1 
 
LOGIC 
 
 DEDUCTIVE AND INDUCTIVE 
 
First Edition, June 1898 (Grant Richards) 
 
 Second Edition, November 1901 (Grant Richards) 
 
 Third Edition, January igo6 (A. Moring Ltd.) 
 
 Reprinted, January 1908 (A. Moring Ltd.) 
 
 Reprinted, May 1909 (A. Moring Ltd.) 
 
LOGIC 
 
 DEDUCTIVE AND INDUCTIVE 
 
 BY 
 
 CARVETH READ, M.A. 
 
 THIRD EDITION, REVISED AND ENLARGED 
 
 LONDON 
 ALEXANDER MORING LIMITED 
 
 THE DE LA MORE PRESS 
 32 GEORGE STREET HANOVER SQUARE W 
 
 1909 
 
PREFACE 
 
 SEPARATION of the facts and laws of Nature into departments 
 for the convenience of study, has been one of the chief con- 
 ditions of scientific progress. It is true that such separation is 
 made for our convenience and does not exist in Nature. Yet 
 it has been the means of revealing the unity of Nature, the 
 connection of facts, the harmony of laws : analysis has been 
 the necessary preliminary to an intelligent synthesis. No 
 further apology need be offered for the separation of Logic, in 
 the present volume, from all other studies, and especially from 
 Psychology and Metaphysics, with greater vigour than has been 
 usual in logical treatises : carrying out the plan that elsewhere 
 has always proved advantageous. 
 
 The instructed reader will easily see that I have been chiefly 
 indebted to Mill's System of Logic, Professor Bain's Logic, Dr. 
 Venn's Empirical Logic, and Dr. Keyne's Formal Logic. What- 
 ever is due to other authors has been acknowledged as occasion 
 arose. In every case I have tried to make the property con- 
 veyed my own : an excuse for theft that must seem odd to a 
 lawyer, but is well recognised in the courts of literature. 
 
 For the comprehensive study of contemporary opinion on 
 Logic, several books besides the above-mentioned are needed : 
 especially Mr. Bradley's Principles of Logic, Mr. Alfred Sidg- 
 wick's Process of Argument, and Mr. Bosanquet's Logic: or the 
 Morphology of Knowledge. The last author's Essentials of 
 Logic is expressly intended to popularise his views. Mr. Hob- 
 house's Theory of Knowledge, an original and valuable treatise, 
 did not come into my hands until this book was finished (now 
 some time ago) : else, probably, I should often have referred 
 to it. Those who, not reading German, desire to see a sample 
 
 188173 
 
vi PREFACE 
 
 of the present state of Logic in the empire, may be referred 
 to Professor Sigwart's Logic, recently translated. Ueberweg's 
 System of Logic, and History of Logical Doctrines is invaluable 
 in its historical passages. 
 
 I owe a great deal to Mr. Alfred Sidgwick, Mr. Thomas 
 Whittaker, and Professor C. M. Thompson, who have been 
 at pains to advise me upon portions of the MS. and proofs. 
 Most of the chapters, however, no one but myself has seen ; 
 so that whatever errors the critic may find must occur in those 
 unsponsored chapters ; and it is, therefore, needless to say 
 which they are. 
 
 CARVETH READ. 
 
 LONDON, May 1898. 
 
 PREFACE TO THE SECOND EDITION 
 
 THE alterations made in this edition are numerous ; but most 
 of them amount only to the excision of a redundant word or 
 sentence, or some small addition to clear up the meaning or 
 guard against misunderstanding. The most important changes 
 will be found in c. ii. 2 ; c. vii. 4 ; c. ix. 5 ; c. xiv. 2 ; 
 c, xv. 5 ; c. xvi. 4-5 ; c. xviii. . 3 ; c. xix. 3. 
 
 Some of these improvements are due to the advice of friendly 
 reviewers, a few of them even to the comments of reviewers 
 who were friends in disguise ; others were privately suggested 
 to me by Prof. Sully, and the rest by my own conscience. 
 
 C. R. 
 
 October 19, igoi. 
 
PREFACE TO THE THIRD EDITION 
 
 THE necessity of reprinting this book as fast as possible has 
 left me no time to do more than to give a list of errata and 
 
 add a few questions at the end. 
 
 C. R. 
 
 October 19, 1905. 
 
 ERRATA 
 
 Page viii, line 5, for " categoremetric " read " categorematic," and 
 
 for " syncategoremetric " read " syncategorematic." 
 xi, line 15, for " Antimony " read " Antinomy." 
 xv, line 4, for "fraction proportion " read "fraction or proportion." 
 
 4, line 3, for " How do we know " read " May it not be." 
 
 n, 2, /or "in" read "is." 
 
 1 7) 36, for " innuendos " read " innuendoes." 
 
 34, 8, for " autonomasia " read " antonomasia." 
 
 40, ,, 16, for " denotation " read " connotation." 
 
 49, 1 1, for "purgatory " read\" Purgatory." 
 
 49) i> J 5> f or "un-wise" read "not-wise." 
 
 53) > 25, /or "most" read "Most." 
 
 69, 9> for " A is not not- A " read " B is not both A and not-A ." 
 
 69, n, for " not A " read " not-A." 
 
 76, 26, for " predicate " read ' predication." 
 
 80, 19, /or "4" read" 6." 
 
 8o ? > 34) / or " 4 5 since S " read " 6 ; since S." 
 
 83, 24, /or " overtend " read " obvertend." 
 
 85, 2 9 ,/ r"4"rmrf"6." 
 
 8 7> i) 5) f or " alleging " read " alledging." 
 
 87, 17, after the first" Some" insert " S." 
 
 87, 19, after the first " Some " /wser< " S." 
 
ERRATA 
 
 Page 89, line i8,/or "Some a is b" read "Some a is B" 
 
 89, 3 6,/or 4 "m*d"6." 
 
 9> J 5> f r " opposition " read " Opposition ." 
 
 ,. 105, i,> " 4" *"*" 6" 
 
 I0 7, 35, /or " middle " raxd " Middle." 
 
 118, 2$, for "E" read "A." 
 
 121, 4,/or"AEO"mzd"EAO." 
 
 124, 28, for "i P" rmrf u is P." 
 
 T 53 7, / or " Hypothetical " tead " Hypotheticals; 
 
 186, 7, /or " situtation " read " situation." 
 
 J 89, 35, /or " chap. xii. I " rm^ " chap. xiii. 2 .' 
 
 250, n, after " established" insert " as a cause." 
 
 283, 8, 6c/orc " unexplained " insert " the." 
 
 287, 16, /or " Here " read " Hence." 
 
 287, 36, /or he " read " the." 
 
 291, 19, for "deductions" read "inductions." 
 
 321. 14, for " Canines" read "canines." 
 
 344, 18, for " corrected " read " collected." 
 
 347, 3i,/or "absortion" r^arf "absorption." 
 
CONTENTS 
 
 PAGE 
 
 PREFACE v 
 
 CHAPTER I 
 
 INTRODUCTORY 
 
 i. Definition of Logic i 
 
 2. General character of proof 2 
 
 3. Division of the subject 4 
 
 4. Uses of Logic 5 
 
 5. Relation of Logic to other sciences 7 
 
 to Mathematics (p. 7) ; to concrete Sciences (p. 9) ; to 
 
 Metaphysics (p. 9) ; to regulative sciences (p. 10) 
 
 6. Schools of Logicians 10 
 
 Relation to Psychology (p. u) 
 
 CHAPTER II 
 
 GENERAL ANALYSIS OF PROPOSITIONS 
 
 i. Propositions and Sentences 15 
 
 2. Subject, Predicate and Copula 16 
 
 3. Compound Propositions 16 
 
 4. Import of Propositions 18 
 
 5. Form and Matter 21 
 
 6. Formal and Material Logic 22 
 
 7. Symbols used in Logic 23 
 
viii CONTENTS 
 
 CHAPTER III 
 
 OF TERMS AND THEIR DENOTATION 
 
 PAGE 
 
 i. Some Account of Language necessary . / 2 ^ 
 
 2. Logic, Grammar and Rhetoric . . . / . . . 27 
 
 3. Words are Categoremejric or Syncategoremet^ic . . 28 
 
 4. Terms Concrete or Abstract 29 
 
 5. Concrete Terms, Singular, General or Collective . . 32 
 
 CHAPTER IV 
 
 THE CONNOTATION OF TERMS 
 
 I. Connotation of General Names 36 
 
 2. Question of Proper Names 37 
 
 other Singular Names (p. 39) 
 
 3. Question of Abstract Terms 39 
 
 4. Uni vocal and Equivocal Terms 40 
 
 Connotation determined by the suppositio (p. 42) 
 
 5. Absolute and Relative Terms 42 
 
 6. Relation of Denotation to Connotation .... 45 
 
 7. Contradictory Terms 46 
 
 8. Positive and Negative Terms ,48 
 
 Infinites ; Privitives ; Contraries (p. 49) 
 
 CHAPTER V 
 
 CLASSIFICATION OF PROPOSITIONS 
 
 i. As to Quantity . 51 
 
 Quantity of the Predicate (p. 54) 
 2. As to Quality . . 54 
 
 Infinite Propositions (p. 55) 
 3. A. I. E. O. . 5 6 
 
CONTENTS ix 
 
 PACK 
 
 4. As to Relation 57 
 
 Change of Relation (p. 58) 
 
 5. As to Modality 62 
 
 6. Verbal and Real Propositions 63 
 
 CHAPTER VI 
 
 CONDITIONS OF IMMEDIATE INFERENCE 
 
 i. Meaning of Inference 66 
 
 2. Immediate and Mediate Inference 67 
 
 3. The Laws of Thought 69 
 
 4. Identity 70 
 
 5. Contradiction and Excluded Middle 71 
 
 6. The Scope of Formal Inference 73 
 
 CHAPTER VII 
 
 IMMEDIATE INFERENCES 
 
 i. Plan of the Chapter 76 
 
 2. Subalternation 76 
 
 3. Connotative Subalternation 77 
 
 4. Conversion 79 
 
 Reciprocality (p. 81) 
 
 5. Obversion 82 
 
 6. Contrary Opposition 83 
 
 7. Contradictory Opposition 84 
 
 8. Subcontrary Opposition 85 
 
 9. The Square of Opposition 86 
 
 10. Secondary modes of Immediate Inference .... 87 
 
 11. Immediate Lnieiences from Conditionals .... 9 
 
CONTENTS 
 
 CHAPTER VIII 
 
 ORDER OF TERMS. EULER J S DIAGRAMS. LOGICAL EQUATIONS. 
 EXISTENTIAL IMPORT OF PROPOSITIONS 
 
 FACE 
 
 i. Order of Terms in a proposition 92 
 
 2. Euler's Diagrams 93 
 
 3. Propositions considered as Equations 97 
 
 4. Existential Import of Propositions 100 
 
 CHAPTER IX 
 
 FORMAL CONDITIONS OF MEDIATE INFERENCE 
 
 i. Nature of Mediate Inference and Syllogism .... 103 
 
 2. General Canons of the Syllogism 104 
 
 Definitions of Categorical Syllogism; Middle Term; 
 Minor Term; Major Term; Minor and Major Pre- 
 mise (p. 105) 
 
 Illicit Process (p. 106) ; Distribution of the Middle 
 (p. 106) ; Negative Premises (p. 108) ; Particular 
 Premises (p. 109) 
 
 3. Dictum de omni et nullo no 
 
 4. Syllogism in relation to the Laws of Thought . . . in 
 5. Other Kinds of Mediate Inference 113 
 
 CHAPTER X 
 
 CATEGORICAL SYLLOGISMS 
 
 i. Illustrations of the Syllogism ...... 116 
 
 2. Of Figures 117 
 
 3. Of Moods 118 
 
 4. How valid Moods are determined . . . . .119 
 
CONTENTS xi 
 
 PAGE 
 
 5. Special Canons of the Four Figures . . . . .121 
 
 6. Ostensive Reduction and the Mnemonic Verses . . 122 
 
 7. Another version of the Mnemonic Verses . . . .126 
 
 8. Indirect Reduction ........ 127 
 
 9. Uses of the several Figures 128 
 
 10. Scientific Value of Reduction 130 
 
 ii. Euler's Diagrams for the Syllogism 131 
 
 CHAPTER XI 
 
 ABBREVIATED AND COMPOUND ARGUMENTS 
 
 i. Popular Arguments Informal 133 
 
 2. The Enthymeme 134 
 
 3. Monosyllogism, Poly syllogism, Prosy llogism, Episyllogism . 136 
 
 4. The Epicheirema 136 
 
 5. The Sorites 137 
 
 6. The AntirAoi^y 139 
 
 *L "+ 
 
 CHAPTER XII 
 
 CONDITIONAL SYLLOGISMS 
 
 i. The Hypothetical Syllogism 142 
 
 2. The Disjunctive Syllogism 146 
 
 3. The Dilemma 149 
 
 CHAPTER XIII 
 
 TRANSITION TO INDUCTION 
 
 i. Formal Consistency and Material Truth .... 154 
 2. Real General Propositions assert more than is directly 
 
 known 155 
 
xii CONTENTS 
 
 3. Hence, formally, a Syllogism's Premises seem to beg the 
 
 Conclusion 157 
 
 4. Materially, a Syllogism turns upon the resemblance of the 
 Minor to the Middle Term ; and thus extends the Major 
 
 Premise to new cases 158 
 
 5. Restatement of the Dictum : equivalent to the Nota note . 159 
 
 6, Material Subalternation 160 
 
 7. Uses of the Syllogism 160 
 
 8. Materially, a Syllogism trusts to the Uniformity of Nature . 162 
 
 9. The Uniformity of Nature analysed 163 
 
 CHAPTER XIV 
 
 CAUSATION 
 
 i. The most important aspect of Uniformity in relation to In- 
 duction is Causation 168 
 
 2. Definition of " Cause " explained : five marks of Causation 169 
 
 3. Hew strictly the conception of Cause can be applied depends 
 
 upon the subject under investigation 176 
 
 4 Scientific conception of Effect. Plurality of Causes . . 178 
 
 5. Some condition, but not the whole cause, may long precede 
 the Effect ; and some co-effect, but not the whole effect, 
 may long survive the Cause 180 
 
 6. Mechanical Causes and the homogeneous Intermixture of 
 Effects; Chemical Causes and the heteropathic Inter- 
 mixture of Effects 181 
 
 7. Tendency, Resultant, Counteraction, Elimination, Resolu- 
 tion, Analysis, Reciprocity ...... 182 
 
 CHAPTER XV 
 
 INDUCTIVE METHOD 
 
 i. Outline of Inductive investigation ..... 185 
 2. Induction defined 189 
 
CONTENTS xiii 
 
 PAGE 
 
 3. " Perfect Induction " 189 
 
 4. Imperfect Induction methodical or immethodical . . 190 
 5. Observation and Experiment, the material ground of Induc- 
 tion, compared 191 
 
 6. The principle of Causation is the formal ground of Induction 193 
 7. The Inductive Canons are derived from the principle of 
 
 Causation, the more readily to detect it in facts observed 195 
 
 CHAPTER XVI 
 
 THE CANONS OF DIRECT INDUCTION 
 
 i. The Canon of Agreement 198 
 
 Negative Instances (p. 200) ; Plurality of Causes (p. 200) 
 Agreement may show connection without direct Causa 
 tion (p. 201) 
 
 2. The Canon of Agreement in Presence and in Absence . . 203 
 It tends to disprove a Plurality of Causes (p. 204) 
 
 3. The Canon of Difference 207 
 
 May be applied to observations (p. 211) 
 
 4. The Canon of Variations 212 
 
 How related to Agreement and Difference (pp. 214-5) ; 
 
 The Graphic Method (p. 217) ; Gradations (p. 219) 
 5. The Canon of Residues 221 
 
 CHAPTER XVII 
 
 COMBINATION OF INDUCTION WITH DEDUCTION 
 
 i. Deductive character of Formal Induction .... 225 
 
 2. Further complication of Deduction with Induction . . 227 
 
 3. The Direct Deductive (or Physical) Method . . .228 
 
 4. Opportunities of Error in the Physical Method . . . 232 
 
 5. The Inverse Deductive (or Historical) Method . . . 234 
 
 6. Precautions in using the Historical Method . . . 239 
 
xiv CONTENTS 
 
 CHAPTER XVIII 
 
 HYPOTHESES 
 
 PAGE 
 
 i. Hypothesis defined and distinguished from Theory . . 244 
 
 2. An Hypothesis must be verifiable 246 
 
 3. Proof of Hypotheses 248 
 
 (1) Must an hypothetical agent be directly observable ? 
 
 (p. 248) ; Vera causa (p. 249) 
 
 (2) An Hypothesis must be adequate to its pretensions 
 
 (p. 250) ; Excepiio firobat regulam (p. 252) 
 
 (3) Every competing Hypothesis must be excluded 
 
 (p. 253) ; Crucial instance (p. 255) 
 
 (4) Hypotheses must agree with the laws of Nature 
 
 (P- 256) 
 4. Hypotheses necessary in scientific investigation . . . 257 
 
 5. The Method of Abstractions 261 
 
 Method of Limits (p. 262) ; In what sense all knowledge 
 is hypothetical (p. 264) 
 
 CHAPTER XIX 
 LAWS CLASSIFIED; CO-EXISTENCE; EXPLANATION; ANALOGY 
 
 i. Axioms; Primary Laws; Secondary Laws, Derivative or 
 
 Empirical ; Facts 266 
 
 2. Secondary Laws either Invariable or Approximate Generali- 
 sations 269 
 
 3. Secondary Laws trustworthy only in ' Adjacent Cases ' . 271 
 
 4. Secondary Laws of Succession or of Co-existence . . 273 
 Natural Kinds (p. 273) ; Co-existence of concrete things 
 to be deduced from Causation (p. 275) 
 
 5. Explanation consists in tracing resemblance, especially of 
 
 Causation 276 
 
 6. Three modes of Explanation 279 
 
 Analysis (p. 279) ; Concatenation (p. 279) ; Subsumption 
 (p. 280) 
 
 7. Limits of Explanation 282 
 
 8. Analogy 283 
 
CONTENTS xv 
 
 CHAPTER XX 
 
 PROBABILITY 
 
 . 
 
 PAGE 
 
 i. Meaning of Chance and Probability 286 
 
 2. Probability as a fraction /proportion 288 
 
 3. Probability depends upon experience and statistics . . 288 
 4. It is a kind of Induction, and pre-supposes Causation . . 291 
 5. Of Averages and ' Errors ' 293 
 
 Personal Equation (p. 294) ; meaning of ' Expectation ' 
 
 (P- 295) 
 6. Rules of the combination of Probabilities .... 295 
 
 Detection of a hidden Cause (p. 296) ; oral tradition 
 (p. 297); circumstantial and analogical evidence (p. 298) 
 
 CHAPTER XXI 
 
 DIVISION AND CLASSIFICATION 
 
 i. Classification, scientific, special and popular . , . 300 
 
 2. Uses of classification 302 
 
 3. Classification, Deductive and Inductive .... 304 
 
 4. Division, or Deductive Classification : its Rules . . . 305 
 
 5. Rules for testing a Division 307 
 
 6. Inductive Classification 309 
 
 7. Difficulty of Natural Classification 310 
 
 8. Darwin's influence on the theory of Classification . . 312 
 9. Classification of Inorganic Bodies also dependent on Causa- 
 tion, . 316 
 
 CHAPTER XXII 
 
 NOMENCLATURE; DEFINITION; PREDICABLES 
 
 i. Precise thinking needs precise language .... 317 
 
 2. Nomenclature and Terminology 318 
 
 3. Definition 320 
 
 4. Rules for testing a Definition 321 
 
xvi CONTENTS 
 
 PAGE 
 
 5. Every Definition is relative to a Classification . . . 322 
 
 6. Difficulties of Definition 325 
 
 Proposal to substitute the Type (p. 325) 
 
 7. The Limits of Definition 326 
 
 8. The five Predicables 327 
 
 Porphpyry's Tree (p. 330) 
 
 9. Realism and Nominalism . 333 
 
 10. The Predicaments 335 
 
 CHAPTER XXIII 
 
 DEFINITION OF COMMON TERMS 
 
 i. The rigour of scientific method must be qualified . . 338 
 2. Still, Language comprises the Nomenclature of an imperfect 
 
 Classification, to which every Definition is relative ; 339 
 
 3. and an imperfect Terminology 343 
 
 4. Maxims and precautions of Definition 344 
 
 5. Words of common language in scientific use . . . 347 
 
 6. How Definitions affect the cogency of arguments . . 350 
 
 CHAPTER XXIV 
 
 FALLACIES 
 
 i. Fallacy defined and divided 355 
 
 2. Formal Fallacies of Deduction 355 
 
 3. Formal Fallacies of Induction . . . . . 358 
 
 4. Material Fallacies classified 363 
 
 5. Fallacies of Observation 364 
 
 6. Begging the Question 365 
 
 7. Surreptitious Conclusion 367 
 
 8. Ambiguity 369 
 
 9. Fallacies, a natural rank growth of the Human Mind, not 
 
 easy to classify, or exterminate 372 
 
 QUESTIONS 375 
 
OF THE 
 
 ( UNIVERSITY ] 
 
 CHAPTER I 
 INTRODUCTORY 
 
 i. Logic is the science that explains what conditions 
 must be fulfilled in order that a proposition may be proved, 
 if it admits of proof. Not, indeed, every such proposition ; for 
 as to those that declare the equality or inequality of numbers 
 or other magnitudes, to explain the conditions of their proof 
 belongs to Mathematics : they are said to be quantitative. 
 But as to all other propositions, called qualitative, like most 
 of those that we meet with in conversation, in literature, in 
 politics, and even in the sciences that are not treated mathe- 
 matically (say, Botany and Psychology); propositions that 
 merely tell us that something happens (as that salt dissolves in 
 water], or that something has a certain property (as that the 
 east wind is baneful), or that something is related to a class of 
 things (as that Englishmen are good sailors) : as to these, it 
 belongs to Logic to show how we may judge whether they are 
 true, or false, or doubtful. When propositions are expressed 
 with the universality and definiteness that belongs to scientific 
 statements, they are called laws ; and laws, so far as they are 
 not laws of quantity, are tested by the principles of Logic, if 
 they at all admit of proof. 
 
 But it is plain that the process of proving cannot go on for 
 ever ; something must be taken for granted ; and this is usually 
 considered to be the case with those highest laws that are 
 called * axioms ' or ' first principles,' of which we can only say 
 that we know of no exceptions to them, that we cannot help 
 believing them, and that they are indispensable to science and 
 
2 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 to consistent thought. Logic, then, may be briefly defined as 
 the science of proof with respect to qualitative laws and propo- 
 sitions, except those that are axiomatic. 
 
 2. Proof may be of different degrees or stages of com- 
 pleteness. Absolute proof would require that a proposition 
 should be shown to agree with all experience and with the 
 systematic explanation of experience, to be a necessary part 
 of an all-embracing and self-consistent philosophy or theory of 
 the universe ; but as no one hitherto has been able to frame 
 such a philosophy, we must at present put up with something 
 less than absolute proof. Logic, assuming certain principles 
 to be true of experience, or at least to be conditions of con- 
 sistent discourse, distinguishes the kinds of propositions that 
 can be shown to agree with these principles, and explains by 
 what means the agreement can best be exhibited. These 
 principles will be found in chaps, vi., ix., xiii., xiv. To bring a 
 proposition or an argument under them, or to show that it 
 agrees with them, is logical proof. 
 
 The extent to which proof is requisite, again, depends upon 
 circumstances ; whether our aim be general truth for its own 
 sake, or merely to compare a proposition with our own convic- 
 tions, or to satisfy the doubts of a friend. If A and B are 
 conversing, and A asserts that some white races have straight 
 black hair, and B doubts this, but is willing to grant that some 
 races with straight black hair are white, A may perhaps prove 
 his point to the satisfaction of B by showing that these two pro- 
 positions are intrinsically the same, as only differing in the order 
 of the words. This is called proof by Immediate Inference, or 
 by equivalence of meaning. 
 
 Again, if B is ready to admit that the Basques and Finns 
 
 are white races, and also that they have straight black hair, then 
 
 when A puts these two propositions together thus 
 
 The Basques and Finns have straight black hair ; 
 
 The Basques and Finns are white races ; 
 
 Therefore, some white races have straight black hair 
 
 the truth of the last proposition is not likely to be disputed any 
 
 , then 
 
INTRODUCTORY 3 
 
 longer. And this is called proof by Mediate Inference : that is 
 to say, a connection between * some white faces ' and * straight 
 black hair ' is supposed not to be directly perceivable, but to be 
 discovered by finding that both are connected in a certain way 
 with, ' Basques and Finns. 1 
 
 If, however, B does not grant that the Basques or the Finns 
 are a white race, or that they have straight black hair, and A 
 tries to prove these propositions, his difficulties greatly increase 
 and may become insuperable. He must collect ethnological 
 evidence, and convince B of its sufficiency ; and if his friend 
 be of a sceptical turn of mind, or desire a reputation for ingenuity 
 rather than for good sense, the conclusion that some white races 
 have straight black hair may be indefinitely postponed. In 
 fact, to follow out this illustration would be altogether unsuit- 
 able to an introductory chapter \ we had better turn to a 
 simpler case. 
 
 Suppose that A holds in his hand a piece of yellow metal, 
 which he asserts to be copper, and that B doubts this, perhaps 
 suggesting that it is really gold. Then A may propose to dip 
 it in vinegar ; and we will suppose B to agree that, if it then 
 turns green, it is copper and not gold. On trying this experi- 
 ment the metal does turn green ; so that we may put A's 
 argument in this way : 
 
 Whatever yellow metal turns green in vinegar is copper ; 
 This yellow metal turns green in vinegar ; 
 Therefore, this yellow metal is copper. 
 
 Now, however, it may occur to B that the liquid in which the 
 metal was dipped was not vinegar, or not pure vinegar, and 
 that the greenness was due to the impurity. A must thereupon 
 show by some means that the vinegar was pure ; and then his 
 argument will be that, since nothing but the vinegar came in 
 contact with the metal, the greenness was due to the vinegar ; 
 or, in other words, that contact with that vinegar was the cause 
 of the metal turning green. 
 
 Still, on second thoughts, B may suspect that he had 
 formerly conceded too much ; he may reflect that, although it 
 
LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 often been shown that copper turned green in vinegar, 
 whilst gold did not, yet the same might not always happen. 
 How-do -wHcew, he might ask, that just at this moment, and 
 perhaps always for the future gold turns, and will turn green in 
 vinegar, whilst copper does not and never will again ? A will 
 probably reply that this is to doubt the uniformity of causation : 
 he may hope that B is not serious : he may point out to his 
 friend that in every action of his life he takes such uniformity 
 for granted. But he will be obliged to admit that, whatever he 
 may say to induce his friend to assent to the principle of Nature's 
 uniformity, his arguments will not amount to logical proof, 
 because every argument in some way assumes that principle. 
 He has come, in fact, to the limits of Logic. Just as the mathe- 
 matician does not try to prove that * two magnitudes equal to 
 the same third are equal to one another,' so the Logician (as 
 such) does not attempt to prove the uniformity of causation 
 and the other principles of his science. 
 
 3. Two departments of Logic are usually recognised, De- 
 duction and Induction ; that is, to describe them briefly, proof 
 from principles, and proof from facts. Classification is some- 
 times made a third department ; sometimes its topics are dis- 
 tributed amongst those of the former two. In the present 
 manual the order adopted is, Deduction in chaps, ii. to xiii, : 
 Induction in chaps, xiii. to xx. ; and lastly, Classification. But 
 such divisions do not represent fundamentally distinct and 
 opposed aspects of the science. For although, in discussing 
 any question with an opponent who makes admissions, it may 
 be possible to combat his views with merely deductive argu- 
 ments based upon his admissions; yet in any question of 
 general truth, Induction and Deduction are mutually dependent 
 and imply one another. 
 
 This may be seen in one of the above examples. A argues 
 that a certain metal is copper, because every metal is copper 
 that turns green when dipped in vinegar. So far his proof 
 appeals to a general proposition, and is deductive. But if B 
 asks how he knows the general proposition to be true, A alleges 
 
 
INTRODUCTORY 5 
 
 experiments or facts ; and this is inductive evidence. De- 
 duction then depends on Induction. But when B asks, again, 
 how any number of past experiments can prove a general pro- 
 position, which must be good for the future as well as for the 
 past, A invokes the uniformity of causation ; that is, he appeals 
 to a principle, and that again is deductive proof. Induction 
 then depends upon Deduction. 
 
 We may put it in this way : Deduction depends on Induc- 
 tion, if general propositions are only known to us through the 
 facts : Induction depends on Deduction, because one fact can 
 never prove another, except so far as what is true of the one 
 is true of the other and of any other of the same kind ; and 
 because, to exhibit this resemblance of the facts, it must be 
 stated in a general proposition. 
 
 4. The use of Logic is often disputed : those who have 
 not studied it, often feel confident of their ability to do without 
 it ; those who have studied it, are sometimes disgusted with 
 what they consider to be its superficial analysis of the grounds 
 of evidence, or needless technicality in the discussion of details. 
 As to those who, not having studied Logic, yet despise it, 
 there will be time enough to discuss its utility with them, when 
 they know something about it ; and as for those who, having 
 studied it, turn away in disgust, whether they are justified 
 every man must judge for himself, when he has attained to 
 equal proficiency in the subject. Meanwhile, the following 
 considerations may be offered as inducements to persevere in 
 the study : 
 
 (a) Logic states, and partly explains and applies, certain 
 abstract principles which all other sciences take for granted ; 
 namely, the axioms above mentioned. 
 
 (b) By exercising the student in the apprehension of these 
 truths, and in the application of them to particular proposi- 
 tions, it educates the power cf abstract thought. For this 
 reason Logic is the best propaedeutic to Philosophy, that is, to 
 Metaphysics and speculative Ethics. 
 
 (c) Every science, when well expounded, is a model cf 
 
6 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 method, and a discipline in close and consecutive thinking. 
 This merit Logic ought to possess in a high degree. 
 
 (d) As the science of proof, Logic gives an account of 
 the general nature of evidence deductive and inductive, as 
 applied in the physical and social sciences and in the affairs 
 of life. Observe: the general nature of such evidence. It 
 would be absurd of the Logician to pretend to instruct the 
 Chemist, Economist and Merchant, as to the special character 
 of the evidence requisite in their several spheres of judgment. 
 Still, by investigating the general conditions of proof, he sets 
 every man upon his guard against insufficient evidence. 
 
 Of course, Logic does not, in the first place, teach us to 
 reason. We learn to reason, as we learn to walk and talk, 
 by the natural growth of our powers, with some assistance 
 from friends and neighbours. But, to be frank, few of us 
 walk, talk or reason remarkably well ; and, as to reasoning, 
 Logic certainly quickens our sense of bad reasoning, both 
 in others and in ourselves. It helps us to avoid being misled 
 by others, and to correct our own mistakes. A man who 
 reasons deliberately, manages it better after studying Logic 
 than he could before if he tries to, if he has not a perverse 
 liking for sophistry, and if he has the sense to know when 
 formalities are out of place. There are some mental qualities 
 that a man can only get from hTsHfaTEeTland mother. 
 
 (e) One application of the science of proof deserves special 
 mention : I mean, to that department of Rhetoric that has 
 been the most developed, relating to persuasion by means of 
 oratory, leader-writing, or pamphleteering. It is usually said 
 that Logic is useful to convince the judgment, not to persuade 
 the will : but one way of persuading the will is to convince the 
 judgment that a certain course is advantageous ; and although 
 this is not always the readiest way, it is the most honourabl 
 and leads to the most enduring results. Logic, in fact, is the 
 backbone of Rhetoric. 
 
 Now, it is in view of these last four uses of Logic (, c, d, e) 
 that it may be treated as an Art. As a Science, it explains the 
 
 fr 
 
 : 
 
INTRODUCTORY 7 
 
 relations of truths to one another, especially to certain first 
 principles : as an Art, it regards Truth as an end desired, and 
 points out some of the means of attaining it; namely, to 
 proceed by a regular method, to test any proposition by 
 the principles of Logic, and to distrust whatever cannot be 
 made consistent with them. It does not give any one 
 originality and fertility of invention; but it enables us to 
 check our inferences, revise our conclusions, and chasten 
 the vagaries of ambitious speculation. On account of this 
 corrective function, Logic is sometimes called a Regulative 
 Science. 
 
 (/) Finally, Logic is at least a refined mental exercise. And 
 it needs no telescopes, microscopes, retorts or scalpels ; no 
 observatories, laboratories, or museums : it is, therefore, cheap 
 and convenient. Moreover, it is of old and honourable 
 descent; a man studies Logic in very good company. It 
 is the warp upon which nearly the whole web of ancient, 
 mediaeval and modern philosophy has been woven; and is 
 therefore manifestly indispensable to a liberal education. 
 
 5. The relation of Logic to other sciences may be indicated 
 thus: 
 
 (a) Logic is regarded by Spencer as co-ordinate with Mathe- 
 matics, both being Abstract Sciences that is, sciences of the 
 relations in which things stand to one another, whatever the 
 particular things may be that are so related; and this view 
 seems to me to be, on the whole, just subject, however, to 
 a qualification that will appear presently. 
 
 Mathematics treats of the relations of all sorts of things 
 considered as quantities, namely, as equal to, or greater or 
 less than, one another. Things may be quantitatively equal 
 or unequal in degree^ as in comparing the temperature of 
 bodies; or in duration; or in spatial magnitude, as with 
 lines, superficies, solids; or in number. And it is assumed 
 that the equality or inequality of things that cannot be directly 
 compared, may be proved indirectly on the assumption that 
 ' things equal to the same thing are equal,' etc. 
 
8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Logic also treats of the relations of all sorts of things, 
 but not as to their quantity. It considers (i) that one thing 
 may be like or unlike another in certain attributes, as that 
 a shark is in many ways like a ray, and in many ways unlike 
 a star-fish : (ii) that attributes co-exist or coinhere (or not) in 
 the same subject, as ihe having several rows of teeth and a 
 backbone prolonged into the upper lobe of the tail coinhere 
 in a shark : and (iii) that one event follows another (or is the 
 effect of it), as that the placing of iron in water causes it to 
 rust. The relations of likeness and of coinherence are most 
 prominent in the department of Classification; for it is by 
 resemblance of coinhering attributes that things form classes : 
 the relation of succession, in the mode of causation, is the 
 chief subject of the department of Induction. It is usual 
 to group together these relations of attributes and of order 
 in time, and call them qualitative, in order to contrast them 
 with the quantitative which belong to Mathematics. And it is 
 assumed that qualitative relations of things, when they cannot 
 be directly perceived, may be proved indirectly by assuming 
 the axiom of the Syllogism (chap, ix.) and the law of Causation 
 (chap. xiv.). 
 
 So far, then, Logic and Mathematics appear to be co- 
 ordinate and distinct sciences. But we shall see hereafter 
 that the satisfactory treatment of that special order of events 
 in time which constitutes Causation, requires a combination of 
 Logic with Mathematics. On the other hand, Logic may be 
 said to be in some respects 4 prior to ' or * above ' Mathematics 
 as usually treated. For the Mathematics assume that one 
 magnitude must be either equal or unequal to another, and 
 that it cannot be both equal and unequal to it, and thus 
 take for granted the principles of Contradiction and Excluded 
 Middle ; but the statement and elucidation of these principles 
 is left to Logic (chap. vi.). The Mathematics also classify and 
 define magnitudes, as (in Geometry) triangles, squares, cubes, 
 spheres ; but the principles of classification and definition 
 remain for Logic to discuss. 
 
 
INTRODUCTORY 9 
 
 (b) As to the concrete Sciences, such as Astronomy, 
 Chemistry, Zoology, Politics Logic (as well as Mathematics) 
 is implied in them all ; for all the propositions of which they 
 consist involve causation, co-existence, and class-likeness. 
 Logic is therefore said to be prior to them or above them : 
 meaning by prior ' not that it should be studied earlier, for 
 that is not a good plan ; meaning by ' above ' not in dignity, 
 for distinctions of dignity amongst liberal studies are absurd. 
 But it is a philosophical idiom to call the abstract ' prior to,' 
 or 'higher than,' the concrete (see Porphyry's Tree, chap. 
 xxii. 8); and Logic is more abstract than Astronomy or 
 Politics, Philosophy may thank that idiom for many a foolish 
 notion. 
 
 (c) But, as we have seen, Logic does not investigate the truth, 
 trustworthiness, or validity of its own principles ; nor does 
 Mathematics : this task belongs to Metaphysics, the criticism 
 of knowledge and beliefs. 
 
 Logic assumes, for example, that things are what to a careful 
 scrutiny they seem to be ; that animals, trees, mountains, 
 planets, are bodies with various attributes, existing in space 
 and changing in time; and that certain principles, such as 
 Contradiction and Causation, are true of things and events. 
 But Metaphysicians have raised many plausible objections to 
 these assumptions. It has been urged that natural objects do 
 not really exist on their own account, but only in dependence 
 on some mind that contemplates them, and that even space 
 and time are only our way of perceiving things ; or, again, that 
 although things do really exist on their own account, it is in an 
 entirely different way from that in which we know them. As 
 to the principle of Contradiction that if an object has an 
 attribute, it cannot at the same time and in the same way 
 be without it (e.g., if an animal is conscious, it is false that it 
 is not conscious) it has been contended that the speciousness 
 of this principle is only due to the narrowness of our minds, or 
 even to the poverty of language, which cannot make the fine 
 distinctions that exist in Nature. And as to Causation, it is 
 
io LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 sometimes doubted whether events always have physical 
 causes; and it is often suggested that, granting they have 
 physical causes, yet these are such as we can neither perceive 
 nor conceive; belonging not to the order of Nature as we 
 know it, but to the secret inwardness and reality of Nature, 
 to the wells and reservoirs of power, not to the spray of 
 the fountain that glitters in our eyes 'occult causes,' in 
 short. Now these doubts and surmises are metaphysical 
 spectres which it remains for Metaphysics to lay. Logic 
 has no direct concern with them (although, of course, meta- 
 physical discussion is usually expected to be logical), but 
 keeps the plain path of plain beliefs, level with the com- 
 prehension of plain men. Metaphysics, as examining the 
 grounds of Logic itself, is sometimes regarded as * the higher 
 Logic.' 
 
 (d) The relation of Logic to Psychology will be discussed in 
 the next section. 
 
 (e) As a Regulative Science, pointing out the conditions of 
 true inference (within its own sphere), Logic is co-ordinate 
 with (i) Ethics, considered as assigning the conditions of 
 right conduct, and with (ii) ^Esthetics, considered as deter- 
 mining the principles of criticism and good taste. 
 
 6. Three principal schools of Logicians are commonly 
 recognised : Nominalist, Conceptualist, and Materialist, who 
 differ as to what it is that Logic really treats of : the Nomi- 
 nalists say, ' of language ' ; the Conceptualists, ' of thought ' ; 
 the Materialists, 'of relations of fact.' To illustrate these 
 positions let us take authors who, if some of them are now 
 neglected, have the merit of stating their contrasted views with 
 a distinctness that later refinements tend to obscure. 
 
 (a) Whately, a well-known Nominalist, regards Logic as the 
 Science and Art of Reasoning, but at the same time as 
 " entirely conversant about language " ; that is to say, it is the 
 business of Logic to discover those modes of statement which 
 shall ensure the cogency of an argument, no matter what may be 
 the subject under discussion. Thus, All fish are cold-blooded, .'. 
 
 
INTRODUCTORY n 
 
 some cold-blooded things are fish : this is a sound inference by the 
 mere manner of expression ; and equally sound itf the inference, 
 All fish are warm-blooded, .'. some warm-blooded things are fish. 
 The latter proposition may be false, but it follows; and 
 (according to this doctrine) Logic is only concerned with the 
 consistent use of words : the truth or falsity of the proposition 
 itself is a question for Zoology. 
 
 (b) Hamilton, our best-known Conceptualist, regards Logic 
 as the science of the "formal laws of thought," and "of 
 thought as thought," that is, without regard to the matter 
 thought about. Just as Whately regards Logic as concerned 
 merely with cogent forms of statement, so Hamilton treats it 
 as concerned merely with the necessary relations of thought. 
 This doctrine is called Conceptualism, because the simplest 
 element of thought is the Concept ; that is, an abstract idea, 
 such as is signified by the word man, planet, colour, virtue ; 
 not a representative or generic image, but the thought of all 
 attributes common to any class of things. Men, planets, 
 colours, virtuous actions or characters, have, severally, some- 
 thing in common on account of which they bear these general 
 names ; and the thought of what they have in common, as the 
 ground of these names, is a Concept. To affirm or deny one con- 
 cept of another, as Some men are virtuous, No man is perfectly 
 virtuous, is to form a Judgment, corresponding to the Proposition 
 of which the other schools of Logic discourse. Conceptualism, 
 then, investigates the conditions of consistent judgments. 
 
 To distinguish Logic from Psychology is most important in 
 connection with Conceptualism. Concepts and Judgments 
 being mental acts, or products of mental activity, it is often 
 thought that Logic must be a department of Psychology. It 
 is recognised, of course, that Psychology deals with much 
 more than Logic does, with sensation, pleasure and pain, 
 emotion, volition ; but in the region of the intellect, especially 
 in its most deliberate and elaborate processes, namely, con- 
 ception, judgment, and reasoning, it is supposed that Logic 
 and Psychology occupy some common ground. In fact, 
 
12 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 however, the two sciences have little in common except a few 
 general terms, and even these they employ in different senses. 
 It is usual to point out that Psychology tries to explain the 
 subjective processes of conception, judgment and reasoning 
 (say, according to the Laws of Association) and to give their 
 natural history ; but that Logic is wholly concerned with the 
 results of such processes, with concepts, judgments and 
 reasonings, and merely with the validity of the results, that is, 
 with their truth or consistency ; whilst Psychology has nothing 
 to do with their validity, but only with their causes. Besides, 
 the logical judgment is (in Formal Logic at least) quite a 
 different thing from the psychological : the latter involves feel- 
 ing and belief, whereas the former is merely a given relation 
 of concepts. S is P : that is a model logical judgment ; there 
 can be no question of believing it ; but it is logically valid if 
 M is P and S is M. If, again, belief has any place in Logic, 
 it depends upon evidence; whereas, in Psychology belief is 
 shown to depend upon causes which may have evidentiary 
 value or may not ; for Psychology explains quite impartially 
 the growth of scientific insight and the growth of prejudice. 
 
 (c) Mill, Bain, and Venn are the chief Materialist logicians; 
 and to guard against the error of confounding Materialism in 
 Logic with the ontological doctrine that nothing exists but 
 Matter, it may suffice to remember that in Metaphysics all 
 these philosophers are Idealists. Materialism in Logic consists 
 in regarding propositions as affirming or denying relations 
 (rf- 5) between matters-of-fact ; in treating the first principles 
 of Contradiction and Causation as true of things so far as they 
 are known to us, and not merely as conditions or tendencies of 
 thought ; and, indeed, in taking these principles as conditions 
 of right thinking, because they seem to hold good of Nature. 
 
 To these differences of opinion it will be necessary to recur 
 in the next chapter ( 4) ; but here I may observe that it is 
 easy to exaggerate their importance in mere Logic. There is 
 really little at issue between schools of logicians as such, and 
 as far as their doctrines run parallel ; it is on the metaphysical 
 
INTRODUCTORY 13 
 
 grounds of their study, or as to its scope and comprehension, 
 that they find a battle-field. As for the present work, it 
 generally proceeds upon the third, or Materialist doctrine. If 
 Deduction and Induction are regarded as mutually dependent 
 parts of one science, uniting the discipline of consistent dis- 
 course with the method of investigating laws of physical 
 phenomena, the Materialist doctrine, that the principles of 
 Logic are founded on fact, seems to be the most natural way 
 of thinking. But if the unity of Deduction and Induction is 
 not disputed by the other schools, the Materialist may regard 
 them as allies exhibiting in their own way the same body of 
 truths. The Nominalist may certainly claim that his doctrine 
 is indispensable : consistently cogent forms of statement are 
 necessary both to the Conceptualist and to the Materialist ; 
 neither the relations of thought nor those of fact can be 
 arrested or presented without the aid of language or some 
 equivalent system of signs. The Conceptualist may urge that 
 the Nominalist's forms of statement and argument exist for the 
 sake of their meaning, namely, judgments and reasonings ; 
 and that the Materialist's laws of Nature are only judgments 
 founded upon our conceptions of Nature ; that the truth of 
 observations and experiments depends upon our powers of 
 perception ; that perception is inseparable from understanding, 
 and that s. system of Induction may be constructed upon the 
 axiom of Causation, regarded as a principle of Reason, just 
 as well as by considering it as a law of Nature, and upon much 
 the same lines. The Materialist, admitting all this, may say 
 that the other schools have not hitherto been eager to recognise 
 the unity of Deduction and Induction or to investigate the 
 conditions of trustworthy experiments and observations within 
 the limits of human understanding ; that thought is itself a 
 sort of fact, as complex in its structure, as profound in its 
 relations, as subtle in its changes as any other fact, and there- 
 fore at least as hard to know ; that to turn away from the full 
 reality of thought in perception, and to confine Logic to 
 artificially limited concepts, is to abandon the effort to push 
 
14 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 method to the utmost and to get as near truth as possible ; 
 and that as to Causation being a principle of Reason rather 
 than of Nature, the distinction escapes his apprehension, since 
 Nature seems to be that to which our private minds turn upon 
 questions of Causation for correction and instruction ; so that 
 if he does not call Nature the Universal Reason, it is because 
 he loves severity of style. 
 
CHAPTER II 
 GENERAL ANALYSIS OF PROPOSITIONS 
 
 i. Since Logic discusses the proof or disproof, or (briefly) 
 the testing of propositions, we must begin by explaining their 
 nature. A proposition, then, may first be described in the 
 language of grammar as a sentence indicative ; and it is usually 
 expressed in the present tense. 
 
 It is true that other kinds of sentences, optative, imperative, 
 interrogative, exclamatory, if they express or imply an asser- 
 tion, are not beyond the view of Logic ; but before treating 
 such sentences, Logic, for greater precision, reduces them to 
 their equivalent sentences indicative. Thus, / wish it were 
 summer may be understood to mean, The coming of summer is 
 an object of my desire. Thou shalt not kill may be interpreted 
 as Murderers are in danger of the judgment. Interrogatories, 
 when used in argument, if their form is affirmative, have 
 negative force, and affirmative force if their form is negative. 
 Thus, Do hypocrites love virtue ? anticipates the answer, No. 
 Are not traitors the vilest of mankind ? anticipates the answer, 
 Yes. So that the logical form of these sentences is, Hypocrites 
 are not lovers of virtue; Traitors are the vilest of mankind. 
 Impersonal propositions, such as // rains, are easily rendered 
 into logical forms of equivalent meaning, thus: Rain is falling; 
 or, if this be tautology, The clouds are raining. Exclamations 
 may seem capricious, but are often part of the argument. 
 Shade of Chatham ! usually means Chatham^ being aware of 
 our present foreign policy ', is much disgusted. It is, in fact, an 
 
16 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 appeal to authority, without the inconvenience of stating what 
 exactly it is that the authority declares. 
 
 2. But even sentences indicative may not be expressed 
 in the way most convenient to logicians. Salt dissolves in 
 water is a plain enough statement for ordinary purposes; 
 but the logician prefers to have it thus : Salt is soluble in 
 water. For he says that a proposition is analysable into 
 three elements : (i) a Subject (as Salt) about which something 
 is asserted or denied; (2) a Predicate (as soluble in water) 
 which is asserted or denied of the Subject, and (3) the 
 Copula (is or are, or is not or are not), the sign of relation 
 between the Subject and Predicate. The Subject and Pre- 
 dicate are called the Terms of the proposition : and the Copula 
 may be called the sign of predication, using the verb ' to 
 predicate ' indefinitely for either * to affirm ' or * to deny.' 
 Thus S is P means the term P is given as related in some way 
 to the term S. We may, therefore, further define a Proposition 
 as 'a sentence in which one term is predicated of another.' 
 
 In such a proposition as Salt dissolves, the copula (is) is 
 contained in the predicate, and, besides the subject, only 
 one element is exhibited : it is therefore said to be secuntfi 
 adjacentis. When all three parts are exhibited, as in Salt is 
 soluble, the proposition is said to be tertli adjacentis. 
 
 For the ordinary purposes of Logic, in predicating attributes 
 of a class, the copula is, or is not, sufficiently represents the 
 relation of subject and predicate ; but when it is desirable to 
 realise fully the nature of the relation involved, it may be better 
 to use a more explicit form. Instead of saying Salt is soluble, 
 we may say Solubility coinheres with the nature of salt, or 
 The putting of salt in water is a cause of its dissolving: thus 
 expanding the copula into a full expression of the relation we 
 have in view, whether coinherence or causation. 
 
 3. The sentences of ordinary discourse are, indeed, for 
 the most part, longer and more complicated than the logical 
 form of propositions ; it is in order to prove them, or to use 
 them in the proof of other propositions, that they are in Logic 
 
GENERAL ANALYSIS OF PROPOSITIONS 17 
 
 reduced as nearly as possible to such simple but explicit 
 expressions as the above (tertii adjacentis). A Compound 
 Proposition, reducible to two or more simple ones, is said to 
 be exponible. 
 
 The meansTiy which sentences are compounded may be seen 
 analysed in any book of grammar. One of the commonest 
 forms is the copulative, such as Salt is both savoury and 
 wholesome, equivalent to two simple propositions : Salt is 
 savoury ; Salt is ivholesome. Pure water is neither sapid nor 
 odorous, equivalent to Water is not sapid ; Water is not 
 odorous. Or, again, Tobacco is injurious, but not when used in 
 moderation, equivalent to Much tobacco is injurious ; a little is 
 not. (The word but, however, sometimes needs a third pro- 
 position to bring out its meaning, as in this case : Other 
 nations change, but not the Chinese an assertion of 
 superiority.) 
 
 Another form of Exponible is the Exceptive, as Klad- 
 deradatsch is published daily, except on week-days, equivalent to 
 Kladderadatsch is published on Sunday ; it is not published 
 any other day. Still another Exponible is the Exclusive, as 
 Only men use fire, equivalent to Men are users of fire ; ~No other 
 animals are. Exceptive and exclusive sentences are, however, 
 equivalent forms ; for we may say, Kladderadatsch is published 
 only on Sunday ; and No animals use fire, except men. 
 
 There are other compound sentences that are not exponible, 
 since, though they contain two or more verbal clauses, the 
 construction shows that these are inseparable. Thus, If cats 
 are scarce, mice are plentiful, contains two verbal clauses ; but 
 if cats are scarce is conditional, not indicative; and mice are 
 plentiful is subject to the condition that cats are scarce. Hence 
 the whole sentence is called a Conditional Proposition. For 
 the various forms of Conditional Propositions see chap. v. 4. 
 
 But, in fact, to find the logical force of recognised 
 grammatical forms is the least of a logician's difficulties in 
 bringing the discourses of men to a plain issue. Metaphors, 
 epigrams, innuendos and other figures of speech present far 
 
 ' 
 
i8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 greater obstacles to a lucid reduction whether for approval or 
 refutation. No rules can be given for finding everybody's 
 meaning. The poets have their own way of expressing them- 
 selves ; sophists, too, have their own way. And the point often 
 lies in what is unexpressed. Thus, " barbarous nations make, 
 the civilised write history," means that civilised nations do not 
 make history, which none is so brazen as openly to assert. Or 
 again, " Alcibiades is dead, but X is still with us." The whole 
 meaning of this * Exponible ' is that X would be the lesser loss 
 to society. Even an epithet or a suffix may imply a propo- 
 sition : This personage may mean X is a pretentious nobody. 
 
 How shall we consider such illusive predications except by 
 cultivating our literary perceptions? The obtuse man who 
 misses the meaning of an epigram may escape some pain ; but 
 * the higher pain ' is good for him. At any rate, to disentangle 
 the compound propositions, and to expand the abbreviations 
 of literature and conversation, is a useful logical exercise. And 
 if it seem a laborious task thus to reduce^to its logical elements 
 a long argument in a speech or treatise, it should be observed 
 that, as a rule, in a long discourse only a few sentences are of 
 principal importance to the reasoning, the rest being explana- 
 tory or illustrative digression, and that a close scrutiny of these 
 cardinal sentences will frequently dispense us from giving much 
 attention to the rest. 
 
 4. But now, returning to the definition of a Proposition 
 given in 2, that it is 'a sentence in which one term is 
 predicated of another,' we must consider what is the import 
 of such predication. For the definition, as it stands, seems 
 to be purely Nominalist. Is a proposition nothing more than 
 a certain synthesis of words ; or, is it meant to correspond 
 with something further, a synthesis of ideas, or a relation of 
 facts ? 
 
 Conceptualist logicians, who speak of judgments instead 
 of propositions, of course define the judgment in their own 
 language. According to Hamilton, it is " a recognition of the 
 relation of congruence or confliction in which two concepts 
 
GENERAL ANALYSIS OF PROPOSITIONS 
 
 stand to each other." To lighten the sentence, I have omitted 
 one or two qualifications (Hamilton's Lectures on Logic, xiii.). 
 "Thus," he goes on, "if we compare the thoughts water, 
 iron, and rusting, we find them congruent, and connect them 
 into a single thought, thus : water rusts iron in that case we 
 form a judgment." When a judgment is expressed in words, 
 he says, it is called a proposition. 
 
 There seems at first to be a merely verbal difference upon 
 this point between the three Schools (chap i. 6); for 
 Whately begins by describing a proposition as " a judgment 
 expressed in words," though he prefers to define it as " a 
 sentence indicative." Mill, again, defines it as " a portion of 
 discourse in which a predicate is affirmed or denied of a 
 subject." (Logic, Book I., chap. iv. i.) But further 
 differences come to light when Whately observes that his 
 definition "relates entirely to the words," and when Mill 
 goes on to inquire into the import of propositions. (Book I., 
 chap, v.) 
 
 Mill finds three classes of propositions : (a) those in which 
 one proper name is predicated of another; and of these 
 Hobbes's Nominalist definition is adequate, namely, that a 
 proposition asserts or denies that the predicate is a name for 
 the same thing as the subject, as Tully is Cicero. 
 
 (b) Propositions in which the predicate means a part (or 
 the whole) of what the subject means, as Horses are animals, 
 Man is a rational animal. These are Verbal Propositions 
 (see below : chap. v. 6), and their import consists in 
 affirming or denying a coincidence between the meanings 
 of names, as The meaning of ' animal' is part of the meaning 
 of l horse*. 
 
 But (c) there are also Real Propositions, whose predicates 
 do not mean the same as their subjects, and whose import 
 consists in affirming or denying one of five different kinds 
 of matter of fact: (i) That the subject exists, or does not; 
 as if we say The bison exists, The great auk is extinct. (2) 
 Co-existence, as Man is mortal; that is, the being subject to 
 
20 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 death coinheres with the qualities on account of which we call 
 certain objects men. (3) Succession, as The military precedes 
 the industrial regime. (4) Causation (a particular kind of 
 Succession), as Water rusts iron. (5) Resemblance, as The 
 colour of this geranium is like that of a soldier's coat, or A = B. 
 
 On comparing this list of real predications with the list 
 of logical relations given above (chap. i. 5^), it will be 
 seen that the two differ only in this, that I have there omitted 
 simple Existence. In fact nothing simply exists, unrelated 
 either in Nature or in knowledge. Still, such a proposition 
 as The bison exists may, no doubt, be used in Logic (subject 
 to interpretation) for the sake of custom or for the sake of 
 brevity. 
 
 Into the question of the Import of Propositions it would 
 be unsuitable to enter further. This controversy really turns 
 upon a difference of opinion as to the scope of Logic and 
 the foundations of knowledge. Mill was dissatisfied with 
 the " congruity " of concepts as the basis of a judgment. 
 Clearly, mere congruity does not justify belief. In the pro- 
 position Water rusts iron, the concepts water, rust and 
 iron may be congruous, but does any one assert their con- 
 nection on that ground ? In the proposition Murderers are 
 haunted by the ghosts of their victims, the concepts victim, 
 murderer, ghost have a high degree of congruity; yet, un- 
 fortunately, I cannot believe it : there seems to be no such 
 cheap defence of innocence. Now, Mill held that Logic 
 is concerned with the grounds of belief, and that the scope 
 of Logic includes Induction as well as Deduction; whereas, 
 according to Hamilton, Induction is only Modified Logic, 
 a mere appendix to the theory of the "forms of thought 
 as thought." Indeed, Mill endeavoured in his Logic to probe 
 the grounds of belief deeper than the science should pretend 
 to penetrate, and introduced a good deal of Metaphysics 
 certainly, either too much or not enough. But, at any rate, 
 his great point was that belief, and therefore (for the most 
 part) the Real Proposition, is concerned not merely wit* 
 
GENERAL ANALYSIS OF PROPOSITIONS 21 
 
 the relations of words, or even of ideas (though, of course, 
 propositions are judgments expressed in words), but with 
 matters of fact; that is, both propositions and judgments 
 point to something further, to the relations of things which 
 we can examine, not merely by thinking about them (com- 
 paring them in thought), but by observing them with the 
 united powers of thought and perception. This is what 
 convinces us that water rusts iron : and the difficulty of 
 doing this is what prevents our feeling sure that murderers 
 are haunted by the ghosts of their victims. Hence, although 
 Mill's definition of a proposition, given above, is adequate 
 for propositions in general ; yet that kind of proposition 
 (the Real) with regard to which Logic (in Mill's view) inves- 
 tigates the conditions of proof, may be more explicitly and 
 pertinently defined as * a predication concerning the relation 
 of matters of fact.' 
 
 5. This leads to a very important distinction to which 
 we shall often have to refer in subsequent pages namely, 
 the distinction between the Form and the Matter of a pro- 
 position or of an argument. The distinction between Form 
 and Matter, as it is ordinarily employed, is easily understood. 
 An apple growing in the orchard and a waxen apple on the 
 table may have the same shape, but consist of different 
 materials ; two real apples may have the same shape, but 
 contain distinct ounces of apple-stuff, so that after one is 
 eaten the other remains to be eaten. Similarly, tables may 
 have the same shape, though one be made of marble, 
 another of oak, another of iron. The form is common to 
 several things, the matter is peculiar to each. Metaphysicians 
 have, by analogy, carried the distinction further : apples, they 
 say, may have not only the same outward shape, but the same 
 inward constitution, which, therefore, may be called the Form 
 of apple-stuff namely, a certain pulpiness, juiciness, sweetness, 
 etc. ; qualities common to all dessert apples : yet their Matter 
 is different, one being here, another there differing in place 
 or time, if in nothing else. 
 
22 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 To apply this distinction to the things of Logic : it is easy 
 to see how two propositions may have the same Form but 
 different Matter : not using ' Form ' in the sense of ' shape,' 
 but for that which is common to many things, in contrast 
 with that which is peculiar to each. Thus, All male lions have 
 tufted tails and All water is liquid at 50 Fahrenheit, are two 
 propositions that have the same form, though their matter i^ 
 entirely different. They both predicate something of the whole 
 of their subjects, though their subjects are different, and so are 
 the things predicated of them. Again, All male lions have 
 tufted tails and All male lions have manes, are two propositions 
 having the same form and in their subjects the same matter, 
 but different matter in their predicates. If, however, we take 
 two such propositions as these : All male lions have manes and 
 Some male lions have manes, here the matter is the same in 
 both, but the form is different in the first, predication 
 is made concerning every male lion ; in the second of only some 
 male lions; the first is universal, the second is particular. 
 Or, again, if we take Some tigers are man-eaters and Some 
 tigers are not man-eaters, here too the matter is the same, 
 but the form is different ; for the first proposition is affirma- 
 tive, whilst the second is negative. 
 
 6. Now, according to Hamilton and Whately, pure Logic 
 has to do only with the Form of propositions and arguments. 
 As to their Matter, whether they are really true in fact, that is 
 a question, they said, not for Logic, but for experience, or for 
 the special sciences. But Mill desired so to extend logical 
 method as to test the material truth of propositions : he thought 
 that he could expound a method by which experience itself 
 and the conclusions of the special sciences may be examined. 
 
 To this method, however, some critics persistently object, 
 that the claim to determine Material Truth takes for granted 
 that the order of Nature will remain unchanged, that (for ex- 
 ample) water not only at present is a liquid at 50 Fahrenheit, 
 but will always be so ; whereas (although we have no reason to 
 expect such a thing) the order of Nature may alter it is 
 
GENERAL ANALYSIS OF PROPOSITIONS 23 
 
 least supposable and in that event water may freeze at such a 
 temperature. On the other hand, they urge that a certain 
 kind of Formal Truth may be placed beyond even the suppo- 
 sition of possible error. An apple, for example, is either green 
 all over, or it is not : if we affirm the one alternative we must 
 deny the other; this is necessary to all intelligible use of 
 language and to all clearness of thought. But upon the ques- 
 tion of material truth, as to the apple being really green all 
 over, a certain dubiousness is defensible and not undignified. 
 For what, after all, is meant by an apple ' green all over ' ? What 
 is 'green' ? To whom is it green ? Not to the colour-blind. In what 
 circumstances ? Not in the dark. Any matter of fact must depend 
 on observation, either directly, or by inference as when some- 
 thing is asserted about atoms or ether. But observation and 
 material inference are subject to the limitations of our faculties ; 
 and however we may aid observation by microscopes and 
 micrometers, it is still observation; and however we may 
 correct our observations by repetition, comparison and refined 
 mathematical methods of making allowances, the correction 
 of error is only an approximation to accuracy. Outside of 
 Formal Reasoning, suspense of judgment is your only attitude. 
 
 It is not to be supposed that such reflections did not occur 
 to Mill, though he may have thought them strained and 
 negligible. Here, however, it seems to me right to allow them 
 some weight ; and accordingly prominence will be given to the 
 character of Logic as a Formal Science. It will also be shown 
 that Induction may be included in Logic and treated formally. 
 But it will be assumed that logical forms are only valuable so 
 far as they represent the actual relations of natural phenomena. 
 
 7. Symbols are often used in Logic instead of concrete 
 terms, not only in Symbolic Logic where the science is treated 
 algebraically (as by Dr. Venn in his Symbolic Logic\ but in 
 ordinary manuals ; so that it may be well to explain the use of 
 them before going further. 
 
 It is a common and convenient practice to illustrate logical 
 doctrines by examples : to show what is meant by a Propositioo 
 
24 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 we may give salt is soluble, or water rusts iron : the copulative 
 exponible is exemplified by salt is savoury and wholesome ; and 
 so on. But this procedure has some disadvantages : it is often 
 cumbrous ; and it may distract the reader's attention from the 
 point to be explained by exciting his interest in the special fact 
 of the illustration. Clearly, too, if Logic is only formal, no 
 particular matter of fact can adequately illustrate any of its 
 doctrines. Accordingly, writers on Logic employ letters of the 
 alphabet instead of concrete terms, (say) X instead of salt or 
 instead of iron, and (say) Y instead of soluble or instead of 
 rusted by water ; and then a proposition may be represented by 
 X is Y. It is still more usual to represent a proposition by 5 is 
 (or is not) P, S being the initial of Subject and P of Predicate ; 
 though this has the drawback that if we argue S is P, 
 therefore P is S, the symbols in the latter proposition no longer 
 have the same significance, since the former subject is now the 
 predicate. 
 
 Again, negative terms frequently occur in Logic, such as not- 
 water, or not-iron, and then if water or iron be expressed by X, 
 the corresponding negative may be expressed by x ; or, generally, 
 if a capital letter stand for a positive term, the corresponding 
 small letter represents the negative. 
 
 And as terms are often compounded, it may be convenient 
 to express them by a combination of letters : instead of 
 illustrating such a case by boiling water or water that is boiling^ 
 we may write XY ; or since positive and negative terms may be 
 compounded, instead of illustrating this by water that is not 
 boiling, we may write Xy. 
 
 The convenience of this is obvious ; but it is more than con- 
 venient ; for, if one of the chief uses of Logic is to dicipline 
 the power of abstract thought, this can be done far more 
 effectually by symbolic than by concrete examples ; and if such 
 discipline were the only use of Logic it might be best to 
 discard concrete illustrations altogether, at least In advanced 
 text-books, though no doubt the practice would be too severe 
 for elementary manuals. But on the other hand, to teach 
 
GENERAL ANALYSIS OF PROPOSITIONS 25 
 
 the practical applicability of Logic to the arguments and 
 proofs of actual life, or even of the concrete sciences, merely 
 symbolic illustration may be not only useless but even mis- 
 leading. When we speak of politics, or poetry, or species, or 
 the weather, the terms that must be used can rarely have the 
 distinctness and isolation of X and Y ; so that the perfunctory 
 use of symbolic illustration makes argument and proof appear 
 to be much simpler and easier matters than they really are. 
 Indeed, in this connection, it is impossible to illustrate Logic 
 sufficiently : the reader who is in earnest about the cogency of 
 arguments and the limitation of proofs, and is scrupulous as to 
 the degrees of assent that they require, must constantly look 
 for illustrations of the science in his own experience and rely 
 at last upon his own sagacity. 
 
CHAPTER III 
 OF TERMS AND THEIR DENOTATION 
 
 i. In treating of Deductive Logic it is usual to recognise 
 three divisions of the subject: first, the doctrine of Terms, 
 words, or other signs used as subjects or predicates ; secondly, 
 the doctrine of Propositions, in which terms are combined ; 
 and, thirdly, the doctrine of the Syllogism in which proposi- 
 tions are combined as the grounds of a conclusion. 
 
 The terms employed are either letters of the alphabet, or 
 the words of common language, or the technicalities of science ; 
 and since the words of 'common language are most in use, it is 
 necessary to give some account of common language as sub- 
 serving the purposes of Logic. It has been urged 'that we 
 cannot think or reason at all without words, or some substitute 
 for them, such as the signs of algebra; and although this 
 opinion is too sweeping, since minds greatly differ, and some 
 think in definite and comprehensive picturiags, and we all 
 draw many simple inferences by means of mental imagery, and 
 even animals do so when judging of prey, or enemies, or friends 
 by their scent or by the noises they make; yet the more 
 elaborate inferences, and especially the grouping and concate- 
 nation of inferences, which we call reasoning, seem to be 
 impossible without language or some equivalent system of 
 signs. It is not merely that we need language to express our 
 reasonings and communicate them to others : in solitary 
 thought we depend on words 'talk to ourselves,' in fact; 
 though the words or sentences that then pass through our 
 minds are not always fully formed or articulated. In Logic, 
 
 
OF TERMS AND THEIR DENOTATION *; 
 
 moreover, we have carefully to examine the grounds (at least 
 the formal and proximate grounds) of our conclusions ; and 
 plainly this cannot be done unless the conclusions in question 
 are explicitly stated and recorded. 
 
 Conceptualists say that Logic deals not with the process of 
 thinking (which belongs t.o Psychology) but with its results ; not 
 with conceiving but with concepts ; not with judging but with 
 judgments. Is the concept self-consistent or adequate, Logic 
 asks-f 'f's the judgment capable of proof ? Now, it is only by 
 fording ouj thoughts in language that it becomes possible to 
 'distinguish between the process and the result of thought. As 
 a mere train of mental imagery, the act and the product of 
 thinking would be identical and equally evanescent. But by 
 carrying on the:proqess in language and"remembering or other- 
 wise recording it, we obtain a result which may be examined 
 according to the principles of Logic. 
 
 2. As Logic, then, must give some account of language, it 
 seems desirable to explain how its treatment of language differs 
 from that of Grammar and from that of Rhetoric. 
 
 Grammar is the study of the words of some language, their 
 classification and derivation, and of the rules of combining 
 them -according to the usage at any time recognised and 
 followed by those who are considered good authors. Composi- 
 tion may be faultless in its grammar, though dull and absurd. 
 
 Rhetoric is the study of language with a view to obtaining 
 some special eSect in the communication of ideas or feelings, 
 such* as picturesqueness in description, vivacity in narration, 
 lucidity in exposition, vehjsmence in persuasion, or literary 
 charm. Some of these ends are often gained in spite of faulty 
 syntax or faulty logic ; but since the few whom bad grammar 
 saddens or incoherent arguments divert are not carried away 
 as they else might be by an unsophisticated orator, Grammar 
 and Logic are 'pecessary to the perfection of Rhetoric. Not 
 that Rhetoric is in bondage to those other sciences ; for foreign 
 idioms and such figures as the ellipsis, the anacoluthon, the 
 oxymoron, the hyperbole, and violent inversions have their 
 
2 8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 places in the magnificent style ; but authors unacquainted with 
 Grammar and Logic are not likely to place such figures well 
 and wisely. Indeed, common idioms, though both grammati- 
 cally and rhetorically justifiable, both correct and effective, 
 often seem illogical. ' To fall asleep,' for example, is a perfect 
 English phrase ; yet if we examine severally the words it 
 consists of, it may seem strange that their combination should 
 mean anything at all. 
 
 But Logic only studies language so far as necessary in order 
 to state, understand, and check the evidence and reasonings 
 that are usually embodied in language. And as long as 
 meanings are clear, good Logic is compatible with false con- 
 cords and inelegance of style. 
 
 3. Terms are either Simple or Composite : that is to say, 
 they may consist either of a single word, as 'Chaucer,' 
 1 civilisation ' ; or of more than one, as ' the father of English 
 poetry,' or * modern civilised nations.' Logicians classify words 
 according to their uses in forming propositions ; or, rather* 
 they classify the uses of words as terms, not the words them- 
 selves ; for the same word may fall into different classes of 
 terms according to the way in which it is used. (Cf. Mr. 
 Alfred Sidgwick's Distinction and the Criticism of Beliefs^ 
 chap, xiv.) 
 
 Thus words are classified as Categorematic or Syncategore- 
 matic. A word is Categorematic if used singly as a term 
 without the support of other words: it is Syncategorematic 
 when joined with other words in order to constitute the 
 subject or predicate of a proposition. If we say Venus is a 
 planet whose orbit is inside the Earth's^ the subject, ' Venus,' is 
 a word used categorematically as a simple term ; the predicate 
 is a composite term whose constituent words (whether sub- 
 stantive, relative, verb, or preposition) are used syncategorema- 
 tically. 
 
 Prepositions, conjunctions, articles, adverbs, relative pro- 
 nouns, in their ordinary use, can only enter into terms along 
 with other words having a substantive, adjectival or participial 
 
OF TERMS AND THEIR DENOTATION 29 
 
 force ; but when they are themselves the things spoken of and 
 are used substantively (suppositio materialis), they are categore- 
 matic. In the proposition, Of was used more indefinitely three 
 hundred years ago than it is now, 'of is categorematic. On 
 the other hand, all substantives may be used categorematically ; 
 and the same self-sufficiency is usually recognised in adjectives 
 and participles. Some, however, hold that the categorematic 
 use of adjectives and participles is due to an ellipsis which the 
 logician should fill up ; that instead of Gold is heavy, he should 
 say Gold is a heavy metal ; instead of The sun is shining, The 
 sun is a body shining. But in these cases the words ' metal ' 
 and 'body' are 'unmistakable tautology, since 'metal' is 
 implied in gold and ' body ' in sun. But, as we have seen, 
 any of these kinds of words, substantive, adjective, or'participle, 
 may occur syncategorematically in connection with others to 
 form a composite term. 
 
 4. Most terms (the exceptions and doubtful cases will be 
 discussed hereafter) have two functions, a denotative and a 
 connotative. A term's denotative function is, to be the name 
 or sign of something or some multitude of things, which are 
 said to be called or denoted by the term. Its connotative 
 function is, to suggest certain qualities and characteristics of 
 the things denoted, so that it cannot be used literally as the 
 name of any other things ; which qualities and characteristics 
 are said to be implied or connoted by the term. Thus 
 * sheep ' is the name of certain animals, and its meaning pre- 
 vents its being used of any others. That which a term directly 
 indicates, then, is its Denotation ; that sense or customary use 
 of it which limits the Denotation is its Connotation (ch. iv.). 
 Hamilton and others use * Extension ' in the sense of Denota- 
 tion, and ' Intension ' or * Comprehension ' in the sense of 
 Connotation. Now, terms may be classified, first, according 
 to what they stand for or denote ; that is, according to their 
 ^Denotation. In this respect, the use of a term is said to be 
 either Concrete or Abstract. 
 
 A term is Concrete when it denotes a ' thing ' ; that is, any 
 
30 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 person, object, fact, event, feeling or imagination, considered 
 as capable of having (or consisting of) qualities and a deter- 
 minate existence. Thus 'cricket ball' denotes any object 
 having a certain size, weight, shape, colour, etc. (which are its 
 qualities), and being at any given time in some place and 
 related to other objects in the bowler's hands, on the grass, 
 in a shop window. Any ' feeling of warmth ' has a certain 
 intensity, is pleasurable or painful, occurs at a certain time, 
 and affects some part or the whole of some animal. An 
 imagination, indeed (say, of a fairy), cannot be said in the 
 same sense to have locality ; but it depends on the thinking of 
 some man who has locality, and is definitely related to his 
 other thoughts and feelings. 
 
 A term is Abstract, on the other hand, when it denotes a 
 quality (or qualities), considered by itself and without deter- 
 minate existence in time, place, or relation to other things. 
 1 Size,' ' shape,' ' weight,' ' colour,' * intensity,' ' pleasurableness,' 
 are terms used to denote such qualities, and are then abstract 
 in their denotation. * Weight,' you observe, is not something 
 with a determinate existence at a given time; it exists not 
 merely in some particular place, but wherever there is a heavy 
 thing ; and, as to relation, at the same moment it combines in 
 iron with hardness and in mercury with liquidity. In fact, a 
 quality is a point of agreement in a multitude of different 
 things ; as all heavy things agree in weight, all round things in 
 roundness, all red things in redness ; and an abstract term 
 denotes such a point (or points) of agreement among the things 
 denoted by concrete terms. Thus the use of abstract terms 
 results from the analysis of concrete things into their qualities ; 
 and conversely a concrete term may be viewed as denoting a 
 synthesis of qualities in individual things. When several things 
 agree in more than one quality, there may be an abstract term 
 denoting the union of qualities in which they agree, but not 
 their peculiarities ; as ' human nature ' denotes the common 
 qualities of men, ' civilisation ' the common conditions of 
 civilised peoples. 
 
OF TERMS AND THEIR DENOTATION 31 
 
 Every general name, if used as a concrete term, has, or may 
 have, a corresponding abstract term. Sometimes the concrete 
 term is modified to form the abstract, as ' greedy greediness/ 
 * vain vanity ' ; sometimes a word is adapted from another 
 language, as ' man humanity ' ; sometimes a composite term 
 is used, as * mercury the nature of mercury,' etc. The same 
 concrete may have several abstract correlatives, as * man 
 manhood, humanity, human nature ' ; * heavy weight, gravity, 
 ponderosity ' ; but in such cases the abstract terms are not 
 used quite synonymously ; that is, they imply different ways of 
 considering the concrete. 
 
 Whether a word is used as a concrete or abstract term is in 
 most instances plain from the word itself, the use of most 
 words being pretty regular one way or the other ; but some- 
 times we must judge by the context. 'Weight' may be used 
 in the abstract for ' gravity,' or in the concrete for a measure ; 
 but in the latter sense it is syncategorematic (in the singular), 
 needing at least the article * a (or the) weight.' * Government ' 
 may mean c supreme political authority,' and is then abstract ; 
 or, the set of men who happen to be ministers, and is then 
 concrete ; but in this case, too, the article is usually prefixed. 
 ' The life ' of any man may mean his vitality (abstract), as in 
 " Thus following life in creatures we dissect " ; or, the series of 
 events through which he passes (concrete), as in ' the life of 
 Nelson as narrated by Southey.' 
 
 It has been made a question whether the denotation of an 
 abstract term may itself be the subject of qualities. Apparently 
 ' weight ' may be greater or less, * government ' good or bad, 
 ' vitality ' intense or dull. But if every subject is modified by 
 a quality, a quality is also modified by making it the subject of 
 another ; and, if so, it seems then to become a new quality. 
 The compound terms * great weight,' * bad government,' * dull 
 vitality,' have not the same denotation as the simple terms 
 ' weight,' * government,' * vitality ' : they imply, and may be 
 said to connote, more special concrete experience, such as the 
 effort felt in lifting a trunk, disgust at the conduct of officials, 
 
32 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 sluggish movements of an animal when irritated. It is to such 
 concrete terms that we have always to refer in order fully to 
 realise the meaning of abstract terms, and therefore, of course, 
 to understand any qualification of them. 
 
 5. Concrete terms may be subdivided according to the 
 number of things they denote and the way in which they 
 denote them. A term may denote one thing or many : if one, 
 it is called Singular; if many, it may do so distributively, 
 and then it is General; or, as taken all together, and 
 then it is Collective : one, then ; any one of many ; many in 
 one. 
 
 Among Singular Terms, each denoting a single thing, the 
 most obvious are Proper Names, such as Gibraltar or George 
 Washington, which are merely marks of individual things or 
 persons, and often form no part of the common language of a 
 country. They are thus distinguished from other Singular 
 Terms, which consist of common words so combined as to 
 restrict their denotation to some individual, such as, 'the 
 strongest man on earth.' 
 
 Proper Terms are often said to be arbitrary signs, because 
 their use does not depend upon any reason that may be given 
 for them. Gibraltar had a meaning among the Moors when 
 originally conferred; but no one now knows what it was, 
 unless he happens to have looked it up ; yet the name serves 
 its purpose as well as if it were "Rooke's Nest." Every 
 Newton or Newport year by year grows old, but to alter the 
 name would cause only confusion. If such names were given 
 by mere caprice it would make no difference ; and they could 
 not be more cumbrous, ugly, or absurd than many of those that 
 are given * for reasons.' 
 
 The remaining kinds of Singular Terms, drawn from the 
 common resources of the language, derive their denotative 
 force from their usual meanings. Thus the pronouns 'he,' 'she/ 
 'it,' are singular terms, whose present denotation is determined 
 by the occasion and context of discourse : so with demonstrative 
 phrases ' this man,' ' that horse.' Descriptive names may be 
 
 
OF TERMS AND THEIR DENOTATION 33 
 
 more complex, as 'the wisest man of Gotham,' which is limited 
 to some individual by the superlative suffix; or 'the German 
 Emperor,' which is limited by the definite article the general 
 term * German Emperor' being thereby restricted either to 
 the reigning monarch or lo the one we happen to be dis- 
 cussing. Instead of the definite, the indefinite article may 
 be used to make general terms singular, as ' a German 
 Emperor was crowned at Versailles ' (individua vagd). 
 
 Abstract Terms are ostensively singular : ' whiteness ' (e.g.) 
 is one quality. But their full meaning is general : ' whiteness ' 
 stands for all white things, so far as white. Abstract terms, in 
 fact, are only formally singular. 
 
 General Terms are words, or combinations of words, used to 
 denote any one of many things that resemble one another in 
 certain respects. * George III.' is a Singular Term denoting 
 one man ; but ' King ' is a General Term denoting him and 
 all other men of the same rank ; whilst the compound 'crowned 
 head ' is still more general, denoting kings and also emperors. 
 It is the nature of a general term, then, to be used in the same 
 sense of whatever it denotes ; and its most characteristic form 
 is the Class-name, whether of objects, such as 'king,' 'sheep,' 
 ' ghost ' ; or of events, such as ' accession,' ' purchase,' ' mani- 
 festation.' Things and events are known by their qualities 
 and relations ; and every such aspect, being a point of re 
 semblance to some other things, becomes a ground of general 
 isation, and therefore a ground for the need and use of general 
 terms. Hence general terms are far the most important sort 
 of terms in Logic, since in them general propositions are ex- 
 pressed ; and, moreover (with rare exceptions), all predicates 
 are general. For, besides these typical class-names, attributive 
 words are general terms, such as ' royal,' ' ruling,' ' woolly,' 
 * bleating,' ' impalpable,' ' vanishing.' 
 
 Infinitives may also be used as general terms, as " To err is 
 human " ; but are best translated into equivalent substantive 
 forms, as Foolish actions are characteristic of mankind. Abstract 
 terms, too, are (as I observed) equivalent to general terms : 
 
 c 
 
34 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 * folly ' is abstract for ' foolish actions.' * Honesty is the best 
 policy* means people who are honest may hope to find their 
 account in being so ; that is, in the effects of their honest actions, 
 provided they are wise in other ways, and no misfortunes attend 
 them. The abstract form is often much the more succinct and 
 forcible, but for logical treatment it needs to be interpreted in 
 the general form. 
 
 By autonomasia proper names may become general terms, 
 as if we say c A Johnson ' would not hat? written such 
 a book i.e., any man of his genius for elaborate elo- 
 quence. 
 
 A Collective Term denotes a multitude of similar things, not 
 distributively, but considered as forming one whole, as ' regi- 
 ment,' * flock,' 'nation.' If in a multitude of things there is 
 no resemblance, except the fact of being considered as parts 
 of one whole, as ' the world,' or * the town of Nottingham ' 
 (meaning its streets and houses, open spaces, people, and 
 civic organisation), the term denoting them as a whole is 
 Singular ; but ' the world ' or ' town of Nottingham,' meaning 
 the inhabitants only, is Collective. 
 
 In their strictly collective use, all such expressions 
 are equivalent to singular terms; but many of them may 
 also be used as general terms, as when we speak of c so 
 many regiments of the line,' or discuss the ' plurality of 
 worlds'; and in this general use they denote any of a 
 multitude of things of the same kind regiments, or habitable 
 worlds. 
 
 Names of substances, such as 'gold,' 'air,' 'water,' may 
 be employed as singular, collective, or general terms ; though, 
 perhaps, as singular terms only figuratively, as when we say 
 Gold is king. If we say with Thales, ' Water is the source of 
 all things* ' water ' seems to be used collectively. But sub- 
 stantive names are frequently used as general terms. For ex- 
 ample, Gold is heavy means ' in comparison with other things/ 
 such as water. And, plainly, it does not mean that the 
 aggregate of gold is heavier than the aggregate of water, but 
 
OF TERMS AND THEIR DENOTATION 35 
 
 only that its specific gravity is greater ; that is, bulk for bulk, 
 any piece of gold is heavier than water. 
 
 Finally, any class-name may be used collectively if we wish 
 to assert something of the things denoted by it, not distri- 
 butively but altogether, as that Sheep are more numerous than 
 
CHAPTER IV 
 THE CONNOTATION OF TEfiMS 
 
 i. Terms are next to be classified according to their 
 Connotation that is, according to what they imply as 
 characteristic of the things denoted. We have seen that 
 general names are used to denote many things in the same 
 sense, because the things denoted resemble one another in 
 certain ways : it is this resemblance in certain points that leads 
 us to class the things together and call them by the same 
 name ; and therefore the points of resemblance constitute the 
 sense or meaning of the name, or its Connotation, and limit 
 its applicability to such things as have these characteristic 
 qualities. * Sheep/ fa' example, is used in the same sense, 
 to denote any of a multitude of animals that resemble one 
 another : their size, shape, woolly coats, cloven hoofs, innocent 
 ways and edibility are well known. When we apply to 
 anything the term * sheep/ we imply that it has these qualities: 
 ' sheep/ denoting the animal, connotes its possessing these 
 characteristics ; and, of course, it cannot, without a figure of 
 speech or a blunder, be used to denote anything that does not 
 possess all these qualities. It is by a figure of speech that the 
 term * sheep ' is applied to some men ; and to apply it to goats 
 would be a blunder. 
 
 Most people are very imperfectly aware of the connotation 
 of the words they use, and are guided in using them merely by 
 the custom of the language. A man who employs a word 
 quite correctly may be sadly posed by a request to explain or 
 define it. Moreover, so far as we are aware of the connotation 
 
THE CONNOTATION OF TERMS 37 
 
 of terms, the number and the kind of attributes we think of, 
 in any given case, vary with the depth of our interest, and with 
 the nature of our interest in the things denoted. ' Sheep ' has 
 one meaning to a touring townsman, a much fuller one to a 
 farmer, and yet a different one to a zoologist. But this does 
 not prevent them agreeing in the use of the word, as long as 
 the qualities they severally include in its meaning are not 
 incompatible. 
 
 All general names, and therefore not only class-names, like 
 * sheep,' but all attributives, have some connotation. 'Woolly' 
 denotes anything that bears wool, and connotes the fact of 
 bearing wool ; ' innocent ' denotes anything that habitually 
 does no harm (or has not been guilty of a particular offence), 
 and connotes a harmless character (or freedom from particular 
 guilt); * edible' denotes whatever can be eaten with good 
 results, and connotes its suitability for mastication, deglutition, 
 digestion, and assimilation. 
 
 2. But whether all terms must connote as well as denote 
 something, has been much debated. Proper names, according 
 to what seems the better opinion, are, in their ordinary use, not 
 connotative. To say that they have no meaning may seem 
 violent : if any one is called Alphonso Schultze (which name 
 I invent, hoping that no man bears it), this name, no doubt, 
 means a great deal to his friends and neighbours, reminding 
 them of his stature and physiognomy, his air and gait, his wit 
 and wisdom, some queer stories, and an indefinite number of 
 other things. But all this significance is local or accidental ; 
 it only exists for those who know the individual or have heard 
 him described: whereas a general name gives information 
 about any thing or person it denotes to everybody who under- 
 stands the language, without any particular knowledge of the 
 individual. 
 
 We must distinguish, in fact, between the peculiar associa- 
 tions of the proper name and the commonly recognised meaning 
 of the general name. This is why proper names are not in the 
 dictionary. Such a name as London, to be sure, or Napoleon 
 
38 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Buonaparte, has a significance not merely local; still, it is 
 accidental. c London ' suggests very different things to a 
 Londoner, to his country cousin, and to a merchant in Buenos 
 Ayres. * Napoleon Buonaparte* excites different ideas in 
 France and in Germany, ; and had another meaning for our 
 grandfathers than it has for us. Moreover, these names are 
 borne by other places and persons than those that have ren- 
 dered them famous. There are Londons in various latitudes, 
 and, no doubt, many Napoleon Buonapartes in Louisiana; 
 and each name has in its several denotations an altogether 
 different suggestiveness. For its suggestiveness is in each 
 application determined by the peculiarities of the place or 
 person denoted, and had any other name been given it would 
 have gathered much the same associations. If the French 
 hero had gone by some flat and vulgar appellation, it would 
 have impoverished the romance of history ; but the great bulk 
 of its significance for us would now be the same. 
 
 However, the scientific grounds of the doctrine that proper 
 names are non-connotative, are these : The peculiarities that 
 distinguish an individual person or thing are admitted to be 
 infinite, and anything less than a complete enumeration of 
 these peculiarities may fail to distinguish and identify the 
 individual. For, short of a complete enumeration of them, 
 the description may be satisfied by two or more individuals ; 
 and in that case the term denoting them, if limited by such 
 a description, is not a proper but a general name, since it is 
 applicable to two or more in the same sense. The existence 
 of other individuals to whom it might apply may be highly 
 improbable; but, if it be logically possible, that is enough. 
 On the other hand, the enumeration of infinite peculiarities 
 is certainly impossible. Therefore proper names have no 
 assignable connotation. The only escape from this reasoning 
 lies in falling back upon time and place, the principles of 
 individuation, as constituting the connotation of proper names. 
 Two things cannot be at the same time in the same place : 
 hence * the man who was at a certain spot on the bridge of 
 
THE CONNOTATION OF TERMS 39 
 
 Lodi at a certain instant in a certain year ' suffices to identify 
 Napoleon Buonaparte for that instant. Supposing no one else 
 to have borne the name, then, is this its connotation ? No one, 
 I think, has ever said so. And, at any rate, time and place are 
 only extrinsic determinations (suitable indeed to events like 
 the battle of Lodi, or to places themselves like London); 
 whereas the connotation of a general term, like * sheep,' consists 
 of intrinsic qualities. Hence, then, the scholastic doctrine 
 ' that individuals have no essence ' (see chap. xxii. 9), and 
 Hamilton's dictum * that every concept is inadequate to the 
 individual/ are justified. 
 
 General names, when used as proper names, lose their 
 connotation, as Euxine or Newfoundland. 
 
 Singular terms, other than Proper, have connotation ; either 
 in themselves, like the singular pronouns ' he/ * she/ * it/ which 
 are general in their applicability, though singular in applica- 
 tion ; or, derivatively, from the general names that combine to 
 form them, as in * the first Emperor of the French ' or the 
 ' Capital of the British Empire.' 
 
 3. Whether Abstract Terms have any connotation is 
 another disputed question. We have seen that they denote a 
 quality or qualities of something, and that is precisely what 
 general terms connote : ' honesty ' denotes a quality of some 
 men ; * honest ' connotes the same quality, whilst denoting the 
 men who have it. 
 
 The denotation of abstract terms thus seems to exhaust 
 their force or meaning. It has been proposed, however, to 
 regard them as connoting the qualities they directly stand for, 
 and not denoting anything ; but surely this is too violent. To 
 denote something is the same thing as to be the name of some- 
 thing (whether real or unreal), which every term must be. It 
 is a better proposal to regard their denotation and connota- 
 tion as coinciding; though open to the objection that 'connote' 
 means ' to mark along with ' something else, and this plan 
 leaves nothing else. Mill thought that abstract terms are 
 connotative when, besides denoting a quality, they suggest a 
 
40 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 quality of that quality (as ' fault ' implies * hurtfulness ') ; but 
 against this it may be urged that one quality cannot bear 
 another, since every qualification of a quality constitutes a 
 distinct quality in the total (' milk-whiteness ' is distinct from 
 ' whiteness,' cf. chap. iii. 4). After all, if it is the most con- 
 sistent plan, why not say that abstract, like proper, terms have 
 no connotation ? 
 
 But if abstract terms must be made to connote something, 
 should it not be those things, indefinitely suggested, to which 
 the qualities belong ? Thus ' whiteness ' may be supposed to 
 connote either snow or vapour, or any white thing, apart from 
 one or other of which the quality has no existence; whose 
 existence therefore it implies. By this course the denotation 
 and connotation of abstract and of general names would be 
 exactly reversed. Just as the denotation of a general name is 
 limited by the qualities connoted, so the uicnfllaltoTl of an 
 abstract name is determined by the things in which that 
 denotation is realised. But the whole difficulty may be 
 avoided by making it a rule to translate, for logical purposes, 
 all abstract into the corresponding general terms. 
 
 4. If we ask how the connotation of a term is to be 
 known, here again the answer depends upon the way it is used. 
 If used scientifically, its connotation is determined by, and is 
 the same as, its definition ; and the definition is determined 
 by examining the things to be denoted, as we shall see in 
 chap. xxii. If the same word is used as a term in different 
 sciences, as ' property ' in Law and in Logic, it will be dif- 
 ferently defined by them, and will have, in each use, a corre- 
 spondingly different connotation. But terms used in popular 
 discourse should, as far as possible, have their connotations 
 determined by classical usage, *.*., by the sense in which they 
 are used by writers and speakers who are acknowledged masters 
 of the language, such as Dryden and Burke. In this case the 
 classical connotation determines the definition ; so that to 
 define terms thus used is nothing else than to analyse their 
 accepted meanings. 
 
THE CONNOTATION OF TERMS 41 
 
 It must not, however, be supposed that in popular use the 
 connotation of any word is invariable. Logicians have at- 
 tempted to classify terms into Univocal (having only one 
 meaning) and ^Equivocal (or ambiguous) ; and no doubt some 
 words (like ' civil,' ' natural,' ' proud,' ' liberal,' ' humorous ') are 
 more manifestly liable to ambiguous use than some others. 
 But in truth all general terms are popularly and classically 
 used in different senses. 
 
 Figurative or tropical language chiefly consists in the transfer 
 of words to new senses, as by metaphor or metonymy. In the 
 course of years, too, words change their meanings ; and before 
 the time of Dryden our whole vocabulary was much more fluid 
 and adaptable than it has since become. Such authors as 
 Bacon, Milton, and Sir Thomas Browne often used words 
 derived from the Latin in some sense they originally had in 
 Latin, though in English they had acquired another meaning. 
 Spenser and Shakespeare, besides this practice, sometimes use 
 words in a way that can only be justified by their choosing to 
 have it so; whilst their contemporaries, Beaumont and Fletcher, 
 write the perfect modern language, as Dryden observed. Lapse 
 of time is not the chief cause of variation in the sense of words. 
 The matters which terms are used to denote are often so com- 
 plicated or so refined in the assemblage, interfusion, or gradation 
 of their qualities, that terms do not exist in sufficient abundance 
 and discriminativeness to denote the things, and, at the same 
 time, convey by connotation a determinate sense of their agree- 
 ments and differences. In discussing politics, religion, ethics, 
 aesthetics, this imperfection of language is continually felt ; and 
 the only escape from it, short of coining new words (which, 
 forsooth, is inelegant) is to use such words as we have, now in 
 one sense, now in another somewhat different, and to trust to 
 the context, or to the resources of the literary art, to convey the 
 true meaning, or perhaps to insinuate a deceptive one. Against 
 this evil the having been born since Dryden is no protection. 
 It behoves us, then, to remember that terms are not classifiable 
 into Univocal and ^Equivocal, but that all terms are susceptible 
 
42 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 of being used sequivocally, and that honesty and lucidity re- 
 quire us to try, as well as we can, to uie each term univocally in 
 the same context. 
 
 The context of any proposition always proceeds upon some 
 assumption or understanding as to the scope of the discussion, 
 which controls the interpretation of every statement and of 
 every word. This was called by De Morgan the " universe of 
 discourse " : an older name for it, revived by Dr. Venn, and 
 surely a better one, is suppositio. If now we are talking of 
 children, and 'play' is mentioned, the suppositio limits the 
 suggestiveness of the word in one way ; whilst if Monaco is 
 the subject of conversation, the same word ' play/ under the 
 influence of a different suppositio^ excites altogether different 
 ideas. Hence to ignore the suppositio is a great source of 
 fallacies of equivocation. 'Man' is generally defined as a 
 kind of animal ; but ' animal ' is often used as opposed to and 
 excluding man. 'Liberal' has one meaning under the suppositio 
 of politics, another with regard to culture, and still another as 
 to the disposal of one's private means. Clearly, therefore, the 
 connotation of general terms is relative to .the suppositio^ or 
 " universe of discourse." 
 
 5. Relative and Absolute Terms. Some words go in 
 couples or groups : like ' up-down,' ' former-latter,' ' father- 
 mother-children,' ' hunter-prey,' ' cause-effect,' etc. These are 
 called Relative Terms, and their nature, explained by Mill, 
 is that the connotations of the members of such a pair or group 
 are derived from the same set of facts (the fundamentum re- 
 latwnis). There cannot be an ' up' without a ' down,' a 'father' 
 without a ' mother ' and ' child ' ; there cannot be a ' hunter ' 
 without something hunted, nor 'prey without a pursuer. 
 What makes a man a ' hunter ' is his activities in pursuit ; and 
 what turns a chamois into 'prey' is its interest in these 
 activities. The meaning of both terms, therefore, is derived 
 from the same set of facts ; neither term can be explained 
 without explaining the other, and neither can with propriety be 
 
 
THE CONNOTATION OF TERMS 43 
 
 used without reference to the other, or to some equivalent, as 
 ' game ' for ' prey.' 
 
 In contrast with such Relative Terms, others have been 
 called Absolute or Non-relative. Whilst 'hunter' and 'prey* 
 are relative, { man ' and ' chamois ' have been considered abso- 
 lute, as we may use them without thinking of any special 
 connection between their meanings. However, if we believe ui 
 the unity of Nature and in the relativity of knowledge (that is, 
 that all knowledge depends upon comparison, or a perception 
 of the resemblances and differences of things), it follows that 
 nothing can be completely understood except through its 
 agreements or contrasts with everything else, and that all 
 terms derive their connotation from the same set of facts, 
 namely, from general experience. Thus both man and chamois 
 are animals ; this fact is an important part of the meaning of 
 both terms, and to that extent they are relative terms. ' Five 
 yards ' and * five minutes ' are very different notions, yet they 
 are profoundly related ; for their very difference helps to make 
 both notions distinct ; and their intimate connection is shown 
 in this, that five yards are traversed in a certain time, and that 
 five minutes are measured by the motion of an index over some 
 fraction of a yard upon the dial. 
 
 The distinction, then, between relative and non-relative 
 terms must rest, not upon a fundamental difference between 
 them (since, in fact, all words are relative), but upon the 
 way in which words are used. We have seen that some 
 words, such as * up-down,' * cause-effect,' can only be 
 used relatively ; and these might, for distinction, be called 
 Correlatives. But other words, whose meanings are only 
 partially interdependent, may often be used without attending 
 to their relativity, and may then be considered as Absolute. 
 We cannot say ' the hunter returned empty handed,' without 
 implying that ' the prey escaped ' ; but we may say ' the man 
 went supperless to bed,' without implying that * the chamois re- 
 joiced upon the mountain.' Such words as ' man' and 'chamois' 
 may, then, in their use, be, as to one another, non-relative. 
 
44 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 To illustrate further the relativity of terms, we may mention 
 some of the chief classes of them. 
 
 Numerical order : ist, 2nd, 3rd, etc. Note that ist implies 
 2nd, and 2nd ist; and that 3rd implies ist and 2nd, but these 
 do not imply 3rd ; and so on. 
 
 in Time or Place : before-after; early-punctual-late ; 
 right-middle-left ; North-South, etc. 
 
 As to Extent, Volume, and Degree: greater-equal-less; 
 large-medium-small ; whole and part. 
 
 Genus and Species are a peculiar case of whole and part 
 (cf. chaps, xxi.-ii.-iii.). Sometimes a term connotes all the attri- 
 butes that another does, and more besides, which, as distin- 
 guishing it, are called differential. Thus ' man ' connotes all 
 that * animal ' does, and also (as differentia} the erect attitude, 
 articulate speech, and other attributes. In such a case as this, 
 where we have well-marked natural classes, the term whose 
 connotation is included in the others' is called a Genus of that 
 Species. Thus we have a Genus, triangle; and a Species, 
 isosceles, marked off from all other triangles by the differential 
 quality of having two equal sides. Or, again : Genus, book ; 
 Species, quarto ; Difference, having each sheet folded into four 
 leaves. 
 
 There are other cases where these expressions ' genus ' and 
 ' species ' cannot be so applied without a departure from usage, 
 as, e.g., if we call snow a species of the genus ' white,' for ' white ' 
 is not a recognised class. The connotation of white (/.*., 
 whiteness) is, however, part of the connotation of snow, just as 
 the qualities of ' animal ' are amongst those of ' man ' ; and for 
 logical purposes it is desirable to use ' genus and species ' to 
 express that relativity of terms which consists in the connotation 
 of one being part of the connotation of the other. 
 
 Two or more terms whose connotations severally include 
 that of another term, whilst at the same time exceeding it, are 
 (in relation to that other term) called Co-ordinate. Thus in 
 relation to ' white,' snow and silver are co-ordinate ; in relation 
 to colour, yellow and red and blue are co-ordinate. And when 
 
THE CONNOTATION OF TERMS 45 
 
 all the terms thus related stand for recognised natural classes, 
 the co-ordinate terms are called co-ordinate species ; thus man 
 and chamois are (in Logic) co-ordinate species of the genus 
 animal. 
 
 6. From such examples of terms whose connotations are 
 related as whole and part, it is easy to see the general truth of 
 the doctrine that as connotation decreases, denotation increases: 
 for 'animal,' with less connotation than man or chamois, 
 denotes many more objects ; * white,' with less connotation 
 than snow or silver, denotes many more things. It is not, 
 however, certain that this doctrine is always true in the con- 
 crete : as there may be a term connoting two or more 
 qualities, all of which qualities are peculiar to all the things it 
 denotes ; and, if so, by subtracting one of the qualities from 
 its connotation, we should not increase its denotation. If 
 'man,' for example, has among mammals the two peculiar 
 attributes of erectness and articulate speech, then, by omitting 
 1 articulate speech ' from the connotation of man, we could not 
 apply the name to any more of the existing mammalia than we 
 can at present. Still we might have been able to do so ; there 
 might have been an erect inarticulate ape, and perhaps there 
 once was one ; and, if so, to omit ' articulate ' from the con- 
 notation of man would make the term 'man' denote that 
 animal (supposing that there was no other difference to exclude 
 it). Hence, potentially, an increase of the connotation of any 
 term implies a decrease of its denotation. And, on the other 
 hand, we can only increase the denotation of a term, or apply 
 it to more objects, by decreasing its connotation ; for, if the 
 new things denoted by the term had already possessed its whole 
 connotation, they must already have been denoted by it. How- 
 ever, we may increase the known denotation without decreasing 
 the connotation, if we can discover the full connotation in 
 things not formerly supposed to have it ; or if we can impose 
 the requisite qualities upon new individuals, as when by 
 annexing some millions of Africans we extend the denotation 
 of ' British subject ' without altering its connotation. 
 
46 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Many of the things noticed in this chapter, especially in this 
 section and the preceding, will be discussed at greater length 
 in the chapters on Classification and Definition. 
 
 7. Contradictory Relatives. Every term has, or may have, 
 another corresponding with it in such a way that, whatever 
 differential qualities ( 5) it connotes, this other connotes 
 merely their absence; so that one or the other is always 
 formally predicable of any Subject, but both these terms are 
 never predicable of the same Subject in the same relation : 
 such pairs of terms are called Contradictories. Whatever 
 Subject we take, it is either visible or invisible, but not both ; 
 either human or non-human, but not both. 
 
 This at least is true formally, though in practice we should 
 think ourselves trifled with if any one told us that * A mountain 
 is either human or non-human, but not both/ It is symbolic 
 terms, such as X and x, that are properly said to be contra- 
 dictories in relation to any subject whatever, S or M. For, as 
 we have seen, the ordinary use of terms is limited by some 
 suppositio^ and this is true of Contradictories. Human and 
 non-human may refer to zoological classification, or to the 
 scope of physical, mental, or moral powers as if we ask 
 whether to flourish a dumb-bell of a ton weight, or to know 
 the future by intuition, or impeccability, be human or non- 
 human. Similarly, visible and invisible refer either to the 
 power of reflecting light, so that they have no hold upon a 
 sound or a smell, or else to power of vision and such qualifi- 
 cations as * with the naked eye ' or * with a microscope.' 
 
 Again, the above definition of Contradictories tells us that 
 they cannot be predicated of the same Subject " in the same 
 relation"; that is, at the same time or place, or under the 
 same conditions. The lamp is visible to me now, but will be 
 invisible if I turn it out ; one side of it is now visible, but the 
 other is not : therefore without this restriction, " in the same 
 relation," few or no terms would be contradictory. 
 
 If a man is called wise, it may mean ' on the whole ' or * in a 
 certain action ' ; and clearly a man may for once be wise (or 
 
THE CONNOTATION OF TERMS 47 
 
 act wisely) who, on the whole, is not-wise. So that here again, 
 by this ambiguity, terms that seem contradictory are predicable 
 of the same subject, but not "in the same relation." In order 
 to avoid the ambiguity, however, we have only to construct the 
 term so as to express the relation, as c wise on the whole ' ; and 
 this immediately generates the contradictory ' not-wise on the 
 whole.' Similarly, at one age a man may have black hair, at 
 another not-black hair ; but the difficulty is practically remov- 
 able by stating the age referred to. 
 
 Still, this case easily leads us to a real difficulty in the use of 
 contradictory terms, a difficulty arising from the continuous 
 change or ' flux ' of natural phenomena. If things are con- 
 tinually changing, it may be urged that contradictory terms are 
 always applicable to the same subject, at least as fast as we 
 can utter them : for if we say a man's hair is black, since (like 
 everything else) his hair is changing, it must now be not-black, 
 though (to be sure) it may still seem black. The difficulty, it 
 may be said, lies in this, that the human mind and its 
 instrument language are not equal to the subtlety of Nature. 
 All things flow, but the terms of human discourse assume a 
 certain fixity of things ; everything at every moment changes, 
 but for the most part we can neither perceive this change nor 
 express it in ordinary language. 
 
 This paradox, however, may, I suppose, be easily overstated. 
 The change that continually goes on in Nature consists in the 
 movements of masses or molecules, and such movements of 
 things are compatible with a considerable persistence of their 
 qualities. Not only are the molecular changes always going 
 on in a piece of gold compatible with its remaining yellow, but 
 its persistent yellowness depends on the continuance of some 
 of those changes. And as much may be said for the blackness 
 of a man's hair, though, no doubt, at a certain age its colour 
 may begin to be problematical, and the applicability to it of 
 ' black ' or ' not-black ' may become a matter of genuine anxiety. 
 Whilst being on our guard, then, against fallacies of contra- 
 diction arising from the imperfect correspondence of fact with 
 
48 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 thought and language, we shall often have to put up with it. 
 Candour and humility being satisfied with the above acknow- 
 ledgment of the subtlety of Nature, this book will henceforward 
 proceed upon the postulate that it is possible to use contra- 
 dictory terms such as cannot both be predicated of the same 
 subject in the same relation, though one of them may be ; that, 
 for example, it may be truly said of a man for some years that 
 his hair is black ; and, if so, that during those years to call it 
 not-black is false or extremely misleading. 
 
 It must be observed that the most opposed terms of the 
 literary vocabulary, such as * wise-foolish,' * old-young,' ' sweet- 
 bitter,' are rarely true contradictories : wise and foolish, indeed, 
 cannot be predicated of the same man in the same relation ; 
 but there are many middling men, of whom neither can be 
 predicated on the whole. For the comparison of quantities, 
 again, we have three correlative terms, * greater equal less/ 
 and none of these is the contradictory of either of the others. 
 In fact, the contradictory of any term is one that denotes the 
 sum of its co-ordinates ( 6) ; and to obtain a contradictory, 
 the surest way is to coin one by prefixing to the given terra 
 the particle * not ' or (sometimes) * non ' : as * wise-not-wise/ 
 ' human-non-human,' { greater-not-greater.' 
 
 The separate word * not ' is surer to constitute a contradictory 
 than the usual prefixes of negation, ' un-' or * in-', or even ' non.' 
 Since compounds of these are generally warped by common use 
 from a purely negative meaning. Thus, * Nonconformist ' does 
 not denote everybody who fails to conform. * Unwise ' is not 
 equivalent to * not-wise,' but means ' rather foolish ' a very 
 foolish action is not-wise, but can only be called unwise by 
 meiosis or irony. Still, negatives formed by * in ' or * un ' or 
 1 non ' are sometimes really contradictory of their positives ; as 
 1 visible-invisible,' ' equal-unequal.' 
 
 8. The distinction between Positive and Negative terms is 
 not of much value in Logic, what importance would else 
 attach to it being absorbed by the more definite distinction of 
 contradictories. For contradictories are positive and negative 
 
 ; 
 
THE CONNOTATION OF TERMS 49 
 
 in essence and, when least ambiguously stated, also in form. 
 And, on the other hand, as we have seen, when positive and 
 negative terms are not contradictory, they are misleading. 
 As with ' wise-unwise,' so with many others, such as ' happy- 
 unhappy ' ; which are not contradictories ; since a man may 
 be neither happy nor unhappy, but indifferent, or (again) 
 so miserable that he can only be called unhappy by a figure 
 of speech. In fact, in the common vocabulary a formal 
 negative often has a limited positive sense; and this is the 
 case with unhappy, signifying the state of feeling in the milder 
 shades of purgatory. 
 
 When a Negative term is fully contradictory of its Positive, it 
 is said to be Infinite ; because it denotes an unascertained multi- 
 tude of things, a multitude only limited by the positive term and 
 the suppositio ; thus '$S?4vise ' denotes all except the wise, within 
 the suppositio of ' intelligent beings.' Indeed, formally (dis- 
 regarding any suppositio), such a negative term stands for all 
 possible terms except its positive : x denotes everything but 
 X ; and ' not-wise ' may be taken to include stones, triangles 
 and hippogriffs. In this sense every negative term has some 
 positive meaning, though a very indefinite one, not a specific 
 positive force like 'unwise' or 'unhappy.' It denotes any 
 and everything that has not the attributes connoted by the 
 corresponding positive term. 
 
 Privative Terms connote the absence of a quality that 
 normally belongs to the thing denoted, as ' blind ' or ' deaf.' 
 We may predicate 'blind* or 'deaf of a man, dog or cow that 
 happens not to be able to see or hear, because the powers of 
 seeing and hearing generally belong to these species ; but of a 
 stone or idol these terms can only be used figuratively. 
 Indeed, since the contradictory of a privative carries with it 
 the privative limitation, a stone is strictly ' not-blind ' : that is, 
 it is ' not-something-that-normally-having-sight-wants-it.' 
 
 Contrary Terms are those that (within a certain genus or 
 suppositio] severally connote differential qualities that are in 
 fact mutually incompatible in the same relation to the same 
 
 D 
 
50 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 thing, and therefore cannot be predicated of the same subject 
 in the same relation ; and, so far, they resemble Contradictory 
 Terms : but they differ from contradictory terms in this, that 
 the differential quality connoted by each of them is positive, 
 and, therefore, not infinite but limited (formally) to part of the 
 suppositio excluded by the others ; so that, possibly, neither of 
 two Contraries is truly predicable of a given subject. Thus 
 ' blue ' and * red ' are Contraries, for they cannot both be 
 predicated of the same thing in the same relation ; but are not 
 Contradictories, since, in a given case, neither may be pre- 
 dicable : if a flower is blue in a certain part, it cannot in 
 the same part be red ; but it may be neither blue nor red, but 
 yellow; though it is certainly either blue or not-blue. All 
 co-ordinate terms are formal Contraries, but if, in fact, a series 
 of co-ordinates comprises only two (as male-female), they are 
 Contradictories; since each includes all that area of the 
 suppositio which the other excludes. 
 
 The extremes of a series of co-ordinate terms are Opposites; 
 as, in a list of colours, white and black, the most strongly 
 contrasted, are said to be opposites, or as among moods of 
 feeling, rapture and misery are opposites. But this distinc- 
 tion is of slight logical importance. Imperfect Positive and 
 Negative couples, like 'happy and unhappy,' which (as we 
 have seen) are not contradictories, are often called Opposites. 
 
 The members of any series of Contraries are all included 
 by any one of them and its contradictory, as all colours come 
 under ' red ' and { not-red,' all moods of feeling under ' happy ' 
 and ' not-happy. 1 
 
CHAPTER V 
 THE CLASSIFICATION OF PROPOSITIONS 
 
 i. Logicians classify Propositions according to Quantity, 
 Quality, Relation and Modality. 
 
 As to Quantity, propositions are either Universal or Par- 
 ticular ; that is to say, the predicate is affirmed or denied 
 either of the whole subject or of a part of it of All or of 
 Some S. 
 
 All Sis P (that is, P is predicated of all S). 
 Some S is P (that is, P is predicated of some S). 
 
 An Universal Proposition may have for its subject a singular 
 term, a collective, a general term distributed, or an abstract 
 term. 
 
 (1) A proposition having a singular term for its subject, as 
 The Queen has gone to France, is called a Singular Proposition ; 
 and some Logicians regard this as a third species of propo- 
 sition with respect to quantity, distinct from the Universal and 
 Particular ; but this is needless. 
 
 (2) A collective term may be the subject, as The Black 
 Watch is ordered to India. In this case, as well as in singular 
 
 propositions, a predication is made concerning the whole 
 subject as a whole. 
 
 (3) The subject may be a general term taken in its full 
 denotation, as All apes are sagacious; and in this case a 
 predication is made concerning the whole subject distribu- 
 tively; that is, of each and everything the subject stands ibi. 
 
 (4) Propositions whose subjects are abstract terms, though 
 they may seem to be formally Singular, are really as to their 
 
52 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 meaning distributive Universals ; since whatever is true of a 
 quality is true of whatever thing has that quality so far as that 
 quality is concerned. Truth will prevail means that All true 
 propositions are accepted at last (by sheer force of being true, in 
 spite of interests, prejudices, ignorance and indifference). To 
 bear this in mind may make one cautious in the use of abstract 
 terms. 
 
 In the above paragraphs a distinction is implied between 
 Singular and Distributive Universals ; but it is very important 
 to remember that, technically, every term, whether subject or 
 predicate, when taken in its full denotation (or universally), is 
 said to be 'distributed/ although this word, in its ordinary 
 sense, would be directly applicable only to general terms. In 
 the above examples, then, ' Queen,' * Black Watch,' ' apes/ 
 and ' truth ' are all distributed terms. Indeed, a simple defi- 
 nition of the Universal Proposition is { one;whose subject is 
 distributed.' 
 
 A Particular Proposition is one that has a general term for 
 its subject, whilst its predicate is not affirmed or denied of every- 
 thing the subject denotes ; in other words,, it is one whose 
 subject is not distributed : as Some lions inhabit Africa. 
 
 In ordinary discourse it is not always explicitly stated whether 
 predication is universal or particular ; it would be very natural 
 to say Lions inhabit Africa, leaving it, as far as the words go, 
 uncertain whether we mean all or some lions. Propositions 
 whose quantity is thus left indefinite are technically called 
 1 preindesignate,' their quantity not being stated or designated 
 by any introductory expression ; whilst propositions whose 
 quantity is expressed, as All Foundling-hospitals have a high 
 death-rate, or Some wine is made from grapes, are said to be 
 * predesignate.' Now, the rule is that preindesignate propositions 
 are, for logical purposes, to be treated as particular; since 
 it is an obvious precaution of the science of proof, in any 
 practical application, not to go beyond the evidence. Still the 
 rule may be relaxed if the universal quantity of a preindesignate 
 proposition is well known or admitted, as in Planets shine with 
 
THE CLASSIFICATION OF PROPOSITIONS 53 
 
 reflected light, or Sinners are wretched, though, indeed, the 
 former of these examples, I suppose, may not be true under all 
 conditions. Again, such a proposition as Man is the paragon 
 of animals is not a preindesignate, but an abstract proposition ; 
 the subject being elliptical for Man according to his proper nature ; 
 and the translation of it into a general proposition is not All 
 men are paragons ; nor can Some men be sufficient, since 
 an abstract can only be adequately rendered by a distributed 
 term ; but we must say, All men who approach the ideal. 
 
 The marks or predesignations of Quantity commonly 
 used in Logic are : for Universals, All, Any, Every, Whatever 
 (in the negative No or No one, see next ) ; for Particulars, 
 Some. 
 
 It should be carefully noted that Some, technically used, 
 does not mean Some only, but Some at least (it may be one, or 
 more, or all). If it meant * Some only' every particular propo- 
 sition would be an exclusive exponible (chap. ii. 3) ; since 
 Only some men are wise implies that Some men are not wise. 
 Besides, it may often happen in an investigation that all 
 the instances we have observed come under a certain rule, 
 though we do not yet feel justified in regarding the rule as 
 universal ; and this situation is exactly met by the expression 
 Some (it may be all). 
 
 The words Many,^ Most, Few are generally interpreted to 
 mean Some ; but as 4nost signifies that exceptions are known, 
 and Few that the exceptions are the more numerous, proposi- 
 tions thus predesignate are in fact exponibles, amounting to 
 Some are and Some are not. If to work with both forms is too 
 cumbrous, so that we must choose one, apparently Few are 
 should be treated as Some are not. The scientific course to 
 adopt with propositions predesignate by Most or Few, is to 
 collect statistics and determine the percentage ; thus, Few men 
 are wise say 2 J per cent. 
 
 The Quantity of a proposition, then, is usually determined 
 entirely by the quantity of the subject, whether all or some 
 Still, the quantity of the predicate is often an important 
 
54 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 consideration ; and though in ordinary usage the predicate 
 is never predesignate, Logicians agree that in every Negative 
 Proposition (see 2) the predicate is ' distributed,' that is to 
 say, is denied altogether of the subject, and that this is in- 
 volved in the form of denial. To say Some men are not brave, 
 is to declare that the quality for which men may be called 
 brave is not at all found in the Some men referred to : and, 
 similarly, to say No men are proof against flattery > cuts off the 
 being * proof against flattery ' entirely from the list of human 
 attributes. On the other hand, every Affirmative Proposition 
 is regarded as having an undistributed predicate; that is to 
 say, its predicate is not affirmed exclusively of the subject. 
 Some men are wise does not mean that * wise ' cannot be 
 predicated of any other beings ; it is equivalent to Some 
 men are wise (whoever else may be). And All elephants are 
 sagacious does not limit sagacity to elephants: regarding 
 1 sagacious ' as possibly denoting many animals of many species 
 that exhibit the quality, this proposition is equivalent to * All 
 elephants are some sagacious animals.' Clearly, the affirmative 
 predication of a quality does not imply exclusive possession of 
 it as denial implies its complete absence ; and, therefore, to 
 regard the predicate of an affirmative proposition as distributed 
 would be to go beyond the evidence and to take for granted 
 what had never been alleged. 
 
 Some Logicians, seeing that the quantity of predicates, 
 though not distinctly expressed, is recognised, and holding 
 that it is the part of Logic "to make explicit in language 
 whatever is implicit in thought," have proposed to exhibit 
 the quantity of predicates by predesignation, thus : * Some 
 men are some wise (beings) ' ; * some men are not any brave 
 (beings); etc. This is called the Quantification of the Pre- 
 dicate, and leads to some modifications of Deductive Logic 
 which will be referred to, but not developed, hereafter. (See 
 3 ; and chap. vii. 4.) 
 
 2. As to Quality, Propositions are either Affirmative or 
 Negative. An Affirmative Proposition is, formally, one whose 
 
THE CLASSIFICATION OF PROPOSITIONS 55 
 
 copula is affirmative (or, has no negative sign), as S is P t All 
 men are partial to themselves. A Negative Proposition is 
 one whose copula is negative (or, has a negative sign), as 
 .S is not /*, Some men are not proof against flattery. When, 
 indeed, a Negative Proposition is of Universal Quantity, it is 
 stated thus : No S is P, No men are proof against flattery ; 
 but, in this case, the detachment of the negative sign from the 
 copula and its association with the subject is merely an accident 
 of our idiom ; the proposition is the same as All men are not 
 proof against flattery. It must be distinguished, therefore, 
 from such an expression as Not every man is proof against 
 flattery ; for here the negative sign really qualifies the subject, 
 and the proposition is Particular, being equivalent to Some 
 men are not proof against flattery. 
 
 When the negative sign is associated with the predicate 
 so as to make this an Infinite Term (chap. iv. 8), the 
 proposition is called an Infinite Proposition, as 5 is not-P 
 (or p\ All men are incapable of resisting flattery, or are 
 not-proof against flattery. 
 
 Infinite propositions, when the copula is affirmative, are, 
 formally, themselves affirmative, although their force is chiefly 
 negative ; for, as the last example shows, the difference 
 between an infinite and a negative proposition may depend 
 upon a hyphen. It has been proposed, indeed, with a view to 
 superficial simplification, to turn all Negatives into Infinites, 
 and thus render all propositions Affirmative in Quality. But 
 although every proposition both affirms and denies something 
 according to the aspect in which you regard it (as Snow is 
 white denies that it is any other colour, and Snow is not blue 
 affirms that it is some other colour), yet there is a great 
 difference between the definite affirmation of a genuine 
 affirmative and the vague affirmation of a negative or infinite ; 
 so that materially an affirmative infinite is the same as a 
 negative. 
 
 Generally Mill's remark is true, that affirmation and denial 
 stand for distinctions of facts that cannot be got rid of by 
 
56 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 manipulation of words. Whether granite sinks in water, or 
 not ; whether the rook lives a hundred years, or not ; whether 
 a man has a hundred dollars in his pocket, or not ; whether 
 human bones have ever been found in tertiary strata, or not ; 
 such alternatives require distinct forms of expression. At the 
 same time, it may be granted that many facts admit of being 
 stated with nearly equal propriety in either Quality, as No man 
 is proof against flattery t or All men are open to flattery. 
 
 But whatever . advantage there is in occasionally changing 
 the Quality of a proposition may be gained by the process of 
 Obversion (chap. vii. 5); whilst to use only one Quality 
 would impair the elasticity of logical expression. It is a 
 postulate of Logic that the negative sign may be transferred 
 from the copula to the predicate, or from the predicate to the 
 copula, without altering the sense of a proposition ; and this is 
 justified by the experience that not to have an attribute and to 
 be without it are the same thing. 
 
 3. A. I. E. O. Combining the two kinds of Quantity 
 Universal and Particular, with the two kinds of Quality, 
 Affirmative and Negative, we get four simple types of pro- 
 position, which it is usual to symbolise by the letters A. I. E. O., 
 thus: 
 
 A. Universal Affirmative All S is P. 
 I. Particular Affirmative Some S is P. 
 E. Universal Negative No S is P. 
 O. Particular Negative Some S is not P. 
 
 These symbols are exceedingly useful in abbreviating the 
 exposition of Logic; and they should be so learnt as to 
 suggest their meaning without the least need for an effort of 
 recollection. As an aid to this, observe that A. and I. are 
 the first two vowels in affirmo and that E. and O. are the 
 vowels in nego. 
 
 Those Logicians who explicitly quantify the predicate 
 obtain, in all, eight forms of proposition according to Quantity 
 and Quality : 
 
THE CLASSIFICATION OF PROPOSITIONS 57 
 
 U. Toto-total Affirmative All X is all Y. 
 
 A. Toto-partial Affirmative All X is some Y. 
 
 Y. Parti-total Affirmative Some X is all Y. 
 
 I. Parti-partial Affirmative Some X is some Y. 
 
 E. Toto-total Negative No X is any Y. 
 
 ij. Toto-partial Negative No X is some Y 
 
 O. Parti-total Negative Some X is not any Y. 
 
 w. Parti-partial Negative Some X is not some Y. 
 Here A. I. E. O. correspond with those similarly symbolised 
 in the usual list, merely designating in the predicates the 
 quantity which was formerly treated as implicit. 
 
 4. As to Relation, propositions are either Categorical or 
 Conditional. A Categorical Proposition is one in which the 
 predicate is directly affirmed or denied of the subject without 
 any limitation of time, place, or circumstance, extraneous to 
 the subject, as All men in England are secure of justice ; in 
 which proposition, though there is a limitation of place (' in 
 England'), it is included in the subject. Of this kind are 
 nearly all the examples that have yet been given, according to 
 the form S is P. 
 
 A Conditional Proposition is so called because the predica- 
 tion is made under some limitation or condition not included 
 in the subject, as If a man lives in England he is secure of 
 justice. Here the limitation ' living in England ' is put into a 
 conditional sentence extraneous to the subject, 'he,' repre- 
 senting any man. 
 
 Conditional propositions, again, are of two kinds Hypo- 
 thetical and Disjunctive. Hypothetical propositions are those 
 that are limited by an explicit conditional sentence, as above, 
 or thus : If Joe Smith was a prophet his followers have been 
 unjustly persecuted. Or in symbols thus : 
 If A is, B is ; 
 If A is B, AisC; 
 If A is B, C is D. 
 
 Disjunctive propositions are those in which the condition 
 under which predication is made is not explicit but only 
 
58 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 implied under the disguise of an alternative proposition, as 
 foe Smith was either a prophet or an impostor. Here there is 
 no direct predication concerning Joe Smith, but only a predi- 
 cation of one of the alternatives conditionally on the other 
 being denied, as, If Joe Smith was not a prophet he was an 
 impostor ; or, If he was not an impostor ; he was a prophet. 
 Symbolically, Conditionals may be represented thus : 
 
 A is either B or C, 
 . Either A is B or C is D. 
 
 Now, formally, every Conditional may be expressed as a 
 Categorical. For our last example shows how a Disjunctive 
 may be reduced to two Hypotheticals (of which one is 
 redundant, being the contrapositive of the other ; see chap. vii. 
 10). And a Hypothetical is reducible to a Categorical thus : 
 If rain falls on St. Swithirfs Day, it falls every day for the next 
 forty ; or, in other words, The case of rain falling on St. 
 Swithiris Day is a case of rain falling for the next forty. But 
 this, though the common plan of stating the Categorical 
 equivalent, is portentously clumsy. It would be better to say: 
 Whenever rain falls upon St. Swit kin's Day, it falls for the next 
 forty. Or, recalling Mill's remark that the essence of a Hypo- 
 thetical is to state that one clause of it (the indicative) may be 
 inferred from the other (the conditional), we may write : The 
 falling of rain upon St. Swit kin's Day is a sign of its falling for 
 the next forty. Or, similarly, Proof of Joe Smiths prophetic 
 mission is a proof of his not being an impostor. 
 
 This turning of Conditionals into Categoricals is called a 
 Change of Relation; and the process may be reversed : All the 
 wise are virtuous may be written, If any man is wise he is 
 virtuous ; or, again, Either a man is not wise or he is virtuous. 
 But the categorical form is usually the simplest. 
 
 If, then, as substitutes for the corresponding conditionals, 
 categoricals are formally adequate, though sometimes inelegant, 
 it may be urged that Logic has nothing to do with elegance ,; 
 or that, at any rate, the chief elegance of science is economy, 
 and that therefore, for scientific purposes, whatever we may 
 
THE CLASSIFICATION OF PROPOSITIONS 59 
 
 write further about conditionals must be an ugly excrescence. 
 The scientific purpose of Logic is to assign the conditions of 
 proof. Can we, then, in the conditional form prove anything 
 that cannot be proved in the categorical? Or does a con- 
 ditional require to be itself proved by any method not applic- 
 able to the Categorical ? If not, why go on with the discussion 
 of Conditionals ? For all laws of Nature, however stated, are 
 essentially categorical. c lf a straight line falls on another 
 straight line, the adjacent angles are together equal to two 
 right angles'; 'If a body is unsupported, it falls ' ; * If population 
 increases rents tend to rise ' : here c if ' means * whenever ' or 
 1 all cases in which ' ; for to raise a doubt whether a straight 
 line is ever conceived to fall upon another, whether bodies are 
 ever unsupported, or population ever increases, is a superfluity 
 of scepticism ; and plainly the hypothetical form has nothing 
 to do with the proof of such propositions, nor with inference 
 from them. 
 
 Still, the disjunctive form is useful in stating a Division 
 (chap, xxi.), whether formal (as A is B or not-B) or material 
 (as Cats are white, or black, or tortoiseshell, or tabby). And in 
 some cases the hypoihetical form may be useful. One of these 
 occurs where it is important to draw attention to the condition, 
 as something especially requiring examination. If there is a 
 resisting medium in space, the earth will fall into the sun ; If the 
 Corn Laws are to be re-enacted, we had better sell railways and 
 buy land: here the hypothetical form draws attention to the 
 questions whether there is a resisting medium in space, whether 
 the Corn Laws are likely to be re-enacted ; but as to methods 
 of inference and proof, the hypothetical form has nothing to do 
 with them. The propositions predicate causation : A resisting 
 medium in space is a condition of the earth's falling into the sun ; 
 A Corn Law is a condition of the rise of rents, and the fall of 
 railway profits. 
 
 A second case in which the hypothetical is a specially 
 appropriate form of statement occurs where a proposition relates 
 to a particular matter and to future time, as If there be a storm 
 
60 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 to-morrow, we shall miss our picnic. It is in such cases (which 
 are of very slight logical value) that the categorical form seems 
 most strained and inelegant; but even then it is logically 
 adequate ; and the true reasons why conditionals have to be 
 discussed here and hereinafter are, that it is usual to do so, and 
 that they furnish valuable exercises in formal thinking. Most 
 people find them more difficult to manipulate than categoricals, 
 and therefore they should be more zealously mastered. 
 
 In discussing Conditional Propositions, the conditional 
 sentence of a Hypothetical, or the first alternative of a Dis- 
 junctive, is called the Antecedent ; the indicative sentence of 
 a Hypothetical, or the second alternative of a Disjunctive, is 
 called the Consequent. 
 
 Hypotheticals, like Categoricals, may be classed according 
 to Quantity and Quality. Premising that the quantity of a 
 Hypothetical depends on the quantity of its Antecedent 
 (which determines its limitation), whilst its quality depends 
 on the quality of its consequent (which makes the predication), 
 we may exhibit four forms : 
 
 A. If A is B, Cis D; 
 
 I. Sometimes when A is B, C is D ; 
 
 E. If A is B, C is not D ; 
 
 0. Sometimes when A is B> C is not D. 
 But I. and O. are rarely used. 
 
 As for Disjunctives, it is easy to distinguish the two quantities 
 thus : 
 
 A. Either A is B, or C is D ; 
 
 1. Sometimes either A is B or C is D. 
 
 But I. is rarely used. The distinction of quality, however, 
 cannot be made : there are no true negative forms. If we 
 write : 
 
 Neither is A B, nor C D, 
 
 there is here no alternative predication, but only an Exponible 
 equivalent to No A is B, and No C is D. And if we 
 write : 
 
 Either A is not B, or C is not D, 
 
THE CLASSIFICATION OF PROPOSITIONS 61 
 
 this is affirmative as to the alternation, and is for all methods 
 of treatment equivalent to A. 
 
 Logicians are divided in opinion as to the interpretation of 
 the conjunction ' either, or ' ; some holding that it means * not 
 both,' others that it means * it may be both.' Grammatical 
 usage, upon which the question is sometimes argued, does not 
 seem to be established in favour of either view. If we say 
 A man so precise in his walk and conversation is either a saint or 
 a consummate hypocrite; or, again, One who is happy in a 
 solitary life is either more or less than man ; we cannot in such 
 cases mean that the subject may be both. On the other 
 hand, if it be said that the author of 1 A Tale of a Tub ' is either a 
 misanthrope or a dyspeptic, the alternatives are not incompatible. 
 Or, again, given that X. is a lunatic, or a lover, or a poet, the 
 three predicates have much congruity. 
 
 It has been urged, however, that in Logic, language should be 
 made as exact and definite as possible, and that this requires 
 the exclusive interpretation ' not both.' But it seems a better 
 argument, that Logic, as the science of evidence, must not 
 assume more than is given ; and, therefore, to be on the safe 
 side, must in doubtful cases assume the least, just as it 
 generally assumes a preindesignate term to be of particular 
 quantity. According to this argument, * either, or ' means * one, 
 or the other, or both.' 
 
 However, when both the alternative propositions have the 
 same subject, as either A is B, or A is C, if the two predicates are 
 contrary or contradictory terms (as ' saint ' and * hypocrite,' or 
 'saint' and 'not-saint'), they cannot in their nature be predicable 
 in the same way of the same subject, and, therefore, in such a 
 case ' either, or ' means one or the other, but not both in the 
 same relation. Hence it seems necessary to admit that the 
 conjunction ' either, or ' may sometimes require one interpre- 
 tation, sometimes the other ; and the rule seems to be that it 
 implies the further possibility * or both,' except when both 
 alternatives have the same subject whilst the predicates are 
 contraries or contradictories. 
 
62 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 If, then, the disjunctive A is either B or C (B and C being 
 contraries) implies that both alternatives cannot be true, it can 
 only be adequately rendered in hypotheticals by the two forms 
 (i) If A is B, it is not <7, and (2) If A is not B, it is C. But 
 if the disjunctive A is either B or C (B and C not being con- 
 traries) implies that both may be true, it will be adequately 
 translated into a hypothetical by the single form, If A is not B, 
 it is C. We cannot translate it into If A is B, it is not C , 
 for, by our supposition, if ' A is B ' is true, it does not follow 
 that 'AtsC' must be false. 
 
 It may be observed that these conditional forms often cover 
 assertions that are not true complex propositions, but a sort of 
 enthymemes (chap. xi. 2), arguments abbreviated and rhetori- 
 cally disguised. The hypothetical, * If Plato was not mistaken 
 poets are dangerous citizens? may be considered as an argument 
 against the laureateship, and may be expanded (informally) 
 thus : ' All Plato's opinions deserve respect ; one of them was 
 that poets are bad citizens ; therefore it behoves us to be chary 
 of encouraging poetry.' Or take this disjunctive, * Either 
 Bacon wrote the works ascribed to Shakespeare, or there were 
 two men of the highest genius in the same age and country! This 
 means that it is not likely there should be two such men, that 
 we are sure of Bacon, and therefore ought to give him all the 
 glory. Now, if it is the part of Logic ' to make explicit in 
 language all that is implicit in thought,' or to put arguments 
 into the form in which they can best be examined, such 
 propositions as the above ought to be analysed in the way 
 suggested, and confirmed or refuted according to their real 
 intention. 
 
 5. As to Modality, propositions are divided into Pure and 
 Modal. A Modal proposition is one in which the predicate is 
 affirmed or denied, not simply but cum modo, with a qualifica- 
 tion. And some Logicians have considered any adverb 
 occurring in the predicate, or any sign of past or future 
 tense, enough to constitute a modal : as ' Petroleum is dan- 
 gerously inflammable ' ; * English will be the universal language/ 
 
THE CLASSIFICATION OF PROPOSITIONS 63 
 
 But far the most important kind of modality, and the only 
 one we need consider, is that which is signified by some 
 qualification of the predicate as to the degree of certainty 
 with which it is affirmed or denied. Thus, ,* The bite of 
 the cobra is probably mortal,' is called a Contingent or Pro- 
 blematic Modal : * Water is certainly composed of oxygen and 
 hydrogen ' is an Assertory or Certain Modal : ' Two straight 
 lines cannot enclose a space' is a Necessary or Apodeictic 
 Modal (the opposite being inconceivable). Propositions not 
 thus qualified are called Pure. 
 
 Modal propositions have had a long and eventful history, 
 but they have not been found tractable by the resources of 
 ordinary Logic, and are now generally neglected by the authors 
 of text-books. Accordingly, I shall not enlarge upon the 
 merely logical treatment of them in the present work. No 
 doubt such propositions are common in ordinary discourse, 
 and in some rough way we combine them and draw inferences 
 from them. It is understood that a combination of assertory 
 or of apodeictic premises may warrant an assertory or an 
 apodeictic conclusion ; but that if we combine either of these 
 witha problematic premise our conclusion becomes problematic; 
 whilst the combination of two problematic premises gives a 
 conclusion less certain than either. But if we ask ' How much 
 less certain ? ' we are left to sheer guessing. That the modality 
 of a conclusion follows the less certain of the premises com- 
 bined is inadequate for scientific guidance ; so that, as ordinary 
 Logic can get no farther than this, it is now generally agreed 
 to abandon the discussion of Modals. The true scientific 
 course with regard to them is, to endeavour to determine the 
 degree of certainty attaching to a proposition by collecting 
 statistics with regard to it. Thus, instead of ' The cobra's bite 
 is probably fatal,' we might find that it is fatal 80 times in 100. 
 Then, if we know that of those who go to India 3 in 1000 are 
 bitten, we can calculate what the chances are that any one 
 going to India will die of a cobra's bite (chap. xx.). 
 
 6. Verbal and Real Propositions. Another important 
 
64 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 division of propositions turns upon the relation of the predi- 
 cate to the subject in respect of their connotations. We 
 saw, when discussing Relative Terms, that the connotation of 
 one term often implies that of another; sometimes recipro- 
 cally, like ' master ' and * slave ' ; or by inclusion, like species 
 and genus ; or by exclusion, like contraries and contradictories. 
 When terms so related appear as subject and predicate of the 
 same proposition, the result is often tautology e.g., The master 
 has authority over his slave ; A horse is an animal ; Red is not 
 blue ; British is not foreign. Whoever knows the meaning of 
 1 master/ ' horse,' ' red,' ' British,' learns nothing from these 
 propositions. Hence they are called Verbal propositions, as 
 only expounding the sense of words, or as if they were propo- 
 sitions only by satisfying the forms of language, not by fulfilling 
 the function of propositions in conveying a knowledge of facts. 
 They are also called * Analytic ' and ' Explicative,' when 
 they separate and disengage the elements of the connotation 
 of the subject. Doubtless, such propositions are very useful to 
 one who does not know the language ; and Definitions, which 
 are verbal propositions whose predicates analyse the whole 
 connotations of their subjects, are indispensable instruments 
 of science (see chap. xxii.). 
 
 Of course, hypothetical propositions may also be verbal, as 
 If the soul be material it is extended ; for 'extension' is connoted 
 by * matter ' : and, therefore, the corresponding disjunctive is 
 verbal. But a true divisional disjunctive can never be verbal 
 (chap. xxi. 4, rule i). 
 
 On the other hand, when there is no such direct relation 
 between subject and predicate that their connotations imply 
 one another, but the predicate connotes something that cannot 
 be learnt from the connotation of the subject, there is no longer 
 tautology, but an enlargement of meaning e.g., Masters are 
 degraded by their slaves ; The horse is the noblest animal ; Red is 
 the favourite colour of the British army. Such propositions are 
 called Real, Synthetic, or Ampliative, because they are propo- 
 sitions for which a mere understanding of their subjects would 
 
THE CLASSIFICATION OF PROPOSITIONS 65 
 
 be no substitute, since the predicate adds a meaning of its own 
 concerning matter of fact. 
 
 It has been seriously questioned whether a verbal propo- 
 sition deserves to be called a proposition at all. We may ask 
 whether, to any one who understands the language, a verbal 
 proposition can ever be an inference or conclusion from 
 evidence ; or whether a verbal proposition can ever furnish 
 grounds for an inference, which might not just as well be 
 found in the meaning of the subject? We shall see hereafter 
 that, without an answer to these questions, some important 
 problems must remain unsolved. The whole subject of real 
 and verbal propositions will inevitably recur in the chapters on 
 Definition ; but verbal propositions are such common blemishes 
 in composition, and such frequent and fatal pitfalls in argument, 
 that attention cannot be drawn to them too early or too often. 
 
CHAPTER VI 
 CONDITIONS OF IMMEDIATE INFERENCE 
 
 i. The word Inference is used in two different senses, 
 which are often confused but should be carefully distinguished. 
 In the first sense, it means a process of thought or reasoning 
 by which the mind passes from facts or statements presented, 
 to some opinion or expectation. The data may be very vague 
 and slight, prompting no more than a guess or surmise; as 
 when we look up at the sky and form some expectation about 
 the weather, or from the trick of a man's face entertain some 
 prejudice as to his character. Or the data may be important 
 and strongly significant, like the footprint that frightened 
 Crusoe, or as when news of war makes the city expect that 
 Consols will fall. These are examples of the act of inferring, 
 or of inference as a process ; and with inference in this sense 
 Logic has nothing to do ; it belongs to Psychology to explain 
 how it is that our minds pass from one perception or thought 
 to another thought, and how we come to conjecture, conclude 
 and believe (cf. chap. i. 6). 
 
 In the second sense, 'inference' means not this process of 
 guessing or opining, but the result of it ; the surmise, opinion, 
 or belief when formed ; in a word, the conclusion : and it is in 
 this sense that Inference is treated of in Logic. The subject- 
 matter of Logic is an inference, judgment or conclusion con- 
 cerning facts, embodied in a proposition, which is to be 
 examined in relation to the evidence that may be adduced for 
 it. in order to determine whether, or how far, the evidence 
 amounts to proof. Logic is the science of Reasoning in the 
 
CONDITIONS OF IMMEDIATE INFERENCE 67 
 
 sense in which * reasoning ' means giving reasons, for it shows 
 what sort of reasons are good. Whilst Psychology explains how 
 the mind goes forward from data to conclusions, Logic takes a 
 conclusion and goes back to the data, inquiring whether those 
 data, together with any other evidence (facts or principles) that 
 can be collected, are of a nature to warrant the conclusion. If 
 we think that the night will be stormy, that A. Schultze is of an 
 amiable disposition, that water expands in freezing, or that one 
 means to national prosperity is popular education, and wish to 
 know whether we have evidence sufficient to justify us in 
 holding these opinions, Logic can tell us what form the 
 evidence should assume in order to be conclusive. Observe : 
 I say what form the evidence should assume, not that Logic 
 tells us what facts are proper evidence in any of these cases ; 
 that is a question for the man of special experience in life, or 
 in science, or in business. But whatever the facts are that 
 constitute the evidence, they must, in order to prove the point, 
 admit of being stated in conformity with certain principles or 
 conditions ; and of these principles or conditions Logic is the 
 science. It deals, then, not with the subjective process of 
 inferring, but with the objective grounds that justify or discredit 
 the inference. 
 
 2. Inferences, in the Logical sense, are divided into two 
 great classes, the Immediate and the Mediate, according to the 
 character of the evidence offered in proof of them. In fact, to 
 speak of inferences, in the sense of conclusions, as immediate 
 or mediate, is an abuse of language, derived from times before 
 the distinction between inference as process and inference as 
 result was generally felt. No doubt we ought rather to speak 
 of Immediate and Mediate Evidence ; but it is of little use to 
 attempt to alter the traditional expressions of the science. 
 
 An Immediate Inference, then, is one that depends for its proof 
 upon only one other proposition which has the same, or more 
 extensive, terms (or matter). Thus that one means to national 
 prosperity is popular education is an immediate inference, if 
 the evidence for it is no more than the admission that popular 
 
68 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 education is a means to national prosperity : Similarly, 3t is an 
 immediate inference that Some authors are vain, if it be granted 
 that All authors are vain. 
 
 An Immediate Inference, indeed, is little else than a verbal 
 transformation ; and some Logicians dispute its claims to be 
 called an inference at all, on the ground that it is identical with 
 the pretended evidence. If we attend to the meaning, say 
 they, an immediate inference does not really express any new 
 judgment ; the fact expressed by it is either the same as its 
 evidence, or is even less significant. If from No men are gods 
 we prove that No gods are men, this is nugatory ; if we prove 
 from it that Some men are not gods, this is to emasculate the 
 sense, to waste valuable information, to lose the commanding 
 sweep of our universal proposition. 
 
 Still, in Formal Logic, it is often found that an immediate 
 inference expresses our knowledge in a more convenient form 
 than that of the evidentiary proposition, as will appear in the 
 chapter on Syllogisms and elsewhere. And in transforming an 
 universal into a particular proposition, as No men are gods, 
 therefore, Some men are not gods, the latter statement, though 
 weaker, is far more easily proved; since a single instance 
 suffices. 
 
 A Mediate Inference, on the other hand, depends for its 
 evidence upon a plurality of other propositions (two or more) 
 which are connected together on logical principles. If we 
 argue 
 
 No men are gods ; 
 Alexander the Great is a man ; 
 .*. Alexander the Great is not a god : 
 
 this is a Mediate Inference. The evidence consists of two 
 propositions connected by the term * man,' which is common 
 to both (a Middle Term), mediating between * gods ' and 
 'Alexander.' Mediate Inferences comprise Syllogisms with 
 their developments, and Inductions ; and to discuss them 
 further at present would be to anticipate future chapters. We 
 must now deal with the principles or conditions on which 
 
CONDITIONS OF IMMEDIATE INFERENCE 69 
 
 Immediate Inferences are valid : commonly called the " Laws 
 of Thought." 
 
 3. The Laws of Thought are conditions of the logical 
 statement and criticism of all sorts of evidence; but as to 
 Immediate Inference, they may be regarded as the only 
 conditions it need satisfy. They are three : (i) The principle 
 of Identity (usually stated as * Whatever is, is,' or ' A is A ') ; 
 (2) The principle of Contradiction ( ; It is impossible for the 
 same thing to be and not be,' or ' A is not not- A ') ; (3) The 
 principle of Excluded Middle (' Anything must either be or 
 not be,' or ' B is either A or not A '). These principles are 
 manifestly not * laws ' of thought in the sense in which ' law ' 
 is used in Psychology ; they do not, like the laws of the 
 association of ideas, profess to give an account of the actual 
 mental processes that uniformly take place in judgment or 
 reasoning. If they were such natural laws of thought, it 
 would be impossible for anybody to mistake one thing for 
 another or assume that the same thing may both be and 
 not be ; whereas we know that people frequently make such 
 mistakes. In relation to thought, therefore, these principles 
 can only be regarded as laws when stated as precepts, the 
 observance of which (consciously or not) is necessary to clear 
 and consistent thinking: e.g., Never assume that the same 
 thing can both be and not be. 
 
 However, in this book, Logic is treated as the science of 
 thought only as embodied in propositions, in respect of which 
 evidence is to be adduced, or which are to be used as evi- 
 dence of other propositions ; and, accordingly, the above laws 
 or principles must be restated as the conditions of consistent 
 argument in such terms as to be directly applicable to propo- 
 sitions. Now, it was shown in the chapter on the connotation 
 of terms, that terms are assumed by Logicians to be capable of 
 definite meaning, and of being used um'vocally in the same 
 context : if, or in so far as, this is not the case, we cannot 
 understand one another's reasons nor even pursue in solitary 
 meditation any coherent train of argument. We saw, too, 
 
70 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 that the meanings of terms were related to one another: 
 some being full correlatives; others partially inclusive one 
 of another, as species of genus ; others mutually incompatible, 
 as contraries ; or alternatively predicable, as contradictories. 
 We now assume that propositions are capable of definite 
 meaning according to the meaning of their component terms 
 and of the relation between them ; that the meaning, the fact 
 asserted or denied, is what we are really concerned to prove or 
 disprove ; that a mere change in the words that constitute our 
 terms, or of construction, does not affect the truth of a propo- 
 sition as long as the meaning is not altered, or (rather) as long 
 as no fresh meaning is introduced ; and that if the meaning of 
 any proposition is true, any other proposition that denies it is 
 false. This postulate is plainly necessary to consistency of 
 statement and discourse ; and consistency is necessary, if our 
 thought or speech is to correspond with the unity and co- 
 herence of Nature and experience ; and the Laws of Thought 
 or Conditions of Immediate Inference are an analysis of this 
 postulate. 
 
 4. The principle of Identity is usually written symbolically 
 thus : A is A ; not- A is not-A. It assumes that something is, 
 and that it may be represented by a term. We need not here 
 raise any metaphysical question whether after all anything can 
 be said really to &, to be self-identical and sempiternal. Logic 
 takes for granted a certain relative identity and persistence of 
 things. Socrates in his father's workshop, at the battle of 
 Delium, and in prison, is assumed to be the same man 
 denotable by the same name; and similarly, elephant, or 
 justice, or fairy, in the same con f e\t, is to be understood of 
 the same thing under the same suppositio. 
 
 But, further, it is assumed that of the same term another 
 term may be predicated again and again in the same sense 
 under the same conditions ; that (in other words) we may 
 epeak of the identity of meaning in a proposition as well as in a 
 term. To symbolise this we ought to alter the usual formula 
 for Identity and write it thus : If B is A, B is A ; if B is 
 
CONDITIONS OF IMMEDIATE INFERENCE 71 
 
 not- A, B is not- A. If Socrates is wise, he is wise ; if fairies 
 frequent the moonlight, they do ; if Justice is not of this world, 
 it is not. Whatever affirmation or denial we make concerning 
 any subject, we are bound to adhere to it for the purposes of 
 the current argument or investigation. Of course, if our 
 assertion turns out to be false, we must not adhere to it ; but 
 then we must repudiate all that we formerly deduced from it 
 and begin again with a clean slate. 
 
 Again, whatever is true or false in one form of words is 
 true or false in any other : this is undeniable ; but in Formal 
 Logic it is not very convenient. If Socrates is wise, is it an 
 identity to say * Therefore the master of Plato is .wise ' ; or, 
 further, that he ' takes enlightened views of life ' ? If Every 
 man is fallible, is it an identical proposition that Every man 
 is liable to error ? It seems pedantic to demand a separate 
 proposition that Fallible is liable to error. But, on the other 
 hand, the insidious substitution of one term for another 
 speciously identical, is a chief occasion of fallacy. How if 
 we go on to argue : therefore, Every man is apt to blunder, 
 prone to confusion of thought, inured to self-contradiction? 
 Practically, I am afraid that the substitution of identities 
 must be left to candour and good-sense ; and may they 
 increase among us. But Formal Logic is, no doubt, safest 
 with symbols ; should, perhaps, content itself with A and B ; 
 or, at least, hardly venture beyond Kand Z. 
 
 5. The principle of Contradiction is usually written 
 symbolically, thus : A is not not-A. But, since this formula 
 seems to be adapted to a single term, whereas we want 
 one that is applicable to propositions, it may be better 
 to write it thus : B is not both A and not-A. That is to 
 say : if any term may be affirmed of a subject, the contra- 
 dictory term may be denied of it in the same relation. A 
 leaf that is green on one side of it may be not-green on the 
 other ; but it is not both green and not-green on the same 
 surface, at the same time, and in the same light. If a stick is 
 straight, it is false that it is at the same time not-straight: 
 
72 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 having granted that two angles are equal, we must deny that 
 they are unequal. 
 
 But is it necessarily false that the stick is * crooked ' ; must we 
 deny that either angle is ' greater or less' than the other ? How 
 far is it permissible to substitute any other term for the formal 
 contradictory? Clearly, the principle of Contradiction takes 
 for granted the principle of Identity and is subject to the 
 same difficulties in its practical application. As a matter of 
 fact and common sense, if we affirm any term, we are bound 
 to deny not only the contradictory but all synonyms for this, 
 and also all contraries and opposites ; which, of course, are 
 included in the contradictory. But who shall determine what 
 these are? Without an authoritative Logical Dictionary to 
 refer to, where all contradictories, synonyms, and contraries 
 may be found on record, Formal Logic will hardly sanction the 
 free play of common sense. 
 
 The principle of Excluded Middle is usually written : B is 
 either A or not-A ; that is, if any term be denied of a subject, 
 the contradictory term may be affirmed in the same relation. 
 Of course, we may deny that a leaf is green on one side 
 without being bound to affirm that it is not-green on the 
 other. But in the same relation a leaf is either green or not- 
 green ; at the same time, a stick is either bent or not-bent. If 
 we deny that A is greater than B, we must affirm that it is not- 
 greater than B. 
 
 Whilst, then, the principle of Contradiction (that ' of contra- 
 dictory predicates, one being affirmed, the other is denied') 
 might seem to leave open a third or middle course, the 
 denying of both contradictories, the principle of Excluded 
 Middle derives its name from the excluding of this middle 
 course, by declaring that the one or the other must be 
 affirmed. Hence the principle of Excluded Middle does 
 not hold good of mere contrary terms. If we deny that a 
 leaf is green, we are not bound to affirm it to be yellow; 
 for it may be red ; and, therefore, we may deny both con- 
 traries, yellow and green. In fact two contraries do not 
 
CONDITIONS OF IMMEDIATE INFERENCE 73 
 
 between them cover the whole predicable area, but contra- 
 dictories do : the form of their expression is such that (within 
 the suppositio) each includes all that the other excludes ; so 
 that the subject (if brought within the suppositio] must fall 
 under the one or the other. It may seem absurd to say that 
 Mont Blanc is either wise or not-wise ; but how comes any 
 mind so ill-organised as to introduce Mont Blanc into this 
 strange company? Being there, however, the principle is 
 inexorable : Mont Blanc, alas ! is not-wise. 
 
 In fact, the principles of Contradiction and Excluded 
 Middle are inseparable ; they are implicit in all distinct 
 experience, and may be regarded as indicating the two aspects 
 of Negation. The principle of Contradiction says : B is not 
 both A and not- A, as if not- A might be nothing at all ; this is 
 abstract negation. But the principle of Excluded Middle says : 
 Granting that B is not A^ it is still something namely, not- A ; 
 thus bringing us back to the concrete experience of a con- 
 tinuum in which the absence of one thing implies the presence 
 of something else. Symbolically : to deny that B is A is to 
 affirm that B is not A, and this only differs by a hyphen from 
 B is not- A. But if any one holds that the hyphen makes all 
 the difference, I give it up. 
 
 These principles, which were necessarily to some extent 
 anticipated in chap. iv. 7, the next chapter will further 
 illustrate. 
 
 6. But first we must draw attention to a maxim (also 
 already mentioned), which is strictly applicable to Immediate 
 Inferences, though (as we shall see) in other kinds of proof it 
 may be only a formal condition : this is the general caution 
 not to go beyond the evidence. An immediate inference 
 ought to contain nothing that is not contained (or formally 
 implied) in the proposition by which it is proved. With 
 respect to quantity in denotation, this caution is embodied 
 in the rule ' not to distribute any term that is not given distri- 
 buted.' Thus, if there is a predication concerning ' Some S,' 
 or ' Some men,' as in the forms I. and O., we cannot infer any- 
 
74 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 thing concerning * All S,' or c All men ' ; and, as we have seen, 
 if a term is given us preindesignate, we are generally to take it 
 as of particular quantity. Similarly, in the case of affirmative 
 propositions, we saw that this rule requires us to assume that 
 their predicates are undistributed. 
 
 As to the grounds of this maxim, not to go beyond the 
 evidence, not to distribute a term that is given as undistri- 
 buted, it is one of the things so plain that to try to justify 
 is only to obscure them. We might indeed say that such 
 a leap from the particular to the general is not sanctioned by 
 any of the three Laws of Thought. The caution against it 
 may particularly be viewed as supplementary to the principle 
 of Identity, that whatever is true in one form of words is true 
 in any other ; since if for * Some S ' we substitute * All S,' we 
 no longer have the same sense as the given form of words. It 
 is a gratuitous assumption, a mere non-sequitur ; and if any 
 controvertist demands permission to make it, the Formal 
 Logician can only " hold up his hands in respectful amaze- 
 ment." 
 
 Still we must here state explicitly what Formal Logic 
 assumes to be contained or implied in the evidence afforded 
 by any proposition, such as 'All S is P.' If we remember 
 that in chap. iv. 7, it was assumed that every term may 
 have a contradictory ; and if we bear in mind the principles 
 of Contradiction and Excluded Middle, it will appear that 
 such a proposition as ' All S is P ' tells us something not only 
 about the relations of ' S ' and * P ', but also of their relations 
 to * not-S ' and ' not-P ' ; as, for example, that ' S is not not-P ', 
 and that ' not-P is not-S.' It will be shown in the next chapter 
 how Logicians have developed these implications in series of 
 Immediate Inferences. 
 
 If it be asked whether it is true that every term, itself 
 significant, has a significant contradictory, and not merely a 
 formal contradictory, generated by force of the word ' not,' it is 
 difficult to give any better answer than was indicated in 3-5, 
 without venturing further into Metaphysics. I shall merely 
 
CONDITIONS OF IMMEDIATE INFERENCE 75 
 
 say, therefore, that, granting that some such term as 'Uni- 
 verse ' or ' Being ' may have no significant contradictory, if it 
 stand for 'whatever can be perceived or thought of; yet 
 every term that stands for less than ' Universe ' or ' Being ' 
 has, of course, a contradictory which denotes the rest of the 
 universe. And since every argument or train of thought is 
 carried on within a special ' universe of discourse,' or under a 
 certain suppositio^ we may say that within the special universe or 
 suppositio every term has a contradictory, and that every pre- 
 dication concerning a term implies some predication concern- 
 ing its contradictory. But the name of the suppositio itself 
 has no contradictory, except with reference to a wider and 
 inclusive suppositio >. 
 
CHAPTER VII 
 
 IMMEDIATE INFERENCES 
 
 i. Under the general title of Immediate Inference 
 Logicians discuss three subjects, namely, Opposition, Con- 
 version, and Obversion ; to which some writers add other 
 forms, such as Whole and Part in Connotation, Contraposi- 
 tion, Inversion, etc. Of Opposition, again, all recognise four 
 modes : Subalternation, Contradiction, Contrariety and Sub- 
 contrariety. The only peculiarities of the exposition upon 
 which we are now entering are, that it follows the lead of the 
 three Laws of Thought, taking first those modes of Immediate 
 Inference in which Identity is most important, then those 
 which plainly involve Contradiction and Excluded Middle ; 
 and that this method results in separating the modes of Oppo- 
 sition, connecting Subalternation with Conversion, and the 
 other modes with Obversion. To make up for this departure 
 from usage, the four modes of Opposition will be brought 
 together again in 9. 
 
 2. Subalternation. Opposition being the relation of 
 propositions that have the same matter and differ only in 
 form (as A., E., I., O.), propositions of the forms A. and I. are 
 said to be Subalterns in relation to one another, and so are E. 
 and O. ; the universal of each quality being distinguished as 
 ' subalternans,' and the particular as ' sub-alternate.' 
 
 It follows from the principle of Identity that, the matter of the 
 propositions being the same, if A. is true I. is true, and that if 
 E. is true O. is true ; for A. and E. predicate something of All 
 S or Allmen ; and since I. and O. make the same predicate of 
 
IMMEDIATE INFERENCES 77 
 
 Some S or Some men, the sense of these particular propositions 
 has already been predicated in A. or E. If All S is P, Some 
 S is P; if No S is P, Some S is not P ; or, if All men are fond 
 of laughing. Some men are ; if No men are exempt from ridicule, 
 Some men are not. 
 
 Similarly, if I. is false A. is false ; if O. is false E. is false. 
 If we deny any predication about Some S, we must deny it of 
 All S ; since in denying it of Some, we have denied it of at 
 least part of All ; and whatever is false in one form of words is 
 false in any other. 
 
 On the other hand, if I. is true, we do not know that A. is ; 
 nor if O. is true, that E. is ; for to infer from Some to All would 
 be going beyond the evidence. We shall see in discussing 
 Induction that the great problem of that part of Logic is, to 
 determine the conditions under which we may in reality 
 transcend this rule and infer from Some to All; though even 
 there it will appear that, formally, the rule is observed. For the 
 present it is enough that I. is an immediate inference from A., 
 and O. from E. ; but that A. is not an immediate inference 
 from I., nor E. from O. 
 
 3. Connotative Subalternation. We have seen (chap. iv. 
 6) that if the connotation of one term is only part of another's 
 its denotation is greater and includes that other's. Hence 
 genus and species stand in subaltern relation, and whatever is 
 true of the genus is true of the species : If All animal life is 
 dependent on vegetation, All human life is dependent on vegetation. 
 On the other hand, whatever is not true of the species or 
 narrower term, cannot be true of the whole genus : If it is 
 false that ' All human life is happy J it is false that ' All animal 
 life is happy* 
 
 Similar inferences may be drawn from the subaltern rela- 
 tion of predicates ; affirming the species we affirm the genus. 
 To take Mill's example, if Socrates is a man, Socrates is a 
 living creature. On the other hand, denying the genus we 
 deny the species : if Socrates is not vicious, Socrates is not 
 drunken. 
 
78 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 It cannot be said that such cases as these are generally 
 recognised by Logicians as immediate inferences coming under 
 the principle of Identity. They are so regarded by Mill and 
 Bain ; but probably most authorities upon our science would 
 treat them as imperfect syllogisms, requiring another premise to 
 legitimate the conclusion, as thus : 
 
 All animal life is dependent on vegetation ; 
 All human life is animal life ; 
 .: All human life is dependent on "vegetation. 
 Or again : 
 
 All men are living creatures ; 
 Socrates is a man ; 
 .*. Socrates is a living creature. 
 
 The decision of this issue seems to turn upon the question (cf. 
 chap. vi. 3) how far a Logician is entitled to assume that the 
 terms he uses are understood, and that the identities involved 
 in their meanings will be recognised. And to this question, 
 for the sake of consistency, one of two answers is required, 
 failing which there remains the rule of thumb. First, it may 
 be held that no term is understood except those that are defined 
 in expounding the science, such as * genus ' and * species/ 
 * connotation ' and * denotation.' But very few Logicians 
 observe this limitation ; few would hesitate to substitute ' not- 
 wise* for * foolish.' Yet by what right? Malvolio being 
 foolish, to prove that he is not-wise, we may construct the 
 following syllogism : 
 
 Foolish is not-wise ; 
 Malvolio is foolish; 
 .'. Malvolio is not-wise. 
 Is this necessary ? If not, why not ? 
 
 Secondly, it may be held that all terms may be assumed as 
 understood (amongst those native to the language) unless a 
 definition is challenged. This principle will justify the sub- 
 stitution of ' not-wise ' for * foolish ' ; but it will also legitimate 
 the above cases (concerning ' human life ' and ' Socrates ') as 
 immediate inferences, with innumerable others that might be 
 
 
IMMEDIATE INFERENCES 79 
 
 based upon the doctrine of relative names, as, for example, 
 The hunter missed his aim : therefore, The prey escaped. And 
 from this principle it will further follow that all apparent 
 syllogisms, having one premise a verbal proposition, are 
 immediate inferences (cf. chap. ix. 4). 
 
 Closely connected with such cases as the above are those 
 mentioned by Archbishop Thomson as "Immediate Inferences 
 by added Determinants " (Laws of Thought, 87). He takes 
 the case : * A negro is a fellow -creature : therefore, A negro in 
 suffering is a fellow-creature in suffering? This rests upon the 
 principle that to increase the connotations of two terms by the 
 same attribute or determinant does not affect the relationship 
 of their denotations, since it must equally diminish (if at all) 
 the denotations of both classes, by excluding the same 
 individuals, if any want the given attribute. But, of course, 
 this principle is true only when the added attribute is not 
 merely the same verbally, but has the same significance in 
 qualifying both terms. We cannot argue A mouse is an animal; 
 therefore, A large mouse is a large animal ; for ' large ' is an 
 attribute relative to the normal magnitude of the thing 
 described. 
 
 4. Conversion is Immediate Inference by transposing the 
 terms of a given proposition without altering its quality. If 
 the quantity is also unaltered, the inference is called * Simple 
 Conversion ' ; but if the quantity is changed from universal to 
 particular, it is called ' Conversion by limitation ' or ' per 
 accidens? The given proposition is called the ' convertend ' ; 
 that which is derived from it, the ' converse.' 
 
 Departing from the usual order of exposition, I have taken 
 up Conversion next to Subalternation, because it is generally 
 thought to rest upon the principle of Identity, and because it 
 seems to be a good method to exhaust the forms that come 
 only under Identity before going on to those that involve 
 Contradiction and Excluded Middle. Some, indeed, dispute 
 the claims of Conversion to illustrate the principle of Identity ; 
 and if the sufficient statement of that principle be ' A is A,' it 
 
8o LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 may be a question how Conversion or any other mode of 
 inference can be referred to it. But if we state it as above 
 (chap. vi. 3), that whatever is true in one form of words is true 
 in any other, there is no difficulty in applying it to Conver- 
 sion. 
 
 Thus, to take the simple conversion of I., 
 
 Some S is P ; .'. Some P is S. 
 
 Some poets are men of business ; .*. Some men of business are 
 
 poets. 
 
 Here the convertend and the converse say the same thing, and 
 this is true if that is. 
 
 We have, then, two cases of simple conversion : of I. (as 
 above) and of E. For E. : 
 
 No Sis P; .'.No Pis S. 
 
 No ruminants are carnivores; .*. No carnivores are 
 
 ruminants. 
 
 In converting I., the predicate (P) when taken as the new 
 subject, being preindesignate, is treated as particular, according 
 to the rule, ' not to go beyond the evidence ' (chap. vi. 4) ; 
 and in converting K, the predicate (P), when taken as the 
 new subject, is treated as universal, according to the rule in 
 chap. iv. i. 
 
 A. is the one case of conversion by limitation : 
 
 All S is P; .'. Some P is S. 
 
 All cats are animals ; .'. Some animals are cats. 
 And here the treatment of the predicate as particular, when 
 taking it for the new subject, is according to the rule in chap. iv. 
 i. Palpably, to infer that All animals are cats would never 
 do. The validity of conversion by limitation may be shown 
 thus : if, All S is P, then, by subalternation, Some S is P, and 
 therefore, by simple conversion, Some P is S. 
 
 O. cannot be truly converted. If we take the proposition : 
 Some S is not P, to convert this into No P is S, or Some P is 
 not S, would break the rule in chap. vi. 4 ; since S, undis- 
 tributed in the convertend, would be distributed in the con- 
 verse. If we are told that S<wie men are not cooks,, we cannot 
 
IMMEDIATE INFERENCES 81 
 
 infer that Some cooks are not men. This would be to assume 
 that ' Some men ' are identical with ' All men' 
 
 By quantifying the predicate, indeed, we may convert O. 
 simply, thus : 
 
 Some men are not cooks .'. No cooks are some men. 
 And the same plan has some advantage in converting A. ; for 
 by the usual method per accidens, the converse of A. being I., 
 if we convert this again it is still I., and therefore means less 
 than our original convertend. Thus : 
 
 All S is P .'. Some P is S .'. Some S is P. 
 Such knowledge, as that All S (the whole of it) is P, is too 
 precious a thing to be squandered in pure Logic ; and it may 
 be preserved by quantifying the predicate ; for if we convert 
 A. to Y., thus 
 
 All S is P .*. Some P is all S 
 
 we may reconvert Y. to A. without any loss of meaning. It is 
 perhaps the chief use of quantifying the predicate that, thereby, 
 every proposition is capable of Simple Conversion. 
 
 The conversion of propositions in which the relation of 
 terms is inadequately expressed by the ordinary copula (is or 
 is not) needs a special rule. To argue thus 
 
 A is followed by B .'. Something followed by B is A 
 is clumsy formalism. We usually say, and ought to say 
 
 A is followed by B : 
 .'. B follows A (or is preceded by A). 
 
 Now, any relation between two terms may be viewed from 
 either side A : B or B : A. It is in both cases the same fact ; 
 but, with the altered point of view, it may present a dif- 
 ferent character. For example, in the Immediate Inference 
 A>B .'. B<A a diminishing turns into an increasing ratio, 
 whilst the fact predicated remains the same. Given, then, a 
 relation between two terms as viewed from one to the other, 
 the same relation viewed from the other to the one may be 
 called the Reciprocal. In the cases of Equality, Co-existence 
 and Simultaneity, the given relation and its reciprocal are not 
 only the same fact, but they also have the same character : in 
 
 F 
 
82 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 the cases of Greater and Less and Sequence, the character 
 alters. 
 
 We may, then, state the following rule for the conversion of 
 propositions in which the whole relation explicitly stated is 
 taken as the copula : Transpose the terms, and for the given 
 relation substitute its reciprocal. Thus 
 
 A is the cause of B :. Bis the effect of A. 
 The rule assumes that the reciprocal of a given relation is 
 definitely known ; and so far as this is true it may be extended 
 to more concrete relations 
 
 A is a genus of B .'. B is a species of A 
 A is the father of B .'. B is a child of A. 
 But not every relational expression has only one definite 
 reciprocal. If we are told that A is the brother of B, we can 
 only infer that B is either the brother or the sister of A. Of 
 course all reciprocal relations must be given in the projected 
 Logical Dictionary. 
 
 5. Obversion (otherwise called Permutation or ^quipol- 
 lence) is Immediate Inference by changing the quality of 
 the given proposition and substituting for its predicate the 
 contradictory term. The given proposition is called the 
 1 obvertend,' and the inference from it the ' obverse.' Thus the 
 obvertend being Some philosophers are consistent reasoners^ the 
 obverse will be Some philosophers are not inconsistent reasoners. 
 The legitimacy of this mode of reasoning follows, in the 
 case of affirmative propositions, from the principle of Con- 
 tradiction, that if any term be affirmed of a subject, the 
 contradictory term may be denied (chap. VL 3). To obvert 
 affirmative propositions, then, the rule is Add the negative 
 sign to the copula, and for the predicate substitute its contra- 
 dictory. 
 
 A. All S is P .'. No S is not-P 
 
 All men are fallible .'. JVo men are infallibk. 
 I. Some S is P .\ some S is not not-P 
 
 Some philosophers are consistent .'. Some philosophers 
 are not inconsistent. 
 

 
 - 
 DIATE INFERENCES 
 
 IMMEDIATE INFERENCES 83 
 
 In agreement with this mode of inference, we have the rule 
 of modern English grammar, that 'two negatives make an 
 affirmative.' 
 
 Again, by the principle of Excluded Middle, if any term be 
 denied of a subject, its contradictory may be affirmed: to 
 obvert negative propositions, then, the rule is Remove the 
 negative sign from the copula, and for the predicate substitute 
 its contradictor)'. 
 
 E. No S is P .'. All S is not-P 
 
 No matter is destructible .'. All matter is indestructible. 
 
 O. Some S is not P .'. Seme S is not-P 
 
 Some ideals are not attainable .'. Some ideals are unat- 
 tainable. 
 
 Thus, by obversion, each of the four propositions retains its 
 quantity but changes its quality : A. to E., I. to O., E. to A., 
 O. to I. And all the obverses are Infinite Propositions, the 
 affirmative infinities having the sense of negatives, and the 
 negative infinities having the sense of affirmatives. 
 
 Again, having obtained the obverse of a given proposition, 
 it may be desirable to recover the obvertend ; or it may at any 
 time be requisite to change a given Infinite into the corre- 
 sponding direct Affirmative or Negative ; and in such cases the 
 process is still obversion. Thus, if No S is not-P be given us to 
 recover the overtend or to find the corresponding Affirmative ; 
 the proposition being formally negative, we apply the rule for 
 obverting negatives : * Remove the negative sign from the 
 copula, and for the predicate substitute its contradictory.' 
 This yields the affirmative All S is P. Similarly, to obtain 
 the obvertend of All S is not-P, apply the rule for obverting 
 Affirmatives ; and this yields No S is P. 
 
 6. Contrariety. We have seen in chap. iv. 8, that con- 
 trary terms are such that no two of them are predicable in the 
 3 ame way of the same subject, whilst perhaps neither may be 
 predicable of it. Similarly, Contrary Propositions may be 
 defined as those of which no two are ever both true together, 
 whilst perhaps neither may be true ; or, in other wordr, both 
 
84 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 may be false. This is the relation between A. and E. when 
 concerned with the same matter : as A. All men are wise ; 
 E. No men are wise. Such propositions cannot both be 
 true; but they may both be false, for some men may be wise 
 and some not. Contrary relation may be viewed as according 
 with the principle of Contradiction : if it may be affirmed that 
 All men are wise, it may be denied that All men are not-wise : 
 and this is the obverse of No men are wise, which therefore 
 may also be denied. 
 
 At the same time we cannot apply to A. and E. the principle 
 of Excluded Middle, so as to show that one of them must 
 be true of the same matter. For if we deny that All men are 
 wise, we do not necessarily deny the attribute ( wise ' of each 
 and evei-y man : to say that Not all are wise may mean no 
 more than that Some are not. This gives a proposition in the 
 form of O. ; which, as we have seen, does not imply its subal- 
 ternans, E. 
 
 If, however, two Singular Propositions, having the same 
 matter, but differing in quality, are to be treated as universals, 
 and therefore as A. and E., they are, nevertheless, contradic- 
 tories and not merely contraries ; for one of them must be 
 false and the other true. 
 
 7. Contradiction, however, is a relation between two pro- 
 positions analogous to that between contradictory terms (one 
 of which being affirmed of a subject the other is denied) such, 
 namely, that one of them is false and the other true. This is 
 the case with the forms A. and O., and E. and I., in the same 
 matter. If it be true that All men are wise, it is false that 
 borne men are not wise (equivalent by obversion to Some men 
 are not-wise) ; or else, since the ' Some men ' are included in 
 the * All men,' we should be predicating of the same men that 
 they are both * wise ' and ' not-wise ' ; which would violate the 
 principle of Contradiction. Similarly, No men are wise, being 
 by obversion equivalent to All men are not-wise, is incom- 
 patible with Some men are wise, by the same principle of Con- 
 tradiction. 
 
 
IMMEDIATE INFERENCES 85 
 
 But, again, if it be false that All men are wise, it is always 
 true that Some are not wise ; for though in denying that ' wise ' 
 is a predicate of ' All men ' we do not deny it of each and 
 every man, yet we deny it of ' Some men.' Of ' Some men,' 
 therefore, by the principle of Excluded Middle, ' not<wise ' is 
 to be affirmed ; and Some men are not-wise, is by obversion 
 equivalent to Some men are not wise. Similarly, if it be false 
 that No men are wise, which by obversion is equivalent to All 
 men are not-wise, then it is true at least that Some men are 
 wise. 
 
 I may here observe that by extending and enforcing the 
 doctrine of relative terms, certain other inferences are implied 
 in the contrary and contradictory relations of propositions. We 
 have seen in chap. iv. that the contradictory of a given term 
 includes all its contraries : ' not-blue,' for example, includes 
 red and yellow. Hence, since The sky is blue becomes by 
 obversion, The sky is not not-blue, we may also infer The sky is 
 not red, etc. From the truth, then, of any proposition predica- 
 ting a given term, we may infer the falsity of all propositions 
 predicating the contrary terms in the same relation. But, on 
 the other hand, from the falsity of a proposition predicating a 
 given term, we cannot infer the truth of the predication of any 
 particular contrary term. If it be false that The sky is red, we 
 cannot formally infer that The sky is blue (cf. chap. vi. 3). 
 
 8. Sub-contrariety is the relation of two propositions, con- 
 cerning the same matter, that may both be true but are never 
 both false. This is the case with I. and O. If it be true that 
 Some men are wise, it may also be true that Some (other) men 
 are not wise. This follows from the maxim in chap. vi. 4, 
 not to go beyond the evidence. 
 
 For if it be true that Some men are wise, it may indeed be 
 true that All are (this being the subalternans) : and if All are, 
 it is (by contradiction) false that Some are not ; but as we are 
 only told that Some men are, it is illicit to infer the falsity of 
 Some are not, which could only be justified by evidence con- 
 cerning All men. 
 
86 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 But if it be false that Some men are wise, it is true that 
 Some men dre not wise ; for, by contradiction, if Some men are 
 wise is false, No men are wise is true; and, therefore, by 
 subalternation, Some men are not wise is true. 
 
 9. The Square of Opposition. By their relations of 
 Subalternation, Contrariety, Contradiction, and Sub-contrariety, 
 the forms A. I. E. O. (having the same matter) are said to stand 
 in Opposition : and Logicians represent these relations by a 
 square having A. I. E. O. at its corners, thus : 
 
 Contraries 
 
 E. 
 
 C/3 
 
 g- 
 
 P 
 
 
 I. 
 
 Sub-contraries 
 
 O. 
 
 As an aid to the memory, this diagram is useful ; but as an 
 attempt to represent the logical relations of propositions, it is 
 useless, and indeed, misleading. For, standing at corners of 
 the same square, A. and E., A. and L, E. and O., and I. and O., 
 seem to be couples bearing the same relation to one another ; 
 whereas we have seen that their relations are entirely different. 
 The following traditional summary of their relations in respect 
 of truth and falsity is much more to the purpose : 
 
 (1) If A. is true, 
 
 (2) If A. is false, 
 
 (3) If I. is true, 
 
 (4) If I. is false, 
 
 I. is true, 
 I. is unknown, 
 A. is unknown, 
 A. is false, 
 
 E. is false, 
 E. is unknown, 
 E. is false, 
 E. is true, 
 
 O. is false. 
 O. is true. 
 O. is unknown. 
 O. is true. 
 
IMMEDIATE INFERENCES 87 
 
 (5) If E. is true, 
 (6) If E. is false, 
 (7) If O. is true, 
 (8) If O. is false, 
 
 A. is false, 
 A. is unknown, 
 A. is false, 
 A. is true, 
 
 I. is false, 
 I. is true, 
 I. is unknown, 
 I. is true, 
 
 O. is true. 
 O. is unknown. 
 E. is unknown. 
 E. is false. 
 
 Where, however, as in cases 2, 3, 6, 7, alleging either the 
 falsity of universals or the truth of particulars, it follows that 
 two of the three Opposites ?re unknown, we may conclude 
 further that one of them must be true and the other false, 
 because the two unknown are always Contradictories. 
 
 10. Secondary modes of Immediate Inference are obtained 
 by applying the process of Conversion or Obversion to the 
 results already obtained by the other process. The best known 
 secondary form of Immediate Inference is the Contrapositive, 
 and this isjthe converse of the obverse of a given proposition. 
 Thus: 
 
 A. All S is P .'. No S is not-P .. No not-P is S 
 
 I. Some is P /. Some S is not not-P /. (none) 
 
 E. No S is P .'. All S is not-P .-. Some not-P is S 
 
 O. Some is not P /. Some S is not-P .'. Some not-P is S 
 
 There is no contrapositive of I., because the obverse of I. is in 
 the form of O., and we have seen that O. cannot be converted. 
 O., however, has a contrapositive (Some not-P is S) ; and this 
 is sometimes given instead of the converse, and called the 
 ' converse by negation.' 
 
 Contraposition needs no justification by the Laws of Thought, 
 as it is nothing but a compounding of conversion with obver- 
 sion, both of which processes have already been justified. I 
 give a table of the other ways of compounding these primary 
 modes of Immediate Inference. 
 
*s "s "s 8 * 
 
 2 
 
 1 1 1 f 
 
 ST' *"* 1 I I 
 
 ^ ** 
 
 ja g Js o 
 O 
 
 1 
 
 *o 'o w 
 
 * 
 
 w "U CU 
 
 2 
 
 <3 j2 
 
 ^ : i i i 
 
 > d 
 
 5 
 
 6 
 
 
 
 2 " u 
 
 4) <U QJ > 
 
 1 i *i 1 
 
 > > > O 
 
 
 
 1 * 
 
 *0 oJ 
 
 III 
 
 111 
 
 2 
 
 - l '1 1 
 
 r 
 
 ll 
 
 i 
 
 g rt 
 
 10 '- 1 
 
 > fl 
 
 s 11 11 
 
 O O 
 
 ^ CO CO 
 
 S > 
 
 ^ 1 ^ 
 
 
 * 1 kTS fcTN 
 
 O OT 
 
 o 
 
 o g, 
 
 S II 
 
 <*-! 
 
 rf 
 
 to 53 
 
 OJ > 
 
 * 1 
 
 y 
 
 So So ^ 
 
 * s 
 Co Co "^ 
 
 i 
 
 OQ 5 
 
 ^> 
 
 en | 
 
 g 
 
 
 
 U 
 
 r r 
 
 | 
 
 *** ** 
 
 
 
 O 
 
 o 1 1 S 8 * 
 
 ^ to ^ co 
 
 
 ^ . ^ . ^ . 
 
 
 M E3 ^ S ^ o 
 
 
 
 "^ Co ^ Co 
 
IMMEDIATE INFERENCES 89 
 
 In this table a and b stand for not-A and not-B and had 
 better be read thus : for No A is b, No A is not-B ; for All 
 b is a (col. 6), All not-B is not-A ; and so on. 
 
 It may not, at first, be obvious why the process of alternately 
 obverting and converting any proposition should ever come to 
 an end ; though it will, no doubt, be considered a very for- 
 tunate circumstance that it always does end. On examining 
 the results, it will be found that the cause of its ending is the 
 inconvertibility of O. For E., when obverted, becomes A.; 
 every A., when converted, degenerates into I. ; every I., when 
 obverted, becomes O. ; O cannot be converted, and to obvert 
 it again is merely to restore the former proposition : so that the 
 whole process moves on to inevitable dissolution. I. and O. 
 are exhausted by three transformations, whilst A. and E. will 
 each endure seven. 
 
 Except Obversion, Conversion and Contraposition, it has 
 not been usual to bestow special names on these processes or 
 their results. But the form in columns 7 and 10 (Some a is b 
 Some a is not B ), where the original predicate is affirmed or 
 denied of the contradictory of the original subject, has been 
 thought by Dr. Keynes to deserve a distinctive title, and he 
 has called it the 'Inverse.' Observe, however, that, although 
 the Inverse is one form, Inversion is not one process, but is 
 obtained by different processes from E. and A. respectively. 
 In this it differs from Obversion, Conversion, and Contraposi- 
 tion, each of which stands for one process. 
 
 The Inverse form has been objected to on the ground that 
 the inference All A is B .: Some not-A is not B, distributes B 
 (as predicate of a negative proposition), though it was given as 
 undistributed (as predicate of an affirmative proposition). But 
 Dr. Keynes defends it on the ground that (i) it is obtained 
 
 <* obversions and conversions which are all legitimate ; and 
 
 that although All A is B does not distribute B in relation to 
 
 yi, it does distribute B in relation to some not-A (namely, in 
 
 relation to whatever not-A is not-J3). This is one reason why, in 
 
 stating the rule in chap. vi. 4, I have written : " an immediate 
 
go LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 inference ought to contain nothing that is not contained, or 
 formally implied^ in the proposition from which it is inferred " ; 
 and have maintained that every term formally implies its 
 contradictory. 
 
 ii. Immediate Inferences from Conditionals are those 
 which consist (i) in changing a Disjunctive into a Hypo- 
 thetical, or a Hypothetical into a Disjunctive, or either into a 
 Categorical; and (2) in the relations of Opposition and the 
 equivalences of Obversion, Conversion, and secondary or 
 compound processes, which we have already examined in 
 respect of Categoricals. As no new principles are involved, 
 it may suffice to exhibit some of the results. 
 
 We have already seen (chap, v. 4) how Disjunctives may 
 be read as Hypotheticals and Hypothetical as Categoricals. 
 And, as to opposition, if we recognise four forms of Hypo- 
 thetical A. I. E. O., these plainly stand to one another in a 
 Square of Opposition, just as Categoricals do. Thus A. and E. 
 (If A is B) C is D) and If A is B, C is not D) are contraries, 
 but not contradictories ; since both may be false (C may 
 sometimes be D, and sometimes not), though they cannot 
 both be true. And if they are both false, their subalter- 
 nates are both true, being respectively the contradictories of 
 the universals of opposite quality, namely, I. of E., and O. 
 of A. But in the case of Disjunctives, we cannot set out 
 a satisfactory Square of Opposition ; because, as we saw (chap. 
 v. 4), the forms required for E. and O. are not to 
 iunctives, but Exponibles. 
 
 The Obverse, Converse, and Contrapositive, > 
 theticals are exhibited thus : 
 
 DATUM, OBVERSS. 
 
 A. IfAisB.C is D IfAisB.C is not a\ 
 
 I. Sometimes when A is B, C is D Sometimes when A is 
 
 E. If A is B, C is not D If A is B, C is d 
 
 O. Sometimes when A is B, C is not D Sometimes when A is 
 
IMMEDIATE INFERENCES 91 
 
 CONVERSE. CONTRAPOSITIVE. 
 
 Sometimes when C is D, A is B If C is d, A is not B 
 Sometimes when C is D, A is B (none) 
 
 IfC is D, A is not B Sometimes when C is d, A is B 
 
 (none) Sometimes when C is d, A is B 
 
 As to Disjunctives, the attempt to put them through these 
 different forms immediately destroys their disjunctive character. 
 Still, given any proposition in the form A is either B or C, we 
 can state the propositions that give the sense of obversion, 
 conversion, etc., thus : 
 
 OBVERSE. A is not both b and c ; 
 CONVERSE. Something either B or C is A ; 
 CONTRAPOSITIVE. Nothing that is both b and c is A. 
 
 For a Disjunctive in I., of course, there is no Contrapositive. 
 Given a Disjunctive in the form either A is B or C is D, we 
 may write for its Obverse In no case is A b> and C at the same 
 time d. But no Converse or Contrapositive of such a Dis- 
 junctive can be obtained, except by first casting it into the 
 hypothetical or categorical form. 
 
 The reader who wishes to pursue this subject further, will 
 find it elaborately treated in Dr. Keynes' Formal Logic, 
 Part II. ; to which work the above chapter is indebted. 
 
CHAPTER VIII. 
 
 ORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL 
 EQUATIONS, EXISTENTIAL IMPORT OF PROPOSITIONS 
 
 i. Which Term is the Subject and which the Predicate of 
 a proposition ? In most of the exemplary propositions cited 
 by Logicians it will be found that the subject is a substantive 
 and the predicate an adjective, as in Men are mortal. But, in 
 literature, sentences in which the adjective comes first are not 
 uncommon, as Loud was the applause, Dark is the fate of man, 
 Great is tfie glory of the conquering sword. Here, then, ' loud,' 
 4 dark ' and * great ' occupy the place of the logical subject. 
 Are they really the. subject, or must we alter the order of such 
 sentences into The applause was loud, etc.t If we do, and 
 then proceed to convert, we get Loud was the applause, or 
 (more scrupulously) Some loud noise was the applause. The 
 last form, it is true, gives the subject a substantive word, but 
 * applause' has become the predicate; and if the substantive 
 ' noise ' was not implied in the first form, Loud is the applause^ 
 by what right is it now inserted ? The recognition of Conver- 
 sion, in fact, requires us to admit that, formally, in a logical 
 proposition, the term preceding the copula is subject and the 
 one following is predicate. And, of course, materially con- 
 sidered, the mere order of terms in a proposition can make no 
 difference in the method of proving it, nor in the inferences 
 that can be drawn from it. 
 
 Still, if the question is, how we may best cast a literary sen- 
 tence into logical form, good grounds for a definite answer may 
 perhaps be found. We must not try to stand upon the 
 
EULER'S DIAGRAMS 93 
 
 naturalness of expression, for Dark is the fate of man is quite as 
 natural as Man is mortal. When the purpose is not merely to 
 state a fact, but also to express our feelings about it, to place 
 the grammatical predicate first may be perfectly natural and 
 most effective. But the grounds of a logical order of statement 
 must be found in its adaptation to the purposes of proof and 
 inference. Now general propositions are those from which 
 most inferences can be drawn, which, therefore, it is most 
 important to establish if true ; and they are also the easiest to 
 disprove if false, since a single negative instance suffices to 
 establish the contradictory. It follows that, in re-casting a 
 literary or colloquial sentence for logical purposes, we should 
 try to obtain a form in which the subject is distributed is 
 either a singular term or a general term predesignate as ' All ' 
 or ' No.' Seeing, then, that most adjectives connote a single 
 attribute, whilst most substantives connote more than one 
 attribute ; and that therefore the denotation of adjectives is 
 usually wider than that of substantives ; in any proposition, 
 one term of which is an adjective and the other a substantive, 
 if either can be distributed in relation to the other, it is nearly 
 sure to be the substantive ; so that to take the substantive term 
 for subject is our best chance of obtaining an universal pro- 
 position. These considerations seem to justify the practice of 
 Logicians in selecting their examples. 
 
 For similar reasons, if both terms of a proposition are sub- 
 stantive, the one with the lesser denotation is (at least in 
 affirmative propositions) the more suitable subject, as Cats are 
 carnivores. And if one term is abstract, that is the more 
 suitable subject ; for, as we have seen, an abstract term may be 
 interpreted by a corresponding concrete one distributed, as 
 Kindness is infectious ; that is, All kind actions suggest imitation. 
 
 If, however, a controvertist has no other object in view than 
 to refute some general proposition laid down by an opponent, 
 a particular proposition is all that he need disentangle from 
 any statement that serves his purpose. 
 
 2. Toward understanding clearly the relations of the terms 
 
94 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 of a proposition, it is often found useful to employ diagrams \ 
 and the diagrams most in use are the circles of Euler. 
 
 These circles represent the denotation of the terms. Suppose 
 the proposition to be All hollow-horned animals ruminate : then, 
 if we could collect all ruminants upon a prairie, and enclose 
 them with a circular palisade; and segregate from amongst 
 them all the hollow-horned beasts, and enclose them with 
 another ring-fence inside the other ; one way of interpreting the 
 proposition (namely, in denotation) would be figured to us 
 thus : 
 
 FIG. i. 
 
 An Universal Affirmative may also state a relation between 
 two terms whose denotation is co-extensive. A definition 
 always does this, as Man is a rational animal ; and this, of 
 course, we cannot represent by two distinct circles, but at best 
 by one with a thick circumference, to suggest that two coincide, 
 thus: 
 
 FIG. 2. 
 
 MEN 
 
 OR 
 RATIONAL 
 
 ANIMALS 
 
 The Particular Affirmative Proposition may be represented 
 in several ways. In the first place, bearing in mind that 
 'Some' means ' some at least, it may be all,' an I. proposition 
 may be represented by Figs, i and 2 ; for it is true that Some 
 
 
EULER'S DIAGRAMS 95 
 
 horned animals ruminate, and that Some men are rational. 
 Secondly, there is the case in which the 'Some things' of 
 which a predication is made are, in fact, not all ; whilst the 
 predicate, though not given as distributed, yet might be so 
 given if we wished to state the whole truth ; as if we say Some 
 men are Chinese. This case is also represented by Fig. i, the 
 outside circle representing ' Men,' and the inside one * Chinese.' 
 Thirdly, the predicate may appertain to some only of the 
 subject, but to a great many other things, as in Some horned 
 beasts are domestic ; for it is true that some are not, and that 
 certain other kinds of animals are, domestic. This case, there- 
 fore, must be illustrated by overlapping circles, thus : 
 
 FIG. 3. 
 
 The Universal Negative is sufficiently represented by a single 
 Fig. (4) : two circles mutually exclusive, thus : 
 
 FIG. 4. 
 
 That is, No horned beasts are carnivorous. 
 
 Lastly, the Particular Negative may be represented by any 
 of the Figs, i, 3, and 4 ; for it is true that Some ruminants are 
 not hollow-horned, that Some horned animals are not domestic, 
 and that Some horned beasts are not carnivorous. 
 
96 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Besides their use in illustrating the denotative force of pro- 
 positions, these circles may also be used to verify the results of 
 Obversion, Conversion, and the secondary modes of Immediate 
 Inference. Thus the Obverse of A. is clear enough on glancing 
 at Figs, i and 2 ; for if we agree that whatever term's denota- 
 tion is represented by a given circle, the denotation of the 
 contradictory term shall be represented by the space outside 
 that circle ; then, of course, if it is true that All hollow-horned 
 animals are ruminants, it is at the same time true that No 
 hollow-horned animals are not-ruminants ; since none of the 
 hollow-horned are found outside the palisade that encloses 
 the ruminants. The Obverse of I., E. or O. may be verified in 
 a similar manner. 
 
 As to the Converse, a Definition is of course susceptible of 
 Simple Conversion, and this is shown by Fig. 2 : ' Men are 
 rational animals ' and ' Rational animals are men.' But any 
 other A. proposition is presumably convertible only by limita- 
 tion, and this is shown by Fig. i ; where All hollow-horned 
 animals are ruminants, but we can only say that Some 
 ruminants are hollow-horned. 
 
 That I. may be simply converted may be seen in Fig. 3, 
 which represents the least that an I. proposition can mean ; 
 and that E. may be simply converted is manifest in Fig. 4. 
 
 As for O., we know that it cannot be converted, and this is 
 made plain enough by glancing at Fig. i ; for that represents 
 the O., Some ruminants are not hollow -horned, but also shows 
 this to be compatible with All hollow-horned animals are 
 ruminants (A.). Now in conversion there is (by definition) no 
 change of quality. The converse, then, of Some ruminants 
 are not hollow-horned must be a negative proposition, having 
 'hollow-horned ' for its subject, either in E. or O. ; but these 
 would be respectively the contrary and contradictory of All 
 hollow-horned animals are ruminants ; and, therefore, if this 
 is true, they must both be false. 
 
 But (referring still to Fig. i) the legitimacy of contrapositing 
 O. is equally clear ; for if Some ruminants are not hollow- 
 
LOGICAL EQUATIONS 97 
 
 horned, Some animals that are not hollow-horned are ruminants, 
 namely, all the animals between the two ring-fences. Similar 
 inferences may be illustrated from Figs. 3 and 4. And the 
 Contraposition of A. may be verified by Figs, i and 2, and the 
 Contraposition of E. by Fig. 4. 
 
 Lastly, the Inverse of A. is plain from Fig. i Some things 
 that are not hollow-horned are not ruminants, namely, all things 
 that lie outside the outer circle and are neither * ruminants ' nor 
 'hollow-horned.' And the Inverse of E. may be studied in 
 Fig. 4 Some things that are not-horned beasts are carnivorous. 
 
 Notwithstanding the facility and clearness of the demon- 
 strations thus obtained, it may be said that a diagrammatic 
 method, representing denotations, is not properly logical, It 
 seems to be agreed that fundamentally the relation asserted (or 
 denied) to exist between the terms of a proposition, is a relation 
 between the terms as determined by their attributes or conno- 
 tation ; whether we take Mill's view, that a proposition asserts 
 that the connotation of the subject is a mark of the connotation 
 of the predicate ; or Dr. Venn's view, that things denoted by 
 the subject (as having its connotation) have (or have not) the 
 attribute connoted by the predicate; or, the Conceptualist 
 view, that a judgment is a relation of concepts (that is, of con- 
 notations). At any rate, it is certain that, with a few exceptions 
 artificially framed (such as ' kings now reigning in Europe '), 
 the denotation of a term is never directly and exhaustively 
 known, but consists merely in ' all things that have the conno- 
 tation.' And I venture to think that the value of logical 
 training depends very much upon our habituating ourselves to 
 construe propositions, and to realise the force of inferences 
 from them, according to the connotation of their terms ; and 
 that, therefore, a student does well not to turn too hastily to 
 the circles, but rather to regard them as means of verifying in 
 denotation the conclusions that he has already learnt to recog- 
 nise as necessary in connotation. (Keynes: Formal Logic, 
 Part II. c. 4.) 
 
 3. The equational treatment of propositions is closely 
 
$8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 connected with the diagrammatic. Hamilton thought it a 
 great merit of his plan of quantifying the predicate, that 
 thereby every proposition is reduced to its true form an 
 equation. According to this doctrine, the proposition All X 
 is all Y(U.) equates X and Y; the proposition All X is some 
 y(A.) equates X with some part of Y; and similarly with the 
 other affirmatives (Y. and I.). And so far it is easy to follow 
 his meaning: the Xs are identical with some or all the Ys. 
 But, coming to the negatives, the equational interpretation 
 is certainly less obvious. The proposition No X is Y (E.) 
 cannot be said in any sense to equate X and Y ; though, if we 
 obvert it into All X is some not- V, we have (in the same sense, 
 of course, as the above affirmative forms) X equated with part 
 at least of ' not-Y.' 
 
 But what is the sense ? Clearly not the same as that in 
 which mathematical terms are equated, namely, in respect of 
 some mode of quantity. For if we may say Some X is some Y t 
 these Xs that are also Ys are not merely the same in number, 
 or mass, or figure ; they are the same in every respect, both 
 quantitative and qualitative, have the same .positions in time 
 and place, are in fact identical. The proposition 2 + 2 = 4 
 means that any two things added to any other two are, in 
 respect of number, equal to any three things added to one 
 other ; and this is true of all things that can be counted, how- 
 ever much they may differ in other ways. But AH X is all Y 
 means that Xs and Ys are the same things, although they have 
 different names when viewed in different aspects or relations. 
 Thus all equilateral triangles are equiangular triangles ; but 
 in one case they are named from the equality of their angles, 
 and in the other from the equality of their sides. Similarly, 
 'British subjects' and * subjects of Queen Victoria' are the 
 same people, named in one case from the person of the 
 Crown, and in the other from the Imperial Government. 
 These logical equations, then, are in truth identities of deno- 
 tation ; and they are fully illustrated by the relations of circles 
 described in the previous section. 
 
LOGICAL EQUATIONS 99 
 
 When we are told that logical propositions are to be con- 
 sidered as equations, we naturally expect to be shown some 
 interesting developments of method in analogy with the 
 equations of Mathematics; but from Hamilton's innovations 
 no such thing results. This cannot be said, however, of the 
 equations of Symbolic Logic ; which are the starting-point of 
 very remarkable processes of ratiocination. As the subject 
 of Symbolic Logic, as a whole, lies beyond the compass of 
 this work, it will be enough to give Dr. Venn's equations cor- 
 responding with the four propositional forms of common Logic. 
 
 According to this system, universal propositions are to be 
 regarded as not necessarily implying the existence of their 
 terms ; and therefore, instead of giving them a positive form, 
 they are translated into symbols that express what they deny. 
 For example, the proposition All devils are ugly need not 
 imply that any such things as * devils' really exist; but it 
 certainly does imply that Devils that are not ugly do not exist. 
 Similarly, the proposition No angels are ugly implies that 
 Angels that are ugly do not exist. Therefore, writing x for 
 
 * devils,' y for 'ugly,' and y for ' not-ugly,' we may express A., 
 the universal affirmative, thus : 
 
 A. xy = o. 
 
 That is, x that is not y is nothing ; or, Devils that are not-ugly 
 do not exist. And, similarly, writing x for * angels ' and y for 
 
 * ugly,' we may express E., the universal negative, thus : 
 
 E. xy = o. 
 
 That is, x that isy is nothing; or, Angels that are ugly do not exist. 
 On the other hand, particular propositions are regarded as 
 implying the existence of their terms, and the corresponding 
 equations are so framed as to express existence. With this 
 end in view, the symbol v is adopted to represent ' something/ 
 or indeterminate reality, or more than nothing. Then, taking 
 any particular affirmative, such as Some metaphysicians are 
 obscure, and writing x for ' metaphysicians,' and y for * obscure/ 
 we may express it thus : 
 
 I. xy = v. 
 
ioo LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 That is, x that is y is something ; or, Metaphysicians that are 
 obscure do occur in experience (however few they may be, or 
 whether they be all obscure). And, similarly, taking any 
 particular negative, such as Some giants are not cruel^ and 
 writing x for * giants ' and y for ' not-cruel,' we may express it 
 thus: 
 
 O. xy = v. 
 
 That is, x that is not y is something ; or, giants that are not-cruel 
 do occur in romances, if nowhere else. 
 
 Clearly, these equations are, like Hamilton's, concerned with 
 denotation. A. and E. affirm that the compound terms xy 
 and xy have no denotation ; and I. and O. declare that xy 
 and xy have denotation, or stand for something. He-re, how- 
 ever, the resemblance to Hamilton's system ceases ; for the 
 Symbolic Logic, by operating upon more than two terms 
 simultaneously, by adopting the algebraic signs of operation, 
 + > ~ > x > = (with a special signification), and manipulating 
 the symbols by quasi-algebraic processes, obtains results which 
 the common Logic reaches (if at all) with much greater 
 difficulty. If, indeed, the value of logical systems were to be 
 judged of by the results obtainable, formal deductive Logic 
 would probably be superseded. And, as a mental discipline, 
 there is much to be said in favour of the symbolic method. 
 But, as an introduction to philosophy, the common Logic must 
 hold its ground. (Venn's Symbolic Logic, c. 7.) 
 
 4. Whether Formal Logic involves any general assumption 
 as to the real existence of the terms of propositions is a ques- 
 tion that has lately excited some interest, so that a few remarks 
 upon it will be expected here. But if my treatment of it seem 
 somewhat dogmatic, brevity must be my excuse. 
 
 I observe, then, in the first place, that Logic treats primarily 
 of the relations implied in propositions. This follows from its 
 being the science of proof for all sorts of (qualitative) proposi- 
 tions ; since all sorts of propositions have nothing in common 
 except the relations they imply. 
 
 But, secondly, relations without terms of some sort are not 
 
EXISTENTIAL IMPORT 101 
 
 to be thought of; and, hence, even the most formal illustra- 
 tions of logical doctrines comprise such terms as S and P, 
 X and Y, or x and y, in a symbolic or representative character. 
 Terms, therefore, of some sort are assumed to exist (together 
 with their negatives or contradictories)^ the purposes of logical 
 manipulation. 
 
 Thirdly, however, that Formal Logic cannot directly involve 
 the existence of any particular concrete terms, such as * man ' 
 or ' mountain/ is implied in the word * formal,' that is, * con- 
 fined to what is common or abstract ' ; since the only thing 
 common to all terms is to be related in some way to other 
 terms. The actual existence of any concrete thing can only be 
 known by experience, as with * man ' or ' mountain ' ; or by 
 methodically justifiable inference from experience, as with 
 ' atom ' or * ether.' 
 
 Nevertheless, fourthly, the existence or non-existence of par- 
 ticular terms may come to be implied : namely, wherever the 
 very fact of existence, or of some condition of existence, is an 
 hypothesis or datum. Thus, given the proposition All S is P, 
 to be P is made a condition of the existence of S : whence it 
 follows that an S that is not P does not exist (xy = o). On the 
 further hypothesis that S exists, it follows that P exists. On 
 the hypothesis that S does not exist, the existence of P is 
 problematic ; but, then, if P does exist we cannot convert the 
 proposition ; since Some P is S (P existing) would involve the 
 existence of S ; which is contrary to the hypothesis. 
 
 Assuming that Universals do nof, whilst Particulars do, imply 
 the existence of their subjects, we cannot infer the subalternate 
 (I. or O.) from the subalternans (A. or E.), for that is to ground 
 the actual on the problematic ; and for the same reason we 
 cannot convert A. per acddens. 
 
 Assuming, again, a certain suppositio or universe, to which 
 in a given discussion every argument shall refer, then, any pro- 
 positions whose terms lie outside that suppositio are irrelevant, 
 and for the purposes of that discussion may be called false. 
 Thus propositions which, according to the doctrine of Opposi- 
 
102 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 tion, appear to be Contradictories, may then cease to be so ; 
 for of Contradictories one is true and the other false ; but, in 
 the case supposed, both are technically false. If the subject 
 of discussion be Zoology, all propositions about centaurs or 
 unicorns are absurd; and such specious Contradictories as 
 No centaurs play the lyre Some centaurs do play the lyre ; or 
 All unicorns fight with lions Some unicorns do not fight with 
 lions, are both false or meaningless, because in Zoology there 
 are no centaurs nor unicorns ; and, therefore, in this reference, 
 the propositions are not really contradictory. But if the subject 
 of discussion or suppositio be Mythology or Heraldry, such 
 propositions as the above are to the purpose, and form 
 legitimate pairs of Contradictories. 
 
 In Formal Logic, in short, we may make at discretion any 
 assumption whatever as to the existence, or as to any condition 
 of the existence of any particular term or terms ; and then 
 certain implications and conclusions follow in consistency with 
 that hypothesis or datum. Still, our conclusions will them- 
 selves be only hypothetical, depending on the truth of the 
 datum ; and, of course, until this is empirically ascertained, we 
 are as far as ever from empirical reality. (Venn : Symbolic 
 Logic, c. 6 ; Keynes : formal Logic> Part II. c. 7.) 
 
CHAPTER IX 
 FORMAL CONDITIONS OF MEDIATE INFERENCE 
 
 i. A Mediate Inference is a proposition that depends for 
 proof upon two or more other propositions, so connected 
 together by one or more terms (which the evidentiary proposi- 
 tions, or each pair of them, have in common) as to justify a 
 certain conclusion, namely, the proposition in question. The 
 type or (more properly) the unit of all such modes of proof, 
 when of a strictly logical kind, is the Syllogism, to which we 
 shall see that all other modes are reducible. It may be 
 exhibited symbolically thus : 
 
 MisP; 
 SisM: 
 .-. S is P. 
 
 Syllogisms may be classified, as to quantity, into Universal 
 or Particular, according to the quantity of the conclusion ; as 
 to quality, into Affirmative or Negative, according to the 
 quality of the conclusion ; and, as to relation, into Categorical, 
 Hypothetical and Disjunctive, according as all their proposi- 
 tions are categorical, or one (at least) of their evidentiary 
 propositions is a hypothetical or a disjunctive. 
 
 We will begin with Categorical Syllogisms, of which the 
 following is a concrete example : 
 
 All authors are vain ; 
 Cicero is an author : 
 .*. Cicero is vain. 
 
 Here we may suppose that there are no direct means of know- 
 ing that Cicero is vain ; but we happen to know that all authors 
 
104 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 are vain and that he is an author ; and these two propositions 
 put together unmistakably imply that he is vain. In other 
 words, we do not at first know any relation between Cicero ' 
 and 'vanity'; but we know that these two terms are severally 
 related to a third term, ' author/ hence called a Middle Term ; 
 and thus we perceive, by mediate evidence, that they are re- 
 lated to one another. This sort of proof bears an obvious re- 
 semblance to the mathematical proof of equality between two 
 quantities, that cannot be directly compared, by showing the 
 equality of each of them to some third quantity : A = B = C 
 .-. A = C. Here B is a middle term. 
 
 We have to inquire, then, what conditions must be satisfied 
 in order that a Syllogism may be formally conclusive or valid. 
 A specious Syllogism that is not really valid is called a 
 Para syllogism. 
 
 2. General Canons of the Syllogism. 
 
 (1) A Syllogism contains three, and no more, distinct pro- 
 positions. 
 
 (2) A Syllogism contains three, and no more, distinct uni- 
 vocal terms. 
 
 These two Canons imply one another. Three propositions 
 with less than three terms can only be connected in some of the 
 modes of Immediate Inference. Three propositions with more 
 than three terms do not show that connection of two terms by 
 means of a third, which is the desideratum for proving a 
 Mediate Inference. If we write 
 
 All authors are vain ; 
 
 Cicero is a statesman 
 
 there are four terms and no middle term, and therefore there 
 is no proof. Or if we write 
 
 All authors are vain ; 
 
 Cicero is an author ; 
 .'. Cicero is a statesman 
 
 here the term ' statesman ' occurs without any voucher ; it 
 appears in the inference but not in the evidence, and therefore 
 violates the maxim of all formal proof, 'not to go beyond 
 
CONDITIONS OF MEDIATE INFERENCE 105 
 
 the evidence' (chap. vi. 4). It is true that if any one 
 argued 
 
 All authors are vain ; 
 Cicero wrote on philosophy ; 
 /. Cicero is vain 
 
 this could not be called a bad argument or a material fallacy ; 
 but it would be a needless departure from the form of 
 expression in which the connection between the evidence and 
 the inference is most easily seen ; it would generally be called a 
 formal fallacy. 
 
 Still a mere adherence to the same form of words in the 
 expression of terms is not enough : we must also attend to 
 their meaning. For if the same words be used ambiguously 
 (as ' author ' now for ' father ' and anon for ' man of letters ') it 
 becomes as to its meaning two terms ; so that we have four in 
 all. Then, if the ambiguous term be the Middle, no connection 
 is shown between the other two ; if either of the others be 
 ambiguous, something seems to be inferred which has never 
 been really given in evidence. 
 
 The above two Canons are, indeed, involved in the definition 
 of a categorical syllogism, which may be thus stated : A Cate- 
 gorical Syllogism is a form of proof or reasoning (way of giving 
 reasons) in which one categorical proposition is established by 
 comparing two others that contain together only three terms, or 
 that have one and only one term in common. 
 
 The proposition established, derived, or inferred, is called 
 the Conclusion : the evidentiary propositions by which it is 
 proved are called the Premises. 
 
 The term common to the premises, by means of which the 
 other terms are compared, is called the Middle Term. For 
 the other terms, the subject of the conclusion is called the 
 Minor Term ; the predicate of the conclusion, the Major 
 Term. 
 
 The premise in which the minor term occurs is called the 
 Minor Premise ; that in which the major term occurs is called 
 the Major Premise. And a Syllogism is usually written thus : 
 
106 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Major Premise All Authors (Middle) are vain (Major) ; 
 Minor Premise Cicero (Minor) is an author (Middle) : 
 Conclusion .*. Cicero (Minor) is vain (Major). 
 Here we have three propositions with three terms, each term 
 occurring twice. The Minor and Major Terms are so called, 
 because, when the conclusion is an universal affirmative (which 
 only occurs in Barbara ; see chap. x. 6), its subject and 
 predicate are respectively the less and the greater in extent or 
 denotation. It should be carefully noticed that the premises 
 are called after the peculiar terms they contain : the expressions 
 ' Major Premise ' and * Minor Premise ' have nothing to do 
 with the order in which the premises are presented ; though 
 it is usual to place the Major first. 
 
 (3) No term must be distributed in the conclusion unless it 
 is distributed in the premises. 
 
 It is usual to give this as one of the General Canons of the 
 Syllogism ; but we have seen (chap. vi. 6) that it is of wider 
 application. Indeed, ' not to go beyond the evidence ' belongs 
 to the definition of formal proof. A breech of this rule in a 
 syllogism is the fallacy of Illicit Process of the Minor, or of the 
 Major, according to which term has been unwarrantably distri- 
 buted. The following parasyllogism illicitly distributes both 
 terms of the conclusion : 
 
 All poets are pathetic ; 
 Some orators are not poets ; 
 .*. No orators are pathetic. 
 
 (4) The Middle Term must be distributed at least once in 
 the premises. 
 
 For the use of mediate evidence is to show the relation of 
 terms that cannot be directly compared ; this is only possible 
 if the Middle Term furnishes the ground of comparison ; and 
 this (in Logic) requires that the whole denotation of the Middle 
 should be either included or excluded by one of the others ; 
 since if we only know that the other terms are related to some 
 of the Middle, their respective relations may not be with the 
 same part of it. Indeed, if the Middle is undistributed in both 
 
CONDITIONS OF MEDIATE INFERENCE 107 
 
 premises, Whately regards it as ambiguous ; in which case the 
 pretended syllogism depending on it has four terms ; so that 
 this 4th Canon may be regarded as reducible to the 2nd. 
 
 It is true that in what has been strangely called the 
 " numerically definite syllogism," an inference may be drawn, 
 though our canon seems to be violated. Thus : 
 
 60 sheep in 100 are horned ; 
 
 60 sheep in 100 are blackfaced ; 
 .*. at least 20 blackfaced sheep in 100 are horned. 
 But such an argument, though I presume it may be correct 
 Arithmetic, is not Logic at all ; and when such numerical 
 evidence is obtainable the comparatively indefinite arguments 
 of Logic are needless. Another apparent exception more to 
 the purpose is the following : 
 
 Most men are 5 feet high ; 
 
 Most men are semi-rational ; 
 .-. Some semi-rational things are 5 feet high. 
 Here the Middle Term (men) is distributed in neither premise, 
 yet the indisputable conclusion is a logical proposition. 
 Observe, however, that the premises are really arithmetical ; 
 for ' most ' means ' more than half,' or more than 50 per cent. 
 For Mediate Inference depending on truly logical premises, 
 then, it is necessary that one premise should distribute the 
 Middle Term ; and the reason of this may be illustrated even 
 by the above supposed exceptions. For in them the premises 
 are such that, though neither premise by itself distributes the 
 Middle, yet they always do so between them, and that with a 
 certain surplus. For if each premise dealt with exactly half 
 the Middle, thus barely distributing it between them, there 
 would be no logical proposition inferrible (though, of course, 
 there might be a conclusion of numerical probability). We 
 require that the Middle, as used in one premise, should 
 necessarily overlap the Middle as used in the other, so as to 
 furnish common ground for comparing the other terms. Hence 
 I have defined the middle as * that Term common to both 
 premises by means of which the other terms are compared. 1 
 
loS LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (5) One at least of the premises must be affirmative; or 
 from two negative premises nothing can be inferred. 
 
 The fourth Canon required that the middle term should be 
 given us distributed, or in its whole extent, in order to afford 
 sure ground of comparison for the others. But that such 
 comparison may be effected, something more is requisite ; the 
 relation of the other terms to the Middle must be of a certain 
 character. One at least of them must be, as to its extent or 
 denotation, partially or wholly identified with the Middle ; so 
 that to that extent it may be known to bear to the other term, 
 whatever relation we are told that so much of the Middle bears 
 to that other term. Now, identity of denotation can only be 
 predicated in an affirmative proposition : one premise, then, 
 must be affirmative. 
 
 If, however, both premises are negative, we only know that 
 both the other terms are partly or wholly excluded from the 
 Middle, or are not identical with it in denotation : where they 
 lie, then, in relation to one another we have no means of 
 knowing. Similarly, in the mediate comparison of quantities, 
 if we are told that A and C are both of them unequal to B, we 
 can infer nothing as to the relation of C to A. Hence the 
 premises 
 
 No electors are sober ; 
 No electors are independent 
 
 however suggestive; do not formally justify us in inferring any 
 connection between sobriety and independence. Formally to 
 draw a conclusion, we must have affirmative grounds, such as 
 in this case we may obtain by obverting both premises : 
 All electors are not-sober ; 
 All electors are not-independent ; 
 .-. Some who are not-independent are not-sober. 
 
 (6) (a) If one premise be negative, the conclusion must be 
 negative : and (ft) to prove a negative conclusion, one premise 
 must be negative. 
 
 (a) For we have seen that one premise must be affirmative, 
 and that thus one term must be partly (at least) identified with 
 
CONDITIONS OF MEDIATE INFERENCE 109 
 
 the Middle. If, then, the other premise, being negative, 
 predicates the exclusion of the other term from the middle, 
 this other term must be excluded from the first term, so lar as 
 we know the first to be identical with the Middle : and this 
 exclusion will be expressed by a negative conclusion. The 
 analogy of the mediate comparison of quantities may here 
 again be noticed : if A is equal to B, and B is unequal to C, 
 A is unequal to C. 
 
 (3) If both premises are affirmative, the relations of both 
 terms to the Middle are more or less inclusive, and therefore 
 furnish no ground for an exclusive inference. This also follows 
 from the function of the Middle term. 
 
 For the more convenient application of these canons to the 
 testing of syllogisms, it is usual to derive from them three 
 Corollaries : 
 
 (i) Two particular premises yield no conclusion. 
 
 For if both premises are affirmative all their terms are undis- 
 tributed, the subjects by predesignation, the predicates by 
 position (chap. v. i) ; and therefore the middle must be 
 undistributed, and there can be no conclusion. 
 
 If one premise is negative, its predicate is distributed by 
 position : the other terms remaining undistributed. But, by 
 Canon 6, the conclusion (if any be possible) must be negative ; 
 and therefore its predicate, the major term, will be distributed. 
 In the premises, therefore, both the middle and the major 
 terms should be distributed, which is impossible: e.g., 
 Some M is not P ; 
 Some S is M ; 
 .'. Some S is not P. 
 
 Here, indeed, the major term is legitimately distributed (though 
 the negative premise might have been the minor) ; but M, the 
 middle term, is distributed in neither premise, and therefore 
 there can be no conclusion. 
 
 (ii) If one premise be particular, so is the conclusion. 
 
 For, again, if both premises are affirmative, they only dis- 
 tribute one term, the subject of the universal premise, and this 
 
no LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 must be the middle term. The minor term, therefore, is 
 undistributed, and the conclusion must be particular. 
 
 If one premise is negative, the two premises together can 
 distribute only two terms, the subject of the universal and the 
 predicate of the negative (which may be the same premise). 
 One of these terms must be the middle ; the other (since the con- 
 clusion is negative) must be the major. The minor term, there- 
 fore, is undistributed, and the conclusion must be particular. 
 
 (iii) From a particular major and a negative minor premise 
 nothing can be inferred. 
 
 For the minor premise being negative, the major premise 
 must be affirmative (5th Canon); and therefore, being par- 
 ticular, distributes the major term neither in its subject nor in 
 its predicate. But since the conclusion must be negative (6th 
 Canon), a distributed major term is demanded, e.g., 
 Some M is P ; 
 No S is M ; 
 
 Here the minor and the middle terms are both distributed, but 
 not the major (P) ; and, therefore, a negative conclusion is 
 impossible. 
 
 3. First Principle or Axiom of the Syllogism. Hitherto 
 in this chapter we have been analysing the conditions of valid 
 mediate inference. We have seen that a single step of such 
 inference, a Syllogism, contains when fully expressed in lan- 
 guage three propositions and three terms, and that these terms 
 must stand to one another in the relations required by the 
 fourth, fifth, and sixth Canons. We now come to a principle 
 which conveniently sums up these conditions ; it is called the 
 Dictujn de omni et nullo, and may be stated thus : 
 
 Whatever is predicated (affirmatively or negatively) of a 
 
 Term distributed, 
 In which Term another is given as (partly or wholly) 
 
 included, 
 
 May be predicated in like manner of (part or all of) the 
 latter Term. 
 
CONDITIONS OF MEDIATE INFERENCE in 
 
 Thus stated (nearly as by Whately in the introduction to his 
 Logic) the Dictum follows line by line the course of a Syllogism 
 in the First Figure (see chap. x. 2). To return to our former 
 example : All authors are vain is the same as Vanity is pre- 
 dicated of all authors ; Cicero is an author is the same as 
 Cicero is included amongst authors ; therefore Cicero is vain, 
 or Vanity may be predicated of Cicero. The Dictum then 
 requires : (i) three propositions ; (2) three terms; (3) that the 
 middle term be distributed ; (4) that one premise be affirmative, 
 since only by an affirmative proposition can one term be given 
 as included in another ; (5) that if one premise is negative the 
 conclusion be so too, since whatever is predicated of the middle 
 term is predicated in like manner of the minor. 
 
 Thus far, then, the Dictum is wholly analytic or verbal, 
 expressing no more than is implied in the definitions of 
 * Syllogism ' and * Middle Term ' ; since (as we have seen) 
 all the General Canons (except the third, which is a still 
 more general condition of formal proof) are derivable from 
 those definitions. However, the -Dictum makes a further 
 statement of a synthetic or real character, namely, that when 
 these conditions are fulfilled an inference is justified ; that then 
 the major and minor terms are brought into comparison 
 through the middle, and that the major term may be predi- 
 cated affirmatively or negatively of all or part of the minor. It 
 is this real assertion that justifies us in calling the Dictum an 
 Axiom. 
 
 4. Whether the Laws of Thought may not fully explain 
 the Syllogism without the need of any synthetic principle has, 
 however, been made a question. Take such a syllogism as the 
 following : 
 
 All domesticated animals are useful ; 
 All pugs are domesticated animals : 
 .*. All pugs are useful. 
 
 Here (an ingenious man might urge), having once identified 
 pugs with domestic animals, that they are useful follows from 
 the Law of Identity. If we attend to the meaning, and 
 
1 12 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 remember that what is true in one form of words is true in 
 any other form, then, all domesticated animals being useful, of 
 course pugs are. It is merely a case of subalternation : we 
 may put it in this way : 
 
 All domesticated animals are useful ; 
 .*. Some domesticated animals (e.g., pugs) are useful. 
 The derivation of negative syllogisms from the Law of Contra- 
 diction (he might add) may be shown in a similar manner. 
 
 But the force of this ingenious argument depends on the 
 participial clause * having once identified pugs with domestic 
 animals.' If this is a distinct step of the reasoning, the above 
 syllogism cannot be reduced to one step, cannot be exhibited 
 as mere subalternation, nor be brought directly under the law 
 of Identity. If 'pug,' Domestic,' and * useful' are distinct 
 terms ; and if ' pug ' and * useful ' are only known to be 
 connected because of their relations to * domestic ' : this is 
 something more than the Laws of Thought provide for : it is 
 not Immediate Inference, but Mediate ; and to justify it, 
 scientific method requires that its conditions be generalised. 
 The Dictum, then, as we have seen, does .generalise these 
 conditions, and declares that when such conditions are satisfied 
 a Mediate Inference is valid. 
 
 But, after all (to go back a little), consider again that pro- 
 position All pugs are domesticated animals : is it a distinct step 
 of the reasoning ; that is to say, is it a Real Proposition ? If, 
 indeed, * domesticated ' is no part of the definition of ' pug/ the 
 proposition is real, and is a distinct part of the argument. 
 But take such a case as this : 
 
 All dogs are useful ; 
 All pugs are dogs. 
 
 Here we clearly have, in the minor premise, only a verbal pro- 
 position : to be a dog is certainly part of the definition of 
 * pug.' But, if so, the inference ' All pugs are useful ' involves 
 no real mediation, and the argument is no more than this : 
 
 All dogs are useful ; 
 .-. Some dogs (e.g., pugs) are useful. 
 
 
CONDITIONS OF MEDIATE INFERENCE 113 
 
 Similarly, if the major premise be verbal, thus : 
 All men are rational ; 
 Socrates is a man 
 
 to conclude that * Socrates is rational ' is no Mediate In- 
 ference ; for so much was implied in the minor premise, 
 'Socrates is a man,' and the major premise adds nothing to 
 this. 
 
 Hence I conclude (as by anticipation in chap. vii. 3) that 
 'any apparent syllogism, having one premise a verbal pro- 
 position, is really an Immediate Inference ' ; but that, if both 
 premises are real propositions, the Inference is Mediate, and 
 demands for its explanation something more than the Laws of 
 Thought. I have not, however, always refrained from using 
 Verbal Syllogisms as formal illustrations^ 
 
 5. Other kinds of Mediate Inference exist, yielding valid 
 conclusions, without being truly syllogistic. Such are mathe- 
 matical inferences of Equality, as 
 
 A = B = C /. A = C. 
 
 Here, according to the usual logical analysis, there are strictly 
 four terms (i) A, (2) equal to B, (3) B, (4) equal to C. 
 
 Similarly with the argument bfortiori, 
 
 A>B>C .: (much more) A>C. 
 
 This also is said to contain four terms : (i) A, (2) greater than 
 B, (3) B, (4) greater than C. Such inferences are nevertheless 
 intuitively sound, may be verified by trial (within the limits of 
 sense-perception), and are generalised in appropriate axioms 
 of their own, corresponding to the Dictum of the syllogism ; 
 as ' Things equal to the same thing are equal to one another, 1 
 etc. 
 
 Now, surely, this is an erroneous application of the usual 
 logical analysis of propositions. Both Logic and Mathematics 
 treat of the relations of terms ; but whilst Mathematics employs 
 the sign = for only one kind of relation, and for that relation 
 exclusive of the terms ; Logic employs the same signs (is or is 
 not) for all relations, recognising only a difference of quality in 
 predication, and treating every other difference of relation as 
 
 H 
 
n 4 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 belonging to one of the terms related. Thus Logicians read 
 A is equal to B : as if equal to B could possibly be a term 
 co-relative with A. Whence it follows that the argument 
 A = jB=C .'. A=C contains four terms ; though everybody 
 sees that there are only three. 
 
 In fact (as observed in chap. ii. 2) the sign of logical relation 
 (is or is not), whilst usually adequate for class-reasoning (coin- 
 herence) and sometimes extensible to causation (because a 
 cause implies a class of events), should never be stretched to 
 include other relations in such a way as to sacrifice intelligence 
 to formalism. And, besides mathematical or quantitative 
 relations, there are others (usually considered qualitative 
 because indefinite) which cannot be justly expressed by the 
 logical copula. We ought to read : 
 
 B is before C ; 
 
 A is before B : 
 
 .-. A is before C. 
 
 And in like manner A is simultaneous with B ; etc. Such 
 arguments (as well as the mathematical) are intuitively sound 
 and verifiable, and might be generalised in axioms if it were 
 worth while : but it is not, because no method could be founded 
 on such axioms. 
 
 Custom justifies some Mediate Inferences, as, The Father of 
 a father is a grand-father. 
 
 Some cases, however, that at first seem obvious, are really 
 delusive unless further data be supplied. Thus A co-exists 
 with B) B with C ; .'. A with C is not sound unless B is 
 an instantaneous event ; for if B is perdurable, A may co-exist 
 with it at one time and C at another. 
 
 Again : A is to the left of B, B of C; .'. A of C. This may 
 pass ; but it is not a parallel argument that if A is north of B 
 and B west of C, then A is north-west of C : for suppose that 
 A is a mile to the north of B, and B a yard to the west of C, 
 then A is practically north of C ; at least its westward position 
 cannot be expressed in terms of the manner's compass. In 
 such a case we require to know not only the directions but the 
 
 
CONDITIONS OF MEDIATE INFERENCE 115 
 
 distances of A and C from B ; and then the exact direction o 
 A from C is an affair of mathematical calculation. 
 
 Qualitative reasoning concerning position is only applicable 
 to things in one dimension of space, or in time considered as 
 having one dimension. Under this condition we may frame 
 the following generalisation concerning all Mediate Inferences : 
 Two terms definitely related to a third, and one of them 
 positively, are related to one another as the other term is 
 related to the third (that is, positively or negatively) ; provided 
 that the relations given are of the same kind (that is, of Time, 
 or Coinherence, or Likeness, or Equality). 
 
 Thus, to illustrate by relations of Time 
 B is simultaneous with C ; 
 A is not simultaneous with B : 
 .*. A is not simultaneous with C. 
 
 Here the relations are of the same kind but of different logical 
 quality, and (as in the syllogism) a negative copula in the 
 premises leads to a negative conclusion. 
 
 An examination in detail of particular cases would show that 
 the above generalisation concerning all Mediate Inferences is 
 subject to too many qualifications to be called an Axiom; it 
 stands to the real Axioms (the Dictum^ etc.) as the notion of 
 the Uniformity of Nature does to the definite principles of 
 natural order (cf. chap. xiii. 9). 
 
CHAPTER X 
 CATEGORICAL SYLLOGISMS 
 
 i. The type of logical, deductive, mediate, categorical 
 Inference is a Syllogism directly conformable with the Dictum : 
 as 
 
 All carnivores (M) are excitable (P) ; 
 Cats (S) are carnivores (M) : 
 .'. Cats (S) are excitable (P). 
 
 In this example P is predicated of M, a term distributed ; in 
 which term, M, S is given as included ; so that P may be pre- 
 dicated of S. 
 
 Many arguments, however, are of a type superficially different 
 from the above : as 
 
 No wise man (P) fears death (M) ; 
 Balbus (S) fears death (M) : 
 .*. Balbus (S) is not a wise man (P). 
 
 In this example, instead of P being predicated of M, M is pre- 
 dicated of P, and yet S is given as included not in P, but in 
 M. The divergence of such a syllogism from the Dictum 
 may, however, be easily shown to be superficial by writing, 
 instead of No wise man fears death> the simple converse, No 
 man who fears death is wise. 
 Again : 
 
 Some dogs (M) are friendly to man (P) ; 
 
 All dogs (M) are carnivores (S) : 
 
 .-. Some carnivores (S) are friendly to man (P). 
 
 Here P is predicated of M undistributed; and instead of S 
 
 being included in M, M is included in S : so that the diver- 
 
CATEGORICAL SYLLOGISMS 117 
 
 gence from the type of syllogism to which the Dictum directly 
 applies is still greater than in the former case. But if we 
 transpose the premises, taking first 
 
 All dogs (M) are carnivores (P), 
 
 then P is predicated of M distributed ; and, simply converting 
 the other premise, we get 
 
 Some things friendly to man (S) are dogs (M) : 
 whence it follows that 
 
 Some things friendly to man (S) are carnivores (P) ; 
 and this is the simple converse of the original conclusion. 
 Once more : 
 
 No pigs (P) are philosophers (M) ; 
 
 Some philosophers (M) are hedonists (S) : 
 .'. Some hedonists (S) are not pigs (P). 
 
 In this case, instead of P being predicated of M distributed, 
 M is predicated of P distributed ; and instead of S (or part of 
 it) being included in M, we are told that some M is included 
 in S. Still there is no real difficulty. To show that it is all 
 right, simply convert both the premises. Then we have : 
 
 No philosophers (M) are pigs (P) ; 
 
 Some hedonists (S) are philosophers (M). 
 Whence the same conclusion follows ; and the whole syllogism 
 plainly conforms directly to the Dictum. 
 
 Such departures as these from the normal syllogistic form 
 are said to constitute differences of Figure (to be further de- 
 fined in 2) ; and the processes by which they are shown to 
 be unessential differences are called Reduction (for a fuller 
 account of which, see 6). 
 
 2. Figure is determined by the position of the Middle 
 Term in the premises ; of which position there are four possible 
 variations. The middle term may be subject of the major 
 premise, and predicate of the minor, as in the first example 
 above; and this position, being directly conformable to the 
 requirements of the Dictum, is called the First Figure. Or the 
 middle term may be predicate of both premises, as in the 
 second of the above examples ; and this is called the Second 
 
n8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Figure. Or the middle term may be subject of both premises, 
 as in the third of the above examples ; and this is called the 
 Third Figure. Or, finally, the middle term may be predicate 
 of the major premise, and subject of the minor, as in the fourth 
 example given above ; and this is the Fourth Figure. 
 
 It may facilitate the recollection of this most important point 
 if we schematise the figures thus : 
 
 SL 
 
 II. 
 P iM 
 
 s IM 
 
 in. 
 
 Mi P 
 Ml S 
 
 IV. 
 P -y M 
 M -S 
 
 The horizontal lines represent the premises, and at the angles 
 formed with them by the slanting or by the perpendicular lines 
 the Middle Term occurs. Note further that the schema of 
 the Fourth and last Figure resembles Z, the last letter of the 
 alphabet : this helps one to remember it in contrast with the 
 First, which is thereby also remembered. Figures II. and III. 
 seem to stand back to back. 
 
 3. The Moods of each Figure are the modifications of it 
 which arise from different combinations of propositions accord- 
 ing to Quantity and Quality. In the First Figure, for example, 
 four Moods are recognised ; A. A. A., E. A. E., A. 1. 1., E. I. O. 
 
 A. AllMisP; 
 A. All S is M : 
 A. .'. All S is P. 
 
 E. No M is P ; 
 A. All S is M : 
 E. /. No S is P. 
 
 E. All M is P ; 
 I. Some S is M : 
 I. /. Some S is P. 
 
 E. No M is P ; 
 
 I. Some S is M : 
 
 O. .'. Some S is not P : 
 
CATEGORICAL SYLLOGISMS 119 
 
 Now, remembering that there are four Figures, and four kinds 
 of propositions (A. I. E. O.), each of which propositions maybe 
 Major Premise, Minor Premise, or Conclusion of a syllogism, 
 it appears that in each Figure there may be 64 Moods, and 
 therefore 256 in all. On examining these 256 Moods, how- 
 ever, we find that only 24 of them are valid (i.e., of such a 
 character that the conclusion strictly follows from the pre- 
 mises), whilst 5 of these 24 are needless, because their con- 
 clusions are 'weaker* or less extensive than the premises 
 warrant ; that is to say, they are particular when they might be 
 universal. Thus, in the First Figure, besides the above 4 
 Moods, A. A. I. and E. A. O. are valid in the sense of being 
 conclusive ; but they are superfluous, because included in 
 A. A. A. and E. A. E. Omitting then these 5 needless Moods, 
 which are called ' Subalterns ' because their conclusions are 
 subaltern (chap. vii. 2) to those of other Moods, there remain 
 1 9 Moods that are valid and generally recognised. 
 
 4. How these 19 Moods are determined must be our next 
 inquiry. There are several ways more or less ingenious and 
 interesting ; but all depend on the application, directly or 
 indirectly, of the Six Canons, which were shown in the last 
 chapter to be the conditions of Mediate Inference. 
 
 (i) One way is to begin by finding what Moods of the First 
 Figure conform to the Dictum. Now, the Dictum requires 
 that, in the major premise, P be predicated of a term dis- 
 tributed, from which it follows that no Mood can be valid 
 whose major premise is particular, as in I. A. I. or O. A. O. 
 Again, the Dictum requires that the minor premise be affirma- 
 tive (" in which term a third is given as included ") ; so that no 
 Mood can be valid whose minor premise is negative, as in 
 A. E. E. or A. O. O. By these considerations we find that in 
 the First Figure, out of 64 Moods possible, only six are valid, 
 namely, those above-mentioned in 3, including the two 
 Subalterns. The second step of this method is to test the 
 Moods of the Second, Third, and Fourth Figures, by trying 
 whether they can be reduced to one or other of the four Moods 
 
120 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 of the First (as briefly illustrated in i, and to be further 
 explained in 6). 
 
 (2) Another way is to take the above six General or 
 Common Canons, and to deduce from them Special Canons 
 for testing each Figure : an interesting method, which, on 
 account of its length, will be treated of separately in the next 
 section. 
 
 (3) Direct application of the Common Canons is, perhaps, the 
 simplest plan. First write out the 64 Moods that are possible 
 without regard to Figure, and then cross out those which 
 violate any of the Canons or Corollaries, thus : 
 
 A A A, :S~AHE. (6th Cad. fy A A I. 7n*-9> (6th Can. b}. 
 -&-&A (6th Can. a) A E E^Tt-B-l (6th Can. a} A E O, 
 7t-J-A-(Cor. if.) 3*(6th Can. o>, A 1 1. -ft~Fa(6th Can. 6) 
 
 Cao. a } 1r&& (Cor. ii.lT%-G-t (6th Can. a) A O O. 
 
 Whoever has the patience to go through the remaining 48 
 Moods will discover that of the whole 64 only 1 1 are valid, 
 namely : 
 
 A. A. A., A. A. I., A. E. E., A. E. O., A. 1. 1., A. O. O., 
 E. A. E., E. A. O., E. I. O., I. A. I., O. A. O. 
 
 These n Moods have next to be examined in each 
 Figure, and if valid in every Figure there will still be 44 moods 
 in all. We find, however, that in the First Figure, A. E. E., 
 A. E. O., A. O. O. involve illicit process of the Major Term 
 (3rd Can.) ; I. A. I., O. A. O. involve undistributed Middle 
 (4th Can.) ; and A. A. I., E. A. O. are Subalterns. In the Second 
 Figure all the affirmative Moods, A. A. A., A. A. I., A.I.I., I.A.I., 
 involve undistributed Middle ; O. A. O. involves illicit process 
 of the Major; and A. E.G., E. A. O. are Subalterns. In the 
 Third Figure, A. A. A., E. A. E., involve illicit process of the 
 Minor (3rd Can.); A. E. E., A. E. O., A. O. O. involve illicit pro- 
 cess of the Major. In the Fourth Figure, A. A. A. involves 
 illicit process of the Minor ; A. I. I., A. O. O. involve undis- 
 tributed Middle ; O. A. O. involves illicit process of the Major; 
 and A. E. O. is Subaltern. 
 
CATEGORICAL SYLLOGISMS 121 
 
 Those moods of each Figure which, when tried by these 
 tests, are not rejected, are valid, namely : 
 
 Fig. I. A. A. A., E.A.E., A. 1. 1., E.I.O. (A. A. I., 
 A. E. O., Subaltern) ; 
 
 Fig. II. E. A. E., A. E. E., E. I. O., A. O. O. (E. A. O., 
 A. E. O., Subaltern) ; 
 
 Fig. III. A.A.I., LA. I,, A. 1. 1., E. A. O., O.A.O., 
 E. I. O. ; 
 
 Fig. IV. A. A. I., A.E. E., I.A.I., E.A.O., E.I.O. 
 (A. E. O., Subaltern). v 
 
 Thus, including subaltern Moods, there are six valid in each 
 Figure. In Fig. III. alone there is no subaltern Mood, 
 because in that Figure there can be no universal conclusion. 
 
 5. Special Canons of the several Figures, deduced from 
 the Common Canons, enable us to arrive at the same result by 
 a somewhat different course. 
 
 The Special Canons are not, perhaps, necessary to the 
 Science, but they afford a very useful means of enabling one 
 to thoroughly appreciate the character of formal syllogistic 
 reasoning. Accordingly, I shall indicate the proof of each 
 rule, leaving its elaboration to the reader. In this he can find 
 no difficulty, if he bears in mind that Figure is determined by 
 the position of the Middle Term. 
 
 Fig. I., Rule (a) : The minor premise must be affirmative. 
 
 For, if not, in negative Moods there will be illicit process of 
 the major term. Applying this rule to the eleven possible 
 Moods given in 4, as remaining after application of the 
 Common Canons, it eliminates A. E. E., A. E. O., A. O. O. 
 
 (b) The major premise must be universal. 
 
 For, if not, the minor being affirmative, the middle term will 
 be undistributed. This rule eliminates I.A.I., O. A. O. ; 
 leaving six Moods, including two Subalterns. 
 
 Fig. II. (a) One premise must be negative. 
 
 For else neither premise will distribute the middle term. 
 This rule eliminates A. A. A., A. A. I., A. 1. 1., I. A. I. 
 
122 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (b) The major premise must be universal. 
 
 For else, the conclusion being negative, there will be illicit 
 process of the major term. This eliminates I. A. I., O. A. O. ; 
 leaving six Moods, including two Subalterns. 
 
 Fig. III. (a) The minor premise must be affirmative. 
 
 For else, in negative moods there will be illicit process of 
 the major term. This rule eliminates A. E. E., A. E. O., 
 A. O. O. 
 
 (b) The conclusion must be particular. 
 
 For else, the minor premise being affirmative, there will be 
 illicit process of the minor term. This eliminates A. A. A., 
 A. E. E., E. A. E. ; leaving six Moods. 
 
 Fig. IV. (a) When the major premise is affirmative, the minor 
 must be universal. 
 
 For else the middle term is undistributed. This eliminates 
 A. 1. 1., A. O. O. 
 
 (b) When the minor premise is affirmative the conclusion must 
 be particular. 
 
 For else there will be illicit process of the minor term. This 
 eliminates A. A. A., E. A. E. 
 
 (c) When either premise is negative, the major must be 
 universal. 
 
 For else, the conclusion being negative, there will be illicit 
 process of the major term. This eliminates O. A. O. ; leaving 
 six Moods, including one Subaltern. 
 
 6. Reduction is either (i) Ostensive or (2) Indirect. 
 Ostensive Reduction consists in showing that an argument 
 given in one Mood can also be stated in another ; the process 
 is especially used to show that the Moods of the second, third, 
 and fourth Figures are equivalent to one or another Mood of 
 the first Figure. It thus proves the validity of the former 
 Moods by showing that they also essentially conform to the 
 Dictum^ and that all Categorical Syllogisms are only superficial 
 varieties of one type of proof. 
 
 To facilitate Reduction, the recognised Moods have all had 
 names given them; which names, again, have been strung 
 
CATEGORICAL SYLLOGISMS 123 
 
 together into mnemonic verses of great force and preg- 
 nancy : 
 
 Barbara, Celarent, Darii, Ferioque prioris : 
 Cesare, Camestres, Festino, Baroco, secundae: 
 Tertia, Darapti, Disamis, Datisi, Felapton, 
 Bocardo, Ferison, habet : Quarta insuper addit 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison. 
 
 In the above verses the names of the Moods of Fig. I. begin 
 with the first four consonants B, C, D, F, in alphabetical 
 order ; and the names of all other Moods likewise begin with 
 these letters, thus signifying (except in Baroco and Bocardo) 
 the Mood of Fig. I., to which each is equivalent, and to which 
 it is to be reduced : as Bramantip to Barbara, Camestres to 
 Celarent, and so forth. 
 
 The vowels A, E, I, O, occurring in the several names, give 
 the Quantity and Quality of major premise, minor premise, 
 and conclusion in the usual order. 
 
 The consonants s and p, occurring after a vowel, show that 
 the proposition which the vowel stands for is to be converted 
 either (s) simply or (p) per accidens ; except where s or p 
 occurs after the third vowel of a name, the conclusion : then it 
 refers not to the conclusion of the given Mood (say Disamis), 
 but to the conclusion of that Mood of the first Figure to which 
 the given Mood is reduced (Darii). 
 
 M (mutare, metathesis) means ' transpose the premises ' (as 
 of Cawestres). 
 
 C means * substitute the contradictory of the conclusion for 
 the foregoing premise,' a process of the Indirect Reduction to 
 be presently explained (see Baroco, 8). 
 
 The other consonants r, n, t (with b and d, when not initial), 
 occurring here and there, have no mnemonic significance. 
 
 What now is the problem of Reduction ? The difference of 
 Figures depends upon the position of the Middle Term. To 
 reduce a Mood of any other Figure to the form of the First, 
 then, we must so manipulate its premises that the Middle 
 
124 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Term shall be subject of the major premise and predicate of 
 the minor premise. 
 
 Now in Fig. II. the Middle Term is predicate of both pre- 
 mises ; so that the minor premise may need no alteration, and 
 to convert the major premise may suffice. This is the case 
 with Cesare, which reduces to Celarent by simply converting 
 the major premise ; and with Festino, which by the same pro- 
 cess becomes Ferio. In Camestres, however, the minor pre- 
 mise is negative ; and, as this is impossible in Fig. I., the 
 premises must be transposed, and the new major premise must 
 be simply converted : then, since the transposition of the pre- 
 mises will have transposed the terms of the conclusion (accord- 
 ing to the usual reading of syllogisms), the new conclusion 
 must be simply converted in order to prove the validity of the 
 original conclusion. The process may be thus represented 
 (s.f. meaning * simply convert ') : 
 
 Camestres. Celarent. 
 
 AllPisM; ^^ ^^- NoMisS; 
 
 NoSisM: ' ^* All Pis M: 
 
 .-. No S is P. * CT No P is S. 
 
 The Ostensive Reduction of Baroco also needs special ex- 
 planation ; for as it used to be reduced indirectly, its name gives 
 no indication of the ostensive process. To reduce it osten- 
 sively let us call it Faksnoko, where k means * obvert the 
 foregoing premise.' By thus obverting (k) and simply convert- 
 ing (s) (in sum, contrapositing) the major premise, and obvert- 
 ing the minor premise, we get a syllogism in Ferio, thus : 
 
 Baroco or Faksnoko. Ferio. 
 
 AllPisM; contra?, ^ No m (not-M) i P; 
 
 Some S is not M : > Some S is m (not-M): 
 
 ,*. Some S is not P. .*. Some S is not P. 
 
CATEGORICAL SYLLOGISMS 125 
 
 In Fig. III. the middle term is subject of both premises ; so 
 that, to reduce its Moods to the First Figure, it may be enough 
 to convert the minor premise. This is the case with Darapti, 
 Datisi, Felapton and Ferison. But, with Disamis, since the 
 major premise must in the First Figure be universal, we must 
 transpose the premises, and then simply convert the new minor 
 premise ; and, lastly, since the major and minor terms have 
 now changed places, we must simply convert the new conclu- 
 sion in order to verify the old one. Thus : 
 
 Disamis. Darii. 
 
 Some M is P ; ^ All M is S ; 
 
 All M is S : ^^ ^-^v Some P is M : 
 
 , Some S is P. * !L * .'. Some P is S. 
 
 Bocardo, like Baroco, indicates by its name the indirect 
 process. To reduce it ostensively let its name be Doksamrosk, 
 and proceed thus : 
 
 Bocardo or Doksamrosk. Darii. 
 
 Some M is not P ; ^ _^* All M is S ; 
 
 All M is S : - ^ Some p (not-P) is M : 
 
 .*. Some S is not P. * conyert & obvert ^ Some p (not . p) is s> 
 
 In Fig. IV. the position of the middle term is, in both 
 premises, the reverse of what it is in the First Figure ; we may 
 therefore reduce its Moods either by transposing the premises, 
 as with Bramantip, Camenes, and Dimaris ; or by converting 
 both premises, the course pursued with Fesapo and Fresison. 
 It may suffice to illustrate by the case of Bramantip : 
 
126 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Bramantip. Barbara. 
 
 AllPisM; ^_ ^r AllMisS. 
 
 All M is S : ^ All P is M : 
 
 .-. Some S is P. < >**'l*r*' ... All P is S. 
 
 This case shows that a final significant consonant (s, p, or 
 sk) in the name of any Mood refers to the conclusion of the 
 new syllogism in the First Figure ; since p in Bramantip cannot 
 refer to its own conclusion in I.; which being already particular, 
 cannot be converted /<?? accidens. 
 
 Finally, in Fig. I., Darii and Ferio differ respectively from 
 Barbara and Celarent only in this, that their minor premises, 
 and consequently their conclusions, are subaltern to the 
 corresponding propositions of the universal Moods ; a difference 
 which seems insufficient to give them rank as distinct forms of 
 demonstration. And as for Barbara and Celarent, they are 
 easily reducible to one another by ob verting their major 
 premises and the new conclusion, thus : 
 
 Barbara. 
 
 obv. 
 All M is P ; > No M is p (not-P) ; 
 
 AllSisM: >. AllSisM: 
 
 061;. 
 .-. All S is P. < .-. No S is p (not-P). 
 
 7. A new version of the mnemonic lines was suggested in 
 Mind No. 27, with the object of (i) freeing them from all 
 meaningless letters, (2) showing by the name of each Mood 
 the Figure to which it belongs, (3) giving names to indicate 
 the ostensive reduction of Baroco and Bocardo. To obtain 
 the first two objects, / is used as the mark of Fig. I., n of Fig. II., 
 r of Fig. III., / of Fig. IV. The verses (to be scanned 
 discreetly) are as follows : 
 
 
CATEGORICAL SYLLOGISMS I2 7 
 
 Balala, Celalel, Dalii, Felioque prioris : 
 
 /Faksnoko secundae: 
 Cesane, Camenes, Fesmon, |g 
 
 Tertia, Darapri, Drisamis, Darisi, Ferapro, 
 
 Doksamrosk -> 
 
 Bocaro j ' Fensor habet : Q uarta insuper addit 
 
 Bamatip, Gametes, Dimatis, Fesapto, Fesistot. 
 
 De Morgan praised the old verses as " more full of meaning 
 than any others that ever were made " ; and in defence of the 
 above alteration it may be said that they now deserve that praise 
 still more. 
 
 8. Indirect reduction is the process of proving a Mood to 
 be valid by showing that the supposition of its invalidity involves 
 a contradiction. Take Baroco, and (since the doubt as to its 
 validity is concerned not with the truth of the premises, but 
 with their relation to the conclusion) assume the premises to 
 be true. Then, if the conclusion be false, its contradictory is 
 true. The conclusion being in O., its contradictory will be in 
 A. Substituting this A. for the minor premise of Baroco, we 
 have the premises of a syllogism in Barbara, which will be 
 found to give a conclusion in A., contradictory of the original 
 minor premise ; thus : 
 
 Baroco. Barbara. 
 
 All P is M ; . All P is M ; 
 
 Some S is not M : *^^ i-*L^* AllSisP: 
 
 /. Some S is not P. - ^-** x> ^~*^. .-. All S is M. 
 
 But the original minor premise, Some S is not M t is true by 
 hypothesis ; and therefore the conclusion of Barbara, All S is 
 M t is false. This falsity cannot, however, be due to the form 
 of Barbara, which we know to be valid ; nor to the major pre- 
 mise, which, being taken from Baroco, is true by hypothesis : 
 
128 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 it must, therefore, be in the minor premise of Barbara. All S 
 is P ; and since this is contradictory of the conclusion of 
 Baroco Some S is not P, that conclusion was true. 
 
 Similarly with Bocardo, the Indirect Reduction proceeds by 
 substituting for the major premise the contradictory of the 
 conclusion ; thus again obtaining the premises of a syllogism 
 in Barbara, whose conclusion is contradictory of the original 
 major premise. Hence the initial B in Baroco and Bocardo : 
 it points to a syllogism in Barbara as the means of Indirect 
 Reduction (Reductio ad impossibile). 
 
 Any other Mood may be reduced indirectly : as, for example, 
 Dimaris. If this is supposed to be invalid and the conclusion 
 false, substitute the contradictory of the conclusion for the 
 major premise, thus obtaining the premises of Celarent : 
 
 Celarent. 
 No S is P ; 
 
 Dimaris. 
 Some P is M ; 
 
 All M is S : 
 .. Some S is P. 
 
 The conclusion of Celarent, simply converted, contradicts the 
 original major premise of Dimaris, and is therefore false. 
 Therefore the major premise of Celarent is false, and the con- 
 clusion of Dimaris is true. We might, of course, construct 
 mnemonic names for the Indirect Reduction of all the Moods: 
 the name of Dimaris would then be Cicari. 
 
 9. The need or use of any Figure but the First has been 
 much discussed by Logicians. Since, in actual debate, argu- 
 ments are rarely stated in syllogistic form ; and, therefore, if 
 reduced to that form for closer scrutiny, generally have to be 
 treated with some freedom ; why not always throw them at 
 once into the First Figure ? That Figure has manifest advan- 
 
CATEGORICAL SYLLOGISMS 129 
 
 tages : it agrees directly with the Dictum ; it gives conclusions 
 in all four prepositional forms, and therefore serves every pur- 
 pose of full affirmation or denial, of showing agreement or 
 difference (total or partial), of establishing the contradictories 
 of universal statements ; and it is the only Figure in which the 
 subject and predicate of the conclusion occupy the same posi- 
 tions in the premises, so that the course of argument has in its 
 mere expression an easy and natural flow. 
 
 Still, the Second Figure also has a very natural air in some 
 kinds of negative arguments. The parallelism of the twc 
 premises, with the middle term as predicate in both, brings out 
 very forcibly the necessary difference between the major and 
 minor terms that is involved in their opposite relations to the 
 middle term. P is not, whilst S is, M, says Cesare : that very 
 neatly drives home the conviction that S is not P. Or perhaps 
 even more naturally in Camestres : Deer do, oxen do not, shed 
 t/ieir horns. What is the conclusion ? 
 
 The Third Figure, again, furnishes in Darapti and Felapton, 
 the most natural forms of stating arguments in which the 
 middle term is singular : 
 
 Socrates was truthful ; 
 
 Socrates was a Greek : 
 
 /. Some Greek was truthful. 
 
 Reducing this to Fig I., we should get for the minor premise, 
 Some Greek was Socrates : which is certainly inelegant. Still, it 
 might be urged that, in the science of proof, elegance is an alto- 
 gether extraneous consideration. And as for the other advantage 
 claimed for Fig. III. that, as it yields only particular con- 
 clusions, it is useful in establishing contradictories against 
 universals I do not see that for that purpose any of its Moods 
 have superiority over Darii and Ferio. 
 
 As for Fig. IV., no particular advantage is claimed for it It 
 is of comparatively late recognition (sometimes called the 
 'Galenian,' after Galen, its supposed discoverer); and its 
 scientific claim to exist at all is disputed. It is said to be a 
 
 I 
 
130 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 mere inversion of Fig. I. ; which is not true in any sense in 
 which Figs. II. and III. may not be condemned as partial 
 inversions of Fig. I., and as having therefore still less claim to 
 recognition. It is also said to invert the order of thought ; as 
 if thought had only one order, or as if the mere order of 
 thought had anything to do with Formal Logic. The truth 
 is that, if distinction of Figure be recognised at all, the 
 Fourth Figure is scientifically necessary, because it is inevitably 
 generated by an analysis of the possible positions of the middle 
 term. 
 
 10. Is Reduction necessary, however ; or have not all the 
 Figures equal and independent validity? In one sense not 
 only every Figure but each Mood has independent validity : 
 for any one capable of abstract thinking sees its validity by 
 direct inspection. But this is true not only of the abstract 
 Moods, but very commonly of particular concrete arguments. 
 Science, however, aims at unifying knowledge ; and after 
 reducing all possible arguments that form categorical 
 syllogisms to the nineteen Moods, it is but another step in 
 the same direction to reduce these Moods to one form. This 
 is the very nature of science : and, accordingly, I cannot look 
 without wonder at the efforts of some Logicians to expound 
 separate principles of each Figure. Grant that they succeed ; 
 and what can the next step be, but either to reduce these 
 principles to the Dictum, or the Dictum and the rest to one of 
 these principles ? Unless this can be done there is no science 
 of Formal Logic. If it is done, what is gained by reducing 
 the principles of the other Figures to the Dictum, instead of 
 the Moods of the other Figures to those of the first Figure ? 
 It may, perhaps, be said that to show (i) that the Moods of 
 the second, third, and fourth Figures flow from their own 
 principles (though, in fact, these principles are laboriously 
 adapted to the Moods) ; and (2) that these principles may be 
 derived from the Dictum, is the more uncompromisingly 
 gradual and regular method : but, on the whole, is not Forma' 
 Logic already sufficiently encumbered with formalities ? 
 
CATEGORICAL SYLLOGISMS 131 
 
 ii. Euler's diagrams may be used to illustrate the 
 syllogism, thus : 
 
 FIG. 5. 
 
 Barbara 
 
 FIG. 6. 
 
 Celarent 
 
 Remembering that 'Some* means 'It may be all,' it is plain 
 that any one of these diagrams in Fig. 7, or the one given 
 above for Barbara, may represent the denotative relations of 
 P, M, and S in Darii ; though no doubt the diagram we 
 generally think of as representing Darii is No. i in Fig. 7. 
 
132 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 FIG. 8. 
 
 Ferio 
 
 Here, again, I suppose, we generally think of No. i as the 
 diagram representing Ferio ; but 2, or 3, or that given above 
 for Celarent, is compatible with the premises. 
 
 It is instructive to work out the diagrams for the Moods of 
 the other Figures, noticing how they stand related to the 
 above. 
 
CHAPTER XI 
 ABBREVIATED AND COMPOUND ARGUMENTS 
 
 i. In ordinary discussion, whether oral or written, it is 
 but rarely that the forms of Logic are closely adhered to. We 
 often leave wide gaps in the structure of our arguments, trust- 
 ing the intelligence of those addressed to bridge them over ; 
 or we invert the regular order of propositions, beginning with 
 the conclusion, and mentioning the premises, perhaps, a good 
 while after, confident that the sagacity of our audience will 
 make all smooth. Sometimes a full style, like Macaulay's, 
 may, by means of amplification and illustration, spread the 
 elements of a single syllogism over several pages a penny- 
 worth of logic steeped in so much eloquence. These practices 
 give a great advantage to sophists ; who would find it very 
 inconvenient to state explicitly in Mood and Figure the preten- 
 tious antilogies which they foist upon the public ; and, indeed, 
 such licences of composition often prevent honest men from 
 detecting errors into which they themselves have unwittingly 
 fallen, and which, with the best intentions, they strive to com- 
 municate to others : but we put up with these drawbacks to 
 avoid the inelegance (forsooth !) and the tedium of a long dis- 
 course in accurate syllogisms. 
 
 Many departures from the strictly logical statement of 
 reasonings consist in the use of vague or figurative language, 
 or in the substitution for one another of expressions supposed 
 to be equivalent though, in fact, dangerously discrepant. 
 Against such occasions of error the logician can provide no 
 safeguard, except the advice to be careful and discriminating 
 
i 3 4 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 in what you say or hear. But as to any derangement of the 
 elements of an argument, or the omission of them, Logic 
 effectually aids the task of restoration ; for it has shown what 
 the elements are that enter into the explicit statement of most 
 ratiocinations, namely, the four forms of propositions ; and 
 what that connected order of propositions is which most easily 
 and surely exposes the validity or invalidity of reasoning, 
 namely, the premises and conclusion of the Syllogism. Logic 
 has even gone so far as to name certain abbreviated forms of 
 proof, which may be regarded as general types of those that 
 actually occur in debate, in leading articles, pamphlets and 
 other persuasive or polemic writings namely, the Enthy- 
 meme, Epicheirema and Sorites'. 
 
 2. The Enthymeme, according to Aristotle, is the Syllo- 
 gism of probable reasoning about practical affairs and matters 
 of opinion, in contrast with the Syllogism of theoretical de- 
 monstration upon necessary grounds. But, as now commonly 
 treated, it is an argument with one of its elements omitted ; 
 a Categorical Syllogism, having one or other of its premises, 
 or else its conclusion, suppressed. If the Major Premise is 
 suppressed, it is called an Enthymeme of the First Order ; if 
 the Minor Premise is wanting, it is said to be of the Second 
 Order ; if the Conclusion is left to be understood, there is an 
 Enthymeme of the Third Order. 
 
 Let the following be a complete Syllogism : 
 All free nations are enterprising : 
 The Dutch are a free nation : 
 .'.The Dutch are enterprising. 
 
 Reduced to Enthymemes this argument may be put thus : 
 
 In the First Order : 
 
 The Dutch are a free nation : 
 .'. The Dutch are enterprising. 
 
 la the Second Order 
 
 All free nations are enterprising : 
 .*. The Dutch are enterprising. 
 
 
ABBREVIATED ARGUMENTS 135 
 
 In the Third Order- 
 All free nations are enterprising ; 
 And the Dutch are a free nation. 
 
 It is certainly very common to meet with arguments whose 
 statement may be represented by one or other of these three 
 forms ; indeed, the Enthymeme is the natural substitute for a 
 full syllogism in oratory : whence the transition from Aristotle's 
 to the modern meaning of the term. The most unschooled of 
 men readily apprehend its force ; and a student of Logic can 
 easily supply the proposition that may be wanted in any case to 
 complete a syllogism, and thereby test the argument's formal 
 validity. In any Enthymeme of the Third Order, especially, 
 to supply the conclusion cannot present any difficulty at all ; 
 and hence it is a favourite vehicle of innuendo, as in Hamil- 
 ton's example : 
 
 Every liar is a coward ; 
 
 And Caius is a liar. 
 
 The frankness of this statement and its reticence, together, 
 make it a biting sarcasm upon Caius. 
 
 To find the missing premise in an Enthymeme of either the 
 First or Second Order, a simple rule may be given : Take that 
 Term of the given Premise that does not occur in the Conclu- 
 sion (and which must therefore be the Middle), and combine it 
 with that Term of the Conclusion which does not occur in the 
 given Premise; the proposition thus formed is the Premise 
 which was requisite to complete the Syllogism. If the premise 
 thus constituted contain the predicate of the conclusion, the 
 Enthymeme was of the First Order ; if it contain the subject of 
 the conclusion, the Enthymeme was of the Second Order. 
 
 That a statement in the form of a Hypothetical Proposition 
 may really be an Enthymeme (as observed in chap. v. 4) can 
 easily be shown by recasting one of the above Enthyniemes 
 thus : Jf all free nations are enterprising, the Dutch are enter- 
 prising. Such statements should be treated according to their 
 true nature. 
 
136 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 To reduce the argument of any ordinary discourse to logical 
 form, the first care should be to make it clear to oneself what 
 exactly the conclusion is, and to state it adequately but as 
 succinctly as possible. Then look for the evidence. This 
 may be of an inductive character, consisting of instances, 
 examples, analogies ; and, if so, of course its cogency must be 
 evalued by the principles of Induction, which we shall pre- 
 sently investigate. But if the evidence is deductive, it will 
 probably consist of an Enthymeme, or of several Enthymemes 
 one depending on another. Each Enthymeme may be isolated 
 and expanded into a syllogism. And we may then inquire : 
 (i) whether the syllogisms are formally correct according to 
 Barbara (or whatever the appropriate Mood) ; (2) whether the 
 premises, or the ultimate premises, are true in fact. 
 
 3. A Monosyllogism is a syllogism considered as standing 
 alone or without relation to other arguments. But, of course, 
 a disputant may be asked to prove the premises of any syllo- 
 gism ; in which case other syllogisms may be advanced for 
 that purpose. When the conclusion of one syllogism is used 
 to prove another, we have a chain-argument ; which, stated at 
 full length, is a Polysyllogism. In any Poly syllogism, again, 
 a syllogism whose conclusion is used as the premise of another, 
 is called in relation to that other a Prosyllogism ; whilst a syllo- 
 gism, one of whose premises is the conclusion of another 
 syllogism, is in relation to that other an Episyllogism. Two 
 modes of abbreviating a Polysyllogism are usually discussed, 
 the Epicheirema and the Sorites. 
 
 4. An Epicheirema is a syllogism for one or both of whose 
 premises a reason is added ; as 
 
 All men are mortal, for they are animals ; 
 Socrates is a man, for rational bipeds are men ; 
 .*. Socrates is mortal. 
 
 The Epicheirema is called Single or Double, says Hamilton, 
 according as an " adscititious proposition " attaches to one or 
 both of the premises. The above example is of the double 
 
ABBREVIATED ARGUMENTS 137 
 
 kind. The Single are said to be of the First Order, if the 
 adscititious proposition attaches to the Major Premise ; if to the 
 Minor, of the Second Order. (Hamilton : Lecture xix.) 
 
 An Epicheirema then is an abbreviated chain of reasoning, 
 or Polysyllogism, comprising an Episyllogism with one or two 
 enthymematic Prosyllogisms. The major premise in the above 
 case, All men are mortal, for they are animals, is an Enthymeme 
 of the First Order, suppressing its own major premise, and may 
 
 be restored thus : 
 
 All animals are mortal ; 
 All men are animals ; 
 .*. All men are mortal. 
 
 The minor premise, however, is an Enthymeme of the Second 
 Order, suppressing its own minor premise, and may be restored 
 
 thus: 
 
 All rational bipeds are men ; 
 Socrates is a rational biped ; 
 /. Socrates is a man. 
 
 5. The Sorites is a Polysyllogism in which the Conclu- 
 sions, and even some of the Premises, are suppressed until the 
 argument ends. If the chain of arguments were freed of its 
 enthymematic character, the suppressed conclusions would of 
 course appear as premises of Episyllogisms. 
 
 Two varieties of Sorites are recognised, the Aristotelian (so 
 called, though not treated of by Aristotle), and the Goclenian 
 (named after its discoverer, Goclenius of Marburg, who flourished 
 about 1600 A.D.). In order to compare these two forms of 
 argument, it will be convenient to place side by side Hamilton's 
 classical examples of them. 
 
 Aristotelian. Goclenian. 
 
 Bucephalus is a horse ; An animal is a substance ; 
 
 A horse is a quadruped ; A quadruped is an animal ; 
 
 A quadruped is an animal ; A horse is a quadruped ; 
 
 An animal is a substance ; Bucephalus is a horse ; 
 
 /. Bucephalus is a substance. .-. Bucephalus is a substance. 
 
138 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 The reader wonders what is the difference between these two 
 forms. Of course, in the Aristotelian Sorites the minor term 
 occurs in the first premise, and the major term in the last ; 
 whilst in the Goclenian the major term occurs in the first, and 
 the minor in the last. But since the character of premises is 
 fixed by their terms, not by the order in which they are 
 written, there cannot be a better example of a distinction with- 
 out a difference. At a first glance, indeed, there may seem to 
 be a more important point involved ; the premises of the 
 Aristotelian Sorites seem to proceed in the order of the Fourth 
 Figure. But if that were really so the conclusion would be, 
 Some substance is Bucephalus. That, on the contrary, every one 
 writes the conclusion, Bucephalns is a substance, proves that 
 the logical order of the premises is in the First Figure. Logi- 
 cally, therefore, there is absolutely no difference between these 
 two forms, and pure reason requires either that the "Aris- 
 totelian Sorites " disappear from the text-books, or that it be 
 regarded as in the Fourth Figure, and its conclusion converted. 
 It is the shining merit of Goclenius to have restored the pre- 
 mises of the Sorites to the usual order of Fig. .1. : whereby he 
 has raised to himself a monument more durable than brass, 
 and secured indeed the very cheapest immortality. How ex- 
 pensive, compared with this, was the method of that Ephesian 
 incendiary ! 
 
 The common Sorites, then, being in the First Figure, its 
 rules follow from those of the First Figure : 
 
 (1) Only one premise can be particular; and, if any, only 
 that in which the minor term occurs. 
 
 For, just as in Fig. I., a particular premise anywhere else 
 involves Undistributed Middle. 
 
 (2) Only one premise can be negative ; and, if any, only 
 that in which the major term occurs. 
 
 For if there were two negative premises, at the point where 
 the second entered the chain of argument there must be a 
 syllogism with two negative premises, which is contrary to 
 Rule 5 ; whilst if one premise be negative it must be that 
 
ABBREVIATED ARGUMENTS 139 
 
 which contains the major term, for the same reason as in Fig. I., 
 namely, that the conclusion will be negative, and that therefore 
 only a negative major premise can prevent Illicit Process of 
 the Major Term. 
 
 If we expand a Sorites into its constituent syllogisms, the 
 conclusions successively suppressed will reappear as major pre- 
 mises ; thus : 
 
 (1) An animal is a substance ; 
 A quadruped is an animal ; 
 
 .*. A quadruped is a substance. 
 
 (2) A quadruped is a substance ; 
 A horse is a quadruped ; 
 
 .'. A horse is a substance. 
 
 (3) A horse is a substance : 
 Bucephalus is a horse ; 
 
 .'. Bucephalus is a substance. 
 
 This suffices to show that the Protosyllogism of a Goclenian 
 Sorites is an Enthymeme of the Third Order ; after which the 
 argument is a chain of Enthymemes of the First Order, or 
 even of the First and Third combined, since the conclusions 
 as well as the major premises are omitted, except in the last 
 one. 
 
 Lest it should be thought that the Sorites is only good for 
 arguments so frivolous as the above, I subjoin an example 
 collected from various parts of Mill's Political Economy : 
 
 The cost of labour depends on the efficiency of labour; 
 The rate of profits depends on the cost of labour ; 
 The investment of capital depends on the rate of profits ; 
 Wages depend on the investment of capital ; 
 /. Wages depend on the efficiency of labour. 
 
 Had it occurred to Mill to construct this Sorites, he would 
 have modified his doctrine of the Wages-Fund, and would have 
 saved many critics from the malignant joy of refuting him. 
 6. The Antinomy is a combination of arguments by which 
 
140 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 contradictory attributes are proved to be predicable of the same 
 subject. In symbols, thus : 
 
 All M is P All N is p 
 
 All S is M All S is N 
 
 All S is P All S is p 
 
 Now, by the principle of Contradiction, S cannot be P and p 
 (not-P) : therefore, if both of the above syllogisms are sound, 
 S cannot exist at all. The contradictory conclusions are called, 
 respectively, Thesis and Antithesis. 
 
 To come to particulars, we may argue : (i) that a constitu- 
 tion which is at once a monarchy, an aristocracy and a de- 
 mocracy, must comprise the best elements of all three forms ; 
 and must, therefore, be the best of all forms of government : 
 ^the British Constitution is, therefore, the best of all. But 
 (2) such a constitution must also comprise the worst elements 
 of monarchy, aristocracy and democracy ; and, therefore, must 
 be the worst of all forms. Are we, then, driven to conclude 
 that the British Constitution, thus proved to be both the best 
 and worst, does not really exist at all, being, logically impos- 
 sible ? For the proofs seem to me equally good. 
 
 Again, 
 
 (1) Every being who is responsible for his actions is free; 
 Man is responsible for his actions : 
 
 .*. Man is free. 
 
 (2) Every being whose actions enter into the course of nature 
 
 is not free ; 
 Man is such a being : 
 .'. Man is not free. 
 
 Does it, then, follow that ' Man,' as the subject of contradictory 
 attributes, is a nonentity? This doctrine, or something like 
 it, has been seriously entertained ; but if to any reader it seems 
 extravagant (as it certainly does to me), he will no doubt find 
 an error in the above arguments. 
 
ABBREVIATED ARGUMENTS 141 
 
 For other examples it is enough to refer to the Critique of 
 Pure Reason, where Kant sets out the Antinomies of Rational 
 Cosmology. But even if we do not agree with Kant that the 
 human understanding, in attempting to deal with certain 
 subjects beyond its reach, inevitably falls into such contradic- 
 tory reasonings ; yet it can hardly be doubted that we not 
 unfrequently hold opinions which, if logically developed, result 
 in Antinomies. And, accordingly, the Antinomy, if it cannot 
 be imputed to Reason herself, may be a very fair, and a very 
 wholesome argumentum ad hominem. It was the favourite 
 weapon of the Pyrrhonists against the dogmatic philosophies 
 that flourished after the death of Aristotle. 
 
CHAPTER XII 
 CONDITIONAL SYLLOGISMS 
 
 i. Conditional Syllogisms may be generally described, AS 
 those that contain conditional propositions. They are usually 
 divided into two classes, Hypothetical and Disjunctive. 
 
 A Hypothetical Syllogism is one that consists of a Hypo- 
 thetical Major Premise, a Categorical Minor Premise, and a 
 Categorical Conclusion. Two Moods are usually recognised : 
 
 (1) Modus ponens t or Constructive. 
 
 If A is B, Cis D; 
 
 A is B: 
 /. C is D. 
 
 If Aristotle's reasoning is conclusive, Plato's theory of Ideas 
 
 is erroneous ; 
 
 Aristotle's reasoning is conclusive : 
 .*. Plato's theory of Ideas is erroneous. 
 
 Rule of the Modus ponens : The antecedent of the Major 
 Premise being affirmed in the Minor Premise, the Consequent 
 is also affirmed in the Conclusion. 
 
 (2) Modus tollens, or Destructive. 
 
 If A is B, C is D ; 
 
 C is not D ; 
 .-. A is not B. 
 
 If Pythagoras is to be trusted, Justice is a number; 
 
 Justice is not a number : 
 .'. Pythagoras is not to be trusted. 
 
CONDITIONAL SYLLOGISMS 143 
 
 Rule of the Modus tollens : The Consequent of the Major 
 Premise being denied in the Minor Premise, the Antecedent 
 is denied in the Conclusion. 
 
 By using negative major premises two other forms are 
 obtainable : then, either by affirming the Antecedent or by 
 denying the Consequent, we draw a negative conclusion. 
 
 Thus (Modus ponens) : (Modus tollens) : 
 
 If A is B, C is not D ; If A is B, C is not D ; 
 
 A is B : C is D : 
 
 /. C is not D. .'. A is not B. 
 
 Further, since the Antecedent of the major premise, taken 
 by itself, may be negative, it seems possible to obtain four 
 more forms, two in each Mood, from the following major 
 premises : 
 
 (1) If A is not B, Cis D; 
 
 (2) If A is not B, C is not D. 
 
 But since the quality of a Hypothetical Proposition is deter- 
 mined by the quality of its Consequent, not at all by the 
 quality of its Antecedent, I do not see how we can get from 
 these two major premises any really new Moods, that is to say, 
 Moods exhibiting any formal difference from the four pre- 
 viously expounded. Recognising these four, however, would 
 it not be well to make the names * Constructive ' and ' Destruc- 
 tive ' not synonymous with Modus ponens and Modus tollens 
 respectively, but applicable thus : * Constructive ' to that form 
 of the Modus ponens that has an affirmative conclusion, and 
 * Destructive ' to the other three Syllogisms that conclude in 
 the negative ? 
 
 It must be carefully observed that, given the hypothetical 
 major premise 
 
 If A is B, C is D 
 
 we cannot by denying the Antecedent infer a denial of the 
 Consequent. That A is B, is a mark of C being D ; but we 
 are not told that it is the sole and indispensable condition of 
 
i 4 4 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 it. If men read good books, they acquire knowledge; but 
 they may acquire knowledge by other means, as by observation. 
 For the same reason, we cannot by affirming the Consequent 
 infer the affirmation of the Antecedent: Caius may have 
 acquired knowledge ; but we cannot thence conclude that he 
 has read good books. 
 
 To see this in another light, let us recall chap. v. 4, where 
 it was shown that a hypothetical proposition may be translated 
 into a categorical one ; whence it follows that a Hypothetical 
 Syllogism may be translated into a Categorical Syllogism. 
 Treating the above examples thus, we find that the Modus 
 ponens takes the form of Barbara, and the Modus tollens the 
 form of Camestres : * 
 
 Modus ponens. 
 If A is B, C is D ; 
 
 AisB: 
 .-. C is D. 
 
 Barbara. 
 
 The case of A being B is a case of C 
 
 being D : 
 
 This is a case of A being B : 
 .*. This is a case of C being D. 
 
 Now if, instead of this, we affirm the Consequent, to form 
 the new minor premise, 
 
 This is a case of C being D, 
 
 there will be a Syllogism in the Second Figure with two 
 affirmative premises, and therefore the fallacy of Undistributed 
 Middle. Again : 
 
 Modus tollens. Camestres. 
 
 If A is B, C is D ; The case of A being B is a case of C 
 
 being D : 
 
 C is not D : This is not a case of C being D : 
 
 .". A is not B. /. This is not a case of A being B. 
 
 But if, instead of this, we deny the Antecedent, to form the 
 new minor premise, 
 
 This is not a case of A being B, 
 there arises a syllogism in the First Figure with a negative 
 
 
CONDITIONAL SYLLOGISMS 145 
 
 minor premise, and therefore the fallacy of Illicit Process of 
 the Major Term. 
 
 By thus reducing the Hypothetical Syllogism to the Cate- 
 gorical form, what is lost in elegance is gained in intelligibility. 
 For, first, we may justify ourselves in speaking of the Hypo- 
 thetical Premise as the Major, and of the Categorical Premise 
 as the Minor; since in the Categorical form they contain 
 respectively the Major and Minor Terms. And, secondly, we 
 may justify ourselves in treating the Hypothetical Syllogism 
 as a kind of Mediate Inference, in spite of the fact that in the 
 Hypothetical Syllogism there are not two Terms compared 
 by means of a third ; since in the Categorical form such Terms 
 distinctly appear : a new Term (' This ') emerges in the position 
 of the Minor ; the place of the Middle is filled by the Ante- 
 cedent of the Major Premise in the Modus pojiens, and by the 
 Consequent in the Modus tollens. 
 
 The mediate element of the inference in a Hypothetical 
 Syllogism consists in asserting, or denying, the fulfilment of a 
 given condition. In the hypothetical proposition 
 
 If A is B, C is D 
 
 the Antecedent, A is B, is the conditio sufficiens, or mark, of 
 the Consequent, C is D ; and therefore the Consequent, 
 C is D, is a conditio sine qua non of the antecedent, A is B ; 
 and it is by means of affirming the former condition, or else 
 denying the latter, that a conclusion is rendered possible. 
 
 Indeed, we need not say that the element of mediation con- 
 sists in affirming, or denying, the fulfilment of a given con- 
 dition : it is enough to say ' in affirming.' For thus to explain 
 the Modus totlens, reduce it to the Modus ponens (contra- 
 positing the major premise) : 
 
 Celarent. 
 
 If A is B, C is D : The case of C not being D is a 
 
 .'. If C is not D, A is not B ; case of A not being B ; 
 
 C is not D : This is a case of C not being D : 
 
 /. A is not B. .'. This is a case of A not being B. 
 
 K 
 
146 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 The above four forms commonly treated of as Hypothetical 
 Syllogisms, are called by Ueberweg and Dr. Keynes ' Hypo- 
 thetico-Categorical.' Ueberweg restricts the name 'Hypo- 
 thetical ' simply (and Dr. Keynes the name ' Conditional ') to 
 such Syllogisms as the following, having two Hypothetical 
 Premises : 
 
 IfCis D, EisF; 
 If A is B, C is D : 
 .-.If A is B, EisF. 
 
 If we recognise particular hypothetical propositions (see 
 chap. v. 4), it is obvious that such Syllogisms may be 
 constructed in all the Moods ,and Figures of the Categorical 
 Syllogism ; and of course they may be translated into Cate- 
 goricals. We often reason in this hypothetical way. For 
 example : 
 
 If the margin of cultivation be extended, rents will rise ; 
 
 If prices of produce rise, the margin of cultivation will be 
 
 extended: 
 /. If prices of produce rise, rents will rise. 
 
 But it may be noticed that the purpose of the Hypothetical 
 Syllogism (commonly so called), as also of the Disjunctive (to 
 be discussed in the next section) is to get rid of the conditional 
 element, to pass from doubt to certainty, and obtain a decisive 
 Categorical Conclusion ; whereas these Syllogisms with two 
 hypothetical premises leave us still with a hypothetical con- 
 clusion. This circumstance seems to me to ally them more 
 closely with Categorical Syllogisms than with those that are 
 discussed in the present chapter. That they are Categoricals 
 in disguise may be seen by considering that the above syllogism 
 is not materially significant, unless in each proposition the 
 word 'If is equivalent to 'Whenever.' Accordingly, in 
 applying the name ' Hypothetical Syllogism,' I have not seen 
 fit to depart from the older usage. 
 
 2. A Disjunctive Syllogism consists of a Disjunctive Major 
 
 jor 
 
CONDITIONAL SYLLOGISMS 147 
 
 Premise, a Categorical Minor Premise, and a Categorical Con- 
 clusion. 
 
 How many Moods are to be recognised in this kind of 
 argument depends on whether the alternatives of the Dis- 
 junctive Premise are regarded as mutually exclusive or possibly 
 coincident. In saying ' Either A is B, or C is D,' do we mean 
 * either, but not both,' or ' either, it may be both ' ? (see chap. v. 
 
 4.) 
 
 When the alternatives of the Disjunctive are not exclusive, 
 we have only the 
 
 Modus tollendo ponens. 
 Either A is B, or C is D ; 
 
 A is not B (or C is not D) : 
 . -.CisD (or A is B). 
 
 Either wages fall, or the weaker hands are dismissed ; 
 
 Wages do not fall : 
 .-. The weaker hands are dismissed. 
 But we cannot argue 
 
 Wages fall : 
 
 /. The weaker hands are not dismissed ; 
 since in ' hard times ' both events may happen together. 
 
 Rule of the Modus tollendo ponens : If one alternative be 
 denied, the other is affirmed. 
 
 When, however, the alternatives of the Disjunctive are 
 mutually exclusive, we have also the 
 
 Modus ponendo tollens. 
 
 Either A is B, or C is D ; 
 
 A is B (or C is D) : 
 .-. C is not D (or A is not B). 
 
 Either the Tories or the Whigs win the election ; 
 
 The Tories win : 
 .. The Whigs do not win. 
 
 We may also, of course, argue as above in the Modus tolkndo 
 ponens 
 
143 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 The Tories do not win : 
 /.The Whigs do. 
 
 But in this example, to make the Modus tolkndo ponens 
 materially valid, it must be impossible that the election should 
 result in a tie. The danger of the Disjunctive Proposition is 
 that the alternatives may not, between them, exhaust the pos- 
 sible cases. Only contradictory alternatives are sure to cover 
 the whole ground. 
 
 Rule of the Modus ponendo to ! lens : If one alternative be 
 affirmed, the other is denied. 
 
 Since a disjunctive proposition may be turned into a hypo- 
 thetical proposition (chap. v. 4), a Disjunctive Syllogism may 
 be turned into a Hypothetical Syllogism : 
 
 Modus tollendo ponens. Modus ponens. 
 
 Either A is B, or C is D ; If A is not B, C is D ; 
 
 A is not B : A is not B : 
 
 .-.CisD. . \CisD. 
 
 Similarly the Modus ponendo tollens is equivalent to that kind 
 of Modus ponens which may be formed with a negative major 
 premise ; for if the alternatives of a disjunctive proposition be 
 exclusive, the corresponding hypothetical may be affirmative 
 or negative : 
 
 Modus ponendo tollens. Modus ponens. 
 
 Either A is B, or C is D ; If A is B, C is not D ; 
 
 A is B ; A is B ; 
 
 .-.CisnotD. /. C is not D. 
 
 Hence, finally, a Disjunctive Syllogism being equivalent to a 
 Hypothetical, and a Hypothetical to a Categorical; a Dis- 
 junctive Syllogism is equivalent and reducible to a Categorical. 
 It is a form of Mediate Inference in the same sense as the 
 Hypothetical Syllogism is ; that is to say, the conclusion 
 depends upon an affirmation, or denial, of the fulfilment of a 
 condition implied in the disjunctive major premise. 
 
 
CONDITIONAL SYLLOGISMS 149 
 
 3. The Dilemma is perhaps the most popularly interesting 
 of all forms of proof. It is a favourite weapon of orators and 
 wits ; and "impaled upon the horns of a dilemma" is a painful 
 situation in which every one delights to see his adversary. 
 It seems to have been described by Rhetoricians before finding 
 its way into works on Logic ; and Logicians, to judge from 
 their diverse ways of defining it, have found some difficulty in 
 making up their minds as to its exact character. 
 
 There is a famous Dilemma employed by Demosthenes, from 
 which the general nature of the argument may be gathered : 
 If j^Eschines joined in the public rejoicings, he is inconsis- 
 tent ; if he did not, he is unpatriotic ; 
 But either he joined, or he did not join : 
 Therefore he is either inconsistent or unpatriotic. 
 That is, reduced to symbols : 
 
 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 (Complex Constructive). 
 Now, plainly, this is a compound Conditional Syllogism, 
 which may be analysed as follows : 
 
 Either A is B or E is F. 
 
 Suppose that E is not F : Suppose that A is not B : 
 
 Then A is B. Then E is F. 
 
 But if A is B, C is D ; But if E is F, G is H ; 
 
 (A is B) : (E is F) : 
 
 .-. C is D. .-. G is H. 
 
 .-. Either C is D or G is H. 
 
 A Dilemma, then, is a compound Conditional Syllogism, 
 having for its Major Premise two Hypothetical Propositions, 
 and for its Minor Premise a Disjunctive Proposition, whose 
 alternative terms either affirm the Antecedents or deny the 
 Consequents of the two Hypothetical Propositions forming the 
 Major Premise. 
 
 The hypothetical propositions in the major premise, may 
 have all four terms distinct (as in the above example) ; and 
 
i5o LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 then the conclusion is a disjunctive proposition, and the 
 Dilemma is said to be Complex. 
 
 Or the two hypothetical propositions may have a common 
 antecedent or a common consequent ; and then the conclusion 
 is a categorical proposition, and the Dilemma is said to be 
 Simple. 
 
 Again, the alternatives of the disjunctive minor premise may 
 be affirmative or negative. If they are affirmative, the Dilemma 
 is called Constructive; and if negative, Destructive. However, 
 seeing that the Dilemma is a compound Conditional Syllogism, 
 it would surely ! be better to name its Moods after the corre- 
 sponding Moods of the Hypothetical Syllogism Modus ponens 
 and Modus tollens. 
 
 If, then, we only use affirmative hypothetical propositions in 
 the major premise, there are four Moods : 
 
 1. The Simple Modus ponens (or, Constructive). 
 
 If A is B, CisD; and if E is F, C is D : 
 
 But either A is B, or E is F : 
 /. C is D. 
 
 If the Tories win the election, the Government will avoid 
 innovation; and if the Whigs win, the House of Lords 
 will prevent them innovating ; 
 But either the Tories or the Whigs will win ; 
 /. There will be no innovation. 
 
 2. The Complex Modus ponens (or, Constructive). 
 
 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. 
 
 If appearance is all that exists, reality is a delusion ; and if 
 there is a substance beyond consciousness, knowledge of 
 reality is impossible : 
 But either appearance is all, or there is a substance beyond 
 
 consciousness : 
 
 .'.Either reality is a delusion, or a knowledge of it is im- 
 possible. 
 
 3. Simple Modus tollens (or Destructive). 
 
CONDITIONAL SYLLOGISMS 151 
 
 If A is B, C is D ; and if A is B, E is F: 
 But either C is not D, or E is not F : 
 /. A is not B. 
 If table-rappers are to be trusted, the departed are spirits ; 
 
 and they also exert mechanical energy : 
 But either the departed are not spirits, or they do not exert 
 
 mechanical energy : 
 .'. Table-rappers are not to be trusted. 
 
 4 . Complex Modus tollens (or, Destructive). 
 
 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. 
 If poetic justice is observed, virtue is rewarded ; and if the 
 
 mirror is held up to Nature, the villain triumphs ; 
 But either virtue is not rewarded, or the villain does not 
 
 triumph : 
 .'. Either poetic justice is not observed, or the mirror is not 
 
 held up to Nature. 
 
 These then are the four Moods of the Dilemma that emerge 
 if we use only affirmative hypotheticals for the major premise ; 
 but, certainly, it is often quite as natural to employ two nega- 
 tive hypotheticals (indeed, one might be affirmative and the 
 other negative ; but waive that) ; and then four more moods 
 emerge, all having negative conclusions. But it is needless to 
 intimidate the reader by drawing up these four moods in battle 
 array. Of course, they always admit of reduction to the fore- 
 going moods by obverting the hypotheticals ; but by the same 
 process we may greatly decrease the number of moods of the 
 Categorical Syllogism ; so that I am afraid that this objection 
 to them will be thought to prove too much. Just as some 
 Syllogisms are most simply expressed in Celarent or Cesare, so 
 some Dilemmas are most simply stated with negative major 
 premises e.g., The Modus ponens above given would run 
 more naturally thus : If the Tories win, the Government will 
 not innovate ; and if the Whigs, the Lords will not let them : 
 and similarly Demosthenes' Dilemma If ^Eschines joined, he is 
 
152 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 not consistent ; and if he did not, he is not patriotic. Moreover, 
 the propriety of recognising Dilemmas with negative major 
 premises, follows from the above analysis of the Dilemma into 
 a combination of Conditional Syllogisms, even if (as in i of 
 this chapter) we take account of only four Moods of the 
 Hypothetical Syllogism. 
 
 In the rhetorical use of the Dilemma, it may be observed 
 that the Disjunction in the minor premise ought to be obvious, 
 or (at any rate) easily acceptable to the audience. Thus, 
 Either the Tories or the Whigs will win; Either ^Eschines joined 
 in the rejoicings, or he did not ; such propositions are not likely 
 to be disputed. But if the orator must stop to prove his minor 
 premise, the smacking effect of this figure (if the expression be 
 allowed) will be lost. Hence the minor premises of other 
 examples given above are only fit for a select audience, like 
 students of Logic. That Either ghosts are not spirits, or they 
 do not exert mechanical energy, supposes a knowledge of the 
 principle, generally taught by physical philosophers, that only 
 matter is the vehicle of energy ; and that Either appearance is 
 all, or there is substance beyond consciousness, is a doctrine which 
 only metaphysical philosophers could be expected to under- 
 stand, and upon which they could not be expected to agree. 
 However, the chief danger is that a plausible disjunction may 
 not be really such as to exclude any middle ground : Either 
 the Tories or the Whigs win, is bad, if a tie be possible ; though 
 in the above argument this is negligible, seeing that a tie 
 cannot directly cause innovations. Either ^Eschines joined in the 
 rejoicings, or he did not, does not allow for a decent conformity 
 with the public movement where resistance would be vain ; 
 yet such conformity as need not be inconsistent with subsequent 
 condemnation of the proceedings, nor incompatible with 
 patriotic reserve founded on a belief that the rejoicings are 
 premature and ominous. 
 
 Another rhetorical consideration is, that the alternatives of 
 the Disjunctive Conclusion of a Complex Dilemma should 
 both point the same way, should be equally distasteful or 
 
CONDITIONAL SYLLOGISMS 153 
 
 paradoxical. ' Either inconsistent or unpatriotic ' : horrid words 
 to a politician ! ' Either no reality or no possible knowledge ' : 
 very disappointing to an anxious inquirer ! Thus the Disjunc- 
 tive Conclusion is as bad for an opponent as the Categorical 
 one in a Simple Dilemma. 
 
 Logicians further speak of the Trilemma, with three Hypo- 
 thetical and a corresponding triple Disjunction ; and of a 
 Folylemma, with any further number of perplexities. But any 
 one who has a taste for mere logical forms may have it amply 
 gratified in numerous text-books. Indeed there are so many 
 opportunities of developing such forms that, if ingenious 
 enough, a man may still hope to discover some quite new 
 ones : and quite innocently, as long as he does not publish 
 them. 
 
CHAPTER XIII 
 
 
 
 TRANSITION TO INDUCTION 
 
 i. Having now discussed Terms, Propositions, Immediate 
 and Mediate Inferences, and investigated the conditions frf 
 Formal Truth or Consistency, we have next to consider the 
 conditions of Material Truth : whether (or how far) it is 
 possible to arrive at propositions that represent the course of 
 nature and human life. Hitherto we have dealt with no sort 
 of proof that gives any such assurance. A valid syllogism 
 guarantees the truth of its conclusion, provided the premises 
 be true : but what of the premises ? The relation, between the 
 premises of a valid syllogism and its conclusion is indeed the 
 same as the relation between the antecedent and consequent 
 of a hypothetical proposition. If A is B, C is D : grant that 
 A is B, and it follows that C is D ; and, similarly, grant the 
 premises of a syllogism, and the conclusion follows. Again, 
 grant that C is not D, and it follows that A is not B ; and, 
 similarly, if the conclusion of a valid syllogism be false, it 
 follows that one, or other, or both of the premises must be 
 false. But, once more, grant that C is D, and it does not 
 follow that A is B ; so neither, if the conclusion of a syllogism 
 be true, does it follow that the premises are. For example : 
 
 Geology is an exact science ; 
 
 Mathematics is a branch of Geology ; 
 .*. Mathematics is an exact science. 
 
 Here the conclusion is true although the premises are absurd. 
 Or again : 
 
TRANSITION TO INDUCTION 155 
 
 Mathematics is an exact science ; 
 Geology is a branch of Mathematics ; 
 .*. Geology is an exact science. 
 
 Here the major premise is true, but the minor is false, and the 
 conclusion is false. In both cases, however, whether the con- 
 clusion be true or false, it equally follows from the premises, if 
 there is any cogency in Barbara. The explanation of this is, 
 that Barbara has only formal cogency ; and that whether the 
 conclusion of that, or any other valid mood, shall be true 
 according to fact and experience, depends upon how the form 
 is rilled up. How to establish the premises, then, is a most 
 important problem ; and it still remains to be solved. 
 
 2. We may begin by recalling the distinction between the 
 Denotation and Connotation of a General Term : the denota- 
 tion comprising the things or events which the term is a name 
 for; the connotation comprising the common qualities on 
 account of which these things are called by the same name. 
 Obviously, there are very few general terms whose denotation 
 is exhaustively known ; since the denotation of a general term 
 comprises all the things that have its connotation, or that ever 
 have had, or that ever will have it, whether they exist here, or 
 in Australia, or in the Moon, or in the utmost stars. No one 
 has examined all men, all dogs, all falling bodies, all cases of 
 fever, all crystals, all mammoths, all revolutions, all stars nor 
 even all planets, since from time to time new ones are discerned. 
 We have names for animals that existed long before there were 
 men to observe them, and of which we know only a few bones, 
 the remains of multitudinous species : others may continue to 
 exist when men have disappeared from the earth. 
 
 If, indeed, we definitely limit the time, or place, or quantity 
 of matter to be explored, we may sometimes learn, within the 
 given limits, all that we are concerned about : as all the bones 
 of a particular animal, or the list of English monarchs hitherto, 
 or the names of all the members of the House of Commons 
 at the present time. Such cases, however, do not invalidate 
 the above logical truth that few general terms are exhaustively 
 
156 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 known in their denotation ; for the very fact of assigning limits 
 of time and place impairs the generality of a term. The 
 bones of a certain animal may be all examined, but not the 
 bones of all animals, nor even of one species. The English 
 monarchs that have reigned hitherto may be known, but there 
 may be many still to reign. 
 
 The General Terms, then, with which Logic is chiefly 
 concerned, the names of Causes and Kinds, such as gravita- 
 tion, diseases, social events, minerals, plants and animals, 
 stand for some facts that are, or have been, known, and for a 
 great many other similar ones that have not been, and never 
 will be, known. Hence the use of a general term depends 
 not upon our direct knowledge of everything comprised in its 
 denotation, but upon our readiness to apply it to anything 
 that has its connotation, whether we have seen the thing or not, 
 and even though we never can see it ; as when a man talks 
 freely of the ichthyosaurus, or of the central heat of planets, or 
 of atoms and ether. 
 
 Hence Universal Propositions, which consist of general 
 terms, deceive us, if we suppose that their predicates are 
 directly known to be related to all the facts denoted by their 
 subjects. In exceptional cases, in which the denotation of a 
 subject is intentionally limited, such exhaustive direct know- 
 ledge may be possible ; as that " all the bones of a certain 
 animal consist of phosphate of lime," or that every member of 
 the present Parliament wears a black silk hat. But what 
 predication is possible concerning the hats of all members of 
 Parliament from the beginning ? Ordinarily, then, whilst the 
 relation of predicate to subject has been observed in some 
 cases, in much the greater number of cases our belief about it 
 depends upon other evidence than observation, or may be said 
 (in a certain sense) to be taken on trust. 
 
 ' All rabbits are herbivorous ' : why do we believe that ? 
 We may have seen a few wild rabbits feeding : or have kept 
 tame ones, and tried experiments with their diet ; or have read 
 of their habits in a book of Natural History ; or have studied 
 
TRANSITION TO INDUCTION 157 
 
 the physiology of digestion in many sorts of animals : but with 
 whatever care we add testimony and scientific method to our 
 own observation, it still remains true that the rabbits observed 
 by ourselves and others are few in comparison with those that 
 live, have lived and will live. And the same truth might 
 be shown to hold good of any other Universal Proposition ; 
 for it plainly follows from the fact that the general terms 
 of which such propositions consist, are never exhaustively 
 known in their denotation. What right have we then to state 
 Universal Propositions ? That is the problem of Inductive 
 Logic. 
 
 3. Universal Propositions, of course, cannot always be 
 proved by syllogisms ; because to prove a universal pro- 
 position by a syllogism, its premises must be universal 
 propositions ; and, then, these must be proved by others, and 
 so on for ever. In fact the Formal Syllogism is itself mis- 
 leading if the Universal Proposition is so : if we think that 
 the premises prove the conclusion because they have been 
 established by detailed observation, we are mistaken. The 
 consideration of any example will show this. Suppose any 
 one to argue : 
 
 All ruminants are herbivorous ; 
 Camels are ruminants : 
 .*. Camels are herbivorous. 
 
 Have we, then, qxamined all ruminants ? If so, we must 
 have examined all camels, and cannot need a syllogism to 
 prove their herbivorous nature : instead of the major premise 
 proving the conclusion, the proof of the conclusion must then 
 be part of the proof of the major premise. But if we have not 
 examined all ruminants, having omitted most giraffes, most 
 deer, most camels, how do we know that the unexamined (say, 
 some camels) are not exceptional ? Camels are vicious enough 
 to be carnivorous ; and indeed it is said that Bactrian camels 
 will eat flesh rather than starve, though of course their habit 
 is herbivorous. 
 
 Or, again, it is sometimes urged that 
 
158 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 All empires decay : 
 .*. Britain will decay. 
 
 This is manifestly a prediction : at present Britain flourishes, 
 and shows no signs of decay. Yet a knowledge of its decay 
 seems necessary, to justify any one in asserting the given 
 premise. If it is a question whether Britain will decay, to 
 attempt (while several empires still flourish) to settle the 
 matter by asserting that all empires decay, seems to be ' a 
 begging of the question.' But although this latter case is a 
 manifest prediction, it does not really differ from the former 
 one ; for the proof that camels are herbivorous has no limits in 
 time. If valid, it shows not only that they are, but also that 
 they will be, herbivorous. 
 
 Hence, to resort to a dilemma, it may be urged : If all the 
 facts of the major premise of any syllogism have been examined, 
 the syllogism is needless ; and if some of them have not been 
 examined, it is a petitio principii. But either all have been 
 examined, or some have not. Therefore, the syllogism is 
 either useless or fallacious. 
 
 4. A way of escape from this dilemma is provided, how- 
 ever, by distinguishing between the formal and material 
 aspects of the syllogism considered as a means of proof. It 
 begs the question formally, but not materially ; that is to say, 
 if it be a question whether camels are herbivorous, and to 
 decide it we are told that ' all ruminants are/ laying stress 
 upon the ' all,' as if all had been examined, though in fact 
 camels have not been, then the question as to camels is 
 begged. The form of a universal proposition is then offered 
 as evidence, when in fact the evidence has not been universally 
 ascertained. But if in urging that 'all ruminants are herb- 
 ivorous ' no more is meant than that so many other ruminants 
 of different species are known to be herbivorous, and that the 
 ruminant stomach is so well adapted to a coarse vegetable 
 diet, that the same habit may be expected in other ruminants, 
 such as camels, the argument then rests upon material 
 evidence without unfairly implying the case in question. 
 
TRANSITION TO INDUCTION 159 
 
 Now the nature of the material evidence is plainly this, that 
 the resemblance of camels to deer, oxen, etc.> in the fact of 
 chewing the cud, justifies us in believing that they have a 
 further resemblance in the fact of feeding on herbs; in 
 other words, we assume that resemblance is a ground of 
 inference. 
 
 Another way of putting this difficulty with regard to syllo- 
 gistic evidence, which we have just been discussing, is to 
 object that by the Laws of Syllogism a conclusion must never 
 go beyond the premises, and that therefore no progress in 
 knowledge can ever be established, except by direct observa- 
 tion. Now, taking the syllogism formally, this is true : if the 
 conclusions go beyond the premises, there must be either four 
 terms, or illicit process of the major or minor term. But 
 taking it materially, the conclusion may cover facts which were 
 not in view when the major premise was laid down ; facts of 
 which we predicate something not as the result of direct obser- 
 vation, but because they resemble in a certain way those facts 
 which had been shown to carry the predicate when the major 
 premise was formed. 
 
 ' What sort of resemblance is a sufficient ground of infer- 
 ence^ is, therefore, the important question alike in material 
 Deduction and in Induction ; and we shall presently endeavour 
 to answer it. In the above cases, the fact of chewing the cud 
 is a strong ground for inferring vegetarianism ; the resemblance 
 of Britain to other empires is a much less substantial basis for 
 expecting her ultimate downfall. 
 
 5. If, now, the material character of syllogistic proof is 
 such as we have above described, in order to generalise it the 
 axiom de omni et nullo needs to be restated. " That whatever 
 is true of a whole class is true of everything the class includes," 
 seems from our present point of view to be a dictum designed 
 to justify the begging of the question. That whatever is true 
 of all is true of some, is a merely formal subaltern inference : 
 knowing ' all,' how can there be any question about the 
 * some ' ? But if we do not know ' all,' not really the ' whole 
 
160 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 class/ we must write the dictum thus : Whatever we have reason 
 to regard as constantly connected with the nature or connotation 
 of a class or class-name, we may expect to be similarly connected 
 with whatever can be shown to have that nature or connotation. 
 Thus the feeding upon herbage, being connected with the 
 nature of ruminants, is connected with camels, because they 
 ruminate. 
 
 Another way of putting this principle is Nota notce, nota 
 rei ipsius, ' the mark of a mark is a mark of the thing itself,' or 
 * whatever has a mark has what it is a mark of.' A mark is 
 anything (A) that is never found without something else (B) ; 
 so that where we find A, B may be expected. Now a camel 
 is a mark of ruminating ; and ruminating is a mark of feeding 
 upon herbage : therefore a camel is a mark of feeding upon 
 herbage. 
 
 6. I must add that, as we distinguish between the formal 
 and material character of the Syllogism, so we ought in the 
 case of Subalternation. To infer I from A may imply a real 
 advance of knowledge, if the ' Some ' of the I were not in view 
 when ' All ' was attached to the subject of the A. Thus Britain 
 will decay goes beyond the material grounds of All empires decay, 
 namely, those known to have decayed: nevertheless it is a 
 subaltern not a mediate inference ; since such a minor premise 
 as Britain is an empire (only true in the form ' the British 
 empire is an empire ') is a verbal proposition in disguise, and 
 adds nothing to the argument. If the inference Britain will 
 decay is doubtful, it is not because a false minor premise has 
 oeen omitted by enthymeme, but because the subalternans is 
 doubtful, because the empires that have been known to decay 
 may not be fair examples of all empires. It should be 
 expressed All empires having such or such characteristics. 
 There is then room for a real minor premise The British 
 empire has these characteristics; and on whether that is 
 true, or not, depends the value of the inference Britain will 
 decay. 
 
 7. The Syllogism has sometimes been discarded by those 
 
TRANSITION TO INDUCTION 161 
 
 who have only seen that, as formally stated, it is either useless 
 or fallacious : but those who also perceive its material grounds 
 retain and defend it. In fact, great advantages are gained by 
 stating an argument as a formal syllogism. For, in the first 
 place, we can then examine separately the three cond'tions on 
 which the validity of the argument depends : 
 
 (1) Are the Premises so connected that, if they are true, the 
 Conclusion follows ? This depends upon the formal principles 
 of chap. x. 
 
 (2) Is the Minor Premise true ? This question can only 
 arise when the minor premise is a real proposition. That 
 Britain is an empire affords no matter for doubt or inquiry ; 
 but whether Britain resembles Egypt, Assyria, Rome in 
 those circumstances that led to their decay is a very difficult 
 subject for investigation. That Camels are ruminants is 
 now a verbal proposition to a Zoologist, but not to the rest 
 of us ; and even to the Zoologist the ascertaining of the rela- 
 tion in which camels stanr 1 to such ruminants as oxen and 
 deer, is not a matter of analysing words but of dissecting 
 specimens. 
 
 (3) Is the Major Premise true ? Are all ruminants herbi- 
 vorous? If there be any exceptions to the rule, camels are 
 likely enough to be among the exceptions. And here the 
 need of Induction is most conspicuous : how can we prove our 
 premises when they are universal propositions ? 
 
 A second advantage of the syllogism is, that it makes us 
 fully aware of what an inference implies. An inference must 
 have some grounds, or else it is a mere prejudice ; but what- i W 
 
 ' 
 
 ever the grounds are, if thej are sufficient in a particular case f 
 they must be_j5ufficient for all similar c&ses,, thfty must admit 
 of being generalised; and to generalise the grounds of the 
 inference, is nothing else than to state tne Major Premise. If 
 the evidence is sufficient to justify the argument that camels 
 are herbivorous because they are ruminanrs, it must also justify 
 the major premise, All ruminants are herbivorous ; for else -7 
 
 the inference cannot really depend merely upon the fact of 
 
 L 
 
162 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 ruminating. To state our evidence syllogistically, then, must 
 be possible, if the evidence is mediate and of a logical kind ; 
 and to state it in this formal way, as depending on the truth of 
 a general principle (the major premise) increases our sense of 
 responsibility for the inference that is thus seen to imply so 
 much ; and if there are any negative instances within our 
 knowledge, we are the more likely to remember them. The 
 use of syllogisms therefore is likely to strengthen our reason- 
 ings. 
 
 A third advantage is, that an accurate generalisation may be 
 useful to others : it is indeed part of the systematic procedure 
 of science. The memoranda of our major premises, or reasons 
 for believing anything, may be referred to by those who come 
 after us, and either confirmed or refuted. When such a memo- 
 randum is used for further inferences, these inferences are said, 
 in the language of Formal Logic, to be drawn from it, as if the 
 conclusion were contained in our knowledge of the major 
 premise ; but, considering the limited extent of the material 
 evidence, it is better to say that the inference is drawn according 
 to the memorandum or major premise, since the grounds of 
 the major premise and of the conclusion are in fact the 
 same. 
 
 We shall see hereafter that inductive proofs may be stated 
 in Syllogisms, and that inductive inferences are drawn according 
 to the Law of Causation. 
 
 8. Of the above three conditions on which the validity of 
 an argument depends, namely, (i) its formal correctness as 
 a syllogism, (2) the truth of the Minor, and (3) the truth of the 
 Major Premise, the most difficult to ensure are clearly the 
 second and third, and especially the third. And here lies one 
 important connection between Deduction and Induction. How 
 can we know whether the premises of a deductive argument are 
 true ? By Induction. Sometimes, indeed, premises may be 
 deduced by Prosyllogisms : All men are mortal, it may be said, 
 because All animals are mortal ; and All animals are mortal^ 
 because All composite bodies are subject to dissolution. But if 
 
 
TRANSITION TO INDUCTION 163 
 
 there were no limit to this process proof would involve a regres- 
 sus ad infinitum, for which life is too short ; and, besides, con- 
 venient Prosyllogisms are not always to be found. Accordingly, 
 Logic accepts certain Principles, Axioms, or ultimate Major 
 Premises, such as the Laws of Thought and Causation, as con- 
 ditions of all reasoning, leaving it to Metaphysics to investigate 
 their grounds ; whilst the common run of general propositions, 
 laws, or premises, if they have any scientific grounds, are either 
 obtained by Induction from facts with the aid of the ultimate 
 Axioms and Principles, or else are Hypotheses (that is, pre- 
 mises provisionally assumed). 
 
 For example, how do we know that all ruminants are herbi- 
 vorous ? We have only directly observed that great multitudes 
 are so ; the examination of a few specimens shows that their 
 organisation is adapted to a vegetable diet, and we infer that 
 unobserved ruminants are also herbivorous, by assuming that 
 resemblance (in ruminating) is a ground of inference (to the 
 property of feeding on herbage). If you ask, Why ? the usual 
 answer is, 'Because of the Uniformity of Nature.' This is 
 considered to be an ultimate principle, for which it is need- 
 less and useless to ask a reason, but with the help of which 
 our ordinary major premises may be obtained by Induction 
 from facts. And in the same way (as we saw in 4) the 
 conclusion oC a syllogism is obtained from the material 
 evidence embodied in the major premise, namely, by assuming 
 that resemblance is a ground of inference, or that Nature is 
 uniform. 
 
 9. The Uniformity of Nature cannot be defined and is there- 
 fore liable to be misunderstood. In many ways Nature seems 
 not to be uniform : there is great variety in the sizes, shapes, 
 colours and all other properties of things : bodies falling in the 
 open air pebbles, slates, feathers descend in different lines 
 and at different rates ; the wind and weather are proverbially 
 uncertain ; the course of trade or of politics, is full of surprises. 
 Yet common maxims, even when absurd, testify to a popular 
 belief that the relations of things are constant : the doctrine of 
 
 UNIVERSITY 1 
 
164 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 St. Swithin and the rhyme beginning ' Evening red and morning 
 grey,' show that the weather is held to be not wholly impre- 
 dictable ; as to human affairs, it is said that ' a green Yule 
 makes a fat churchyard,' that ' trade follows the flag,' and that 
 * history repeats itself; and Superstition knows that witches 
 cannot enter a stable-door if a horse-shoe is nailed over it, and 
 that the devil cannot cross a threshold inscribed with a perfect 
 pentagon. But the surest proof of a belief in the Uniformity 
 of Nature is given by the conduct of men and animals ; by that 
 adherence to habit, custom and tradition, to which in quiet 
 times they chiefly owe their safety, but which would daily dis- 
 appoint and destroy them, if it were not generally true that 
 things may be found where they have been left and that in 
 similar circumstances there are similar events. 
 
 Now this general belief, seldom distinctly conceived, for the 
 most part quite unconscious (as a principle), merely implied in 
 what men do, is also the foundation of all the Sciences, which 
 are entirely occupied in seeking the Laws (that is, the Uni- 
 formities) of Nature. And Philosophy, endeavouring, as its 
 nature is, to generalise to the utmost, whilst retaining the 
 definiteness of scientific thought, resolves the comprehensive 
 but indeterminate notion of Uniformity into a number of First 
 Principles, which may be indicated as follows : 
 
 (1) The Principles of Contradiction and Excluded Middle 
 (ch. vi. 3). These are called Laws of Thought ; and so they 
 are : for, in the first place, it is true of thoughts, as of every- 
 thing else, that they have a certain content or not ; occur in a 
 certain order, or do not : and, in the second place, thought, in 
 reference to an object thought about, is bound to observe these 
 laws, on pain of else going wrong. But the reason why the 
 above principles are laws of thought in this secondary sense 
 (that is, as rules or imperatives) is, that they are laws of things 
 in the primary sense of ' laws ' (as uniformities) ; for else they 
 would misdirect us, and it would be (literally) madness to con- 
 form to them. 
 
 (2) Certain Axioms of Mediate Evidence : as, in Mathe- 
 
TRANSITION TO INDUCTION 165 
 
 matics, 'that magnitudes equal to the same magnitude are 
 equal to one another ' ; and, in Logic, the Dictum or its 
 equivalent 'the mark of a mark is a mark of the thing 
 itself.' 
 
 (3) That all Times and all Spaces are commensurable; 
 although in certain relations of space (as TT) the unit of r , *~ 
 measurement must be infinitely small. If Time really r *d*^ 
 trotted with one man and galloped with another, as it ** **t~ 
 seems to ; if space really swelled in places, as De Quincey 
 dreamed that it did ; life could not be regulated, experience ^ ' 
 could not be compared and science would be impossible. 
 
 The Mathematical Axioms would then never be applicable 
 to space or time, or to the objects or processes that fill 
 them. 
 
 (4) The Persistence of Matter and Energy : the physical 
 principle that, in all changes of the universe, the quantities 
 
 of Matter and Energy (actual and potential, so-called) remain , * If ** 
 the same. For example, as to matter, although dew is found r * 
 on the grass at morning without any apparent cause, and p" 
 although a candle seems to burn away to a scrap of blackened < 
 wick, yet every one knows that the dew has been condensed f 
 from vapour in the air, and that the candle has only turned 
 into gas and smoke. As to energy, although a stone thrown 
 up to the housetop and resting there has lost actual energy, 
 it has gained such a position that the slightest touch may 
 bring it to the earth again in the same time as it took to 
 travel upwards; and in that position it is said to have 
 potential energy. When a boiler works an engine, every 
 time the piston is thrust forward (having actual energy), an 
 equivalent in heat (molecular energy) is lost. But for the 
 elucidation of these principles, readers must refer to treatises 
 of Chemistry and Physics. 
 
 (5) Causation, a special form of the foregoing principles ^ 
 
 (4), we shall discuss in the next chapter. ^"t 1 * 
 
 (6) Certain Uniformities of Co-existence ; but for want oi 
 a general principle of Co-existence, corresponding to Causatioa 
 
166 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (the principle of Succession), we can only classify these uni- 
 formities as follows : 
 
 (a) The Geometrical ; as that, in a four-sided figure, if the 
 opposite angles are equal, the opposite sides are equal and 
 parallel Countless similar uniformities of co-existence are 
 disclosed by Geometry. The co-existent facts do not cause 
 one another, nor are they jointly caused by something else ; 
 they are mutually involved : such is the nature of space. 
 
 (b) Universal co-existences among the properties of 
 concrete things. The chief example is the co-existence of 
 gravity with inertia in all material bodies. There is, I 
 believe, no other entirely satisfactory case; but some good 
 approximations to "such uniformity are known to physical 
 science. 
 
 (c) Co-existence due to Causation ; such as the positions of 
 objects in space at any time. The houses of a town are where 
 they are, because they were put there ; and they remain in 
 their place as long as no other causes arise strong enough 
 to remove or destroy them. Similarly, the relative positions 
 of rocks in geological strata, and of trees in a forest, are due to 
 causes. 
 
 (d) The co-existence of properties in Natural Kinds ; which 
 we call the constitution, defining characters, or specific nature 
 of such things. Oxygen, platinum, sulphur and the other 
 elements ; water, common salt, alcohol and other com- 
 pounds ; the various species of plants and animals : all these 
 are known to us as different groups of co-existent properties. 
 It may be conjectured, indeed, that these groupings of proper- 
 ties are also due to causation, and sometimes the causes can 
 be traced : but very often the causes are still unknown ; and, 
 at any rate, these cases of co-existence form a sufficiently well- 
 marked class to be separately mentioned. 
 
 (<?) There are also a few cases in which properties co-exist 
 in an unaccountable way, without being co-extensive with any 
 one species, genus, or order : as most metals are whitish, and 
 scarlet flowers are wanting in fragrance. 
 
TRANSITION TO INDUCTION 167 
 
 So much, then, as to the Uniformity of Nature in general j 
 some of its constituent principles have already been discussed : 
 and Causation is such an important one as to require a 
 chapter to itself. 
 
 (On this , see Venn's Empirical Logic, c. 4.) 
 
CHAPTER XIV 
 CAUSATION 
 
 i. For the theory of Induction, the specially important 
 aspect of the Uniformity of Nature is Causation. 
 
 For (i) the Principles of Contradiction and Excluded Middle 
 are implied in all logical operations, and need no further expli- 
 cation. 
 
 (2) That one thing is a mark of ariother (except in the 
 ultimate modes of Uniformity such as the Law of Causation 
 itself which are assumed in Logic) must be established by 
 Induction ; and the surest of all marks is a Cause. So that 
 the application of the Nota notes in particular cases requires, 
 when most valid, a previous appeal to Causation. And if we 
 find that the Nota notce is itself appealed to in showing that 
 any given related phenomena are Cause and Effect, it will only 
 be in the same way as in all syllogisms, that is to say, as an 
 Axiom. 
 
 (3) The uniformity of Space and Time is, of course, involved 
 in Causation, if we conceive Causation as essentially matter in 
 motion ; for motion is only known as a traversing of space in 
 time ; so that if space and time were not uniform, causation 
 would be irregular. But, though always assumed, this principle 
 need not be explicitly appealed to in any particular investiga- 
 tion ; since it is only a formal condition ; for time and space 
 are not agents, though they are conditions of every agent's 
 operation 
 
 (4) The general persistence of Matter and Energy, again, 
 
CAUSATION 169 
 
 although it is nothing else than Causation in the movement of 
 the world, is yet too wide a principle to use in establishing the 
 cause of a particular limited phenomenon, such as a soap- 
 bubble, or a thunder-storm, or the tide. 
 
 (5) As to co-existences, the Geometrical do not belong to 
 Logic : those involved in the existence of plants, animals, and 
 inorganic bodies, must, as far as possible, be traced to causes ; 
 and so, of course, must the relative positions of objects in space 
 at any time : and what Co-existences remain do not admit of 
 methodical inductive treatment ; they will be briefly discussed 
 in chap. xvii. 
 
 We may assume, then, that Causation is that mode or aspect 
 of the Uniformity of Nature which especially concerns us in 
 Induction; and we must, therefore, make it as definite as 
 possible. 
 
 2, A Cause, according to Mill, is, " the invariable uncon- 
 ditional antecedent " of a given phenomenon. This definition 
 Deeds careful attention. 
 
 (1) A Cause is relative to a given phenomenon, called the 
 Effect. Logic has no method for investigating the cause of 
 the universe as a whole, but only of a part or epoch of it : we 
 select from the infinite continuum of Nature any portion that 
 is neither too large nor too small for a trained mind to com- 
 prehend. The magnitude of the phenomenon may be a matter 
 of convenience. If the cause of disease in general is too wide 
 a problem, can fevers be dealt with ; or, if that be too much, 
 is typhus within the reach of inquiry ? In short, how much 
 can we deal with accurately ? 
 
 (2) The given phenomenon is always an event ; that is to 
 say, not a new thing (nothing is wholly new), but a change in 
 something or in the relative position of things. We may ask 
 the cause of the phases of the moon, of the freezing of water, 
 of a deposit of chalk, of the differentiation of species. To 
 inquire the cause of France being a republic, or Russia an 
 autocracy, implies that these countries were once otherwise 
 governed, or had no government : to inquire the cause of the 
 
170 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 earth being shaped like an orange, implies that the matter of 
 .the earth had once another shape. 
 
 (3) The Cause is antecedent to the Effect, which accordingly 
 is often called its consequent. This is often misunderstood 
 and sometimes disputed. It has been said that the meaning 
 of 'cause' implies an ' effect,' so that until an effect occurs 
 there can be no cause. But this is a blunder ; for whilst the 
 word ' cause ' implies ' effect,' it also implies the relative 
 futurity of the effect ; and effect implies the relative priority 
 of the cause. The connotation of the words, therefore, agrees 
 well enough with Mill's doctrine. In fact, the danger is that 
 any pair of contrasted words may suggest too strongly that the 
 phenomena denoted "are separate in Nature; whereas every 
 natural process is continuous. If water, dripping from the 
 roof, wears away a stone, it fell on the roof as rain ; the rain 
 came from a condensing cloud ; the cloud was driven by the 
 wind from the sea, whence it exhaled ; and so on. There is 
 no beginning to this, and no break in it. We may take any 
 one of these changes, call it an effect, and ask for its cause ; 
 or call it a cause, and ask for its effect. There is not in 
 Nature one set of things called causes and another called 
 effects ; but everything is both cause of the future and effect of 
 the past ; and whether we consider an event as the one or the 
 other, depends upon the direction of our curiosity or interest. 
 
 Still, taking the event as effect, its cause is the antecedent 
 process ; or, taking it as a cause, its effect is the consequent 
 process. This follows from the conception of causation as 
 essentially motion ; for that motion takes time is (from the way 
 our perceptive powers grow) an ultimate intuition. But, for 
 the same reason, there is no interval of time between cause 
 and effect ; since all the time is filled up with motion. 
 
 Nor must it be supposed that the whole cause is antecedent 
 to the effect as a whole : for we often take the phenomenon on 
 such a scale that minutes, days, years, may elapse before we 
 consider the cause as exhausted (e.g., an earthquake, a battle, 
 an expansion of credit) ; and all that time the effect has been 
 
 
CAUSATION 171 
 
 accumulating. But we may further consider such a cause as 
 made up of moments or minute factors, and the effect as made 
 up of corresponding moments ; and then the cause, taken in 
 its moments, is antecedent throughout to the effect, taken in 
 its corresponding moments. JLj 
 
 
 
 (4) The Cause is the invariable antecedent of fo 
 that is to say, whenever a given cause occurs it always has the 6 ' l< 
 same effect : in this, in fact, consists the Uniformity of Causa- n*' 
 tion. Accordingly, not every antecedent of an event is its Jflf* 
 Cause : to assume that it is so, is the familiar fallacy of arguing 
 * post hoc ergo propter hoc.' But every event has an infinite 
 number of antecedents that have no ascertainable connection 
 with it : if a picture falls from the wall in this room, there may 
 have been, just before, an earthquake in New Zealand, an 
 explosion in a Japanese arsenal, a religious riot in India, a 
 political assassination in Russia and a vote of censure in the 
 House of Commons, besides millions of other less noticeable 
 events, between none of which and the falling of the picture 
 can any direct causation be detected ; though, no doubt, they 
 are all necessary occurrences in the general world-process, and 
 remotely connected. The cause, however, was that a door 
 slammed violently in the room above, and that the picture 
 was heavy and the cord old and rotten. Even if two events 
 invariably occur one after the other, as day follows night, or 
 the report follows the flash of a gun, they may not be cause 
 and effect, though it is highly probable that they are closely 
 connected by causation ; and in these two examples the events 
 are of course co-effects of a common cause, and may be re- 
 garded as elements of its total effect. Still, whilst it is not 
 true that every antecedent, or that every invariable antecedent, 
 of an event is its cause, it is held to be true that the cause is 
 something, or some state and process of things, such that when- 
 ever it exactly recurs the same event invariably follows. At 
 the same time, it must be acknowledged that, if we consider 
 the antecedent state and process of things very widely and 
 minutely, it never does exactly recur. So that to construe the 
 
1 72 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Law of Causation too strictly, is to render it inapplicable not 
 only in practice but also in scientific inquiry. The requisite 
 qualifications will appear in the next paragraph. 
 
 (5) The Cause is the Unconditional Antecedent. ' Con- 
 dition ' means any necessary factor of a Cause : any thing 
 or agent that exerts, impedes, or deflects energy; or any rela- 
 tion of time or space in which agents stand to one another. 
 A positive condition is one that cannot be omitted without 
 frustrating the effect ; a negative condition is one that cannot 
 be introduced without frustrating the effect. In the falling of 
 the picture, e.g., the positive conditions were the picture (as 
 being heavy) and the slamming door ; the negative conditions 
 were that the pictufe should have no support but the cord, 
 and that the cord should not be sound. When Mill, then, 
 defines the Cause of any event as its " unconditional " ante- 
 cedent, he means that it is that group of conditions (state and 
 process of things) which, without any further condition, is 
 followed by the event in question : it is the least antecedent 
 that suffices, positive conditions being present and negative 
 absent. 
 
 Now this enables us to distinguish a true cause from an 
 unconnected antecedent. Earthquakes have happened in New 
 Zealand and votes of censure in the House of Commons 
 without a picture's falling in this room : they were not un- 
 conditional antecedents ; something else was needed to bring 
 down a picture. It also distinguishes a true icause from an 
 invariable antecedent that is only a co-effect : for when day 
 follows night something else happens ; the Earth rotates upon 
 her axis : a flash even of gunpowder is not an unconditional 
 antecedent of a report ; the powder must be ignited in a closed 
 chamber. 
 
 By common experience, and more precisely by experiment, 
 it is found possible to select from among the antecedents of an 
 event a certain number upon which, so far as can be perceived, 
 it is dependent, and to neglect the rest. Remote conditions 
 may indeed modify the event in ways so refined as to escape 
 
CAUSATION 173 
 
 our notice : business and science are alike subject to the limi- 
 tations of our human faculties. Subject to these limitations, 
 however, we are able in many cases to secure an unconditional 
 antecedent upon which a certain event invariably follows. In 
 ordinary affairs everybody takes this for granted : if the gas 
 will not burn, or a gun will not go off, we wonder ' what can be 
 wrong with it/ that is, what positive condition is wanting, or 
 what negative one is present. And these conditions are 
 definitely and narrowly conceived. No one now supposes 
 that gunnery depends upon those " remotest of all causes," 
 the stars, or upon the sun being in Sagittarius rather than in 
 Aquarius, or that one shoots straightest with a silver bullet, or 
 after saying the alphabet backwards. 
 
 (6) That the Cause of any event is an Immediate Ante- 
 cedent follows from its being an unconditional one. For if 
 there are three events, ABC, causally connected, it is plain 
 that A is not the unconditional antecedent of C, but requires 
 the further condition of first giving rise to B. But that is not 
 all ; for the B that gives rise to C is never merely the effect of 
 A ; it involves something further. Take such a simple case as 
 the motion of the earth round the sun (neglecting all other 
 conditions, the other planets, etc.) ; and let the earth's motion at 
 three successive moments be A B C : A is not the whole cause 
 of B in velocity and direction ; we must add relation to the 
 sun, say x. But then, again, the cause of C will not be merely 
 Bx, for the relation to the sun will have altered ; so that we 
 must represent it as Bx'. The series, therefore, is Ax Bx' C. 
 What is called a "remote cause" is, therefore, doubly con- 
 ditional ; first, because it supposes an intervening cause ; and 
 secondly, because it only in part determines the conditions 
 that constitute this intervening cause. 
 
 But though the immediacy of a cause is implied in its 
 unconditionalness, it is often so important a clue to it as to 
 deserve separate mention. At the same time, it must be 
 acknowledged that, as far as the detection of causes depends 
 upon sense-perception, our knowledge of immediacy is subject 
 
i 7 4 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 to the limitations of our perceptive powers, which (however 
 aided by instruments) are unequal to the subtlety of Nature. 
 Between the event and what seems to us the immediate 
 antecedent many things (molecular changes) may happen (say) 
 in Chemistry. And where phenomena are treated upon a 
 large scale, as in the biological and social sciences, immediacy, 
 as a mark of causation, must be liberally interpreted. So far, 
 then, as to the qualitative character of Causation. 
 
 (7) But to complete our account of it, we must briefly con- 
 sider its quantitative character. As to the Matter contained, 
 and as to the Energy embodied, Cause and Effect are conceived 
 to be equal. As to matter, indeed, they may be more properly 
 called identical ; since the effect is nothing but the cause 
 redistributed. When oxygen combines with hydrogen to form 
 water, or with mercury to form red precipitate, the weight 
 of the compound is exactly equal to the weight of the elements 
 combined in it ; when a shell explodes and knocks down a 
 wall, the materials of the shell and wall are scattered about. 
 As to energy, we see that in the heavenly bodies, which meet 
 with no sensible impediment, it remains the same from age to 
 age: with things 'below the moon' we have to allow for 
 the more or less rapid conversion of the visible motion of a 
 mass into other forms of energy, such as sound and heat. 
 But the right understanding of this point involves physical 
 considerations of some difficulty, as to which the reader must 
 refer to appropriate books, such as Balfour Stewart's on The 
 Conservation of Energy. 
 
 The comprehension of the quantitative aspect of causation 
 is, however, greatly aided by Professor Bain's analysis of any 
 cause into a * Moving Power ' and a ' Collocation ' of circum- 
 stances. When a demagogue by making a speech stirs up a 
 mob to a riot, the speech is the Moving or Inciting Power ; 
 the mob already in a state of smouldering passion, and a street 
 convenient to be wrecked, are the Collocation. When a small 
 quantity of strychnine kills a man, the strychnine is the Inciting 
 Power; the nature of his nervo-muscular system, apt to be 
 
CAUSATION 175 
 
 thrown into spasms by that drug, and all the organs of his 
 body dependent on that system, are the Collocation. Now 
 any one who thinks only of the speech, or the drug, in these 
 cases, may express astonishment at the disproportion of cause 
 and effect : 
 
 " What great events from trivial causes spring ! " 
 
 But, remembering that the whole cause of the riot included the 
 excited mob, every one sees that its muscular power is enough 
 to wreck a street ; and remembering that breathing depends 
 upon the normal action of the intercostal muscles, it is plain 
 that if this action is stopped by strychnine, a man must die. 
 Again, a slight rise of temperature may be a sufficient Inciting 
 Power to occasion extensive chemical changes in a Collocation 
 of elements otherwise stable. Hence, when sufficient energy 
 to account for any effect cannot be found in the Inciting 
 Power, or manifestly active condition, we must look for it in 
 the Collocation which is often supposed to be passive. 
 
 And that reminds us of another common misapprehension, 
 namely, that in Nature some things are passive and others 
 active : the distinction between * agent ' and ' patient.' This 
 is a merely relative distinction : in Nature all concrete things 
 are active. To the eye some things seem at rest and others in 
 motion ; but we know that nothing is really at rest, that every- 
 thing palpitates with molecular change, and whirls with the 
 planet through space ; and the quietest-looking object (say, a 
 moss-covered stone), if we try to push or lift it, pushes or pulls 
 us back, assuring us that ' action and reaction are equal and 
 opposite.' * Inertia ' does not mean want of vigour, but the 
 exact contrary ; and may be metaphorically described as the 
 inexpugnable resolve of everything to have its own way. Such 
 reflections enable any one to understand how cause and effect 
 are equal when regarded as a transformation of matter and 
 energy. 
 
 It may be observed that the equality of cause and effect 
 defines and interprets the unconditionality of causation. The 
 
176 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 cause, we have seen, is that group of conditions which, without 
 any further condition, is followed by a given event. But how 
 is such a group to be conceived ? Unqualified, it admits only 
 of a general description : quantified, it must mean a group of 
 conditions equal to the effect. For, if not, it must be either 
 always greater or less than the effect, or else sometimes one 
 and sometimes the other. But the last supposition is excluded 
 by reason, that is, by uniformity : whilst, on the first supposi- 
 tion, the world and all its operations would continually diminish; 
 and, on the second, continually increase. Therefore, unless 
 one of these alternatives is true, the unconditional cause is that 
 which is equal to the effect ; and the equality of cause and 
 effect can only be measured in units of matter and energy. 
 
 The transformation of matter and energy, then, is the 
 essence of causation : because it is continuous, causation is 
 immediate ; and because in the same circumstances the trans- 
 formation always follows the same course, a cause has invari- 
 ably the same effect. If a fire is lit morning after morning in 
 the same grate, with coal, wood, and paper of the same quality 
 and similarly arranged, there will be each day the same 
 flaming of paper, crackling of wood and glowing of coal, 
 followed in about the same time by the same reduction of the 
 whole mass partly to ashes and partly to gases that have gone 
 up the chimney. The flaming, crackling and glpwing are, 
 physically, so many modes of energy ; and the change of 
 materials into gas and ashes is a chemical and physical redis- 
 tribution : and, if some one is present, he will be aware of all 
 this; and then, besides the physical changes, there will be 
 sensations of light, sound and heat ; and these again will be 
 always the same in the same circumstances. 
 
 The Cause of any event, then, when exactly ascertainable, 
 has five marks : it is (quantitatively) equal to the effect, and is 
 (qualitatively) its immediate, unconditional^ invariable ante- 
 cedent. 
 
 3. This scientific conception of causation, however, has 
 been developed and rendered definite by the investigations of 
 
CAUSATION 177 
 
 those physical sciences that can avail themselves of exact 
 experiments and mathematical calculation ; and it is there, in 
 Chemistry, Optics, Thermotics and Dynamics, that it is most 
 completely applicable. The conception can indeed be carried 
 into the Biological and Social Sciences, even in its quantitative 
 form, by making the proper allowances. For the limbs of 
 animals are levers, and act upon mechanical principles ; and 
 digestion and the aeration of the blood by breathing are 
 partly chemical processes. There is a quantitative relation 
 between the food a man eats and the amount of work he can 
 do. The numbers of any species of plant or animal depend 
 upon the food supply. The value of a country's imports is 
 equal to the value of its exports and of the services it renders 
 to foreigners. But, generally, the less experiment and exact 
 calculation are practicable in any branch of inquiry, the less 
 rigorously can the conception of causation be applied there ; 
 the more, too, will its application depend upon the qualitative 
 marks, and the more need there will be to use it judiciously. 
 In every inquiry the greatest possible precision must be aimed 
 at ; but it is unreasonable to expect in any case more precise 
 proofs than the subject admits of. 
 
 Wherever mental action is involved, there is a special 
 difficulty in applying the physical notion of causation. For, 
 clearly, if a Cause is conceived as matter in motion, a thought, 
 or feeling, or volition can be neither Cause nor Effect. And 
 since mental action is involved in all social affairs, and in 
 the life of all men and animals, it may seem impossible to 
 interpret social or vital changes according to laws of causa- 
 tion. Still, animals and men are moving bodies ; and it is 
 recognised that their thoughts and feelings are so connected 
 with their movements and with the movements of other things 
 acting upon them, that we can judge of one case by another ; 
 although the connection is by no means well understood, and 
 the best words (such as all can agree to use) have not yet been 
 found to express even what we know about it. Hence, a 
 regular connection being granted, I have not hesitated, to use 
 
 M 
 
178 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 biological and social events and the laws of them, to illustrate 
 Causation and Induction ; because, though less exact than 
 chemical or mechanical examples, they are to most people 
 more familiar and interesting. 
 
 In practical affairs, it is felt that everything depends upon 
 causation ; how to play the fiddle, or sail a yacht, or get one's 
 living, or defeat the enemy. The price of pig-iron six months 
 hence, the prospects of the harvest, the issue in a Coroner's 
 court, Home Rule and Socialism, are all questions of causation. 
 But, in such cases, the conception of a cause is rarely applied 
 in its full scientific acceptation, as the unconditional ante- 
 cedent, or ' all the conditions ' (neither more nor less) upon 
 which the event depends. This is not because men of business 
 are bad logicians, or incapable of scientific comprehension ; 
 for very often the reverse is conspicuously true ; but because 
 practical affairs call for promptitude and a decisive seizing upon 
 what is predominantly important. How learn to play the fiddle ? 
 " Go to a good teacher." (Then, beginning young enough, 
 with natural aptitude and great diligence, all may be well.) 
 How defeat the enemy ? " Be two to one at the critical 
 juncture." (Then, if the men are brave, disciplined, well 
 armed and well fed, there is a good chance of victory.) Will 
 the price of iron improve ? " Yes : for the market is over- 
 sold " : (that is, many have sold iron who have none to deliver, 
 and must at some time buy it back ; and that will put up the 
 price if the stock is not too great, if the demand does not 
 fall off, and if those who have bought what they cannot pay for 
 are not in the meanwhile obliged to sell.) These prompt and 
 decisive judgments as to what is the Cause, or predominantly 
 important condition, of any event, are not as good as a scientific 
 estimate of all the conditions, when this can be obtained; 
 but, when time is short, the insight of trained sagacity may 
 be much better than an imperfect theoretical treatment of 
 such problems. 
 
 4. To regard the Effect of certain antecedents in a narrow 
 selective way, is another common mistake. In the full scientific 
 
CAUSATION 1 79 
 
 conception of an Effect, it is the sum of the unconditional 
 consequences of a given state and process of things : the 
 consequences immediately flowing from that situation without 
 further conditions. Always to take account of all the con- 
 sequences of any cause would no doubt be impracticable ; still 
 the practical, as well as the scientific interest, often requires 
 that we should enlarge our views of them. An important 
 consequence of eating is to satisfy hunger, and this is the 
 ordinary motive to eat ; but it is a poor account of the effect, 
 including its physiological consequences. All sorts of food 
 ' satisfy hunger ' ; but for health and strength some sorts are 
 much better than others. An important consequence of firing 
 a gun is the propulsion of the bullet or shell ; but there are 
 many other consequences in the whole effect, and one of 
 them is the heating of the gun, which, accumulating with rapid 
 firing, may at last put the gun out of action. The tides have 
 consequences to shipping and in the wear and tear of the coast 
 that draw every one's attention ; but we are told that they also 
 retard the rotation of the earth, and at last may cause it to 
 present always the same face to the sun, and, therefore, to be 
 uninhabitable. Such concurrent consequences of any cause 
 may be called its Co-effects : the Effect being the sum of them. 
 The neglect to take account of the whole Effect (that is, 
 of all the co-effects) in any case of causation is perhaps the 
 reason why many philosophers have maintained the doctrine 
 of a " Plurality of Causes " : meaning not that more than one 
 condition is operative in the antecedent of every event (which 
 is true), but that the same event may be due at different times 
 to different antecedents, that in fact there may be vicarious 
 causes. If, however, we take any effect as a whole, this does 
 not seem to be true. A fire may certainly be lit in many ways : 
 with a match or a flint and steel, or by rubbing sticks together, 
 or by a flash of lightning : have we not here a plurality of 
 causes ? Not if we take account of the whole effect ; for then 
 we shall find it modified in each case according to the 
 difference of the cause. In one case there will be a burnt 
 
i8o LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 match, in another a warm flint, in the last a changed slate of 
 electrical tension. And similar differences would be found in 
 cases of death under different conditions, as stabbing, hanging, 
 cholera; or of shipwreck from explosion, scuttling, tempest. 
 In short, if we knew the facts minutely enough, it would be 
 found that there is only one Cause (sum of conditions) for each 
 Effect (sum of co-effects), and that the order of events is as 
 uniform backwards as forwards. 
 
 Still, as we are far from knowing events minutely, it is 
 necessary in practical affairs, and even in the more complex and 
 unmanageable scientific investigations, especially those that deal 
 with human life, to acknowledge a possible plurality of causes 
 for any effect. Indeed, forgetfulness of this leads to many rash 
 generalisations ; as that ' revolutions always begin in hunger ' ; 
 or that * myths are a disease of language.' Then there is great 
 waste of ingenuity in reconciling such propositions with the 
 recalcitrant facts. A scientific method recognises that there 
 may be other causes of effects thus vaguely conceived, and 
 then proceeds to distinguish in each class of effects the 
 peculiarities due to different causes. 
 
 5. The understanding of the complex nature of Causes 
 and Effects helps us to overcome some other difficulties that 
 perplex the use of these words. We have seen that the true 
 cause is an immediate antecedent; but if the cause is con- 
 founded with one of its constituent conditions, it may seem to 
 have long preceded the event which is regarded as its effect. 
 Thus, if one man's death is ascribed to another's desire of 
 revenge, this desire may have been entertained for years before 
 the assassination occurred : similarly, if a^ shipwreck is ascribed 
 to a sunken reef, the rock was waiting for ages before the ship 
 sailed that way. But, of course, neither the desire of revenge 
 nor the sunken nock was ' the sum of the conditions ' on which 
 the one or the other event depended. 
 
 We have also seen that the true effect of any state or process 
 of things is the immediate consequence ; but if the effect is 
 confounded with one of its constituent factors, it may seem to 
 
CAUSATION 181 
 
 long outlive the cessation of the cause. Thus, in nearly every 
 process of human industry and art, one factor of the effect a 
 road, a house, a tool, a picture may, and generally does, 
 remain long after the work has ceased : but such a result is 
 not the whole effect of the operations that produce it. The 
 other factors may be, and some always are, evanescent. In 
 most of such works some heat is produced by hammering or 
 friction, and the labourers are fatigued ; but these consequences 
 soon pass off. Hence the effect as a whole only momentarily 
 survives the cause. Consider a pendulum which, having been 
 once set agoing, swings to and fro in an arc, under the joint 
 control of the shaft, gravitation and its own inertia : at every 
 moment its speed and direction change ; and each change may 
 be considered as an effect, of which the antecedent change was 
 one condition. In such a case as this, which, though a very 
 simple, is a perfectly fair example of all causation, the duration 
 of either cause or effect is quite insensible : so that, as Dr. 
 Venn says, an Effect, rigorously conceived, is only " the initial 
 tendency " of its Cause. 
 
 6. Mill contrasted two forms under which causation appears 
 to us : that is to say, the conditions constituting a cause may 
 be modified or ' intermixed ' in the effect in two ways, which 
 are typified respectively by Mechanical and Chemical action. 
 In mechanical causation, which is found in Astronomy and all 
 branches of Physics, the effects are all reducible to modes of 
 Energy, and are therefore commensurable with their causes. 
 They are either directly commensurable, as in the cases treated 
 of in the consideration of the mechanical powers ; or, if 
 different forms of energy enter into cause and effect, such as 
 mechanical energy, electrical energy, heat, these different forms 
 are severally reducible to units, between which equivalents have 
 been established. Hence Mill calls this the " homogeneous 
 intermixture of effects," because the antecedents and conse- 
 quents are fundamentally of the same kind. 
 
 In chemical causation, on the other hand, cause and effect 
 (at least as they present themselves to us) differ in almost 
 
182 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 every way : in the act of combination the properties of the 
 elements disappear, and are superseded by others in the com- 
 pound. If, for example, mercury (a heavy, silvery liquid) be 
 heated in contact with oxygen (a colourless gas), oxide of 
 mercury is formed (red precipitate, which is a powder). This 
 compound presents very different phenomena from those of its 
 elements ; and hence Mill called this class of cases " the hetero- 
 pathic intermixture of effects." Still, in chemical action, the 
 effect is not (in Nature) heterogeneous with the cause : for the 
 weight of a compound is equal to the sum of the weights of the 
 elements that are merged in it ; and an equivalence has been 
 ascertained between the energy of chemical combination and 
 the heat, light, etc., produced in the act of combination. 
 
 The heteropathic intermixture of effects is also found in 
 organic processes (which, indeed, are partly chemical) : as 
 when a man eats bread and milk, and by digestion and 
 assimilation converts them into nerve, muscle and bone. 
 Such phenomena may make us wonder that people should 
 ever have believed that * effects resemble their causes.' A dim 
 recognition of the equivalence of cause and effect in respect 
 of matter and motion may have aided the belief: and the 
 resemblance of offspring to parents may have helped ; but it 
 has been thought to be chiefly due to a confusing of the order 
 of images in the mind with the order of events in nature. After 
 enough experience, the thought of any event makes us anticipate 
 its consequences, or form a picture of them before they happen ; 
 but again, any image in the mind often reminds us of something 
 similar, and this may be mistaken for the anticipation of an 
 effect. Hence, whistling is seriously regarded as a means of 
 raising the wind, because the wind whistles ; and barbarous 
 rain-makers sometimes torment a child to tears that the clouds 
 also may weep. (See Tylor's Primitive Culture, ch. 4.) 
 
 7. There is another consideration arising out of the com- 
 plex character of causes and effects. When a cause consists 
 of two or more conditions or forces, we may consider what 
 effect any one of them would have if it operated alone, that is 
 
CAUSATION 183 
 
 to say, its Tendency. This, now, is best illustrated by the 
 Parallelogram of Forces : if two forces acting upon a point; 
 but not in the same direction, be represented by straight lines 
 drawn in the direction of the forces, and in length propor- 
 tional to their magnitudes, these lines, meeting in an angle, 
 represent severally the Tendencies of the forces ; whilst if the 
 parallelogram be completed on these lines, the diagonal drawn 
 from the point in which they meet represents their Resultant 
 or effect. 
 
 Again, considering the tendency of any force if it operated 
 alone, we may say that, when combined with another force 
 (not in the same direction) in any resultant, its tendency is 
 counteracted either partially or wholly. If the other force be 
 equal and opposite, the resultant is equilibrium ; if it be in 
 the same direction, the two are merely added together. 
 Counteraction is only one mode of combination. 
 
 Sometimes the separate tendencies of combined forces can 
 only be theoretically distinguished : as when the motion of a 
 projectile is analysed into a tendency to travel in the straight 
 line of its discharge, and a tendency to fall straight to the 
 ground. But sometimes a tendency can be isolated : as when, 
 after dropping a feather in some place sheltered from the 
 wind, and watching it drift to and fro, as the air, offering 
 unequal resistances to its uneven surface, counteracts its weight 
 with varying success, until it slowly settles upon the ground, 
 we take it up and drop it again in a vacuum, when it falls like 
 lead. Here we have the Tendency of a certain Cause (namely, 
 the relation between the feather and the earth) free from 
 Counteraction: and this is called the Elimination of the 
 counteracting circumstances. In this case indeed there is 
 physical elimination ; whereas, in the case of a projectile, when 
 we say that its actual motion is resolvable (neglecting the 
 resistance of the air) into two tendencies, one in the line of 
 discharge, the other earthwards, there is only theoretically 
 elimination of either tendency, considered as counteracting 
 the other ; and this is more specifically called the Resolution 
 
1 84 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 or Analysis of the total effect into its component conditions. 
 Now, Elimination and Resolution may be said to be the 
 essential process of Induction in the widest sense of the term, 
 as including the combination of Induction with Deduction. 
 
 The several conditions constituting any cause, then, by 
 aiding or counteracting one another's tendencies, jointly 
 determine the total effect. Hence, viewed in relation one to 
 another, they may be ssaul 'to stand in Reciprocity or mutual 
 influence. This relation is itself one of co-existence, though it 
 is conceived with reference to a possible effect. As Kant says, 
 all substances, as perceived in space at the same time, are in 
 reciprocal activity. And what is true of the world of things at 
 any moment (as connected, say, by gravity) is true of any 
 selected group of circumstances which we regard as the 
 particular cause of any event to come. The use of the concept 
 of Reciprocity, then, lies in the analysis of a cause : but we 
 must not think of Reciprocity as obtaining in the succession 
 of cause and effect, as if the effect could turn back upon its 
 cause ; for as the effect arises its cause disappears, and is 
 irrecoverable by Nature or Magic. 
 
CHAPTER XV 
 
 INDUCTIVE METHOD 
 
 T . It is necessary to describe briefly the process of investi- 
 gating laws of causation, not with the notion of teaching 
 any one the Art of Discovery, which each man pursues for 
 himself according to his natural gifts and his experience in 
 the methods of his own science, but merely to cast some light 
 upon the contents of the next few chapters. Logic is here 
 treated as a process of proof; proof supposes that some 
 general proposition has been suggested as requiring proof; 
 and the search for such propositions springs from scientific 
 curiosity. 
 
 We may, as Professor Bain observes (Logic : B. iii. ch. 5), 
 desire to detect a process of causation either first, amidst 
 circumstances that have no influence upon the process but only 
 obscure it ; as when, being pleased with a certain scent in a 
 garden, we wish to know from what flower it rises ; or, being 
 attracted by the sound of some instrument in an orchestra, we 
 desire to know which it is : or, secondly, amidst circumstances 
 that alter the effect from what it would have been by the sole 
 operation of some cause ; as when the air deflects a falling 
 feather ; or in some more complex case, such as the problem 
 now (1895) exciting so much interest, the fall of prices that has 
 gone on during the last twenty years. 
 
 To begin with, we must form definite ideas as to what the 
 phenomenon is that we are about to investigate ; and in a case 
 of any complexity this is best done by writing a detailed 
 description of it : e.g., to investigate the cause of a recent fall of 
 
1 86 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 prices, we must describe exactly the course of the phenomenon, 
 dating the period over which it extends, recording the successive 
 fluctuations of prices, with their maxima and minima, and 
 noting the classes of goods or securities that were more or less 
 affected, etc. 
 
 Then the first step of Elimination (as Professor Bain further 
 observes) is " to analyse the situtation mentally," in the light 
 of analogies suggested by our experience or previous know- 
 ledge. Dew, for example, is moisture formed upon the surface 
 of bodies from no apparent source. But two possible sources 
 are easily suggested by common experience : is it deposited 
 from the air, like the moisture upon a mirror when we breathe 
 upon it ; or does it -exude from the bodies themselves, like 
 gum or turpentine ? Or, again, as to the fall of prices, a little 
 experience, in business, or knowledge of Economics, readily 
 suggests two possible explanations : either cheaper production 
 in making goods or carrying them; or a scarcity of that in 
 which the purchasing power of the chief commercial nations is 
 directly expressed, namely, gold. 
 
 Having thus analysed the situation and considered the 
 possibility of one, two, three, or more possible causes, we fix 
 upon one of them for further investigation ; that is to say, we 
 frame an Hypothesis that this is the Cause. When an Effect 
 is given to find its Cause, an inquirer nearly always begins his 
 investigations by thus framing an Hypothesis as to the 
 Cause. 
 
 The next step is to try to verify this Hypothesis. This 
 we may sometimes do by varying the circumstances of the 
 phenomenon, according to the Canons of Inductive Proof 
 to be discussed in the next chapter ; that is to say, by observing 
 or experimenting in such a way as to get rid of or eliminate 
 the obscuring or disturbing conditions. Thus, to find out 
 which flower in a garden gives a certain scent, it is usually 
 enough to rely on observation, going up to the likely flowers 
 one after the other and smelling them : at close quarters, the 
 greater relative intensity of the smell is sufficiently decisive. 
 
INDUCTIVE METHOD 187 
 
 Or we may resort to a sort of experiment, plucking a likely 
 flower, as to which we frame the hypothesis (this is the cause) 
 and carrying it to some place where the air is free from con- 
 flicting odours. 
 
 But if the phenomenon is so complex and extensive as 
 the recent fall of prices, direct observation or experiment is 
 a useless or impossible method ; and we must then resort 
 to Deduction. If, for example, we take the hypothesis that 
 the fall is due to a scarcity of gold, we must show that there 
 is a scarcity ; what effect such a scarcity may be expected to 
 have upon prices from the acknowledged laws of prices, and 
 from the analogy of other cases of an expanded or restricted 
 currency; that this expectation agrees with the statistics of 
 recent commerce : and finally, that the alternative hypothesis 
 that the fall is due to cheaper production is not true ; either 
 because there has not been a sufficient cheapening of general 
 production ; or because, if there has been, the results to be 
 rationally expected from it are not such as to agree with the 
 statistics of recent commerce. (Ch. xviii.) 
 
 But now suppose that, a phenomenon having been suggested 
 for explanation, we are unable at the time to think of any 
 Cause to frame any Hypothesis about it ; we must then wait 
 for the phenomenon to occur again, and, once more observing 
 its course and accompaniments and trying to recall its ante- 
 cedents, do our best to conceive an Hypothesis, and 
 proceed as before. Thus, in the recent epidemic of influenza, 
 some doctors framed the hypothesis that it was due to a 
 deluge in China, others to a volcanic eruption near Java ; some 
 thought it a mild fown of Asiatic plague, and others caught a 
 specific microbe. As the disease often recurred, there were 
 fresh opportunities of framing hypotheses. I do not know 
 whether any one of them has been established. If not, we 
 must wait for the next epidemic. 
 
 Again, however, the investigation may take a different form : 
 given a supposed Cause to find its Effect ; e.g., a new chemical 
 element, to find what compounds it forms witb other elements; 
 
1 88 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 or, the spots on the sun, have they any influence upon our 
 weather ? 
 
 Here, then, if the cause is under control, as a new element 
 may be, it is possible to try experiments with it according 
 to the Canons of Inductive Proof. The inquirer may form 
 some hypothesis or expectation as to the effects, to guide his 
 observation of them, but will be careful not to hold his expec- 
 tion so confidently as to falsify his observation of what actually 
 happens. 
 
 But if the cause is, like the sun-spots, not under control, 
 the inquirer will watch on all sides what events follow their 
 appearance and development ; he must watch for consequences 
 of the new cause he is ^studying in many different circumstances, 
 that his observations may satisfy the canons of proof. But he 
 will also resort for guidance to Deduction ; arguing from the 
 nature of the cause, if anything is known of its nature, what 
 consequences may be expected, and comparing the results of 
 this deduction with any consequent which he suspects to be 
 connected with the cause; and of course, if the results of 
 Deduction and Observation agree, he will still consider 
 whether the facts observed may not be due to some other 
 cause. 
 
 A cause, however, may be under control and yet be too 
 dangerous to experiment with ; such as a proposed change of 
 the constitution by legislation ; or even some minor Act of 
 Parliament, for altering the Poor Law, or regulating the hours 
 of labour. Here the first step must be Deductive. We must 
 ask what consequences are to be expected from the nature of 
 the change (comparing it with similar changes), and from the 
 laws of the special circumstances in which it is to operate? 
 And sometimes we may partially verify our deduction by 
 trying experiments upon a small scale or in a mild form. 
 There are conflicting deductions as to the probable effect of 
 giving Home Rule to Ireland; and experiments have been 
 made in more or less similar cases, as in the Colonies and 
 in some foreign countries. As to the proposal to make eight 
 
INDUCTIVE METHOD 189 
 
 hours the legal limit of a day's labour in all trades, we have 
 all tried to forecast the consequences of this ; and by way of 
 verification we might begin with nine hours; or we might 
 induce some other country to try the experiment first. Still, 
 no verification by experiments on a small scale, or in a mild 
 form, or in somewhat similar yet very different circumstances, 
 can be considered logically conclusive. What proofs are con- 
 clusive we shall see in the following chapters. 
 
 2. To begin with the conditions of direct Induction. An 
 Induction is an universal real proposition, based on observa- 
 tion, in reliance on the uniformity of Nature : when well ascer- 
 tained, it is called a Law. Thus, that all life depends on the 
 presence of oxygen is (i) an universal proposition ; (2) a 
 real one, since the 'presence of oxygen' is not connoted 
 by * life ' ; (3) it is based on observation ; (4) it relies on 
 the uniformity of Nature, since all cases of life have not been 
 examined. 
 
 It should be observed that such a proposition is here called 
 ' an Induction,' when it is inductively proved ; that is, proved 
 by facts, not deduced from more general premises (except the 
 premise of Nature's uniformity) : and by the ' process of Induc- 
 tion' is meant the method of inductive proof. The phrase 
 1 process of Induction ' is often used in another sense, namely, 
 for the inference or judgment by which such propositions are 
 arrived at. But it is better to call this ' the process of 
 hypothesis,' and to regard it as a preliminary to the process 
 of Induction (that is, proof), as furnishing the hypothesis 
 which, if it can stand the proper tests, becomes an Induction 
 or Law. 
 
 3. Inductive proofs are usually classed as Perfect and Im- 
 perfect. They are said to be Perfect when all the instances 
 within the scope of the given proposition have been severally 
 examined, and the proposition has been found true in each 
 case. But we have seen (chap. xii. i) that the instances 
 included in universal propositions concerning Causes and Kinds 
 cannot be exhaustively examined : we do not know all planets, 
 
IQO LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 all heat, all liquids, all life, etc. ; and we never can, since a 
 man's life is never long enough. It is only in such cases as 
 those formerly quoted from Jevons, that examination can be 
 exhaustive ; or else if a class is artificially limited, such as, ' the 
 present House of Commons.' There perfect induction might 
 show (say) that every member has two Christian names. The 
 argument is sometimes exhibited as a Syllogism in Darapti 
 with a Minor premise in U., which legitimates a Conclusion in 
 A., thus : 
 
 A.B. to Z have two Christian names ; 
 A.B. to Z are all the present M.P.s : 
 
 /. All the present M.P.s have two Christian names. 
 But in such an investigation there is no need of logical method 
 to find the major premise; it is mere counting : and to carry 
 out the syllogism is a hollow formality. Accordingly, our 
 definition of Induction excludes the kind unfortunately called 
 Perfect, by including in the notion of Induction a reliance on 
 the uniformity of Nature ; for this would be superfluous if 
 every instance in question had been severally examined. Im- 
 perfect Induction, then, is what we have to deal with : the 
 method of showing the credibility of an universal real proposi- 
 tion by an examination of some of the instances it includes, 
 generally a small fraction of them. 
 
 4. Imperfect Induction is either Methodical or Imme- 
 thodical. Now, Method is procedure upon a principle ; and if 
 the method is to be precise and conclusive, the principle must 
 be clear and definite. 
 
 There is a Geometrical Method, because the axioms of 
 Geometry are clear and definite, and by their means, with 
 the aid of definitions, laws are deduced of the equality of lines 
 and angles and other relations of position and magnitude in 
 space. The process of proof is purely Deductive (the axioms 
 and definitions being granted). Diagrams are used not as facts 
 for observation, but merely to fix our attention in following the 
 general argument ; so that it matters little how badly they are 
 drawn, as long as their divergence from the conditions of the 
 
UNIVERSITY 
 
 INDUCTIVE METHOD 191 
 
 proposition to be proved is not distracting. Even the appeal 
 to " superposition " to prove the equality of magnitudes (as in 
 Euclid I. 4), is not an appeal to observation, but to our judg- 
 ment of what is implied in the foregoing conditions. Hence 
 no inference is required from the special case to all similar 
 ones ; for they are all proved at once. 
 
 There is also, as we have seen, a method of Deductive Logic 
 resting on the Principles of Consistency and the Dictum de 
 omni et nullo. And we shall find that there is a method of 
 Inductive Logic, resting on the principle of Causation. 
 
 But there are a good many general propositions, more or 
 less trustworthy within a certain range of conditions, which 
 cannot be methodically proved for want of a precise principle 
 by which they may be tested ; and they, therefore, depend 
 upon Immethodical Induction, that is, upon the examination 
 of as many instances as can be found, relying for the rest upon 
 the mere undefinable principle of the Uniformity of Nature, 
 since we are not able to connect them with any of its definite 
 modes enumerated in chap. xiii. 9. To this subject we shall 
 return in chap, xix., after treating of Methodical Induction, or 
 the means of determining that a relation of events is of the 
 nature of Cause and Effect, because the relation can be shown 
 to have the marks of causation, or some of them. 
 
 5. Observations and Experiments are the material grounds 
 of Induction. An experiment is an observation made under 
 prepared, and therefore known, conditions ; and, when obtain- 
 able, it is much to be preferred. Simple observation shows 
 that the burning of the fire depends, for one thing, on the 
 supply of air ; but it cannot show us that it depends on oxygen. 
 To prove this we must make experiments; as by obtaining 
 pure oxygen and pure nitrogen (which, mixed in the proportion 
 of one to four, form the air) in separate vessels, and then 
 plunging a burning taper into the oxygen when it will blaze 
 fiercely, and again plunging it into the nitrogen when it will 
 be extinguished. This shows that the greater part of the air 
 does nothing to keep the fire alight, except by diminishing its 
 
392 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 intensity and so making it last longer. Experiments, now, are 
 more perfect the more carefully they are prepared, and the 
 more completely the conditions are known under which the 
 given phenomenon is to be observed. Plainly, however s 
 experiments are only possible when some knowledge has 
 already been gained by observation, for else the preparation 
 which they require would be impossible. 
 
 Observation, then, was the first material ground of Induc- 
 tion, and in some sciences it remains the chief ground. The 
 heavenly bodies, the winds and tides, the strata of the earth, 
 and the movements of history, are beyond our power to experi- 
 ment with. Experiments upon the living body or mind are 
 indeed resorted to when practicable, even in the case of man, 
 as in Psycho-physics, and the investigation of Hypnotism; 
 but, if of a grave nature, they are usually thought unjustifiable. 
 And in political affairs experiments are hindered by the 
 reflection, that those whose interests are affected must bear 
 the consequences and may resent them. Hence, it is in 
 physical and chemical inquiries that direct experiment is most 
 useful. 
 
 Where direct experiment is possible, however, it has many 
 advantages over unaided observation. If one experiment does 
 not enable us to observe the phenomenon satisfactorily, we 
 may try again and again ; whereas the mere observer, who 
 wishes to study the bright spots on Mars, or a commercial 
 crisis, must wait for a favourable opportunity. Again, in 
 making experiments we can often vary the conditions of the 
 phenomenon, so as to observe its different behaviour in each 
 case ; whereas he who depends solely on observation must 
 trust the bounty of nature to supply him with a suitable diver- 
 sity of instances. It is a particular advantage of experiment 
 that a phenomenon may sometimes be 'isolated,' that is, 
 removed from the influence of all agents except that whose 
 operation we desire to observe, or except those whose opera- 
 tion is already known : whereas a simple observer, who has no 
 control over the conditions of the subject he studies, can never 
 
INDUCTIVE METHOD 193 
 
 be quite sure that its movements or changes are not due to 
 causes that have never been conspicuous enough to draw his 
 attention. Finally, experiment enables us to observe coolly 
 and circumspectly and to be precise as to what happens, the 
 time of its occurrence, the order of successive events, their 
 duration, intensity and extent. 
 
 But whether we proceed by observation or experiment, the 
 utmost attainable exactness of measurement and calculation is 
 requisite ; and these presuppose some Unit, in multiples or 
 divisions of which the result may be expressed. This unit 
 cannot be an abstract number as in Arithmetic, but must be 
 one something an hour, or a yard, or a pound according to 
 the nature of the phenomenon to be measured. But what is 
 an hour, or a yard, or a pound ? There must in each case be 
 some particular constant Standard of reference to give assur- 
 ance that the unit may always have the same value. " The 
 English pound is defined by a certain lump of platinum pre- 
 served at Westminster." The unit may be identical with the 
 standard or some division or multiple of it ; and, in measuring 
 the same kind of phenomena, different units may be used for 
 different purposes as long as each bears a constant relation to 
 the standard. Thus, taking the rotation of the earth as the 
 standard of Time, the convenient unit for long periods is a 
 year (which is a multiple) ; for shorter periods, a day (which is 
 identical) ; for shorter still, an hour (which is a division), or 
 even seconds or thousandths of a second. (See Jevons' 
 Principles of Science, ch. 14.) 
 
 6. The principle of Causation is the formal ground of 
 Induction ; and the Inductive Canons derived from it are 
 means of testing the formal sufficiency of observations to 
 justify the statement of a Law. If we can observe the 
 process of cause and effect in nature we may generalise our 
 observation into a law, because that process is invariable. 
 First, then, can we observe the course of cause and effect ? 
 Our power to do so is plainly limited by the refinement of our 
 senses, aided by instruments such as lenses, thermometer!}, 
 
 N 
 
i 9 4 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 balances, etc. If the causal process is essentially molecular 
 change, as in the maintenance of combustion by oxygen, we 
 cannot directly observe it ; if the process is partly cerebral or 
 mental, as in social movements which depend on feeling and 
 opinion, it can but remotely be inferred ; even if the process is a 
 collision of moving masses (billiard-balls), we cannot really 
 observe what happens, the elastic yielding and recoil and the 
 internal changes that result ; though no doubt photography will 
 throw some light upon this, as it has done upon the galloping 
 of horses and the impact of projectiles. Direct observation is 
 limited to the effect which any change in a phenomenon (or its 
 index) produces^ upon our senses ; and what we believe to be 
 the causal process is a matter of inference and calculation. It 
 is to be regretted, if the meagre and abstract outlines of Induc- 
 tive Logic foster the notion, that the evidence on which Science 
 (or even common opinion) rests is simple: it is amazingly 
 intricate and cumulative. 
 
 Secondly, then, so far as we can observe the process of 
 nature, how shall we judge whether a true causal instance, a 
 relation of Cause and Effect, is before us ? By looking for the 
 five marks of Causation. Thus, in the experiment above 
 described, showing that oxygen supports combustion, we find 
 (i) that the taper which only glowed before being plunged 
 into the oxygen, bursts into flame when there Sequence; 
 (2) that this begins to happen at once without perceptible 
 interval Immediacy; (3) that no other agent or disturbing 
 circumstance was present (the preparation of the experiment 
 having excluded any such thing) Unconditionalness ; (4) the 
 experiment may be repeated as often as we like with the 
 same result Invariableness. Invariableness, indeed, I do not 
 regard as formally necessary to be shown, supposing the other 
 marks to be clear; for it can only be proved within our 
 experience ; and the very object of Induction is to find grounds 
 of belief beyond actual experience. However, for material 
 assurance, to guard against his own liability to error, the 
 inquirer will of course repeat his experiments. 
 
INDUCTIVE METHOD 195 
 
 The above four are the qualitative marks of Causation : the 
 fifth and quantitative mark is the Equality of Cause and Effect ; 
 and this, in the above example, the Chemist determines by 
 showing that, instead of the oxygen and wax that have dis- 
 appeared during combustion, an equivalent amount of carbonic 
 acid, water, etc., has been formed. 
 
 Here, then, we have all the marks of causation ; but in the 
 ordinary judgments of life, in history, politics, criticism, 
 business, we must not expect such clear and direct proofs ; 
 and we shall see in subsequent, chapters how different kinds 
 of evidence are combined in different departments of investi- 
 gation. 
 
 7. The Inductive Canons, to be explained in the next 
 chapter, describe the character of observations and experiments 
 that justify us in drawing conclusions about causation ; and, 
 as we have observed, they are derived ftom the principle of 
 Causation itself. According to that principle, cause and effect 
 are invariably, immediately and unconditionally antecedent 
 and consequent, and are equal as to the matter and energy 
 embodied. 
 
 Invariability can only be observed, in any of the methods 
 of induction, by collecting more and more instances, or 
 repeating experiments. Of course it can never be exhaustively 
 observed. 
 
 Immediacy, too, in direct Induction, is a matter for the 
 most exact observation that is possible. 
 
 Succession, or the relation itself of antecedent and conse- 
 quent, must either be directly observed ; or else ascertained by 
 showing that energy gained by one phenomenon has been lost 
 by another, for this implies succession. 
 
 But the Unconditionality of Causation, to determine that is 
 the great object of the methods, and for that purpose the 
 meaning of unconditionality may be further explicated by the 
 following rules : 
 
196 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 I. FOR POSITIVE INSTANCES. 
 
 To find a Cause : (a) Any agent whose introduction among 
 certain conditions (without further change) is followed by a 
 given phenomenon ; or, (b) whose removal is followed by the 
 cessation (or modification) of that phenomenon, is (so far) the 
 cause or an indispensable condition of it. 
 
 To find the Effect : (c) Any event that follows a given 
 phenomenon, when there is no further change ; or, (d) that 
 does not occur when the conditions of a former occurrence are 
 exactly the same, except for the absence of that phenomenon,, 
 is the effect of it (or is dependent on it). 
 
 II. FOR NEGATIVE INSTANCES. 
 
 To exclude a supposed Cause : (a) Any agent that can be 
 introduced among certain conditions without being followed 
 by a given phenomenon (or that is found without that pheno- 
 menon) ; or (b) that can be removed when that phenomenon 
 is present without impairing it (or that is absent when that 
 phenomenon is present), is not the cause, or does not com- 
 plete the cause, of that phenomenon in those circumstances. 
 
 To exclude a supposed Effect : (c) Any event that occurs 
 without the introduction (or presence) of a given phenomenon ; 
 or (d) that does not occur when that phenomenon is introduced 
 (or is present), is not the effect of that phenomenon. 
 
 Subject to the conditions thus somewhat cumbrously stated, 
 the rules may be briefly put as follows : 
 
 I. (a) That which (without further change) is followed by a 
 given event is its cause. 
 
 II. (a) That which is not so followed is not the cause. 
 
 I. (b) That which cannot be left out without impairing a 
 phenomenon is a condition of it. 
 
 II. (b) That which can be left out is not a condition of it. 
 
INDUCTIVE METHOD 197 
 
 The Equality of Cause and Effect may be further explained 
 by these rules : 
 
 III. (a) When a cause (or effect) increases or decreases, so 
 does its effect (or cause). 
 
 III. (b) If two phenomena, having the other marks of cause 
 and effect, seem unequal, the less contains an unexplored 
 factor. 
 
 III. (c) If an antecedent and consequent do not increase or 
 decrease correspondingly, they are not cause and effect, so far 
 as they vary. 
 
 It will next be shown that these propositions are variously 
 combined in Mill's five Canons of Induction. 
 
CHAPTER XVI 
 THE CANONS OF DIRECT INDUCTION 
 
 i. Let me begin by borrowing an example from Professor 
 Bain (Logic : B.* III. c. 6). The North-East wind is generally 
 detested in this country : as long as it blows few people feel 
 at their best. Occasional well-known causes of a wind being 
 injurious are violence, excessive heat or cold, excessive dry ness 
 or moisture, electrical condition, the being laden with dust or 
 exhalations. Let the hypothesis be that the last is the cause of 
 the North-East wind's unwholesome quality ; since we know it 
 is a ground current setting from the pole toward the equator 
 and bent westward by the rotation of the earth ; so that, 
 reaching us over thousands of miles of land, it may well be 
 fraught with dust, effluvia, and microbes. Now, examining 
 many cases of North-East wind, we find that this is the only 
 circumstance in which all the instances agree : for it is some- 
 times cold, sometimes hot ; generally dry, but sometimes wet ; 
 sometimes light, sometimes violent, and of all electrical con- 
 ditions. Each of the other circumstances, then, can be 
 omitted without the N.E. wind ceasing to be noxious ; but one 
 circumstance is never absent, namely, that it is a ground 
 current. That circumstance, therefore, is probably the Cause 
 of its injuriousness. This case illustrates : 
 
 (i) THE CANON OF AGREEMENT. 
 
 If tivo or more instances of a phenomenon under investigation 
 have only one other circumstance (antecedent or consequent] in 
 
 \ 
 
 ' 
 
THE CANONS OF DIRECT INDUCTION 199 
 
 common^ that circumstance is the cause (or an indispensable part 
 of the cause) or the effect of the phenomenon. 
 
 This rule of proof (so far as it is used to establish direct 
 causation) depends, first, upon observation of an invariable 
 connection between the given phenomenon and one other 
 circumstance ; and, secondly, upon I. (a) and II. (b} among the 
 propositions obtained from the unconditionality of causation at 
 the close of the last chapter. 
 
 Let us suppose two instances of the occurrence of a given 
 phenomenon A, an antecedent, or /, a consequent, with 
 concomitant facts or events and let us represent them thus : 
 ABC A D E (antecedents) 
 
 p q r p t s (consequents) ; 
 
 and let us suppose that, 111 tiud case, the immediate succession 
 of events can be observed. Then A is the cause of p. For, 
 as far as our instances go, A is the invariable antecedent of p ; 
 and/ is the invariable consequent of A. But the two instances 
 of A or p agree in no other circumstance. Therefore A is (or 
 completes) the unconditional antecedent of p. For B and C 
 are not the causes of /, being absent in the second instance 
 (Rule II. (ft)}, nor are D and E, being absent in the first 
 instance. Moreover, q and r are not effects of A, being 
 absent in the second instance (Rule II. (d) ) ; nor are s and /, 
 being absent in the first instance. 
 
 It should be observed that the cogency of the proof depends 
 entirely upon its tending to show the unconditicnality of the 
 sequence K-p. That / follows A, even immediately, is nothing 
 by itself : if a man sits down to study and, on the instant, a 
 hand-organ begins under his window, he must not infer malice 
 in the musician : thousands of things follow one another every 
 moment without traceable connection ; and this we call ' acci- 
 dental.' Even invariable sequence is not enough to prove 
 direct causation ; for, in our experience, does not night invari- 
 ably follow day? The proof requires that the instances be 
 such as to show not merely what events are in invariable 
 sequence, but also what are not. From among the occasional 
 
200 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 antecedents of p (or consequents of A) we have to eliminate 
 the accidental ones. And this is done by finding or making 
 ' negative instances ' in respect of each of them. Thus the 
 
 instance f is a negative instance of B and C considered 
 
 as supposable causes of p (and of q and r as supposable 
 effects of A) ; for it shows that they are absent when / (or A) 
 is present. 
 
 To insist upon the cogency of * negative instances' was 
 Bacon's great contribution to Inductive Logic. If we neglect 
 them, and merely collect examples of the sequence A-/, this is 
 * simple enumeration ' ; and although simple enumeration, when, 
 the instances of agreement are numerous enough, may give 
 rise to a strong belief in the connection of phenomena, yet it 
 can never be a methodical or logical proof of causation, since 
 it does not indicate the unconditionalness of the sequence. 
 For simple enumeration of the sequence h.-p leaves open the 
 possibility that, besides A, there is always some other antecedent 
 of /, say X ; and then X may be the cause of/. To disprove 
 it, we must find, or make, a negative instance of X where 
 p occurs, but X is absent. 
 
 If indeed (or whenever) we recognise the possibility of a 
 plurality of causes, this method of Agreement cannot be quite 
 satisfactory. For then, in such instances as the above, although 
 D is absent in the first, and B in the second, it does not follow 
 that they are not the causes of p ; for they may be alternative 
 causes : B may have produced p in the first instance, and D in 
 the second ; A being in both cases an accidental circumstance 
 in relation to p. To remedy this shortcoming by the method 
 of Agreement itself (we shall see other remedies hereafter) the 
 only course is to find more instances of/. We may never find 
 a negative instance of A ; and, if not, the probability that A is 
 the cause of p increases with the number of instances. But if 
 there be no antecedent that we cannot sometimes exclude, yet 
 the collection of instances will probably give at last all the 
 causes of p ; and by finding the proportion of instances in 
 
THE CANONS OF DIRECT INDUCTION 201 
 
 which A, B, or X precedes p, we may estimate the probability 
 of any one of them being the cause of p in any given case of 
 its occurrence. 
 
 Again, though we have assumed that, in the instances sup- 
 posed above, immediate sequence is observable, yet in many 
 cases it may not be so, if we rely only on the canon of Agree- 
 ment ; if instances cannot be obtained by experiment, and we 
 have to depend on observation. The phenomena may then 
 be so mixed together that A and p seem to be merely con- 
 comitant ; so that, though connection of some sort may be 
 rendered highly probable, we may not be able to say which is 
 cause and which is effect. We must then try (as Bain says) to 
 trace the expenditure of energy : if / gains when A loses, the 
 course of events is from A to / ; but here we are anticipating 
 the method of Variations ( 4). 
 
 Moreover, where succession cannot be traced, the method 
 of Agreement may point to a connection between two facts 
 (perhaps as co-effects of a remote cause) where direct causation 
 seems to be out of the question : e.g., that Negroes, though of 
 different tribes, different localities, customs, etc., are both 
 prognathous and dolichocephalic. But such an investigation 
 belongs to the theory of Definition rather than to our present 
 subject. 
 
 Men often use arguments which, if they knew it, might be 
 shown to conform more or less to this canon ; for they collect 
 many instances to show that two events are connected; but 
 usually neglect to bring out the negative side of their proof ; 
 so that their arguments only amount to simple enumeration. 
 Thus Ascham in his Toxophilus, insisting on the national 
 importance of archery, argues that victory has always depended 
 on superiority in shooting ; and, to prove it, he shows how the 
 Parthians checked the Romans, Sesostris conquered great part 
 of the known world, Tiberius overcame Arminius, the Turks 
 established their empire, and the English defeated the French 
 (with many like examples) all by superior archery. But 
 having cited these cases to his purpose, he is content ; whereas 
 
202 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 he might have greatly strengthened his proof by showing how 
 one or the other instance excludes other possible causes of 
 success. Thus : the cause was nor discipline, for the Romans 
 were better disciplined than the Parthians ; nor yet the boasted 
 superiority of a northern habitat, for Sesostris issued from the 
 south; nor better manhood, for here the Germans probably 
 had the advantage of the Romans ; nor superior civilisation, 
 for the Turks were less civilised than most of those they con- 
 quered ; nor numbers, nor even a good cause, for the French 
 were more numerous than the English, and were shamefully 
 attacked by Henry V. on their own soil. Many an argument 
 from simple enumeration may thus be turned into an induction 
 of greater plausibility according to the canon of Agreement. 
 
 Still, in the above case, the effect (victory) is so vaguely 
 conceived, that a plurality of causes must be allowed for : 
 although, e.g., discipline did not enable the Romans to conquer 
 the Parthians, it may have been their chief advantage over the 
 Germans ; and it was certainly important to the English under 
 Henry V. in their war with the French. 
 
 Here is another argument, somewhat similar to the above, 
 put forward by Mr. Spencer with a full consciousness of its 
 logical character. States that make war their chief object, he 
 says, assume a certain type of organisation, involving the 
 growth of the warrior class and the treatment of labourers as 
 existing solely to sustain the warriors ; the complete subordina- 
 tion of individuals to the will of the despotic soldier-king, their 
 property, liberty and life being at the service of the State ; the 
 regimentation of society not only for military but also for civil 
 purposes ; the suppression of all private associations, etc. This 
 is the case in Dahomey and in Russia, and it was so at Sparta, 
 in Egypt, and in the empire of the Yncas. But the similarity 
 of organisation in these States cannot have been due to race, 
 for they are all of different races ; nor to size, for some are 
 small, some large ; nor to climate or other circumstances of 
 habitat, for here again they differ widely : the one thing they 
 have in common is the military purpose ; and this, therefore, 
 
THE CANONS OF DIRECT INDUCTION 203 
 
 must be the cause of their similar organisation. (Political 
 Institutions.} 
 
 By this method, then, to prove that one thing is causally 
 connected with another, say A with /, we show, first, that in all 
 instances of /, A is present ; and, secondly, that any other 
 supposable cause of/ may be absent without disturbing/. We 
 next come to a method the use of which greatly strengthens the 
 foregoing, by showing that where p is absent A is also absent, 
 and (if possible) that A is the only supposable cause that is 
 always absent along with p. 
 
 2. THE CANON OF THE JOINT METHOD OF AGREE- 
 MENT IN PRESENCE AND IN ABSENCE. 
 
 If (i) two or more instances in which a phenomenon occurs 
 have only one other circumstance (antecedent or consequent) in 
 common, while (2) two or more instances in which it does not 
 occur (though in some important points they resemble the former 
 set of instances) have nothing else in common save the absence of 
 that circumstance the circumstance in which alone the two sets 
 of instances differ throughout (being present in the first set and 
 absent in the second) is the effect or the cause, or an indispensable 
 part of the cause^ of the phenomenon. 
 
 The first clause of this Canon is the same as that of the 
 method of Agreement, and its significance depends upon the 
 same propositions concerning causation. The second clause, 
 relating to instances in which the phenomenon is absent, 
 depends for its probative force upon Prop. II. (#), and I. (b). 
 Let the two sets of instances be represented as follows : 
 
 Instances of Presence. Instances of Absence. 
 
 ABC CHF 
 
 p q r r x w 
 
 AD E B DK 
 
 p s t q y z 
 
 AFG EGM 
 
 p u v t / n 
 
204 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Then A is the cause of /, or p the effect of A : first, by the 
 Canon of Agreement in Presence, as represented by the first set 
 of instances ; and, secondly, by Agreement in Absence in the 
 second set of instances. For there we see that C, H, F, B, D, 
 K, E, G, M occur without the phenomenon /, and therefore (by 
 Prop. II. (a) ) are not its cause, or not the whole cause, unless 
 they have been counteracted (which is a point for further 
 investigation). We also see that r, x, w, q, y, z, t, f, n occur 
 without A, and therefore are not the effects of A. And, further, 
 if the negative instances represent all possible cases, we see that 
 (according to Prop. I. (b) ) A is the cause of/, because it cannot 
 be omitted without the cessation of p. The inference that A 
 and p are cause and effect, suggested by their being present 
 throughout the first set of instances, is therefore strengthened 
 by their being both absent throughout the second set. 
 
 As this Double Method, like the Single Method of Agree- 
 ment, relies mainly on observation, sequence may not be per- 
 ceptible in the instances observed, and then, direct causation 
 cannot be proved by it, but only the probability of causal con- 
 nection. It has, however, one peculiar advantage, namely, 
 that if the second list of instances (in which the phenomenon 
 and its supposed antecedent are both absent) can be made 
 exhaustive, it precludes any hypothesis of a plurality of causes ; 
 since all possible antecedents will have been included in this 
 list without producing the phenomenon. Thus, in the above 
 symbolic example, taking the first set of instances, the suppo- 
 sition is left open that B, C, D, E, F, G may, at one time or 
 another, have been the cause of p ; but, in the second list, 
 these antecedents all occur here or there without producing /, 
 and therefore (unless counteracted in some way) cannot be the 
 cause of/. A, then, stands out as the one thing that is present 
 whenever/ is present, and absent whenever/ is absent. 
 
 Stated in this abstract way, the Double Method may seem 
 very elaborate, complicated and difficult ; yet, in fact, we all 
 use it in our ordinary reasonings. If a man finds that whenever 
 he eats cucumber he suffers from indigestion, this indicates by 
 
THE CANONS OF DIRECT INDUCTION 205 
 
 Agreement that cucumber is the cause of his grief. But, if he 
 is fond of cucumber, he will put the fault upon other ingredients 
 of his diet taken at the same time, such as cheese, salmon or 
 pastry, which he likes less. Making, however, a second list of 
 dinners (say) when visiting, at which cucumber is not served, 
 whilst cheese, salmon, pastry, etc., all occur, and finding that he 
 does not suffer from indigestion, the conclusion seems to be 
 forced upon him that cucumber is the only pleasure of the 
 table that must be bought with pain. In this case sequence 
 can be observed. Again, if, whilst a certain oarsman is stroke 
 of a boat whose crew often changes, it always wins ; whilst, 
 after he retires, it always loses (in spite of other changes) ; his 
 admirers will certainly argue according to this Method that, 
 since his presence brought victory and his absence brings 
 defeat, success was due to him and to him alone. 
 
 There are some instructive applications of this Double 
 Method in Dr. Wallace's Darwinism. In chap, viii., for 
 example, on Colour in Animals, he observes, that the useful- 
 ness of their colouration to animals is shown by the fact that, 
 "as a rule, colour and marking are constant in each species of 
 wild animal, while, in almost every domesticated animal, there 
 arises great variability. We see this in our horses and cattle, 
 our dogs and cats, our pigeons and poultry. Now the essen- 
 tial difference between the conditions of life of domesticated 
 and wild animals is, that the former are protected by man, 
 while the latter have to protect themselves." Wild animals 
 protect themselves by acquiring qualities adapted to their mode 
 of life. Now colouration is a very important quality, its chief, 
 though not its only use, being concealment. Hence a useful 
 colouration having been established in any species, though 
 individuals may occasionally vary from it, they will generally 
 perish ; whilst among domestic animals variation of colour or 
 marking is subject to no check except the taste of owners. We 
 have, then, two lists of instances : first, innumerable species of 
 wild animals in which the colouration is constant and which 
 depend upon their own qualities for existence ; secondly, 
 
206 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 several species of domestic animals in which the colouration is 
 not constant, and which do not depend upon their own qualities 
 for existence. In the former list two circumstances are present 
 together (under all sorts of conditions) ; in the latter they are 
 absent together. The argument may be further strengthened 
 by adding a third list, parallel to the first, comprising domestic 
 animals in which colouration is approximately constant, but 
 where (as we know) it is made a condition of existence by 
 owners, who only breed from those specimens that come up to 
 a certain standard of colouration. 
 
 Dr. Wallace goes on to discuss the colouring of arctic 
 animals ; I will slightly condense his statement. In the arctic 
 regions some animals are wholly white all the year round, such 
 as the polar bear, the American polar hare, the snowy owl and 
 the Greenland falcon : these live amidst almost perpetual 
 snow. Others, who live where the snow melts in summer, 
 only turn white in winter, such as the arctic hare, the arctic 
 fox, the ermine and the ptarmigan. In all these cases the 
 white colouring is useful, concealing the herbivores from their 
 enemies, and also the carnivores in approaching their prey; 
 this usefulness, therefore, is the cause of the white colouring. 
 Two other explanations have, however, been suggested : first, 
 that the prevalent white of the arctic regions directly colours 
 the animals, either by some photographic or chemical action 
 on the skin, or by a reflex action through vision (as in the 
 chameleon) ; secondly, that a white skin checks radiation and 
 keeps the animals warm. But there are some exceptions to 
 the rule of white colouring in arctic animals which refute these 
 hypotheses, and confirm the author's. The sable remains 
 brown throughout the winter; but it frequents trees, with 
 whose bark its colour assimilates. The musk-sheep is brown 
 and conspicuous ; but it is gregarious, and its safety depends 
 upon being able to recognise its kind and keep with the herd. 
 The raven is always black ; but it fears no enemy and feeds on 
 carrion, and therefore does not need concealment for either 
 defence or attack. The colour of the sable, then, though not 
 
THE CANONS OF DIRECT INDUCTION 207 
 
 white, serves for concealment ; the colour of the musk-sheep 
 serves a purpose more important than concealment ; the raven 
 needs no concealment. There are thus two sets of instances : 
 in one set the animals are white ; (a) all the year ; (b) in 
 winter, and white conceals them (a) all the year, (b) in winter ; 
 in the other set, the animals are not white, and to them either 
 whiteness would not give concealment, or concealment would 
 not be advantageous. And this second list refutes the rival 
 hypotheses : for the musk-sheep and the raven are as much 
 exposed to the glare of the snow, and to the cold, as the other 
 animals are. 
 
 3. THE CANON OF DIFFERENCE. 
 
 If an instance in which a phenomenon occurs, and an instance 
 in which it does not occur, have every other circumstance in 
 common save one, that o?te (whether consequent or antecedent) 
 occurring only in the former ; the circumstance in which alone 
 the two instances differ is the effect, or the cause, or an indispen- 
 sable condition of the phenomenon. 
 
 This follows from Props. I. (a) and (b), in chapter xv. 7. 
 Let two instances, such as the Canon requires, be represented 
 thus : 
 
 ABC BC 
 
 p q r q r 
 
 Then A is the cause of p. For, in the first instance, A being 
 introduced (without further change), p arises (Prop. I. (a) ) ; 
 and, in the second instance, A having been removed (without 
 other change), / disappears (Prop. I. (b) ). Similarly we may 
 prove, by the same instances, that / is the effect of A. 
 
 Which of two phenomena thus shown to be connected is 
 cause, and which effect (if we have no prior knowledge of their 
 nature, and are not experimenting, but relying on simple obser- 
 vation) must be determined by observing the order in which 
 they occur ; and the immediacy of their connection is also a 
 matter for observation, aided by whatever instruments and 
 methods of inspection and measurement may be available. 
 
208 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 As to the invariability of the connection, it may of course 
 be tested by collecting more instances or making more experi- 
 ments ; but it has been maintained, that a single experiment 
 according to this method, if satisfactorily performed, is suf- 
 ficient to prove causation, and therefore implies invariabi- 
 lity (since causation is uniform), though no other instances 
 should ever be obtainable; because a single perfect experi- 
 ment establishes the unconditionality of the connection. Now, 
 formally this is true; but in any actual investigation how 
 shall we decide what is a satisfactory or perfect experiment ? 
 
 T> /~ 
 
 Such an experiment requires that in the negative instance r , 
 
 B C shall be the least assemblage of conditions necessary 
 to co-operate with A in producing p ; and that it is so cannot 
 be ascertained without either general prior knowledge of the 
 nature of the case or special experiments for the purpose. So 
 that invariability will not really be inferred from a single expe- 
 riment ; besides that, every prudent inquirer repeats his experi- 
 ments, if only to guard against his own liability to error. 
 
 The supposed plurality of causes does not affect the 
 method of Difference. In the above symbolic case, A is 
 clearly one cause (or condition) of p, whatever other causes 
 may be possible ; whereas in the former case of the Single 
 Method of Agreement, it remained doubtful (admitting a 
 plurality of causes) whether A, in spite of being always present 
 with /, was ever a cause or condition of it. 
 
 Now this method of Difference is perhaps oftener than any 
 other, though without our being distinctly aware of it, the basis 
 of ordinary judgments. That the sun gives light and heat, that 
 food nourishes and fire burns, that a stone will break a window 
 or kill a bird, that turning a tap hastens or checks the flow of 
 water or of gas, and thousands of other propositions are known 
 to be true by rough but often emphatic applications of this 
 method in common experience. 
 
 It should be noticed that there are two ways in which this 
 application may be made : either (a) by observation, taking for 
 
THE CANONS OF DIRECT INDUCTION 209 
 
 our two instances distinct assemblages of conditions, differing 
 only in one phenomenon together with its antecedent or con- 
 sequent ; or (b) by experiment, regarding as our two instances 
 the same assemblage of conditions, before and after the intro- 
 duction of a certain agent. If, for example, there are two men 
 of closely similar age, health, clothing and habits, one of whom 
 stands in the shade and feels cool, whilst the other stands in 
 the sun and feels warm, this shows in the former way, by 
 observation, that the sun gives heat ; but if, instead of this, 
 the man who stands in the shade merely steps into the sun- 
 shine and feels warm, the same proposition is proved in the 
 latter way, by experiment. The experimental way is the better 
 when, as in this case, an immediate sequence can be obtained, 
 because it gives a greater certainty of there being no difference 
 between the two instances except the intervention of the given 
 agent. For, when there are two separate sets of conditions, it 
 may be very difficult to make sure that they are exactly similar 
 except in one circumstance with its antecedent or consequent. 
 On the other hand, the experimental method is unsatisfactory 
 if some time must elapse between the introduction of the agent 
 and the manifestation of its effects ; for then other changes 
 may have occurred meanwhile to which these effects are really 
 due. If you throw a stone at a window and the window breaks 
 (nothing else having happened apparently), it will be thought 
 pretty clear that the missile was the immediate unconditional 
 antecedent of the fracture : but if, feeling out of sorts, you 
 take a drug and some time afterwards feel better, it is not 
 clear on this ground alone that the drug was the cause of 
 recovery, for other curative processes may have been active 
 meanwhile food, or sleep, or exercise. 
 
 Any book on some branch of Physics or on Chemistry will 
 furnish scores of examples of the method of Difference : such 
 as Galileo's experiment to show that air has weight, by first 
 weighing a vessel filled with ordinary air, and then filling it 
 with condensed air and weighing it again ; when the increased 
 weight can only be due to the greater quantity of air con- 
 
 o 
 
2io LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 tained. The melting-point of solids is determined by heating 
 them until they do melt (as silver at 1000 C., gold at 1250, 
 platinum at 2000) ; for the only difference between bodies at 
 the time of melting and just before is the addition of so much 
 heat. Similarly with the boiling-point of liquids. That the 
 transmission of sound depends upon the continuity of an 
 elastic ponderable medium, is proved by letting a clock strike 
 in a vacuum (under a glass from which the air has been with- 
 drawn by an air-pump), and standing upon a non-elastic 
 pedestal : when the clock may be seen to strike, but makes 
 only such a faint sound as may be due to the imperfections of 
 the vacuum and.the pedestal. 
 
 The experiments by which the chemical analysis or synthesis 
 of various forms of matter is demonstrated are simple or com- 
 pound applications of this method of Difference, together with 
 the quantitative mark of causation (that cause and effect are 
 equal) ; since the bodies resulting from an analysis are equal 
 in weight to the body analysed, and the body resulting from a 
 synthesis is equal in weight to the bodies synthesised. That 
 an electric current resolves water into oxygen and hydrogen 
 may be proved by inserting the poles of a galvanic battery in 
 a vessel of water ; when this one change is followed by another, 
 the rise of bubbles from each pole and the very gradual decrease 
 of the water. If the bubbles are caught in receivers placed 
 over them, it can be shown that the joint weight of the two 
 bodies of gas thus formed is equal to the weight of the water 
 that has disappeared; and that the gases are respectively 
 oxygen and hydrogen may then be shown by proving that they 
 have the properties of those gases according to further experi- 
 ments by the method of Difference ; as (e.g.) that one of them 
 is oxygen, because it supports combustion, and combines in 
 certain definite proportions with carbon, sulphur, etc. 
 
 In the more complex sciences the method of Difference is 
 not so generally applicable, because of the greater difficulty of 
 being sure that only one circumstance at a time has altered ; 
 still, it is frequently used. Thus, if by dividing a certain nerve 
 
THE CANONS OF DIRECT INDUCTION 211 
 
 certain muscles are paralysed, it is shown that normally that 
 nerve controls those muscles. In his work on Earthworms^ 
 Darwin argues that, though sensitive to mechanical tremors, 
 they are deaf (or, at least, not sensitive to sonorous vibrations 
 transmitted through the air), by the following experiment. He 
 placed a pot containing a worm that had come to the surface, 
 as usual at night, upon a table, whilst close by a piano was 
 violently played ; but the worm took no notice of the noise. 
 He then placed the pot upon the piano whilst it was being 
 played, when the worm, feeling the vibrations, hastily slid back 
 into its burrow. 
 
 When, instead of altering one circumstance in an instance 
 (which we have done our best not otherwise to disturb) and 
 then watching what follows, we try to find two ready-made 
 instances of a phenomenon, which only differ in one other 
 circumstance, it is, of course, still more difficult to be sure that 
 there is really only one other circumstance in which they differ. 
 It may be worth while, however, to do our best to find such 
 instances. Thus, that the temperature of ocean currents in- 
 fluences the climate of the shores they wash, seems to be 
 shown by the fact that the average temperature of Newfound- 
 land is lower than that of the Norwegian coast some 15 
 farther north. Both regions have great continents at their back ; 
 and as the mountains of Norway are higher and capped with 
 perennial snow, we might expect a colder climate there : but 
 the shore of Norway is visited by the Gulf Stream, whilst the 
 shore of Newfoundland is traversed by a cold current from 
 Greenland. Again, when in 1841 the railway from Rouen to 
 Paris was being built, gangs of English and gangs of French 
 workmen were employed upon it, and the English got through 
 about one-third more work per man than the French. It was 
 suspected that this difference was due to one other difference, 
 namely, that the English fed better, preferring beef to thin 
 soup. Now, logically, it might have been objected that the 
 evidence was unsatisfactory, seeing that the men differed in 
 other things besides diet in * race ' (say), which explains so 
 
212 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 much and so easily. But the Frenchmen, having been induced 
 to try the same diet as the English, were, in a few days, able 
 to do as much work : so that the " two instances " were better 
 than they looked. It often happens that evidence, though 
 logically questionable, is good when used by experts, whose 
 familiarity with the subject makes it good. 
 
 4. THE CANON OF CONCOMITANT VARIATIONS. 
 
 Whatever phenomenon varies in any manner whenever another 
 phenomenon (consequent or antecedent) varies in some particular 
 manner \no other* change having concurred} is either a cause or 
 effect of that phenomenon \pr is connected with it through some 
 fact of causation\ 
 
 This is not an entirely fresh method, but may be regarded 
 as a special case either of Agreement or of Difference, to prove 
 the cause or effect, not of a phenomenon as a whole, but of 
 some modification of it. There are certain forces, such as 
 gravitation, cohesion, heat, friction, that can never be elimi- 
 nated altogether, and therefore can only be studied in their 
 degrees. To such phenomena the method of Difference can 
 never be fully applied, because there are no negative instances. 
 But we may obtain negative instances of a given quantity of 
 such a phenomenon (say, heat), and may apply the method of 
 Difference to that quantity. Thus, if the heat of a body in- 
 creases 10 degrees, from 60 to 70, the former temperature of 
 60 was a negative instance in respect of those 10 degrees; and 
 if only one other circumstance (say, friction) has altered at the 
 same time, that circumstance (if an antecedent) is the cause. 
 Accordingly, if in the above Canon we insert, after ' particular 
 manner', "[no other change having concurred,] " it is a state- 
 ment of the method of Difference as applicable to the in- 
 crement of a phenomenon instead of to the phenomenon as a 
 whole ; and we may then omit the last clause " [or is con- 
 nected, etc.]" For these words are inserted to provide for the 
 case of co-effects of a common cause (such as the flash and 
 
THE CANONS OF DIRECT INDUCTION 213 
 
 report of a gun) ; but if no other change (such as the discharge 
 of a gun) has concurred with the variations of two phenomena, 
 there cannot have been a common cause, and they are therefore 
 cause and effect. 
 
 If, on the other hand, we omit the clause " [no other change 
 having concurred,] " the Canon is a statement of the method of 
 Agreement as applicable to the increment of a phenomenon 
 instead of to the phenomenon as a whole; and it is then 
 subject to the imperfections of that method : that is to say, it 
 leaves open the possibilities, that an inquirer may overlook 
 a plurality of causes ; or may mistake a connection of two 
 phenomena, which (like the flash and report of a gun) are 
 co-effects of a common cause, for a direct relation of cause and 
 effect. 
 
 It may occur to the reader that we ought also to distinguish 
 Qualitative and Quantitative Variations as two orders of 
 phenomena to which the present method is applicable. But, 
 in fact, Qualitative Variations may be adequately dealt with by 
 the foregoing methods of Agreement, Double Agreement, and 
 Difference; because a change of quality or property entirely 
 gets rid of the former phase of that quality, or substitutes one 
 for another; as when the ptarmigan changes from brown to 
 white in winter, or as when a stag grows and sheds its antlers 
 with the course of the seasons. The peculiar use of the method 
 of Variations, however, is (as already observed) to formulate 
 the conditions of proof in respect of those causes or effects 
 which cannot be entirely got rid of, but can be obtained only 
 in greater or less amount ; and such phenomena are, of course, 
 quantitative. 
 
 Even when there are two parallel series of phenomena, the 
 one quantitative and the other qualitative like the rate of air 
 vibration and the pitch of sound, or the rate of ether-vibration 
 and the colour-series of the spectrum the method of Variations 
 is not applicable. For (i) two such series cannot be said to 
 vary together, since the qualitative variations are heterogeneous : 
 512:576 is a definite ratio ; but the corresponding notes, C, D, 
 
214 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 in the treble clef, present only a difference. Hence (2) the 
 correspondence of each note with each number is a distinct 
 fact. Each octave even is a distinct fact ; there is a difference 
 between C 64 and C 128 that could never have been anticipated 
 without the appropriate experience. There is, therefore, no 
 such law of these parallel series as there is for temperature and 
 change of volume (say) in mercury. Similar remarks apply to 
 the physical and sensitive light-series. 
 
 We may, then, illustrate the two cases of the method thus 
 (putting a dash against any letter, A' or /', to signify an increase 
 or decrease of the phenomenon the letter stands for) : Agree- 
 ment in Variations (other changes being admissible) 
 ABC A' D E A" F G 
 
 / q r p' s t p" u v 
 
 Here the accompanying phenomena (B C q r> D E s /, FG u v) 
 change from time to time, and the one thing in which the 
 instances agree throughout is that any increase of A (A' or A") is 
 followed or accompanied by an increase of/ (p' or/") : whence 
 it is argued that A is the cause of/, according to Prop. III. (a) 
 (ch. xv. 7). Still, it is supposable that, in the second in- 
 stance, D or E may be the cause of the increment of / ; and 
 that, in the third instance, F or G may be its cause : though the 
 probability of such vicarious causation decreases rapidly with 
 the increase of instances in which A and / vary together. And, 
 since an actual investigation of this type must rely on observa- 
 tion, it is further possible that some undiscovered cause, X, is 
 the real determinant of both A and / and of their concomitant 
 variations. 
 
 Professor Ferri, in his Criminal Sociology, observes : " I have 
 shown that in France there is a manifest correspondence of 
 increase and decrease between the number of homicides, 
 assaults and malicious wounding, and the more or less abundant 
 vintage, especially in the years of extraordinary variations, 
 whether of failure of the vintage (1853-5, 1859, 1867, 1873, 
 1878-80), attended by a remarkable diminution of crime 
 (assaults and wounding), or of abundant vintages (1850, 1856-8, 
 
THE CANONS OF DIRECT INDUCTION 215 
 
 1862-3. 1865, 1868, 1874-5), attended by an increase of crime" 
 (p. 117, Eng. trans.). And earlier he had remarked that such 
 crimes also " in their oscillations from month to month display 
 a characteristic increase during the vintage periods, from June 
 to December, notwithstanding the constant diminution of other 
 offences" (p. 77). 
 
 This is necessarily an appeal to the canon of Concomitant 
 Variations, because France is never without her annual vintage, 
 nor yet without her annual statistics of crime. We can only 
 faintly imagine what would happen if there were no vintage ! 
 Still, it is an argument whose cogency is only that of Agree- 
 ment, showing that very probably the abuse of the vintage is a 
 cause of crimes of violence, but leaving open the supposition, 
 that some other circumstance or circumstances, arising or 
 varying from year to year, may determine the increase or 
 decrease of crime ; or that there is some unconsidered agent 
 which affects both the vintage and crimes of violence. French 
 sunshine, it might be urged, whilst it matures the generous 
 grape, also excites a morbid fermentation in the human 
 mind. 
 
 Difference in Variations may be symbolically represented 
 thus (no other change having concurred) : 
 
 AB A'B A"B 
 
 pq* / q ' f q' 
 
 n 
 
 Here the accompanying phenomena are always the same ; 
 
 and the only point in which the successive instances differ is in 
 the increments of A (A', A") followed by corresponding incre- 
 ments of/ (/', p") : hence the increment of A is the cause of 
 the increment of/. 
 
 For examples of the application of this method, the reader 
 should refer to some work of exact science. He will find in 
 Deschanel's Natural Philosophy > c. 32, an account of some 
 experiments by which the connection between Heat and 
 Mechanical Work has been established. It is there shown that 
 " whenever work is performed by the agency of heat " [as in 
 
216 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 driving an engine], "an amount of heat disappears equivalent 
 to the work performed ; and whenever mechanical work is spent 
 in generating heat " [as in rubbing two sticks together], " the 
 heat generated is equivalent to the work thus spent." And an 
 experiment of Joule's is described, which consisted in fixing a 
 rod with paddles in a vessel of water, and making it revolve 
 and agitate the water by means of a string wound round the 
 rod, passed over a pulley and attached to a weight that was 
 allowed to fall. The descent of the weight was measured by a 
 graduated rule, and the rise of the water's temperature by a 
 thermometer. " It was found that the heat communicated to 
 the water by the agitation amounted to one pound-degree 
 Fahrenheit for every 772 foot-pounds of work" expended by 
 the falling weight. As no other material change seems to take 
 place during such an experiment, it shows that the progressive 
 expenditure of mechanical energy is the cause of the progressive 
 heating of the water. 
 
 The Thermometer itself illustrates this method. It has 
 been found that the application of heat to mercury expands it 
 according to a law ; and hence the volume of the mercury, 
 measured by a graduated index, is used to indicate the tempera- 
 ture of the air, water, animal body, etc.* in which the thermo- 
 meter is immersed, or with which it is brought in contact. In 
 such cases, if no other change has taken place, the heat of the 
 air, water, or body is the cause of the rise of the mercury in 
 its tube. If some other substance (say spirit) be substituted 
 for mercury in constructing a thermometer, it serves the same 
 purpose, provided the index be graduated according to the 
 law of the expansion of that substance by heat, as experi- 
 mentally determined. 
 
 It may be added that instances of phenomena that do not 
 vary together indicate the exclusion of a supposed cause (by 
 Prop. III. (<:)). The stature of the human race has been 
 supposed to depend on temperature ; but there is no corre- 
 spondence. The " not varying together," however, must not 
 be confused with "varying inversely," which when regular 
 
THE CANONS OF DIRECT INDUCTION 217 
 
 indicates a true concomitance. Indeed it is often a matter of 
 convenience whether we regard concomitant phenomena as 
 varying directly or inversely. It is usual to say ' the greater 
 the friction the less the speed ' ; but it is really more intelligible 
 to say 'the greater the friction the more rapidly molar is 
 converted into molecular motion.' 
 
 The Graphic Method is an interesting way of exhibiting 
 Concomitant Variations to the eye, and is extensively used in 
 physical and statistical inquiries. Along a horizontal line (the 
 abscissa) is measured one of the conditions (or agents) with 
 which the inquiry is concerned, called the Variable ; and along 
 perpendiculars (ordinates) is measured some phenomenon to be 
 compared with it, called the Variant. 
 
 Thus, the expansion of a liquid by heat may be represented 
 by measuring degrees of temperature along the horizontal, and 
 
 FIG. 9. 
 
 <*e 60 so 70 eo eo reo T 
 
 Degrees of Temperature. 
 
 the expansion of a column of the liquid in units of length along 
 the perpendicular. 
 
 In the next diagram, reduced from one given by Mr. C. H. 
 Denyer in an article on the price of tea (Economic Journal^ 
 No. 9), the condition measured horizontally is Time; and, 
 vertically, three variants are measured simultaneously, so that 
 their relations to one another from time to time may be seen 
 at a glance. 
 
 From this it is evident that, as the Duty on Tea falls, the 
 Price of Tea falls, whilst the Consumption of Tea rises ; and, 
 in spite of some irregularity of correspondence in the courses 
 of the three phenomena, their general causal connection can 
 
2i8 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 4) O 
 
 ^ 
 
 Jl 
 
 Jo* 
 
 fl 
 Jl 
 
 5 *H a) 
 
 | ^ 
 
 7 ^ 
 
 1 "o 
 
 1 <D 
 
 I 2 
 
 "^^ JM 
 
 d 
 
 
 i 
 
 \ 
 
 \ 
 
 C^, 
 
 \ 
 
THE CANONS OF DIRECT INDUCTION 919 
 
 hardly be mistaken. However, the causal connection may 
 also be inferred by general reasoning ; the statistical Induction 
 can be confirmed by a Deduction ; thus illustrating the com- 
 bined method of proof to be discussed in the next chapter. 
 Without such confirmation the proof by Concomitant Varia- 
 tions would not be complete ; because, from the complexity 
 of the circumstances, social statistics can only yield evidence 
 according to the method of Agreement in Variations. For, 
 besides the agents that are measured, there may always be 
 some other important influence at work. During the last fifty 
 years, for example, crime has decreased whilst education has 
 increased : true ; but at the same time wages have risen and 
 many other things have happened. 
 
 It will be noticed that in the diagram the three lines, 
 especially those of Price and Consumption (which may be con- 
 sidered natural resultants, in contrast with the arbitrary fixa- 
 tion of a Tax), do not depart widely from regular curves ; and 
 accordingly, assuming the causes at work to vary continuously 
 during the intervals between points of measurement, curves 
 may be substituted. In fact, a curve often represents the 
 course of a phenomenon more truthfully than can be done by 
 a line that zigzags along the exact measurements ; because it 
 is less influenced by temporary and extraordinary causes that 
 may obscure the operation of those that are being investigated. 
 On the other hand, the abrupt deviations of a punctilious 
 zigzag may have their own logical value, as will appear in the 
 next section. 
 
 The Method of Gradations or Serial Arrangement, much 
 used in Biology and Sociology, is based upon the principle of 
 Concomitant Variations. 
 
 Finish in the manufacture of spear-heads depends (material 
 being given) upon the workman's having (a) a definite idea of 
 the thing to be made, and (b) mechanical craftsmanship. As 
 different workmen have these prerequisites in different degrees 
 their work will approach or stop short of perfection, much as 
 if the best workman should abandon his tasks at various stages 
 
220 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 of incompleteness. Now at successive stages of culture the 
 average workman will produce spear-heads corresponding in 
 finish to the imperfect products of apprentices and inferior 
 journeymen (in all degrees) of the best age. Hence, arranging 
 flint spear-heads in a series from the best types downwards, we 
 have a rough index of the progress of culture ; and we are 
 also able to infer with confidence that many crude specimens 
 are really hand-made which, but for the continuity of the series, 
 we might have regarded as pieces of flint accidentally chipped 
 and worn. To confirm such inferences by laying ancient 
 spear-heads side by side with the work of existing savages is 
 the Comparative Method. 
 
 Similarly to show the possibility that some extraordinary 
 organic phenomena, such as the eyes in the Peacock's tail, 
 have been produced by a natural process (say, Sexual 
 Selection), similar phenomena in various grades of develop- 
 ment may be pointed out, such as the decoration of the wings 
 of Argus Pheasants, and ocelli in other genera of Phasianida. 
 The argument is that the gradual and cumulative operation 
 of similar conditions produces increasing manifestations of 
 similar effects. The Peacock's ocelli must have passed 
 through all stages of development; but the earlier stages 
 are, of course, lost and irrecoverable. (Darwin : Descent of 
 Man, c. 14.) 
 
 To arrange phenomena in graduated series (if possible) in 
 order to study them is, perhaps, the most definite maxim in 
 the Art of Discovery, (Bain : Induction^ c. 6, and App. II.) 
 If their causes are unknown it is likely to suggest hypotheses : 
 and if the causes are partly known, variation in the character 
 of the series is likely to suggest a corresponding variation of 
 the conditions ; as in investigating the development of the 
 forelimbs of vertebrates or the natural history of clothes. 
 
THE CANONS OF DIRECT INDUCTION 
 
 5. THE CANON OF RESIDUES. 
 
 Subduct from any pheno??ienon such part as previous induc- 
 tions have shown to be the effect of certain antecedents^ and the 
 residue of the phenomenon is the effect of the remaining ante- 
 cedents. 
 
 Th'e phenomenon is here assumed to be an effect : a similar 
 Canon may be framed for residuary causes. 
 
 This also is not a fresh method, but a special case of the 
 method of Difference. For if we suppose the phenomenon to 
 be p q r, and the antecedent to be A B C, and that we already 
 know B and C to have (either severally or together) the con- 
 sequents q r t in which their efficacy is exhausted ; we may 
 
 T> r* 
 
 regard - as an instance of the absence of/ obtained deduc- 
 
 A B f 
 
 lively from the whole phenomenon by our knowledge of 
 
 A R f* 
 
 the laws of B and C ; so that p- is an instance of the 
 
 B f 
 
 presence of /, differing otherwise from - in nothing except 
 
 that A is also present. By the Canon of Difference, there- 
 fore A is the cause of /. Or, again, when phenomena thus 
 treated are strictly quantitative, the method may be based on 
 Prop. III. (3), ch. xv. 7. 
 
 Of course, if A can be obtained apart from B C and directly 
 experimented with so as to produce/, so much the better ; and 
 this may often be done ; but the special value of the method 
 of Residues appears, when some complex phenomenon has been 
 for the most part accounted for by known causes, whilst there 
 remains some excess, or shortcoming, or deviation from the 
 result which those causes alone would lead us to expect, and 
 this residuary fact has to be explained in relation to the whole. 
 Here the negative instance is constituted by deduction, showing 
 what would happen but for the interference of some unknown 
 
222 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 cause which is to be investigated ; and this prominence of the 
 deductive process has led some writers to class the method as 
 deductive. But we have seen that all the Canons involve 
 deduction ; and, considering how much in every experiment is 
 assumed as already known (what circumstances are * material,' 
 and when conditions may be called ' the same '), the wonder 
 is that no one has insisted upon regarding every method as 
 concerned with residues. In fact, as scientific explanation 
 progresses, the phenomena that may be considered as residuary 
 become more numerous and the importance of this method 
 increases. 
 
 Examples : Tbe recorded dates of ancient eclipses having 
 been found to differ from those assigned by calculation, it has 
 been surmised that the average length of a day may in the 
 meanwhile have increased. If so, this is a residuary pheno- 
 menon not accounted for by the causes formerly recognised as 
 determining the rotation of the earth on its axis ; and it may 
 be explained by the doctrine that the tides, by their friction, 
 are reducing the rate of the earth's rotation, and thereby 
 lengthening the day. 
 
 Capillarity seems to be a striking exception to the principle 
 that water (or any liquid) ' finds its level,' that being the con- 
 dition of equilibrium ; yet capillarity proves to be only a 
 refined case of equilibrium when account is taken of the forces 
 of adhesion by different kinds of bodies in contact. 
 
 " Many of the new elements of Chemistry," says Herschel, 
 "have been detected in the investigation of residual phe- 
 nomena." Thus, Lord Rayleigh found that nitrogen from the 
 atmosphere was slightly heavier than nitrogen got from chemical 
 sources. The search for the cause of this difference led to the 
 discovery of argon. 
 
 The Economist shows that when a country imports goods 
 the chief means of paying for them is to export other goods. 
 If this were all, imports and exports would be of equal value : 
 yet the United Kingdom imports about ^400,000,000 annually, 
 and exports about ^300,000,000. Here, then, is a residuary 
 
THE CANONS OF DIRECT INDUCTION 223 
 
 phenomenon of ; 100,000,000 to be accounted for. But foreign 
 countries owe us about ^50,000,000 for the use of shipping, 
 and ; 7 0,000,000 as interest on the capital we have lent them, 
 and ;i 5,000,000 in commissions upon business transacted for 
 them. These sums added together amount to ^135,000,000 ; 
 and that is ,35,000,000 too much. Thus another residuary 
 phenomenon emerges ; for whilst foreigners seem to owe us 
 ^435,000,000 they only send us ^400,000,000 of imports. 
 To account for these ^35,000,000 we may suppose that they 
 represent the annual investment of our capital abroad, in return 
 for which no immediate payment is due; and, these being 
 omitted, exports and imports balance. 
 
 When, in pursuing the method of Variations, the phenomena 
 compared do not always correspond in their fluctuations, the 
 irregular movements of that phenomenon which we regard as 
 the effect may often be explained by treating them as residuary 
 phenomena, and then seeking for exceptional causes, whose 
 temporary interference has obscured the influence of the 
 general cause. Thus, returning to the diagram of the Price 
 of Tea in 4, it is clear that generally the Price falls as the 
 Duty falls; but in Mr. Denyer's more minutely wrought 
 diagram, from which this is reduced, it may be seen that 
 in 1840 the Price of Tea rose from 3*. gd. to 4*. gd. without 
 any increase of Duty. This, however, is readily explained 
 by the Chinese War of that year, which, of course, checked 
 the trade. Again, from 1869 to 1889 the Duty was con- 
 stant, whilst the Price of Tea fell as much as %d. per Ib. ; but 
 this residuary phenomenon is explained by the prodigiously 
 increased production of Tea during that period in India and 
 Ceylon. 
 
 The above examples of the method of Residues are all 
 quantitative ; but the method is often employed where exact 
 estimates are unobtainable. 
 
 Darwin, having found certain modifications of animals in 
 form, colouration and habits, that were not clearly derivable 
 from their struggle for existence in relation to other species or 
 
224 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 to external conditions, suggested that they were due to Sexual 
 Selection. 
 
 The ' vestiges ' and ' survivals ' so common in Biology and 
 Sociology are residuary phenomena. It is a general inference 
 from the doctrine of Natural Selection that every organ and 
 function of a plant, animal, or society is in some way useful to 
 it. There occur, however, organs and functions that have at 
 present no assignable utility, are at least wasteful, and some- 
 times even injurious. And the explanation is that formerly 
 they were useful ; but that, their uses having lapsed, they are 
 now retained by the force of heredity or tradition, 
 
CHAPTER XVII 
 COMBINATION OF INDUCTION WITH DEDUCTION 
 
 i. We have now reviewed Mill's five Canons of Inductive 
 Proof. At bottom, as he observes, there are only two, namely, 
 Agreement and Difference : since the Double Method, Varia- 
 tions and Residues are (as we have seen) only special forms of 
 the other two. And indeed it may almost be said that in final 
 analysis they are all reducible to one, namely, Difference ; foi 
 the cogency of the method of Agreement (as distinguished from 
 a simple enumeration of instances agreeing in the coincidence 
 of a supposed cause and its effect), depends upon the omission, 
 in one instance after another, of all other circumstances ; which 
 omission is a point of difference. 
 
 Now, the Canons are an analysis of the conditions of 
 proving directly, by means of observation or experiment, any 
 proposition that predicates causation. But if we say * by means 
 of observation or experiment,' it is not to be understood that 
 these are the only means and that nothing else is involved ; for 
 it has been shown that the Law of Causation is itself an indis- 
 pensable foundation of the evidence. In fact Inductive Logic 
 may be considered as haying a purely formal character. It 
 consists, first, in a statement of the Law of Cause and Effect ; 
 secondly, in certain immediate inferences from this Law, 
 expanded into the Canons ; thirdly, in the syllogistic applica- 
 tion of the Canons to special propositions of causation by 
 means of minor premises, showing that certain instances satisfy 
 the Canons. 
 
220 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 At the risk of some pedantry, we may exhibit the process as 
 follows (cf. Prof. Ray's Logic : Appendix D) : 
 
 Whatever relation of events has certain marks is a case of 
 Causation ; 
 
 The relation A : p has some or all of these marks (as shown 
 by observation and by the conformity of instances to 
 such or such a Canon) : 
 
 Therefore, the relation A : p is a case of Causation. 
 Now, the parenthesis, "as shown by the conformity, etc." is an 
 adscititious member of an Epicheirema, which may be stated, 
 as a Prosyllogism, thus : 
 
 If an instance, etc. (Canon of Difference) ; 
 
 A Tl C* Ti f~* 
 
 The instances > - are of the kind required : 
 
 p q r q r 
 
 Therefore, A, present where p occurs and absent where it 
 does not occur, is an indispensable antecedent of/. 
 
 Such is the bare Logic of Induction : so that, strictly 
 speaking, observation or experiment is no part of the logic, 
 but a means of applying the logic to actual, that is, not merely 
 symbolical, propositions. The Formal Logic of Induction is 
 essentially deductive ; and it has been much questioned 
 whether any transition from the formal to the material 
 conditions of proof is possible. As long as we are content to 
 illustrate the Canons with symbols, such as A and /, all goes 
 well ; but can we in any actual investigation show that the 
 relevant facts or f instances ' correspond with those symbols ? 
 
 In the first place, as Dr. Venn shows, natural phenomena 
 want the distinctness and capability of isolation that belong to 
 symbols. Secondly, the observing whether instances conform 
 to a Canon, must always be subject at last to the limits of our 
 faculties. How can we ascertain exact equality, immediate 
 sequence? The Canon of Difference, in its experimental 
 application, is usually considered the most cogent sort of 
 proof: yet when can the two sequent instances, before and 
 after the introduction of a certain agent, be said to differ in 
 nothing else ? Are not earth and stars always changing posi- 
 
COMBINED INDUCTION AND DEDUCTION 227 
 
 tion ; is not every molecule in the room and apparatus always 
 oscillating? It is true that our senses are now aided by 
 elaborate instruments ; but the construction of these depends 
 on scientific theories, which again depend on experiments. 
 
 It is right to touch upon this well-known sceptical topic ; 
 but to insist much upon it is not a sign of good sense. The 
 works of Herschel, Whewell, and Jevons should be consulted 
 for the various methods of correcting observations, by repeating 
 them, averaging them, verifying one experimental process by 
 another, always refining the methods of exact measurement, 
 multiplying the opportunities of error (that if any exist it may 
 at last show itself), and by other devices of what may be called 
 Material Logic or Methodology. But, probably, only many 
 years spent in the study and personal manipulation of scientific 
 processes, can give a just sense of their effectiveness ; and to 
 stand by, suggesting academic doubts, is easier and more 
 amusing. 
 
 2. Still, it is not so much in laws based upon direct obser- 
 vation or experiment, that the material validity of scientific 
 reasoning appears, as in the cumulative evidence that arises 
 from the co-ordination of laws within each science, and the 
 growing harmony and coherence of all sciences. This requires 
 a more elaborate combination of deduction with observation 
 and experiment. During the last three hundred years many 
 departments of science have been reduced under principles of 
 the greatest generality, such as the Law of Gravitation, the 
 Undulatory theory of Light, the Conservation of Energy, and 
 the Theory of Natural Selection ; connecting and explaining 
 the less general laws, which, again, are said to connect and 
 explain the facts. Meanwhile, those sciences that were the 
 first to make progress have been useful in developing others 
 which, like Biology and Sociology, present greater difficulties. 
 In fact it is more and more apparent that the distinctions 
 drawn among Sciences are entirely for the convenience of 
 study, and that all Sciences tend to merge in one universal 
 Science of Nature. Now, this process of the ' unification of 
 
228 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 knowledge ' is almost another name for deduction ; but at the 
 same time it depends for its reality and solidity upon a 
 constant reference to observation and experiment. Of the 
 logical character of this process only a very inadequate notion 
 can be given in the ensuing chapters. 
 
 Let us begin by returning to some earlier considerations. 
 We have seen in chap. xiv. 6, that when two or more agents 
 or forces combine to produce a phenomenon, their effects are 
 intermixed in it, and this in one of two ways according to their 
 nature. In chemical action and in vegetable and animal life, 
 the causal agents concerned are blended in their results in 
 such a way that most of the qualities which they exhibited 
 severally are lost, whilst new qualities appear instead. Thus 
 chlorine (a gas) and sodium (a metal), in a certain combina- 
 tion, form common salt ; which is quite unlike either of them : 
 a man eats bread, and it becomes muscle, nerve and bone. In 
 such cases we cannot trace the qualities of the causal agents in 
 the qualities of the effects ; given such causes, we can prove by 
 experimental analysis and synthesis, according to the canons 
 of induction, that they have such effects ; but we may not be 
 able in any new case to calculate what the effects will be. 
 
 On the other hand, in Astronomy and Physics, the causes 
 treated of are mechanical ; at least, it is the aim of Physics to 
 attain to a mechanical conception of phenomena ; so that, in 
 every new combination of forces, the intermixed effect, or re- 
 sultant, may be calculated beforehand ; provided that the forces 
 concerned admit of being quantitatively estimated, and that 
 the conditions of their combination are not so complex as to 
 baffle the powers of mathematicians. In such cases, therefore, 
 when direct observation or experiment is insufficient to resolve 
 an effect into the laws of its conditions, the general method is 
 to calculate what may be expected from a combination of its 
 conditions, either as known or hypothetically assumed, and to 
 compare this anticipation with the actual phenomenon. 
 
 3. This is what Mill calls the Direct Deductive Method ; 
 or, the Physical Method, because it is so much relied on in 
 
COMBINED INDUCTION AND DEDUCTION 229 
 
 j\*u- 
 deal/ 
 :ady >. 
 knit ' \ 
 
 treating of Light, Heat, Sound, etc. ; though it is also the 
 usual method of Astronomy and Economics : Deduction 
 leads the way, and its results are tested by inductive experi- 
 ments or observations. Given any complex mechanica^ / 
 phenomenon, the inquirer considers (i) what laws already 
 ascertained by induction seem likely to apply to it (in default 
 of known laws, hypotheses are substituted : cf. chap, xviii.) ; he 
 then (2) computes the effect that will follow from these laws 
 in circumstances similar to the case before him ; and (3) he 
 verifies his conclusion by comparing it with the actual pheno- 
 menon. 
 
 A well-tried and staunch example of this method is the 
 explanation of the rise of water in the * common pump.' We 
 know three laws applicable to this case: (a) that the atmosphere 
 weighs upon the water outside the pump with a pressure of 
 15 Ib. to the square inch; (b) that a liquid (and therefore the 
 water) transmits pressure equally in all directions (upwards as 
 well as downwards and sideways) ; and (c) that pressure upon 
 a body in any direction, if not counteracted by an opposite 
 pressure, produces motion. Hence, when the rise of the 
 piston of the pump removes the pressure upon the water within 
 the cylinder, tending to produce a vacuum there, this water is 
 pushed up by the pressure of the air upon the water outside 
 the cylinder, and follows the rising piston, until the column of 
 water inside the cylinder exerts a pressure equal to that of the 
 atmosphere upon a given area. So much for the computation; 
 does it correspond with the fact ? It is found that at the sea- 
 level water can be pumped to the height of 33 feet ; and that 
 such a column of water has a pressure of 15 Ib. to the square 
 inch. We may show further that, at the sea level, spirits of 
 wine may be pumped higher, according to its less specific 
 gravity ; and that if we attempt to pump water at successive 
 altitudes above the sea level, we can only raise it to less and 
 less heights, corresponding with the lessened atmospheric pres- 
 sure at those altitudes, where the column of air producing the 
 pressure is shorter. Finally, if we try to work a pump, having 
 
250 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 first produced a vacuum over the water outside the cylinder, we 
 shall find that the water inside will not rise at all ; the piston 
 can be raised, but the water does not follow it. The verifica- 
 tion thus shows that the computed effect corresponds with the 
 phenomenon to be explained ; that the result does not depend 
 upon the nature of water only, but is true (allowing for differ- 
 ences of specific gravity) of other liquids ; that if the pressure 
 of the outside air is diminished, the height of pumping is so 
 too (canon of Variations) ; and that if that pressure is. entirely 
 removed, pumping becomes impossible (canon of Difference). 
 
 Any text-book of Astronomy or Physics furnishes numerous 
 illustrations of this method. Take, for example, the first chap- 
 ter of Deschanel's Optics^ where are given three methods of 
 determining the velocity of Light. This was first deduced from 
 observation of Jupiter's satellites. The one nearest the planet 
 passes behind it, or into its shadow, and is eclipsed at intervals 
 of about 42 \ hours. But it can be shown that, when Jupiter 
 and the Earth are nearest together on the same side of the Sun, 
 an eclipse of this satellite is visible from the earth 16 min. 26-6 
 sec. earlier than when Jupiter and the Earth are furthest apart 
 on opposite sides of the Sun : 16 min. 26*6 sec., then, is the 
 time in which light traverses the diameter of the Earth's orbit. 
 Therefore, supposing the Earth's distance from the Sun to be 
 91 J millions of miles, light travels about 185,500 miles a second. 
 Another deduction, agreeing with this, starts from the fact of 
 aberration, or the displacement of the apparent from the actual 
 position of the stars in the direction of the earth's motion. 
 Aberration depends partly on the velocity of light, partly on 
 the velocity of the Earth ; and the latter being known, the 
 former can be computed. Now, these two deductive arguments, 
 verifying each other, have also been verified experimentally. 
 Foucault's experiment to measure the velocity of light is too 
 elaborate to be described here : a full account of it will be 
 found in the treatise above cited, 687. 
 
 When the phenomena to be explained are of such a 
 -"'* character, so vast in extent, power or duration, that it is 
 
COMBINED INDUCTION AND DEDUCTION 231 
 
 impossible, in the actual circumstances of the case, to frame 
 experiments in order to verify a deductive explanation, it may 
 still be possible to reproduce a similar phenomenon upon a 
 smaller scale. Thus Monge's explanation of mirage by the 
 great heat of the desert sand, which makes the lowest stratum 
 of air less dense than those above it, so that rays of light 
 from distant objects are refracted in descending, until they 
 are actually turned upwards again to the eye of the beholder, 
 giving him inverted images of the objects as if they were 
 reflected in water, is manifestly incapable of being verified by 
 experiment in the natural conditions of the phenomenon. But 
 by heating the bottom of " a sheet-iron box, with its ends cut 
 away," the rarefied air at the bottom of the box may sometimes 
 be made to yield reflections ; and this shows at least that the 
 supposed cause is a possible one (Deschanel, Optics, 726). 
 Similarly as to the vastest of all phenomena, the evolution of 
 the stellar system, and of the solar system as part of it, from an 
 immense cloudlike volume of matter : Mr. Spencer, in his 
 Essay on 2"he Nebular Hypothesis (Essays, I. vi.), says, amidst 
 a great array of deductive arguments from mechanical principles, 
 that " this a priori reasoning harmonises with the results of 
 experiment. Dr. Plateau has shown that when a mass of fluid 
 is, as far as may be, protected from the action of external Torces, 
 it will, if made to rotate with adequate velocity, form detached 
 rings ; and that these rings will break up into spheroids, which 
 turn on their axes in the same direction with the central mass." 
 The theory of the evolution of species of plants and animals by 
 Natural Selection, again, though, of course, it cannot be verified 
 by direct experiment (since experiment implies artificial arrange- 
 ment), and the process is too slow for observation, is, never- 
 theless, to some extent confirmed by the practice of gardeners 
 and breeders of animals : since, by taking advantage o 
 accidental variations of form and colour in the plants or 
 animals under their care, and relying on the heritability of 
 these variations, they obtain extensive modifications of the 
 original stocks, and adapt them to the various purposes for 
 
232 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 which flowers and cereals, poultry, dogs and cattle are domes- 
 ticated. This shows, at least, that living forms are plastic and 
 extensively modifiable in a comparatively short time. 
 
 4. Suppose, however, that, in verifying a deductive argu- 
 ment, the effect as computed from the laws of the causes 
 assigned, does not correspond with the facts observed ; there 
 must then be an error somewhere. If the fact has been 
 accurately observed, the error must lie either in the process of 
 deduction and computation, or else in the premises. As to 
 the process of deduction, it may be very simple and easily 
 revised, as in the above explanation of the common pump ; or 
 it may be very involved and comprise long trains of mathe- 
 matical calculation. If, however, on re-examining the compu- 
 tations, we find them correct, it remains to look for some 
 mistake in the premises. 
 
 (1) We may not have accurately ascertained the laws, or the 
 modes of operation, of the forces present. Thus, the rate at 
 which bodies fall was formerly believed to vary in proportion 
 to their relative weights ; and any estimate based upon this 
 belief is not likely to have agreed with the facts. Again, the 
 corpuscular theory of light, namely, that the physical cause of 
 light is a stream of fine particles projected in straight lines 
 from the luminous object, though it seemed adequate to the 
 explanation of many optical phenomena, could not be made to 
 agree with the facts of interference and double refraction. 
 
 (2) The circumstances in which the agents are combined 
 may not have been correctly conceived. When Newton began 
 to inquire whether the attraction of the earth determined the 
 orbit of the moon, he was at first disappointed. '* According 
 to Newton's calculations, made at this time," says Whewell, 
 " the moon, by her motion in her orbit, was deflected from the 
 tangent every minute through a space of thirteen feet. But 
 by noticing the space which bodies would fall in one minute 
 at the earth's surface, and supposing this to be diminished in 
 the ratio of the inverse square, it appeared that gravity would, 
 at the moon's orbit, draw a body through more than fifteen 
 
COMBINED INDUCTION AND DEDUCTION 233 
 
 feet." In view of this discrepancy he gave up the inquiry for 
 sixteen years, until in 1682, having obtained better data, he 
 successfully renewed it. " He had been mistaken in the 
 magnitude of the earth, and consequently in the distance of 
 the moon, which is determined by measurements of which the 
 earth's radius is the base." It was not, therefore a mistake as 
 to the law or nature of the forces concerned (namely, the law 
 of the inverse square and the identity of celestial with terrestrial 
 gravity), but as to the circumstances in which the agents (earth 
 and moon) were combined, that prevented his calculations 
 being verified. (Hist. 2nd. Sc. : VII. ii. 3.) 
 
 (3) One or more of the agents affecting the result may have 
 been overlooked and omitted from the estimate. Thus, an 
 attempt to explain the tides by taking account only of the 
 earth and the moon, will not entirely agree with the facts, since 
 the sun also influences the tides. This illustration, however, 
 shows that when the conclusion of a deductive explanation does 
 not entirely agree with the facts, it is not always to be inferred 
 that the reasoning is, properly speaking, wrong ; it may be 
 right as far as it goes, and merely inadequate. Hence (a) it is 
 often in just such cases that an opportunity occurs of applying 
 the Method of Residues, by discovering the agent that must 
 be allowed for in order to complete the explanation. And 
 (b) the investigation of a phenomenon is often designedly begun 
 upon an imperfect basis for the sake of simplicity ; the result 
 being regarded as a first approximation, to be afterwards 
 corrected by including one by one the remaining agents or 
 circumstances affecting the phenomenon, until the theory is 
 complete ; that is, until its agreement with the facts is satis- 
 factory. 
 
 (4) We may have included among the data of our reason- 
 ings agents or circumstances that do not exist or do not affect 
 the phenomenon in question. In the early days of science 
 purely fanciful powers were much relied upon : such as the 
 solid spheres that carried the planets and stars ; the influence 
 of the planets upon human destiny ; the tendency of every- 
 
234 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 thing to seek " its own place," so that fire rises to heaven, and 
 solids fall to the earth ; the " plastic virtue " of the soil, which 
 was once thought to have produced fossils. It may be said, 
 however, that when such conceptions hindered the progress of 
 explanation, it was not so much by vitiating the deductive 
 method as by putting men off from exact inquiries. More to 
 our present purpose were the supposed cataclysms, or extra- 
 ordinary convulsions of the earth, a belief in which long 
 hindered the progress of Geology. Again, in Biology, Psycho- 
 logy, and Sociology many explanations have depended upon 
 the doctrine that any improvement of structure or faculty 
 acquired by an individual may be inherited by his descendants : 
 as that, if an animal learns to climb trees, his offspring have a 
 greater aptitude for that mode of life ; that if a man tries to 
 be good, his children find it easier to be virtuous ; that if the 
 inhabitants of a district carry on cloth-work, it becomes easier 
 for each successive generation to acquire dexterity in that art. 
 But now the heritability of powers acquired by the individual 
 through his own efforts, is disputed; and, if the denial be 
 made good, all such explanations as the above must be 
 revised. 
 
 Clearly, then, if the premises of a deductive argument be 
 vitiated in any of these four ways, its conclusion will fail to 
 agree with the results of observation and experiment, unless, 
 of course, one kind of error happen to be cancelled by another 
 that is ' equal and opposite.' We now come to a variation of 
 the method of combining Induction with Deduction, so im- 
 portant as to require separate treatment. 
 
 5. The Inverse or Historical Method has of late years 
 become remarkably fruitful. When the forces determining a 
 phenomenon are too numerous, or too indefinite, to be com- 
 bined in a direct deduction, we. may begin by collecting an 
 empirical law of the phenomenon!^ that * the democracies of 
 City-states are arbitrary and fickle'), and then endeavour to 
 show by deductions from " the nature of the case," that is, 
 from a consideration of the circumstances and forces known 
 
COMBINED INDUCTION AND DEDUCTION 235 
 
 to be operative (of which, in the above instance, the most 
 important is sympathetic contagion), that such a law was to 
 be expected.Y Deduction is thus called in to verify a previous 
 >Iahietron~; whereas in the ' Physical Method ' a Deduction 
 Sr was verified by comparing it with an Induction or an experi- 
 ment ; hence the Method now to be discussed has been named 
 the Inverse Deductive Method. 
 
 But although it is true that, in such inquiries as we are now 
 dealing with, Induction generally takes the lead ; yet I cannot 
 think that the mere order in which the two logical processes 
 occur is the essential distinction between the two ways of 
 combining them. For, in the first place, in investigations of 
 any complexity both Induction and Deduction recur again 
 and again in whatever order may be most convenient ; and, in 
 the second place, the so-called ' inverse order ' is sometimes 
 resorted to in Astronomy and Physics. For example, Kepler'TX 
 Laws were first collected empirically from observations of the \ 
 planetary motions, and afterwards deduced by Newton from 
 the Law of Gravitation ; this, then, was the Inverse Method r^^ 
 but the result is something very different from any that can be 
 obtained by the Historical Method. The essential difference 
 . between the Physical and Historical Methods is that, in the 
 f f former, whether Direct or Inverse, the deductive process,\ 
 ^T owhen complete, amounts to exact demonstration; whereas, in ) 
 the latter, the deductions consist of qualitative reasonings, andy 
 ""the results are indefinite/'- j^They establish (i) a priori a 
 merely probable connection between the phenomena according 
 to the empirical law (say, between City-democracy and fickle 
 politics) ; (2) connect this with other historical or social 
 generalisations, by showing that they all alike flow from the 
 same causes, namely, from the nature of races of men under 
 certain social and geographical conditions; and (3) explain 
 why such empirical laws may fail, according to the differences 
 that prevail among races of men and among the conditions 
 under which they live. Thus, seeing how rapidly excitement 
 is propagated by the chatter, grimacing, and gesticulation of 
 
236 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 townsmen, it is probable enough that the democracy of a City- 
 state should be fickle (and arbitrary, because irresponsible). 
 A similar phenomenon of panic, sympathetic hope and despair, 
 is exhibited by every stock-exchange, and is not peculiar to 
 political life. And when political opinion is not manufactured 
 solely in the reverberating furnace of a city, fickleness ceases 
 to characterise Democracy ; and, in fact, is not found in 
 Switzerland or the United States, nor even in France so far as 
 politics depend upon the peasantry. 
 
 This is called the Historical Method, then, because it is 
 more useful than any other in explaining the movements of 
 history, and iri verifying the generalisations of political and 
 social science. We must not, however, suppose that its use is 
 confined to such studies. Only a ridiculous pedantry would 
 allot to each subject its own method and forbid the use of any 
 other ; as if it were not our capital object to establish truth by 
 any means. Wherever the forces determining a phenomenon 
 are too numerous or too indefinite to be combined in a 
 deductive demonstration, there the Historical Method is 
 likely to be useful ; and this seems often to be the case in 
 Geology and Biology, as well as in the Science of History, or 
 Sociology, and its various subsidiary studies. 
 
 Consider upon what causes historical events depend : 
 customs, character, and opinions of all the people concerned ; 
 the organisation of their government, and the character of 
 their religious institutions ; the development of industry among 
 them, of the military art, of fine art, literature and science ; 
 their relations, commercial, political and social with other 
 nations ; the physical conditions of climate and geographical 
 position amidst which they live. Hardly an event of importance 
 occurs in any nation that is not, directly or indirectly, influenced 
 by every one of mese circumstances, and that does not react 
 upon them. Now, from the nature of the Inductive Methods, 
 it is plain that, in such a complex and tangled situation as 
 history presents, a satisfactory employment of them is rarely 
 possible ; for they all require the actual or virtual isolation of 
 
COMBINED INDUCTION AND DEDUCTION 237 
 
 the phenomenon under investigation. They also require the 
 greatest attainable immediacy of connection between cause 
 and effect ; whereas the causes of social events may accumulate 
 during hundreds of years. Clearly, therefore, in collecting 
 empirical laws from history, only very rough inductions can be 
 hoped for, and we may have to be content with simple 
 enumeration. Hence the importance of supporting such laws 
 by deduction from the nature of the case, however faint a pro- 
 bability of the asserted connection is thereby raised ; and this 
 even if each law is valued merely for its own sake. Still more, 
 if anything worth the name of Historical Science is to be con- 
 structed, must a mere collection of such empiricisms fail to 
 content us; and the only way to give them a scientific 
 character is to show deductively their common dependence 
 upon various combinations of the same causes. Yet even 
 those who profess to employ the Historical Method often omit 
 the deductive half of it ; and of course ' practical politicians ' 
 boast of their entire contentment with what they call ' the facts. 1 
 Sometimes, however, politicians, venturing upon deductive 
 reasoning have fallen into the opposite error of omitting to 
 test their results by any comparison with the facts : arguing 
 from certain ' Rights of Man,' or * Interests of Classes,' or 
 * Laws of Supply and Demand,' that this or that event will 
 happen, or ought to happen, without troubling themselves to 
 observe whether it does happen or ever has happened. This 
 method of Deduction without any empirical verification, is 
 called by Mill the Geometrical ; and, plainly, it can be trust- 
 worthy only where there is no actual conflict of forces to be 
 considered. In pure mathematical reasoning about space, 
 time, and number, provided the premises and the reasoning 
 be correct, verification by a comparison with the facts may 
 be needless, because there is no possibility of counteraction. 
 But when we deal with actual causes, no computation of their 
 effects can be relied upon without comparing our conclusions 
 with the facts : not even in Astronomy and Physics, least of 
 all in Politics. 
 
238 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Burke, then, has well said that "without the guide and 
 light of sound, well-understood principles all our reasoning in 
 politics, as in everything else, would be only a confused jumble 
 of particular facts and details without the means of drawing 
 any sort of theoretical or practical conclusion " ; but that, on 
 the other hand, the statesman, who does not take account of 
 circumstances, infinite and infinitely combined, "is not 
 erroneous, but stark mad he is metaphysically mad" (On the 
 Petition of the Unitarians). There is, or ought to be, no 
 logical difference between the evidence required by a states- 
 man and that appealed to by a philosopher ; and since, as we 
 have seen, the combination of principles with circumstances 
 cannot, in solving problems of social science, be made with 
 the demonstrative precision that belongs to astronomical and 
 physical investigations, there remains the Historical Method as 
 above described. 
 
 Examples of the empirical laws ffom which this method 
 begins will occur to every one. They abound in histories, 
 newspapers, and political discussions, and are of all shades of 
 truth or half-truth : as that ' History consists in the biographies 
 of great men ' ; in other words, that the movements of society 
 are due to exceptional personal powers, not to general causes ; 
 That at certain epochs great men occur in groups ; That every 
 Fine Art passes through periods of development, culmination 
 and decline; That Democracies tend to change into Des- 
 potisms ; That the possession of power, whether by classes or 
 despots, corrupts the possessor ; That ' the governments most 
 distinguished for sustained vigour and abilities have generally 
 been aristocracies ' ; That l revolutions always begin in 
 hunger ' ; That civilisation is inimical to individuality ; That 
 the civilisation of the country proceeds from the town ; That 
 1 the movement of progressive societies has hitherto been a 
 movement from Status to Contract (/.*., from a condition in 
 which the individual's rights and duties depend on his caste, 
 or position in his family as slave, child, or patriarch, to a 
 condition in which his rights and duties are largely determined 
 
COMBINED INDUCTION AND DEDUCTION 239 
 
 by the voluntary agreements he enters into) ; and this last is 
 treated by Mr. Spencer as one aspect of the law first stated by 
 Comte, that the progress of societies is from the military to the 
 industrial state. 
 
 The deductive process we may illustrate by Mr. Spencer's 
 explanation a priori of the co-existence in the military state of 
 those specific characters, the inductive proof of which furnished 
 an illustration of the method of Agreement (ch. xvi. i). The 
 type of the military State involves the growth of the warrior 
 class, and the treatment of labourers as existing solely to 
 support the warriors ; the complete subordination of all indi- 
 viduals to the will of the despotic soldier-king, their property, 
 liberty and life being at the service of the State ; the regimen- 
 tation of society, not only for military, but also for civil 
 purposes ; the suppression of all private associations, etc. 
 Now all these characteristics arise from their utility for the 
 purpose of war, a utility amounting to necessity if war is the 
 State's chief purpose. For every purpose is best served when 
 the whole available force co-operates toward it : other things 
 equal, the bigger the army the better ; and to increase it, men 
 must be taken from industry until only just enough remain to 
 feed and equip the soldiers. As this arrangement is not to 
 everybody's taste, there must be despotic control; and this 
 control is most effective through regimentation by grades of 
 command. Private associations, of course, cannot live openly 
 in such a State, because they may have wills of their own and 
 are convenient for conspiracy. Thus the induction of charac- 
 teristics is verified by a deduction of them from the nature of 
 the case. 
 
 r 6. The greater indefiniteness of the Historical, compared 
 with the Physical Method, both in its inductions and in its 
 deductions, makes it, perhaps, even more difficult to work 
 with. It wants much sagacity and more sincerity; for the 
 demon of Party is generally too much with us. Our first care 
 should be to make the empirical law as nearly true as pos- 
 sible, collecting as many as we can of the facts which the law 
 
24 o LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 is supposed to generalise, and examining them according to the 
 canons of Induction, with due allowance for the imperfect 
 applicability of those canons to such complex, unwieldy, and 
 indefinite instances. 
 
 Turning to the examples of such laws given above, it is 
 clear that in some cases no pains have been taken to examine 
 the facts. What is the inductive evidence that Democracies 
 change into Despotisms ; that revolutions always begin in 
 hunger ; or that civilisation is inimical to individuality ? Even 
 Mill's often quoted saying, " that the governments remarkable 
 in history for; sustained vigour and ability have generally been 
 aristocracies," is oddly over-stated. For if you turn to the 
 passage (Rep. Gov. chap, vi.), the next sentence tells you that 
 such governments have always been aristocracies of public 
 functionaries ; and the next sentence but one restricts, appa- 
 rently, the list of such remarkable governments to two Rome 
 and Venice. Whence, then, comes the word " generally " into 
 Mill's law? 
 
 As to deducing our empirical law from a consideration of 
 the nature of the case, it is obvious that we ought (a) to 
 take account of all the important conditions; (b) to allow 
 weight to them severally in proportion to their importance; 
 and (c) not to include in our estimates any condition which we 
 cannot show to be probably present and operative. Thus the 
 Great-Man-Theory of history must surely be admitted to 
 assign a real condition of national success. The great man 
 organises, directs, inspires : is that nothing ? On the other 
 hand, to recognise no other condition of national success is the 
 manifest frenzy of a mind in the mythopoeie age. We must 
 allow the great man his due weight, and then inquire into the 
 general conditions that (a) bring him to birth in one nation 
 rather than another, and (b) give him his opportunity. 
 
 Mill's explanation of the success of the aristocratic govern- 
 ments of Rome and Venice is, that they were, in fact, bureau- 
 cracies; that is to say, their members were trained in the 
 science and art of administration and command. Here, again, 
 
COMBINED INDUCTION AND DEDUCTION 241 
 
 we have, no doubt, a real condition ; but is it the only one ? 
 The public mind, which little relishes the scaling down of 
 Mill's original law to those two remote cases, is persuaded that 
 an aristocracy is the depository of hereditary virtue, especially 
 with reference to government, and would at once ascribe to 
 this circumstance the greater part of the success of any aristo- 
 cratic government. Now, if the effects of training are inherited, 
 they must, in an hereditary aristocracy, increase the energy of 
 the cause assigned by Mill ; but, if not, such heredity is a con- 
 dition "not present or not operative." Still, if families are 
 ennobled for their extraordinary natural powers of administra- 
 tion or command (and this sometimes happens), it is agreed on 
 all hands that innate qualities are heritable ; at least, if care be 
 taken to intermarry with families similarly distinguished, and if 
 by natural or artificial selection all the failures among the off- 
 spring be eliminated. The Spartans had some crude notion of 
 both these precautions ; and if such measures had been widely 
 adopted, we might deduce from the doctrine of heredity a pro- 
 bability in favour of Mill's original proposition, and thereby 
 verify it in its generality, if it could be collected from the facts. 
 The Historical Method may be further illustrated by the 
 course adopted in that branch of Social Science which has been 
 found susceptible of the most extensive independent develop- 
 ment, namely, Economics. First, by way of contrast, I should 
 say that the general, abstract, or theoretical treatment of 
 Economics is according to the Physical Method ; because, as 
 Mill explains, although the phenomena of industry are no 
 doubt influenced, like other social affairs, by all the other cir- 
 cumstances of Society, government, religion, war, art, etc. ; yet, 
 where industry is most developed, as in England and the 
 United States, certain special conditions affecting it are so much 
 the most important that, for the purpose at least of a first out- 
 line of the science, they may conveniently be considered as the 
 only ones. These conditions are : (i) the general disposition 
 of men to obtain wealth with as little trouble as possible, and 
 (2) to spend it so as to obtain the greatest satisfaction of their 
 
 Q 
 
242 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 various desires ; (3) the facts that determine population, and 
 (4) the tendency of extractive industry, when pushed beyond a 
 certain limit without any improvement in the industrial arts, to 
 yield " diminishing returns." From these premises it is easy to 
 infer the general laws of prices, of wages and interest (which 
 are the prices of labour and of the use of capital), and of rent ; 
 and it remains to verify these by comparing them with the facts 
 in each case ; and (if they fail to agree with the facts) to amend 
 them, according to the Method of Residues, by taking account 
 of those influential conditions which were omitted from the first 
 draft of the theory. 
 
 Whilst, h6wever, this is usually the procedure of those 
 inquirers who have done most to give Economics its scientific 
 character, to insist that no other plan shall be adopted would 
 be sheer pedantry ; and Dr. Keynes has shown, in his Scope 
 and Method of Political Economy, that Mill has him self some- 
 times solved economic problems by the Historical Method. 
 With an analysis of his treatment of Peasant Proprietorship in 
 Book II., cc. 7 and 8 of his Principles of Political Economy, 
 we may close this chapter. Mill first shows inductively, by 
 collecting evidence from Switzerland, Germany, Norway, 
 Belgium, and France, that peasant proprietors are super- 
 humanly industrious, intelligent cultivators, and generally 
 intelligent men, prudent, temperate, and |ndee^entand that 
 they exercise self-control in avoiding inrpTovldSnt marriages. 
 This group of empirical generalisations as to the character of 
 peasant proprietors he then deduces from the nature of the 
 case : their industry, he says, is a natural consequence of the 
 fact that, however much they produce, it is all their own ; they 
 cultivate intelligently, because for generations they have given 
 their whole mind to it; they are generally intelligent men, 
 because the variety of work involved in small farming, requir- 
 ing foresight and calculation, necessarily promotes intelligence ; 
 they are prudent, because they have something to save, and by 
 saving can improve their station and perhaps buy more land ; 
 they are temperate, because intemperance is incompatible with 
 
 
COMBINED INDUCTION AND DEDUCTION 243 
 
 industry and prudence ; they are independent, because secure 
 of the necessaries of life, and from ( having property to fall back 
 upon ; and they avoid improvidence in marriage, because the 
 extent and fertility of their fields is always plainly before them, 
 and therefore how many children they can maintain is easily 
 calculated. The worst of them is that they work too hard and 
 deny themselves too much : but, over the greater part of the 
 world, other peasantry work too hard ; though they can scarcely 
 be said to deny themselves too much, since all their labour for 
 others brings them no surplus to squander upon self-indulgence. 
 
CHAPTER XVIII 
 HYPOTHESES 
 
 i. An Hypothesis, sometimes employed instead of a 
 known law* as a premise in the deductive investigation of 
 nature, is denned by Mill as " any supposition which we make 
 (either without actual evidence, or on evidence avowedly 
 insufficient) in order to endeavour to deduce from it con- 
 clusions in accordance with facts which are known to be 
 real ; under the idea that if the conclusions to which the 
 hypothesis leads are known truths, the hypothesis itself either 
 must be, or at least is likely to be, true." The deduction of 
 known truths from an hypothesis is its Verification ; and when 
 this has been accomplished in a good many cases, and there 
 are no manifest failures, the hypothesis is often called a 
 Theory ; though this term is also used for the whole system of 
 laws of a certain class of phenomena, as when Astronomy is 
 called the ' theory of the heavens.' Between hypothesis and 
 theory in the former sense no distinct line can be drawn ; for 
 the complete proof of a certain speculation may take a long 
 time, and meanwhile the gradually accumulating evidence pro- 
 duces in different minds very different degrees of satisfaction ; 
 so that the sanguine begin to talk of ' the theory,' whilst the 
 melancholic continue to call it l the hypothesis.' 
 
 An Hypothesis may be made concerning (i) an Agent, such 
 as the ether ; or (2) a Collocation, such as the plan of our solar 
 system whether geocentric or heliocentric ; or (3) a Law of 
 an agent's operation, as that light is transmitted by a wave- 
 motion. 
 
HYPOTHESES 245 
 
 The received explanation of Light involves both an agent, 
 the ether, as an all-pervading elastic fluid, and also the law of 
 its operation as transmitting light in waves of definite form 
 and lengths, with definite velocity. The agreement between 
 the calculated results of this complex hypothesis and the 
 observed phenomena of light is the chief part of the verifica- 
 tion, which has now been so successfully accomplished that we 
 generally hear of the * Undulatory Theory.' Sometimes a new 
 agent only is proposed ; as the planet Neptune was at first 
 assumed to exist in order to account for perturbations in the 
 movements of Uranus, influencing it according to the already 
 established law of Gravitation. Sometimes the agents are 
 known, and only the law of their operation is hypothetical, as 
 was at first the case with the law of Gravitation itself. For the 
 agents, namely, Earth, falling bodies on the Earth, Moon, Sun, 
 and planets were manifest ; and the hypothesis was that their 
 motions might be due to their attracting one another with a 
 force proportional to the product of their masses and inversely 
 proportional to the squares of the distances between them. In 
 the Ptolemaic Astronomy, again, there was an hypothesis as to 
 the collocation of the heavenly bodies (namely, that our Earth 
 was the centre of the universe, and that Moon, Sun, planets 
 and stars revolved around her) : in the early form of the system 
 there was also an hypothesis concerning agents upon which 
 this arrangement depended (namely, the crystalline spheres in 
 which the heavenly bodies were fixed, though these were after- 
 wards declared to be imaginary) ; and an hypothesis concerning 
 the law of operation (namely, that circular motion is the most 
 perfect and eternal, and therefore proper to celestial things). 
 
 Hypotheses, of course, are by no means confined to the 
 physical sciences : we all make them freely in private life. In 
 searching for anything, we guess where it may be before going 
 to look : the search for the North Pole is likewise guided by 
 hypotheses how best to get there. In estimating the characters 
 or explaining the conduct of acquaintances or of public men, 
 we frame hypotheses as to their dispositions and principles. 
 
246 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 * That we should not impute motives ' is a peculiarly absurd 
 maxim, as there is no other way of understanding human life. 
 To impute bad motives, indeed, when good are just as pro- 
 bable, is to be wanting in the scientific spirit, which views 
 every subject in 'a dry light.' Nor can we help 'judging 
 others by ourselves ' ; for self-knowledge is the only possible 
 starting-point when we set out to interpret the lives of others. 
 But to understand the manifold combinations of which the 
 elements of character are susceptible, and how these are deter- 
 mined by the breeding of race or family under various con- 
 ditions, and again by the circumstances of each man's life, 
 demands an extraordinary union of sympathetic imagination 
 with scientific habits of thought. Such should be the equip- 
 ment of the historian, who pursues the same method of 
 hypothesis when he attempts to explain (say) the state of 
 parties upon the Exclusion Bill, or the policy of Louis XI. 
 Problems such as the former of these are the easier ; because, 
 amidst the compromises of a party, personal peculiarities 
 obliterate one another, and expose a simpler scheme of human 
 nature with fewer fig-leaves. Much more hazardous hypo- 
 theses are necessary in interpreting the customs of savages, and 
 the feelings of all sorts of animals. Thus the method of our 
 every-day thoughts is identical with that of our most refined 
 speculations. Literary criticisms, again, abound with hypo- 
 theses : e.g.) as to the composition of the Homeric poems, the 
 order of the Platonic dialogues, the authorship of the Caed- 
 monic poems, or the Ossianic, or of the letters of Junius. And 
 in all these cases we have to ask whether the hypothesis 
 accounts for the facts. 
 
 2. It follows from the definition of an hypothesis that 
 none is of any use that does not admit of verification (proof or 
 disproof), by comparing the results that may be deduced from 
 it with facts or laws. If so framed as to elude every attempt 
 to test it by facts, it can never be proved by them nor add 
 anything to our understanding of them. 
 
 Suppose that a conjurer asserts that his table is controlled 
 
 
HYPOTHESES 247 
 
 by the spirit of your deceased relative of virtuous memory, and 
 makes it rap out an account of some domestic adventure that 
 could hardly have been expected to be within a stranger's 
 knowledge. So far good. Then, trying again, the table raps 
 out some absurd blunder about your family history which the 
 deceased relative could not have committed ; but the conjurer 
 explains that 'a lying spirit' sometimes possesses the table. 
 Plainly, this amendment of the hypothesis makes it equally 
 compatible with success and with failure. It has been said of a 
 certain supposed biological agent, "It would seem that by a 
 little skilful manipulation it can be made to account for any- 
 thing that has ever been observed, or is ever likely to be 
 observed. It is one of those convenient invisibles that will do 
 anything that you desire." And whatever the justice of this 
 criticism, it shows a sound conception of what is to be required 
 of an hypothesis. Very similar was the case of the Ptolemaic 
 Astronomy : by perpetual tinkering, its hypothesis was made 
 to correspond with accumulating observations of the celestial 
 motions ; so that, until the telescope was invented, it may be 
 said to have been almost unverifiable. Consider, again, the 
 sociological hypothesis, that civil order was at first founded on 
 a Contract which remains binding upon all mankind : this is 
 reconcilable with the most opposite institutions. For we have 
 no record of such an event; and if the institutions of one State 
 (say the British) include ceremonies, such as the coronation 
 oath and oath of allegiance, which may be remnants of an 
 original contract, they may nevertheless be of comparatively 
 recent origin : whereas if the institutions of another State (say 
 the Russian) contain nothing that admits of similar interpreta- 
 tion, yet traces of the contract once existing may long since 
 have been obliterated. Moreover, the actual contents of the 
 contract not having been preserved, every adherent of this 
 hypothesis supplies them at his own discretion, * according to 
 the dictates of Reason ' ; and so one derives from it the duty 
 of passive obedience, and another with equal cogency estab- 
 lishes the right of rebellion. 
 
248 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 To be verifiable, then, an hypothesis must be definite; if 
 somewhat vague in its first conception (which is reasonably to 
 be expected), it must be made definite in order to be put to 
 the proof. But, except this condition of verifiability, and 
 denniteness for the sake of verifiability, without which a 
 proposition does not deserve the name of an hypothesis, it 
 seems inadvisable to lay down rules for a ' legitimate ' hypo- 
 thesis. 
 
 The epithet is infelicitous. It suggests that the Logician 
 makes rules for scientific inquirers ; whereas his business is to 
 discover the principles which they, in fact, employ in what are 
 acknowledged to be their most successful investigations. If 
 he did make rules for them, and they treated him seriously, 
 they might be discouraged in the exercise of that liberty of 
 hypothesising which is the condition of all originality ; whilst 
 if they paid no attention to him, he must suffer some loss of 
 dignity. To say that a ' legitimate hypothesis ' must explain 
 all the facts, at least in the department for which it is invented, 
 is decidedly discouraging. No doubt it may be expected to 
 do this in the long run when (if ever) it is completely 
 established ; but this may take a long time : Is it meanwhile 
 illegitimate? Or can this adjective be applied to Newton's 
 corpuscular theory of light, even though it has failed to explain 
 all the facts ? 
 
 3. Given a verifiable hypothesis, however, what constitutes 
 proof or disproof ? 
 
 (i) If a new agent be proposed, it is desirable that we 
 should be able directly to observe it, or at least to obtain 
 some evidence of its existence of a different kind from the 
 very facts which it has been invented to explain. Thus, in the 
 discovery of Neptune, after the existence of such a planet 
 outside the orbit of Uranus had been conjectured (to account 
 for the movement of the latter), the place in the heavens which 
 such a body should occupy at a certain time was calculated, 
 and there by means of the telescope it was actually seen. 
 
 Agents, however, are assumed and reasoned upon very 
 
HYPOTHESES 249 
 
 successfully which, by their nature, never can be objects of 
 perception : such are the atoms of Chemistry and the ether 
 of Optics. But the severer Methodologists regard them with 
 suspicion: Mill was never completely convinced about the 
 ether. He was willing, however, to make the most of the 
 evidence that has been adduced as indicating a certain property 
 of it distinct from those by which it transmits radiation, namely, 
 mechanical inertia, whereby it has been supposed to retard the 
 career of the heavenly bodies, as shown especially by the 
 history of Encke's comet. This comet returned sooner than it 
 should, as calculated from the usual data ; the difference was 
 ascribed to the influence of a resisting medium in reducing the 
 extent of its orbit ; and such a medium may be the ether. If 
 this conjecture (now of less credit) should gain acceptance, 
 the ether might be regarded as a vera causa (that is, a condition 
 whose existence may be proved independently of the pheno- 
 mena it was intended to explain), in spite of its being excluded 
 by its nature from the sphere of direct perception. 
 
 After all, it is very difficult to say what is within the sphere 
 of direct perception. Waiving this question, however, Science 
 is not a way of perceiving things, but essentially a way of 
 thinking about them. It starts, indeed, from perception and 
 returns to it, and its thinking is controlled by the analogies of 
 perception. Atoms and ether are thought about as if they 
 could be seen or felt, not as noumena ; and if they are found 
 necessary to connect and explain perceptions, those who can 
 understand the explanation will no doubt be reconciled to 
 them. For most men of Science, I suppose, their existence is 
 as good as axiomatic. 
 
 On the other hand, a great many agents, once assumed in 
 order to explain phenomena, have since been explained away. 
 Of course, a fact can never be ' explained away ' : the phrase 
 is properly applicable to the fate of erroneous hypotheses, 
 when, not only are they disproved, but others are established in 
 their places, Of the Aristotelian spheres, which were supposed 
 to support and translate sun, moon and planets, no trace has 
 
250 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 ever been found : they would have been very much in the way of 
 the comets. Phlogiston, again, an agent much in favour with 
 the earlier Chemists, was found, Whewell tells us, when their 
 theories were tested by exact weighing, to be not merely non- 
 existent but a minus quantity ; that is to say, it required the 
 assumption of its absolute lightness " so that it diminished the 
 weight of the compounds into which it entered.'* These agents, 
 then, the spheres and phlogiston, have been explained away, 
 and instead of them we have the laws of motion and oxygen. 
 
 (2) Whether the hypothetical agent be perceptible or not, it 
 cannot be established, nor can a supposed law of such an 
 agent be accepted as sufficient to the given inquiry, unless it 
 is adequate to account for the effects which it is called upon to 
 explain, at least so far as it pretends to explain them. The 
 general truth of this is sufficiently obvious, since to explain the 
 facts is the purpose of an hypothesis ; and we have seen that 
 Newton gave up his hypothesis that the moon was a falling 
 body, as long as he was unable to show that the amount of its 
 deflection from a tangent (or its fall) in a given time, was 
 exactly what it should be, if the Moon was controlled by the 
 same force as falling bodies on the Earth. 
 
 It is worth while, however, to observe the limitations to 
 which this canon is subject. In the first place, it says that, 
 unless adequate to explain the facts in question, an hypothesis 
 cannot be 'established* ': but, for all that, such an hypothesis 
 may be a very promising one, not to be hastily rejected, since 
 it may take a very long time fully to verify an hypothesis. 
 Some facts may not be obtainable that are necessary to show 
 the connection of others : as, for example, the hypothesis that 
 all species of animals have arisen from earlier ones by some 
 process of gradual change, can be only imperfectly verified by 
 collecting the fossil remains of extinct species, because immense 
 depths and expanses of fossiliferous strata have been destroyed. 
 Or, again, the general state of culture may be such as to pre- 
 vent men from tracing the consequences of an hypothesis ; for 
 which reason, apparently, the doctrine that the Sun is the 
 
 
HYPOTHESES 251 
 
 centre of our planetary system remained a discredited hypo- 
 thesis for 2000 years. Surely, this should instruct us not to 
 regard an hypothesis as necessarily erroneous or illegitimate 
 merely because we cannot yet see how it works out : but 
 neither can we in such a case regard it as established, unless 
 we take somebody's word for it. 
 
 Secondly, the canon says that an hypothesis is not estab- 
 lished, unless it accounts for the phenomena so far as it 
 professes to. But it implies a complete misunderstanding to 
 assail a doctrine for not explaining what lies beyond its 
 scope. Thus, it is no objection to a theory of the origin of 
 species, that it does not explain the origin of life : it does not 
 profess to. For the same reason, it is no objection to the 
 theory of Natural Selection, that it does not account for the 
 variations which selection presupposes. But such objections 
 might be perfectly fair against a general doctrine of Evolu- 
 tion. 
 
 An interesting case in Mr. Wallace's Darwinism (chap, x.) 
 will illustrate the importance of attending to the exact condi- 
 tions of an hypothesis. He says that in those groups of 
 " birds that need protection from enemies," "when the male is 
 brightly coloured and the female sits exposed on the nest, she 
 is always less brilliant and generally of quite sober and protec- 
 tive hues " ; and his hypothesis is, that these sober hues have 
 been acquired or preserved by Natural Selection, because it is 
 important to the family that the sitting bird should be incon- 
 spicuous. Now to this it might be objected that in some birds 
 both sexes are brilliant or conspicuous ; but the answer is that 
 the female of such species does not sit exposed on the nest ; for 
 the nests are either domed over, or made in a hole ; so that 
 the sitting bird does not need protective colouring. If it be 
 objected, again, that some sober-coloured birds build domed 
 nests, it may be replied that the proposition ' All conspicuously 
 coloured birds are concealed in the nest,' is not to be converted 
 simply into ' All birds that sit concealed in the nest are con- 
 spicuously coloured.' In the cases alleged the domed nests 
 
252 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 are a protection against the weather, and the sober colouring is 
 a general protection to the bird, which inhabits an open 
 country. It may be urged, however, that jays, crows, and 
 magpies are conspicuous birds, and yet build open nests : but 
 these are aggressive birds, not needing protection from enemies. 
 Finally, there are cases, it must be confessed, in which the 
 female is more brilliant than the male, and which yet have open 
 nests ! Yes : but then the male sits upon the eggs, and the female 
 is stronger and more pugnacious ! 
 
 Thus every objection is shown to imply some inattention to 
 the conditions of the problem ; and in each case it may be said, 
 exceptio probat regulam the exception tests the rule. (Of 
 course, the usual translation " proves the rule," in the restricted 
 modern sense of " prove," is absurd.) That is to say, it appears 
 on examination : (i) that the alleged exception is not really 
 one, and (2) that it stands in such relation to the rule as to 
 confirm it. For, you will notice that, to all the above objec- 
 tions it is replied that, granting the phenomenon in question 
 (special protective colouring for the female) to be absent, the 
 alleged cause (need of protection) is also absent ; so that the 
 proof is, by means of the objections, extended, from being one 
 by the method of Agreement, into one by the Double Method. 
 Unfortunately, it is not always that an assailant's neglect to 
 observe the exact conditions of the doctrine in dispute can be 
 turned to such good account. 
 
 Thirdly, an hypothesis originally intended to account for 
 the whole of a phenomenon and failing to do so, though it 
 cannot be established in that sense, may nevertheless contain 
 an essential part of the explanation. 
 
 Thus the Neptunian Hypothesis in Geology, was an attempt 
 to explain the formation of the Earth's outer crust, as having 
 been deposited from an universal ocean of mud. In the 
 progress of the science other causes, seismic, fluvial and atmo- 
 spheric, have been found necessary in order to complete the 
 theory of the history of the Earth's crust : but it remains true 
 that the stratified rocks, and some that have lost their straiified 
 
 
HYPOTHESES 253 
 
 character, were originally deposited under water. Inadequacy, 
 therefore, is not a reason for entirely rejecting an hypothesis or 
 treating it as illegitimate. 
 
 (3) Granting that the hypothetical cause is real and ade- 
 quate, the investigation is not complete. Agreement with the 
 facts is a very persuasive circumstance, the more so the more 
 extensive the agreement, especially if no exceptions are known. 
 Still, if this is all that can be said in favour of an hypothesis, it 
 amounts to proof by the method of Agreement only ; it does 
 not exclude the possibility of vicarious causes ; and if the 
 hypothesis proposes a new agent that cannot be directly 
 observed, an equally plausible hypothesis about another 
 imagined agent may perhaps be invented. 
 
 According to Whewell, it is a strong mark of the truth of an 
 hypothesis when it agrees with distinct inductions concerning 
 different classes of facts, and he calls this the * Consilience of 
 Inductions,' because they jump together in the unity of the 
 hypothesis. It is particularly convincing when this Consilience 
 takes place easily and naturally without necessitating the 
 mending and tinkering of the hypothesis ; and he cites the 
 Theory of Gravitation and the Undulatory Theory of Light as 
 the most conspicuous examples of such ever-victorious hypo- 
 theses. Thus, Gravitation explains the fall of bodies on the 
 Earth, and the orbits of the planets and their satellites ; it 
 applies to the tides, the comets, the double stars, and gives 
 consistency to the Nebular Hypothesis, whence flow important 
 Geological inferences ; and all this without any need of amend- 
 ment. Nevertheless, Mill, with his rigorous sense of duty, 
 points out, that an Induction is merely a proposition concerning 
 many facts, and that a consilience of Inductions is merely a 
 multiplication of the facts explained; and that, therefore, if 
 the proof is merely Agreement in each case, there can be no 
 more in the totality : the possibility of vicarious causes is not 
 precluded; and the hypothesis may, after all, describe an 
 accidental circumstance. 
 
 Whewell also laid great stress upon Prediction as a mark of 
 
254 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 a true hypothesis. Thus, Astronomers predict eclipses, 
 occultations, transits, long beforehand with the greatest pre- 
 cision ; and the prediction of the place of Neptune by sheer 
 force of deduction is one of the most astonishing things in the 
 history of science. Yet Mill persisted in showing that a pre- 
 dicted fact is only another fact, and that it is really not very 
 extraordinary that an hypothesis that happens to agree with 
 many known facts should also agree with some still undis- 
 covered. And, I must say, there seems to be some illusion in 
 the common belief in the probative force of prediction. Pre- 
 diction surprises us, puts us off our guard, and renders per- 
 suasion easy,; in this it resembles the force of an epigram in 
 rhetoric. But cases can be produced in which erroneous 
 hypotheses have led to prediction ; and Whewell himself pro- 
 duces them. Thus, he says that the Ptolemaic theory was 
 confirmed by its predicting eclipses and other celestial pheno- 
 mena, and by leading to the construction of Tables in which 
 the places of the heavenly bodies were given at every moment 
 of time. Similarly, both Newton's theory of Light and the 
 Chemical doctrine of Phlogiston led to predictions which came 
 true. 
 
 What sound method demands in the proof of an hypip- 
 thesis, then, is not merely that it be shown to agree with the 
 facts, but that every other hypothesis be excluded. This, to 
 be sure, may be beyond our power ; there may in some cases 
 be no such negative proof except the exhaustion of human 
 ingenuity in the course of time. 
 
 The present theory of colour has in its favour the failure of 
 Newton's corpuscular hypothesis and of Goethe's anti-mathe- 
 matical hypothesis ; but the field of conjecture remains open. 
 On the other hand, Newton's proof that the solar system is 
 controlled by a central force, he supported by the demonstra- 
 tion that a force having any other direction could not have 
 results agreeing with Kepler's second law of the planetary 
 motions, namely, that, as a planet moves in its orbit, the areas 
 described by a line drawn from the sun to the planet are 
 
HYPOTHESES 255 
 
 proportional to the times occupied in the planet's motion. 
 When a planet is nearest to the sun, the area described by such 
 a line is least for any given distance traversed by the planet ; 
 and then the planet moves fastest : when the planet is furthest 
 from the sun, the area described by such a line is greatest for 
 an equal distance traversed ; and then the planet moves slowest. 
 This law may be deduced from the hypothesis of a central 
 fo^:e, but not from any other ; the proof, therefore, as Mill 
 says, satisfies the method of Difference. 
 
 Apparently, to such completeness of demonstration certain 
 conditions are necessary : the possibilities must lie between 
 alternatives, such as A or not-A, or amongst some definite list 
 of cases that may be exhausted, such as equal, greater or less. 
 He whose hypothesis cannot be brought to such a definite 
 issue, must try to refute whatever other hypotheses are offered, 
 and naturally he will attack first the strongest rivals. With 
 this object in view he looks about for a " crucial instance," 
 that is, an observation or experiment that stands like a cross 
 (sign-post) at the parting of the ways to guide us into the right 
 way, or, in plain words, an instance that can be explained by 
 one hypothesis but not by another. 
 
 Thus the phases of Venus, similar to those of the Moon, but 
 concurring with great changes of apparent size, when dis- 
 covered by Galileo, presented a crucial instance in favour of 
 the Copernican hypothesis, as against the Ptolemaic, so far at 
 least as to prove that Venus revolved around the Sun inside 
 the orbit of the Earth. Foucault's experiment determining the 
 velocity of Light (cited in the last chapter) was at first intended 
 as an experimentum cruets to decide between the corpuscular 
 and undulatory theories ; and answered this purpose, by show- 
 ing that the velocity of a beam passed through water was less 
 than it should be by the former, but in agreement with the 
 latter doctrine (Deschanel : 813). 
 
 Perhaps experiments of this decisive character are com- 
 monest in Chemistry : chemical tests, says Herschel, " are 
 almost universally crucial experiments." The following is 
 
256 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 abridged from Playfair (Encycl Met., Diss. III.): The 
 Chemists of last century observed that metals were rendered 
 heavier by calcination ; and there were two ways of accounting 
 for this : either something had been added in the process, 
 though what, they could not imagine ; or, something had been 
 driven off that was in its nature light, namely, Phlogiston. To 
 decide between these hypotheses, Lavoisier hermetically sealed 
 some tin in a glass retort, and weighed the whole. He then 
 heated it ; and, when the tin was calcined, weighed the whole 
 again, and found it the same as before. No substance, there- 
 fore, either light or heavy, had escaped. Further, when the 
 retort was cooled and opened, the air rushed in, showing that 
 some of the air formerly within had disappeared or lost its 
 elasticity. On weighing the whole again, its weight was now 
 found to have increased by ten grains ; so that ten grains of 
 air had entered when it was opened. The calcined tin was 
 then weighed separately, and proved to be exactly ten grains 
 heavier than when it was placed in the retort ; showing that 
 the ten grains of air that had disappeared had combined with 
 the metal during calcination. This experiment, then, decided 
 against Phlogiston, and led afterwards to an analysis of common 
 air confirming Priestley's discovery of oxygen. 
 
 (4) An hypothesis must agree with the rest of the laws of 
 Nature ; and, if not itself of the highest generality, must be 
 derivable from primary laws (chap. xix. i). 
 
 Thus gravitation and the diffusion of heat, light and sound 
 from a centre, all follow the " law of the inverse square," and 
 agree with the relation of the radius of a sphere to its surface. 
 Any one who should think that he had discovered a new 
 central force would naturally begin to investigate it on the 
 hypothesis that it conformed to the same law as gravitation or 
 light. A Chemist, again, who should believe himself to have 
 discovered a new element, would expect it to fill one of the 
 vacant places in the "Periodic System." Conformity, in such 
 cases, is strong confirmation, and disagreement is an occasion 
 of misgivings. 
 
HYPOTHESES 257 
 
 A narrower hypothesis, as * that the toad's ugliness is pro- 
 tective ', would be supported by the general theory of protective 
 colouring and figure, and by the still more general theory of 
 Natural Selection, if facts could be adduced to show that the 
 toad's appearance does really deter its enemies. Such an 
 hypothesis resembles an Empirical Law in its need of deriva- 
 tion (chap. xix. i, 2). If underivable from, or irreconcil- 
 able with, known laws, it is a mere conjecture or prejudice. 
 The absolute levitation of Phlogiston, in contrast with the 
 gravitation of all other forms of matter, was discreditable to 
 that supposed agent. That Macpherson should have found 
 the Ossianic poems extant in the Gaelic memory, was contrary 
 to the nature of oral tradition; except where tradition is 
 organised, as it was for ages among the Brahmins. The sug- 
 gestion that xanthochroid Aryans were " bleached " by exposure 
 during the glacial period, does not agree with Wallace's doc- 
 trine concerning the colouration of Arctic animals. That our 
 forefathers being predatory, like bears, white variations amongst 
 them were then selected by the advantage of concealment, is a 
 more plausible hypothesis. 
 
 Although, then, the consilience of Inductions or Hypo- 
 theses is not a sufficient proof of their truth, it is still a 
 condition of it ; nonconsilience is a suspicious circumstance, 
 and resilience (so to speak), or mutual repugnance, is fatal to 
 one or all. 
 
 4. We have now seen that an hypothesis must, to deserve 
 the name in science, be verifiable and therefore definite ; and 
 that to establish itself as a true theory, it must present some 
 symptom of reality, and be adequate and unconditional and in 
 harmony with the system of experience. Thus guarded, hypo- 
 theses seem harmless enough; but, certainly, people some- 
 times have a strong prejudice against them, as against a tribe 
 of savages without government, or laws, or any decent regard 
 for vested interests. It is well known, too, that Bacon and 
 Newton disparaged them. But Bacon in his examples of an 
 investigation according to his own method, is obliged after a 
 
 B 
 
258 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 preliminary classification of facts, to resort to an hypothesis, 
 calling it permissio intellectus, interpretatio inchoata or vinde- 
 miatio prima. And what Newton meant by hypotheses non 
 fingo, seeing that he invented so many, is itself fair game for 
 an hypothesis. At any rate, it is plain that hypotheses are 
 essential aids to discovery : indeed, speaking generally, 
 deliberate investigation depends wholly upon the use of 
 them. 
 
 It is true that we may sometimes observe a train of events 
 that chances to pass before us, either when we are idle or 
 engaged with some other inquiry, and so obtain a new glimpse 
 of the course of nature. ^Or we may try experiments hap- 
 hazard, and watch the results. But, even in these cases, 
 before our new notions can be considered knowledge, they 
 must be definitely framed hi hypotheses and reobserved or 
 experimented upon, with whatever calculations or precautions 
 may be necessary to ensure accuracy or isolation. As a rule, 
 however, when inquiring deliberately into the cause of an 
 event, whether in nature or in history, we first reflect upon the 
 circumstances of the case and compare it with similar ones 
 previously investigated, and so are guided by a preconception 
 more or less definite of * what to look for/ what the cause is 
 likely to be, that is, by an hypothesis. Then, if our precon- 
 ception is justified, or something which we observe leads to a 
 new hypothesis, either we look for other instances to satisfy 
 the canons of Agreement : or (if the matter admits of experi- 
 ment) we endeavour, under known conditions according to the 
 canons of Difference and Variations, to reproduce the event 
 by means of that which our hypothesis assigns as the cause ; or 
 we draw remote inferences from our hypothesis, and try to test 
 these by the Inductive Canons. 
 
 If we argue from an hypothesis and express ourselves 
 formally, it will usually appear as the Major Premise ; but this 
 is not always the case. In extending ascertained laws to fresh 
 cases, the Minor Premise may be an hypothesis, as in testing 
 the chemical constitution of any doubtful substance, such as a 
 
 
HYPOTHESES 259 
 
 piece of ore. Some solution or preparation, A, is generally 
 made which (it is known) will, on the introduction of a certain 
 agent, B, give a reaction, C, if the preparation contains a given 
 substance, X. The major premise, then, is the law of 
 reaction 
 
 Whenever A is X, if treated with B it is C. 
 The minor premise is an hypothesis that the preparation con- 
 tains X. An experiment then treats A with B. If C results, a 
 probability is raised in favour of the hypothesis that A is X ; 
 or a certainty, if we know that C results on that condition 
 only. 
 
 So important are hypotheses to science, that Whewell insists 
 that they have often been extremely valuable even though 
 erroneous. Of the Ptolemaic system he says, " We can hardly 
 imagine that Astronomy could, in its outset, have made so great 
 a progress under any other form." It served to connect men's 
 thoughts on the subject and to sustain their interest in working 
 it out; by successive corrections "to save appearances," it 
 attained at last to a descriptive sort of truth, which was of 
 great practical utility; it also occasioned the invention of 
 technical terms, and, in general, digested the whole body of 
 observations and prepared them for assimilation by a better 
 hypothesis in the fulness of time. Whewell even defends 
 the maxim that " Nature abhors a vacuum," as having 
 formerly served to connect many facts that differ widely in 
 their first aspect. "And in reality is it not true," he asks, 
 " that nature does abhor a vacuum, and does all she can to 
 avoid it ? " Let no forlorn cause despair of a champion ! 
 Yet no one has accused Whewell of Quixotry; and the 
 sense of his position is that the human mind, of course, is a 
 rather feeble affair, which can hardly begin thinking except 
 with blunders. 
 
 The progress of science may be plausibly attributed to a pro- 
 cess of Natural Selection ; hypotheses are produced in abund- 
 ance and variety, and those unfit to bear verification are 
 destroyed, until only the fittest survive. Wallace, a practical 
 
260 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 naturalist, if there ever was one, as well as an eminent theorist, 
 takes the same view as Whewell of such inadequate conjec- 
 tures. Of * Lemuria,' a hypothetical continent in the Indian 
 Ocean, once supposed to be traceable in the islands of 
 Madagascar, Seychelles and Mauritius, its surviving frag- 
 ments, and named from the Lemurs, its characteristic denizens, 
 he says (Island Life, chap, xix.) that it was " essentially a 
 provisional hypothesis, very useful in calling attention to a 
 remarkable series of problems in geographical distribution [oi 
 plants and animals], but not affording the true solution oi 
 those problems." We see, then, that ' provisional hypotheses,' 
 though erroneous, may be very useful or (as Whewell says) 
 necessary. 
 
 Hence, to be prolific of hypotheses is the first attribute 
 of scientific genius ; the first, because without it no progress 
 whatever can be made. And some men seem to have a 
 marked felicity, a sort of instinctive judgment even in their 
 guesses, as if their heads were made according to Nature. 
 But others among the greatest, like Kepler, guess often and 
 are often wrong before they hit upon the truth, and them- 
 selves, like Nature, destroy many vain shoots and seedlings 
 of science for one that they find fit to live. If this is 
 how the mind works in scientific inquiry (as it certainly is, 
 with most men, in poetry, in fine art, and in the scheming 
 of business), it is useless to repine. We should rather recog- 
 nise a place for fool's hypotheses, as Darwin did for " fool's 
 experiments." 
 
 But to complete the scientific character, there must be great 
 patience, accuracy, and impartiality in examining and testing 
 these conjectures, as well as great ingenuity in devising 
 experiments to that end. It is the want of these qualities 
 that leads to crudity and public failure and brings hypotheses 
 into derision. Not partially and hastily to believe in one's 
 own guesses, nor petulantly and hastily to reject them, but 
 to consider the matter, to suspend judgment, is the mora 
 lesson of science : difficult, distasteful, and rarely mastered. 
 
HYPOTHESES 261 
 
 Everybody, according to his lights, makes haste to frame 
 hypotheses, whether for scientific or private uses ; because, as 
 Whewell says, "man is prone to become a deductive reasoner," 
 and hypotheses, anticipating the laborious induction of highly 
 general laws, are a short cut to deduction. There are two sides 
 to this proneness of our nature, a good and a bad. The good 
 is that hypothesis and deduction have in fact been the great 
 means of explaining or enabling us to understand the world ; 
 so that our instinctive resort to them is a predisposition to 
 science. The bad is that this method encourages superficiality. 
 Deduction is generally easier than Induction, because it is 
 carried on far more by means of signs, whether in Mathematics 
 or common language. To wield the higher Mathematics needs 
 a distinguished head ; but this power cannot be put into com- 
 petition with the lucid and comprehensive imagination neces- 
 sary to represent masses of facts for inductive analysis. For 
 the great use of language and of all symbols in thinking, is to 
 economise this energy of imagination. Without such devices 
 the human race could never have developed: for who can 
 imagine the purport in denotation of a single general name ? 
 But these devices show * the defects of their qualities ' by often 
 quite superseding thought and degenerating into gibberish. 
 Whether, indeed, this is ever true of the higher Mathematics is 
 not for me to say ; but everybody knows how true it is of 
 common speech. 
 
 5. The word ' hypothesis ' is often also used for the scientific 
 device of treating an Abstraction as, for the purposes of argu- 
 ment, equivalent to the concrete facts. Thus, in Geometry, a 
 line is treated as having no breadth ; in Mechanics, a bar may 
 be supposed absolutely rigid, or a machine to work without 
 friction ; in Economics (as we saw in the last chapter), man 
 is sometimes regarded as actuated solely by love of gain and 
 dislike of exertion. The results reached by such reasoning 
 may be made applicable to the concrete facts, if allowance be 
 made for the omitted circumstances or properties, in the 
 several cases of lines, bars, and men; but otherwise all 
 
262 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 conclusions from abstract terms are limited by their defini- 
 tions. Abstract reasoning, then (that is, reasoning limited by 
 definitions), is often said to imply * the hypothesis ' that things 
 exist as their names are denned, having no properties but 
 those enumerated in their definitions. This seems, however, 
 a needless and confusing extension of the term ; for an 
 hypothesis proposes an agent, collocation, er law hitherto 
 unknown; whereas abstract reasoning proposes to exclude 
 from consideration a good deal that is well known. There 
 seems no reason why the latter device should not be plainly 
 called an Abstraction. 
 
 Such Abstractions are, of course, also necessary to science ; 
 for no object is comprehensible by us in all its properties at 
 once. But if we forget the limitations of our abstract data, 
 we are liable to make strange blunders by mistaking the 
 character of the results: treating the results as simply true 
 of actual things, instead of as true of actual things only so far 
 as they are represented by the Abstractions. In addressing 
 abstract reasoning, therefore, to those especially who are 
 unfamiliar with scientific methods, pains should.be taken to 
 make it clear what the Abstractions are, what are the con- 
 sequent limitations upon the argument and its conclusions, 
 and what corrections and allowances are necessary in order to 
 turn the conclusions into an adequate account of the concrete 
 facts. The greater the number, variety, and subtlety of the 
 properties possessed by any object (such as human nature), 
 the greater the qualifications required in the conclusions of 
 abstract reasoning, before they can hold true of such an object 
 in practical affairs. 
 
 Closely allied to this method of Abstraction is the Mathe- 
 matical Method of Limits. In his History of Scientific Ideas 
 (B. II. c. 12), Whewell says : 
 
 " The Idea of a Limit supplies a new mode of establishing 
 mathematical truths. Thus with regard to the length of any 
 portion of a curve, a problem which we have just mentioned ; 
 a curve is not made up of straight lines, and therefore we 
 
HYPOTHESES 263 
 
 cannot by means of any of the doctrines of elementary 
 geometry measure the length of any curve. But we may make 
 up a figure nearly resembling any curve by putting together 
 many short straight lines, just as a polygonal building of very 
 many sides may nearly resemble a circular room. And in 
 order to approach nearer and nearer to a curve, we may make 
 the sides more and more small, more and more numerous. 
 We may then possibly find some mode of measurement, some 
 relation of these small lines to other lines, which is not dis- 
 turbed by the multiplication of the sides, however far it be 
 carried. And thus we may do what is equivalent to measuring 
 the curve itself; for by multiplying the sides we may approach 
 more and more closely to the curve till no appreciable difference 
 remains. The curve line is the Limit of the polygon ; and in 
 this process we proceed on the Axiom that * What is true up 
 to the Limit is true at the Limit.' " 
 
 Now, what Whewell calls the Axiom here, others might call 
 an Hypothesis ; but perhaps it is properly a Postulate. And 
 it is just the obverse of the Postulate implied in the Method of 
 Abstractions, namely, that ' What is true of the Abstraction is 
 true of concrete cases the more nearly they approach the 
 Abstraction.' What is true of the * Economic Man ' is truer 
 of a broker than of a farmer, of a farmer than of a labourer, of 
 a labourer than of the artist of romance. Hence the Abstrac- 
 tion may be called a Limit or limiting case, in the sense that 
 it stands to concrete individuals, as a curve does to the figures 
 made up " by putting together many short straight lines." 
 Correspondingly, the Proper Name may be called the Limit 
 of the class-name ; since its attributes are infinite, whereas any 
 name whose attributes are less than infinite stands for a 
 possible class. In short, for logical purposes, a Limit may 
 be defined as any extreme case to which actual examples may 
 approach without ever reaching it. And in this sense 
 'Method of Limits' might be used as a term including the 
 Method of Abstractions ; though it would be better to speak 
 of them generically as * Methods of Approximations.' 
 
264 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 We may also notice the Assumptions (as they may be called) 
 that are sometimes resorted to to facilitate an investigation, 
 because some definite ground must be taken and nothing 
 better can be thought of : as in estimating national wealth, 
 that furniture is half the value of the houses. 
 
 It is easy to conceive of an objector urging that such 
 devices as the above are merely ways of avoiding the actual 
 problems, and that they display more cunning than skill. But 
 Science, like good sense, puts up with the best that can be 
 had; and, like prudence, does not reject the half-loaf. The 
 position, that a conceivable case that can be dealt with may, 
 under certain conditions, be substituted for one that is 
 unworkable, is a touchstone of intelligence. To stand out for 
 ideals that are known to be impossible, is only an excuse for 
 doing nothing at all. 
 
 In another sense, again, the whole of Science is sometimes 
 said to be hypothetical, because it takes for granted the 
 Uniformity of Nature; for this, in its various aspects, can 
 only be directly ascertained by us as far as our experience 
 extends ; whereas the whole value of the principle of 
 Uniformity consists in its furnishing a formula for the 
 extension of our other beliefs beyond our actual experience. 
 Transcendentalists, indeed, call it a form of Reason, just 
 because it is presupposed in all knowledge; and they and 
 the Empiricists agree that to adduce material evidence for 
 it, in its full extent, is impossible. If, then, material evidence 
 is demanded by any one, he cannot regard the conclusions of 
 Mathematics and physical Science as depending on what is 
 itself unproved ; he must, with Mill, regard these conclusions 
 as drawn " not from but according to " the axioms of Equality 
 and Causation. That is to say, if the axioms are true, the 
 conclusions are ; the material evidence for both the axioms 
 and the conclusions being the same, namely, uncontradicted 
 experience. Now when we say, * If Nature is uniform, 
 Science is true ', the hypothetical character of Science appea 
 in the form of the statement. Nevertheless, it seems und 
 
 : 
 
HYPOTHESES 265 
 
 sirable to call our confidence in Nature's uniformity an * hypo- 
 thesis ': it is incongruous to use the same term for our 
 tentative conjectures and for our most indispensable beliefs. 
 ' The Universal Postulate ' is a better term for the principle 
 which, in some form or other, every generalisation takes for 
 granted. 
 
CHAPTER XIX 
 
 LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; 
 ANALOGY 
 
 i. Laws are classified, according to their degrees of 
 generality, as higher and lower, though the grades may not 
 be decisively distinguishable. 
 
 First, there are Axioms or Principles, that is real, universal, 
 self-evident propositions. They are (i) real propositions ; 
 not, like 'The whole is greater than any of its parts/ 
 merely definitions, or implied in definitions. (2) They are 
 regarded as universally true of phenomena, as far as the form 
 of their expression extends ; that is, for example,. Axioms con- 
 cerning quantity are true of everything that is considered in 
 its quantitative aspect, though not (of course) in its qualitative 
 aspect. (3) They are self-evident ; that is, each rests upon 
 its own evidence (whatever that may be) ; they cannot be 
 derived from one another, nor from any more general law. 
 Some, indeed, are more general than others : the Logical 
 Principle of Contradiction, ' if A is B, it is not not-B ', is true 
 of qualities as well as of quantities ; whereas the Axioms of 
 Mathematics apply only to quantities. The Mathematical 
 Axioms, again, apply to time, space, mental phenomena, and 
 matter and energy ; whereas the Law of Causation is only true 
 of concrete events in the redistribution of matter and energy : 
 such, at least, is the strict limit of Causation, if we identify it 
 with the Conservation of Energy ; although our imperfect 
 knowledge of life and mind often drives us to speak of feelings, 
 ideas, volitions, as causes. Still, the Law of Causation cannot 
 
LAWS CLASSIFIED 267 
 
 be derived from the Mathematical Axioms, nor these from the 
 Logical. The kind of evidence upon which Axioms rest, or 
 whether any evidence can be given for them, is (as before 
 observed) a question for Metaphysics, not for Logic. Axioms 
 are the upward limit of Logic, which, like all the special 
 Sciences, necessarily takes them for granted, as the starting 
 point of all deduction and the goal of all generalisation. 
 
 Next to Axioms, come Primary Laws of Nature : these are 
 of less generality than the Axioms, and are subject to the 
 conditions of methodical proof; being universally true only 
 of certain forces or properties of matter, or of nature under 
 certain conditions ; so that proof of them by logical or 
 mathematical reasoning is expected, because they depend upon 
 the Axioms for their formal evidence. Such are the law of 
 Gravitation, in Astronomy; the law of definite Proportions, in 
 Chemistry ; the law of Heredity, in Biology ; and in Psycho- 
 logy, the law of Relativity. 
 
 Then, there are Secondary Laws, of still less generality, 
 resulting from a combination of primary conditions or forces 
 in given circumstances, and therefore conceivably derivable 
 from the laws of those conditions or forces, if we can 
 discover them and compute their united effects. Accordingly, 
 Secondary Laws are either (i) Derivative, having been 
 analysed into, and deduced from, Primary Laws ; or (2) Em- 
 pirical, those that have not yet been deduced (though from 
 their comparatively special and complex character, it seems 
 probable they may be, given sufficient time and ingenuity), 
 and that meanwhile rest upon some unsatisfactory sort of 
 induction by Agreement or Simple Enumeration. 
 
 Whether laws proved only by the canon of Difference are to 
 be considered Empirical, is perhaps a question : their proof 
 derives them from the principle of Causation ; but, being of 
 narrow scope, some more special account of them seems 
 requisite in relation to the Primary Laws before we can call 
 them Derivative in the technical sense. 
 
 Many Secondary Laws, again, are partially or imperfectly 
 
268 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Derivative; we can give general reasons for them, without 
 being able to determine theoretically the precise relations of 
 the phenomena they describe. Thus, Meteorologists can 
 explain the general conditions of all sorts of weather, but have 
 made but little progress toward predicting the actual course of 
 it (at least, for our island) : Geologists know the general causes 
 of mountain ranges, but not why they rise just where we find 
 them : Economists explain the general course of a commercial 
 crisis, but not why the great crises recur at intervals of about 
 ten years. 
 
 Derivative Laws make up the body of the exact Sciences, 
 having been assimilated and organised ; whilst Empirical Laws 
 are the undigested materials of Science. The theorems of 
 Euclid are good examples of Derivative Laws in Mathematics ; 
 in Astronomy, Kepler's laws and the laws of the tides; in 
 Physics, the laws of shadows, of perspective, of harmony ; in 
 Biology, the law of Natural Selection, and others from this ; 
 in Economics, the laws of prices, rents, wages, interest. 
 
 Empirical Laws are such as Bode's law of the planetary 
 distances ; the laws of the expansion of different bodies by 
 heat, and formulae expressing the electrical conductivity of 
 each substance as a function of the temperature. Strictly 
 speaking, I suppose, all the laws of chemical combination are 
 Empirical : the law of definite proportions is found true in all 
 cases that have been examined, except for variations that may 
 be ascribed to errors of experiment. Much the same is true 
 in Biology ; most of the secondary laws are Empirical, except 
 so far as structures or functions may be regarded as specialised 
 cases in Physics or Chemistry and deducible from these 
 Sciences. The theory of Natural Selection, however, has been 
 the means of rendering many laws, that were once wholly 
 Empirical, at least partially Derivative ; namely, the laws of 
 the Geographical distribution of plants and animals, and of 
 their adaptation in organisation, form and colour, habits and 
 instincts, to their various conditions of life. The laws that 
 remain Empirical in Biology are of all degrees of generality 
 
LAWS CLASSIFIED 269 
 
 from that of the tendency to variation in size and in every 
 character shown by all (or nearly all) species (though as to the 
 reason of this there are promising hypotheses), down to such 
 curious cases as that the colour of roses and carnations never 
 varies into blue, that scarlet flowers are never sweet-scented, 
 that bullfinches fed on hemp-seed turn black, that the young 
 of white, yellow and dun pigeons are born almost naked 
 (whilst others have plenty of down) ; and so on. The deriva- 
 tion of Empirical Laws is the greater part of the Explanation 
 of Nature ( 5, 6). 
 
 A ' Fact,' in the common use of the word, is a particular 
 Observation : it is the material of science in its rawest state. 
 As perceived by a mind, it is, of course, never absolutely 
 particular: for we cannot possibly perceive anything without 
 classing it, more or less definitely, with things already known 
 to us ; nor describe it without using connotative terms which 
 imply a classification of the things denoted. Still, we may 
 consider an Observation as particular, in comparison with a 
 Law that includes it with numerous others in one general 
 proposition. To turn an Observation into an Experiment, 
 or (where experiment is impracticable) to repeat it with all 
 possible precautions and exactness, and to describe it as to 
 the duration, quantity, quality and order of occurrence of its 
 phenomena, is the first stage of scientific manufacture. Then 
 comes the formulation of an Empirical Law; and lastly, if 
 possible, deduction or derivation, either from higher laws 
 previously ascertained, or from an hypothesis. However, as a 
 word is used in various senses, we often speak of laws as 
 ' facts ' : we say the law of Gravitation is a fact, meaning that 
 it is real, or verifiable by observations or experiments. 
 
 2. Secondary Laws may also be classified according to 
 their constancy into (i) the Invariable (as far as experience 
 reaches), and (2) Approximate Generalisations in the form 
 Most X's are Y. Of the Invariable we have given examples 
 above. The following are Approximate Generalisations : Most 
 comets gp round the Sun from East to West ; Most metals are 
 
270 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 solid at ordinary temperatures ; Most marsupials are Austral- 
 asian ; Most arctic animals are white in winter ; Most cases of 
 plague are fatal ; Most men think first of their own interests. 
 Some of these laws are empirical, as that * Most metals are 
 solid at ordinary temperatures ' : at present no reason can be 
 given for this ; nor do we know why most cases of plague are 
 fatal. Others, however, are at least partially derivative, as 
 that * Most arctic animals are white ' ; for this seems to be due 
 to the advantage of concealment in the snow; whether, as 
 with the bear, the better to surprise its prey, or, with the hare, 
 to escape the notice of its enemies. 
 
 But the, scientific treatment of such a proposition requires 
 that we should also explain the exceptions : if ' Most are ', this 
 implies that ' Some are not ' ; why not, then ? Now, if we can 
 give reasons for all the exceptions, the Approximate Generali- 
 sation may be converted into an universal one, thus : * All 
 arctic animals are white, unless (like the raven) they need no 
 concealment either to prey or to escape; or unless mutual 
 recognition is more important to them than concealment (as 
 with the musk-sheep) '. The same end of universal statement 
 may be gained by including the conditions on which the 
 phenomenon depends, thus : ' All arctic animals to whom con- 
 cealment is of the utmost utility are white '. 
 
 When Statistics are obtainable, it is proper to convert an 
 Approximate Generalisation into a proportional statement of 
 the fact, thus : instead of l Most attacks of plague are fatal ', we 
 might find that in a certain country 70 per cent, were so. 
 Then, if we found that in another country the percentage of 
 deaths was 60, in another 40, we might discover, in the 
 different conditions of these countries, a clue to the high rate 
 of mortality from this disease. Indeed, even if the proportion 
 of cases in which two facts are connected does not amount to 
 * Most', yet, if any definite percentage is obtainable, the pro- 
 position has a higher scientific value than a vague ' Some ' : as 
 if we know that 2 per cent, of the deaths in England are due 
 to suicide, this may be compared with the rates of suicide in 
 
LAWS CLASSIFIED 271 
 
 other countries ; from which perhaps inferences may be drawn 
 as to the causes of suicide. 
 
 In one department of life, namely, Politics, there is a special 
 advantage in true Approximate Generalisations amounting to 
 1 Most cases '. The citizens of any State are so various in 
 character, enlightenment, and conditions of life, that we can 
 expect to find few propositions universally true of them : so 
 that propositions true of the majority must be trusted as the 
 bases of legislation. If most men are deterred from crime by 
 the fear of punishment; if most men will idle if they can 
 obtain support without industry ; if most jurymen will refuse 
 to convict of a crime for which the prescribed penalties seem 
 to them too severe ; these are most useful truths, though there 
 should be numerous exceptions to them all. 
 
 3. Secondary Laws can only be trusted in ' Adjacent 
 Cases ' ; that is, where the circumstances are similar to those 
 in which the laws are known to be true. A Derivative Law 
 will be true wherever the forces concerned exist in the combi- 
 nations upon which the law depends, if there are no counter- 
 acting conditions. 
 
 Thus, that water can be pumped to about 33 feet at the sea- 
 level, is a derivative law on this planet : is it true in Mars ? 
 That depends on whether there are in Mars bodies of a liquid 
 similar to our water ; whether there is an atmosphere there ; 
 and how great its pressure is; which will vary with its height 
 and density. If there is no atmosphere, there can be no 
 pumping ; or if there is an atmosphere of less pressure than 
 ours, water such as ours can only be pumped to a less height 
 than 33 feet. Again, we know that there are arctic regions in 
 Mars ; if there are also arctic animals, are they white ? That 
 may depend upon whether there are any beasts of prey. If 
 not, concealment seems to us of no use. 
 
 An Empirical Law, being one whose conditions we do not 
 know, the extent of its prevalence is still less ascertainable. 
 Where it has not been actually observed to be true, we 
 cannot trust it unless the circumstances, on the whole, 
 
272 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 resemole so closely those amongst which it has been observed, 
 that the unknown causes, whatever they may be, are likely to 
 prevail there. And, even then, we cannot have much confidence 
 in it ; for there may be unknown circumstances which entirely 
 frustrate the effect. 
 
 The first naturalist who travelled (say) from Singapore east- 
 ward by Sumatra and Java, or Borneo, and found the mam- 
 malia there similar to those of Asia, may naturally have 
 expected the same thing in Celebes and Papua ; but, if so, he 
 was entirely disappointed ; for in Papua the mammalia are 
 marsupials like those of Australia. Thus his empirical law, 
 * The mammalia of the Eastern Archipelago are Asiatic,' would 
 have failed for no apparent reason. According to Mr. Wallace, 
 there is a reason for it, though such as could only be dis- 
 covered by extensive researches : namely, that the sea is deep 
 between Borneo and Celebes, so that they must have been 
 separated for many ages ; whereas it is shallow from Borneo 
 westward to Asia, and also southward from Papua to Australia ; 
 so that these regions, respectively, may have been recently 
 united : and the true law is that similar mammalia belong to 
 those tracts which at comparatively recent dates have formed 
 parts of the same continents. 
 
 A considerable lapse of time may make an empirical law no 
 longer trustworthy ; for the forces from whose combination it 
 resulted may have ceased to operate, or to operate in the same 
 combination ; and since we do not know what those forces 
 were, even the knowledge that great changes have taken place 
 in the meantime cannot enable us, after an interval, to judge 
 whether or not the law still holds true. New stars shine in the 
 sky and go out ; species of plants and animals become extinct ; 
 diseases die out and fresh ones afflict mankind : all these 
 things doubtless have their causes, but if we do not know what 
 they are, we have no measure of the effects, and cannot tell 
 when or where they will happen. 
 
 Laws of Concomitant Variations may hold good only within 
 certain limits. That bodies contract as the temperature falls, 
 
CO-EXISTENCE 273 
 
 is not true of water a little above freezing point. In Psychology, 
 Weber's Law is only true within the middle range of sensation- 
 intensities, not for very faint, nor for very strong, stimuli. 
 In such cases the failure of the laws may depend upon some- 
 thing imperfectly understood in the collocation : as to water, 
 on its molecular constitution ; as to sensation, upon the 
 structure of the nervous system. 
 
 4. Secondary Laws, again, are either of Succession or of 
 Co-existence. 
 
 Those of Succession are either (i) of direct causation, as 
 that ' Water quenches fire ', or (more strictly) that 'Evaporation 
 reduces temperature ' ; or (2) of the effect of a remote cause, as 
 ' Bad harvests tend to raise the price of bread ' ; or (3) of the 
 joint effects of the same cause, as that ' Night follows day ' 
 (from the revolution of the earth), or the course of the seasons 
 (from the inclination of the earth's axis). 
 
 Laws of Co-existence are of several classes, (i) One has 
 the generality of a Primary Law, though it is proved only by 
 Agreement, namely, ' All gravitating bodies are inert '. Others, 
 though less general than this, are of very extensive range, as 
 that * All gases that are not decomposed by rise of temperature 
 have the same rate of expansion ' ; and, in Botany, again, 
 that * All monocotyledonous plants are endogenous '. These 
 laws of Co-existence are concerned with the most fundamental 
 properties of bodies. 
 
 (2) Next come laws of the Co-existence of those properties 
 which are comprised in the definitions of Natural Kinds. 
 Mill distinguished between (a) classes of things that agree 
 among themselves and differ from others only in one or a 
 few attributes (such as c red things ', * musical notes ', * car- 
 nivorous animals ', * soldiers '), and (/3) classes of things that 
 agree among themselves and differ from others in a multitude 
 of characters : and the latter he calls Natural Kinds. These 
 comprise the chemical elements and their pure compounds 
 (such as water, alcohol, rock-salt, chalk), and the species of 
 plants and animals. Clearly, each of these is constituted by 
 
274 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 the co-existence or co-inherence of a multitude of properties, 
 some of which are selected as the basis of their definitions. 
 Thus, Gold is a metal of high specific gravity, high melting 
 point, low chemical affinities, great ductility, yellow colour, etc. : 
 a Horse has ' a vertebral column, mammae, a placental embryo, 
 four legs, a single well-developed toe in each foot provided with 
 a hoof, a bushy tail, and callosities on the inner sides of both 
 the fore and the hind legs ' (Huxley). 
 
 Since Darwinism has obtained general acceptance, some 
 Logicians have doubted the propriety ot calling the organic 
 species * Kinds,' on the grounds that they are not, as to definite- 
 ness and permanence, on a par with the chemical elements or 
 such compounds as water and rock-salt; that thejr vary 
 extensively, and that it is only by the loss of former generations 
 of animals that we are able to distinguish species at all. But 
 to this it may be replied that species (so-called) are often 
 approximately constant for immense periods of time, and may 
 be called permanent in comparison with human generations ; 
 and that, although the leading principles of Logic are perhaps 
 eternal truths, yet upon a detail such as this, the science may 
 condescend to recognise a distinction if it is good for (say) 
 only 100,000 years. That if former generations of plants and 
 animals were not lost, all distinctions of species would dis- 
 appear, may be true; but they are lost for the most part 
 beyond hope of recovery ; and accordingly the distinction of 
 species is still recognised ; although there are cases, chiefly at 
 the lower stages of organisation, in which so many varieties 
 occur as to make adjacent species almost or quite indistinguish- 
 able. So far as species are recognised, then, they present a 
 complex co-existence of qualities, which is certainly a logical 
 problem; and, coming more naturally under the head of 
 Natural Kinds than any other, they must be mentioned in this 
 place. 
 
 (3) There are, again, certain coincidences of qualities not 
 essential to any kind, and sometimes prevailing amongst many 
 different kinds : such as ' Insects of nauseous taste have vivid 
 
CO-EXISTENCE 275 
 
 (warning) colours' ; * White tom-cats with blue eyes are deaf; 
 * White spots and patches, when they appear in domestic 
 animals, are most frequent on the left side.' 
 
 (4) Finally, there may be constancy of relative position, as 
 of sides and angles in Geometry ; and also among concrete 
 things (at least for long periods of time), as of the planetary 
 orbits, the apparent positions of fixed stars in the sky, the 
 distribution of land and water on the globe, opposite seasons 
 in opposite hemispheres. 
 
 All these cases of Co-existence (except the Geometrical) 
 present the problem of deriving them from Causation ; for 
 there is no general Law of Co-existence from which they can 
 be derived ; and, indeed, if we conceive of the external world 
 as a perpetual redistribution of matter and energy, it follows 
 that the whole state of Nature at any instant, and therefore 
 every Co-existence included in it, is due to Causation issuing 
 from some earlier distribution of matter and energy. Hence, 
 indeed, it is not likely that the problems of Co-existence as a 
 whole will ever be solved, since the original distribution of 
 matter is, of course, unknown. Still, starting with any given 
 state of Nature, we may hope to explain some of the co- 
 existences in any subsequent state. We do not, indeed, know 
 why heavy bodies are always inert, nor why the chemical 
 elements are what they are; but it is known that "the 
 properties of the elements are functions of their atomic 
 weight," which (though, at present, only an empirical law) 
 may be a clue to some deeper explanation. As to plants and 
 animals, we know the conditions of their generation, and can 
 trace a connection between most of their characteristics and 
 the conditions of their life : as that the teeth and stomach of 
 animals vary with their food, and that their colour generally 
 varies with their habitat. 
 
 Geometrical Co-existence, when it is not a matter of 
 definition (as ' a square is a rectangle with four equal sides '), 
 is deduced from the Definitions and Axioms : as when it is 
 shown that in triangles the greater side is opposite the greater 
 
276 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 angle. The deductions of theorems or secondary laws, in 
 Geometry is a type of what is desirable in the Physical 
 Sciences : the demonstration, namely, that all the connections 
 of phenomena, whether successive or co-existent, are conse- 
 quences of the redistribution of matter and energy according 
 to the principle of Causation. 
 
 Coincidences of Co-existence (Group (3)) may sometimes 
 be deduced and sometimes not. That * nauseous insects have 
 vivid coloration ' comes under the general law of * protective 
 coloration ' ; as they are easily recognised and therefore 
 avoided by insectivorous birds and other animals. But why 
 white tom-cats with blue-eyes should be deaf, is (I believe) 
 unknown. When Co-existences cannot be derived from 
 Causation, they can only be proved by collecting examples 
 and trusting vaguely to the Uniformity of Nature. If no 
 exceptions are found, we have an empirical law of considerable 
 probability within the range of our exploration. If exceptions 
 occur, we have at most an Approximate Generalisation, as that 
 * Most metals are whitish,' or * Most domestic cats are 
 tabbies' (but this is probably the ancestral colouring). We 
 may then resort to staiistics for greater definiteness, and find 
 that in Hampshire (say) 90 per cent, of the domestic cats are 
 tabby. 
 
 5. Scientific Explanation consists in discovering, deducing, 
 and assimilating the laws of phenomena ; it is the analysis of 
 that Heracleitan 'flux' which so many philosophers have 
 regarded as intractable to human inquiry. In the ordinary use 
 of the word, ' explanation ' means the satisfying a man's under- 
 standing; and what may serve this purpose depends partly 
 upon the natural soundness of his understanding, and partly 
 on his education ; but it is always at last an appeal to the 
 primary functions of cognition, discrimination and assimila- 
 tion. 
 
 Generally, what we are accustomed to seems to need no 
 explanation, unless our curiosity is particularly directed to it. 
 That boys climb trees and throw stones, and that men go fox- 
 
CO-EXISTENCE 277 
 
 hunting, may easily pass for matters of course. If any one is 
 so exacting as to ask the reason, there is a ready answer in 
 the ' need of exercise.' On reflection, however, this will not 
 explain the peculiar zest of those exercises, which is something 
 quite different from our feelings whilst swinging dumb-bells or 
 tramping the highway. Others, more sophisticated, tell us 
 that the civilised individual retains in his nature the instincts 
 of his remote ancestors, and that these assert themselves at 
 stages of his growth corresponding with ancestral periods of 
 culture or savagery : so that if we delight to climb trees, throw 
 stones, and hunt, it is because our forefathers once lived in 
 trees, had no missiles but stones, and depended for a livelihood 
 upon killing something. To some of us, again, this seems an 
 explanation ; to others it merely gives annoyance, as a super- 
 fluous hypothesis, the fruit of a wanton imagination and too 
 much leisure. 
 
 However, what we are not accustomed to immediately 
 excites curiosity. If it were exceptional to climb trees, throw 
 stones, ride after foxes, whoever did such things would be 
 viewed with suspicion. An eclipse, a shooting star, a solitary 
 boulder on the heath, a strange animal, or a Chinaman in the 
 street, calls for explanation ; and among some nations, eclipses 
 have been explained by supposing a dragon to devour the sun 
 or moon ; solitary boulders, as the missiles of a giant ; and so 
 on. Such explanations, plainly, are attempts to regard rare 
 phenomena as similar to others that are better known ; a snake 
 having been seen to swallow a rabbit, a bigger one may swallow 
 the sun : a giant is supposed to bear much the same relation 
 to a boulder as a boy does to half a brick. When any very 
 common thing seems to need no explanation, it is because the 
 several instances of its occurrence are a sufficient basis cf 
 assimilation to satisfy most of us. Still, if a reason for such a 
 thing is demanded, the commonest answer has the same 
 implication, namely, that assimilation or classification is a 
 sufficient reason for it. Thus, if climbing trees is referred to 
 the need of exercise, it is assimilated to running, rowing, etc. \ 
 
278 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 if the customs of a savage tribe are referred to the command 
 of its gods, they are assimilated to those things that are done 
 at the command of chieftains. 
 
 Explanation, then, is a kind of classification ; it is the finding 
 of resemblance between the phenomenon in question and other 
 phenomena. In Mathematics, the explanation of a theorem is 
 the same as its proof, and consists in showing that it repeats, 
 under different conditions, the definitions and axioms already 
 assumed and the theorems already demonstrated. 
 
 In Concrete Sciences, to discover the cause of a pheno- 
 menon, or to derive an empirical law from laws of causation, 
 is *to explain it ; because a cause is an invariable antecedent, 
 and therefore reminds us of, or enables us to conceive, an 
 indefinite number of cases similar to the present one wherever 
 the cause exists ; and, as we have seen that the discovery of 
 the laws of nature is essentially the discovery of causes, the 
 discovery and derivation of laws is scientific explanation. 
 
 The discovery of quantitative laws is especially satisfactory, 
 because it not only explains why an event happens at all, but 
 why it happens just in this direction, degree, or amount; so 
 that (the only likeness between quantities, as such, being 
 equality), the cause is shown to be equal not only to other causes 
 but to its own effect ; wherefore, whether the conservation of 
 matter and energy be universally true or not, it must still be 
 an universal postulate of scientific explanation. 
 
 The mere discovery of an empirical law of co-existence, as 
 that ' white tom-cats with blue eyes are deaf ', is indeed 
 something better than an isolated fact : every general propo- 
 sition relieves the mind of a load of facts ; and, for many 
 people, to be able to say ' It is always so ' may be enough ; 
 but for scientific explanation we require to know the reason of 
 it, that is, the cause. Still, if asked to explain an Axiom, we 
 can only say, * It is always so : ' though it is some relief to point 
 out particular instances of its realisation, or to exhibit the 
 similarity of its form to that of other axioms as of the nota 
 note to the axiom of equality. 
 
EXPLANATION 279 
 
 6. There are three modes of scientific Explanation ; First, 
 the analysis of a phenomenon into the laws of its causes and 
 the concurrence of these causes. 
 
 The pumping of water implies (i) pressure of the air, (2) 
 distribution of pressure in a liquid, (3) that motion takes the 
 direction of least resistance. Similarly, that thunder follows 
 forked lightning, and that the report of a gun follows the flash, 
 are resolvable into (i) the discharge of electricity, or the ex- 
 plosion of gunpowder ; (2) distance of the observer from the 
 event ; (3) that light travels faster than sound. The planetary 
 orbits are analysable into the tendency of planets to fall into 
 the sun, and their tendency to travel in a straight line. When 
 this conception is helped out by swinging a ball round by a 
 string, and then letting it go, to show what would happen to 
 the earth if gravitation ceased, we see how the recognition of 
 resemblance lies at the bottom of explanation. 
 
 Secondly, the discovery of steps of causation between a cause 
 and its remote effects ; the interpolation and concatenation of 
 causes. 
 
 The maxim ' No cats no clover ' is explained by assigning 
 the intermediate steps in the following series ; that the fructi- 
 fication of red clover depends on the visits of humble-bees, 
 who scatter the pollen in seeking honey ; that if field-mice are 
 numerous they destroy the humble-bees' nests ; and that (owls 
 and weasels being exterminated by game-keepers) the destruc- 
 tion of field-mice depends upon the supply of cats ; which, there- 
 fore, are a remote condition of the clover crop. Again, the com- 
 munication of thought by speech is an example of something 
 so common that it seems to need no explanation; yet to 
 explain it is a long story. A thought in one man's mind is the 
 remote cause of a similar thought in another's : Here we have 
 (i) a thought associated with mental words ; (2) a connection 
 between these thoughts and some tracts of the brain ; (3) a 
 connection between these tracts of the brain and the muscles 
 of the larynx, the tongue and the lips ; (4) movements of the 
 chest, larynx and mouth, propelling and modifying waves of 
 
280 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 air ; (5) the impinging of these air-waves upon another man's 
 ear, and by a complex mechanism exciting the aural nerve ; 
 
 (6) the transfer of this excitation to certain tracts of his brain ; 
 
 (7) a connection there with sounds of words and their 
 associated thoughts. If one of these links fail, there is no 
 communication. 
 
 Thirdly, the Subsumption of several laws under one more 
 general expression. 
 
 Thus the tendency of bodies to fall to the earth and the 
 tendency of the earth itself (with the other planets) to fall into 
 the sun, are subsumed under the general law that ' All matter 
 gravitates.' The same law subsumes the movements of the 
 tide. By means of the notion of specific gravity, it includes 
 ' levitation,' or the actual rising of some bodies, as of corks in 
 water, of balloons, or flames in the air ; the fact being that 
 these things do not tend to rise, but to fall like everything 
 else ; only as the water or air weighs more in proportion to its 
 volume than corks or balloons, the latter are pushed up. 
 
 This process of Subsumption bears the same relation to 
 Secondary Laws, that these do to particular facts. The 
 generalisation of many particular facts (that is, a statement of 
 that in which they agree) is a law ; and the generalisation of 
 these laws (that is, again, a statement of that in which they 
 agree) is a higher law; and this process, upwards or down- 
 wards, is essentially the course of scientific progress. The 
 perfecting of any science consists in comprehending more and 
 more of the facts within its province, and in showing that they 
 all exemplify a smaller and smaller number of principles, 
 which express their most profound resemblances. 
 
 It can easily be shown that these three modes of explanation 
 all consist in generalising or assimilating the phenomena. 
 
 The pressure of the air, of a liquid, and motion in the direc- 
 tion of least resistance, are all commoner facts than pumping ; 
 that light travels faster than sound is a commoner fact than a 
 thunder-storm or gun-firing. Each of the laws 'Cats kill 
 mice,' ' Mice destroy humble-bees' nests,' * Humble-bees 
 
EXPLANATION 281 
 
 fructify red clover' is wider and expresses the resemblance 
 of more numerous cases than the law that ' Clover depends on 
 cats ' ; because each of them is less subject to further condi- 
 tions. Similarly, every step in the communication of thought 
 by language is less conditional, and therefore more general, 
 than the completion of the process. 
 
 In all the above cases, again, each law into which the 
 phenomenon (whether pumping or conversation) is resolved, 
 suggests a host of related resemblances : as the modifying of 
 air-waves by the larynx and lips suggests the various devices 
 by which the strings and orifices of musical instruments modify 
 the character of notes. 
 
 As for Subsumption (case (3)), it consists entirely in proving 
 the existence of an essential similarity between things where it 
 was formerly not observed : as that the gyrations of the moon, 
 the fall of apples, and the flotation of bubbles are all examples 
 of gravitation : or that the purifying of the blood by breathing, 
 the burning of a candle, and the rusting of iron are all cases 
 of oxidation : or that the colouring of the underside of a red- 
 admiral's wings, the spots of the giraffe, the shape of a stick- 
 caterpillar, the transparency of deep-sea animals, and countless 
 other cases, though superficially so different, agree in this, that 
 they conceal and thereby protect the organism. 
 
 Not any sort of likeness, however, suffices for scientific 
 explanation : it must be ' fundamental ' ; or (as this is a vague 
 expression) we may say that the only satisfactory explanation 
 of concrete things or events, is to discover their likeness to 
 others in respect of Causation. Hence attempts to help the 
 understanding by familiar comparisons are often worse than 
 useless. Any of the above examples will show that explana- 
 tion, instead of making a phenomenon seem familiar, puts (as 
 the saying is) ' quite a new face upon it.' The proneness to 
 substitute familiarisation for radical explanation, is the easily 
 besetting sin of human understanding : the most plausible of 
 fallacies, the most attractive, the most difficult to avoid even 
 when we are on our guard against it. 
 
282 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 7. The explanation of Nature (if it be admitted to consist 
 in generalisation, or the discovery of resemblance amidst 
 differences) can never be completed. For (i) there are (as 
 Mill says) facts, namely, fundamental states or processes of 
 consciousness, which are distinct ; in other words, they do not 
 resemble one another, and therefore cannot be generalised 
 or subsumed under one explanation. Colour, heat, smell, 
 sound, touch, pleasure and pain, are so different that there is 
 one group of conditions to be sought for each ; and the laws 
 of these conditions cannot be subsumed under a more general 
 one "without leaving out the very facts to be explained. A 
 general condition of sensation, such as the stimulating of the 
 sensory organs of a living animal, gives no account of the 
 special characters of colour, smell, etc. ; which are, however, the 
 phenomena in question : and each of them has its own law. 
 Nay, each distinct sensation, quality, or degree must have its 
 own law ; for in each ultimate difference there is something 
 that cannot be assimilated. Such differences amount, accord- 
 ing to experimental Psychologists, to more than 40,000. 
 
 (2) When physical science is treated objectively (that is, 
 with as little reference as possible to the fact that all pheno- 
 mena are only known in relation to the human mind), colour, 
 heat, smell, sound (considered as sensations) are neglected, 
 and attention is fixed upon certain of their conditions : Ex- 
 tension, Figure, Resistance, Weight, Motion, with their 
 derivatives, Density, Elasticity, etc. These are called the 
 Primary Qualities of Matter; and it is assumed that they 
 belong to matter by itself, whether we look on or not : whilst 
 colour, heat, sound, etc., are called Secondary Qualities, as 
 depending entirely upon the reaction of some conscious 
 animal. From this point of view, the world is considered 
 in the abstract, as a perpetual redistribution of matter and 
 energy. 
 
 But, not to dwell upon the difficulty of reducing the activi- 
 ties of life and chemistry to mechanical principles, and even 
 the modes of mechanical and physical energy to one another 
 
EXPLANATION 283 
 
 (for, as Dr. Croll observed, equivalence is not identity) even 
 if this were done, complete explanation could not be attained. 
 For (a) as explanation is the discovery of causes, we no 
 sooner succeed in assigning the causes of the present state of 
 the world than we have to inquire into the causes of those 
 causes, and again the still earlier causes, and so on to infinity. 
 But, this being impossible, we must be content, wherever we 
 stop, to contemplate the uncaused, that is, unexplained ; and 
 then all that follows is really unexplained. 
 
 Besides this difficulty, however, there is another that 
 prevents the perfecting of any theory of the abstract material 
 world, namely (), that it involves more than one first principle. 
 For we have seen that the Uniformity of Nature is not really a 
 principle, but a merely nominal generalisation, since it cannot 
 be definitely stated ; and, therefore, the principles of Contra- 
 diction, Mediate Equality, and Causation remain incapable of 
 subsumption ; nor can any one of them be reduced to another : 
 so that they remain unexplained. 
 
 (3) Another limit to explanation lies in the infinite character 
 of every particular fact; so that we may know the laws of 
 many of its properties and yet come far short of understanding 
 it as a whole. A lump of sandstone in the road : we may 
 know a good deal about its specific gravity, temperature, 
 chemical composition, geological conditions ; but if we inquire 
 the causes of the particular modifications it exhibits of these 
 properties, and further why it is just so big, containing so 
 many molecules, neither more nor less, disposed in just such 
 relations to one another as to give it this particular figure, why 
 it lies exactly there rather than a yard off, and so forth, we 
 shall get no explanation of all this. The causes determining 
 each particular phenomenon are infinite, and can never be 
 computed ; and, therefore, it can never be fully explained. 
 
 8. Analogy is a kind of probable proof based upon 
 imperfect similarity (as the best that can be discovered) 
 between the data of comparison and the subject of our 
 inference. Like Deduction and Induction, it assumes that 
 
2 S 4 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 things which are alike in some respects are also alike in 
 others ; but it differs from them in not appealing to a definite 
 general law assigning the essential points of resemblance upon 
 which the argument relies. In Deductive proof, this is done 
 by the major premise of every syllogism : if the major says 
 that ' All fat men are humourists,' and we can establish the 
 minor, * X is a fat man,' we have secured the essential 
 resemblance that carries the conclusion. In Induction, the 
 Law of Causation and its representatives, the Canons, serve 
 the same purpose, specifying the essential marks of a cause. 
 But/in Analogy, the resemblance relied on cannot be stated 
 categorically. 
 
 If we argue that Mars is inhabited because it resembles the 
 datum, our Earth, (i) in being a planet, (2) neither too hot 
 nor too cold for life, (3) having an atmosphere, (4) sea and 
 land, etc., we are not prepared to say that ' All planets having 
 these characteristics are inhabited.' It is, therefore, not a 
 deduction ; and since we do not know the original causes of 
 life on the Earth, we certainly cannot show by induction that 
 adequate causes exist in Mars. We rely, then, upon some 
 such vague notion of Uniformity as that * Things alike in some 
 points are alike in others ' ; which, plainly, is either false or 
 nugatory. But, of course, if the linear markings upon the 
 surface of Mars indicate a system of canals, the inference that 
 he has intelligent inhabitants is no longer analogical, since 
 canals can have no other cause. 
 
 The cogency of any proof depends upon the character and 
 definiteness of the likeness which one phenomenon bears to 
 another ; but Analogy trusts to the general quantity of likeness 
 between them, in ignorance of what may be the really important 
 likeness. 
 
 If, having tried with a stone, an apple, a bullet, etc., we find 
 that they all break an ordinary window, and thence infer that 
 a cricket ball will do so, we do not reason by Analogy, but 
 make instinctively a deductive extension of an induction, 
 merely omitting the explicit generalisation, * All missiles of a 
 
ANALOGY 285 
 
 certain weight, size and solidity break windows.' But if, 
 knowing nothing of snakes except that the viper is venomous, 
 a child runs away from a grass-snake, he argues by Analogy ; 
 and, though his conduct is prudentially justifiable, his inference 
 is wrong : for there is no law that ' All snakes are venomous/ 
 but only that those are venomous that have a certain structure 
 of fang ; a point which he did not stay to examine. 
 
 Analogical argument, therefore, is only probable, and that in 
 various degrees. 
 
 (i) The greater the number and importance of the points 
 of agreement, the more probable is the inference. (2) The 
 greater the number and importance of the points of difference, 
 the less probable is the inference. (3) The greater the number 
 of unknown properties in the subject of our argument, the 
 less the value of any inference from those that we do know. 
 Of course the number of unknown properties can itself be 
 estimated only by Analogy. In the case of Mars, they are 
 probably very numerous; and, apart from the evidence of 
 canals, the prevalent assumption that there are intelligent 
 beings in that planet, seems to rest less upon probability than 
 on a curiously imaginative extension of the gregarious senti- 
 ment, the chilly discomfort of mankind at the thought of being 
 alone in the universe, and a hope that there may be conversable 
 and ' clubable ' souls nearer than the Dog-star. 
 
CHAPTER XX 
 PROBABILITY 
 
 Y Chance was once believed to be a distinct power in the 
 world, disturbing the regularity of Nature ; though, according 
 to Aristotle, it was only operative in occurrences below the 
 sphere of the moon. As, however, it is now admitted that 
 every event in the world is due to some cause, if we can only 
 trace the connection, whilst nevertheless the notion of Chance 
 is still useful when rightly conceived, we have to find some 
 other ground for it than that of a spontaneous capricious force 
 inherent in things. For such a conception can have no place 
 in any logical interpretation of Nature : it can never be inferred 
 from a principle, seeing that every principle expresses an 
 uniformity ; nor, again, if the existence of a capricious power 
 be granted, can any inference be drawn from it. Impossible 
 alike as premise and as conclusion, for Reason it is nothing at 
 all. 
 
 Every event is a result of causes : but the multitude of forces 
 and the variety of collocations being immeasurably great, the 
 overwhelming majority of events occurring about the same time 
 are only related by Causation so remotely that the connection 
 cannot be follo\Nfcd. Whilst my pen moves along the paper, a cab 
 rattles down the street, bells in the neighbouring steeple chime 
 the quarter, a girl in the next house is practising her scales, 
 and throughout the world innumerable events are happening 
 which may never happen together again ; so that should one of 
 them recur, we have no reason to expect any of the others. 
 This is Chance, or chance coincidence. The word coincidence 
 
 
PROBABILITY 287 
 
 is vulgarly used only for the inexplicable concurrence of in- 
 teresting events " quite a coincidence ! " 
 
 On the other hand, many things are now happening together 
 or coinciding, that will do so, for assignable reasons, again and 
 again ; thousands of men are leaving the City, who leave at 
 the same hour five days a week. But this is not chance ; it is 
 causal coincidence due to the custom of business in this country, 
 as determined by our latitude and longitude and other circum- 
 stances. No doubt the above chance coincidences writing, 
 cab-rattiing, chimes, scales, etc. are causally connected at some 
 point of past time. They were predetermined by the condition 
 of the world ten minutes ago ; and that was due to earlier con- 
 ditions, one behind the other, even to the formation of the 
 planet. But whatever connection there may have been, we 
 have no such knowledge of it as to be able to deduce the 
 coincidence, or calculate its recurrence. Here Chance is 
 defined by Mill to be : Coincidence giving no ground to infer 
 uniformity. 
 
 However, in fact, some chance coincidences do recur ac- 
 cording to laws of their own : I say some, but it may be all. If 
 the world is finite, the possible combinations of its elements 
 are exhaustible ; and, in time, whatever conditions of the world 
 have concurred will concur again, and in the same relation to 
 former conditions. This writing, that cab, those chimes, those 
 scales will coincide again : the Argonautic expedition, and the 
 Trojan war, and all our other troubles will be renewed. But, 
 to avoid melancholy, let us consider some more manageable 
 instance, such as the throwing of dice. Every one who has 
 played much with dice knows (so I am told) that double sixes 
 are sometimes thrown, and sometimes double aces. Such 
 coincidences do not happen once and only once ; they occur 
 again and again, and a great number of trials will show that, 
 though their recurrence has not the regularity of cause and 
 effect, it yet has a law of its own, namely a tendency to average 
 regularity. In 10,000 throws there will be some number of 
 double sixes ; and the greater the number of throws he 
 
288 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 more closely will the average recurrence of double sixes, or 
 double aces, approximate to one in thirty-six. Such a law 
 of average recurrence is the basis of Probability. Chance 
 being the fact of coincidence without assignable cause, Proba- 
 bility is expectation based on the average frequency of its 
 happening. 
 
 2. Probability is an ambiguous term. Usually, when we 
 say that an event is ' probable,' we mean that it is more likely 
 than not to happen. But, scientifically, an event is probable 
 if our expectation of its occurrence is less than certainty, as 
 long as the event is not impossible. Probability thus conceived 
 is represented by a fraction. Taking i to stand for certainty, 
 and o for impossibility, probability may be -f^f t r TTTUTJ"* or 
 (generally) ~. The denominator, of course, represents the 
 number of times that an event happens, and the numerator the 
 number of times that it coincides with another event. In 
 throwing a die, the probability of ace turning up is expressed 
 by putting the number of throws for the denominator and the 
 number of times that ace is thrown for the numerator ; and we 
 may assume that the more trials we make the . nearer will the 
 resulting fraction approximate to . 
 
 Instead of speaking of the ' throwing of the die ' and its 
 * turning up ace ' as two events, the former is often called ' the 
 event ' and the latter * the way of its happening.' And these 
 expressions may easily be extended to cover relations of distinct 
 events ; as when two men shoot at a mark and we desire to 
 represent the probability of both hitting the bull's eye together, 
 each shot may count as an event (denominator) and the 
 coincidence of ' bull's-eyes ' as the way of its happening 
 (numerator). 
 
 It is also common to speak of probability as a proportion. 
 If the fraction expressing the probability of ace being cast is , 
 the proportion of cases in which it happens is i to 5 ; or (as it 
 is, perhaps, still more commonly put) ' the chances are 5 to i 
 against it.' 
 
 3. As to the grounds of probability opinions differ. 
 
PROBABILITY 289 
 
 According to one view the ground is subjective : probability 
 depends, it is said, upon the quantity of our Belief in the 
 happening of a certain event, or in its happening in a particular 
 way. According to the other view the ground is objective, and, 
 in fact, is nothing else than experience, which is most trust- 
 worthy when carefully expressed in statistics. 
 
 To the subjective view it may be objected, (a) that Belief 
 cannot by itself be satisfactorily measured. Surely, no one 
 will maintain that Belief, merely as a state of mind, always has 
 a definite numerical value of which one is conscious, as T J^ or 
 y 1 ^. Let anybody mix a number of letters in a bag, knowing 
 nothing of them except that one of them is X, and then draw 
 them one by one, endeavouring each time to estimate the value 
 of his belief that the next will be X ; can he say that his belief 
 in the drawing of X regularly increases as the number of letters 
 left decreases ? 
 
 If not, we see that (b) Belief does not uniformly correspond 
 with the state of the facts. If in such a trial as proposed above, 
 we really wish to draw X, as when looking for something in a 
 number of boxes, how common it is after a few failures to feel 
 quite hopeless and to say : " Oh, of course it will be in the last." 
 For belief is subject to hope and fear, temperament, passion, 
 and prejudice, and not merely to rational considerations. And 
 it is useless to appeal to ' the Wise Man,' the purely rational 
 judge of probability, unless he is producible. Or, if it be said 
 that belief is a short cut to the evaluation of experience, be- 
 cause in fact it is the resultant of all past experience, we may 
 reply that this is not true. For everybody knows that one 
 striking experience, or two or three recent ones, will immensely 
 outweigh a great number of faint or remote experiences. More- 
 over, the experience of two men may be practically equal, whilst 
 their beliefs upon any question greatly differ. Any two English- 
 men have about the same experience, personal and ancestral, 
 of the weather ; yet their beliefs in the saw that ' if it rain on 
 St. Swithin's Day it will rain for forty days after,' may differ as 
 confident expectation and sheer scepticism. Upon which of 
 
290 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 these beliefs shall we ground the probability of forty days' 
 rain? 
 
 But (<;), at any rate, if Probability is to be connected with 
 Inductive Logic, it ought surely to rest upon the same 
 ground, namely Observation. Induction, in any particular- 
 case, is not content with beliefs or opinions, but aims at 
 probing, testing, verifying or correcting them by appealing 
 to the facts ; and Probability has the same object and the 
 same basis. 
 
 There are, indeed, cases in which the conditions of an event 
 are "supposed to be mathematically predetermined, as in tossing 
 a penny, throwing dice, dealing cards. In throwing a die, the 
 ways of happening are six ; in tossing a penny only two, head 
 and tail : and we usually assume that the odds with a die are 
 fairly 5 to i against ace, whilst with a penny ' the betting is 
 even' on head or tail. Still, this assumption rests upon another, 
 that the die is perfectly fair, or that the head and tail of a penny 
 are exactly alike ; and this is not true. With an ordinary die 
 or penny, a very great number of trials would, no doubt, give 
 an average approximating to J- or \ ; yet might always leave a 
 certain excess one way or the other, which would also become 
 more definite as the trials went on ; thus showing that the die 
 or penny did not satisfy the mathematical hypothesis. Bufton 
 is said to have tossed a coin 4040 times, obtaining 1992 heads 
 and 2048 tails; a pupil of De Morgan tossed 4092 times, 
 obtaining 2048 heads and 2044 tails. 
 
 There are other important cases in which probability is 
 estimated and numerically expressed, although statistical 
 evidence directly bearing upon the point in question cannot be 
 obtained ; as in betting upon a race ; or in the prices of stocks 
 and shares, which are supposed to represent the probability of 
 their paying, or continuing to pay, a certain rate of interest. 
 But the judgment of experts in such matters is certainly based 
 upon experience; and great pains are taken to make the 
 evidence as definite as possible by comparing records of speed, 
 or by financial estimates ; though something must still be 
 
PROBABILITY 291 
 
 allowed for reports of the condition of horses, or of the prospects 
 of war, etc. 
 
 However, where statistical evidence is obtainable, no one 
 dreams of preferring to estimate probability by the quantity of 
 his belief. Insurance offices, dealing with fire, shipwreck, 
 death, accident, etc., prepare elaborate statistics of these 
 events, and regulate their rates accordingly. Apart from 
 statistics, at what rate ought the lives of men aged 40 to be 
 insured, in order to leave a profit of 5 per cent, upon jiooo 
 payable at each man's death ? Is l quantity of belief ' a suffi 
 cient basis for doing this sum ? 
 
 4. The ground of probability is experience, then, and, 
 whenever possible, statistics ; which are a kind of inductions. 
 It has indeed been urged that induction is itself based upon 
 probability ; that the subtlety, complexity and secrecy of 
 nature are such, that we are never quite sure that we fully 
 know even what we have observed ; and that, as for laws, the 
 conditions of the universe at large may at any moment be 
 completely changed; so that all imperfect deductions, in- 
 cluding the law of Causation itself, are only probable. But, 
 clearly, this doctrine turns upon another ambiguity in the word 
 * probable.' It may be used in the sense of * less than abso- 
 lutely certain'; and such doubtless is the condition of all 
 human knowledge, in comparison with the comprehensive 
 intuition of archangels : or it may mean * less than certain 
 according to our standard of certainty,' that is, in comparison 
 with the law of Causation and its derivatives. 
 
 We may suppose some one to object that " by this relative 
 standard even empirical laws cannot be called * only probable ' 
 as long as we * know no exception to them ' ; for that is all that 
 can be said for the boasted law of Causation; and that, 
 accordingly, we can frame no fraction to represent their 
 probability. That * all swans are white ' was at one time, from 
 this point of view, not probable but certain ; though we now 
 know it to be false. It would have been an indecorum to call 
 it only probable as long as no other-coloured swan was 
 
292 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 known ; not merely because the quantity of belief amounted to 
 certainty, but because the number of events (seeing a swan) 
 and the number of their happenings in a certain way (being 
 white) were equal, and therefore the evidence amounted to i 
 or certainty." 
 
 But we reply, that such an empirical law is only probable, 
 and that the estimate of its probability must be based on the 
 number of times that similar laws have been found liable to 
 exceptions. White crows, though rare, are exceptions to the 
 law that crows are black ; and it is not uncommon to find 
 allied varieties of animals differing in colour in different 
 localities. Had the evidence been known and duly weighed, 
 then, it could never have seemed more than probable that ' all 
 swans are white.' But what law, similar in rank to the law of 
 Causation, presents any exceptions ? 
 
 It ought not to be difficult to see that induction, ' humanly 
 speaking/ does not rest on probability ; but that the probability 
 of concrete events (not of mere mathematical abstractions like 
 the falling of absolutely true dice) rests on induction and, 
 therefore, on causation. 
 
 The inductive evidence underlying an estimate of probability 
 may be of three kinds: (a) direct statistics of the events in 
 question ; as when we find that, at the age of 20, the average 
 expectation of life is 39-40 years. This is an empirical law, 
 and, if we do not know the causes of any event, we must be 
 content with an empirical law. But (b) if we do know the 
 causes of an event, and the causes which may prevent its 
 happening, and can estimate the comparative frequency of 
 their occurring, we may deduce the probability that the effect 
 (that is, the event in question) will occur. Or (c) we may 
 combine these two methods, verifying each by means of the 
 other. Now either the method (b) or (a fortiori) the method 
 (c) (both depending on causation) is more trustworthy than the 
 method (a) by itself. 
 
 But, further, a merely empirical statistical law will only be 
 true as long as the causes influencing the event remain the 
 
PROBABILITY 293 
 
 same. A die may be found to turn ace once in six throws, on 
 the average, in close accordance with mathematical theory ; 
 but if we load it on that facet the results will be very different. 
 So it is with the expectation of life, or fire, or shipwreck. The 
 increased virulence of some epidemic such as influenza, an 
 outbreak of anarchic incendiarism, a moral epidemic of over- 
 loading ships, may deceive the hopes of insurance offices. 
 Hence we see, again, that probability depends upon causation, 
 not causation upon probability. 
 
 That uncertainty of an event which arises not from ignorance 
 of the law of its cause, but from our not knowing whether the 
 cause itself does or does not occur at any particular time, is 
 Contingency. 
 
 5. The nature of an average supposes deviations from it. 
 These deviations, or 'errors,' conform to the law that the 
 greater are less frequent than the smaller, so that most of the 
 events approximate to the average. The calculation of 
 probabilities, in fact, supposes a class or series of instances or 
 events, subject (as far as known) to somewhat similar con- 
 ditions, though the conditions are not so similar as to result in 
 uniformity. Where the more similar conditions predominate, 
 they produce average instances; where dissimilar conditions 
 occur, but in such a way as to cancel one another, the average 
 again results ; where unusual conditions occur without can- 
 celling, extraordinary instances appear. Hence if the average 
 height of a nation is 5 ft. 6 in., most men will be about that 
 size ; men of 5 ft. and 6. ft. will be rare, and those of 4 ft. 6 in. 
 and 6 ft. 6 in. rarer still; whilst limits to height in both 
 directions seem to be fixed by the nature of things. In casting 
 a die, in sets of six throws, ace will turn up oftener once than 
 twice in each set of throws, oftener twice than three times, 
 though it may appear every time in six, and even in continuous 
 sets of sixes ; and, in such a case, there seems (a priori} to be 
 no necessary limit to the length of sequences that may occur in 
 infinite trials. 
 
 These considerations have an important bearing upon the 
 
294 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 interpretation of probabilities. The average probability for 
 any general class or series of events cannot be confidently 
 applied to any one instance or to any special class of instances, 
 since this one, or this special class, may exhibit a striking error 
 or deviation ; it may, in fact, be subject to special causes. 
 Within the class whose average is first taken, and which is 
 described by general characters as ' a man/ or ' a die,' or ' a 
 rifle shot/ there may be special classes marked by special 
 characters and determined by special influences. Statistics 
 giving the average for * mankind ' may not be true of ' civilised 
 men,' or any still smaller class such as * inhabitants of U.S.A.* 
 Hence life-insurance orifices rely not merely on statistics of life 
 and death in general, but collect special evidence in respect 
 of different ages and sexes, and make further allowance for 
 teetotalism, inherited disease, etc. Similarly for individual 
 cases : the average expectation for a class, whether general or 
 special, is only applicable to any particular case if that case is 
 adequately described by the class characters. In England, for 
 example, the average expectation of life for males at 20 years 
 of age is 39*40; but at 60 it is still 13*14, and at 73 it is 7*07 ; 
 at 100 it is i *6 1. Of men 20 years old those who live more 
 or less than 39*40 years are deviations or errors ; but there are 
 a great many of them. To insure the life of a single man at 
 20, in the expectation of his dying at 60, would be a mere bet, 
 if we had no special knowledge of him ; the safety of an 
 insurance office lies in having so many clients that opposite 
 deviations cancel one another : the more clients the safer the 
 business. It is quite possible that a hundred men aged 20 
 should be insured in one week and all of them die before 25 : 
 this would be ruinous, if others did not live to be So or 90. 
 
 Not only in such a practical affair as insurance, but in 
 matters purely scientific, the minute and subtle peculiarities of 
 individuals have important consequences. Each man has a 
 certain cast of mind, character, physique, giving a distinctive 
 turn to all his actions even when he tries to be normal. In 
 every employment this determines his Personal Equation, or 
 
PROBABILITY 295 
 
 average deviation from the normal. The term Personal 
 Equation is used chiefly in connection with scientific observa- 
 tion, as in Astronomy. Each observer is liable to be a little 
 wrong, and this error has to be allowed for and his observations 
 corrected accordingly. 
 
 The use of the term Expectation,' and of examples drawn 
 from insurance and gambling, is apt to convey the notion that 
 probability relates entirely to future events ; but if it is based 
 on laws and causes it can have no reference to point of time. 
 As long as conditions are the same events will be the same, 
 whether we consider uniformities or averages. We may there- 
 fore draw probable inferences concerning the past as well as 
 the future, subject to the same hypothesis, that the causes 
 affecting the events in question be the same and similarly 
 combined. On the other hand, if we know that conditions 
 bearing on the subject of investigation, have changed since 
 statistics were collected, or were different at some time previous 
 to the collection of evidence, every probable inference based 
 on those statistics must be corrected by allowing for the altered 
 conditions, whether we desire to reason forwards or backwards 
 in time. 
 
 6. The rules for the combination of probabilities are as 
 follows : 
 
 (1) If two events or causes do not concur, the probability of 
 one or the other occurring is the sum of the separate pro- 
 babilities. A die cannot turn up both ace and six ; but the 
 probability in favour of each is J : therefore, the probability in 
 favour of one or the other is J. Death can hardly occur from 
 both burning and drowning : if i in 1000 is burned and 2 in 
 1000 are drowned, the probability of being burnt or drowned 
 
 ic 3 
 
 15 TT5UTF- 
 
 (2) If two events are independent, having neither connection 
 nor repugnance, the probability of their concurring is found 
 by multiplying together the separate probabilities of each 
 occurring. 
 
 If in walking down a certain street I meet A once in four 
 
296 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 times, and B once in three times, I ought (by mere chance) to 
 meet both once in twelve times : for in twelve occasions I meet 
 B four times ; but once in four I meet A. 
 
 This is a very important rule in scientific investigation, 
 since it enables us to detect the presence of causation. For 
 if the coincidence of two events is more or less frequent than 
 it would be if they were entirely independent, there is either 
 connection or repugnance between them. If, e.g., in walking 
 down the street I meet both A and B oftener than once in 
 twelve times, they may be engaged in similar business, calling 
 them from their offices at about the same hour. If I meet 
 them both less often than once in twelve times, they may 
 belong to the same office, where one acts as a substitute fo.T 
 the other. Similarly, if in a multitude of throws a die turns 
 six oftener than once in six times, it is not a fair one : that is, 
 there is a cause favouring the turning of six. 
 
 If of 20,000 people 500 see apparitions and 100 have friends 
 murdered, the chunce of any man having both experiences 
 is -g-enju ; but if each lives on the average 300,000 hours, the 
 chance of both events occurring in the same hour is 
 If tne two events occur in the same hour 
 
 oftener than this, there is more than a chance coincidence. 
 
 The more minute a cause of connection or repugnance 
 between events, the longer the series of trials or instances 
 necessary to bring out its influence. The less a die is loaded, 
 the more casts must be made before it can be shown that a 
 certain side tends to recur oftener than once in six. 
 
 (3) The rule for calculating the probability of a dependent 
 event is clearly the same as the above ; for the concurrence of 
 two independent events is itself dependent upon each of them 
 occurring. My meeting with both A and B in the street is 
 dependent on my walking there and on my meeting one of 
 them. Similarly, if A is sometimes a cause of B (though liable 
 to be frustrated), and B sometimes of C (C and B having no 
 causes independent of B and A respectively), the occurrence of 
 C is dependent on that of B, and that again on the occurrence 
 
PROBABILITY 297 
 
 of A. Hence we may state the rule : If two events are 
 dependent each on another, so that if one occur the second 
 may (or may not), and if the second a third ; whilst the third 
 never occurs without the second, nor the second without the 
 first ; the probability that if the first occur the third will, is found 
 by multiplying together the fractions expressing the probability 
 that the first is a mark of the second and the second of the 
 third. 
 
 Upon this principle the value of hearsay evidence or tradition 
 deteriorates, and generally the cogency of any argument based 
 upon the combination of approximate generalisations dependent 
 on one another or " self-infirmative." If there are two witnesses, 
 A and B, of whom A saw an event, whilst B only heard A 
 relate it (and is therefore dependent on A), what credit is due 
 to B's recital ? Suppose the probability of each man's being 
 correct as to what he says he saw, or heard, is f : then 
 (f x J = T 9 F ) the probability that B's story is true is a little more 
 than J. For if in 16 attestations A is wrong 4 times, B can 
 only be right in f of the remainder, or 9 times in 16. Again, 
 if we have the Approximate Generalisations, ' Most 'attempts 
 to reduce wages are met by strikes,' and ' Most strikes are 
 successful,' and learn, on statistical inquiry, that in every 
 hundred attempts to reduce wages there are 80 strikes, and 
 that 70 p.c. of the strikes are successful, then 56 p.c. of 
 attempts to reduce wages are unsuccessful. 
 
 Of course this method of calculation cannot be quantita- 
 tively applicable if no statistics are obtainable, as in the 
 testimony of witnesses ; and even if a numerical value could 
 be attached to the evidence of a certain class of witnesses, it 
 would be absurd to assume it for particular members of the 
 class without taking account of their education, interest in the 
 case, prejudice, or general capacity. Still, the numerical 
 illustration of the rapid deterioration of hearsay evidence, 
 when less than quite veracious, puts us on our guard against 
 rumour. To retail rumour may be as bad as to invent an 
 original lie. 
 
298 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (4) If an event may coincide with two or more other 
 independent events, the probability that they will together be 
 a sign of it, is found by multiplying together the fractions 
 representing the improbability that each is a sign of it, and 
 subtracting the product from unity. 
 
 This is the rule for estimating the cogency of cumulative 
 testimony, circumstantial evidence, analogical evidence; or, 
 generally, for combining Approximate Generalisations " self 
 corroboratively." 
 
 If, for example, each of two independent witnesses, or cir- 
 cumstances, raises a probability of 6 to i in favour of a certain 
 event; taking i to represent certainty, i- is the improbability 
 of the event, notwithstanding each witness. Then TX^- = ^J-, 
 the improbability of both proving it. Therefore the proba- 
 bility of the event is 48 to i . The matter may be plainer if 
 put thus : A is right 6 times in 7, or 42 in 49 ; in the remain- 
 ing 7 times in 49 B will be right 6 times. Therefore, together 
 they will be right 48 times in 49. 
 
 If in an analogical argument there were 8 points of com- 
 parison, 5 for and 3 against a certain inference, and the 
 probability of each point could be quantified, the total 
 value of the evidence could be estimated by doing a similar 
 sum. 
 
 When approximate generalisations that have not been pre- 
 cisely quantified combine their evidence, the cogency of the 
 argument increases in the same way, though it cannot be 
 made so definite. If it be true that most poets are irritable, 
 and also that most invalids are irritable, a still greater pro- 
 portion will be irritable of those who are both invalids and 
 poets. 
 
 On the whole, from the discussion of probabilities there 
 emerge four principal cautions as to their use : Not to make a 
 pedantic parade of numerical probability, where the numbers 
 have not been ascertained ; Not to trust to our feeling of what 
 is likely, if statistics can be obtained ; Not to apply an average 
 probability to special classes or individuals without inquiring 
 
PROBABILITY 299 
 
 whether they correspond to the average type ; and Not to trust 
 to the empirical probability of events, if their causes can be 
 discovered and made the basis of reasoning which the empirical 
 probability may be used to verify. 
 
 The reader who wishes to pursue this subject further should 
 read a work to which the foregoing chapter is greatly indebted, 
 Dr. Venn's Logic of Chance, 
 
CHAPTER XXI 
 DIVISION AND CLASSIFICATION 
 
 i. Classification, in its widest sense, is a mental grouping 
 of facts or phenomena according to their resemblances and 
 differences, so as best to serve some purpose. I say a 
 " mental grouping " ; for although in museums we often 
 see the things themselves arranged in classes, yet such an 
 arrangement only contains specimens representing a classi- 
 fication. The classification itself may extend to innumerable 
 objects most of which have never been seen at all. Extinct 
 animals, for example, are classified from what we know of 
 their fossils ; and some of the fossils may be seen arranged 
 in a museum ; but the animals themselves have disappeared 
 for many ages. 
 
 Again, things are classed according to their resemblances 
 and differences : that is to say, those that most closely resemble 
 one another are classed together on that ground ; and those 
 that differ from one another in important ways, are distributed 
 into different classes. The more the things differ, the wider 
 apart are their classes both in thought and in the arrangements 
 of a museum. If their differences are very great, as with 
 animals, vegetables and minerals, the classing of them falls to 
 different departments of thought or science, and is often repre- 
 sented in different museums, zoological, botanical, minera- 
 logical. 
 
 We must not, however, suppose that there is only one way 
 of classifying things. The same objects may be classed in 
 
 
DIVISION AND CLASSIFICATION 301 
 
 various ways according to the purpose in view. For gardening, 
 we are usually content to classify plants into trees, shrubs, 
 flowers, grasses and weeds ; the ordinary crops of English agri- 
 culture are distinguished, in settling their rotation, into white 
 and green ; the botanist writes about monocotyledons and 
 dicotyledons. The principle of resemblance and difference is 
 recognised in all these cases; but what resemblances or 
 differences are important depends upon the purpose to be 
 served. 
 
 Purposes may themselves be classified ; and here the most 
 important distinction for Logic is between (a) special or 
 practical purposes, as in gardening or hunting, and (/3) general 
 or scientific, as in Botany or Zoology. The scientific purpose 
 is merely knowledge ; it may indeed subserve all particular or 
 practical ends, but has no other end than knowledge directly 
 in view. And whilst, even for knowledge, different classi- 
 fications may be suitable for different lines of inquiry, 
 in Botany and Zoology the Morphological classification is 
 (I suppose) that which gives the most general and com- 
 prehensive knowledge (see Huxley, On the Classification of 
 Animals i ch. i). Most of what a logician says about classi- 
 fication is applicable to the practical kind ; but the scientific 
 (often called ' Natural Classification '), as the most thorough 
 and comprehensive, is what he keeps most constantly before 
 him. 
 
 Scientific classification, of course, comes late in human 
 history, and at first works over earlier classifications which 
 have been made by the growth of intelligence, of language, and 
 of the practical arts. Even in the distinctions recognised by 
 animals, may be traced the grounds of classification. A cat 
 does not confound a dog with one of its own species, nor 
 water with milk, nor cabbage with fish. But it is in the 
 development of language that the progress of instinctive classi- 
 fication may best be seen. The use of general names implies 
 the recognition of classes of things corresponding to them, 
 which form their denotation, and whose resembling qualities 
 
302 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 so far as recognised, form their connotation ; and such names 
 are of many degrees of generality. The use of abstract names 
 shows that the objects classed have also been analysed, and 
 that their resembling qualities have been recognised amidst 
 diverse groups of qualities: 
 
 Of the classes marked by popular language it is worth while 
 to distinguish two sorts (cf. chap. xix. 4) : Kinds, and those 
 having but few points of agreement. 
 
 But the popular classifications, made by language and the 
 primitive arts, are very imperfect. They omit innumerable 
 things which have not been found useful or noxious, or have 
 been inconspicuous, or have not happened to occur in the 
 region inhabited by those who speak a particular language; 
 and even things recognised and named may have been very 
 superficially examined, and therefore wrongly classed, as when 
 a whale or porpoise is called a fish, or a slowworm is con- 
 founded with snakes. A scientific classification, on the other 
 hand, aims at the utmost comprehensiveness, ransacking the 
 whole world from the depths of the earth to the remotest star 
 for new objects, and scrutinising everything with the aid of 
 crucible and dissecting knife, microscope and spectroscope, to 
 find the qualities and constitution of everything, in order that 
 it may be classed among those things with which it has most 
 in common and distinguished from those other things from 
 which it diners. A scientific classification continually grows 
 more comprehensive, more discriminative, more definitely and 
 systematically coherent. Hence the uses of classification may 
 be easily perceived. 
 
 2. The first use of classification is the better understanding 
 of the facts of Nature (or of any sphere of practice) ; for under- 
 standing consists in perceiving and comprehending the likeness 
 and difference of things, in assimilating and distinguishing 
 them; and in carrying out this process systematically new 
 correlations of properties are continually disclosed. Thus 
 classification is closely analogous to we may say, a kind of 
 explanation. Explanation has been shown (chap. xix. 5) to 
 
DIVISION AND CLASSIFICATION 303 
 
 consist in the discovery of the laws or causes of changes in 
 Nature ; and laws and causes imply similarity, or like changes 
 under like conditions : in the same way classification consists 
 in the discovery of resemblances in the things that undergo 
 change. We may say (subject to subsequent qualifications) 
 that Explanation analyses Nature in its dynamic, Classification 
 in its static aspect. In both cases we have a feeling of relief. 
 When the cause of any event is pointed out, or an object is 
 assigned its place in a system of classes, the gaping wonder, 
 or confusion, or perplexity, occasioned by an unintelligible 
 thing, or (worse) by a multitude of such things, is dissipated. 
 No doubt, some people are more than others susceptible of 
 this pleasure and fastidious about its purity. 
 
 A second use of classification is to aid the memory. It 
 strengthens memory, because one of the conditions of our 
 remembering things is, that they resemble what we last thought 
 of ; so that to be accustomed to study and think of things in 
 classes must greatly facilitate remembrance. But, besides this, 
 it improves the character of memory, by making us more likely 
 to remember what we want. For what we want in any emer- 
 gency is to remember what served the purpose in similar cases ; 
 or to recall cases similar to the present one, as in warding a 
 blow, or solving a problem, or illustrating an essay. Here 
 again, explanation and classification have the same use : they 
 both tend to rationalise the memory, and to organise the mind 
 in correspondence with Nature. 
 
 Every one knows how a poor mind is always repeating itself, 
 going by rote through the same train of words, ideas, actions ; 
 and that such a mind is neither interesting nor practical. It is 
 not practical, because the circumstances of life are rarely 
 exactly repealed, so that it is rarely enough for our present 
 purpose to remember only one former case ; we need several, 
 that by comparing (perhaps automatically) their resemblances 
 and differences with the one before us, we may select a course 
 of action, or a principle, or a parallel, suited to our immediate 
 needs. 
 
304 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Thus, greater fertility and flexibility of thought seem naturally 
 to result from the practice of explanation and classification. 
 But it must be honestly added, that the result depends upon 
 the spirit in which such study is carried on ; for if we are too 
 fond of finality, too eager to believe that we have already 
 attained a greater precision and comprehension than are in 
 fact attainable, nothing can be more petrific than * science,' and 
 our last state may be worse than the first. Of this, students of 
 Logic have often furnished examples. 
 
 3. Classification may be either Deductive or Inductive ; 
 that is to say, in the formation of classes, as in the proof of 
 propositions, we may, on the whole, proceed from the more to 
 the less, or from the less to the more general ; not that these 
 two processes are entirely independent. 
 
 If we begin with some large class, such as * Animal/ and 
 subdivide it deductively into Vertebrate and Invertebrate, yet 
 the principle of division (namely, central structure) has first 
 been reached by a comparison of examples and by generalisa- 
 tion; if, on the other hand, beginning with individuals, we 
 group them inductively into classes, and these again into wider 
 ones (as dogs, cats, horses, whales and monkeys 'into mammalia) 
 we are guided both in special cases by hypotheses as to the 
 best grounds of resemblance, and throughout by the general 
 principle of classification to associate things that are alike 
 and to separate things that are unlike. This principle holds 
 implicitly a place in classification similar to that of causation 
 in inductive proof; and whatever the remote origin or basis of 
 these principles, that is a question for Psychology or for Meta- 
 physics : they are now principles of intelligence, of Logic and 
 of Science. Here, therefore, as in proof, induction is implied 
 in deduction, and deduction in induction. Still, the two modes 
 of procedure may be usefully distinguished : in deduction, we 
 advance from a whole to its parts, from general to special ; in 
 induction, from special (or particular) to general, from the 
 parts to their whole. 
 
DIVISION AND CLASSIFICATION 
 
 4. The process of Deductive Classification, or Formal 
 Division, may be represented thus : 
 
 
 
 A 
 
 1 
 
 
 
 1 
 
 AB 
 
 1 
 
 
 
 1 
 Ab 
 
 I 
 
 1 
 ABC 
 
 1 
 ABc 
 
 1 
 AbC 
 
 1 
 Abe 
 
 Given any class (A) to be divided. 
 
 1. Select one important character, attribute, or quality (B), 
 not common to all the individuals comprehended in the class, 
 as the basis of division (Jundamcntum divisionis). 
 
 2. Proceed by Dichotomy ; that is, cut the given class into 
 two, one having the selected attribute (say, B), the other not 
 having it (b). This, like all formal processes, assumes the 
 principles of Contradiction and Excluded Middle, that * No A 
 is both B and not-B,' and that ' Every A is either B or not-B ' 
 (chap. vi. 3) ; and if these principles are not true, or not 
 applicable, the method fails. 
 
 When a Class is thus subdivided, it may be called, in relation 
 to its subclasses, a Genus ; and in relation to it, the subclasses 
 may be called Species : thus Genus A, Species AB and Ab, 
 etc. 
 
 3. Proceed gradually in the order of the importance of 
 characters ; that is, having divided the given class, subdivide 
 on the same principle the two classes thence arising ; and so 
 again and again, step by step, until all the characters are 
 exhausted : Divisio ne fiat per saltum. 
 
 Suppose we were to attempt an exhaustive classification of 
 things by this method, we must begin with ' All Things,' and 
 divide them (say) into phenomenal and not-phenomenal, and 
 then subdivide phenomena, and so on, thus : 
 
3 o6 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 All Things 
 I 
 
 I I 
 
 Phenomenal Not-phenomenal 
 
 I I 
 
 Extended Unextended 
 
 (e.g., Pleasure and Pain) 
 
 ! 
 
 r I 
 
 Resistant Non-resistant 
 (Matter) (Space) 
 
 I 
 
 I I 
 
 Gravitating Non-gravitating 
 
 . I I 
 
 Simple Compound 
 
 Having subdivided 'Simple 7 by all possible characters, we 
 must then go back and similarly subdivide Not-phenomenal, 
 Unextended, Non-resistant, Non-gravitating, and Compound. 
 Now, if we knew all possible characters, and the order of their 
 importance, we might prepare a priori a classification of all 
 possible things; at least, of all things that come under the 
 principles of Contradiction and Excluded Middle. It might, 
 indeed, appear that many of our compartments had nothing 
 actual answering to them ; there may, for example, be nothing 
 that is not phenomenal to some mind, or nothing that is 
 extended and non-resistant (no vacuum), and so forth. It is 
 true that this implies a breach of the rule, that the dividing 
 quality be not common to the whole class ; but, in fact, doubts 
 have been, and are, seriously entertained whether these com- 
 partments are filled or not. If they are not, we have concepts 
 representing nothing, which have perhaps been generated by 
 the mere force of grammatical negation ; and, on the strength 
 of these empty concepts, we have been misled into dividing 
 by an attribute, which (being universal) cannot be a funda- 
 menfum divisioMs. But though in such a classification places 
 might be empty, there would be a place for everything ; for 
 
DIVISION AND CLASSIFICATION 307 
 
 whatever did not come into some positive class, such as 
 Gravitating, must, at any rate, fall under one of the negative 
 classes (the ' Nots ') that would run down the right-hand side 
 of the Table and of its subdivisions. 
 
 This is the ideal of classification. Unfortunately, however, 
 we have to learn what characters or attributes are possible, by 
 experience and comparison; we are far from knowing them all : 
 and we do not know the order of their importance ; nor are we 
 even clear what ' important ' means in this context, whether 
 ' widely prevalent,' or * ancient,' or ' causally influential,' or 
 ' indicative of others.' Hence, in classifying actual things, the 
 inductive method of beginning with particular things, and 
 sorting them according to their likeness as discovered by 
 investigation of their nature, must clearly always be resorted 
 to. The exceptional cases, in which deduction is really useful, 
 occur where certain limits to the number and combination of 
 qualities happen to be known, as they may be in human 
 institutions, or where there are mathematical conditions. Thus, 
 we might be able to classify orders of Architecture, or the 
 legitimate metres and stanzas of English Poetry ; though, in 
 fact, these things are too free, subtle and complex for deductive 
 treatment : for do not the Arts grow like trees ? The only 
 sure cases are mathematical ; as we may show that there are 
 possible only three kinds of plane triangles, four conic sections, 
 five regular solids, etc. 
 
 5. The rules for testing a Division are as follows : 
 
 i. Each Sub-class, or Species, should comprise less than the 
 Class, or Genus, to be divided. 
 
 This provides that the Division shall be a real one, and not 
 based upon an attribute common to the whole class ; that, 
 therefore, the first rule for making a division shall have been 
 completely adhered to. But, as in 4, we are here met by a 
 logical difficulty. Suppose the class to be divided is A, and 
 we attempt to divide upon the attribute B, into AB and Ab ; 
 is this now a true division, if we do not know any A that is 
 not B ? As far as our knowledge extends, we have not divided 
 
308 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 A at all. But, on the other hand, our knowledge of concrete 
 things is never exhaustive ; so that, although we know of no A 
 that is not B, it may yet exist, and we have seen that it is a 
 logical caution not to assume what we do not know. In a 
 deductive classification, at least, it seems better to regard every 
 attribute as a possible ground of division. Hence, in the 
 above division of 'All Things,' 'Non-phenomenal/ 'Ex- 
 tended-Non-resistant,' * Resistant-Non-gravitating,' appear as 
 negative classes (that is, classes based on the negation of an 
 attribute), although their real existence may be doubtful. But, 
 if this is justifiable, we must either rewrite the first test of a 
 division thus : ' Each sub-class should possibly comprise less 
 than the class to be divided ' ; or else we must confine the rule 
 to (a) thoroughly empirical divisions, as in dividing Colour 
 into Red and Not-red, where we know that both sub-classes 
 are real ; and (b) divisions under demonstrable conditions as 
 in dividing the three kinds of triangles by the quality equi- 
 lateral, we know that it is only applicable to acute-angled 
 triangles, and do not attempt to divide the right-angled or 
 obtuse-angled by it. 
 
 2. The Sub-classes taken together should be equal to the 
 Class to be divided : the sum of the Species constitutes the 
 Genus. This provides that the Division shall be exhaustive ; 
 which is always secured by dichotomy, according to the prin- 
 ciple of Excluded Middle ; because whatever is not in the 
 positive class, must be in the negative : Red and Not-red 
 include all colours. 
 
 3. The Sub-classes must be opposed or mutually exclusive : 
 Species must not overlap. This again is secured by Dichotomy, 
 according to the principle of Contradiction, provided the 
 Division be made upon one attribute at a time. But, if we 
 attempt to divide simultaneously upon two attributes, as 
 ' Musicians ' upon ( nationality ' and ' method,' we get what is 
 called a Cross-division, thus : ' German Musicians/ ' Not- 
 German,' * Classical/ 'Not-Classical/ for these classes may 
 overlap, the same men sometimes appearing in two groups 
 
DIVISION AND CLASSIFICATION 309 
 
 Bach in ' German ' and * Classical,' Pergolesi in ' Not-German 
 and ' Classical.' If, however, we divide Musicians upon these 
 attributes successively, cross division will be avoided, thus : 
 
 Musicians 
 I 
 
 1 
 
 Classical 
 
 1 
 
 1 
 Non-classical 
 1 
 
 1 
 German 
 
 1 
 Non-German 
 
 1 
 German 
 
 1 
 Non-German 
 
 Here no Musician will be found in two classes, unless he has 
 written works in two styles, or unless there are works whose style 
 is undecided. Let this " unless or unless " suggest caution in 
 using dichotomy as a short cut to the classification of realities. 
 
 4. No Sub-class must include anything that is not comprised 
 in the class to be divided : the Genus comprises all the Species. 
 Do not divide Dogs into fox-terriers and dog-fish. 
 
 6. The process of Inductive Classification may be repre- 
 sented thus : 
 
 Given any multitude of individuals to be classified: 
 
 (1) Place together in groups (or in thought) those things that 
 have in common the most, the most widely diffused and the 
 most important qualities. 
 
 (2) Connect those groups which have, as groups, the greater 
 resemblance, and separate those that have the greater 
 difference. 
 
 (3) Demarcate, as forming higher or more general classes, 
 those groups of groups that have important characters in 
 common ; and, if possible, on the same principle, form these 
 higher classes into classes higher still : that is to say, graduate 
 the classification upwards. 
 
 Whilst, in Division the terms ' Genus ' and ' Species ' are 
 entirely relative to one another and have no fixed positions in 
 a gradation of classes, it has been usual, in Inductive Classifi- 
 cation, to confine the term 'Species' to classes regarded as 
 lowest in the scale, to give the term * Genera ' to classes on the 
 
3 io LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 step above, and at each higher step to find some new term 
 such as * Tribe,' ' Order,' ' Sub-kingdom/ ' Kingdom ' ; as may 
 be seen by turning to any book on Botany or Zoology. If, 
 having fixed our Species, we find them subdivisible, it is usual 
 to call the Sub-species * Varieties.' 
 
 Suppose we attempt to classify by this method the objects in 
 an ordinary sitting-room. We see at a glance carpets, mats, 
 curtains, grates, fire-irons, coal-scuttles, chairs, sofas, tables, 
 books, pictures, musical instruments, etc. These we may call 
 
 * Species.' Carpets and mats clearly go together; so do chairs 
 and sofas ; so do grates, fire-irons, and coal-scuttles ; and so on. 
 These greater groups, or higher classes, we may call *' Genera.' 
 Putting together carpets, mats and curtains as * warmth-fabrics '; 
 chairs, sofas and tables as * supports'; books, pictures and 
 musical instruments as * means of culture ' ; these groups we 
 may call Orders. Sum up the whole as, from the housewife's 
 point of view, ' furniture/ If we then subdivide some of the 
 species, as books into poetry, novels, travels, etc. these Sub- 
 species may be considered ' Varieties.' 
 
 A Classification thus made, may be tested by the same rules 
 as those given for testing a Division ; but if it does not stand 
 the test, we must not infer that the classification is a bad one. 
 If the best possible, it is good, though formally imperfect: 
 whatever faults are found must then be charged upon the 
 
 * matter,' which is traditionally perverse and intractable. If, 
 for example, there is a hammock in the room, it must be classed 
 not with the curtains as a warmth-fabric, but with the sofas as 
 a support; and books and pictures may be classed as, in a 
 peculiar sense, means of culture, though all the objects in the 
 room may have been modified and assorted with a view to 
 gratifying and developing good taste. 
 
 7. The difficulty of classifying natural objects is very 
 great. It is not enough to consider their external appearance : 
 exhaustive knowledge of their internal structure is necessary, 
 and of the functions of every part of their structure. This is 
 a matter of immense research, and has occupied many of the 
 
DIVISION AND CLASSIFICATION 311 
 
 greatest minds for very many years. The following is a tabular 
 oucline of the classification of the 
 
 Animal Kingdom 
 
 I I 
 
 SUB-KINGDOM : Vertebrates Invertebrates (5 Sub-kingdoms) 
 
 CLASS : Mam 
 
 
 Sauropsida 
 
 I 
 
 Ichthyopsida 
 
 r~ n 
 
 Amphibia Fishes 
 
 1 1 
 mals Birds Reptiles 
 
 1 
 SOB-CLASS: Placental Implacental 
 1 
 
 I 
 DIVISION : Monodelphia Didelphia 
 
 I 
 
 Ornithodelphia 
 
 I III 
 
 ORDER: Quadrumana Rodentia Carnivora Ungulata Caetacea, etc. 
 
 I ! I 
 
 SECTION: Pinnigrada Plantigrada Digitigrada 
 
 I I 
 
 (Seals, etc.) (Bears, etc.) 
 
 \ I I I I 
 
 GENUS : Mustelidse Viverridae Hysenidae Canidae Felidae 
 
 (Weasels, etc.) (Civets, etc.) 
 
 Ill III 
 
 SPECIES : Lion Tiger Leopard Puma Lynx Cat, etc. 
 
 I 
 
 I I I 
 
 VARIETY : African Syrian Cave-lion (extinct) 
 
 As there is not space enough to tabulate such a classification 
 in full, I have developed at each step the most interesting 
 groups : Vertebrates, Mammals, Monodelphia, Carnivora, Digi- 
 tigrada, Felidse, Lion. Most of the other groups in each grade 
 are also subdivisible, though some of them contain far fewer 
 sub-classes than others. 
 
312 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 To see, however, the true character of this classification, we 
 must consider that it is based chiefly upon knowledge of 
 existing animals. Some extinct animals, known by their 
 fossils, find places in it; for others new places have been 
 made. But it represents, on the whole, a cross-section, or 
 cross-sections, of Nature as developing in time ; and, in order 
 to give a just view of the relations of animals, it must be seen 
 in the light of other considerations. The older systems of 
 classification, and the rules for making them, seem to have 
 assumed that an actual system of classes, or of what Mill calls 
 ' Kinds/ exists in nature, and that the relations of Kinds in 
 this system are determined by quantity of resemblance in 
 co-existent qualities, as the ground of their affinity. 
 
 8. Darwin's doctrine of the origin of species modifies the 
 conception of natural classification in several ways. In the 
 first place, if all living things are blood-relations, modified in 
 the course of ages according to their various conditions of life, 
 * Affinity ' must mean * nearness of common descent ' ; and it 
 seems irrational to propose a classification upon any other 
 basis. We have to consider the Animal (or the Vegetable) 
 Kingdom as a family tree, exhibiting a long line of ancestors, 
 and (descended from them) all sorts of cousins, first, second, 
 third, etc., perhaps once, twice, or oftener 'removed'. Of 
 course, animals in the relation of first cousins must be classed 
 as nearer than second cousins, and so on. 
 
 But, if we accept this principle, and are able to trace 
 relationship, it may not lead to the same results as we should 
 reach by simply relying upon the present * quantity of 
 resemblance ', unless we understand this in a very particular 
 way. For the most obvious features of an animal may have 
 been recently acquired, as often happens with those characters 
 which adapt an animal to its habits of life, as the wings of a 
 bat, or the fish-like shape of a dolphin; or as in cases of 
 'mimicry'. Some butterflies, snakes, etc., have grown to 
 resemble closely, in a superficial way, other butterflies and 
 snakes, from which a stricter investigation widely separates 
 
 
DIVISION AND CLASSIFICATION 313 
 
 them ; and this superficial resemblance is probably a recent 
 acquisition, for the sake of protection : the imitated butterflies 
 being nauseous, and the imitated snakes poisonous. On the 
 other hand, ancient and important traits of structure may, in 
 some species, have dwindled into inconspicuous survivals or 
 be still found only in the embryo ; so that only great know- 
 ledge and sagacity can identify them ; yet upon ancient traits, 
 though hidden, classification depends. The seal seems nearer 
 allied to the porpoise than to the tiger, the shrew nearer to the 
 mouse than to the hedgehog ; and the Tasmanian hyaena, or 
 the Tasmanian devil, looks more like a true hysena, or a badger, 
 than like a kangaroo ; yet the seal is nearer akin to the tiger, 
 the shrew to the hedgehog, and the Tasmanian carnivores are 
 marsupial, like the kangaroo. To overcome this difficulty we 
 must understand the resemblance upon which classification is 
 based to include resemblance of Causation, that is, the fact 
 itself of descent from common ancestors. In the case of 
 organic beings, all other rules of classification are subordinate 
 to one : trace the genealogy of every form. 
 
 By this rule, however, we get a definite meaning for the 
 phrase 'important or fundamental attribute' as determining 
 organic classes; namely, most ancient, or 'best serving to 
 indicate community of origin.' Grades of classification will 
 be determined by such fundamental characters, and may cor- 
 respond approximately to the more general types (now mostly 
 extinct) from which existing animals have descended. 
 
 In the second place, by the hypothesis of development the 
 fixity of species is discredited. The lowest grade of a classifi- 
 cation is made up not of well-defined types unchanging from 
 age to age, but of temporary species, often connected by 
 uncertain and indistinct varieties : some of which may, in 
 turn, if the conditions of their existence alter, undergo such 
 changes as to produce new species. Hence, again, the notion 
 that Kinds exist in organic nature must be greatly modified. 
 During a given period of a few thousand years, Kinds may be 
 recognised, because, under such conditions as now Drevail in 
 
314 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 the world, that period of time is insufficient to bring about 
 great changes. But, if it be true that lions, tigers, and leopards 
 have had a common ancestor, from whose type they have 
 gradually diverged, it is plain that their present distinctness 
 results only from the death of intermediate specimens and the 
 destruction of intermediate varieties. Could we, by the 
 evidence of fossils, restore all the ranks of the great proces- 
 sions that have descended from the common ancestor, we 
 should find nowhere a greater difference than between offspring 
 and parents ; and the appearance of Kinds existing in nature, 
 which is so striking in a museum or zoological garden, would 
 entirely vanish. 
 
 A classification, then, as formerly observed, represents a 
 cross-section of nature as developing in time : could we begin 
 at the beginning and follow this development down the course 
 of time, we should find no classes, but an ever-moving, chang- 
 ing, spreading, branching continuum. It may be represented 
 thus : Suppose an animal (or plant) A, extending over a certain 
 geographical area, subject to different influences and conditions 
 
 ADHK ADHL ACliM 
 
 of climate, food, hill and plain, wood and prairie, enemies and 
 rivals, and undergoing modifications here and there in adapta- 
 tion to the varying conditions of life : then varieties appear. 
 These varieties, diverging more and more, become distinct 
 Species (AB, AC, AD, AX). Some of these Species, the more 
 widely diffused, again produce varieties ; which, in turn, become 
 
DIVISION AND CLASSIFICATION 315 
 
 Species (ABE, ABF, ADG, ADH). From these again, arise, 
 ABFI, ABFJ, ADHK, ADHL, ADHM. Then ABE, ABF, 
 and ADH are Genera (ADG being extinct) ; and the earlier 
 types represent Families and Orders. 
 
 If in this age a classifier appears, he finds seven living 
 Species, which can be grouped into four Genera (ABE, ABF, 
 AC, ADH), and these again into three Families (AB, AC, AD), 
 all forming one Order. If the fossils of ADG and AX can be 
 found, he has two more Species, one more Genus (ADG), and 
 one more Family (AX). For AC, which has persisted un- 
 changed, and AX, which has become extinct, are both of them 
 Families, each represented by only one Species. 
 
 But now suppose that he could find a fossil specimen of 
 every generation (hundreds of thousands of generations), from 
 ABFI, etc., up to A ; then, as each generation would only 
 differ from the preceding as offspring from parents, he would 
 be unable at any point to distinguish a Species ; at most, he 
 would observe a slightly marked variety. ABFI and ABFJ 
 would grow more and more alike, until they became indistin- 
 guishable in ABF ; ABF and ABE would merge into AB ; 
 AB, AC, AD and AX would merge into A. Hence, the 
 appearance of Species is due to our taking cross-sections of 
 time, or comparing forms that belong to periods remote from 
 one another (like AX, ADG, and ADHK, or AD, ADH and 
 ADHK), and this appearance of Species depends upon the 
 destruction of ancestral intermediate forms. 
 
 In the third place, the hypothesis of development modifies 
 the logical character of classification : it no longer consists in 
 a direct induction of co-existent characters, but is largely a 
 deduction of these from the characters of earlier forms, 
 together with the conditions of variation ; in other words, 
 the definition of a species must, with the progress of science, 
 cease to be a mere empirical law of co-existence and become 
 a derivative law of Causation. But, after all, this was already 
 implied in the position that causation is the fundamental 
 principle of the explanation of concrete things ; and, accord- 
 
3i 6 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 ingly, the derivative character of species or kinds extends 
 beyond organic nature. 
 
 9. The classification of inorganic bodies also depends on 
 causation. There is the physical classification into Solids, 
 Liquids, and Gases. But these states of matter are dependent 
 on temperature ; at least, it is known that many bodies may, 
 at different temperatures, exist in ail three states. They 
 cannot therefore be defined as solid, liquid, or gaseous 
 absolutely, but only within certain degrees of temperature, 
 and therefore as dependent upon causation. Similarly, the 
 geological classification of bodies, according to relative anti- 
 quity (primary, secondary, tertiary, with their subdivisions), 
 and mode of formation (igneous and aqueous), rests upon 
 causation ; and so does the chemical classification of com- 
 pound bodies according to the elements that enter into them 
 in definite proportions. Hence, only the classification of the 
 elements themselves (amongst concrete things), at present, 
 depends largely upon empirical Co-existence. If the elements 
 remain irresolvable into anything simpler, the definitions of 
 the co-existent characters that distinguish .them must be 
 reckoned amongst the ultimate Uniformities of Nature. But 
 if a definite theory of their origin both generally and severally, 
 whether out of ether vortices or what-not, shall ever gain 
 acceptance, similarity of genesis or causation will naturally be 
 the leading consideration in classifying the chemical elements. 
 In fact, the ultimate explanation of nature is always causation ; 
 or, in other words, the Law of Causation is the backbone of 
 the system of Experience. 
 
CHAPTER XXII 
 NOMENCLATURE, DEFINITION, PREDICABLES 
 
 i. Precision of thought needs precision of language, not 
 only for recording such thought and for communicating it to 
 others, the two uses most frequently insisted upon, but even 
 for forming general or abstract ideas. It is true that we can 
 often remember with great vividness persons, things, landscapes, 
 changes and actions of persons or things, without the aid of 
 language (though words are often mixed with such trains of 
 imagery), and thus may form judgments and inferences in par- 
 ticular cases ; but for general notions, judgments and inferences 
 not merely about this or that man, Bismarck or Garibaldi, but 
 about all men or all Germans, we need something besides the 
 few images we can form of them from observation or from 
 pictures. Even in those cases where we may possess generic 
 images, say, of * horse ' or ' cat ' (that is, images formed, like 
 composite photographs, by a coalescence of the images of all 
 the horses or cats we have seen, so that their common properties 
 stand out and their differences frustrate and cancel one another), 
 these are useless for precise thought ; for the generic image will 
 not correspond with the general appearance of horse or cat, 
 unless we have had proportional experience of all varieties and 
 have been impartially interested in all ; and, besides, what we 
 want for general thought is not a generic image of the appear- 
 ance of things, though it were much more definite and fairly 
 representative than such images ever are, but a general repre- 
 sentation of their important characters ; which may be con- 
 nected with internal organs, such as none but an anatomist 
 
318 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 ever sees. We require a symbol connected wiih the general 
 character of a thing, or quality, or process, as scientifically 
 determined, whose representative truth may be trusted in 
 ordinary cases, or may be verified whenever doubt arises. 
 Such symbols are for most purposes provided by language ; 
 Mathematics and Chemistry have their own symbols. 
 
 2. First, then, there should be " a name for every important 
 meaning " : (a) A Nomenclature, or system of the names of all 
 classes of objects, adapted to the use of each science. Thus, 
 in Geology there are names for classes of rocks and strata, in 
 Chemistry for the elements and their compounds, in Zoology 
 and Botany for the varieties and species of animals and plants, 
 their genera, families and orders. 
 
 To have such names, however, is not the whole aim in 
 forming a scientific language, it is desirable that they should 
 be systematically significant, and even elegant. Names, like 
 other instruments, ought to be efficient, and the efficiency of 
 names consists in conveying the most meaning with the least 
 effort. In Botany and Zoology this result is obtained by 
 giving to each species a composite name which includes that 
 of the genus to which it belongs. Thus the species of Felidae 
 given in chap. xvii. 7, are called Felis leo (lion), Felis tigris 
 (tiger), Felis leopardus (leopard), Felis concolor (puma), Felis 
 lyncus (European lynx), Felis catus (wild cat). To take another 
 illustration from the nomenclature of Butterflies : Vanessa 
 Atalanta (red admiral), Vanessa lo (peacock), Vanessa poly- 
 cloros (large tortoise-shell), Vanessa urticcz (small tortoise-shell), 
 Vanessa Antiopa (Camberwell beauty), etc. In Chemistry, 
 again, the nomenclature is extremely efficient. Names of the 
 simpler compounds are formed by combining the names of 
 the elements that enter into them ; as Hydrogen Chloride, 
 Hydrogen Sulphide, Carbon Dioxide ; and these can be given 
 still more briefly and efficiently in symbols, as HC1, H 2 S, CO,. 
 The symbolic letters are usually initials of the names of the 
 elements : as C = Carbon, S = Sulphur ; sometimes of the Latin 
 name, when the common name is English, as Fe= Iron. Each 
 
NOMENCLATURE 319 
 
 letter represents a fixed quantity of the element for which it 
 stands, viz., the atomic weight. The number written below a 
 symbol on the right-hand side shows how many atoms of the 
 element denoted enter into a molecule of the compound. 
 
 (b) A Terminology is next required, in order to describe 
 and define the things that constitute the classes designated by 
 the nomenclature, and to describe and explain their actions. 
 
 (i) A name for every integral part of an object, as head, limb, 
 vertebra, heart, nerve, tendon ; stalk, leaf, corolla, stamen, 
 pistil ; plinth, frieze, etc. (ii) A name for every metaphysical 
 part of an object (that is, for every abstract quality of it, or for 
 a quality considered apart from the rest that constitute it), and 
 for their degrees and modes : as extension, figure, solidity, 
 weight ; rough, smooth, elastic, friable ; the various colours, 
 red, blue, yellow, in all their shades and combinations ; and so 
 with- sounds, smells, tastes, temperatures. 
 
 The terms of Geometry are employed to describe the modes 
 of figure, as angular, curved, square, elliptical ; and the terms 
 of Arithmetic to express the degrees of weight, elasticity, tem- 
 perature, pitch of sound. When other means fail, qualities are 
 suggested by the names of things which exhibit them in a 
 salient way : figures by such terms as amphitheatre, bowl-like, 
 pear-shaped, egg-shaped ; colours by lias-blue, sky-blue, 
 gentian-blue, peacock-blue ; and similarly sounds, smells and 
 tastes. It is also important to express by short terms complex 
 qualities, as harmony, fragrance, organisation, sex, symmetry, 
 stratification. 
 
 (iii) In the explanation of Nature we require further suitable 
 names for processes and activities : as deduction, conversion, 
 verification, addition, integration, causation, tendency, momen- 
 tum, gravitation, aberration, refraction, conduction, affinity, 
 combination, germination, respiration, attention, association, 
 development. 
 
 There may be sometimes a difficulty in distinguishing the 
 terms which stand for qualities from those that express 
 activities, since all qualities imply activities. Weight for 
 
320 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 example, implies gravitation ; and the quality heat is also a 
 kind of motion. But the distinction aimed at lies between a 
 quality as perceived by means of an effect upon our senses (as 
 weight is resistance to our effort in lifting ; heat, a sensation 
 when we approach fire), and that property of a body which is 
 conceived to account for its energy (as gravitation that brings a 
 body to the ground, or physical heat that expands an iron bar 
 or works an engine). The former class of words, expressing 
 qualities, are chiefly used in description : the latter class, 
 expressing activities, are chiefly needed in explanation. They 
 correspond respectively, like classification and explanation, with 
 the static and dynamic aspects of Nature 
 
 The terms of ordinary language fall into the same classes as 
 those of science : they stand for things, classes of things, parts, 
 or qualities, or activities of things ; but they are far less precise 
 in their signification. As long as popular thought is vague its 
 language must be vague; nor is it desirable too strictly to 
 correct the language whilst the thought is incorrigible. Much 
 of the effect of poetry and eloquence depends upon the elas- 
 ticity and indirect suggestiveness of common terms. Even in 
 reasoning upon some subjects, it is a mistake to aim at an 
 unattainable precision. It is better to be vaguely right than 
 exactly wrong. In the criticism of manners, of fine art, or of 
 literature, in politics, religion and moral philosophy, what we 
 are anxious to say is often far from clear to ourselves ; and it 
 is better to indicate our meaning approximately, or as we feel 
 about it, than to convey a false meaning, or to lose the warmth 
 and colour that are the life of such reflections. It is hard to 
 decide whether most harm has been done by sophists who 
 take a base advantage of the vagueness of common terms, or 
 by honest paralogists (if I may use the word) who begin by 
 deceiving themselves with a plausible definiteness of expres- 
 sion, and go on to propagate their delusions amongst followers 
 eager for systematic insight but ignorant of the limits of its 
 possibility. 
 
 3. A Definition is necessary (if possible) for every scien- 
 
NOMENCLATURE 321 
 
 dfic name. To define a name is to give a precise statement of 
 its meaning or connotation. The name to be defined is the 
 subject of a proposition, whose predicate is a list of the funda- 
 mental qualities common to the things or processes which the 
 subject denotes, and on account of possessing which qualities 
 this name is given to them. 
 
 Thus, a curve is a line of which no part is straight. The 
 momentum of a moving body is the product of its mass and its 
 velocity (these being expressed in numbers of certain units). 
 Nitrogen is a transparent colourless gas, of specific gravity 
 9713, not readily combining, etc. A Lion maybe defined as 
 a monodelphian mammal, predatory, walking on its toes, of 
 nocturnal habits, with a short rounded head and muzzle ; 
 
 dental formula : Incisors 3 ~ 3 Canines ~ * , praemolars 
 3-3 i - * 
 
 3 " 3 molars T = 30 ; four toes on the hind and five 
 
 2-2 i - i 
 
 on the fore foot, retractile claws, prickly tongue, light and 
 muscular in build, about gj feet from muzzle to tip of tail, 
 tawny in colour, the males maned, with a tufted tail. If any- 
 thing answers to this description, it is called a lion ; if not, 
 not : for this is the meaning of the name. 
 
 For ordinary purposes, it may suffice to give an Incomplete 
 Definition ; that is, a list of qualities not exhaustive, but con- 
 taining enough to identify the things denoted by the given 
 name ; as if we say that a lion is * a large tawny beast of prey 
 with a tufted tail. 1 Such purposes may also be served by a 
 Description ; which is technically, a proposition mentioning 
 properties sufficient to distinguish the things denoted, but not 
 the properties that enter into the definition ; as if a lion is 
 called 'the monarch of the desert that figures in the royal 
 standard,' or * that helps the unicorn to support the crown.' 
 
 4. The rules for testing a Definition are : I. As to its 
 Contents 
 
 (i) It must state the whole connotation of the name to be 
 defined. 
 
322 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (2) It must not include any quality derivative from the con- 
 notation. Such a quality is called a Proprium. 
 
 A breach of this rule can do, indeed, no positive harm, but 
 it is a departure from scientific economy. There is no need to 
 state in the definition what can be derived from it ; and what- 
 ever can be derived by causation, or by mathematical demon- 
 stration, should be exhibited in that manner. 
 
 (3) It must not mention any circumstance that is not a part 
 of the connotation, even though it be universally found in the 
 things denoted. Such a circumstance, if not derivable from 
 the connotation, is called an Accident. 
 
 That, for example, the Lion at present only inhabits the Old 
 World, is (I presume) an Accident : if a species otherwise like 
 a lion were found in Brazil, it would not be refused the name 
 of lion on the score of locality. Whilst, however, the rules of 
 Logic have forbidden the inclusion of Proprium or Accident in 
 a Definition, in fact the definitions of Natural History often 
 mention such attributes when characteristic. Indeed, defini- 
 tions of superordinate classes Families and Orders not 
 infrequently give qualities as generally found in the subordinate 
 classes, and at the same time mention exceptional cases in 
 which they do not occur. 
 
 II. As to its Expression 
 
 (4) A Definition must not include the very term to be 
 defined, nor any cognate. In defining Lion we must not repeat 
 ' lion/ nor use l leonine ' ; it would elucidate nothing. 
 
 (5) It must not be put in vague language. 
 
 (6) It nmst not be in a negative form, if a positive form is 
 obtainable. We must not be content to say that a lion is l no 
 vegetarian/ or ' no lover of daylight.' To define a curve as a 
 line ' always changing its direction ' may be better than as * in 
 no part straight/ 
 
 5. The process of determining a Definition is inseparable 
 from classification. We saw that classification consists in dis- 
 tributing things into groups according to their likenesses and 
 differences, regarding as a class those individuals which have 
 
DEFINITION 323 
 
 most qualities in common. In doing so we must, of course, 
 recognise the common qualities or points of likeness ; and to 
 enumerate these is to define the name of the class. If we 
 discover the qualities upon which a class is based by direct 
 observation and induction, by the same method we discover 
 the definition of its name ; and similarly if we discover the 
 qualities of the class by the help of both observation and 
 deduction, as in the modern classification of plants and 
 animals. 
 
 We saw also that classification is not merely the determina- 
 tion of isolated groups of things, but a systematic arrangement 
 of such groups in relation to one another. Hence, again, 
 Definitions are not independent, but relative to one another ; 
 and, of course, in the same way as classes are relative. That 
 is to say, as a class is placed in subordination to higher or 
 more comprehensive groups, so the definition of its name is 
 subordinate to that of their names ; and as a class stands in 
 contrast with co-ordinate classes (those that are in the same 
 degree of subordination to the same higher groups), so the 
 definition of its name is in contrast or co-ordination with the 
 definitions of their names. 
 
 Lion is subordinate to Fells, to Digitigrade, to Carnivore and 
 so on up to Animal ; and, beyond the Animal Kingdom, to 
 Phenomenon : it is co-ordinate with Tiger, Puma, etc. ; and 
 more remotely it is co-ordinate with Dog, Jackal, Wolf, which 
 come under Cam's a genus co-ordinate with Felts. The 
 definition of Lion, therefore, is subordinate to that of Felts, 
 and to all above it up to Phenomenon ; and is co-ordinate 
 with that of Tiger, and with all species in the same grade. 
 This is the ground of the old method of Definition per genus et 
 differential*. 
 
 The Genus being the next class above any Species, the 
 differentia or Difference consists of the qualities which mark 
 that Species in addition to those that mark the Genus, and 
 which therefore distinguish it from all other Species of the 
 same Genus. In the above definition of Lion, for example, all 
 
324 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 the properties down to " light and muscular in build " are 
 generic, that is, are possessed by the whole Genus, Felis ; and 
 the remaining four (size, colour, tufted tail, and mane in the 
 male) are the Difference, or specific properties, because in 
 those points the Lion contrasts with the other Species of that 
 Genus. Differences may be exhibited thus : 
 
 Lion. 
 
 SIZE : about g feet from nose to 
 
 tip of tail. 
 COLOUR : tawny. 
 TAIL: tufted. 
 MANE : present in the male. 
 
 Tiger. 
 
 About 10 feet. 
 
 Warm tawny, striped with black. 
 
 Tapering. 
 
 Both sexes maneless. 
 
 There are other differences in the shape of the skull. In 
 defining Lion, then, it would have been enough to mention the 
 Genus and the properties making up the Difference ; because 
 the properties of the Genus may be found by turning to the 
 definition of the Genus : and, on the principle of economy, 
 whatever it is enough to do it is right to do. To define * by 
 genus and difference,' then, is a point of elegance, when the 
 genus is known ; but the only way of knowing it is to compare 
 the individuals comprised in it and in co-ordinate genera, 
 according to the methods of scientific classification. It may 
 be added that, as the genus represents ancestral derivation, the 
 predication of genus in a definition indicates the remote causes 
 of the phenomena denoted by the name defined. And this 
 way of defining corresponds with the method of double naming 
 by genus and species : Felis leo, Felis tigris, etc.; Vanessa Ata- 
 lanta, Vanessa Io> etc. 
 
 The so-called Genetic Definition, chiefly used in Mathe- 
 matics, is a rule for constructing that which a name denotes, 
 in such a way as to ensure its possesssing the primary attributes 
 connoted by the name. Thus, for a circle : Take any point 
 and, at any constant distance from it, trace a line returning 
 into itself. In Chemistry a genetic definition of any compound 
 might be given in the form of directions for the requisite 
 synthesis of elements. 
 
DEFINITION 325 
 
 6. The difficulties and limits of Definition must next be 
 considered. The chief difficulty in the definition of scientific 
 names consists in determining exactly the nature of the things 
 denoted by them, as in classifying plants and animals. If 
 organic species are free growths, continually changing, however 
 gradually, according as circumstances give some advantage to 
 one form over others, we may expect to find such species 
 branching into varieties, which differ considerably from one 
 another in some respects, though not enough to constitute 
 distinct species. This is the case ; and, consequently, there 
 arises some uncertainty in collecting from all the varieties those 
 attributes which are common to the species as a whole ; and, 
 therefore, of course, uncertainty in defining the species. The 
 same difficulty may occur in defining a genus, on account of 
 the extent to which some of its species differ from others, 
 whilst having enough of the common character to deter the 
 classifier from forming a distinct genus on their account. On 
 the other hand the occurrence of numerous intermediate varieties 
 may make it difficult to distinguish genera or species at all. 
 Even the Kingdoms of plants and animals cannot be precisely 
 discriminated : sponges and other organisms seeming to belong 
 to one as much as to the other. Now, where there is a difficulty 
 of classification there must be a corresponding difficulty of 
 definition. 
 
 It has been proposed in such cases to substitute a Type for 
 a Definition ; to select some variety of a species, or species of 
 a genus, as exhibiting its character in an eminent degree, and 
 to regard other groups as belonging to the same species or 
 genus, according as they agree more with this Type than with 
 other Types representing other species or genera. But the selec- 
 tion of one group as typical implies a recognition of its attributes 
 as generally prevailing (though not universally) throughout 
 the species or genus ; and to recognise these attributes and 
 yet refuse to enumerate them in a Definition, seems to be no 
 great gain. To enumerate the attributes of the Type as an 
 Approximate Definition of the species or genus, true of most of 
 
326 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 the groups constituting the species or genus, answers the same 
 purpose, is more explicit, and can mislead no one who really 
 attends to the exposition. An Approximate Definition is, 
 indeed, less misleading than the indication of a Type ; for the 
 latter method seems to imply that the group which is now 
 typical has a greater permanence or reality than its co-ordinate 
 groups; whereas, for aught we know, one of the outside 
 varieties or species may even now be superseding and ex- 
 tinguishing it. But the statement of a definition as approxi- 
 mate, is an honest confession that both the definition and 
 the classification are (like a provisional hypothesis) merely the 
 best account we can give of the matter according to our present 
 knowledge. 
 
 7. The limits of Definition are twofold : (a) A name whose 
 meaning cannot be analysed cannot be defined. This limita- 
 tion meets us only in dealing with the names of the meta- 
 physical parts or simple qualities of objects under the second 
 requisite of a Terminology. 
 
 Resistance and weight, colour and its modes, many names of 
 sounds, tastes, smells, heat and cold in fact, whatever stands 
 for an unanalysable perception, cannot be made intelligible to 
 any one who has not had experience of the facts denoted ; 
 they cannot be defined, but only exemplified. A sort of 
 genetic definition may perhaps be attempted, as if we say 
 that colour is the special sensation of the retina, or that blue 
 is the sensation produced by a ray of light vibrating about 
 700,000,000,000,000 times a second ; but such expressions can 
 give no notion of our meaning to a blind man, or to any one 
 who has never seen a blue object. Nor can we explain what 
 heat is like, or the smell of tobacco, to those who have never 
 experienced them ; nor the sound of C 128 to one who knows 
 nothing of the musical scale. 
 
 If, however, we distinguish the property of an object from 
 the sensation it excites in us, we may define any simple pro- 
 perty as * the power of producing the sensation ' ; the colour of 
 a flower as the power of exciting the sensation of colour in us. 
 
 
DEFINITION 327 
 
 Still, this gives no information to the blind nor to the colour- 
 blind. 
 
 (b) The second limit of Definition is the impossibility of 
 exhausting infinity, which would be necessary in order to convey 
 the meaning of the name of any individual thing or person. 
 
 For, as we saw in chap, iv., if in attempting to define a 
 proper name we stop short of infinity, our list of qualities or 
 properties may possibly be found in two individuals, and then 
 it becomes the definition of a class-name or general name, 
 however small the actual class. Hence we can only give a 
 Description of that which a proper name denotes, enumerating 
 enough of its properties to distinguish it from everything else as 
 far as our knowledge goes. 
 
 Abstract names may be defined by defining the correspond- 
 ing concrete : the definition of ' human nature ' is the same as 
 of * man.' But if the corresponding concrete be a simple sen- 
 sation (as blue), this being indefinable, the abstract (blueness) 
 is also indefinable. 
 
 8. The five Predicables (Species, Genus, Difference, Pro- 
 prium, Accident) may best be discussed in connection with 
 Classification and Definition ; and in giving an account of 
 Classification, most of what has to be said about them has 
 been anticipated. Their name indeed connects them with the 
 doctrine of Propositions ; for Predicables are terms that may 
 be predicated, classified according to their connotative relation 
 to the Subject of a proposition (that is, according to the relation 
 in which their connotation stands to the connotation of the 
 Subject) : nevertheless, the significance of the relations of such 
 predicates to a subject is derivative from the general doctrine 
 of classification. 
 
 For example, in the proposition * X is Y,' Y must be one of 
 the five sorts of Predicables in relation to X ; but of what sort, 
 depends upon what X (the subject) is, or means. The subject 
 of the proposition must be either a Definition, or a general 
 Connotative Name, or a Singular Name. 
 
 If X is a Definition, Y must be a Species ; for nothing but a 
 
328 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 general name can be predicated of a Definition : and, strictly 
 speaking, it is only in relation to a Definition (as subject) that 
 Species can be a predicable ; when it is called Species predica- 
 
 If X is a Connotative Name, it is itself a Species (Species 
 subjicibilis) ; and the place of the subject of a proposition is 
 the usual one for Species. The predicate, Y, may then be 
 related to the Species in three different ways. First, it may be 
 a Definition, exactly equivalent to the Species ; in fact, nothing 
 else than the Species in an explicit form, the analysis of its 
 connotation ; so that it seems most reasonable to regard this as 
 a second form of the Species predicabilis. Secondly, the pre- 
 dicate may be, or connote, some part only of the Definition or 
 connotation of the Species ; and then it is either Genus (2), or 
 Difference (3). Thirdly, the predicate may connote no partvl 
 the Definition, and then it is either derivable from it, being a 
 Proprium (4), or not derivable from it, being an Accident (5). 
 These points of doctrine will be expanded and illustrated in 
 subsequent pages. 
 
 If X is a Singular Name, deriving connotation from its con- 
 stituent terms (chap. iv. 2), as ' The present Emperor of 
 China,' it may be treated as a Species subjicibilis. Then that 
 he is * an absolute monarch,' predicates a Genus ; because that 
 is a genus of * Emperor of China,' a part of the Singular Name 
 that gives it connotation. That he wears a yellow robe is a 
 Proprium, derivable from the ceremonial of his court. That 
 he is thirty years of age is an Accident. 
 
 But if X is a Proper Name, having no connotation, Y must 
 always be an Accident ; since there can then be no Definition 
 of X, and therefore neither Species, Genus, Difference, nor 
 Proprium. Hence, that * Alphonso Schultze is a man ' is an 
 Accidental Proposition : ' man ' is not here a Species predica- 
 bilis ; for the name might have been given to a dog or a 
 mountain. That is what enables the proposition to convey 
 information : it would be useless if the Proper Name implied 
 * humanity.' 
 
PREDICABLES 329 
 
 Species is most frequently used (as in Zoology) for the class 
 denoted by a general name ; but in Logic it is better to treat it 
 as a general name used connotatively for the attributes pos- 
 sessed in common by the things denoted, and on account of 
 which they are regarded as a class : it is sometimes called the 
 Essence ( 9). In this connotative sense, a Species is 
 implicitly what the Definition is explicitly ; and therefore the 
 two are always simply convertible. Thus, ' A plane triangle ' 
 (Species) is { a figure enclosed by three straight lines ' (Defini- 
 tion) : clearly we may equally say, * A figure enclosed by three 
 straight lines is a plane triangle.' It is a simple identity. 
 
 A Genus is also commonly viewed denotatively, as a class 
 containing smaller classes, its species ; but in Logic it is, again, 
 better to treat it connotatively, as a name whose definition is 
 part of the definition of a given species. 
 
 A Difference is the remainder of the definition of any species 
 after subtracting a given genus. Hence, the Genus and Dif- 
 ference together make up the Species ; whence the method of 
 definition per genus et differentiam (ante, 5). 
 
 It has already been mentioned, that whilst in the classifica- 
 tory sciences (Botany and Zoology), the species is fixed at the 
 lowest step of the classification (varieties not being reckoned 
 as classes), and the genus is also fixed on the step next above 
 it, in Logic these predicables are treated as movable up and 
 down the ladder : any lower class being species in relation to 
 any higher ; which higher class, wherever taken, thus becomes 
 a genus. Lion may logically be regarded as a species of 
 digitigrade, or mammal, or animal ; and then each of these is 
 a genus as to lion : or, again, digitigrade may be regarded as a 
 species of mammal, or mammal as a species of animal. The 
 highest class, however, is never a species ; wherefore it is 
 called a Summum Genus: and the lowest class is never a 
 genus : wherefore it is called an Infima Species. Between these 
 two any step may be either species or genus, according to the 
 relation to other classes in which it is viewed, and is then 
 called Subaltern. The summum genus, again, may be viewed 
 
330 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 in relation to a given universe or suppositio (that is, any limited 
 area of existence now the object of attention), or to the wJiole 
 universe. If we take the animal kingdom as our suppositio, 
 Animal is the summum genus; but if we take the whole 
 universe, * All things ' is the summum genus. 
 
 "Porphyry's tree" is used to illustrate this doctrine. It 
 begins with a summum genus, 'Substance,' and descends by 
 adding differences, step by step, to the infima species^ ' Man.' 
 It also illustrates Division by Dichotomy. 
 
 SUBSTANCE 
 
 ^S 
 
 CORPOREAL ! INCORPOREAL 
 
 ANIMATE INANIMATE 
 
 SENSIBLE INSENSlBLt 
 
 RATIONAL I IRRATIONAL 
 
 Beginning with ' Substance,' as summum genus, and adding the 
 difference ' Corporeal,' we frame the species ' Body.' Taking 
 1 Body ' as the genus and adding the difference ' Animate,' we 
 frame the species * Living Body ; ' and so on till ' Man ' is 
 reached ; which being infima species, is only subdivisible into 
 
PREDICABLES 331 
 
 individuals. But it should be noted that the division of Man 
 into individuals involves a change of principle : it is a division 
 of the denotation, not an increase of the connotation as in the 
 earlier steps. Only one side of each dichotomy is followed 
 out : if the other side had been taken Incorporeal Substance 
 would be ' Spirit ' ; which might be similarly subdivided. 
 
 Genus and Species, then, have a double relation. In 
 denotation the Genus includes the Species, in connotation 
 the Species includes the Genus. Hence the doctrine that by 
 increasing the connotation of a name you decrease its deno- 
 tation: if, for example, to the definition of 'lion' you add 
 
 * inhabiting Africa,' Asiatic lions are no longer denoted by it. 
 On the other hand, if you use a name to denote objects that it 
 did not formerly apply to, some of the connotation must be 
 dropped : if, for example, the name * lion ' be used to include 
 
 * pumas/ the tufted tail and mane can no longer be part of the 
 meaning of the word ; since pumas have not these properties. 
 
 This doctrine is logically or formally true, but it may not 
 always be true in fact. It is logically true ; because wherever 
 we add to the connotation of a name, it is possible that some 
 things to which it formerly applied are now excluded from its 
 denotation, though we may not know of any such things. 
 Still, as a matter of fact, an object may be discovered to have 
 a property previously unknown, and this property may be 
 fundamental and co-extensive with the denotation of its name, 
 or even more widely prevalent. The discovery that the whale 
 is a mammal did not limit the class ' whale ' ; nor did the dis- 
 covery that lions, dogs, wolves, etc.) walk upon their toes, 
 affect the application of any of these names. 
 
 Similarly, the extension of a name to things not previously 
 denoted by it, may not in fact alter its definition; for the 
 extension may be made on the very ground that the things 
 now first denoted by it have been found to have the pro- 
 perties enumerated in its definition, as when the name 
 ' mammal ' was applied to whales, dolphins, etc. If, however, 
 'mammal' had formerly been understood to apply only to 
 
332 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 land animals, so that its definition included (at least, popularly) 
 the quality of * living on the land,' this part of the connotation 
 was of course lost when the denotation came to include certain 
 aquatic animals. 
 
 A Proprium is an attribute derived from the definition: 
 being either (a) implied in it, or deducible from it, as ' having 
 its three angles equal to two right angles ' may be proved from 
 the definition of a triangle ; or (b) causally dependent on it, as 
 being c dangerous to flocks ' results from the nature of a wolf, 
 and as * moving in an ellipse ' results from the nature of a 
 planet in its relation to the sun. 
 
 An Accident is a property accompanying the defining attri- 
 butes without being deducible from them. The word suggests 
 that such a property is merely ' accidental,' or there 'by 
 chance ' ; but, of course, it only means that we do not under- 
 stand the connection. 
 
 Proprium and Accident bear the same relation to one 
 another as Derivative and Empirical Laws : both Accidents 
 and Empirical Laws present problems, the solution of which 
 consists in reducing them, respectively, to .Propria and 
 Derivative Laws. In fact, the predication of a Proprium is a 
 Derivative Law, and the predication of an Accident is an 
 Empirical Law. Thus the colour of animals was once regarded 
 as an Accident for which no reason could be given ; but now 
 the colour of animals is regarded as an effect of their nature 
 and habits, the most frequent cause of it being the advantage 
 of concealment; whilst in other cases, as among brightly 
 coloured insects and snakes, the cause seems to be the advan- 
 tage of advertising their own noxiousness. If such reasoning 
 is sound, colour is a Proprium (and if so, it cannot logically be 
 included in a Definition ; but it is better to be judicious than 
 formal). 
 
 If the colour of animals is a Proprium, we must recognise a 
 distinction between Inseparable and Separable Propria, accord- 
 ing as they do, or do not, always accompany the essence : for 
 mankind is regarded as one species ; but each colour, white, 
 
ESSENCE 333 
 
 black or yellow, is separable from it under different climatic 
 conditions : whilst tigers are everywhere coloured and striped 
 in much the same way ; so that we may consider their colour- 
 ing as inseparable, in spite of exceptional specimens black or 
 white or clouded. 
 
 The same distinction may be drawn between Accidents. 
 1 Inhabiting Asia ' is an Inseparable Accident of tiger, but a 
 Separable Accident of lion. Even the occasional characteristics 
 and occupations of individuals are sometimes called Separable 
 Accidents of the species ; as, of Man, being colour-blind, car- 
 pentering, or running. 
 
 A Proprium in the original signification of the term ('tiiov) 
 was peculiar to a Species, never found with any other, and was 
 therefore convertible with the Subject ; but this restriction is 
 no longer insisted on. 
 
 9. Any predication of a Genus, Difference or Definition, 
 is a Verbal, Analytic, or Essential proposition : and any pre- 
 dication of a Proprium or Accident, is a Real, Synthetic, or 
 Accidental proposition (chap. v. 6). A Proposition is called 
 Verbal or Analytic when the predicate is a part, or the whole, 
 of the meaning of the subject ; and of course, the subject being 
 species, a genus or difference is part, and a definition is the 
 whole, of its meaning or connotation. Hence such a proposi- 
 tion has also been called explicative. Again, a proposition is 
 called Real or Synthetic when the predicate is no part of the 
 meaning of the subject; and, the subject being species, a pro- 
 prium or accident is no part of its meaning or connotation. 
 Hence such a proposition has been called ampliative. 
 
 As to Essential and Accidental, these terms are derived 
 from the doctrine of Realism. Realists maintain that the 
 Essence of a thing, or that which makes a thing to be what 
 (or of what kind) it is, also makes everything else of the same 
 kind to be what it is. The Essence, they say, is not proper to 
 each thing or separately inherent in it, but is an * Universal ' 
 common to all things of that kind. Some hold that the 
 universal nature of things of any kind is an Idea existing apart 
 
334 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 from the things in the intelligible world, a rather shy corner, 
 invisible to mortal eye and only accessible to thought ; whence 
 the Idea is called a nournenon : that only the Idea is truly 
 real, and that the things (say, men, lions, bedsteads and cities) 
 which appear to us in sense-perception, and which therefore 
 are called phenomena, only exist by participating in, or 
 imitating, the Idea of each kind of them. The standard of 
 this school bears the legend Universalia ante rent. 
 
 But others think that the Universal does not exist apart 
 from particular things, but is their present Essence; gives 
 them actuality as individual substances ; " informs " them, or 
 is their formal cause, and thus makes them to be what they 
 are of their kind according to the definition : the universal 
 lion is in all lions, and is not merely similar, but identical in 
 all ; for thus the Universal Reason thinks and energises in 
 Nature. This school inscribes upon its banners, Universalia 
 in re. 
 
 To define anything, then, is to discover its Essence, whether 
 transcendent or immanent ; and to predicate the definition, or 
 any part of it (genus or difference), is to enounce, an essential 
 proposition. But a proprium, being no part of a definition, 
 though it always goes along with it, does not show what a thing 
 is ; nor of course does an accident ; so that to predicate either 
 of these is to enounce an accidental proposition. 
 
 Another school of Metaphysicians denies the existence of 
 Universal Ideas or Forms ; the real things, according to them, 
 are individuals ; which, so far as any of them resemble one 
 another, are regarded as forming classes : and the only Uni- 
 versal is the class-name, which is applied universally in the 
 same sense. Hence, they are called Nominalists. The sense 
 in which any name is applied, is derived, they say, from a 
 comparison of the individuals, and by abstraction of the pro- 
 perties they have in common ; and thus the definition is formed. 
 Universalia post rem is their motto. Some Nominalists, how- 
 ever, hold that, though Universals do not exist in nature, they 
 do in our minds, as Abstract Ideas or Concepts ; and that to 
 
PREDICAMENTS 335 
 
 define a term is to analyse the Concept it stands for ; whence, 
 these philosophers are called Conceptualists. 
 
 Such questions belong to Metaphysics and Psychology rather 
 than to Logic ; and I have only given a commonplace account 
 of a subject upon every point of which there is much difference 
 of opinion. 
 
 10. The doctrine of the Predicaments, or Categories, is so 
 interwoven with the history of speculation and especially of 
 Logic that, though its vitality is exhausted, it can hardly be 
 passed over unmentioned. The Predicaments of Aristotle are 
 the heads of a classification of terms as possible predicates of 
 a particular thing or individual. Hamilton (Logic : Lect. xi.) 
 has given a classification of them ; which, if it cannot be found 
 in Aristotle, is an aid to the memory, and may be thrown into 
 a table thus (cf. Bain : Logic > App. C.) : 
 
 Substance 
 
 otffla (i) 
 
 i-Quantity 
 
 7ro<r6 (2) 
 
 [Attribute] -Quality 
 
 Troi6v (3) 
 
 '-Relation 
 
 irp6<r TI (4) 
 
 rWhere 
 
 iroO (5) 
 
 Uvhen 
 
 7r6re (6) 
 
 [Modes of Relation] r Action 
 l-Passion 
 
 Troteii/ (7) 
 irdffxeiv (8) 
 
 rPosture 
 
 Keladai (9) 
 
 LHabit 
 
 X" (10) 
 
 Taking a particular thing or individual, as c Socrates,' this is 
 Substance in the proper sense of the word, and can never be a 
 predicate, but is the subject of all predicates. We may assert 
 of him (i) Substance in the secondary sense (species or genus) 
 that he is a man or an animal ; (2) Quantity, of such a height 
 or weight ; (3) Quality, fair or dark ; (4) Relation, shorter or 
 taller than Xanthippe ; (5) Where, at Athens ; (6) When, two 
 thousand and odd years ago ; (7) Action, that he questions 
 or pleads ; (8) Passion, that he is answered or condemned ; 
 (9) Posture, that he sits or stands ; (10) Habit, that he is 
 clothed or armed. 
 
336 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Thus illustrated (Categories : c. 4), the Predicaments seem 
 to be a list of topics, generally useful for the analysis and 
 description of an individual, but wanting in the scientific 
 qualities of rational arrangement, derivation and limitation. 
 Why are there just these heads, and just so many? It has 
 been suggested that they were determined by grammatical 
 forms : for Substance is expressed by a substantive ; Quantity, 
 Quality and Relation are adjectival ; Where and When, 
 adverbial ; and the remaining four are verbal. It is true that 
 the parts of speech were not systematically discriminated until 
 some years after Aristotle's time ; but, as they existed, they 
 may have unconsciously influenced his selection and arrange- 
 ment of the Predicaments. Where a principle is so obscure 
 one feels glad of any clue to it (cf. Grote's Aristotle ', c. 3, and 
 Zeller's Aristotle, c. 6). But whatever the origin and original 
 meaning of the Predicaments, they were for a long time regarded 
 as a classification of things ; and it is in this sense that Mill 
 criticises them (Logic: Bk. I. c. 3). 
 
 If, however, the Predicaments are heads of a classification of 
 terms predicable, we may expect to find some connection with 
 the Predicables ; and, in fact, secondary Substances are species 
 and genus ; whilst the remaining nine forms are generally 
 accidents. But, again, we may expect some agreement between 
 them and the fundamental forms of predication (ante, chap. i. 
 5, and chap. ii. 4) : Substance, whether as the foundation 
 of attributes, or as genus and species, implies the predication 
 of coinherence, which is one mode of Co-existence. Quantity 
 is predicated as equality (or inequality) a mode of Likeness ; 
 and the other mode of Likeness is involved in the predication 
 of Quality. Relation, indeed, is the abstract of all predication, 
 and ought not to appear in a list along with special forms of 
 itself. * Where ' is position, or Co-existence in space ; and 
 * When ' is position in time, or Succession. Action and Passion 
 are the most interesting aspect of Causation. Posture and 
 Habit are complex modes of Co-existence, but too specialised 
 to have any philosophic value. Now, I do not pretend that 
 
PREDICAMENTS 337 
 
 this is what Aristotle meant and was trying to say : but if Like- 
 ness, Co-existence, Succession and Causation are fundamental 
 forms of predication, a good mind analysing the fact of pre- 
 dication is likely to happen upon them in one set of words or 
 another. 
 
 By Kant the word Category has been appropriated to the 
 highest forms of judgment, such as Unity, Reality, Substance 
 and Cause, under which the Understanding reduces pheno- 
 mena to order and thereby constitutes Nature. This change 
 of meaning has not been made without a certain continuity of 
 thought; for forms of judgment are modes of predication. 
 But, besides altering the lists of Categories and greatly improv- 
 ing it, Kant has brought forward under an old title a doctrine 
 so original and suggestive that it has extensively influenced the 
 subsequent history of Philosophy. At the same time, and pro- 
 bably as a result of the vogue of the Kantian philosophy, the 
 word * category ' has been vulgarised as a synonym for ' class/ 
 just as * predicament ' long ago passed from Scholastic Logic 
 into common use as a synonym for ' plight.' A minister is 
 said to be * in a predicament,' or to fall under the ' category of 
 impostors.' 
 
CHAPTER XXIII 
 DEFINITION OF COMMON TERMS 
 
 i. Ordinary words may need definition, if in the course of 
 exposition or argument their meaning is liable to be mistaken. 
 Definition should not be regarded as giving the sense of the 
 word for all occasions of its use. It is an operation of great 
 delicacy. Fixity of meaning in the use of single words is con- 
 trary to the genius of the common vocabulary; since each 
 word, whilst having a certain predominant character, must be 
 used with many shades of significance, in order to express the 
 different thoughts and feelings of multitudes of. men in end- 
 lessly diversified situations ; and its force, whenever it is used, 
 is qualified by the other words with which it is connected in a 
 sentence, by its place in the construction of the sentence, by 
 the emphasis, or by the pitch of its pronunciation compared 
 with the other words. 
 
 Clearly, the requisite of a scientific language, ' that every 
 word shall have one meaning well defined,' is too exacting for 
 popular language ; because the other chief requisite of scientific 
 language cannot be complied with, * that there be no important 
 meaning without a name.' 'Important meanings,' or what 
 seem such, are too numerous to be thus provided for ; and new 
 ones are constantly arising, as each of us pursues his business 
 or his pleasure, his meditations or the excursions of his fancy. 
 It is impossible to have a separate term for each meaning ; 
 and, therefore, the terms we have must admit of variable 
 application. 
 
DEFINITION OF COMMON TERMS 339 
 
 An attempt to introduce new words is generally disgusting. 
 Few men have mastered the uses of half the words already to 
 be found in our classics. Much more would be lost than 
 gained by doubling the dictionary. It is true that, at certain 
 stages in the growth of a people, a need may be widely felt for 
 the adoption of new words : such, in our own case, was the 
 period of the Tudors and early Stuarts. Many fresh words, 
 chiefly from the Latin, then appeared in books, were often 
 received with reprobation and derision, sometimes disappeared 
 again, sometimes established their footing in the language : 
 see The Art of English Poetry (ascribed to Puttenham), 
 Book III. chap. 4, and Ben Jonson's Poetaster, Act v. sc. i. 
 Good judges did not know whether a word was really called 
 for : even Shakespeare thought ' remuneration ' and ' accommo- 
 date ' ridiculous. But such national exigencies rarely arise ; 
 and in our own time great authors distinguish themselves by 
 the plastic power with which they make common words convey 
 uncommon meanings. 
 
 Fluid, however, as the ordinary language is and ought to 
 be, it may be necessary for the sake of clear exposition, or 
 to steady the course of an argument, to avoid either sophistry 
 or unintentional confusion, that words should be defined 
 and discriminated ; and we must discuss the means of doing 
 so. 
 
 2. Scientific method is applicable, with some qualifications, 
 to the definition of ordinary words. Classification is involved 
 in any problem of definition : at least, if our object is to find 
 a meaning that shall be generally acceptable and intelligible. 
 No doubt two disputants may, for their own satisfaction, adopt 
 any arbitrary definition of a word important in their contro- 
 versy ; or any one may define a word as he pleases, at the risk 
 of being misunderstood, provided he has no fraudulent in- 
 tention. But in exposition or argument addressed to the 
 public, where words are used in some of their ordinary senses, 
 it should be recognised that the meaning of each one involves 
 that of many others. For language has grown with the human 
 
340 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 mind, as representing its knowledge of the world: this know- 
 ledge consists of the resemblances and differences of things 
 and of the activities of things, that is, of classes and causes ; 
 and as there is such order in the world, so there must be in 
 language : language, therefore, embodies an irregular classifica- 
 tion of things with their attributes and relations according to 
 our knowledge and beliefs. The best attempt (known to me) 
 to carry out this view is contained in Roget's Thesaurus, 
 which is a classification of English words according to their 
 meaning : founded, as the author tells us, on the models of 
 Zoology and Botany, it has some of the requisites of a Logical 
 Dictionary. 
 
 Popular language, indeed, having grown up with a predomi- 
 nantly practical purpose, represents a very imperfect classifica- 
 tion philosophically considered. Things, or aspects, or pro- 
 cesses of things, that have excited little interest, have often 
 gone unnamed : so that scientific discoverers are obliged, for 
 scientific purposes, to invent thousands of new names. Strong 
 interests, on the other hand, give such a colour to language, 
 that, where they enter, it is difficult to find any indifferent 
 expressions. Consistency being much prized, though often the 
 part of a blockhead, inconsistency implies not merely the 
 absence of the supposed virtue, but a positive vice : Beauty- 
 being attractive and ugliness the reverse, if we invent a word 
 for that which is neither, ' plainness,' it at once becomes tinged 
 with the ugly. In short, we love beauty and morality so much 
 as to be almost incapable of signifying their absence without, 
 expressing aversion. 
 
 Again, the erroneous theories of mankind have often found 
 their way into popular speech, and their terms have remained 
 there long after the rejection of the beliefs they embodied : as 
 lunatic, augury, divination, spell, exorcism : though, to be 
 sure, such words may often be turned to good account, besides 
 the interest of preserving their original sense. Language is a 
 record as well as an index. 
 
 Language, then, being essentially classificatory, any attempt 
 
DEFINITION OF COMMON TERMS 341 
 
 to ascertain the meaning of a word, far from neglecting its 
 relations to others, should be directed toward elucidating 
 them. 
 
 Every word belongs to a group, and this group to some other 
 larger group. A group is sometimes formed by derivation, at 
 least so far as different meanings are marked merely by inflec- 
 tions, as short, shorter, shorten, shortly ; but, for the most part, 
 is a conflux of words from many different sources. Repose, 
 depose, suppose, impose, propose, are not nearly connected in 
 meaning ; but are severally allied in sense much more closely 
 with words philologically remote. Thus repose is allied with 
 rest, sleep, tranquillity; disturbance, unrest, tumult; whilst 
 depose is, in one sense, allied with overthrow, dismiss, dethrone ; 
 restore, confirm, establish; and, in another sense, with de- 
 clare, attest, swear, prove, etc. Groups of words, in fact, 
 depend on their meanings, just as the connection of scientific 
 names follows the resemblance in character of the things 
 denoted. 
 
 Words, accordingly, stand related to one another, for the 
 most part, though very irregularly, as genus, species, and 
 co-ordinate species. 
 
 Taking repose as a genus, we have as species of it, though 
 not exactly co-ordinate with one another, tranquillity with a 
 mental differentia (repose of mind), rest, whether of mind or 
 body, sleep, with the differentia of unconsciousness (privative). 
 
 As this illustration suggests, synonyms are species, or 
 varieties, wherever any difference can be detected in them; 
 and to discriminate them we must first find the generic 
 meaning ; for which there may, or may not, be a single word. 
 Thus, equality, sameness, likeness, similarity, resemblance, identity, 
 are synonyms ; but, if we attend to the ways in which they are 
 actually used, perhaps none of them can claim to be a genus 
 in relation to the rest. If so, we must resort to a compound 
 term for the genus, such as * absence of some sort of difference/ 
 Then equality is absence of difference in quantity ; sameness is 
 often absence of difference in quality, though the usage is not 
 
342 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 strict : likeness, similarity, and resemblance, in their actual use, 
 perhaps, cannot be discriminated ; unless likeness be the more 
 concrete, similarity the more abstract; but they may all be 
 used compatibly with the recognition of more or less difference 
 in the things compared, and even imply this. Identity is the 
 absence of difference of origin, a continuity of existence, with 
 so much sameness from moment to moment as is compatible 
 with changes in the course of nature ; so that egg, caterpillar, 
 chrysalis, butterfly may be identical for the run of an individual 
 life, in spite of differences quantitative and qualitative, as truly 
 as a shilling that all the time lies in a drawer. 
 
 Co-ordinate Species, when positive, have the least contrariety; 
 but there are also opposites, namely negatives, contradictories 
 and fuller contraries. These may be regarded as either 
 co-ordinate genera or the species of co-ordinate genera. Thus, 
 repose being a genus, not-repose is by dichotomy a co-ordinate 
 genus and is a negative and contradictory; then activity 
 (implying an end in view), motion (limited to matter), dis- 
 turbance (implying changes from a state of calm), tumult, etc., 
 are co-ordinate species of not-repose, and are . therefore co- 
 ordinate opposites, or contraries, of the species of repose. 
 
 As for correlative words, like Master and Slave, Husband 
 and Wife, etc., it may seem far-fetched to compare them with 
 the sexes of the same species of plants or animals ; but there 
 is this resemblance between the two cases, that sexual names 
 are correlative, as ' lioness,' and that one sex of a species, like 
 a correlative name, cannot be defined without implying the 
 other ; for if a distinctive attribute of one sex be mentioned 
 (as the lion's mane), it is implied that the other wants it, and 
 apart from this implication the species is not defined : just as 
 the definition of ' master ' implies a ' slave ' to obey. 
 
 Common words, whilst less precise than the terms of a 
 scientific nomenclature, differ from them also in this, that the 
 same word may occur in different genera. Thus, sleep is a 
 species of repose as above ; but it is also a species of uncon- 
 sciousness, with co-ordinate species swoon, hypnotic state, etc. 
 
DEFINITION OF COMMON TERMS 343 
 
 In fact, every word stands under as many distinct genera, 
 at least, as there are simple or indefinable qualities to be 
 enumerated in its definition. 
 
 3. But besides being partly similar to a scientific nomen- 
 clature, ordinary language is, of course, partly a terminology 
 for describing things according to their qualities and structure. 
 Such are all the names of colours, sounds, tastes, contrasts of 
 temperature, of hardness, of pleasantness; in short, all 
 descriptive adjectives, and all names for the parts and processes 
 of things. Any word connoting a quality may be used to 
 describe many very different things, as long as they agree in 
 this quality. This is the generality of a word (sometimes said 
 to make it, or its meaning, universal, chap. xxii. 9), or its 
 general applicability. 
 
 But we must observe, that the quality connoted by a word, 
 and treated as always the same quality, is often only analogically 
 the same. Take the word great : we speak of a great storm, a 
 great man, a great book ; but great is in each case not only 
 relative, implying small, and leaving open the possibility that 
 what we call great is still smaller than something else of its 
 kind, but it is also predicated with reference to some quality or 
 qualities, which may be very different in the several cases of 
 its application. If the book is prized for wisdom, or for 
 imagination, its greatness lies in that quality; if the man is 
 distinguished for influence, or for courage, his greatness is of 
 that nature; if the storm is remarkable for violence, or for 
 duration, its greatness depends on that fact. The word great, 
 therefore, is not used for these things in the same sense, but 
 only analogically and elliptically. Similarly with good, pure, 
 free, strong, rich, and so on. ' Rest ' has not the same meaning 
 in respect of a stone and of an animal, nor ' strong ' in respect 
 of thought and muscle, nor ' sweet ' in respect of sugar and 
 music. But here we come to the border between literal and 
 figurative use: every one sees that figurative epithets are 
 analogical; but by custom any figurative use may become 
 literal. 
 
344 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Again, many general names of widely different meaning, are 
 brought together in describing any concrete object, as an 
 animal, or a landscape, or in defining any specific term. This 
 is the sense of the doctrine, that any concrete thing is a conflux 
 of generalities or universals : it may at least be considered in 
 this way ; though it seems more natural to say, that an object 
 presents these different aspects to a spectator (who, to fully 
 comprehend it, must classify it in every aspect) ; that to name 
 the different qualities or aspects of an object is to give its 
 metaphysical analysis ; and that to name the qualities in 
 which an object represents a class is to define the name of 
 that class. 
 
 4. The process of seeking a definition may be guided by 
 the following maxims : 
 
 (1) Find the usage of good modern authors ; that is (as they 
 rarely define a word explicitly), consider what in various re- 
 lations they use it to denote ; from which uses its connotation 
 may be corrected. 
 
 (2) But if this process yields no satisfactory result, make a 
 list of the things denoted, and of those denoted by the co- 
 ordinate and opposite words; and observe the qualities in 
 which the things denoted agree, and in which they differ from 
 those denoted by the contraries and opposites. If civilisation 
 is to be defined, make lists of civilised peoples, of semi- 
 civilised, of barbarous, and of savage : now, what things are 
 common to civilised peoples and wanting in the others respec- 
 tively ? This is an exercise worth attempting. If poetry is 
 to be defined, survey some typical examples of what good 
 critics recognise as poetry, and compare them with examples 
 of literary prose, oratory, and science. Having determined the 
 characteristics of each kind, it is a good plan to arrange them 
 opposite one another in parallel columns. Whoever tries to 
 define by this method a few important words frequently occur- 
 ing in conversation will find his head the clearer for it, and 
 will collect by the way much information which may be more 
 valuable than the definition itself, should he ever find one. 
 
DEFINITION OF COMMON TERMS 345 
 
 (3) If the genus of a word to be defined is already known, 
 the process may be shortened. Suppose the genus of poetry 
 to be belles lettres (that is, ' appealing to good taste '), this 
 suffices to mark it off from science ; but since literary prose 
 and oratory are also belles lettres^ we must still seek the 
 differentia of poetry by a comparison of it with these co- 
 ordinate species. A compound word often exhibits genus and 
 difference upon its face : as ' re-turn,' ' inter-penetrate,' ' tuning- 
 fork,' ' cricket-bat ' ; but the two last would hardly be under- 
 stood without inspection or further description. And however 
 a definition be discovered, it is well to state it per genus et 
 differentiam. 
 
 (4) In denning any term we should avoid encroaching upon 
 the meaning of any of the co-ordinate terms ; for else their 
 usefulness is lessened : as by making * law ' include * custom,' 
 or ' wealth ' include ' labour ' or ' culture.' 
 
 (5) If two or more terms happen to be exactly synonymous, 
 it may be possible (and, if so, it is a service to the language) 
 to divert one of them to any neighbouring meaning that has 
 no determinate expression. Thus, Wordsworth and Coleridge, 
 at the beginning of this century, took great pains to distinguish 
 between Imagination and Fancy, which at that time had be- 
 come in common usage practically equivalent ; and they sought 
 to limit ' imagination ' to an order of poetic effect, which (they 
 said) had prevailed during the Elizabethan age, but had been 
 almost lost during the Gallo-classic, and which it was their 
 mission to restore. Co-ordinate terms often tend to coalesce 
 and become synonymous, or one almost supersedes the other, 
 to the consequent impoverishment of our speech. At present 
 proposition (that something is the fact) has almost driven out 
 proposal (that it is desirable to co-operate in some course of 
 action). Even good writers and speakers, by their own practice, 
 encourage this confusion : they submit to Parliament certain 
 ' propositions ' (proposals for legislation), or even make ' a pro- 
 position of marriage'. Definition should counteract such a 
 tendency. 
 
346 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (6) We must avoid the temptation to extend the denotation 
 of a word so far as to diminish or destroy its connotation ; or 
 to increase its connotation so much as to render it no longer 
 applicable to things which it formerly denoted: we should 
 neither unduly generalise, nor unduly specialise, a term. Is it 
 desirable to define education so as to include the * lessons of 
 experience ' ; or is it better to restrict it as implying a personal 
 educator? If any word implies blame or praise, we'are apt to 
 extend it to everything we hate or approve. But coward cannot 
 be so denned as to include all bullies, nor noble so as to 
 include every honest man, without some loss in distinctness of 
 thought. 
 
 The same impulses make us specialise words ; for, if two 
 words express approval, we wish to apply both to whatever we 
 admire and to refuse both to whatever displeases us. Thus, 
 a man may resolve to call no one great who is not good: 
 greatness, according to him, connotes goodness : whence it 
 follows that (say) Napoleon I. was not great. Another man 
 is disgusted with greatness : according to him, good and great 
 are mutually exclusive classes, sheep and goats, as in Gray's 
 wretched clench : " Beneath the good how far, yet far above 
 the great." In fact, however, * good ' and ' great ' are descrip- 
 tive terms, sometimes applicable to the same object, some- 
 times to different : but c great ' is the wider term and 
 applicable to goodness itself and also to badness; whereas 
 by making * great ' connote goodness it becomes the nar- 
 rower term. And as we have seen ( 3), such epithets may 
 be applicable to objects on account of different qualities : 
 good is not predicated on the same ground of a man and of 
 a horse. 
 
 ^7) In defining any word, it is desirable to bear in mind its 
 derivation, and to preserve the connection of meaning with its 
 origin ; unless there are preponderant reasons for diverting it, 
 grounded on our need of the word to express a certain sense, 
 and the greater difficulty of finding any other word for the 
 same purpose. Is it better to lean to the classical or to the 
 
DEFINITION OF COMMON TERMS 347 
 
 vulgar sense of ' indifferent,' * impertinent,' ' aggravating,' 
 ' phenomenal ' ? 
 
 (8) Rigorous definition should not be attempted where the 
 subject does not admit of it. Some kinds of things are so 
 complex in their qualities, and each quality may manifest itsel* 
 in so many degrees without ever admitting of exact measure- 
 ment, that we have no means of marking them off precisely 
 from other things nearly allied, similarly complex and similarly 
 variable. If so we cannot precisely define their names. Imagi- 
 nation and fancy are of this nature, civilisation and barbarism, 
 poetry and other kinds of literary expression. As to poetry, 
 some think it only exists in metre, but hardly maintain that the 
 metre must be strictly regular : if not, how much irregularity 
 of rhythm is admissible? Others regard a certain mood of 
 impassioned imagination as the essence of poetry ; but they 
 have never told us how great intensity of this mood is 
 requisite. We also hear that poetry is of such a nature that 
 the enjoyment of it is an end in itself ; but as it is not main- 
 tained that poetry must be wholly impersuasive or uninstructive, 
 there seems to be no means of deciding what amount or pro- 
 minence of persuasion or instruction would transfer the work 
 to the region of oratory or science. Such cases make the 
 method of defining by the aid of a type really useful : the diffi- 
 culty can hardly be got over without pointing to typical 
 examples of each meaning, and admitting that there may be 
 many divergences and unclassifiable instances on the border 
 between allied meanings. 
 
 5. As science began from common knowledge, the terms 
 of the common vocabulary have often been adopted into the 
 sciences, and many are still found there : such as weight, mass, 
 work, attraction, repulsion, diffusion, reflection, absortion, base, 
 salt, and so forth. 
 
 In the more exact sciences, the vague popular associations 
 with such words is hardly any inconvenience ; since those who 
 are addicted to such studies do not expect to master them 
 without undergoing special discipline ; and, having precisely 
 
343 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 defined the terms, they acquire the habit of thinking with them 
 according to their assigned signification in those investigations 
 to which they are appropriate. It is in the Social Sciences, 
 especially Economics and Ethics, that the use of popular ter- 
 minology is at once unavoidable and prejudicial. For the 
 subject-matters, industry and the conduct of life, are every 
 man's business ; and, accordingly, have always been discussed 
 with a consciousness of their direct practical bearing upon 
 public and private interests, and therefore in the common 
 language, in order that everybody may as far as possible benefit 
 by whatever light can be thrown upon them. It is true that 
 Astronomy, Mechanics and Chemistry are of incalculable 
 importance to industry, and to public and private interests: 
 still, their application to practice is generally in the hands of 
 specialists (navigators, engineers, dyers), who may undergo the 
 requisite special training in proportion as their share in any 
 process requires an appreciation of its scientific grounds. But 
 the saying, that 'what is everybody's business is nobody's/ 
 receives melancholy illustration from the popular attitude 
 toward the Science of Wealth and Industry. Is there not 
 another saying that ' a man knows his own business best ' ? 
 He looks, perhaps, into a work on Economics and sees that it 
 is all about Prices, Money, Rent, Wages, Profits. Now, he has 
 received and paid money all his life, and either received or 
 paid rent, wages, and profits: how, then, can things so 
 familiar need any explanation ? He may often say with much 
 truth, that he has made more money than the author. It has 
 been justly observed, however, that nearly all uninstructed and 
 traditionary opinions upon these subjects are curiously wrong : 
 they are not merely erroneous, but perverse and absurd. Yet 
 the obtaining of instruction has been hindered by the very 
 means adopted to facilitate it, the use of common language in 
 a technical sense ; for without special discipline in the use of 
 technicalities, the special meaning of the terms employed will 
 often be confused with the vague meanings that they have in 
 ordinary conversation ; and if their divergence from ordinary 
 
 
DEFINITION OF COMMON TERMS 349 
 
 usage is observed, it is likely enough to give annoyance, or to 
 raise a laugh at the apparent ignorance of the * theorist ' who 
 wrote the book. 
 
 The almost uniform practice of Economists and Moralists, 
 however, shows that, in their judgment, the good derived from 
 writing in the common vocabulary outweighs the evil : though 
 it is sometimes manifest that they themselves have been misled 
 by extra-scientific meanings. To reduce the evil as much as 
 possible, the following precautions seem reasonable : 
 
 (1) To try to find and adopt the central meaning of the 
 word (say Rent or Money) in its current or traditionary appli- 
 cations ; so as to lessen in the greater number of cases the jar 
 of conflicting associations. But if the central popular meaning 
 does not correspond with the scientific conception to be 
 expressed, it may be better to invent a new term. 
 
 (2) To define the term with sufficient accuracy to secure its 
 clear and consistent use for scientific purposes. 
 
 (3) When a popular term has to be used in a sense that 
 departs from the ordinary one in such a way as to incur the 
 danger of misunderstanding, to qualify it by some adjunct or 
 " interpretation-clause." 
 
 It must be confessed that the first of these rules is not 
 always adhered to ; and, in the progress of a science, as subtler 
 and more abstract relations are discovered amongst the facts, 
 the meaning of a term may have to be modified and shifted 
 further and further from its popular use. The term ' Rent,' 
 for example, is used by economists in such a sense, that they 
 have to begin the discussion of the facts it denotes, by explain- 
 ing that it does not imply any actual payment by one man to 
 another. Here, for most readers, the meaning they are 
 accustomed to, seems already to have entirely disappeared ; 
 but worse follows : and we ought, therefore, to pity the sorrows 
 of a plain man of common sense who sits down to study 
 Economics in a railway carriage. Difficulties may, however, be 
 largely overcome by qualifying the term in its various relations, 
 as produce-rents, ground-rents, customary rents, and so forth. 
 
350 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (Cf. Dr. Keynes' Scope and Method of Political Economy, 
 chap. 5.) 
 
 6. Definitions affect the cogency of arguments in many 
 ways, whether we use popular or scientific language. If the 
 definitions of our terms are vague, or are badly abstracted 
 from the facts denoted, of course, all arguments involving these 
 terms are inconclusive. There can be no confidence in 
 reasoning with such terms ; since, if they are vague, there is 
 nothing to protect us from ambiguity ; or, if their meaning has 
 been badly abstracted, we may be led into absurdity as if 
 1 impudence ' be defined in such a way as to confound it with 
 honesty. 
 
 Again, it is by Definitions that we can best distinguish 
 between Verbal and Real Propositions. Whether a term 
 predicated is implied in the definition of the subject, or adds 
 something to its meaning, deserves our constant attention. 
 We often persuade ourselves that statements are profound and 
 important, when, in fact, they are mere verbal propositions. 
 " It is just to give every man his due " ; " the greater good 
 ought to be preferred to the less " ; such dicta sound well 
 indeed, too well ! For ' a man's due ' means nothing else than 
 what it is just to give him ; and * the greater good ' may mean 
 the one that ought to be preferred : these, therefore, are 
 Truisms. The investigation of a definition may be a very 
 valuable service to thought ; but, once found, there is no merit 
 in repeating it. To put forward verbal or analytic propositions, 
 or truisms, as information (except, of course, in actually ex- 
 plaining terms to the uninstructed), shows that we are not think- 
 ing what we say ; for else we must become aware of our own 
 emptiness. Every step forward in knowledge is expressed in 
 a real or synthetic proposition ; and it is only by means of 
 such, propositions that information can be given (except as to 
 the meaning of words) or that an argument or train of reasoning 
 can make any progress. 
 
 Opposed to a truism is a Contradiction in Terms ; that is, 
 the denying of a subject something which it connotes (or which 
 
DEFINITION OF COMMON TERMS 351 
 
 belongs to its definition), or the affirming of it something 
 whose absence it connotes (or which is excluded by its 
 definition). A Verbal Proposition is necessarily true, because 
 it is tautologous; a Contradiction in Terms is necessarily 
 false, because it is inconsistent. Yet, as a rhetorical artifice, 
 or figure, it may be effective : that ' the slave is not bound to 
 obey his master ' may be a way of saying that there ought to be 
 no slaves ; that * property is theft,' is an uncompromising 
 assertion of the communistic ideal. Similarly a truism may 
 have rhetorical value : that * a Negro is a man ' has often been 
 a timely reminder, or even that " a man's a man." It is only 
 when we fall into such contradiction or tautology by lapse of 
 thought, by not fully understanding our own words, that it 
 becomes absurd. 
 
 Real Propositions comprise the predication of Propria and 
 Accidentia. Accidentia, implying (as we have seen) a sort of 
 empirical law, can only be established by direct induction. 
 But propria are deduced from (or rather by means of) the 
 definition with the help of real propositions, and this is what 
 is called 'arguing from a Definition.' Thus, if increasing 
 capacity for co-operation is a specific character of Civilisation, 
 great wealth may be considered as a proprium of civilised as 
 compared with barbarous nations. For co-operation is made 
 most effectual by the division of labour, and that this is the 
 chief condition of producing wealth is a real proposition, 
 established both inductively and deductively. Such arguments 
 from definitions concerning concrete facts and causation, of 
 course, require verification by comparing the conclusion with 
 the facts. The verification of this example is easy, if we do 
 not let ourselves be misled in estimating the wealth of barbarians 
 by the ostentatious " pearl and gold " of kings and nobles, 
 where 99 per cent, of the people live in penury and servitude. 
 The wealth of civilisation is not only great but diffused, and in 
 its diffusion its greatness must be estimated. 
 
 To argue from a Definition may be a process of several 
 degrees of complexity. The simplest case is the establishment 
 
352 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 of a proprium as the direct consequence of some connoted 
 attribute, as in the above example. If the definition has been 
 correctly abstracted from the particulars, the particulars have 
 the attributes summarised in the definition ; and, therefore, they 
 have whatever can be shown to follow from those attributes. 
 But it frequently happens that the argument rests partly on the 
 qualities connoted by the class name and partly on many other 
 facts. 
 
 In Geometry, the proof of a theorem depends not only upon 
 the definition of the figure or figures directly concerned, but 
 also upon one or more axioms, and upon propria or construc- 
 tions already established. Thus, in Euclid's fifth Proposition, 
 the proof that the angles at the base of an isosceles triangle are 
 equal, depends not only on the equality of the opposite sides, 
 but upon this together with the construction that shows how 
 from the greater of two lines a part may be cut off equal to the 
 less, the proof (or assumption) that triangles that can be con- 
 ceived to coincide are equal, and the axiom that if equals be 
 taken from equals the remainders are equal. Similarly, in 
 Biology, if colouring favourable to concealment is a proprium 
 of carnivorous animals, it is not deducible merely from their 
 predatory character or any other attribute entering into the 
 definition of any species of them, but from their predatory 
 character together with the causes summarised in the phrase 
 1 Natural Selection ' ; that is, competition for a livelihood, and 
 the destruction of those that labour under any disadvantages, 
 of which conspicuous colouring would be one. The particular 
 colouration of any given species, again, can only be deduced 
 by further considering its habitat (desert, jungle or snow- 
 field): a circumstance lying wholly outside the definition of 
 the species. 
 
 The validity of an argument based partly or wholly on a 
 Definition depends, in the first place, on the existence of 
 things corresponding with the Definition that is, having the 
 properties connoted by the name defined. If there are no 
 such things as isosceles triangles, Euclid's fifth Proposition is 
 
DEFINITION OF COMMON TERMS 353 
 
 only formally true, like a theorem concerning the fourth 
 dimension of space : merely consistent with his other assump- 
 tions. But if there are any triangles only approximately 
 isosceles, the proof applies to them, making allowance for their 
 concrete imperfection : the nearer their sides approach straight- 
 ness and equality the more nearly equal will the opposite 
 angles be. 
 
 Again, as to the existence of things corresponding with terms 
 defined, Dr. Venn has pointed out that ' existence ' may be 
 understood in several senses: (i) merely for the Reason, like 
 the pure genera and species of Porphyry's tree ; the sole con- 
 dition of whose being is logical consistency : or (2) for the 
 Imagination, like the giants and magicians of romance, the 
 heroes of tragedy and the fairies of popular superstition ; whose 
 properties may be discussed, and verified by appeal to the 
 right documents and authorities (poems and ballads) : or (3) 
 for Perception, like plants, animals, stones and stars. We may 
 argue, therefore, from the definition of a fairy, or a demigod, 
 or a dragon, and deduce various consequences without 
 absurdity, if we are content with poetic consistency and the 
 authority of myths and romances as the test of truth. 
 
 When, however, we pass into the region of concrete objects, 
 whose properties are causes, and not merely determinations of 
 space (as in Geometry), we meet with another condition of the 
 validity of any argument depending on a Definition : there 
 must not only be objects corresponding to the definition ; but 
 there must be no other causes counteracting those qualities on 
 whose agency our argument relies. Thus, though we may 
 infer from the quality of co-operation connoted by civilisation, 
 that a civilised country will be a wealthy one, this may not be 
 found true of such a country recently devastated by war or 
 other calamity. Nor can co-operation always triumph ove 
 disadvantageous circumstances. Scandinavia is so poor in the 
 gifts of nature that are favourable to industry, that it is not 
 wealthy in spite of civilisation : still, it is far wealthier than it 
 would be in the hands of a barbarous people. In short, when 
 
 z 
 
354 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 arguing from a Definition, we can only infer the tendency of 
 any causal characteristics included in it ; the unqualified 
 realisation of such a tendency must depend upon the absence 
 of counteracting causes. As soon as we leave the region of 
 pure conceptions and make any attempt to bring our specula- 
 tions home to the actual phenomena of nature or of human 
 life, the verification of every inference becomes an unremitting 
 obligation. 
 
CHAPTER XXIV 
 FALLACIES 
 
 i. A Fallacy is any failure to fulfil the conditions of 
 Proof. If we neglect or mistake the conditions of proof 
 unintentionally, whether in our private meditations or in 
 addressing others, it is a Paralogism : but if we endeavour to 
 pass off upon others evidence or argument which we know or 
 suspect to be unsound, it is a Sophism. 
 
 Fallacies, whether paralogisms or sophisms, may be divided 
 into two classes : (a) the Formal, or those that can be shown 
 to conflict with one or more of the truths of Logic, whether 
 Deductive or Inductive ; as if we attempt to prove an universal 
 affirmative in the Third Figure ; or to argue that, as the average 
 expectation of life for males at the age of 20 is 39 J years f 
 therefore Alcibiades, being 20 years of age, will die when he 
 is 39i* (&) tne Material, or those that cannot be clearly 
 exhibited as transgressions of any logical principle, but are 
 due to hasty or superficial inquiry or confused reasoning ; 
 as in adopting premises on insufficient authority, or without 
 examining the facts ; or in mistaking the point to be proved. 
 
 2. Formal Fallacies of Deduction and Induction are, 
 all of them, breaches of the rule ' not to go beyond the 
 evidence.' As a detailed account of them would be little 
 else than a repetition of most of the foregoing chapters, it may 
 suffice to recall some of the places at which it is easiest to go 
 astray. 
 
 (i) It is not uncommon to mistake the Contrary for the 
 Contradictory, as A is not taller than B, .*. he is shorter. 
 
356 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (2) To convert A. or O. simply, as 
 
 All Money is Wealth /. All Wealth is Money. 
 or Some Wealth is not Money .'. Some Money is not Wealth. 
 In both these cases, Wealth, though undistributed in the 
 convertend, is distributed in the converse. 
 
 (3) To attempt to syllogise with two premises containing four 
 terms, as 
 
 The Papuans are savages ; 
 
 The Javanese are neighbours of the Papuans : 
 .*. The Javanese are savages. 
 
 Such an argument is excluded by the definition of a Syllogism, 
 and presents no formal evidence whatever. We should naturally 
 assume that any man who advanced it merely meant to raise 
 some probability that c neighbourhood is a sign of community 
 of ideas and customs.' But, if so, he should have been more 
 explicit. There would, of course, be the same failure of con- 
 nection, if a fourth term were introduced into the conclusion, 
 instead of in the premises. 
 
 (4) To distribute in the conclusion a term that was undis- 
 tributed in the premises (an error essentially the same as (2) 
 above), /.*., Illicit process of the major or minor term, as 
 
 Every rational agent is accountable ; 
 Brutes are not rational agents : 
 .*. Brutes are not accountable. 
 
 In this example (from Whately), an illegitimate mood of Fig. I., 
 the major term, ' accountable,' has suffered the illicit process ; 
 since, in the premise, it is predicate of an affirmative proposi- 
 tion and, therefore, undistributed ; but, in the conclusion, of a 
 negative proposition and, therefore, distributed. The fact 
 that nearly everybody would accept the conclusion as true, of 
 course, might lead them to overlook the inconclusiveness of 
 the formal proof. 
 Again, 
 
 All men are two-handed ; 
 All two-handed animals are cooking animals : 
 .*. All cooking animals are men. 
 
 
FALLACIES 357 
 
 Here we have Bramantip concluding in A. ; and there is, 
 formally, an illicit process of the minor ; though the conclusion 
 is true ; and the evidence, such as it is, is materially adequate. 
 (Of course, 'two-handed,' being a peculiar differentia, is 
 nugatory as a middle term, and may be cut out of both pre- 
 mises ; but * cooking ' is a proprium peculiar to the species 
 Man ; so that these terms might be related in U., All men are 
 all cookers ; whence, by conversion, All cookers are men.) 
 
 (5) To omit to distribute the middle term in one or the 
 other premise, as 
 
 All verbal propositions are self evident; 
 
 All axioms are self-evident : 
 .*. All axioms are verbal propositions. 
 
 This is an illegitimate mood in Fig. II.; in which, to give 
 any conclusion, one premise must be negative. It may serve 
 as a formal illustration of Undistributed Middle ; though, as 
 both premises are verbal propositions, it is materially not 
 syllogistic at all, but an error of classification ; a confounding 
 of co-ordinate species by assuming their identity because they 
 have the generic attribute in common. 
 
 (6) To simply convert a hypothetical proposition, as 
 
 If trade is free, it prospers ; 
 .*. If trade prospers, it is free. 
 
 Clearly, this is similar to the simple conversion of the cate- 
 gorical A. ; since it takes for granted that the antecedent is 
 co-extensive with the consequent, or (in other words) that the 
 freedom of trade is the sole condition of, or (at least) insepar- 
 able from, its prosperity. 
 
 The same assumption is made if, in a hypothetical syllogism, 
 we try to ground an inference on the affirmation of the con- 
 sequent or denial of the antecedent, as 
 
 If trade is free it prospers : 
 
 It does prosper ; 
 /. It is free. 
 
 It is not free ; 
 .'. It does not prosper. / 
 
358 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 Neither of these arguments is formally good ; nor, of course, 
 is either of them materially valid, if it be possible for trade to 
 prosper in spite of protective tariffs. 
 
 An important example of this fallacy is the prevalent notion, 
 that if the conclusion of an argument is true the premises must 
 be all right ; or, that if the premises are false the conclusion 
 must be erroneous. For, plainly, that 
 
 If the premises are true, the conclusion is true, 
 is a hypothetical proposition ; and we argue justly 
 
 The premises are true ; 
 /. The conclusion is true ; 
 or, The conclusion is false ; 
 .-. The premises are false. 
 
 This is valid for every argument that is formally correct ; but 
 that we cannot trust the premises on the strength of the con- 
 clusion, nor reject the conclusion because the premises are 
 absurd, the following example will show : 
 
 All who square the circle are great mathematicians ; 
 Newton squared the circle : 
 /. Newton was a great mathematician. 
 
 Here our conclusion is, no doubt, true ; but the premises 
 are intolerable. If, then, to-day the inferences of our favourite 
 orator are very much to our taste, we had better not for that 
 reason embrace his premises without examining them. Another 
 day, in circumstances slightly different, they may have other, 
 less innocent results. 
 
 How the taking of Contraries for Contradictories may vitiate 
 Disjunctive Syllogisms and Dilemmas has been sufficiently 
 explained in the twelfth chapter. 
 
 3. Formal Fallacies of Induction consist in supposing 
 or inferring Causation without attempting to prove it, or in 
 pretending to prove it without satisfying the Canons of 
 observation and experiment : as 
 
 (i) To assign the Cause of anything that is not a concrete 
 event : as, e.g., why two circles can touch^ only in one point. 
 We should give the 'reason'; for this expression includes, 
 
FALLACIES 359 
 
 besides evidence of causation, the principles of formal deduc- 
 tion, logical and mathematical. 
 
 (2) To argue, as if on inductive grounds, concerning the 
 cause of the Universe as a whole. This may be called the 
 fallacy of transcendent inference : since the Canons are only 
 applicable to instances of events that can be compared ; they 
 cannot deal with that which is in its nature unique. 
 
 (3) To mistake co-existent phenomena for cause and effect : 
 as when a man, wearing an amulet and escaping shipwreck, 
 regards the amulet as the cause of his escape. To prove his 
 point, he must either get again into exactly the same circum- 
 stances without his amulet, and then be drowned according 
 to the method of Difference ; or, shirking the only satisfactory 
 test, and putting up with mere Agreement, he must show, (a) 
 that all who are shipwrecked and escape wear amulets, and 
 (b) that their cases agree in nothing else ; and (<:), by the Joint 
 Method, that all who are shipwrecked without amulets are 
 drowned. And even if his evidence, according to Agreement, 
 seemed satisfactory in all these points, it would still be falla- 
 cious to trust to it as proof of direct causation ; since we have 
 seen that unaided observation is never sufficient for this : it is 
 only by experiment in prepared circumstances that we can 
 confidently trace sequence and the transfer of energy. 
 
 There is the reverse error of mistaking causal connection for 
 independent co-existence : as if any one regards it as merely a 
 curious coincidence that great rivers generally flow past great 
 towns. In this case, however, the evidence of connection does 
 not depend merely upon direct Induction. 
 
 (4) Post hoc, ergo propter hoc: to accept the mere sequence 
 of phenomena, even though often repeated, as proving that the 
 phenomena are cause and effect, or connected by causation. 
 This is a very natural error : for although, the antecedents of a 
 phenomenon being numerous, most of them cannot be the 
 cause, yet it is among them that the cause must be sought. 
 Indeed, if there is neither time nor opportunity for analysis, it 
 may seem better to accept any antecedent as a cause, (or, at 
 
360 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 least, as a sign) of an important event than to go without any 
 guide. And, accordingly, the vast and complicated learning of 
 omens, augury, horoscopy and prophetic dreams, relies upon 
 this maxim ; for whatever the origin of such superstitions, a 
 single coincidence in their favour triumphantly confirms them. 
 It is the besetting delusion of everybody who has wishes or 
 prejudices ; that is, of all of us at some time or other ; for then 
 we are ready to believe without evidence. And, plainly, the 
 fallacy consists in judging off-hand, without any attempt, either 
 by deductive or inductive methods, to eliminate the irrelevant 
 antecedents ; which, however, may include all the most striking 
 and specious. 
 
 (5) To regard the Co-Effects (whether simultaneous or 
 successive) of a common cause as standing in the direct rela- 
 tion of cause and effect. Probably no one supposes that the 
 falling of the mercury in his thermometer is the cause of the 
 neighbouring lake's freezing. True, it is the antecedent, and 
 (within a narrow range of experience) may be the invariable 
 antecedent of the frost ; but, besides that the two events are 
 so unequal, every one is aware that there is another antecedent, 
 the fall of temperature, which causes both. Yet in many cases, 
 the same kind of mistake is made from not remembering that, 
 to justify inductively our belief in a cause, the instances com- 
 pared must agree, or differ, in one circumstance only (besides 
 the effect). The flowing tide is an antecedent of the ebbing 
 tide ; it is invariably so, and is equal to it ; but it is not the 
 cause of it : other circumstances are present ; and the moon 
 (chiefly) is the cause of both flow and ebb. In several instances, 
 States that have grown outrageously luxurious have declined in 
 power : that luxury caused the downfall may seem obvious, 
 and capable of furnishing a moral lesson to the young. Hence 
 other important circumstances are overlooked, such as the 
 institution of slavery, the corruption and rapacity of officials 
 and tax- gathers, an army too powerful for discipline ; any or all 
 of which may be present, and sufficient to explain both the 
 luxury and the ruin. 
 
FALLACIES 361 
 
 (6) To mistake one condition of a phenomenon for the whole 
 cause. To speak of an indispensable condition of any phe- 
 nomenon as the cause of it, may be a mere conventional 
 abbreviation ; and in this way such a mode of expression is 
 common not only in popular but also in scientific discussion. 
 Thus we say that a temperature of 33 F. is a cause of the 
 melting of ice; although that ice melts at 33 F., must further 
 depend upon something in the nature of water ; for every solid 
 has its own melting-point. As long, then, as we remember 
 that * cause,' used in this sense, is only a convenient abbrevia- 
 tion, no harm is done ; but, if we forget it, fallacy may result : 
 as when a man says that the cause of a financial crisis was the 
 raising of the rate of discount, neglecting the other conditions 
 of the market ; whereas, in some circumstances, a rise of the 
 Bank-rate may increase public confidence and prevent a crisis. 
 
 Now, we have seen that the direct use of the Canons of 
 Agreement and Difference may only enable us to say that a 
 certain antecedent is a cause or an indispensable condition of 
 the phenomenon under investigation. If, therefore, it is 
 important to find the whole cause, we must either experiment 
 directly upon the other conditions, or resort to the Method of 
 Residues and deductive reasoning ; nor must we be content, 
 without showing where such precision is possible, that the 
 alleged cause and the given phenomenon are equal. 
 
 (7) To mistake a single consequence of a given cause for the 
 whole effect, is a corresponding error ; and none so common. 
 Nearly all the mistakes of private conduct and of legislation 
 are due to it : To cure temporary lassitude by a stimulant, and 
 so derange the liver ; to establish a new industry by protective 
 duties, and thereby impoverish the rest of the country ; to gag 
 the press, and so drive the discontented into conspiracy ; to 
 build an alms-house, and thereby attract paupers into the 
 parish, raise the rates, and discourage industry. 
 
 (8) To demand greater exactness in the estimate of causes 
 or effects than a given subject admits of. In the more complex 
 sciences, Biology, Sociology, Psychology, it is often impossible 
 
362 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 to be confident that all the conditions of a given phenomenon 
 have been assigned, or that all its consequences have been 
 traced. The causes of the great French Revolution have been 
 carefully investigated, and still we may doubt whether they 
 have all been discovered, or whether their comparative import- 
 ance has been rightly determined ; but it would be very un- 
 reasonable to treat that event as monstrous and unintelligible. 
 Aristotle observes in his Ethics, that a properly cultivated mind 
 knows what degree of precision is to be expected in each 
 science. Hence, controvertists, being sufficiently educated 
 and naturally loving fair play, do not comment superciliously 
 upon the absence of mathematical demonstration where it is of 
 course unobtainable. 
 
 (9) To treat an agent or condition remote in time as an 
 unconditional cause : for every moment of time gives an oppor- 
 tunity for new combinations of forces and, therefore, for modi- 
 fications of the effect. Thus, although we often say that 
 Napoleon's Russian expedition was the cause of his downfall, 
 yet the effect was subject to numerous further conditions. Had 
 the natives not burnt Moscow, had the winter been exception- 
 ally mild, had the Prussians and Austrians not risen against 
 him, the event might have been very different. It is rash to 
 trace the liberties of modern Europe to the battle of Marathon. 
 Indeed, our powers of perception are so unequal to the subtlety 
 of nature, that even in experimental science there is time for 
 molecular changes to occur between what we treat as a cause 
 and the effect as we perceive it. In such cases the strictly 
 unconditional cause has not been discovered. 
 
 (10) To neglect the negative conditions to which a cause is 
 subject. When we say that water boils at 212 F., we mean 
 " provided the pressure be the same as that of the atmosphere 
 at about the sea-level " ; for under a greater pressure water will 
 not boil at that temperature, whilst under less pressure it boils 
 at a lower temperature. In the usual statement of a law of 
 causation, what are sometimes called 'disturbing,' 'frustrating/ 
 * counteracting ' circumstances, that is, negative conditions, are 
 
FALLACIES 363 
 
 supposed to be absent ; so that the strict statement of such a 
 law, whether for a remote cause, or for an immediate cause 
 (when only positive conditions are included), is that the agent 
 or assemblage of conditions, tends to produce such an effect, 
 other conditions being favourable, or in the absence of contrary 
 forces. 
 
 (n) It is needless to repeat what has already been said of 
 other fallacies that beset inductive proof; such as the neglect 
 of a possible plurality of causes where the effect has been 
 vaguely conceived; the extension of empirical laws beyond 
 adjacent cases; the chief errors to which the estimate of 
 analogies and probabilities, or the application of the principles 
 of classification are liable ; and the reliance upon direct Induc- 
 tion where the aid of Deduction may be obtained, or upon 
 observation where experiment may be employed. As to formal 
 fallacies, that may be avoided by adhering to the rules of 
 logical method, this may suffice. 
 
 4. There remain many ways in which arguments fall short 
 of a tolerable standard of proof, though they cannot be 
 exhibited as definite breaches of logical principles. Logicians, 
 therefore, might be excused from discussing them ; but out of 
 the abundance of their pity for human infirmity they usually 
 describe and label the chief classes of these 4 extra-logical 
 fallacies,' and gibbet a few examples. 
 
 We may adopt Whately's remark, that a fallacy lies either (i) 
 in the premises, or (2) in the conclusion, or (3) in the attempt 
 to connect a conclusion with the premises. 
 
 (i) Now the premises of a sound argument must either be 
 valid deductions, or valid inductions, or particular observations, 
 or axioms. In an unsound argument, then, whose premises 
 are supported by either deduction or induction, the evidence 
 may be reduced to logical rules ; and its failure is therefore a 
 ' logical fallacy ' such as we have already discussed. It follows 
 that an extra-logical fallacy of the premises must lie in what 
 cannot be reduced to rules of evidence, that is, in bad observa- 
 tions ( 5), or sham axioms ( 6). 
 
364 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 (2) As to the conclusion, this can only be fallacious if 
 some other conclusion has been substituted for that which 
 was to have been proved ( 7). 
 
 (3) Fallacies in the connection between premises and 
 conclusion, if all the propositions are distinctly and explicitly 
 stated, become manifest upon applying the rules of Logic. 
 Fallacies, therefore, which are not thus manifest, and so 
 are extra-logical, must depend upon some sort of slurring, 
 confusion, or ambiguity of thought or speech ( 8). 
 
 5. Amongst Fallacies of Observation, Mill distinguishes 
 (i) those of Non-observation, where either instances of the 
 presence or absence of the phenomenon under investigation, 
 or else some of the circumstances constituting it or attending 
 upon it, though important to the induction, are overlooked. 
 These errors are implied in the Formal Fallacies of Induction 
 already treated of in 3 (paragraphs (3) to (7)). 
 
 Mill's class (2) comprises fallacies of Malobservation. Mai- 
 observation may be due to obtuseness or slowness of percep- 
 tion ; and it is one advantage of the physical sciences as means 
 of education, that the training involved in studying them tends 
 to cure these defects. 
 
 But the occasion of error upon which Mill most insists, 
 is our proneness to substitute a hasty inference for a just 
 representation of the fact before us ; as when a yachtsman, 
 all agog for marvels, sees a line of porpoises and takes 
 them for the sea-serpent. Every one knows what it is to 
 mistake a stranger for a friend, a leaf for a sparrow, one 
 word for another (X persisted in reading Unsertesen as 
 untersetzen). The wonder is that we are not oftener wrong ; 
 considering how small a part present sensation has in percep- 
 tion, and how much of every object observed is supplied by a 
 sort of automatic judgment. You see something brown, which 
 your perceptive mechanism classes with the appearance of a 
 cow at such a distance ; and instantly all the other properties 
 of a cow are supplied from the resources of former experience : 
 but on getting nearer, it turns out to be a log of wood. It is 
 
FALLACIES 365 
 
 some protection against such errors to know that we are 
 subject to them ; and the Logician fulfils his duty in warning 
 us accordingly. But the matter belongs essentially to Psy- 
 chology ; and whoever wishes to pursue it will find a thorough 
 explanation in Prof. Sully's volume on Illusions. 
 
 Another error is the accumulation of useless, irrelevant 
 observations, from which no proof of the point at issue~can"Be~ 
 derived. It has been said that an important part of an induc- 
 tive inquirer's equipment consists in knowing what to observe. 
 The study of any science doubtless educates this power by 
 showing us what observations have been effective in similar 
 cases : but something depends upon genius. Observation is 
 generally guided by hypotheses : he makes the right observa- 
 tions who can frame the right hypotheses ; whilst another over- 
 looks things, or sees them all awry, because he is confused and 
 perverted by wishes, prejudices or other false preconceptions ; 
 and still another gropes about blindly, noting this and docket- 
 ing that to no purpose, because he has no hypothesis, or one 
 so vague and ill-conceived that it sheds no light upon his 
 path. 
 
 6. The second kind of extra-logical Fallacy lying in the 
 premises, consists in offering as evidence some verbal jingle 
 or assertion which is entirely baseless : it is generally known as 
 petitio principii) or begging the question. The question may 
 be begged in three ways : (i) there are what Mill calls 
 Fallacies & priori, mere assertions, pretending to be self- 
 evident, and often sincerely accepted as such by the author 
 and some infatuated disciples, but in which the cool spectator 
 sees either no sense at all, or palpable falsity. 
 
 These sham axioms are (grievous to confess) not uncommon 
 in the writings of the greatest philosophers. There are hun- 
 dreds of them ; and probably every one is familiar with the . , 
 following examples : That circular motion is the most perfect ; 
 That every body strives toward its natural place ; That like 
 cures like ; That every bane has its antidote ; That what is 
 true of our conceptions is true of Nature ; That pleasure is 
 
366 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 nothing but relief from pain ; That the good, the beautiful and 
 the true are inseparable; That, in trade, whatever is some- 
 where gained is somewhere lost ; That only in agriculture does 
 nature assist man ; That a man may do what he will with his 
 own ; That some men are naturally born to rule and others to 
 obey. Now some of these doctrines are specious enough ; 
 whilst, as to others, how they could ever have been entertained 
 arouses a wonder that can only be allayed by a lengthy 
 historical and psychological disquisition. 
 
 (2) Verbal propositions offered as proof of some matter of 
 fact. 
 
 These have, indeed, one attribute of Axioms : they are self- 
 evident to any one who knows the language ; but as they only 
 dissect the meaning of words, nothing but the meaning of words 
 can be inferred from them. If anything further is arrived at, 
 it must be by the help of real propositions. How common is 
 such an argument as this : ' Lying is wrong, because it is 
 vicious' the implied major premise being that 'what is vicious 
 is wrong.' Now if anybody hesitates whether to be a liar or 
 not, good reasons can be given him for abstaining ; but the 
 above argument only shows that lying is called wrong ; and 
 this the impending liar already knew. The argument, there- 
 fore, must be supplemented by a further premise, that * what is 
 called wrong in English is most probably something that ought 
 to be avoided ' : but this is a real proposition, which to a 
 foreigner might seem to need a vast amount of evidence. Let 
 us hope there is some shorter and more cosmopolitan way of 
 justifying the moral law. Still, such arguments, though bad 
 Logic, often have a rhetorical force : to call lying not only 
 wrong but vicious, may be dissuasive by accumulating associa- 
 tions of shame and ignominy. 
 
 Definitions, being the most important of verbal propositions 
 (since they imply the possibility of as many other verbal pro- 
 positions as there are denning attributes and combinations of 
 them), need to be watched with especial care. If two dis- 
 putants define the same word in different ways, with each of 
 
FALLACIES 367 
 
 the different attributes included in their several definitions they 
 may bring in a fresh set of real propositions as to the agency 
 or normal connection of that attribute. Hence their conclu- 
 sions about the things denoted by the word defined, diverge in 
 all directions and to any extent. And it is generally felt that 
 a man who is allowed to define his terms as he pleases, may 
 prove anything to those who, through ignorance or inadvertence 
 grant that the things that those terms stand for have the attri- 
 butes that figure in his definitions. 
 
 (3) Circulus in demonstrando^ the pretence of giving a reason 
 for an assertion, whilst in fact only repeating the assertion 
 itself generally in other words. 
 
 In such cases the original proposition is, perhaps, really 
 regarded as self-evident, but by force of habit a man says 
 
 * because ' ; and then, after vainly fumbling in his empty pocket 
 for the coin of reason, the habit of symbolic thinking in words 
 only, without reference to the facts, comes to his rescue, and 
 he ends with a paraphrase of the same assertion. Thus a man 
 may try to prove the necessity of Causation : ' Every event 
 must have a cause ; because an event is a change of pheno- 
 mena, and this implies a transformation of something pre- 
 existing; which can only have been possible, if there were 
 forces in operation capable of transforming it.' Or, again : 
 
 * We ought not to go to war, because it is wrong to shed blood/ 
 But, plainly, if war did not imply bloodshed, the unlawfulness 
 of this could be nothing against war. The more serious any 
 matter is, the more important it becomes either to reason 
 thoroughly about it, or to content ourselves with wholesome 
 assertions. How many c arguments ' are superfluous ! 
 
 7. The Fallacy of surreptitious conclusion (ignoratio 
 eknchi\ the mistaking or obscuring of the proposition really 
 at issue, whilst proving something else instead. 
 
 This may be done by substituting a particular proposition 
 for an universal, or an universal for a particular. Thus, he who 
 attacks the practice of giving in charity must not be content to 
 show that it has, in this or that case, degraded the recipient ; 
 
LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 who may have been exceptionally weak. Or, again, to dissuade 
 another from giving alms in a particular case, it is not enough 
 to show that the general tendency of almsgiving is injurious ; 
 for, by taking pains, the general tendency may often be 
 counteracted. 
 
 Sometimes an argument establishing a wholly irrelevant con- 
 clusion is substituted for an argumentum ad rem. Macaulay 
 complains of those apologists for Charles I. who try to defend 
 him as a king, by urging that he was a good judge of paintings 
 and indulgent to his wife. 
 
 To this class of Fallacies belongs the argumentum ad 
 hominem, which consists in showing not that a certain proposi- 
 tion is true, but that Critias ought to accept it in consistency 
 with his other opinions. Thus : * In every parish the cost of 
 education ought to be paid out of the rates : you, at least, have 
 said that there can be no sound economy, unless local expenses 
 are defrayed from local funds.' But whether this is a fallacy 
 depends, as Whately observes, upon whether it is urged as 
 actually proving the point at issue, or merely as convicting the 
 opponent of inconsistency. In the latter case, the argument 
 is quite fair : whatever such a conclusion may be worth. 
 
 Similarly with the argumentum ad populum : * this measure 
 is favourable to such or such a class ; let them vote for it.' An 
 appeal to private greed, however base, is not fallacious, as long 
 as the interest of the class is not fraudulently substituted for 
 the good of the nation. And much the same may be said for 
 the argumentum ad verecundiam. When a question of morals 
 is debated as a question of honour among thieves, there is no 
 fallacy, if the moral issue is frankly repudiated. The argument 
 from authority is often brought under this head : ' such is the 
 opinion of Aristotle.' Although this does not establish the 
 truth of any proposition, it may be fairly urged as a reason for 
 not hastily adopting a contrary conclusion : that is, of course, 
 if the subject under discussion be one as to which Aristotle (01 
 whoever the authority may be) had materials for forming a 
 'udgment. 
 
FALLACIES 369 
 
 A negative use of this fallacy is very common. Some general 
 doctrine, such as Positivism, Transcendentalism, Utilitarianism, 
 or Darwinism, is held in common by a group of men ; who, 
 however, all judge independently, and therefore are likely to 
 differ in details. An opponent exhibits their differences of 
 opinion, and thereupon pretends to have refuted the theory 
 they agree in supporting. This is an argumentum ad scholam, 
 and pushes too far the demand for consistency. In fact it 
 recoils upon the Sophist ; for there is no sense in quoting men 
 against one another, unless both (or all) are acknowledged to 
 speak with the authority of learning and judgment, and there- 
 fore the general doctrine which they hold in common is the 
 more confirmed. 
 
 This is an example of the paralogism of * proving too much ' ; 
 when a disputant is so eager to refute an opponent as to lay 
 down, or imply, principles from which an easy inference 
 destroys his own position. To appeal to a principle of greater 
 sweep than the occasion requires may easily open the way to 
 this pitfall : as if a man should urge that * all men are liars,' 
 as the premise of an argument designed to show that another's 
 assertion is less credible than his own. 
 
 A common form of ignoratio elenchi is that which Whately 
 called the ' fallacy of objections ' : it consists in insisting upon 
 all the considerations against any doctrine or proposal, with- 
 out any attempt to weigh them against the considerations in 
 its favour ; amongst which should be reckoned all the con- 
 siderations that tell against the alternative doctrines or pro- 
 posals. Incontestable demonstration can rarely be expected 
 even in science, outside of the Mathematics ; and in practical 
 affairs, as Butler says, ' probability is the very guide of life ' ; 
 so that any conclusion depends upon the balance of evidence, 
 and to allow weight to only a part of it is an evasion of the 
 right issue. 
 
 8. Fallacies in the connection of premises and con- 
 clusion that cannot be detected by reducing the arguments 
 to syllogistic form, must depend upon some juggling with 
 
 2 A 
 
370 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 language to disguise their incoherence. They may be gener- 
 ally described as Fallacies of Ambiguity, whether they turn 
 upon the use of the same word in different senses, or upon 
 ellipsis. 
 
 Thus it may be argued that all works written in a classical 
 language are classical, and that, therefore, the History of 
 Philosophy by Diogenes Laertius, being written in Greek, is a 
 classic. Such ambiguities are sometimes serious enough ; 
 sometimes are little better than jokes. For jokes, as Whately 
 observes, are often fallacies ; and considered as a propoedeutic 
 to the art of sophistry, punning deserves the ignominy that has 
 overtaken it. 
 
 Fallacies of ellipsis usually go by learned names, as ; (i) d 
 dicto secundum quid ad dictum simplidter. It has been argued 
 that since, according to Ricardo, the value of goods depends 
 solely upon the quantity of labour necessary to produce them, 
 the labourers who are employed upon (say) cotton cloth ought 
 to receive as wages the whole price derived from its sale, 
 leaving nothing for interest upon capital. Ricardo, however, 
 explains that by * the quantity of labour necessary to produce 
 goods ' he means not only what is immediately applied to them, 
 but also the labour bestowed upon the implements and build- 
 ings with which the immediate labour is assisted. Now these 
 buildings and implements are capital, the labour which pro- 
 duced them was paid for, and it was far enough from Ricardo's 
 mind to suppose that the capital which assists present labour 
 upon (say) cotton cloth has no claim to remuneration out of 
 the price of it. In this argument, then, the word labour in the 
 premise is used secundum quid> that is, with the suppressed 
 qualification of including past as well as present labour ; but 
 in the inference labour is used simplidter to mean present 
 labour only. 
 
 (2) A dicto secundum quid ad dictum secundum alterum quid. 
 It may be urged that, since the tax on tea is uniform, there- 
 fore all consumers contribute equally to the revenue for their 
 enjoyment of it. But written out fairly this argument runs 
 
FALLACIES 371 
 
 thus : Since tea is taxed uniformly $d. per /., all consumers 
 pay equally for their enjoyment of it whatever quality they use. 
 These qualifications introduced, nobody can be deceived. 
 
 (3) A dicto simpliciter ad dictum secundum quid, also called 
 fallacia accidentis. Thus : To take interest upon a loan is 
 perfectly just, therefore, I do right to exact it from my own 
 father in distress. The popular answer to this sort of 
 blunder is that * circumstances alter cases.' We commit this 
 error in supposing that what is true of the average is likely to 
 be true of each case ; as if one should say : ( The offices are 
 ready to insure my house [with thousands of others] agains 
 fire at a rate per annum which will leave them heavy losers 
 unless it lasts a hundred years ; so, as we are told not to take 
 long views of life, I shall not insure.' 
 
 The Fallacy of Division and Composition consists in sug- 
 gesting, or assuming, that what is true of things severally 
 denoted by a term is true of them taken together. That every 
 man is mortal is generally admitted, but we cannot infer that, 
 therefore, the human race will become extinct. That the 
 remote prospects of the race are tragic may be plausibly argued, 
 but not from that premise. 
 
 Changing the Premises is a fallacy usually placed in this 
 division; although, instead of disguising different meanings 
 under similar words, it generally consists in using words or 
 phrases ostensibly differing, as if they were equivalent : those 
 addressed being expected to renounce their right to reduce 
 the argument to strict forms of proof, as needless pedantry in 
 dealing with an author so palpably straightforward. If an 
 orator says ' Napoleon conquered Europe ; in other words, 
 he murdered five millions of his fellow creatures ' and is 
 allowed to go on, he may infer from the latter of these pro- 
 positions many things which the former of them would hardly 
 have covered This is a sort of hyperbole, and there is a 
 corresponding meiosis, as : ' Mill admits that the Syllogism is 
 useful ' ; when, in fact, that is Mill's contention. It may be 
 supposed that, if a man is fool enough to be imposed upon bv 
 
372 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 such transparent colours, it serves him right ; but this harsh 
 judgment will not be urged by any one who knows and con- 
 siders the weaker brethren. 
 
 9. The above classification of Fallacies is a rearrangement 
 of the plans adopted by Whately and Mill. But Fallacies 
 resemble other spontaneous natural growths in not submitting 
 to precise and definite classification. The same blunders, 
 looked at from different points of view, may seem to belong to 
 different groups. Thus, the example given above to illustrate 
 fallacia accidentis, 'that, since it is just to take interest, it is 
 right to exact it from one's own father,' may also be regarded 
 as petitio prinripn, if we consider the unconditional statement 
 of the premise ' to take interest upon a loan is perfectly just ' ; 
 for, surely, this is only conditionally true. Or, again, the first 
 example given of simple ambiguity ' that whatever is written 
 in a classical language is classical, etc.\ may, if we attend 
 merely to the major premise, be treated as a bad generalisation, 
 an undue extension of an inference, founded upon a simple 
 enumeration of the first few Greek and Latin works that one 
 happened to remember. 
 
 It must also be acknowledged that genuine wild fallacies, 
 roaming the jungle of controversy, are not so easily detected or 
 evaded as specimens seem to be when exhibited in a Logician's 
 collection ; where one surveys them without fear, like a child 
 at a menagerie. To assume the succinct mode of statement 
 that is most convenient for refutation, is not the natural habit 
 of these things. But to give reality to his account of fallacies 
 an author needs a large space, that he may quote no inconsider- 
 able part of literature ancient and modern. 
 
 As to the means of avoiding fallacies, a general increase of 
 sincerity and candour amongst mankind may be freely 
 recommended. With more honesty there would be fewer bad 
 arguments; but there is such a thing as well-meaning inca- 
 pacity that gets unaffectedly fogged in converting A., and 
 regards the refractoriness of O., as more than flesh and blood 
 can endure. Mere indulgence in figurative language, again, is 
 
FALLACIES 373 
 
 a besetting snare. "One of the fathers, in great seventy 
 called poesy vinum damonum? says Bacon : himself too fanciful 
 for a philosopher. Surely, to use a simile for the discovery of 
 truth is like studying beauty in the bowl of a spoon. 
 
 The study of the natural sciences trains and confirms the 
 mind in a habit of good reasoning, which is the surest 
 preservative against paralogism, as long as the terms in use 
 are, like those of science, well defined ; and where they are ill 
 defined, so that it is necessary to guard against ambiguity, a 
 thorough training in politics or metaphysics may be useful. 
 Logic seems to me (I must confess) to serve, to some extent, 
 both these purposes. The conduct of business, or experience, 
 a sufficient time being granted, is indeed the best teacher, but 
 also the most austere and expensive. In the seventeenth century 
 some of the greatest philosophers wrote de intellectus emen- 
 datione ; and if their successors have given over this very 
 practical inquiry, the cause of its abandonment is not success 
 and satiety but despair. Perhaps the right mind is not to be 
 made by instruction, but can only be bred : a slow, haphazard 
 process ; and meanwhile the rogue of a sophist may count on 
 a steady supply of dupes to amuse the tedium of many an age. 
 
 FINIS. 
 
QUESTIONS 
 
 The following questions are chiefly taken from public examination 
 papers: Civil Service [S], Oxford [O], and Cambridge [C]. 
 
 I. TERMS, ETC. 
 
 1. What is a Term ? Explain and illustrate the chief divisions 
 
 of Terms. What is meant by the Connotation of a 
 Term ? Illustrate. [S] 
 
 2. " The connotation and denotation of terms vary inversely." 
 
 Examine this assertion, explaining carefully the limits 
 within which it is true, if at all. [S] 
 
 3. Exemplify the false reasoning arising from the confusion of 
 
 Contrary and Contradictory Terms. [S] 
 
 4. Discuss the claims of the doctrine of Terms to be included 
 
 in a Logical System. Distinguish between a General 
 and an Abstract Term [S] 
 
 5. Explain and illustrate what is meant by the Denotation 
 
 and Connotation of a Term. What terms have both, 
 and what have one only ? [S] 
 
 6. Distinguish between Abstract and Concrete Names. To 
 
 which of these classes belong (a) adjectives, (b) names 
 of states of consciousness? Are any abstract names 
 connotative ? [S] 
 
 7. Distinguish between (a) Proper and Singular Terms, 
 
 (b] Negative and Privative, (c) Absolute and Relative. 
 Illustrate. 
 
376 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 8. What connection is there between the Connotation and the 
 
 Relativity of Names ? 
 
 9. Examine the logical relations between the following pairs 
 
 of terms : (a) happy and happiness ; (b) happy and 
 unhappy; (c) 'the juryman' and 'the jury'; (d) parent 
 and offspring. 
 Explain the technical words used in your answer. [C] 
 
 10. Distinguish between name; part of speech ; term: and 
 illustrate by reference to the following use, useful, 
 usefully. [C] 
 
 xi. Describe the nature of Collective terms; examine in par- 
 ticular any difficulties in distinguishing between these 
 and general or abstract terms. [C] 
 
 12. Distinguish between positive, negative, and privative 
 names. Of what kind are the following, and why 
 parallel, alien, idle, unhappy ? What ambiguity is there 
 in the use of such a term as " not- white " ? [C] 
 
 II. PROPOSITIONS AND IMMEDIATE INFERENCE. 
 
 13. What is meant by (i) the Conversion, and (2) the Contra- 
 position of a proposition ? Apply these processes, as 
 far as admissible, to the following : 
 
 (a) All invertebrates have cold blood. 
 
 (b) Some cold-blooded animals are not invertebrates. 
 
 (c) No wingless birds are songsters. 
 
 (d) Some winged birds are not songsters. 
 
 What can you infer from (a) and (b) jointly, and what from 
 
 (c) and (O jointly? [S] 
 14 "The author actually supposes that, because Professor 
 
 Fawcett denies that all wealth is money, he denies that 
 
 all money is wealth." Analyse the differences of opinion 
 
 implied in the above passage. [S] 
 15. Take any universal affirmative proposition ; convert it by 
 
 obversion (contraposition) ; attach the negative particle 
 
QUESTIONS 377 
 
 to the predicate, and again convert. Interpret the result 
 exactly, and say whether it is or is not equivalent to the 
 original proposition. [S] 
 
 1 6. What information about the term "solid body" can we 
 
 derive from the proposition, " No bodies which are not 
 solids are crystals " ? [S] 
 
 17. Discuss the proposal to treat all propositions as affirma- 
 
 tive. 
 
 1 8. Convert the proposition "A is probably B." What in- 
 
 formation does the proposition give us concerning 
 B? [S] 
 
 19. Show in how many ways you can deny the following asser- 
 
 tions : All cathedral towns are all cities; Canterbury 
 is the Metropolitan see. [S] 
 
 20. Explain the nature of a hypothetical (or conditional) pro- 
 
 position. What do you consider the radical difference 
 between it and a categorical ? [S] 
 
 21. What is the function of the copula ? In what different 
 
 manners has it been treated ? [S] 
 
 22. Convert " A killed C unjustly": "All Knowledge is pro- 
 
 bably useful"; "The exception proves the rule"; 
 " Birds of a feather flock together." [S] 
 
 23. What is modality ? How are modals treated by (a) formal 
 
 logic and (b) by the theory of induction ? [S] 
 
 24. What is the subject of an impersonal proposition ? Give 
 
 reasons for your answer. [S] 
 
 25. Is the categorical proposition sufficiently described as 
 
 referring a thing or things to a class ? [S] 
 
 26. Enumerate the cases in which the truth or falsity of one 
 
 proposition may be formally inferred from the truth or 
 falsity of another. Illustrate these cases, and give to 
 each its technical name. [S] 
 
 27. Illustrate the relation of Immediate Inferences to the Laws 
 
 of Thought. 
 
 28. Explain what is meant by (a) Symbolic Logic; () 
 
 the Logic of Relatives. Describe some method of 
 
378 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 representing propositions by means of diagrams ; and 
 indicate how far any particular theory of the import of 
 propositions is involved in such representation. [S] 
 
 29. Explain the exact nature of the relation between two 
 
 Contradictory propositions ; and define Conversion by 
 Contraposition, determining what kind of propositions 
 admit of such conversion. 
 
 Give the contradictory and the contrapositive of each of 
 the following propositions : 
 
 (a) All equilateral triangles are equiangular ; 
 
 (b) No vertebrate animal has jaws opening sideways ; 
 
 (c) Wherever A and B are both present, either C or D 
 
 is also present. [S] 
 
 30. Define Obversion and Inversion, and apply these processes 
 
 also to the above three propositions. 
 
 31. Propositions can be understood either in extension or in 
 
 intension. Explain this, and discuss the relative value 
 of the two interpretations. [S] 
 
 32. Distinguish between real and verbal propositions; and 
 
 explain the importance of the distinction. 
 
 33. Illustrate the process called ' change of Relation.' 
 
 III. SYLLOGISM AND MEDIATE INFERENCE 
 
 34. What is a Syllogism? Find, without reference to the 
 
 mnemonic verses, in what different ways it is possible 
 to prove syllogistically the conclusion No S is P ; 
 arid show the equivalence between these different ways. 
 (S] 
 
 35. From what points of view can the syllogism be regarded 
 
 (i) as being, (2) as not being, * pctitio principal [S] 
 
 36. What are the figures of syllogism? For what kind of 
 
 arguments are they severally adapted ? [S] 
 
 37. What is meant by Mood and Figure? How can the 
 
 validity of a Mood be tested ? Should there be four 
 Figures or three ? [S] 
 
QUESTIONS 379 
 
 38. Construct syllogisms in Camenes, Datisi and Baroco, and 
 
 reduce them to the corresponding moods of the first 
 figure. 
 
 39. Explain the meaning of "ostensive" and "indirect" Re- 
 
 duction. Show that any Mood of the second Figure 
 may be reduced in either way. 
 
 40. Show that A cannot be proved except in the First Figure. 
 
 Express the following reasoning in as many syllogistic 
 figures as you can : Some theorists cannot be trusted, 
 for they are unwise. [S] 
 
 41. Discuss the possibility of reducing the argument a fortiori 
 
 to the syllogistic form. [S] 
 
 42. Can a false conclusion be reached through true premises, 
 
 or a true conclusion through false premises ? Give 
 reasons for your answer. [S] 
 
 43. Can we under any circumstances infer a relation between 
 
 X and Z from the premises 
 Some Y's are X's 
 Some Y's are Z's? [S] 
 
 44. Take an apparent syllogism subject to the fallacy of 
 
 negative premises, and inquire whether you can correct 
 the reasoning by converting one or both of the premises 
 into the affirmative form. [S] 
 
 45. Enumerate the faults to which a syllogism is liable, giving 
 
 instances of each. [S] 
 
 46. State any Enthymeme, and expand it into (i) a Syllogism, 
 
 (2) an Epicheirema, (3) a Sorites ; and give in each 
 case the technical name of the Mood or Order that 
 results. 
 
 47. State any Disjunctive Syllogism, and change it (i) into a 
 
 Hypothetical, (2) into a Categorical; and discuss the 
 loss or gain, in cogency or significance involved in this 
 process. 
 
 48. Can the Syllogism be treated as merely a consequence 
 
 of the "Laws of Thought"? If not, why not; and 
 what else does it imply ? 
 
3 8o LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 49. Prove that with three given propositions (of the forms 
 
 A., E., I., O.) it is never possible to construct more 
 than one valid syllogism. [C] 
 
 50. Distinguish between a Constructive and a Destructive 
 
 Hypothetical Syllogism; and show how one may be 
 reduced to the other. [C] 
 
 IV. INDUCTION, ETC. 
 
 51. What constitutes a Valid Induction ? Distinguish it from 
 
 a legitimate hypothesis. [S] 
 
 52. Is it possible to form true universal propositions about 
 
 facts if we have not actually observed all the individuals 
 designated by the subject of the proposition? If so 
 how? [S] 
 
 53. "Perfect induction is demonstrative and syllogistic ; imper- 
 
 fect induction is neither." Explain the difference 
 between perfect and imperfect induction, and examine 
 the truth of this assertion. [S] 
 
 54. Why is it that one should not regard night as the cause, 
 
 nor even as a universal condition of day? Explain 
 " cause " and condition. [S] 
 
 55. What do you understand by an experiment? Can you say 
 
 how many experiments are required to establish (i) a 
 fact, (2) a law of nature ? 
 
 56. How would you define antecedent, cause, effect, consequent? 
 
 [S] 
 
 57. England is the richest country in the world, and has a 
 
 gold currency. Russia and India, in proportion to 
 population, are poor countries and have little or no gold 
 currency. How far are such kind of facts logically 
 sufficient to prove that a gold currency is the cause of a 
 nation's wealth ? [S] 
 
 58. A man having been shot through the heart immediately 
 
 falls dead. Investigate the logical value of such a fact 
 
QUESTIONS 381 
 
 as proving that all men shot through the heart will fall 
 dead. [S] 
 
 59. Explain the process of induction called the Method of 
 
 Difference, and give some new instances of its applica- 
 tion. How is it related to the Method of Concomitant 
 Variations ? What is the Major Premise implied in all 
 these methods ? [S] 
 
 60. Explain the logical cogency of experiments in the search 
 
 for physical causes. [S] 
 
 6 1. If the effects of A B C D are fully expressed by a b c d, and 
 
 those of B C D by b c d, what inductive inference can 
 be drawn and on what principle? State the canon 
 according to which it is drawn. [S] 
 
 62. Compare the advantage of observation and experiment as 
 
 means of gaining data for Reasoning. [S] 
 
 63. Compare the cogency of different Inductive Methods, 
 
 showing the kind of evidence each requires, and the 
 principle on which it is based. [S] 
 
 64. Compare the Canons of Agreement and Difference (i) as 
 
 to the difficulty of fitting them with actual " Instances," 
 and (2) as to their conclusiveness. 
 
 65. Describe what is meant by residual phenomena, and 
 
 estimate their value in inductive science. [S] 
 
 66. What is the argument from Analogy? How does it 
 
 differ from (a) Induction, (b) Metaphorical argument ? 
 
 [S] 
 
 67. What are the various senses in which the word Analogy 
 
 has been used? Distinguish, giving instances, between 
 good and bad analogies. [S] 
 
 68. How do you distinguish between what Mill calls the 
 
 Geometrical, Physical and Historical Methods ? 
 
 69. What is meant by a doctrine being unverifiable? If a 
 
 conclusion reached by deduction does not agree with 
 the facts, where must we look for error ? 
 
 70. There are certain cases in which failure of verification is 
 
 fatal to a theory, and other cases in which it is of 
 
382 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 comparatively little cogency. How would you distin- 
 guish between these classes of cases ? [S] 
 
 71. Taking the " evolution," or any other proposed hypothesis, 
 
 how should one proceed (a) to show whether it satisfies 
 the conditions of a legitimate hypothesis sufficiently to 
 entitle it to investigation, and (b) to test it with a view 
 to its acceptance or rejection as a truth of science ? [S] 
 
 72. What do you mean by saying that "a phenomenon has 
 
 been satisfactorily explained " ? 
 
 73. Explain and illustrate the Historical Method of Sociological 
 
 inquiry. [S] 
 
 74. What is the relation of the theory of Probability to Logic ? 
 
 [S] 
 
 75. Explain and discuss the doctrine that Induction is based 
 
 upon the Theory of Probability. [S] 
 
 76. Explain the nature and use of Classification, the means to, 
 
 and tests of, its successful performance. [S] 
 
 77. What is Definition and what is its use? Mention various 
 
 difficulties that occur in the process, and show how they 
 are to be met. [S] 
 
 78. Propose rules for a good Division and a good Definition 
 
 and exemplify the breach of them. [S] 
 
 79. Examine the validity of the idea of Real Kinds. [O] 
 
 80. What kind of words are indefinable, and why ? When do 
 
 we define by negation and by example ? [S] 
 
 8 1. Distinguish between the province and aims of classification 
 
 and (logical) division. Illustrate. [S] 
 
 82. What is an infima species or species sperialissima ? Com- 
 
 pare the use of the terms genus and species in Logic 
 with that which is common in speaking of animals or 
 plants. [S] 
 
 83. How far does the formation of Definitions and Classifica- 
 
 tions constitute the end of Science ? [S] 
 
 84. Examine the methodological relations between Definition, 
 
 Classification and Nomenclature. [S] 
 
 85. Give instances of " Differentia," " Property," " Inseparable 
 
QUESTIONS 383 
 
 Accident"; and examine, with reference to your 
 instances, how far it is possible to distinguish them. [S] 
 
 V. MISCELLANEOUS. 
 
 86. " People can reason without the help of Logic." Why is 
 
 this not a sufficient objection to the study ? In your 
 answer show distinctly why Logic should be studied. 
 [S] 
 
 87. What is the meaning of the assertion that Logic is con- 
 
 cerned with the form, and not with the matter, of 
 thought ? [S] 
 
 88. "Neither by deductive nor inductive reasoning can we 
 
 add a title to our implicit knowledge." (Jevons.) Ex- 
 plain and criticise. [S] 
 
 89. What is the logical foundation of the indirect method or 
 
 reductio ad absurdum ? Is it applicable to non-mathe- 
 matical subjects ? [S] 
 
 90. On what grounds do we believe in the reality of a historical 
 
 event? [S] 
 
 91. "Facts are familiar theories." Explain and discuss this. 
 
 [O] 
 
 92. Wherein lies the difficulty of proving a negative ? [O] 
 
 93. Can any limits be assigned to the possible unification of 
 
 the sciences ? [O] 
 
 94. Are the results of inductive inference necessarily certain ? 
 
 [O] 
 
 95. The method of deductive science is hypothetical. Ex- 
 
 plain and discuss. [O] 
 
 96. " The uniformity of Nature can never be more than a 
 
 working hypothesis." Explain and criticise. 
 
 97. " Without speculation there is no good and original ob- 
 
 servation." Why ? f O] 
 
 98. Can the provinces of induction and deduction be kept 
 
 separate ? [O] 
 
384 LOGIC: DEDUCTIVE AND INDUCTIVE 
 
 99. How far is the relation of logical dependence identical 
 with that of causation ? [O] 
 
 100. State in syllogistic form (mood and figure) the following 
 
 arguments : 
 
 (a) As polygamy is in many countries legal, we may 
 infer the variability of the moral standard. 
 
 (b) If gold is wealth, to export it diminishes the 
 national resources. 
 
 (c) If all good people are happy, unhappiness is an 
 indication of vice. 
 
 (d) One may be sure of the benefits of inuring young 
 children to cold, from the strength exhibited by all men 
 and women thus treated in infancy, 
 
 (e) Where there is no law, there is no injustice. 
 
 (/) " Dissimulation is but a faint kind of policy or 
 wisdom ; for it asketh a strong wit and a strong heart to 
 know when to tell the truth, and to do it ; therefore it 
 is the weaker sort of politicians that are the greatest 
 dissemblers." (Bacon.) 
 
 (g) Money being a barren product, it is contrary to 
 nature to make it reproduce itself. Usury, therefore, is 
 unnatural, and, being unnatural, is unjustifiable. 
 
 (h) The study of mathematics is essential to a com- 
 plete course of education, because it induces a habit of 
 close and regular reasoning. [S] 
 
 101. Explain and illustrate the following terms: Subalternans, 
 
 Vera Causa, Plurality of Causes, Law of Nature, 
 Empirical Law, Summum Genus, Predicament, Arbor 
 Porphyriana, Axiom, Universe of discourse (suppositio\ 
 Antinomy, Dilemma, Realism, Dichotomy. 
 
 102. Is there any distinction and, if so, what, between a com- 
 
 plete Description and an Explanation ? [C] 
 
 103. On what principles have Fallacies been classified? To 
 
 what extent do you think a satisfactory classification of 
 Fallacies possible ? [C] 
 
 104. Examine how far conceptions of Persistence and of 
 
QUESTIONS 385 
 
 Invariable Concomitance of Properties are involved in 
 the methodological application of the conception of 
 Cause. 
 
 Inquire whether the two following propositions can be 
 reconciled with one another : (a) The same conjunc- 
 tion of antecedents is invariably followed by the same 
 consequent ; (fr) We never find the same concurrence 
 of phenomena a second time. [C] 
 
 105. Using the term Logic in a wide sense so as to include 
 
 Methodology, inquire how far a Logic of Observation is 
 possible, and show in what it will consist. [C] 
 
 1 06. What is Proof? 
 
 Explain and discuss the following dicta: (a) Qui 
 nimium probat, nihil probat : (b) A bad proof is worse 
 than no proof ; (c) The exception proves the rule ; 
 (d) Negatives cannot be proved. [C] 
 
 107. Examine how far the rules of immediate and syllogistic 
 
 inference are modified by differences of interpretation 
 of the categorical proposition in respect to the existence 
 of the subject. [S] 
 
 108. "An effect is but the sum of all the partial causes, the 
 
 concurrence of which constitutes its existence." 
 " The cause of an event is its invariable and unconditional 
 antecedent." Explain and compare these two theories 
 of causation. Does either alone exhaust the scientific 
 conception of cause ? [S] 
 
 109. Under what logical conditions are statistical inferences 
 
 authorised, and what is the nature of their conclusions ? 
 [S] 
 no. Distinguish between Psychology, Metaphysics, and Logic; 
 
 and discuss briefly their mutual relations. [S] 
 in. All processes of inference in which the ultimate premises 
 
 are particular cases are equally induction. 
 Induction is an inverse deduction. 
 
 Explain and contrast these two theories of the relation of 
 induction to deduction. [S] 
 
386 LOGIC : DEDUCTIVE AND INDUCTIVE 
 
 112. What are the Fallacies specially incident to Induction? 
 
 or to the application of the theory of Probabilities? 
 
 [S] 
 
 113. What is meant by the personal error (or personal equation) 
 
 in observation ? Discuss its importance in different 
 branches of knowledge. [S] 
 
 114. Define and illustrate: Paralogism, ignoratio elenchi, 
 
 fallacia actidentis, argumentum ad verecundiam^ illicit 
 process, undistributed middle. 
 
 115. State the three fundamental laws of thought, explain 
 
 their meaning, and consider how far they are in- 
 dependent of each other ? [L] 
 
 1 1 6. Enumerate the " Heads of Predicables" and define their 
 
 meaning. Discuss their logical importance. [L] 
 
 117. Upon what grounds has it been asserted that the 
 
 conclusion of a syllogism is drawn, not from, but 
 according to, the major premise ? Are they valid ? [L] 
 
 118. " Experiment is always preferable to observation." Why 
 
 is this ? Explain from the example of any science how 
 observation and experiment supplement each other. 
 
 M 
 
 119. What is a hypothesis? Distinguish between a working 
 
 hypothesis and an established hypothesis, so as to 
 bring out the conditions on which the latter depends. 
 
 [L] 
 
 120. Explain how good scientific nomenclature and termi- 
 
 nology are connected with the purposes of good 
 classification. [Ll 
 
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