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LOGIC 
 
 DEDUCTIVE AND INDUCTIVE 
 
BOOKS BY JOHN GRIER HIBBEN, Ph.D. 
 PUBLISHED BY CHARLES SCRIBNER’S SONS 
 
 LOGIC, DEDUCTIVE AND INDUCTIVE, 
 
 net $1.40 
 
 THE PROBLEMS OF PHILOSOPHY . net 1.00 
 
 HEGEL’S LOGIC net 1.25 
 
 INDUCTIVE LOGIC 1.50 
 
LOGIC 
 
 DEDUCTIVE AND INDUCTIVE 
 
 BY 
 
 JOHN GRIER HIBBEN, Ph.D. 
 
 STUART PROFESSOR OF LOGIC IN PRINCETON UNIVERSITY 
 
 NEW YORK 
 
 CHARLES SCRIBNER’S SONS 
 1906 
 
COPYRIGHT, 1896, 1905, BY 
 CHARLES SCRIBNER'S SONS 
 
 Nortoooh ftrras 
 
 J. S. Cushing & Co. — Berwick & Smith Co. 
 Norwood, Mass., U.S.A, 
 
I lei 
 
 2Ea 
 
 JOHN DAVIDSON 
 
 IN APPRECIATION OF THE VALUABLE SUGGESTIONS 
 RECEIVED IN THE PREPARATION OF THIS BOOK, 
 AND OF THE KINDLY INTEREST EXPRESSED 
 IN MANY WAYS THROUGH YEARS OF 
 AN INTIMATE FRIENDSHIP 
 
“O fxiv yap <Tuv07rrtK05 SiaAe/m/cos, 6 8e ou. 
 
 — Plato : Republic VII, 537 C. 
 
PREFACE 
 
 This book consists of two parts, — the Deductive and 
 the Inductive Logic. The former treats of the general 
 nature of our thought processes as well as the fundamental 
 principles and practice of deduction, and is now published 
 for the first time. The latter is my Inductive Logic which 
 was published in 1896, now revised and incorporated in 
 this volume. It has been my endeavor to present in con- 
 nection with the more formal and traditional treatment of 
 the deductive logic also some considerations which have 
 been contributed by the discussions of the modern logic 
 and which find expression in such works as those of Sig- 
 wart, Lotze, Erdmann, Green, Bosanquet, Venn, and others. 
 
 The illustrations and examples contained in the text are 
 taken as far as possible from the sphere of everyday expe- 
 riences, in order that they may represent modes of actual 
 reasoning pursued by the common run of mankind. With 
 this end in view, all the stock examples which have grown 
 old and infirm in the service of many generations of stu- 
 dents in logic have been omitted. Moreover, the material 
 as well as the formal significance of the judgments em- 
 ployed in reasoning has been emphasized in order that the 
 student may come to regard logic as a living process of 
 thought functioning in a normal and natural manner, and 
 not as an artificial manipulation of certain dead elements 
 mechanically adjusted one to another. 
 
 The illustrations which appear in the Inductive Logic, 
 and which are taken from the experiments of Faraday, 
 Tyndall, Darwin, Pasteur, Lubbock, and others, are quoted 
 
 vii 
 
PREFACE 
 
 viii 
 
 for the most part at considerable length, not merely be- 
 cause in the concrete case the universal principles of rea- 
 soning and of method are often most forcibly discovered, 
 but also because the experiments of such pioneers in re- 
 search actually create these methods of investigation, or 
 at least serve to render them exact and definite. 
 
 In Chapter XIV, Part I, “ A Generalization of Immediate 
 Inferences,” I have presented some original material, — this 
 being an attempt on my part to summarize all the possible 
 transformations of any given proposition according to a 
 scheme suggested by the Aristotelian square of opposition, 
 and developed along similar lines. In addition to the 
 general field usually covered by writers on deductive logic, 
 there is appended a discussion on “ Extra-syllogistic Reason- 
 ing,” being Chapter XVIII, Part I. 
 
 I wish to avail myself of this opportunity to express my 
 appreciation of the suggestions and help which I received 
 from my colleagues, Dean Andrew F. West and Professor 
 Winthrop M. Daniels, in the preparation of the Logical 
 Exercises which appear at the end of Part II. 
 
 Princeton, N.J., 
 December 23, 1904. 
 
 J. G. H. 
 
CONTENTS 
 
 PART I 
 
 DEDUCTIVE LOGIC 
 
 CHAPTER I 
 
 PAGE 
 
 The Nature of Thought 3 
 
 Definition and nature of Logic, 3. Thought as reflection, 4. 
 
 The four functions of thought, 4. Concept, judgment, in- 
 ference, 10. Logic as a normative science, 11. 
 
 CHAPTER II 
 
 The Concept 13 
 
 Relation of identity to diversity in concepts, 13. The 
 
 natural history of the concept, 15. Logical and empirical 
 concepts, 16. Genetic concepts, 22. Thought and lan- 
 guage, 23. 
 
 CHAPTER III 
 
 The Judgment 25 
 
 The essential nature of judgment, 25. Universal and 
 singular judgments, 26. Relation of judgment to reality, 
 
 27. The element of necessity in judgment, 30. The uni- 
 versal element in judgment, 31. Judgment and language, 
 
 33. Subject, predicate, and copula, 33. 
 
 CHAPTER IV 
 
 The Universal Judgment 36 
 
 The categories of Aristotle, 37. Heads of Predicables, 38. 
 Various types of judgment, 40. Extension and intension, 
 denotation and connotation, 42. 
 
 IX 
 
X 
 
 CONTENTS 
 
 CHAPTER V 
 
 PAGE 
 
 Definition . 44 
 
 Nature of definition, 44. Real and nominal definition, 44. 
 
 Rules of definition, 45. Definition by description, 47. 
 Definition for purpose of identification, 48. Genetic defi- 
 nition, 48. 
 
 CHAPTER VI 
 
 Division and Classification 50 
 
 Nature of division, 50. Rules of division, 51. Dichotomy, 
 
 61. Contrary and contradictory, 52. Trichotomy, 53. 
 Empirical and logical divisions, 54. Nature of classifica- 
 tion, 55. Artificial and natural classification, 56. Serial 
 classification, 58. Effect of the doctrine of evolution on 
 theory of classification, 59. Classification of the sciences, 
 
 61. Classifications of Bacon, Comte, and Spencer, 62. 
 
 CHAPTER VII 
 
 The Singular Judgment 67 
 
 Its relation to the universal judgment, 67. Impersonal, 
 perceptive, and demonstrative judgments, 67. Determinate 
 reference, 68. Indeterminate reference, 69. Judgment 
 concerning a proper name, 69. 
 
 CHAPTER VIII 
 
 The Negative Judgment ....... 73 
 
 Nature of the negative judgment, 73. Its function of 
 exact determination, 74. Its positive ground, 75. Signifi- 
 cant negation, 75. Implication in negation, 76. Infinite 
 negation, 77. 
 
 CHAPTER IX 
 
 The Categorical, Hypothetical, and Disjunctive 
 
 Judgments 78 
 
 The nature of each, 78. Their relation to universal and 
 singular judgments, 79. Their relation to the progressive 
 stages of knowledge, 81. Modality of judgments, 83. 
 
CONTENTS 
 
 XI 
 
 CHAPTER X 
 
 PAGE 
 
 The Nature of Inference 85 
 
 Logical and psychological elements in inference, 85. Ob- 
 jective and subjective necessity, 87. Data of perception, 
 
 88. System as ground of inference, 89. The implicit and 
 explicit, 92. Inference mediated through the universal, 93. 
 Conceptual processes, 94. Explanation, 94. Relation of 
 inference to judgment, 95. 
 
 CHAPTER XI 
 
 The Laws of Thought 98 
 
 The law of identity, 98. The law of contradiction, 100. 
 
 The law of excluded middle, 101. The law of sufficient 
 reason, 102. 
 
 CHAPTER XII 
 
 Immediate Inference 103 
 
 Immediate inference, a misnomer, 103. The processes of 
 implication and transformation, 103. The square of opposi- 
 tion, 104. Practical suggestions based on opposition, 108. 
 
 CHAPTER XIII 
 
 On Transformations of Judgment Forms . . .110 
 
 Conversion, 110. Content and form in conversion, 113. 
 Obversion, 114. Contraposition, 114. 
 
 CHAPTER XIV 
 
 A Generalization of Immediate Inferences . . 117 
 
 Summary of possible transformations, 117. The A square, 
 
 118. The E square, 119. The I square, 120. The O 
 square, 120. 
 
 CHAPTER XV 
 
 Mediate Inference — The Syllogism .... 122 
 Structure and functions of the syllogism, 122. Distribu- 
 tion of terms, 125. Rules for criticism of validity of syllo- 
 
CONTENTS 
 
 xii 
 
 PAGE 
 
 gisms, 126. Modification of these rules in special cases, 129. 
 Enthymeme, 130. Prosyllogism, episyllogism, and the 
 sorites, 132. 
 
 CHAPTER XVI 
 
 Mood and Figure 134 
 
 The valid moods, 134. Figure, 137. Mnemonic lines, 
 
 139. Reduction, 140. 
 
 CHAPTER XVII 
 
 The Hypothetical and Disjunctive Syllogisms . . 142 
 
 Hypothetical syllogism, 142. Disjunctive syllogism, 146. 
 Dilemma, 145. Trilemma, 148. 
 
 CHAPTER XVIII 
 
 Extra-syllogistic Reasoning ...... 149 
 
 Reasoning from particulars to particulars, 149. The typi- 
 cal case a disguised universal, 151. Inference based upon 
 given relations, 152. Its relation to the underlying system, 
 
 154. The logic of relatives, 156. 
 
 CHAPTER XIX 
 
 Fallacies 157 
 
 Formal fallacies, 167. Material fallacies, 158. Equivo- 
 cation, 158. Amphiboly, 159. Composition, 159. Divi- 
 sion, 160. Accent, 160. Figure of speech, 160. Accident, 
 
 161. Converse accident, 161. Ignoratio Elenchi, 162. Non 
 sequitur, 164. Petitio Principii , 164. Non causa pro 
 causa, 165. Many questions, 165. 
 
CONTENTS 
 
 xiii 
 
 PART II 
 
 INDUCTIVE LOGIC 
 
 CHAPTER I 
 
 PAGE 
 
 Induction and Deduction 169 
 
 Various opinions concerning their relative importance, 
 
 169. Regarded as different phases of one and same pro- 
 cess, 170. Their relation to the ground of inference as 
 system, 170. Their relation to the universal, 171. Truth 
 and fact, 171. Mutual dependence of deduction and induc- 
 tion, 172. 
 
 CHAPTER II 
 
 The Essentials of Induction 175 
 
 The inductive hazard, 175. Basal postulate of induction, 
 
 176. Its epistemological nature, 177. Reduction, 177. 
 
 Law and rule, 180. Law as a hypothetical universal, 
 
 181. Induction in practical affairs of life, 181. Scientific 
 spirit, 182. 
 
 CHAPTER III 
 
 Types of Inductive Inference 183 
 
 Method of enunciation, 183. (a) Perfect induction, 184. 
 
 ( b ) Incomplete induction, 186. (c) Probability, 186. 
 
 Method of Analogy, 187. Method of Scientific Analysis, 
 
 188. The causal element in these various methods, 189. 
 
 CHAPTER IV 
 
 Causation 195 
 
 Phenomenal significance of causal concept, 196. Philo- 
 sophical significance, 197. Logical significance, 198. Origin 
 of belief in uniformity of nature, 199. Popular and scien- 
 tific idea of cause, 201. Causal analysis, 202. Limitations 
 of knowledge, 203. 
 
XIV 
 
 CONTENTS 
 
 CHAPTER V 
 
 PAGE 
 
 The Method of Causal Analysis and Determination 206 
 Sequence, 206. Concurrence, 207. Coexistence, 208. 
 Collocations, 209. Transfer of energy, 211. Quantitative 
 determination, 211. Observation and experiment, 213. 
 Negative determination, 217. Pseudo-causal connections, 
 
 219. 
 
 CHAPTER VI 
 
 Mill’s Inductive Methods — The Method of Agree- 
 ment 222 
 
 The five methods, 222. Agreement, 224. Symbolical 
 representation, 225. Variation of instances, 227. Obser- 
 vation, 228. Simple enumeration, 228. Sequence and 
 coexistence, 229. Criticism of this method, 229. Agree- 
 ment as a method of suggestion, 232. Illustrations, 232. 
 
 CHAPTER VII 
 
 The Method of Difference 236 
 
 Its relation to agreement, 236. Its characteristic features, 
 
 236. Symbolical representation, 238. Relation to negative 
 determination, 239. Difference and combinations, 239. 
 Criticism of the method, 240. Practical difficulties, 242. 
 Illustrations, 245. Blind experiments, 247. 
 
 CHAPTER VIII 
 
 The Joint Method of Agreement and Difference . 248 
 Relation to method of difference, 248. Its characteristics 
 and symbolical representation, 249. Illustrations, 250. 
 Advantages of this method, 257. 
 
 CHAPTER IX 
 
 The Method of Concomitant Variations . . . 258 
 
 Characteristics and symbolical representation, 258. Quan- 
 titative determination, 259. Graphical representation, 260. 
 Advantages in its psychological impressions, 261. Illustra- 
 tions, 262. Comprehension of unknown forces by this 
 method, 266. Precautions in using this method, 267. 
 
CONTENTS 
 
 XV 
 
 CHAPTER X 
 
 PAGH 
 
 The Method of Residues . 271 
 
 Characteristics and symbolical representation, 271. A 
 deductive method, 272. Its function suggestive, 273. Illus- 
 trations, 273. Its practical value, 277. 
 
 CHAPTER XI 
 
 Prediction and Verification ...... 278 
 
 The inducto-deductive method, 278. Illustrations, 279. 
 Bacon’s anticipations of nature, 283. Scientific thought, 
 
 284. Indirect method of prediction, 286. Exceptional 
 phenomena, 288, Generalization, 289. Mathematical 
 method, 290. 
 
 CHAPTER XII 
 
 Hypothesis 291 
 
 Its relation to induction, 291. Illustrations, 292. Func- 
 tion of the imagination in hypothesis, 299. Analysis and 
 synthesis, 300. Requirements of a logical hypothesis, 301. 
 Consilience of inductions, 309. Experimentum Crucis , 310. 
 
 Mill and Whewell controversy, 312. 
 
 CHAPTER XHI 
 
 Analogy 314 
 
 Analogy and induction, 314. Natural kinds, 314. Anal- 
 ogy and classification, 315. Teleological analogy, 317. 
 Suggestion the chief function of analogy, 323. Require- 
 ments of true analogy, 325. Analogy and probability, 329. 
 
 CHAPTER XIV 
 
 Probability . 330 
 
 Probability and causal determination, 330. Relation to 
 enumerative induction, 332. Various kinds of inference in 
 sphere of probability, 333. Coincidence and cause, 345. 
 Circumstantial evidence, 346. Probability and method of 
 residues, 350. 
 
XVI 
 
 CONTENTS 
 
 CHAPTER XV 
 
 PAGE 
 
 Empirical Laws 351 
 
 Various degrees of probability in inference, 351. Various 
 kinds of empirical laws, 352. Empirical uniformity result- 
 ing from the method of agreement, 357. Empirical laws 
 and laws of an ultimate nature, 357. 
 
 CHAPTER XVI 
 
 Inductive Fallacies 359 
 
 Errors of perception, 360. Errors of judgment, 362. 
 Errors of imagination, 366. Errors of the conceptual pro- 
 cesses, 369. The psychological nature of these fallacies, 372. 
 
 CHAPTER XVII 
 
 The Inductive Methods as applied to the Various 
 
 Sciences 374 
 
 Method varies with different kinds of phenomena, 374. 
 Difficulties in method due to complexity of phenomena, 378. 
 Phenomena of one science interpreted in the light of others, 
 
 380. Deductive method of some sciences replaced by the 
 inductive, 381. 
 
 CHAPTER XVIII 
 
 Historical Sketch of Induction 385 
 
 Socrates, 385. Plato, 385. Aristotle, 386. Roger Bacon, 
 
 387. Leonardo da Vinci, 388. Telesius, 389. Carnpa- 
 nella, 389. The experimental investigators, 390. Francis 
 Bacon, 390. Locke, 392. Newton, 393. Herschel, 394. 
 
 Whewell, 395. Mill, 396. 
 
 Logical Exercises 399 
 
 Index 435 
 
PART I 
 
 DEDUCTIVE LOGIC 
 
CHAPTER I 
 
 THE NATURE OF THOUGHT 
 
 Logic is a word derived from the Greek Aoyos, which 
 means thought or reason ; and in this origin may be found 
 the essential significance of logic, — that it treats of the 
 nature and of the laws of thought. Before it is possible 
 to appreciate the characteristic features of the laws of 
 thought, it is necessary to understand the general nature 
 of the processes of thought themselves. While the process 
 of thought is various, its most common and conspicuous 
 manifestation may be described as that phase of the mind’s 
 activity which regards any specific object which may be 
 presented to it in the light of the general body of knowl- 
 edge. For example, a person may chance to pick up a stone, 
 which he holds in his hand for a moment and immediately 
 throws away. It has been in the focus of his attention for 
 a fleeting moment only, and has excited no activity of 
 thought whatsoever. He has observed but has not thought 
 about it. Suppose, however, it does arrest his attention and 
 he begins to think about it, what is the nature of this 
 thinking which goes on in his mind ? If his knowledge of 
 geology is meagre, the result of the application of it to the 
 special object of inquiry may be merely the assertion that 
 the stone which he holds in his hand is some kind of a 
 fossil. If, however, his knowledge is more extensive and 
 has grown out of a wide experience, he will be able no 
 doubt to refer the fossil in question to its proper geological 
 age, and to give some satisfactory description of the general 
 nature and habits of that species of animals to which it 
 
 3 
 
4 
 
 DEDUCTIVE LOGIC 
 
 belongs, thus, in a measure more or less explicit, recon- 
 structing its probable life history. Thinking, therefore, 
 may be defined in one of its aspects at least as the process 
 of interpreting the special by the general, or the new expe- 
 rience by the old. 
 
 This definition of thought may be further illustrated by 
 the word reflection, which is often used as synonymous 
 with thought. Thus we say that we will reflect about a cer- 
 tain proposition, which is equivalent to saying we will think 
 about it. The process of reflection is essentially one of 
 illumination. The very word reflection suggests the light 
 ray which flashes from one object of vision to another; so, 
 also, in a figurative sense, it signifies the illumination which 
 one object of knowledge sheds upon another. In the reflect- 
 ing mind, the new element of experience, whatever it may 
 be, is held in the focus of the light rays which converge to 
 that point from all the surrounding parts of the general body 
 of knowledge until its essential nature is fully revealed. 
 
 In this process which we call thinking, or reflecting, there 
 are in all four functions involved. 
 
 1. The first function of thought consists in the trans- 
 formation of the crude data of knowledge furnished by 
 the senses into forms of such a nature that they can be 
 readily used in the various operations of our thinking 
 processes. The form which thought necessarily assumes 
 for the prosecution of its own activity is always that of 
 a universal idea; that is, an idea which possesses a one- 
 ness of meaning but admits of an indefinite variety of 
 application. The universal is sometimes called a group 
 idea, or a class idea, by which a number of individuals are 
 embraced under some one general designation. If our body 
 of knowledge consisted merely in the total number of par- 
 ticular experiences arranged in the form of a series wherein 
 each separate term remained distinct and completely uncon- 
 nected with any other term, then obviously new experiences 
 could be added to, but never could be assimilated with, 
 
THE NATURE OF THOUGHT 
 
 5 
 
 such a body of knowledge. Indeed, a disconnected array of 
 isolated experiences would hardly merit the name of knowl- 
 edge at all. On the contrary, the elements constituting the 
 body of our knowledge must be so related and coordinated 
 that similar elements fall together in such a manner that 
 a single thought form shall be able to express them all. 
 Thus, when a geologist says that a certain stone is a fossil, 
 he means that in his general body of knowledge he has 
 framed an idea known by the word symbol “ fossil,” which 
 embraces under it innumerable special cases, and that one 
 of these is the stone in question. Thus objects of per- 
 ception can be grasped by the mind and become definite 
 objects of thought. This grasp of the mind by which a 
 number of special cases are held together by a single idea 
 of a nature so universal as to comprehend them all is known 
 as the process of conception, and the universal idea itself 
 which is the result of that process is known as the concept. 
 This word is from the Latin concapio, to take together. The 
 corresponding German word is Begriff, which has the same 
 root as our English word “ grip.” In the concept the mind 
 grasps all the essential features which characterize a given 
 group or class of objects, and holds them together in such a 
 manner as to constitute an elemental thought form. The 
 process of thinking, therefore, is fundamentally a conceptual 
 process, and this primary function of thought consists in 
 constructing whatever is given through the processes of 
 perception into the forms of concepts. 
 
 2. The second function of thought consists in the reduc- 
 tion of the total mass of concepts to some kind of systematic 
 order. Every concept as it is formed must be received into 
 the general body of knowledge and assigned to its proper 
 place and position. The concepts must be arranged in their 
 due rank and order according to their natural relations of 
 coordination or subordination. In order that our concepts 
 may be used as instruments of knowledge, they must admit 
 of a constant and consistent reference to the general system 
 
6 
 
 DEDUCTIVE LOGIC 
 
 of which they form constituent parts. These elemental 
 forms of thought must have their origin in order and not in 
 chaos. They must be subject to underlying laws of relation, 
 and not to accident or caprice. Thus the botanist not only 
 possesses an idea of the general nature of a certain species 
 of plant, that is, a concept of it, but he knows also definitely 
 its particular relation to the classified system of plants as 
 a whole. He is able therefore to describe the species in 
 question by the relative position which it occupies in the 
 system itself. Knowledge of the species is obtained not 
 merely through an understanding of what it is, but also of 
 what its proper setting may be. 
 
 3. The third function of thought consists in referring 
 whatever may be before the consciousness as the object of 
 thought to its appropriate concept. Such a reference is a 
 process of interpretation, and represents the central and 
 most essential feature of all thinking. This mode of inter- 
 pretation may be brought about in several ways. 
 
 (a) In the first place, any one portion of our general 
 body of knowledge may be interpreted in the light of some 
 other. Thus by way of interpretation or explanation I may 
 refer one concept to another concept which embraces it as 
 a smaller class or group within a larger one ; e.g. the Trap- 
 pists are a Roman Catholic brotherhood. 
 
 ( b ) Again, the concept lends itself to a further use as an 
 instrument of knowledge, by revealing the various charac- 
 teristics which constitute its nature according as the trend 
 of thought at the moment may happen to emphasize one or 
 another of them. In the ordinary processes of thought we 
 never use a concept in the totality of its significance. We 
 attend only to a single phase of the concept’s meaning at a 
 time; and our thought selects always that particular phase 
 of the meaning which is pertinent to the special object of 
 thought under consideration. Thus the concept, govern- 
 ment, is an exceedingly complex idea, and may be consid- 
 ered from various points of view, — as to its general nature, 
 
THE NATURE OF THOUGHT 
 
 7 
 
 whether democratic, monarchial, despotic, etc. ; or as to its 
 special functions, whether that of the judicial, legislative, or 
 executive. The concept as a complex idea may always be 
 subjected to a more precise determination by the concentra- 
 tion of thought upon one or more of its special attributes or 
 relations. 
 
 (c) In the third place, a particular experience in the 
 field of sense perception may be interpreted by referring it 
 to the appropriate concept of which it may be regarded as a 
 special case. The knowledge given through the senses is 
 rendered more definite by this reference of it to a concept 
 which serves to illumine it. 
 
 This process of thought which renders the elements of 
 consciousness more definite by a reference in any one of the 
 three ways mentioned above to some interpreting concept 
 is known as the judgment. There is a universal tendency 
 of thought to transform every concept into the form of a 
 judgment, because the very presence of a concept in con- 
 sciousness challenges our thought to express some definite 
 assertion concerning it, and such an assertion is itself a 
 judgment. As long as there is sustained interest in any 
 concept which occupies the focus of attention, there is a 
 constant play of thought about it ; we turn it over in our 
 minds ; we examine it on all sides ; we put questions to 
 ourselves about it; and the result is a series of judgments 
 as regards its nature and the several relations which it sus- 
 tains to cognate concepts. Thus our general knowledge 
 serves to illumine the specific portion of it which is the 
 special object under contemplation. So also when the 
 object of consciousness is a particular object of sense per- 
 ception, we form a judgment by referring it to its appropri- 
 ate concept. Thus in the judgment, Arsenic is a poison, we 
 have as it were a cross-section of our knowledge in general ; 
 but in the judgment, this substance which is in the test- 
 tube before me contains arsenic, the reference is to a special 
 object in the field of vision which is interpreted by means 
 of its appropriate concept. 
 
8 
 
 DEDUCTIVE LOGIC 
 
 Every new experience which is more than a fleeting im- 
 pression, and which is drawn into the field of our attention, 
 gives rise to one or more judgments of this latter kind. As 
 I am writing, I look out from a hillside which commands a 
 wide prospect; and as I observe the various objects in the 
 field of vision, my thought immediately refers them to their 
 appropriate concepts by way of more definite characteriza- 
 tion. There is the winding road through the valley, sepa- 
 rating the green meadow from the wood beyond; in the 
 meadow cows are grazing; by the side of the road flows a 
 stream, rushing over its rocky bed and losing itself in the 
 dark shadows of the wood ; in the distance are the uplands 
 again bounded by the horizon line, above which the clouds 
 are hanging low and threatening. Such a description of the 
 various objects of perception within a field of vision forms a 
 series of particular instances referred to their corresponding 
 concepts. They are simple judgments of identification, — 
 a reference of an object immediately before us to a familiar 
 idea which through its word symbols satisfactorily describes 
 it. Such a scene however naturally gives rise to more com- 
 plex ideas, which represent the fourth function of thought. 
 
 4. This fourth function of thought consists in the process 
 of unfolding whatever may be necessarily implied in our 
 judgments, but is not explicitly asserted. Thus in the scene 
 described above, I am able to make certain statements which 
 are warranted by the facts, but which are not the result of 
 simple observation. I am led to venture the assertion that 
 there are trout in the stream before me ; that by reasonable 
 skill and perseverance a fisherman may hope to fill his creel 
 there in a few hours ; that the threatening clouds, the east 
 wind, and sultry atmosphere will bring rain; and that it 
 would be wise under such conditions to fish worm rather 
 than fly. Judgments such as these are far more complex 
 than the simple judgments of identification or recognition. 
 We may call them judgments of elaboration. What is actu- 
 ally given is combined with our general knowledge in such 
 
THE NATURE OF THOUGHT 
 
 9 
 
 a manner as to render explicit the full measure of all which 
 is necessarily implied. Thus the assertion that the stream 
 contains trout is based upon an experience of many years, 
 and in this way the past is used as a meaus of interpreting 
 the present. In like manner my past experience of atmos- 
 pheric conditions enables me to interpret the present condi- 
 tions as indicating the approach of rain. Moreover, the 
 dark and stormy day is judged to be more suitable for worm 
 than fly fishing, because on account of the coming rain the 
 natural flies will not be on the wing, and the rain itself will 
 wash from the hillsides and banks into the stream grubs 
 and worms, which the expectant trout will be in readiness 
 to take. My general knowledge has enabled me in this 
 particular case to make statements which go beyond that 
 which is actually perceived, but which nevertheless I am 
 constrained to believe true, because necessitated by what is 
 known. And this is the essential feature of all inference. 
 
 But inference is not confined to the interpretation of that 
 which is given in perception. It may serve also to interpret 
 any part of our general body of knowledge by any other 
 part, or by the whole. Thus two judgments of a universal 
 nature may be brought together in such a manner that their 
 combination furnishes elements of knowledge which are not 
 given by either judgment separately. We know, for in- 
 stance, that the sum of the angles formed on the same side 
 of a straight line at a given point equals two right angles; 
 also, that the exterior angle formed by extending a side of a 
 triangle equals the two opposite and interior angles. These 
 two judgments, when put together, necessitate the infer- 
 ence that the sum of the angles of a triangle equals two 
 right angles. Inference therefore is essentially a process 
 by which our thought combines given elements of knowledge 
 in such a way that the result contains something which the 
 given elements in their isolation fail to disclose. 
 
 There are some general considerations in reference to these 
 four functions of thought which should be presented. In the 
 
10 
 
 DEDUCTIVE LOGIC 
 
 first place, the word function itself is significant. It in- 
 dicates an activity which is dependent upon other activities 
 correlated with it. Each of the four functions of thought is 
 closely connected and coordinated with the other functions, 
 and no one is complete in itself. The concept is an essential 
 element of the judgment, for the j udgmen t is merely the 
 concept rendered definite through assertion. Moreover, in- 
 ferenc e is a process which consists essentially in the expan- 
 sion and elaboration of our judgments. Inference is itself a 
 judgment, only it is a judgment which is reached indirectly. 
 And in the formation of any judgment it is exceedingly 
 difficult to eliminate altogether the inferential elements, 
 inasmuch as every judgment contains more than is actually 
 given in perception, or in a series of perceptions. The result 
 rests largely upon that which is necessitated by our general 
 knowledge, and this is essentially inference. 
 
 In these coordinated relations which unite concept, judg- 
 ment, and inference, it is natural to regard judgment as the 
 central function of thought. From this point of view the 
 concept may then be defined as the judgment in its potential 
 form ; that is, the concept contains in an indefinite way all 
 the possible elements of knowledge which it is the function 
 of the judgment to make explicit. The inference is the 
 judgment, as we have seen, exhibited in its relation to other 
 judgments upon which it depends as the warrant of its 
 validity. The concept is an abridged form of judgment, 
 while the inference is an expanded form ; and the unit of 
 thought, therefore, which lies at the basis of all thought 
 processes is the judgment. It is to thought what the 
 element is to chemistry. 
 
 Again it is to be observed that in the process of inter- 
 preting a given object of knowledge by means of its corre- 
 sponding thought form, it happens that the object in question, 
 say a given object in the field of vision, will in some measure 
 at least modify the thought form to which it is referred. 
 Thus every new experience is both interpreted by our 
 
THE NATURE OE THOUGHT 
 
 11 
 
 general body of knowledge, and also in turn widens the range 
 of that knowledge and changes its nature to a greater or 
 less extent. Especially is this true concerning any object 
 of knowledge which is so new as to be wholly unfamiliar. 
 There is then no appropriate thought form to which we can 
 refer it. We must so analyze the properties of the object in 
 question and compare it with other instances of the same gen- 
 eral kind, as to construct a basis for the formation of a con- 
 cept which shall embrace the new order of phenomena under 
 consideration. Such a new concept has to be fitted into the 
 main body of concepts, and the process of readjustment 
 among the old concepts is sometimes a most complex and 
 difficult one. This is illustrated in a striking manner by 
 the newly formed concept of radium and the various prop- 
 erties of radio-activity. To receive this new concept into 
 the main body of concepts requires a readjustment of our 
 former ideas of matter, conservation of energy, etc., which 
 is almost revolutionary. 
 
 Again, among the philosophical sciences, logic is usually 
 grouped with ethics and aesthetics under the general class 
 of the so-called normative sciences. A normative science is 
 one which refers all its phenomena to some standard, or 
 norm of value to which they are required to conform. The 
 standard in ethics is that of the right or the good; in 
 aesthetics, of beauty ; and in logic, of truth. Truth may 
 be defined as correspondence with reality. The real is the 
 world as it is constructed by us in consciousness. It is 
 coextensive with the whole received body of knowledge. 
 It is the world which is revealed to us through the senses, 
 it is true ; but at the last analysis it is that world as we 
 interpret and understand it. 
 
 To say therefore that the logical demand of our concepts 
 is that they must be true signifies that every concept must 
 clearly and adequately embody the essential features of all 
 the particular instances in experience which have formed 
 the basis of its derivation ; the concept moreover must be 
 
12 
 
 DEDUCTIVE LOGIC 
 
 capable of a constant reference, that is, it must not contain 
 any element of variability which prejudices its integrity as 
 a concept. To say that a judgment must be true signifies 
 that when the judgment expresses the general relation of 
 any concepts to each other within the same system, it must 
 conserve the general order which characterizes the system 
 as a whole, and all interrelated parts of it ; and when the 
 judgment is of the form of a particular experience referred 
 to its appropriate concept, then all such references must be 
 exact. To say that an inference must be true signifies that 
 the conclusion reached through the process of inference 
 must be of such a nature that every element of it will find 
 complete warrant in that which is adduced as its ground. 
 The logical standard, therefore, which must be realized in 
 all cases demands clear and adequate concepts of a constant 
 meaning arranged in an orderly system, so that every 
 reference to it of any particular object of thought must be 
 exact, and every inference based upon it must be valid. 
 While truth may manifest itself in many ways as clearness, 
 adequacy, constancy, consistency, exactness, or validity, 
 nevertheless these are all but various instances of a single 
 elemental principle which underlies the ultimate standard 
 of logical thinking. 
 
CHAPTER II 
 
 THE CONCEPT 
 
 The concept as a form of thought embraces a number 
 of phenomena which, however much they may differ, have 
 nevertheless an underlying unity. The ratio of the elements 
 of similarity to those of diversity in our concepts is by no 
 means a constant one, but admits of considerable variation. 
 
 1. In the first place, the diversity may be reduced sub- 
 stantially to zero, as for instance in such a concept as that 
 of a silver dollar. The differences which exist between the 
 several particular cases of this general concept are so minute 
 as to be overlooked ; the similarity alone attracts the at- 
 tention. Each one is an exact copy of every other, and the 
 idea of any diversity is here practically eliminated. 
 
 In reality, however, no two phenomena are precisely 
 alike. As Leibniz once remarked, “No two leaves on the 
 same tree are alike.” And Plato in the same vein has said 
 that “ If two things were exactly alike, there would not be 
 two but one.” Therefore, while the element of diversity 
 may be reduced to zero as regards its practical relevancy 
 and as regards the essential significance of the concept in 
 question, nevertheless it is always present in some appre- 
 ciable degree and may be discovered to a discriminating 
 observer. 
 
 2. There is a second class of concepts wherein the diver- 
 sity is more apparent, and yet the likeness is quite as 
 obvious. Thus the concept, dog, embodies all the charac- 
 teristic features of the dog race, and yet is so elastic 
 and ample an idea as to hold in one and the same mental 
 grasp such diverse breeds as the mastiff, the bull-dog, 
 
 13 
 
14 
 
 DEDUCTIVE LOGIC 
 
 the French poodle, the greyhound and dachshund. A con- 
 cept such as this is typical of the general run of concepts 
 which require no unusual penetration to disclose the funda- 
 mental elements of similarity in spite of the wide range of 
 differences. 
 
 3. There is, however, a third class of concepts which 
 require more than ordinary insight, it may be the insight of 
 genius, in order to discover the unity which lies hidden be- 
 neath an obscuring mass of manifold differences. It required 
 the analytic mind of a Newton to grasp under one concept 
 such diverse phenomena as the fall of a body to the earth 
 and the moon’s revolution about its orbit. In the one case 
 there is motion in a straight line, in the other the motion 
 is in the path of an ellipse ; in the one the body actually 
 falls to the earth, in the other it is forever falling but never 
 falls. Nevertheless, the two are similar. The course of 
 the moon may be resolved into two distinct motions ; the one 
 centripetal, which is a direct falling toward the earth, the 
 other the centrifugal, which holds the former in check and 
 modifies the direct fall toward the earth so that the result 
 is the present elliptical orbit of the moon. Therefore it may 
 be truly said that the moon is always falling toward the 
 earth in a manner precisely similar to that of the ordinary 
 falling body upon the earth’s surface. The only difference 
 is the counter force which is operative in the one case and 
 not in the other. Such a difference however so obscures 
 the general features of resemblance in the resulting phe- 
 nomena that a surface observation devoid of any deeper 
 reflection may pronounce them so different as to possess no 
 point in common. It is characteristic of the trained mind 
 that it is able to penetrate beneath the surface and discover 
 points of similarity which escape the notice of unreflecting 
 observation. Fortunately for the generality of intelligence, 
 the phenomena of human experience for the most part fall 
 together into natural groups whose underlying bond of unity 
 is perfectly obvious. Nature is so prodigal of her creations 
 
THE CONCEPT 
 
 15 
 
 that innumerable individuals of the same species are forced 
 upon our attention. The common events of life repeat them- 
 selves with a regularity which compels the recognition of a 
 constant and common principle as their basis. Therefore it 
 becomes a natural habit of mind to see things together by 
 reason of their common features. The most primitive of all 
 our judgments, and that which lies at the foundation of all 
 other judgments, is that which is based upon the recognition 
 of similarity among phenomena. The concept has its ori- 
 gin in the recognition of similarity among several percepts . 1 
 As Schopenhauer has remarked, “We get the stuff and 
 content of our concepts from observation.” In our obser- 
 vation, the various instances of some one general kind of 
 phenomena fall together in our minds on account of their 
 similarity. They form a series of similar percepts, each 
 term of which differs from every other term, and yet all in 
 a certain sense are alike. The mind grasps the essential 
 features of similarity, fusing them together according to an 
 underlying unity which persists in spite of the differences. 
 The result is the concept. In such a process, the mind has 
 subjected the various percepts to an analysis which sepa- 
 rates whatever is peculiarly individual in each instance 
 from the elements which are characteristic of the series as 
 a whole. This is essentially a process of abstraction ; it is 
 what Aristotle calls a^mpevi s. There is also a complement- 
 ary process of synthesis, v-poo-Oeais according to Aristotle, 
 which consists in building up the common elements obtained 
 by the analysis into a complete whole. The resulting 
 product is in no sense merely an image in the mind of the 
 blended percepts, but is essentially an ideal construction of 
 thought which is sufficiently comprehensive and elastic to 
 admit of application to all particular cases of it. These 
 processes of separating and uniting, of tearing down and 
 building up, of analysis and synthesis, have become so con- 
 
 1 In the terminology of psychology, the process of perceiving is called 
 perception ; the resulting product, however, is known as the percept. 
 
16 
 
 DEDUCTIVE LOGIC 
 
 firmed a mental habit that we are not conscious of them, but 
 come to regard our concepts in the light of original mental 
 possessions rather than thought forms which we ourselves 
 have fashioned out of the various phenomena in experience. 
 
 The unconscious blending together of the essential charac- 
 teristics of a group of phenomena forms a concept which is 
 at first barely more than a general impression, a vague 
 mental grasp of the kind of objects represented by it. The 
 mind has not yet worked over its first impressions and has 
 not formed the crude data of its perception into clear and 
 adequate concepts. The concept at this preliminary stage 
 of its evolution is called empirical, signifying that it is the 
 result of a superficial experience which has been subjected 
 to no critical analysis whatsoever. The word empirical in 
 philosophy signifies whatever is the result of experience; it 
 has, however, a secondary meaning which implies that the 
 experience in question is a limited one. It is in this sec- 
 ondary sense that the phrase empirical concept is used. 
 On the other hand, the logical or scientific concept, as it 
 is often called, is one which has been formed as the result 
 of some conscious effort to analyze the various phenomena 
 which form the basis of the concept in question so as to 
 obtain a clear and adequate idea of their essential charac- 
 teristics. The logical concept differs from the empirical in 
 the following particulars : — 
 
 1. The logical concept is always characterized by a grow- 
 ing loss of particularity. The preliminary rough draft of 
 our concepts always shows the coloring of the particular 
 instances whence they have arisen. Our first experiences 
 are necessarily few in number, and they are not sufficiently 
 numerous to afford a basis for the elimination of all charac- 
 teristics which are not essential. Certain features which 
 may be common to a limited number of instances will often 
 disappear when that number is increased. The disappear- 
 ance of such characteristics or their appearance in a sporadic 
 manner merely proves that they do not belong to the essence 
 
THE CONCEPT 
 
 17 
 
 of the concept. It is an evidence of an ignorant or untrained 
 mind that it associates its concepts with particular experi- 
 ences. Such an intellect we are pleased to call provincial 
 or insular. The nature of the logical concept is always 
 indicated by its independence of the special case. Thus 
 the concept of gravitation is not confined to the earth’s 
 attraction of bodies upon its surface. It rises above such 
 a particular instance, and presents the idea of universal 
 attraction, of which the force of gravitation upon the earth 
 is but a small and insignificant instance. 
 
 The objection has been urged by Berkeley for instance 
 that this growing loss of particularity in the concept in- 
 dicates an increasing indefiniteness, inasmuch as the elimina- 
 tion of one particular attribute after another tends to reduce 
 the concept itself to a bare form stript of all definite features. 
 Consequently, it is insisted, our concept of a rose must be one 
 devoid of any specific color, form, or fragrance, and our con- 
 cept of a dog must be one of no particular breed, habit, or 
 disposition ; concepts, therefore, are but the spectral forms 
 of real objects. This view, however, is based upon a radical 
 misunderstanding of the essential nature of a concept. For 
 the concept is freed from the particular attributes which 
 characterize the various percepts only in a certain sense. 
 While these attributes are not preserved as such in the 
 concept, they are nevertheless conserved. The particular 
 attribute of color, or of form, or of habit is indeed dropped 
 out of mind in framing the concept, but there is always a 
 compensation for the loss of the particular by substituting 
 in its place the possibility, not only of the attribute in 
 question, but of all others of the same general kind. Instead 
 of the particular we have the potential which admits of an 
 indefinite degree of variation. Thus the concept of a rose 
 admits of any shade of color whatsoever which is compatible 
 with the whole range of experience regarding roses. In 
 this adaptability to all possible varieties of color, the poten- 
 tial color of the concept is vastly richer in content, and far 
 
18 
 
 DEDUCTIVE LOGIC 
 
 more comprehensive, than the single color of any particular 
 rose could possibly be. So, also, the concept of a dog is 
 not confined to a particular breed; it embraces the potential 
 of all the possible breeds of dogs. Indeed, the mental 
 process of constructing a concept may be regarded as that 
 of transforming the various observed attributes of the same 
 general order into a potential attribute which is lodged in 
 our minds as a comprehensive symbol embracing every 
 possible variety of detail. 
 
 This potential variation in any concept should not remain 
 indefinite and vague, but should have definitely prescribed 
 limits. Thus the color possibility of the concept of a rose 
 possesses a very wide range of variation ; that of the violet, 
 however, is narrowly circumscribed. The leaf of a beech 
 tree shows a definite pattern, which is preserved in the 
 midst of a variation which is essentially one of size alone, 
 and that within known and easily recognized limits. In the 
 leaf of the sassafras tree there is a far wider possibility of 
 variation. On one and the same tree of this species there are 
 leaves of three distinct patterns. Whatever may be our con- 
 cept of the sassafras leaf, it must certainly provide for this 
 characteristic variation of form. Moreover, the range of 
 variation may itself be subject to a variation under chang- 
 ing circumstances. The leaf of the maple is in its normal 
 appearance green. It admits of a wide variation of shade but 
 always within the limits of the one color. In the autumn 
 tints, however, there is a remarkable expansion of the range 
 of variation, the green turning into the various shades of 
 brown, yellow, red, gold, and crimson. The possibility of a 
 wide range of variation in the attributes of our concepts 
 render them as thought forms exceedingly elastic in the 
 processes of thinking, while, on the other hand, the definite 
 limitation of their possible variation renders them quite as 
 serviceable for exact reference and determination. There is 
 thus a double gain both of precision and facility in the 
 exercise of our thought activity. 
 
THE CONCEPT 
 
 19 
 
 2. There is a second characteristic of the logical concept 
 in distinction from the roughly generalized empirical con- 
 cept ; namely, that it is freed from all dependence upon any 
 mental picture in order to render it clear and intelligible. 
 This feature of the logical concept grows out of the former 
 given above, — the growing loss of particularity; for the 
 particular can be represented to thought in the form of a 
 memory image of the original experience. Not so, however, 
 with the universal idea which lies at the basis of the concept. 
 The concept is not a composite picture in the mind of a 
 series of percepts. As far as a mental picture might sug- 
 gest resemblances, we would naturally classify together the 
 whale and the fish, or the bat and the bird. Dissociated 
 however from the representations of the outer appearance 
 of these animals, the bat, as regards the essential elements 
 which go to make up the concept, is far more closely allied 
 to the whale than to the bird. The mental picture is in- 
 deed a help to our thinking, but strong minds must learn to 
 forego such adventitious aid. The undeveloped mind — that 
 of the savage, or the child — is dependent upon pictures, 
 symbols, or figurative representations. In the process of 
 education, as the mental activity becomes trained and dis- 
 ciplined, the need of colored chalk, of illustrative diagrams, 
 and of picture-books, becomes less and less in evidence. 
 In the evolution of the religious sentiment, this is notice- 
 able in a marked degree. The early religions, notably that 
 of Judaism, endeavored to convey spiritual truth through 
 an appeal to the senses mediated by a brilliant symbolism. 
 This, however, was superceded by that religion which laid 
 stress upon a worship in spirit and in truth, with no in- 
 direct appeal to the thought through the senses, but by 
 means of ideas which directly enlightened the eyes of the 
 understanding. An appreciation of the truth in this wise is 
 essentially logical inasmuch as the truth appears in a form 
 which appeals immediately to the reason. 
 
 3. A third characteristic of the logical concept is its 
 
20 
 
 DEDUCTIVE LOGIC 
 
 tendency to progressive differentiation ; that is, a breaking up 
 into smaller concepts which are more precisely determined, 
 and more distinctly separated in thought one from the 
 other. The first rough concepts which are formed embrace 
 without discrimination all sorts of individual instances which 
 may happen to present any surface resemblances whatso- 
 ever. The child may have at first but one vague concept 
 which applies equally well to a cow, a horse, and a mule. 
 Later in the growth of knowledge, this indefinite concept 
 breaks up into more definite ones, and the child learns to 
 discriminate between the cow and the horse, and between 
 the horse and the mule. Wherever there is knowledge 
 which is comprehensive and exact, the corresponding con- 
 cepts are nicely differentiated and precisely determined. 
 For most persons, it is a sufficient identification of a bird 
 to recognize it as a hawk. But for the ornithologist such 
 a reference is altogether too general and indefinite. He 
 wishes to know which one of the several different species 
 of hawk the particular bird may happen to be. Nothing is 
 gained however by the mere multiplication of the number 
 of concepts, unless at the same time we are able to discrimi- 
 nate between them. The discriminating mind is essentially 
 the logical mind. The means by which our concepts may 
 receive more precise determination will be discussed later 
 in the chapter on the negative judgment. 
 
 There are two ways by which our concepts may be broken 
 up so as to give rise to new concepts. The one has already 
 been mentioned, — the analysis of the concept into smaller 
 and smaller groups, each group, however small, represent- 
 ing a complete whole, or complex of attributes. The other 
 does not regard a complex of attributes which together 
 constitute the characteristic features of a distinct species of 
 plant or animal ; it regards the rather some single attribute 
 and concentrates the attention upon that. This attribute is 
 first viewed in all the particular instances where it occurs, 
 and then fashioned into the form of a concept by considering 
 
THE CONCEPT 
 
 21 
 
 it, in and by itself, quite apart from any of tbe instances 
 which illustrate it. Such a concept is known as an abstract 
 concept. It is our idea of a particular quality or attribute 
 of a thing apart from the thing itself. The concrete con- 
 cept, on the other hand, is our idea of a thing as composed 
 of a complex of attributes, and none of them separated in 
 thought from the thing in which they all inhere. Thus we 
 have the abstract concept of motion as distinct from the 
 concrete concept of a moving body ; the abstract concept of 
 a sweet or sour flavor as distinct from the concrete concept 
 of sugar, or of a lemon, in which the attributes sweet and 
 sour may find expression. So also we have the abstract 
 concepts of activities apart from any actors, such as speak- 
 ing, swimming, fighting, etc. There may be abstract con- 
 cepts not merely of attributes and activities, but also of 
 relations which may exist between different objects of per- 
 ception, or between concepts as the case may be, quite apart 
 from the objects or concepts thus related, such as the con- 
 cept of cause and effect, of organization, of sequence, or of 
 coexistence. There may be also abstract concepts involving 
 a combination of several attributes, and yet held apart from 
 any definite thing or object of knowledge in which they 
 inhere, such as the complex concepts of freedom, of philan- 
 thropy, of the good, the true, the beautiful. The possi- 
 bility of the various forms of abstract concepts and of the 
 resulting combinations which may be made out of the sepa- 
 rated elements is indeed without limit. Our logical faculty 
 is thus given an indefinite scope. The ability to combine 
 the given elements of knowledge into new forms gives to 
 our thought a mighty instrument of discovery and of 
 progress. 
 
 4. There is still another characteristic of the logical in 
 distinction from the merely empirical concept, a character- 
 istic, however, which is realized only in that higher order 
 of concepts which merit the designation of scientific. The 
 nature of these concepts is radically distinct from that of 
 
22 
 
 DEDUCTIVE LOGIC 
 
 the most accurately formulated concepts of the kind which 
 has so far been described. Instead of representing a corre- 
 lated nexus of common characteristics which discover them- 
 selves to observation in the several special cases, this new 
 order of concepts represent rather the fundamental con- 
 structive principle, which both underlies the actual produc- 
 tion of every particular instance, and also serves to preserve 
 the integrity and constancy of its being as well. Such a prin- 
 ciple may assume various forms. It may express simply 
 the method of producing the different instances which fall 
 under a single concept. Thus the concept of a conic section 
 represents the several sections which may be made of a cone, 
 according as the angle of the cutting plane is varied. There 
 will result consequently either a point, straight line, circle, 
 ellipse, parabola, or hyperbola. A mere observation of the 
 general features of these lines would never disclose their 
 common nature. They fall together in one and the same 
 group on account of their common origin, while a simple 
 variation in the manner of their production gives rise to a 
 pronounced differentiation in the results. 
 
 Again the constructive principle may represent a summa- 
 tion of all the component elements of the object in ques- 
 tion, with possibly the formula of their relative proportions 
 added. Thus the concept of sulphuric acid can be repre- 
 sented by the symbol, H 2 S0 4 , an exact statement of the 
 chemical elements in the proper proportions which consti- 
 tute the essential nature of the compound. A concept of 
 this kind is very different from that concept of sulphuric 
 acid which represents its several properties and affinities. 
 
 Again, this constructive principle may appear in the 
 form of a law which is operative in producing and sustain- 
 ing the various organisms which may be referred to it. 
 Thus the concept of natural sele cti on represents a most 
 comprehensive law, which explains the origin of new 
 species in the evolution of natural organisms. Every 
 species has its own constructive principle, which, if discov- 
 
THE CONCEPT 
 
 23 
 
 ered, would form the truest and most satisfactory concept 
 of that species. These various forms of the concept repre- 
 senting a constructive principle rather than a mere complex 
 of common attributes are known by the one name of gen- 
 etic concepts ; that is, concepts which refer to the com- 
 mon origin of a class of particular instances, rather than 
 to the characteristic features of their common nature. 
 
 There now remains to be considered a topic of consider- 
 able interest and importance, namely, the relation of the 
 concept to the word which serves as its symbol. As a 
 symbol the word does not exist for itself, but only for the 
 meaning which it represents. A symbol always refers to 
 something which lies outside of itself, and language is a 
 system of symbols by means of which thought finds signifi- 
 cant expression. The word Aoyos has a twofold meaning 
 in Greek — (a) the thought itself and ( b ) the word or words 
 which stand for the thought. Aristotle calls the one 6 tau 
 or 6 iv rrj i//v\rj Aoyos, and the other 6 !£a> Aoyos, — that is, 
 the one, the inner logic ; the other, the outer logic. Lan- 
 guage, therefore, is the external symbol of the inner thought. 
 We have seen that the logical concept is characterized by 
 a freedom from all entanglements with any particular per- 
 cepts, or anything like a picture representation of the 
 same. In this respect, the word as a symbol forms a most 
 excellent vehicle for the expression of concepts in their 
 pure thought significance. For the word is perfectly color- 
 less and is freed from all local or temporal associations. 
 The growth of language has paralleled in this respect the 
 growth of thought, inasmuch as there has been a constant 
 tendency for words to lose whatever original associations 
 of a particular or pictorial nature they may have had. The 
 Hebrew word for anger was derived from a root which 
 signified the boiling over of a pot of water, a suggestive 
 picture of the heat and energy of passion. This primitive 
 picture, however, has passed away and only the significant 
 thought remains. So, also, the word green meant, according 
 
24 
 
 DEDUCTIVE LOGIC 
 
 to its derivation, the color of growing things, the green 
 natural objects; but now its meaning has burst these limita- 
 tions and possesses a far wider scope. 
 
 There is also a parallel differentiation of words accom- 
 panying the progressive differentiation of thought. Pro- 
 fessor Max Muller refers to the fact that the Hawaiiaus 
 have only one word to express the various ideas of love, 
 friendship, gratitude, kindness, and respect. To discrimi- 
 nate between the different shades of meaning which these 
 several ideas signify, a corresponding variety of verbal 
 symbols has been found necessary. Thus the inner and the 
 outer thought have progressed together, and the line of prog- 
 ress is always toward a more complete definiteness of mean- 
 ing, in which the finer distinctions of thought may be felt 
 and expressed. 
 
 There is no doubt that clearness of thought is often 
 greatly obscured by the medium of language. Words come 
 to acquire strange twists and turns which are productive of 
 much misunderstanding and error. It is the office of the 
 logical mind to determine the meaning of words, and to use 
 the word which most precisely and adequately expresses the 
 thought. Obscurity in the use of language, however, may 
 usually be traced to obscurity in thought. Clear thinking 
 will always find a medium of clear expression. 
 
CHAPTER III 
 
 THE JUDGMENT 
 
 The essential function of the judgment is to give definite- 
 ness to the concept. When the concept appears in thought, 
 it is never as a complete element in itself, but it is always 
 as a constitutive element of a judgment. The concept 
 exercises no more independent a function apart from the 
 judgment than does the sap separated from the tree whose 
 entire structure it permeates. If we attempt to hold the 
 concept in the focus of thought, it will always appear 
 elusive and indefinite. It becomes definite only as it sug- 
 gests some judgment, or it may be a series of judgments of 
 which it serves to form the basal element. We may seem 
 at times to hold the concept before the mind as a naked, 
 unattached idea ; but it is a barely momentary result which 
 is reached. The concept maintains such a shadowy form, 
 only so long as we do not concentrate our thought upon it. 
 As soon as it becomes in any sense an object of thought, it 
 challenges some assertion either concerning its nature, or its 
 relations to other concepts in our general body of knowledge. 
 If we make a list of various concepts, such as iron, educa- 
 tion, freedom, army, horse, bird, fern, and so on, the eye 
 rapidly traverses such a list, instantly recognizing the mean- 
 ing of each word, as it occurs, and immediately passing on 
 to the next. But in such a process we have not really taken 
 these various concepts into our thought. There has been 
 merely a series of mental reactions in the recognition of the 
 meaning of word symbols. Such a recognition is nothing 
 more than the vague sense of familiarity which the several 
 words are capable of arousing. If, however, an unfamiliar 
 
 25 
 
26 
 
 DEDUCTIVE LOGIC 
 
 word should appear in such a list, it would immediately 
 give us pause; we would begin to think about it, to turn it 
 over in our minds, endeavoring to discover its general nature 
 and the relations which it sustains to our other concepts. 
 This would at once give us a series of judgments. Or if any 
 one of the suggested words should elicit any special interest 
 on our part, the various processes of thought would be found 
 to react upon it in such a manner as again to yield a num- 
 ber of judgments. Thus if we allow our thought to dwell 
 upon such an idea as that of education with something more 
 than a mere passing recognition of a familiar word, then we 
 at once find ourselves constructing some definite assertions 
 concerning this idea, as to its general nature, its various 
 forms, its methods and scope, and the fundamental princi- 
 ples which underlie its essential significance. Whenever a 
 concept swings into the focus of thought, it at once forms a 
 centre whence radiates a series of judgments. The judg- 
 ment may be defined, therefore, as a concept which is ren- 
 dered definite through some assertion concerning it. The 
 concept is a potential judgment, or rather it is the potential 
 of many judgments which are implicitly contained in it. 
 The judgment is the concept in its unfolded form. The 
 concept, moreover, may be regarded as an unstable com- 
 pound which through the barest contact of thought sepa- 
 rates into its elemental parts and relations expressed in the 
 form of judgments. 
 
 There are two ways by which we may render any concept 
 definite through assertion, thus producing two general types 
 of judgment. 
 
 1. The concept may be referred to another concept which 
 forms an essential element in its constitution, or else to one 
 which sustains some essential relation to it. Thus we may 
 have the judgment as follows : The constitution of a nation 
 embodies the fundamental principles underlying the judi- 
 cial, legislative, and executive functions of government. 
 In such a judgment we have the interpretation of one 
 
THE JUDGMENT 
 
 27 
 
 concept by others which enter into its composition as 
 constitutive elements of it. 
 
 We may have also a judgment which expresses relations 
 between concepts as the following : Liberty is not possible 
 in a country where there is no respect for law. 
 
 In both of these illustrations the judgments relate to our 
 knowledge in general. 
 
 2. A concept, however, may be made definite by a reference 
 to some particular instance which illustrates it, or a particu- 
 lar instance in turn may be referred to a concept which in- 
 terprets it. Thus the concept of philanthropy may be made 
 clearer and more definite by a reference to certain specific 
 persons and their deeds ; and on the other hand a special 
 case, as a peculiar light in the northern sky, may be explained 
 by a reference to a familiar concept which serves to interpret 
 it, such as the aurora borealis. Under this head of a refer- 
 ence of the particular experience to its corresponding univer- 
 sal, we have the great body of our judgments of identification 
 or recognition, — such as, This plant is a fringed orchis, 
 or That is a red-winged blackbird, or That substance is com- 
 bustible. In these cases, the particular instance is referred 
 to the appropriate class or group within which it naturally 
 falls, or to a general attribute which characterizes it. 
 
 Of the two forms of judgment, thus outlined, the former 
 represents some phase of our knowledge in general ; the lat- 
 ter, the application of some phase of our general knowledge 
 to some special case. 
 
 Whether the judgment consists of the characterization of 
 our knowledge in general, or the interpretation of a particu- 
 lar experience by means of our general knowledge, it remains 
 true that in either case the judgment itself must rest upon 
 a sound basis of reality. A judgment which cannot show 
 some basis of reality upon which it rests is a judgment in 
 name only. It may be a fancy, a dream, a query, a hope, but 
 it is not a judgment. In this particular respect, the judg- 
 ment may be defined as the reference of a concept to reality. 
 
28 
 
 DEDUCTIVE LOGIC 
 
 This is more obvious in the second form of judgment, where 
 there is a reference of a particular experience to a concept, 
 for in this case the reality which underlies the particular 
 experience in question furnishes the evident basis of reality 
 to the judgment itself. Thus if one should say, That is the 
 wreck of a sailing vessel, then the actual object of perception 
 evidencing its own reality to the senses is to be regarded as 
 referred to the general concept, a wreck of a sailing vessel, 
 which thus identifies and explains it. 
 
 It is well to remark in this connection that every object 
 of perception evidences its own reality to the senses, and 
 this sense of reality attaching to an object is as definite and 
 as clear a quality of the object as its form, size, color, or any 
 of its various properties and activities. 
 
 This attribute of reality must be regarded as a simple, 
 unanalyzable element of consciousness which is immediately 
 given and attested in the very process of perception itself. 
 
 The reference to reality in the first kind of judgment — 
 that is, a judgment which relates to our knowledge in 
 general — is not so patent ; but nevertheless the reality is 
 present as an unseen but secure foundation for the truth 
 of the judgment. In this first form of judgment wherein 
 one universal idea is related to another universal idea, 
 where do we find any basis of reality ? If one idea can be 
 explained by another idea, in that very process it would 
 seem that we had swung clear of reality altogether. This is 
 not so, however. Take the judgment, The collie is an excel- 
 lent sheep-dog ; here the reference to reality is not direct, 
 it is true, but it is indirect. These concepts, collie and 
 sheep-dog, have their origin in a series of perceptual experi- 
 ences, and whatever reality may lie at the basis of the 
 percepts is conserved in the concepts which emerge from 
 them. 
 
 Conceptual reality is based upon perceptual reality. 
 The concept is real in the sense that it traces its origin to 
 the several concrete instances whose reality basis is dis- 
 
THE JUDGMENT 
 
 29 
 
 closed in perception. When the latter is wanting, the 
 possibility of the reference of the concept to reality is at 
 once removed. Thus we may have an assertion which has 
 the form but lacks the substance of a genuine judgment, 
 such as the following: The Centaur is an animal which 
 has the body of a horse with the head and shoulders of a 
 man. Here is a concept, standing as the subject of a judg- 
 ment, which can lay claim to no perceptual ancestry in our 
 experience. We can form a clear mental picture of it ; it 
 can even be rendered intelligible to the understanding of a 
 child ; but there is no real experience at the root of the idea, 
 and therefore it is nothing but a spectral form of a judg- 
 ment. Every true concept in distinction from a pseudo- 
 concept, such as that of a Centaur, or a Jabberwock, and the 
 like, is referable to some real experience in much the same 
 way as the genuine dollar note may be referred to the gold 
 coin which it represents and by which it is redeemable. 
 The counterfeit note presents the same general appearance 
 as the genuine, but it has a different history, and must be 
 traced to another origin which is of such a nature as to 
 render it base and valueless. 
 
 There is, however, a certain phase of reality which char- 
 acterizes many of our judgments, and which underlies the 
 very processes of judgment themselves, but has no origin in 
 perception. This is the reality which is discovered in the 
 very nature of thought itself. It is essentially a thought 
 reality, and as such we become aware of it quite indepen- 
 dently of any particular experience, and only by it indeed 
 is our experience rendered intelligible. This kind of reality 
 is illustrated in those sel f-evident truths which are the com- 
 mon possession of all rational beings, such as the axioms of 
 geometry, the principle of universal causation, the appreci- 
 ative judgments of moral worth or aesthetic value. Such 
 judgments are given as examples of a large group of judg- 
 ments which evidently imply as their basis a form of reality 
 which cannot be traced to an origin in mere perception. 
 
30 
 
 DEDUCTIVE LOGIC 
 
 There is, of course, that school in philosophy which denies 
 the possibility of any reality of this kind, but insists that 
 all forms of reality whatsoever, when completely analyzed, 
 will reveal an ultimate origin in experience, and that the 
 so-called intuitive truths have had their beginnings in con- 
 sciousness at the earliest stages in human development, and 
 have been transmitted through many generations, attaining 
 in each generation more complete expression, and more 
 exact formulation ; consequently for us they appear in 
 thought as judgments which seem to be self-attested and 
 to have no origin in our particular experiences. In the 
 present discussion as to the nature of the reality which 
 underlies our judgments, this question has no direct bear- 
 ing. We find in our consciousness certain judgments which, 
 for us, at least, whatever their remote origin may be, ap- 
 pear as intuitive truths evidencing their own reality with a 
 compulsion of thought quite as irresistible as that which 
 attests the reality of any object which we may see, or hear, 
 or touch. 
 
 These forms of reality whether attested by perception or 
 by the necessity of thought itself have this in common, — 
 they present themselves to consciousness in such a manner 
 that we are constrained to yield them a permanent and 
 constant recognition. To refuse a place to them in thought 
 would mean the denial of our intellectual integrity. Reality, 
 as regards its significance for logic, may be defined as that 
 which we are constrained to think. The real compels our 
 thought. The dream or fancy can be dispelled by the wak- 
 ing consciousness or the commanding will. Not so, how- 
 ever, with the real object of perception, or the necessary 
 implications of thought. The ghost is laid by the reassuring 
 judgments of common sense, but not the lightning, the 
 thunder, the storm which have overtaken us. The child’s 
 world is one in which, there is no sharp distinction between 
 fact and fancy ; especially is this true with the child’s world 
 of play. But contact with the world of growing knowledge 
 
THE JUDGMENT 
 
 31 
 
 brings many disillusions and the reduction of many cher- 
 ished fancies to the impossible and absurd. 
 
 It is not strictly a question of logic, — this question con- 
 cerning the ultimate nature of reality. It is essentially a 
 question of metaphysics, for metaphysics has primarily to 
 do with the ultimate nature of things, — of time, of space, 
 of causation, of God, man, and the world, and therefore of 
 the ultimate nature of the reality itself which underlies 
 these various manifestations of it. The special question 
 which metaphysics puts is this : Does our knowledge of 
 the world represent it really as it is ? May not reality be 
 very different from that which it appears to be in my per- 
 ceptions ? Are the sea, the sky, the wood, portrayed in 
 my thought with an exact correspondence to the reality 
 which constitutes them what they are ? It is evident that 
 there is here room for much discussion, for much difference 
 of opinion, and for much confusion of thought as well. But 
 logic is satisfied from its point of view, if there is assurance 
 that in the body of knowledge which represents our world 
 as we conceive it there are elements which maintain a con- 
 stant character, and that whatever we come to think about 
 them is due to a necessity which underlies their essential 
 nature. Logic therefore is not concerned with the ultimate 
 nature of reality, but it does demand as the basis of all 
 knowledge certain elements which are grounded in neces- 
 sity and admit of a constant reference in thought. 
 
 Moreover, that which appears to the individual as a nec- 
 essary experience, a necessary truth, or a necessary demon- 
 stration receives constantly through intercourse with one’s 
 fellow-men a social confirmation and verification. We find 
 for the most part that our judgments run parallel to those 
 of the generality of mankind. What we think, other men 
 think. What is true for me, I believe is true for you also. 
 The debatable area of conflicting opinion is to be regarded 
 as knowledge in the making. Questions which divided 
 men’s minds a generation or two ago are many of them now 
 
32 
 
 DEDUCTIVE LOGIC 
 
 settled, and the results formulated in universally accepted 
 judgments. Even where there may remain an outstanding 
 difference of opinion, there is always some common ground 
 of necessity which is recognized; and the lack of agree- 
 ment is due to the fact, not that the basis of our knowledge 
 is uncertain and shifting, but that human judgment is 
 fallible, owing to the limitations of experience, the want of 
 insight, the presence of prejudice, or the undue submission 
 to authority. All these disturbing elements enter into the 
 processes of thought and cause perturbations of judgment. 
 In spite however of such disagreements, the presence of 
 an underlying necessity as the basis of knowledge is at- 
 tested and sealed by the general agreement of our judg- 
 ments with those of our fellows. The communication of 
 thought, the communal interests and activities, the indus- 
 trial and social faith which is preserved between man and 
 man, the laws both written and unwritten which command 
 respect and obedience, the universally recognized standards 
 of civilized life, all attest a common recognition of one and 
 the same element of necessity, and a common interpre- 
 tation of the many phases of its manifestation. 
 
 The difference between the man who is sane and one who 
 is not lies in the absence of this social factor of agreeing 
 judgments. With the insane mind there is a feeling of 
 necessity which, however, is without foundation. The world 
 in which he lives and moves and has his being is for him 
 a necessary world. But in it he dwells alone. No one else 
 can enter it, or understand his view of it. He believes that 
 he is Julius Csesar, or Napoleon, and it may be consistently 
 thinks and acts in that character. But for him there is no 
 fellowship in thought, for his experiences are not believed 
 and his judgments stand in conflict with those of all the 
 rest of mankind. 
 
 It is incumbent upon us, therefore, as logical beings, to 
 make sure of the basis of reality which we believe under- 
 lies our judgments. In the investigation of any subject 
 
THE JUDGMENT 
 
 33 
 
 concerning which we regard ourselves entitled to a judg- 
 ment, not only should we seek as wide a range of observa- 
 tion as is possible concerning the facts upon which we 
 found the judgment, but we should acquaint ourselves also 
 with what other men have thought and have written upon 
 the subject. This is to be done, not that we may slavishly 
 acquiesce in their judgments, but that by a critical exami- 
 nation of all that is known and reported we may be the 
 better able to defend our own position, or the more reason- 
 ably to modify or to abandon it as the case may be. 
 
 We come now to discuss the relation of the judgment as 
 a form of thought to its corresponding expression by means 
 of language. The judgment expressed in language is known 
 as a proposition. The grammatical form of a proposition 
 consists of subject, predicate, and copula. The copula is 
 some form of the verb “ to be ” either expressed or implied. 
 It is always implied in any verb which may appear in a 
 proposition. Thus the proposition, He rows a boat, is equiv- 
 alent to the proposition, He is rowing a boat ; wherein the 
 verb “ to row ” breaks up into the participle of the verb com- 
 bined with the auxiliary verb “ to be.” This can occur with 
 any verb whatsoever, and therefore in any verb there is im- 
 plied some form of the verb “ to be ” ; consequently every 
 proposition may be regarded as composed of subject, predi- 
 cate, and copula. 
 
 The logical function of these three parts of speech needs 
 some further exposition. In the first place, there is a dis- 
 tinction between logical subject and predicate on the one 
 hand, and grammatical subject and predicate on the other. 
 The logical subject of every proposition is some phase of 
 reality ; the logical predicate is always the significant idea 
 which the judgment contains applied to this phase of reality 
 in order to characterize or interpret it. The judgment in 
 this connection may be defined as the interpretation of some 
 phase of reality by means of some universal idea. The reality 
 is the logical subject ; the universal idea interpreting it is the 
 
34 
 
 DEDUCTIVE LOGIC 
 
 logical predicate. This statement may be illustrated as fol- 
 lows : Let us take a judgment of the type in which a partic- 
 ular experience is interpreted by means of a concept, — This 
 is an excellent essay on the labor question. Here the sub- 
 ject, denoted by the demonstrative adjective “this,” refers 
 directly to a point of the world of reality, evident to the 
 senses, something visible and tangible ; the predicate is the 
 complex concept, “an excellent essay on the labor question,” 
 which is asserted of the subject in question. The thought 
 form interprets the perceived reality simply. In this type 
 of judgments, the logical subject and predicate coincide 
 with the grammatical subject and predicate. 
 
 In the other form of judgment which is a characterization 
 of some phase of our knowledge in general, the logical sub- 
 ject and predicate do not coincide with the grammatical 
 subject and predicate. For instance, let us consider the 
 proposition, — All permanent reforms emanate from the 
 people. Here the grammatical subject is “ all permanent 
 reforms ” ; the grammatical predicate is that they “ emanate 
 from the people.” 
 
 Now it is the function of the copula to fuse together the 
 grammatical subject and predicate into one idea which forms 
 the heart of the judgment and its real logical predicate. 
 For while language separates the grammatical subject and 
 predicate, the two must be conceived as merely parts of one 
 and the same idea in thought. The grammatical predicate, 
 in this case the phrase “ emanate from the people,” is an 
 essential characteristic of the grammatical subject, “ perma- 
 nent reform ” ; together they form but a single idea, namely, 
 a permanent reform emanating from the people. This is 
 the logical predicate which is affirmed of this particular 
 phase ot that reality which lies at the basis of every true 
 judgment, and though not expressed in the grammatical 
 form of the proposition nevertheless constitutes its logical 
 subject. The logical significance of this judgment, if ex- 
 plicitly expressed, would be somewhat as follows : The 
 
THE JUDGMENT 
 
 35 
 
 world of reality as I am constrained to regard it is such 
 as to necessitate that all permanent reforms should emanate 
 from the people. And this may serve as a type of all our 
 universal judgments ; they affirm of some phase of reality 
 the central idea which constitutes the heart of the judgment 
 itself. A false judgment contains at its heart a central 
 idea to which there is no corresponding subject in the real 
 world of knowledge. 
 
 When we come to put into words the single idea which 
 always lies at the root of the essential unity of the judg- 
 ment, why do we separate this unitary idea into two, the 
 grammatical subject and the grammatical predicate? The 
 reason is that while the idea in question represents a single 
 unified thought, it is nevertheless complex and capable of 
 an analysis into two component elements, one the grammati- 
 cal subject and the other the grammatical predicate. Judg- 
 ment is a process which consists in relating one phase of 
 an idea to another phase of the same idea, and in rendering 
 evident the unity which underlies them. The grammatical 
 subject forms one of these phases; the grammatical predi- 
 cate forms the other. The copula serves to bring them to- 
 gether and to affirm their unity. Thus every proposition 
 is the expression of the complementary processes of analysis 
 and synthesis ; the analysis is expressed by the grammatical 
 subject and predicate, the synthesis by the force of the 
 copula whose function it is to blend the two into one logical 
 idea which forms the very essence of the judgment itself. 
 
 In connection with this discussion of the relation of 
 language to thought, it would be well to call attention to 
 the meaning of the word term in logic. A term is any word 
 or combination of words considered as a part of a proposition, 
 that is, as subject or predicate. The term, therefore, is the 
 expression in language of the concept as an integral part 
 of the judgment. 
 
CHAPTER IV 
 
 THE UNIVERSAL JUDGMENT 
 
 Judgments, as we have seen, are of two kinds. The 
 first represents some one or other of the many phases of 
 our general knowledge. The second serves to interpret the 
 special case in the light of general knowledge. The first 
 type is known as the universal judgment. Our general 
 body of knowledge is composed of judgments of this kind, 
 and if they are to prove serviceable in the interpretation of 
 special cases as they arise, they must together form an 
 orderly system. The concepts which form the constitutive 
 elements of these judgments are all interrelated. Every 
 concept represents a point whence radiate lines of connection 
 with many other concepts. It is impossible to frame a 
 judgment which shall contain a concept out of all relation 
 to other concepts. 
 
 If, for instance, we analyze the full significance of the 
 abstract concept of redness, we at once relate it in our 
 thought to the general color system, which in turn we refer 
 to light as its source. The idea of light at once suggests the 
 ether vibrations which affect the retina of the eye, and this, 
 in turn, the transmission of the physiological disturbance 
 which occurs in the retina to the optic lobes of the brain, 
 and then the resultant reaction which is attended by the 
 consciousness of a color sensation. Thus the examination 
 of any concept will reveal an indefinite number of relations 
 extending into the general body of our knowledge. Their 
 formulation gives rise to a series of descriptive judgments. 
 Our knowledge therefore so far as it is worthy the name 
 
 36 
 
THE UNIVERSAL JUDGMENT 
 
 37 
 
 of knowledge, represents an organized system of relations. 
 Moreover, there are certain general principles which underlie 
 the process of organizing the various elements of knowledge. 
 These principles pertain to the very nature of thought itself, 
 and man has universally employed them in constructing 
 his world of knowledge. These fundamental principles are 
 called the categories of thought. They indicate the various 
 possible ways by which conceptual elements are related so 
 as to form the unitary idea which lies at the basis of the 
 judgment. 
 
 As given by Aristotle, the categories, ten in number, are 
 as follows : — 
 
 e 6 . 7 rore time 
 
 Thus any concept whatever may be regarded from one or 
 more of these points of view, — as to its substance, what it 
 is ; as to its various attributes, its dimensions and weight ; 
 the relations which it sustains ; its space and time condi- 
 tions ; its relative position as regards its surroundings ; as 
 to what it may possess ; as to how it acts ; and how it is 
 acted upon. The list exhausts the possibilities of descrip- 
 tion. The word KarrjyopLa, as used by Aristotle, means as- 
 sertion or predication. The table of the categories presents 
 the possibilities of the various kinds of assertion. We have 
 seen, moreover, that a judgment is a process essentially of 
 assertion. The categories therefore give us the possible 
 varieties of judgment. These categories suggest a cor- 
 responding division of words into the various parts of 
 speech. The substance corresponds to the noun ; quantity, 
 quality, and relation to the adjective ; place, time, and pos- 
 ture to the adverb; having, acting, and being acted upon to 
 the verb. Thus we have outlined the possibilities, not only 
 
 5. nov place 
 
 7. KelcrOtu posture or attitude 
 
 8 . ex etv having 
 
 9. 7 rot£tv acting 
 
 10 . 7 racrx£iv being acted upon 
 
38 
 
 DEDUCTIVE LOGIC 
 
 of thought relations, but of the expression of the same in 
 language. 
 
 There are, moreover, certain considerations in reference to 
 these categories which enable us to coordinate the various 
 portions of our knowledge so as to form out of them a system 
 which shall show unity and order. These considerations 
 are as follows : — 
 
 The first category is substance ; the other nine categories 
 give the various kinds of possible attributes which together 
 serve to determine the essential nature of any concept, that 
 is, its substance, this first of the categories. Of these various 
 attributes, some will be common to a number of concepts. 
 This will enable us to group similar concepts together. 
 Other attributes will be unique as regards some particular 
 concept. They will serve as a distinguishing mark of the 
 concept in question. Others again appear in certain special 
 instances of a concept, but not in all. This serves to mark 
 the distinction between constant and variable attributes, a 
 distinction which is exceedingly valuable from the stand- 
 point of logic ; for it draws the line between attributes and 
 relations which have a universal validity and those which 
 are shifting and uncertain. 
 
 The above considerations are formulated under five tech- 
 nical terms, known in logic as the Heads of Predicables ; 
 that is, the various ways in which a predicate given by any 
 one of the categories may be affirmed of a subject, or of the 
 concept regarded in the light of the first category, substance. 
 These terms are as follows : — 
 
 1. Genus. 
 
 2. Species. 
 
 3. Property. 
 
 4. Differentia, or Specific Difference. 
 
 5. Accident. 1 
 
 1 Aristotle gives but four forms, including “species ’’under “genus,” 
 and instead of “ differentia,” giving “ definition.” 
 
THE UNIVERSAL JUDGMENT 
 
 39 
 
 They are the Heads of Predicables, as given by Porphyry 
 (230-300 a.d.) in his Introduction to Aristotle’s Treatise on 
 the Categories. 
 
 Genus and species are relative terms and can best be 
 defined together. The genus is always a larger class which 
 embraces two or more smaller classes under it by reason of 
 their common attributes. 
 
 The species is any one of the smaller classes which is 
 embraced under the genus. 
 
 The property is an attribute which pertains to the very 
 nature of the concept itself. 
 
 The differentia is that particular property which serves to 
 distinguish a given species from all others belonging to the 
 same genus. 
 
 The accident is an attribute which does not pertain to the 
 essential nature of the concept, and therefore may be present 
 or absent without affecting the integrity of the concept in 
 question. 
 
 These distinctions may be illustrated in the following 
 proposition : — 
 
 Democracy ( species ) is a form of government (genus) in 
 which the supreme power is vested in the people (differ- 
 entia) ; it is attended by certain dangers due to the dissipa- 
 tion of responsibility (property) ; it is regarded in the 
 United States by some as a proved success, by others as 
 still in the experimental stage (accident). 
 
 The several species under one genus are called cognate 
 species. 
 
 A generic property is one which grows out of the idea 
 represented by the genus, and which therefore all cognate 
 species have in common. 
 
 A specific property is one which grows out of the idea 
 represented by the differentia, and belongs therefore only 
 to one of a number of cognate species. 
 
 Genus and species, being relative terms, a concept may 
 be regarded as a species relative to a genus which embraces 
 
40 
 
 DEDUCTIVE LOGIC 
 
 it, but a genus relative to the various species which it 
 embraces. 
 
 There is however the summum genus, which can be re- 
 ferred to no larger class, and also the infima species, which 
 cannot be broken up into any smaller classes. 
 
 In the light of these various distinctions, we may group 
 our judgments in several classes, according to the dif- 
 ferent ways by which the concepts in these judgments are 
 related. 
 
 1. The possibility of referring a species as a subject to 
 its corresponding genus as a predicate ; e.g. The purple 
 martin is a swallow. 
 
 2. The possibility of referring a genus as a subject to the 
 various species under it which together form the predicate ; 
 e.g. The swallow may be a purple martin, a barn swallow, a 
 cliff swallow, etc. 
 
 3. The possibility of describing any species as a subject 
 by one or more of its properties as a predicate ; e.g. Cast 
 iron has a specific gravity of 7.20. 
 
 The special case of this group is where the property 
 chosen is the differentia of the species ; e.g. Capital is 
 wealth which is actually used for producing more wealth. 
 
 4. The possibility of describing a concept by its accident ; 
 e.g. Some animals can swim. 
 
 A judgment in this latter form is known as a particular 
 judgment. It is not a statement in terms of a universal ; 
 neither indeed can it be as long as the predicate is an ac- 
 cident of the concept which appears as subject. 
 
 It must not be overlooked, however, that any predicate 
 which is an accident may be raised to the higher level of a 
 property in reference to any concept, provided that concept 
 is only more specifically limited. Thus if we change the 
 above proposition by inserting the limiting adjective “ web- 
 footed,” the predicate at once becomes the property of the 
 subject thus limited, and instead of a particular judgment, 
 as in the former case, we now have the universal judgment, 
 
THE UNIVERSAL JUDGMENT 
 
 41 
 
 — All web-footed animals can swim. In general it may be 
 said that an accident of any species always becomes the 
 property of that same species under certain definite restric- 
 tions. Every accident, therefore, is a potential property. 
 To call any attribute of a species an accident is a confes- 
 sion of ignorance, for if we only know the corresponding 
 limitation of the species in question, the accident at once is 
 transformed into a property. 
 
 If our knowledge were perfect, we should be able to 
 explain all accidental variations, even the most minute and 
 seemingly insignificant. Each so-called accident could then 
 be regarded as a property and be referred to some constant 
 element within the nature of the concept itself as its cause. 
 Every variation in nature, whether of color, or form, or 
 peculiarities of habit and disposition, has a good and suffi- 
 cient reason why it is what it is and not anything else. To 
 call such variations mere accidents of a species is of course 
 a confession of ignorance. This leads us to the fifth pos- 
 sibility of reference. 
 
 5. The possibility of referring properties of concepts to 
 definite conditions as their cause. The causal relation when 
 expressed or implied in a judgment not only renders that 
 judgment more definite and consequently serves to perfect 
 the order of the general body of knowledge, but it also 
 furnishes the ground for the judgment itself and conse- 
 quently serves to justify it. Take for instance the proposi- 
 tion, A conic section formed by a cutting plane parallel 
 to the base of a cone is always a circle. Here the circle, as 
 regards a conic section in general, is an accident, but as 
 regards a conic section under the condition that the cutting 
 plane is parallel to the base, it is an essential property. 
 The condition determines the property, and the two are 
 related as cause and effect. So, also, to further illustrate 
 this relation, the freezing or boiling of water may be regarded 
 as accidents, so far as the concept of water in general is 
 concerned. They are, however, properties of water when 
 
42 
 
 DEDUCTIVE LOGIC 
 
 specifically determined by the freezing and boiling condi- 
 tions. 
 
 Knowledge, therefore, which is vague and indefinite, gives 
 rise to judgments whose predicates are accidents of the 
 subject concept. Definite knowledge, on the other hand, 
 always gives rise to judgments whose predicates are prop- 
 erties of the subject concept. The bond of connection or 
 inherence between any species and its property forms the 
 ground of the universal judgment. 
 
 In the various relations which concepts may sustain to 
 one another in the general scheme which has been given, 
 there are, in the main, two points of view from which a 
 concept may be regarded, giving rise to two different kinds 
 of judgment. The one point of view is known as that of 
 extension and the other that of intension. The extension 
 of a concept refers to the range of its application. The 
 intension refers to the various properties which constitute 
 its meaning. The term denotation is used as equivalent to 
 extension; and connotation as equivalent to intension. The 
 term content is also used in much the same sense as con- 
 notation or intension. By some writers the terms extension 
 and intension are applied to concepts, while denotation and 
 connotation are applied to terms, the language symbols of 
 concepts. In ordinary usage, however, extension and de- 
 notation are used interchangeably ; so also intension and 
 connotation. Two questions naturally arise in reference to 
 any concept : the first, what is its meaning ? and the sec- 
 ond, to what extent within the range of our knowledge 
 may it be applied ? It is obvious that these two questions 
 are mutually dependent. It is impossible of course, to 
 know the number of special cases to which the concept may 
 be applied if we know nothing of its distinctive properties; 
 and, on the other hand, we can know nothing of the distinc- 
 tive properties unless we possess some knowledge of the 
 special cases illustrating them. 
 
 The distinction between intension and extension gives 
 
THE UNIVERSAL JUDGMENT 
 
 43 
 
 rise to two topics known as definition and division. Defi- 
 nition is the process of unfolding the connotation of any 
 term, and division is the process of unfolding the denotation 
 of a term ; that is, the former tells what it is, the latter to 
 what instances it may be applied. These two processes we 
 will now consider more in detail. 
 
CHAPTER V 
 
 DEFINITION 
 
 Definition is the process of unfolding the connotation 
 of a concept. A statement giving the complete connota- 
 tion, however, would be overloaded and would weigh down 
 our thought and its expression with a superfluous burden. 
 If a definition serves to locate a concept in its proper region 
 within the general body of knowledge, and in addition dis- 
 tinguishes it from all other cognate concepts which may 
 fall within the same general area of thought, then it may 
 be said to perform its function satisfactorily. The function 
 of definition is expressed by the following rule : Definition 
 consists in referring any concept to its proximate genus, i.e. 
 the genus immediately above it, and also in giving its 
 appropriate differentia. 
 
 To define means to set limits or bounds. This rule in- 
 dicates two defining circles : the first, the genus, marks the 
 larger area within whose range the concept belongs ; the 
 second, the differentia, draws a narrower circle which sepa- 
 rates the concept within it from all others which lie within 
 the outer circle, and yet outside this inner circle of more 
 exact specification. This method of defining is a procedure 
 which should always be followed when it is possible. There 
 are other modes of definition which are less complete, but 
 which it is sometimes necessary to employ, as will be shown 
 later. The above method, however, is preferable, as it alone 
 can give what is known as the essential definition. 
 
 A distinction is drawn by some logicians between a real 
 and a nominal definition. The real definition is regarded as 
 one which gives the meaning of the concept ; the nominal, 
 
 44 
 
DEFINITION 
 
 45 
 
 as giving the meaning of the term which is the language 
 symbol of the concept. Some writers, as Sigwart and Mill, 
 declare that there can be no such thing as a real definition, 
 inasmuch as the process of defining consists in unfolding 
 the meaning of words. Definition, from this point of view, is 
 merely the art of fitting the word to the idea which it repre- 
 sents. It seems to me, however, that the process of defini- 
 tion must primarily refer to the meaning of the thought, 
 and only in a secondary sense to the meaning of the word 
 which is the symbol of the thought. For the symbol can 
 have no meaning, except as it represents some thought 
 behind it. And, in the second place, to define means to 
 render definite. Consequently, a definition of terms presup- 
 poses always a preliminary transformation of our ideas from 
 an indefinite to a definite state of determination. It is 
 thought determination alone which can afford a basis for 
 exact verbal definition. To draw a line of distinction be- 
 tween a real and a nominal definition is to misunderstand 
 the relation which obtains between a symbol and that which 
 it symbolizes. 
 
 There are certain rules which should be observed in 
 definition : — 
 
 1. The term defined should be coextensive with the defini- 
 tion, neither greater nor less. The following is an example 
 of the violation of this rule: Logic is a normative science. 
 Here the term “ normative science ” is not coextensive with 
 “ logic,” for it includes ethics and aesthetics as well as logic. 
 
 2. The definition shonld not contain any superfluous 
 material. Take the following definition : — An hallucina- 
 tion is a fancied perception (genus) without basis of fact 
 (differentia), and which indicates an abnormal state of 
 consciousness. The latter clause, while quite true, is alto- 
 gether superfluous. The definition should be always in as 
 concise a form as possible. 
 
 3. The definition should not repeat the term to be defined 
 either explicitly or implicitly. The violation of this rule is 
 
46 
 
 DEDUCTIVE LOGIC 
 
 known as defining in a circle (circulus in definiendo). In an 
 examination recently given the terms “ percept ” and “ con- 
 cept” were deSned as follows: — A percept is that which 
 is perceived. A concept is that which is conceived. These 
 definitions are incorrect also for another reason, because 
 they contain no proper genus. Instead of a true genus to 
 which the term defined is referred there is substituted the 
 indefinite and unsatisfactory phrase “ that which.” 
 
 Under this head of explicit or implicit repetition of the 
 term to be defined may be included all synonyms of the 
 term in question. There is the following remark of Hume 
 which illustrates this. Speaking of the definition of the 
 term “ efficacy,” he says : “ I begin with observing that the 
 terms of efficacy, agency, power, force, energy, necessity, con- 
 nexion, and productive quality are all nearly synonymous ; 
 and therefore it is an absurdity to employ any one of 
 them in defining the rest. By this observation we reject at 
 once all the vulgar definitions which philosophers have given 
 of power and efficacy ; and instead of searching for the idea 
 in these definitions, must look for it in the impressions 
 from which it is originally derived.” 1 
 
 It sometimes happens that in a compound term the in- 
 cidence of the definition falls only upon one of the elements 
 which compose the compound. In such a case, the other 
 element of the compound term may be repeated in the defi- 
 nition. Thus the terms, “ vesper-sparrow,” “ gun-metal,” 
 “armored cruiser,” may be defined by referring each to its 
 appropriate genus, “ sparrow,” “ metal,” “ cruiser,” and then 
 giving its corresponding differentia. 
 
 4 A definition should never be in obscurer language than 
 the term to be defined. The violation of this rule is called 
 “ ignotum per ignotius.” 
 
 An example of this is the following: A state is an 
 ethnic unit which lies within a geographical unit. 
 
 1 Hume, A Treatise of Human Nature. Edited by Green and Grose, 
 p. 451. 
 
DEFINITION 
 
 47 
 
 Sometimes, however, in defining technical terms it is 
 necessary to use technical words, and an impression is 
 given to the uninitiated at least of an obscure definition. 
 Such a definition is Herbert Spencer’s of evolution. “ Evo- 
 lution is a continuous change from an indefinite incoherent 
 homogeneity to a definite coherent heterogeneity through 
 successive differentiations and integrations.” In this defi- 
 nition every term used has a definite connotation with which 
 every student of the subject has become familiar, and there- 
 fore to such an one this definition is exceedingly luminous. 
 
 5. A definition should never contain negative expressions 
 when it is possible to state it by means of the proper posi- 
 tive terms. 
 
 The following is a violation of the rule : — 
 
 A utilitarian is one who does not believe in an intuitional 
 basis of morals. 
 
 It is always desirable to define any term by what it is 
 rather than by what it is not. 
 
 There are certain terms, however, which by their very 
 nature admit of a negative definition only. Such terms 
 are the following, — anarchist, blindness, unarmored cruiser, 
 supernatural, and the like. 
 
 There are other forms of definition which are substituted 
 for the ideal form per genus et differentiam. Sometimes 
 they are mere makeshifts at definition, when one is ignorant 
 of the true genus or differentia; and often for some spe- 
 cial reason they better serve the purpose of a satisfactory 
 definition. 
 
 They are as follows : — 
 
 1. Definition by description. When the genus or the dif- 
 ferentia is unknown, then the concept may be described by 
 its various properties. A person thinks that he has dis- 
 covered a new species of plant. He is in doubt as to its 
 precise differentia. An exact definition is impossible. He 
 wishes, however, to publish some account of it. The only 
 course which is possible under the circumstances is to give 
 
48 
 
 DEDUCTIVE LOGIC 
 
 a complete description of it, especially as regards those prop- 
 erties in which it deviates in any marked degree from the 
 type. The description may serve as a basis for the discovery 
 of the real differentia. 
 
 It often happens when one begins a new study, and the 
 material he has to deal with is unfamiliar, that precise defi- 
 nitions are impossible. At this preliminary period descrip- 
 tion must take the place of definition. Later with the 
 mastery of the subject comes the possibility of framing 
 satisfactory definitions. 
 
 2. Definition for the purpose of identification. Instead of 
 the differentia which may be a property that is not evident 
 to a surface observation, there may be substituted in the 
 definition another property which is readily observable and 
 which serves as a mark of identification. Thus we may de- 
 fine an acid as a chemical compound which turns blue litmus 
 red. It is not a definition of an acid, but it is a most 
 convenient formula of identification. Or we may define 
 sassafras as a tree of the laurel family whose bark has an 
 aromatic odor or taste. Such formulae are most valuable as 
 working definitions. Sometimes the property which best 
 serves as a basis for identification is a very insignificant 
 one. Thus the color markings of birds, such as the white 
 tail-feather of the vesper-sparrow, may furnish a convenient 
 and perfectly satisfactory basis for identification. It may 
 be that the peculiar mode of flight may serve a similar 
 purpose. In all such instances a superficial property is 
 substituted for the differentia. 
 
 3. The genetic definition, which refers the concept to be 
 defined to its origin. The genetic definition, in giving the 
 origin of the concept, furnishes at the same time a method 
 by which special instances of the concept may be produced, 
 and made available for observation and experiment. Thus 
 the genetic definition of sulphuric acid is given by the 
 formula H 2 S0 4 . Here the compound is defined by the com- 
 ponent elements of which its essential nature consists. The 
 
DEFINITION 
 
 49 
 
 genetic definition of a certain dye would be in terms of the 
 formula by means of which the dye may be produced. So 
 also all recipes, prescriptions, and methods of construction 
 may be regarded as definitions of this class. Any concrete 
 instance may be produced at will by following the sugges- 
 tions contained in the definitions. Thus it is a genetic 
 definition of a right cylinder that it is a solid body con- 
 ceived as generated by the rotation of a rectangle about one 
 of its sides as an axis. So also the various colors of the 
 spectrum may be defined in terms of the number of vibra- 
 tions corresponding to each color. 
 
 The genetic definition is one which has always a practical 
 significance inasmuch as it furnishes knowledge in such a 
 form as to subserve the ends of utility. It not only tells 
 us the meaning of certain ideas, but it also indicates how 
 we may apply them in the arts, the sciences, and the practi- 
 cal needs of our lives. 
 
 
CHAPTER VI 
 
 DIVISION AND CLASSIFICATION 
 
 Division is a process by which the denotation of a con- 
 cept is exhibited. The result is that form of judgment in 
 which the subject term represents the concept regarded as a 
 genus, and the predicate term contains the several species 
 which fall under it. The process of definition always 
 underlies that of division, for we must know the differentia 
 of each species before it is possible to consider it as a dis- 
 tinct group under a given genus. In dividing a concept 
 into its appropriate species, one may proceed in a number of 
 different ways according to the point of view he may choose 
 to take. The point of view determines in every case the 
 so-called principle of division ( fundamentum divisionis). 
 
 Thus we may divide the general concept, education, ac- 
 cording to the principle of the progressive stages of educa- 
 tion regarded as a process, as primary, secondary, collegiate, 
 university, and professional ; or the principle chosen may be 
 that of the general nature of the course of studies pursued, 
 such as the common school, academic, scientific, technical, 
 etc. ; or again, the principle of division may be an historical 
 one, giving the periods of ancient, mediaeval, and modern 
 education. It is obvious that the principle of division will 
 vary according to one’s special interest or purpose. There is 
 thus a wide range of possibility as regards the analysis of 
 our various concepts. There is no beaten road for thought 
 to travel, but each one may cut out his own path. In the 
 midst of this variety of choice, however, there are certain 
 rules which logic imposes upon the free play of thought. 
 Within the bounds of these restrictions the inventive spirit 
 
 50 
 
DIVISION AND CLASSIFICATION 
 
 51 
 
 may range at will; but the violation of them brings con- 
 fusion and inconsistency of thought. The rules are : — 
 
 1. There must be but one principle of division. A 
 violation of this rule, for instance, would be such a division 
 as that of the concept “education” into primary, secondary, 
 collegiate, technical, scientific, and professional. 
 
 2. The members of a division should be mutually 
 exclusive ; no two members of a division should overlap. 
 The above example illustrates the violation of this rule also. 
 The following furnishes another illustration : The division 
 of the discontented classes in society into socialists, an- 
 archists, nihilists, and populists. 
 
 While the violation of the first rule produces overlapping 
 divisions, nevertheless the same error may be due to other 
 causes even when the requirements of the first rule are 
 realized. 
 
 3. The division must be exhaustive. No possibility 
 should be overlooked and omitted from the division. Thus 
 if we divide conduct into two classes, the moral and immoral, 
 the division is at fault because of its incompleteness. There 
 is still a third class which is omitted, namely, that of con- 
 duct which is morally indifferent, and concerning which it 
 is not possible to affirm that it is either moral or immoral. 
 
 There is a particular method of division known as Dichot- 
 omy which provides for an exhaustive division under all 
 circumstances. It consists in dividing a concept into two 
 parts, according to the presence or the absence of a 
 differentiating attribute which is chosen as the principle 
 of division. This may be illustrated by the so-called “ Tree 
 of Porphyry,” which exhibits a continued division of that 
 most general and all-comprehensive concept, being. 
 
52 
 
 DEDUCTIVE LOGIC 
 
 Being 
 
 corporeal incorporeal 
 
 animate inanimate 
 
 sensible insensible 
 
 rational irrational 
 
 Plato Aristotle and other individuals 
 
 Such a division is more curious than satisfactory, for one 
 of the members in each successive division is left indefinite, 
 being designated by what it is not, rather than by what it is. 
 Moreover, if a positive term is substituted for the negative, 
 and its precise connotation is attempted, it will in all 
 probability not be a complete opposite of the first term of 
 the dichotomy. If this is the case, the division itself is not 
 complete, for the dividing of a concept into two members 
 which are not exact opposites renders it possible to inter- 
 polate between them one or more possibilities which do not 
 belong to the one or the other of the extremes. In this connec- 
 tion it is necessary to distinguish between contradictory and 
 contrary or opposite terms. 
 
 Contradictory terms are such that they divide the whole 
 universe of thought between them and admit of no middle 
 ground. 
 
 Contrary terms stand opposite to each other as extremes, 
 but there is a possibility of middle ground between them. 
 
 Animate and inanimate are contradictory, bitter and 
 sweet are contrary terms. 
 
 A dichotomous division requires its terms to be related as 
 contradictories. There is perhaps no error in division which 
 is more frequent or more insidious than this, of dividing a 
 
DIVISION AND CLASSIFICATION 
 
 53 
 
 concept into members which sustain contrary rather than 
 contradictory relations to each other. This is seen particu- 
 larly in debate where an opponent will often confront one 
 with a choice of alternatives, either this course or that, 
 when, however, there is a third possibility unnoticed, or 
 purposely ignored. It is the third possibility which we 
 should always have in mind, and endeavor to discover 
 whenever the necessities of a dichotomous division are 
 forced upon us. There can be no free choice of the mind 
 unless all possibilities are presented. 
 
 On this very account division very often takes a threefold 
 form, that of Trichotomy ; because when a concept is divided 
 into two members exhibiting some one or more opposed 
 characteristics, a third member representing a mediating 
 position between the two naturally suggests itself. This 
 form of division which expresses extreme terms in relation 
 to the middle ground between them has played an important 
 role in the history of philosophical thought. For instance 
 Aristotle’s theory of morals was based upon the principle 
 that right conduct always lies between two extremes, neither 
 of which commends itself to the reason. Thus courage, which 
 is the mean between cowardice on the one hand and rash- 
 ness on the other, takes rank as a virtue and is freed from 
 all criticism which is called forth naturally by the extremes. 
 So, also, according to Aristotle, temperance is the virtue 
 which avoids the extremes of ascetic abstinence and un- 
 bridled desire. 
 
 The trichotomous division is further illustrated in the 
 dialectical method which grew out of the teaching of Kant, 
 and which was developed by Fichte and brought to its com- 
 plete expression by Hegel. The meaning of “dialectic” may 
 be gathered from Plato’s usage of the term, which with him 
 signified the process of argument between two disputants, 
 who in their controversy for and against a given proposition 
 render this exceedingly valuable service, namely, that the 
 course of debate brings to light whatever fundamental 
 
54 
 
 DEDUCTIVE LOGIC 
 
 elements of truth the opposed positions may have in com- 
 mon. This idea Hegel has applied to the evolution of all 
 truth which he declares develops progressively through three 
 stages. The first is the thesis, the primary proposition as 
 originally affirmed ; the second is the antithesis, the opposed 
 proposition ; the third is the synthesis, the reconstruction of 
 these two from a higher point of view which discloses the 
 unity underlying the two extreme positions. Hegel insists 
 that a scheme such as this forms a universal programme 
 according to which the evolution of all thought must pro- 
 ceed. 
 
 A distinction is drawn in logic between the so-called 
 empirical and logical divisions. A logical division is one 
 which applies the principle of division to any given concept, 
 and notes all the possible members of the division which 
 result from such a process. The empirical division is the 
 result of a critical examination of the logical division to the 
 end that all members of such a division which cannot be 
 realized actually in experience may be eliminated. A strictly 
 logical division may give certain ideal groups which are 
 rendered impossible actually because of certain necessities 
 of the concrete situation, or because of the general economy 
 of nature. 
 
 As an illustration of the former, the genus, regular poly- 
 hedron, may be divided according to the number of the 
 bounding planes. Now applying to the genus the principle 
 of division which is the number series, and without taking 
 into consideration any other limiting conditions whatso- 
 ever, we get regular polyhedrons according as their faces 
 are : — 
 
 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc. 
 
 However, a second question forces itself upon our consid- 
 eration. Are the space conditions such that all of these 
 supposed regular polyhedrons can be actually constructed? 
 
DIVISION AND CLASSIFICATION 
 
 55 
 
 The answer is that only the following are possible, those 
 having sides as follows : — 
 
 4 , 6 , 8 , 12 , 20 . 
 
 Thus the formal division has been corrected through an 
 appeal to the actual conditions which are imposed by the 
 existent space relations. 
 
 Again to illustrate what may be called the limitations due 
 to the economy of nature, we have the following division 
 of mankind, according to differences of color : White men, 
 black, red, yellow, orange, green, etc. 
 
 Such a division is the result of applying a color principle 
 of division in its full rigor and extent to the concept in 
 question. When, however, we ask in addition the question 
 as to the prodigality of nature in this respect, we find that 
 the actual colors found among the various races of man are 
 limited, and therefore our division must be corrected by 
 striking out such colors as green, orange, etc., which have 
 no empirical confirmation in fact. 
 
 There is a difference as regards order of procedure between 
 dividing a concept simply according to the possible varia- 
 tions of some selected property irrespective of any con- 
 sideration of the actual limitations which may occur in 
 experience, and starting with actual classes as they have 
 been observed in experience, and grouping them together in 
 a system as related members of one and the same genus. 
 This latter process is that of classification which will be 
 considered next. 
 
 Classification is a term which is used for the most part 
 interchangeably with division, but, as regards strictly logical 
 usage, classification is a process which is the inverse of 
 division proper. The problem of classification, therefore, 
 is that of arranging given classes into a system whose 
 unity is such that it can be regarded as forming the under- 
 lying ground of the several classes in question. Moreover, 
 classification proper represents usually a more elaborate 
 
56 
 
 DEDUCTIVE LOGIC 
 
 scheme than simple division. In classification the process 
 of division is many times repeated, so that the original genus 
 not only has its species grouped under it, but each species in 
 turn may be regarded as a new genus, and its corresponding 
 species indicated, and so on until a series of infimaz species is 
 reached. 
 
 A classification may be of two kinds, either artificial or 
 natural. In an artificial classification, the principle of classi- 
 fication selected is some characteristic which is external to 
 the essential nature of the elements to be classified. In a 
 natural classification, the principle of classification selected 
 is a property which forms a constituent part of the essential 
 nature of the elements to be classified. 
 
 1. In an artificial classification the characteristic which is 
 selected as the basis of the classification is either an accident, 
 or at least an unimportant property of the elements to be 
 classified. The consequence is that the various members of 
 the classification which fall together in the same group 
 possess in common only this arbitrary or artificial mark 
 selected as the basis of classification, and are dissimilar in 
 all other respects. 
 
 This kind of a classification is best illustrated by the 
 alphabetical catalogue of books in a library. The initial 
 letter of the author is regarded as a differentiating mark. It 
 brings together in one group an indiscriminate variety of 
 books which have in common merely the one artificial mark. 
 Such a classification, however, serves its purpose most satis- 
 factorily in furnishing a convenient key for reference. 
 
 An artificial classification generally may be said to per- 
 form some such function as this, namely, of realizing some 
 definite and specific purpose, and is therefore essentially a 
 working classification. It must not be thought that an 
 artificial classification is necessarily an imperfect or unsat- 
 isfactory classification. On the contrary, for the end to 
 which it is designed, it serves a most useful purpose. 
 
 2. A natural classification is based upon one or more 
 
DIVISION AND CLASSIFICATION 
 
 57 
 
 properties directly connected with the essential nature of 
 the elements to be classified. In a natural classification the 
 members which fall together in the same group should not 
 only agree as regards the common property which is selected 
 as the basis of the classification, but also as regards a large 
 number of cognate properties. A property therefore should 
 be selected as the basis of classification which has the largest 
 number of correlated properties inseparably connected with 
 it, so that whenever the given property is present, the cor- 
 related properties will always accompany it. Such a 
 property is known as a diagnostic property. It is like the 
 significant symptom which indicates to the physician the 
 nature of a disease, because the symptom in question always 
 has a number of other symptoms correlated with it and which 
 forms therefore a basis of exact diagnosis. A diagnostic 
 attribute, therefore, will bring together in one and the same 
 group members of the classification which have in common 
 not merely a large number of properties, but these proper- 
 ties form a system of correlated and interconnected elements 
 which together constitute what is known as a natural kind. 
 In a natural classification, the various members therefore 
 form these groups of natural kinds, or, as they are sometimes 
 called, real kinds. In a zoological classification we would 
 have such natural kinds as vertebrates, mammals, reptiles, 
 etc. The mammals, for instance, have not merely the dif- 
 ferentiating mark in common, but also a complex system of 
 correlated properties which are built about the central and 
 distinguishing property of the kind. 
 
 Natural classifications obtain in all the sciences, wherein 
 the subject-matter is arranged in groups according to a 
 natural determination of kind. The classifications of ani- 
 mal and plant life are the best illustrations which we have 
 of natural classification. A natural classification furnishes 
 an excellent basis for comparative study, for, in the method 
 of grouping according to kind, resemblances are most easily 
 observed and significant relations suggested, while at the 
 
58 
 
 DEDUCTIVE LOGIC 
 
 same time characteristic differences are rendered most promi- 
 nent. It often happens in a natural classification that the 
 fundamental property chosen as the basis of the classifica- 
 tion, and which is of such a nature as to determine the 
 essential structure or function of a definite kind, is neces- 
 sarily of such a nature that it is not disclosed to a surface 
 observation. Thus the classification of birds, for instance, 
 is based largely upon fundamental differences in anatomical 
 structure. Birds, not as we see them, but as they are when 
 stripped of plumage and in their nakedness, are the real 
 objects of consideration in such a system of classification. 
 The result is that in the same group there will appear side 
 by side a number of birds whose surface markings are 
 exceedingly disparate, such as the blue jay and the crow, 
 or the English sparrow and the cardinal. It is always a 
 broadening experience, as regards our habits of thinking, 
 when we are able to discover some essential similarity at 
 the basis of a marked surface dissimilarity. 
 
 In arranging the various cognate species in any scheme 
 of classification, they should be arranged in some kind of 
 order so that the more closely allied species are placed side 
 by side. It is not only necessary to exhibit the unity under- 
 lying each distinct species, but also the connection which 
 exists between several species closely related to each other. 
 This is especially to be desired when several cognate species 
 together form a series of progressive development. In 
 such a series, every term representing a distinct species 
 should occupy a place in the classification which will at 
 once show its dependence upon the terms preceding it, 
 and its influence in turn upon the terms which follow it. 
 Every term thus looks before and after, and the series as a 
 whole is characterized by an ever increasing complexity of 
 attributes and functions. This principle of an ordered 
 series in classification, which the doctrine of evolution has 
 emphasized, is applicable not merely to the classification of 
 animal and plant life, but has a far wider sphere of applica- 
 
DIVISION AND CLASSIFICATION 
 
 59 
 
 tion. Herbert Spencer has taken the theory of biological 
 evolution, and has applied it with skill and insight to the 
 various branches of knowledge, as politics, sociology, history, 
 psychology, ethics, etc., so that as a result the classification 
 of the subject-matter in these disciplines shows a graded 
 series of progressive development. 
 
 The doctrine of evolution, moreover, has affected the 
 general theory of classification in the further demand that 
 the progressive series should exhibit as far as possible the 
 transition cases between the most closely allied of cognate 
 species. In the traditional view of classification according to 
 natural kinds, it was held most stoutly that each member of a 
 series of cognate species — that is, each natural kind — must 
 be regarded as cut off wholly from every other, even from 
 that with which it is most of kin. It is the ancient doctrine 
 of the immutability of species. The theory of evolution, 
 however, insists that the seemingly distinct species shade 
 off by inappreciable degrees of difference, so that the gap 
 between any two may be filled up by transition cases show- 
 ing the possibility of a continuous transformation from one 
 to the other. These transition cases, or missing links, can- 
 not always be supplied in experience ; but the contention of 
 the evolutionist is that in many cases they have been 
 supplied, and that if our experience were not so limited, 
 they could be supplied in many more. There is an illustra- 
 tion, however, which does show a classification in which the 
 transition cases between groups may be shown perfectly 
 without any defects due to the limitations of experience. 
 This illustration is from the sphere of mathematics, and 
 therefore is relieved of the complexities and consequent 
 difficulties which obtain in reference to natural phenomena. 
 We know that the various conic sections may be divided 
 into the following groups, — the point, straight line, circle, 
 ellipse, parabola, and hyperbola. These are not to be re- 
 garded as distinct classes, each one lying wholly outside 
 of all the others, but as so related that the circle for instance 
 
60 
 
 DEDUCTIVE LOGIC 
 
 may be exhibited as the special case of the ellipse, and that 
 it may be shown how through a continuous transformation 
 the ellipse may become a circle. In like manner, the 
 parabola may pass over into the ellipse on the one hand, 
 or into the hyperbola on the other. 
 
 When also limiting cases between species are forthcoming 
 in biological classification, they serve to form a graduated 
 series in which the presence of transition cases between 
 allied groups discloses their underlying unity. The tradi- 
 tional doctrine of the immutability of species breaks down 
 in the face of such instances. The distinct groups of fishes 
 and amphibians are differentiated by the presence of gills 
 in the one and of lungs in the other. In the case of the 
 so-called group of Dipnoi, the African mud-fish, there were 
 discovered in one and the same animal both lungs and gills. 
 It forms, therefore, an intermediate transition type between 
 the fishes and the amphibians. Moreover, the links which 
 the existing forms of animal life have not been able to 
 supply have been found in many cases in the record of 
 extinct forms preserved in the various geological strata 
 of the earth’s surface. 
 
 The unity of widely divergent species is illustrated by 
 Yon Baer’s law, that the history of evolution of species in 
 the race is repeated in miniature in the development 
 observed in the embryo of each individual. Thus the egg 
 of a bird in the various stages of transformation passes 
 through a series of forms, resembling in a rough way it is 
 true, but still resembling successively a worm, then a fish, 
 then an amphibian, then a reptile, and finally the full- 
 formed bird. That all these variations in form are due to 
 variations in the one constructive basal principle is clearly 
 seen, inasmuch as the different transformations occur within 
 the one organism, bounded by the enveloping wall of the 
 egg. It is the function of classification, therefore, to show 
 whenever it is possible the unity which underlies its various 
 groups, and holds them together in a single system through 
 
DIVISION AND CLASSIFICATION 
 
 61 
 
 bonds not of external relation merely, but of an inner kin- 
 ship. 
 
 Every science naturally seeks to arrange its material in 
 an orderly manner which results in some scheme of classifi- 
 cation. In the sciences such as zoology and botany, the 
 systems of classification are developed to such an extent of 
 detail that the intermediate genera and species between the 
 summum genus and the infima species are specified by a 
 series of terms which serve to indicate a more and more 
 elaborate degree of specification. These terms in their 
 order of specification are as follows : kingdom, group, sphere, 
 class, order, family, tribe, genus, subdivision, species, variety, 
 and finally, the separate individuals. These terms may not 
 all be used in any one system, but they form a kind of 
 skeleton scheme, any parts of which are available for the 
 general purposes of classification. It should be remembered 
 in this connection that the terms genus and species, accord- 
 ing to logical usage, are to be regarded always as relative 
 terms applicable to any classes whatever, which are sub- 
 ordinated one to the other. Thus the term order is a genus 
 as regards the family, but species as regards the class. 
 
 In a system of classification, the names assigned to 
 various species are often compound terms made up of the 
 genus and differentia of the species, e.g. fringed gentian, 
 red-winged blackbird, smooth-coated collie, etc. The name 
 not only indicates its place in the general system of classifi- 
 cation, but is at the same time a shorthand expression of its 
 definition. 
 
 Not only has each science a classification of its own 
 material, but attempts have been made also from time to 
 time to classify the various sciences in some one general 
 system which shall show their essential relations and 
 dependencies. This has proved to be a most engaging 
 problem to philosophical minds, a problem, however, as 
 perplexing as it is absorbing. There have been three 
 attempts in modern times which are of special interest, — 
 
62 
 
 DEDUCTIVE LOGIC 
 
 the classification of the general branches of knowledge by 
 Bacon, and the classifications of the sciences by Comte and 
 Spencer. 
 
 Bacon’s classification of all learning, his so-called “ Intel- 
 lectual Globe,” is based upon the threefold division of the 
 mind, — memory, imagination, and reason, to which corre- 
 spond the three general divisions of learning, history, poetry, 
 and philosophy. The classification in its main lines and 
 without going into all its minute ramifications is shown on 
 facing page . 1 
 
 This classification affords abundant scope for the exercise 
 of one’s critical faculty as regards the validity of the various 
 divisions which Bacon makes in the course of his analysis 
 of human learning. 
 
 Bacon insisted that every classification of human knowl- 
 edge should exhibit its various members as branches con- 
 nected with a common trunk ; the classification of Comte is 
 based upon a principle radically different. His purpose is 
 to show the various sciences in their order of progressive 
 development. He insists that together they form a series 
 of increasing complexity in which each science is dependent 
 upon those before it, and is itself a natural propsedeutic to 
 those which follow it. 
 
 Comte’s classification of the sciences proceeds in the follow- 
 ing order : Mathematics, Astronomy, Physics, Chemistry, 
 Biology, Sociology, the Science of Morals. In order that 
 the significance of this series may be fully appreciated, the 
 following passage from Comte is appended : — 
 
 “ In morals we study human nature for the government 
 of human life. All our real speculations, the most abstract 
 and the most simple not excepted, necessarily converge toward 
 this human domain, for indirectly they help us to the knowl- 
 edge of man under his lower aspects, on which the nobler are 
 dependent. . . . Paramount as the theory of our emotional 
 nature, studied in itself, must ultimately be, without this 
 1 Bacon, The Dignity and Advancement of Learning, Book II, etc. 
 
Human Learning- 
 
 DIVISION AND CLASSIFICATION 
 
 63 
 
G4 
 
 DEDUCTIVE LOGIC 
 
 preliminary step it would have no consistence. Morals thus 
 objectively made dependent on Sociology, the next step is 
 easy and similiar; objectively Sociology becomes dependent 
 on Biology, as our cerebral existence evidently rests on our 
 purely bodily life. These two steps carry us on to the con- 
 ception of Chemistry as the normal basis of Biology, since 
 we allow that vitality depends on the general law of the 
 combination of water. Chemistry again in its turn is ob- 
 jectively subordinate to Physics, by virtue of the influence 
 which the universal properties of matter must always exer- 
 cise on the specific qualities of the different substances. 
 Similarly Physics become subordinate to Astronomy when 
 we recognize the fact that the existence of our terrestrial 
 environment is carried on in perpetual subjection to the condi- 
 tions of our planet as one of the heavenly bodies. Lastly, 
 Astronomy is subordinated to Mathematics by virtue of 
 the evident dependence of the geometrical and mechanical 
 phenomena of the heavens on the universal laws of number, 
 extension, and motion .” 1 
 
 Mr. Spencer takes exception to Comte’s arrangement of 
 the sciences in serial order, insisting that such a grouping 
 of the sciences represents neither their logical dependence 
 or their historical dependence. In this connection he gives 
 his definition of a true classification which may be of inter- 
 est to quote here as we have already emphasized the 
 fundamental principle which lies at its basis. “ A true classi- 
 fication,” says Mr. Spencer, “ includes in each class those 
 objects which have more characteristics in common with one 
 another, than any of them have in common with any objects 
 excluded from the class. Further, the characteristics pos- 
 sessed in common by the colligated objects, and not possessed 
 by other objects, involve more numerous dependent charac- 
 teristics. There are two sides of the same definition. For 
 things possessing the greatest number of attributes in com- 
 mon are things that possess in common those essential at- 
 
 1 Comte, System of Positive Polity, Vol. IV, pp. 161-162. 
 
DIVISION AND CLASSIFICATION 
 
 65 
 
 tributes on which the rest depend; and, conversely, the 
 possession in common of the essential attributes implies the 
 possession in common of the greatest number of attributes .” 1 
 The classification of Mr. Spencer proceeds upon this 
 principle with the following result: — 
 
 that which treats of 
 the forms in which 
 phenomena are 
 known to us 
 
 Abstract Science 
 
 Logic 
 
 Mathematics 
 
 Science is 
 
 or 
 
 that which treats 
 of the phenom- 
 ena themselves 
 
 in their f ^tract- 
 
 elements concrete 
 [ Science 
 
 in their f Concrete 
 totalities | Science 
 
 Mechanics 
 
 Physics 
 
 Chemistry 
 
 etc. 
 
 Astronomy 
 
 Geology 
 
 Biology 
 
 Psychology 
 
 Sociology 
 
 etc. 2 
 
 In the above the terms abstract, abstract-concrete, con- 
 crete, need some further explanation in order that one may 
 understand the sense in which Mr. Spencer uses them. By 
 abstract sciences he would designate those sciences which 
 deal with fundamental principles detached from any par- 
 ticular incidents which may illustrate them ; as, for in- 
 stance, the necessary relations which obtain in logic and 
 mathematics and which maybe proved and formulated quite 
 apart from any concrete demonstration. By the compound 
 term abstract-concrete he means those sciences which are 
 partly concrete inasmuch as they investigate actual phenom- 
 ena themselves, but abstract inasmuch as the phenomena 
 investigated are only detached portions of more complete 
 
 1 Spencer, Essays, Scientific, Political, and Speculative, Vol. II, p. 76. 
 
 2 Ibid., Vol. II, p. 78. 
 
6G 
 
 DEDUCTIVE LOGIC 
 
 wholes, as, for instance, the examination in chemistry of the 
 special properties of oxygen by themselves and apart from 
 the whole body of chemical phenomena. By the purely con- 
 crete sciences, Mr. Spencer refers to those sciences which 
 investigate phenomena pertaining to complete aggregates, 
 and the relation of all separate parts to one combined 
 whole. Thus, as Mr. Spencer says : “ The geologist does not 
 take for his problem only those irregularities of the earth’s 
 crust that are worked by denudation ; or only those which 
 igneous action causes. He does not seek simply to under- 
 stand how sedimentary strata were formed; or how faults 
 were produced ; or how moraines originated ; or how the 
 beds of Alpine lakes were scooped out. But taking into 
 account all agencies cooperating in endless and ever varying 
 combinations, he aims to interpret the entire structure of 
 the earth’s crust. If he studies separately the actions of 
 rain, rivers, glaciers, icebergs, tides, waves, volcanoes, earth- 
 quakes, etc., he does so that he may be better able to 
 comprehend their joint actions as factors in geological 
 phenomena, the object of his science being to generalize 
 these phenomena in all their intricate connexions as parts 
 of one whole.” 1 
 
 These classifications of Bacon, Comte, and Spencer have 
 been given here somewhat at length inasmuch as they pre- 
 sent an excellent idea of the difficulties attending the classi- 
 fication of such complex phenomena, as well as to furnish 
 suitable material for the exercise of one’s critical faculty in 
 respect to the measure in which these systems have realized 
 the rigorous requirements of the laws of classification. 
 
 1 Spencer, Essays, Scientific, Political, and, Speculative, Vol. II, p. 89. 
 
CHAPTER VII 
 
 THE SINGULAR JUDGMENT 
 
 This type of judgment differs from the universal judg- 
 ment in the essential feature that it refers a single object of 
 thought to our general body of knowledge which serves to 
 interpret it, while the universal judgment is concerned solely 
 with the universal characteristics and relations which obtain 
 within the general body of knowledge itself. The singular 
 judgment deals with special eases in the light of our gen- 
 eral knowledge. The universal judgment deals only with 
 the various phases of general knowledge in the light which 
 is reflected from one part to another. The single instance 
 which forms the subject of the singular judgment may be 
 actually present in the field of perception, or it may be re- 
 instated in consciousness through the processes of memory. 
 The change in tense may be regarded as unessential, and 
 the term perceptive judgment is often used as synonymous 
 with singular judgment, whether the given perception is in 
 the past or present time. The so-called narrative judgment 
 is only the perceptive judgment referred to past time, and 
 therefore does not constitute a distinct type of judgment. 
 
 If the whole field of perception is taken in an indefinite 
 manner as the object of thought, and no particular part 
 of it specified for special consideration, then the judgment 
 which results is known as the impersonal judgment, e.g. It 
 is raining, it is hot, it is a charming day, etc. The imper- 
 sonal pronoun in such judgments refers to reality which is 
 present in consciousness in a wholly undifferentiated man- 
 ner. If, however, this indefinite range of reality is more 
 precisely determined by focussing the consciousness at any 
 
 67 
 
68 
 
 DEDUCTIVE LOGIC 
 
 one particular point in the field of perception, we have as a 
 result the so-called demonstrative judgments, introduced by 
 the demonstrative pronoun or adjective, e.g. This is magnetic 
 ore ; this black sand is magnetic ore. The latter is really a 
 combination of two judgments, This is black sand, and it 
 is magnetic. The perceptive judgment always originates at 
 the focal point of the perceptual processes, just as the uni- 
 versal judgment originates at the focal point of the concep- 
 tual processes. A similar variety of assertion is also possible 
 in reference to the perceptive or singular judgment as was 
 found to obtain in reference to the universal judgment. 
 Thus the single subject in perception, or in memory, may 
 be rendered definite by referring it to its appropriate genus 
 or species, or by describing it by its properties, differentia, or 
 accidents. 
 
 There are two functions of the perceptive judgment which 
 correspond in a general way to the two functions of definition 
 and division. Corresponding to definition there is the func- 
 tion of determinate reference. And corresponding to division 
 there is the function of indeterminate reference. 
 
 1. By determinate reference is meant the identification 
 of the single object of perception in question with its ap- 
 propriate genus or species, e.g. That is a fossil of the car- 
 boniferous age. In such a judgment we have satisfactorily 
 disposed of the single object of perception by referring it to 
 the general class to which it belongs. It is a process simi- 
 lar to that of definition. Indeed, this judgment may lead 
 naturally to a definition of the general class to which we refer 
 the specific object before us; for the question may be put, 
 What is a fossil of the carboniferous age ? The answer 
 would be its definition. In every process of referring a 
 single object of perception to the concept which explains it, 
 the knowledge of the definition of the concept employed is 
 always implicit in such a judgment. It is not explicitly 
 stated, however, unless the terms used need to be further 
 explained or illustrated. It should be remembered that a 
 
CHAPTER VIII 
 
 THE NEGATIVE JUDGMENT 
 
 So far in this discussion, judgments of assertion only, or 
 affirmative judgments, have been under consideration. We 
 come now to the examination of the negative judgment. 
 We have seen that the function of the copula in the affirma- 
 tive judgment is to fuse into one the subject and predicate 
 terms of the universal judgment, and in the singular judg- 
 ment to assert that the given object in the field of percep- 
 tion or in memory is one with the concept to which it is 
 referred. The process in either case is essentially con- 
 structive. 
 
 The negative judgment, on the other hand, holds apart the 
 subject and predicate terms. It denies the possibility of 
 explaining the one concept by the other, or of interpreting 
 the single case by the universal in question. The negative 
 judgment stands guard over our general body of knowledge, 
 excluding whatever is altogether false, and also whatever 
 may be false under certain conditions but may be true 
 under others. It is thus through the process of the nega- 
 tive judgment that thought becomes discriminating. Our 
 first judgments upon any unfamiliar subject are most 
 naturally vague and indefinite. The truth which they 
 contain is mingled with much that is erroneous. It may be, 
 as is often the case, that a given object of perception is 
 recognized as belonging to a certain genus, but we do not 
 know to which one of several species under this genus it 
 should be assigned. But as our knowledge grows, the 
 various special cases become distinct through well-recognized 
 differences, which, when stated, constitute a series of negative 
 
 73 
 
74 
 
 DEDUCTIVE LOGIC 
 
 judgments. This process of differentiation serves to render 
 knowledge more exact. This is essentially the method 
 which Socrates pursued with his pupils, asking of them the 
 meaning of some idea, such as virtue, or justice, and then 
 examining the conventional definition given in the light of 
 certain concrete instances of virtue or of justice which 
 differed radically from the definition. Accordingly the 
 definition had to be changed so as to adapt itself to these 
 negative cases. In this manner vague and general notions 
 upon which little thought had been bestowed were trans- 
 formed into clear and precise ideas. The old dictum, Omnis 
 determinatio est negatio, expresses the essential function of 
 the negative judgment as that of exact determination through 
 the process of negation. This process of negation sets a 
 limit beyond which a given concept cannot be applied. A 
 limit thus set serves as a boundary of exact determination. 
 It marks always a line of distinction between what is and 
 what is not as regards the essential nature of any concept. 
 The process of exact determination by means of negation 
 may be analyzed into its three component stages which form 
 the programme of all exact thinking : — 
 
 1. The first rough draft of knowledge, which is neces- 
 sarily vague and indefinite. 
 
 2. The critical limitation of this primary assertion by a 
 number of negative judgments, which show where it breaks 
 down, where it does not apply, and wherein the unessential 
 may be eliminated. 
 
 3. The reconstruction of the original statement modified 
 by the necessary restrictions, which the process of negative 
 criticism has disclosed as essential. The result is knowdedge 
 in exact and definite form. 
 
 Thus the beginner in the study of chemistry has a vague 
 idea of chemical affinity, — that certain elements enter into 
 a number of various combinations to form compounds. But 
 as his knowledge grows, he finds himself face to face with a 
 series of negative facts, which must be reckoned with, — ■ 
 
THE NEGATIVE JUDGMENT 
 
 75 
 
 namely, that all elements indiscriminately do not combine 
 together ; that they which are capable of combining do not do 
 so in any proportions whatsoever ; that combinations which 
 are possible under certain temperature conditions are not in 
 others ; that elements which unite under ordinary circum- 
 stances will not unite in the presence of certain other 
 elements. Consequently, when the idea of chemical affinity 
 comes to be restated in the thought of the advanced student 
 of the subject, it must be necessarily more definite and exact 
 by reason of these very negative instances which have 
 emerged in the course of his investigations. 
 
 Moreover, every negative judgment which possesses any 
 value as knowledge must rest upon some positive ground. 
 Mere denial of itself means nothing. For when pushed for 
 a reason of our denial, we must be prepared to give some 
 positive ground for the conviction that is in us. When we 
 say, It will not rain to-night, our judgment rests upon our 
 interpretation of the actual weather conditions. We venture 
 the negative statement because we are positive concerning 
 the significance of the present atmospheric conditions. And 
 also, if we should say of a certain friend, He did not do 
 the mean act of which he is accused, we rest such a denial 
 upon our knowledge of his character, abundantly tested and 
 proved by years of close companionship. If a person should 
 affirm that he does not expect to be conditioned in a certain 
 examination, and the only ground he could allege for his 
 belief were merely the indefinite feeling that he would 
 not fail, such an uncertain foundation would be absolutely 
 worthless. A definite negation must have the ground of 
 definite knowledge, or otherwise it has no force. 
 
 A distinction moreover is often drawn between signifi- 
 cant and non-significant denial. Significant denial occurs 
 within the region which lies near the line of differentiation 
 between affirmation and negation. The non-significant de- 
 nial occurs in the region remotely separated from this line 
 of differentiation. Thus, to say that a chrysanthemum is 
 
76 
 
 DEDUCTIVE LOGIC 
 
 not an animal would be a non-significant denial. But to 
 say that one of the lower orders of animal such as that of 
 the sea-anemone is not a chrysanthemum would be a sig- 
 nificant denial, because it resembles the chrysanthemum in 
 external appearance. There are so many marks in common 
 that one may fail to recognize at the first glance the 
 differentiating mark which separates the two cases. 
 
 Significant denial often carries with it also the implication 
 that under certain changed conditions the relation or refer- 
 ence which is denied would become true. Thus the state- 
 ment that water does not boil on the top of a mountain at 
 212°, implies that it would boil however at some other tem- 
 perature. If we say that the elements, oxygen and hydrogen, 
 will not unite in a one-to-one proportion, there is the impli- 
 cation that they will unite in some other proportion. Again 
 the statement, that a certain man having made such a politi- 
 cal blunder could not be nominated for governor, implies 
 that had it not been for the political blunder in question, he 
 might have been nominated for governor. A distinction 
 however should be drawn between limiting conditions and 
 conditions whose removal do not alter the force of the 
 original denial. Thus in the statement, Do not trust the 
 Greeks bearing gifts, the phrase “bearing gifts” is not a 
 limiting condition, the removal of which would alter the 
 statement at all. The meaning is, Do not trust the Greeks 
 even though they bear gifts ; that is, do not trust them at 
 all. Likewise the statement, There are no ghosts in mod- 
 ern times, should not be interpreted as meaning that there 
 were ghosts in ancient times. The nearer incompatible con- 
 cepts approach a limit beyond which denial passes over into 
 assertion the more significant does the denial become, and 
 the greater the possible difference of opinion which may 
 arise in reference to it. It is in the field immediately adja- 
 cent to the limiting cases that dispute arises. When I say 
 that the American Beauty rose is not yellow, no one disputes 
 such an assertion ; and, moreover, there is no suggestion in 
 
THE NEGATIVE JUDGMENT 
 
 77 
 
 this statement as to the real color of the American Beauty. 
 But if I say that a certain shade of red does not match a 
 given sample, the denial on my part may provoke a differ- 
 ence of opinion ; and because the range of variation is so 
 narrow, the implication is that the true color must be very 
 near the one mentioned and within the region of the various 
 shades of red. 
 
 If denial asserts an incompatibility between concepts 
 which is absolute, — that is, if there is no common point of 
 similarity at all between them, — the judgment is called an 
 infinite negation. Such judgments being completely with- 
 out significance are always nonsensical ; e.g. A stone has no 
 conscience. A triangle has no lungs. Between the limit on 
 the one hand of the infinite negation, and on the other of 
 the limiting case which separates denial from assertion, 
 there are all grades of denial possible according to the order 
 of their growing significance. Near the limit of assertion 
 denial becomes the subject of dispute and controversy. 
 Further removed the denial is unquestioned. Further still, 
 it becomes a truism, a commonplace of knowledge, soon 
 passing into the region of the grotesquely absurd and mean- 
 ingless. To know just where assertion ends and where 
 denial begins is characteristic of the exact mind ; to know 
 just where denial ceases to be significant is characteristic of 
 the relevant mind. 
 
CHAPTER IX 
 
 THE CATEGORICAL, HYPOTHETICAL, AND DISJUNCTIVE 
 JUDGMENTS 
 
 There are three forms which our judgments may take, — 
 the categorical, hypothetical, and disjunctive. 
 
 The categorical judgment is assertion in its simplest form, 
 unconditioned, unanalyzed, and unexplained ; e.g. That man 
 is a half-breed ; whales are mammals. It expresses either 
 a fact, or else a generalization based upon a number of 
 facts. 
 
 The hypothetical judgment is an assertion subject to a 
 given limitation, or regarded under certain specified condi- 
 tions. It does not refer to a concrete special case, but 
 rather to the abstract universal relations which form the 
 ground of all the possible special cases which may be con- 
 ditioned by the relations ; e.g. If in an isosceles triangle a 
 line is drawn from the apex perpendicular to the base, it 
 will bisect it; if hydrogen, oxygen, and sulphur unite in 
 the proportions H^S0 4 , they will form sulphuric acid. 
 
 Our knowledge, it must be remembered, forms a system 
 of interrelated parts. The hypothetical judgment is con- 
 cerned essentially with the necessary connections which 
 obtain between these various elements. It asserts the 
 fundamental relations which exist between any ground and 
 its consequence. In our body of knowledge regarded as a 
 system, the hypothetical judgments constitute the basal 
 lines of construction ; by them part is related to part, and 
 part to the whole. 
 
 The disjunctive judgment is an indeterminate assertion 
 concerning various possibilities which may exist in refer- 
 
 78 
 
VARIETIES OF JUDGMENT FORMS 79 
 
 ence to a given subject, and which are of such a nature that 
 the establishment of the truth of any one necessarily excludes 
 the others ; e.g. The invading fleet may attack Newport, Cape 
 Cod, or Gloucester. One may travel from New York to 
 Philadelphia by the Reading, or the Pennsylvania rail- 
 roads. 
 
 We have divided all judgments into two general types, 
 — the singular judgment and the universal. Of these, the 
 singular judgment is naturally categorical, for it is an 
 assertion concerning a fact or a group of facts. If the 
 categorical is changed in form so as to make it a hypo- 
 thetical, this is done by reason of a universal hypothetical 
 judgment of which the singular hypothetical judgment in 
 question is merely a special case, and therefore the hypo- 
 thetical nature is due to the universal relation which is as- 
 sumed as underlying it. Thus in the judgment, If this 
 substance is an acid, it will turn blue litmus paper red, we 
 see that the hypothetical relation expressed concerning the 
 special case is merely a single instance of a relation which 
 holds universally. It is only in this indirect manner that 
 a hypothetical judgment can apply to a special case. The 
 hypothetical is essentially a mode of expressing universal 
 relations. There are two cases in which the hypothetical 
 form of judgment is naturally used. 
 
 1 . When we wish to express the necessary connection of 
 cause and e ff ect between any given elements in a system 
 of related parts, e.g. If you double the pressure, you halve 
 the volume of gases. 
 
 2. When we wish to express a more exact differentiation 
 of our concepts by means of a reference to their specific 
 differences, e.g. If a triangle has two of its sides equal, it 
 is an isosceles triangle. The hypothetical form is used also 
 when the differentiating mark cannot be regarded as of the 
 essence of the concept in question, and even when it is abso- 
 lutely arbitrary, provided only it serves to point out unmis- 
 takably the concept in question. Thus the signal of Paul 
 
80 
 
 DEDUCTIVE LOGIC 
 
 Revere was in this form, If the enemy come by land, there 
 will be a single light in the belfry ; if by sea, two lights. 
 
 The essential function of the hypothetical is to show this 
 relation of dependence of any one element upon another in a 
 system of interrelated and coordinated parts. The system it- 
 self may be one of nature, or one arbitrarily assumed or agreed 
 upon by mutual consent, or of common convention. The 
 main thing is that the system should be of such a nature 
 as to render the connection which constitutes the hypotheti- 
 cal relation absolutely uniform and necessary. 
 
 It is of course possible to change any categorical judg- 
 ment of the universal form into a hypothetical. Thus, 
 All crows are black, may be put into the form, If there is a 
 crow, it is black. The hypothetical in this case is however 
 not the natural form of expression, and the reason is that 
 in such a judgment the necessary connection of ground and 
 consequent is not brought to the fore. There must be 
 in the very constitution of the crow a sufficient ground 
 for its customary color ; nevertheless its precise nature is 
 unknown and lies in the background of the simple asser- 
 tion itself. It can be said therefore in general that when 
 a universal judgment presents an unanalyzed content, it 
 takes the categorical form ; when however the content is 
 analyzed so as to exhibit within it the connection of ground 
 and consequent, then it takes the hypothetical form. 
 
 Again, the disjunctive judgment naturally expresses a 
 universal relation. When it refers, as it often does, to a 
 special case, the disjunction is really based upon our knowl- 
 edge of general conditions. When we say, for instance, 
 that a certain line must be equal to, greater than, or less 
 than some other given line, we do so because we know that 
 any line whatsoever must be equal to, greater than, or less 
 than any other given line. So also a physician may pronounce 
 a suspicious case of sore throat to be either scarlet fever or 
 diphtheria. His judgment in this case is grounded wholly 
 upon his knowledge of such cases in general. Therefore, 
 
VARIETIES OF JUDGMENT FORMS 
 
 81 
 
 although the disjunctive judgment may in form deal with 
 a single instance, it always contains by implication a refer- 
 ence to the universal conditions which are illustrated in the 
 special case. 
 
 The disjunctive judgment, moreover, contains both a 
 categorical and a hypothetical element. It is categorical 
 inasmuch as it asserts a definite area of possibility. It is 
 hypothetical inasmuch as the possibilities are related in 
 such a manner that if any one is true, the others are false, 
 and if any one is false, one of the others must be true. 
 Such a hypothetical implication renders the disjunctive 
 judgment significant; otherwise it would be without mean- 
 ing. To illustrate this, let us examine the following dis- 
 junctive judgment, A certain murder was committed by an 
 enemy or by a burglar. The categorical element in this 
 assertion limits the possibilities to the two alternatives 
 mentioned, and excludes suicide or any other possibility. 
 The hypothetical element lies in the implication that if 
 either one of the possibilities is proved, it negatives the 
 other. 
 
 Moreover, the categorical, disjunctive, and hypothetical 
 judgments may be regarded as various stages in the prog- 
 ress of knowledge from that which is indefinite and inde- 
 terminate to that which is definite and determinate. 
 
 The categorical judgment represents the primary stage 
 of vague assertion, wherein the conditions upon which the 
 asserted fact depends have not been fully analyzed. 
 
 The disjunctive is a statement of the various antecedents 
 which may have given rise to the given fact. 
 
 The hypothetical is the critical analysis of these various 
 antecedents, and the determination of that particular one 
 which bears an essential and necessary relation to the fact 
 in question. 
 
 All knowledge necessarily begins with a vague assertion. 
 The very fact that it is a beginning renders the assertion 
 vague. We hear, for instance, that a man has died suddenly 
 
82 
 
 DEDUCTIVE LOGIC 
 
 under suspicious circumstances. Our first statement is 
 merely that a murder has been committed. A closer exam- 
 ination of the surroundings will suggest various possibilities 
 by way of explanation. We settle finally upon the definite 
 conviction that the murder was committed by an enemy; 
 because we know that the dead man had an enemy who 
 had repeatedly threatened to take his life, and we have 
 therefore the general hypothetical principle to guide us, 
 that if a man has an enemy who has repeatedly threatened 
 to take his life, that man’s murder may be presumably 
 traced to this as its explanation, provided there are no 
 other guiding indications. Or if the question should be 
 raised as to which one of several possible species is referred 
 to in any given instance, then we have a series of significant 
 hypothetical to assist us in the exact determination. We 
 may have the disjunctive statement that whales are either 
 sperm whales or right whales. This is more precisely de- 
 termined in our body of general knowledge by means of 
 the two hypotheticals : if the whale does not have in its 
 mouth baleen or whalebone, it is a sperm whale ; but if it 
 has baleen in its mouth, it is a right whale. 
 
 The process of the exact determination of a disjunctive 
 judgment may be effected through a series of negative judg- 
 ments as well as positive. Instead of determining any one 
 member of a disjunction positively, by discovering its differ- 
 entia or necessary condition, we may reach a like result by 
 a process of elimination. If we have given several possible 
 explanations of a certain situation we may examine each in 
 turn and prove it to be impossible, and so narrow the range 
 by successive elimination until one only is left. Negation 
 becomes especially significant when there are but two 
 possibilities in reference to any given situation. The elimi- 
 nation of either one leaves the other in full possession of 
 the field. Thus, if in the case of a murdered man it can be 
 proved negatively that he never had an enemy, and that 
 there was no one who would have sought his life through 
 
VARIETIES OF JUDGMENT FORMS 
 
 83 
 
 hatred or because of an injury received, we are then forced 
 to the explanation that the man was murdered by a burglar 
 or some one other than an enemy. This process of elimina- 
 tion by negation is trustworthy so far as we are sure that 
 the negative judgment is true, and that also we have com- 
 pletely embraced all possibilities in our disjunction. 
 
 We have seen that every process of judgment consists in 
 establishing a unity of some kind among the elements of our 
 thought. Now this unifying bond in judgment admits of 
 a certain degree of variability, being more or less definite in 
 nature. Its degree of variability determines what is known 
 as the modality of judgments. 
 
 If this unifying bond is actual, the judgment is known as 
 an assertorical judgment. If the judgment expresses a pos- 
 sible relation only, it is a pr oblem atical judgment. If the 
 judgment expresses a necessary relation, — that is, where the 
 unifying bond expresses not merely that which is but that 
 which must be, — the judgment is known as a oodei ctic. 
 
 The categorical judgment naturally takes the assertorical 
 form, e.g. x is y. 
 
 The disjunctive judgment naturally takes the problemati- 
 cal form, e.g. x may be y, or 2, or w. 
 
 The hypothetical judgment naturally take the apodeictic 
 form, e.g. If x is y, then 2 must be w. 
 
 There may, however, be a change of modality as regards 
 any one of the forms of judgment, — categorical, disjunctive, 
 or hypothetical. Thus the categorical judgment will be 
 found in the various forms as follows : x is y, x may be y, 
 x must be y. The first of these is the natural way of express- 
 ing the categorical ; for the form, a; may be y, implies other 
 possibilities, and at least the negative possibility that x may 
 not be y. Therefore the problematical mode of the judgment 
 is to be regarded as implying a disjunctive. Moreover, the 
 categorical form, x must be y, implies a hypothetical judg- 
 ment as its basis, for the assertion of necessity naturally 
 implies some knowledge of the fundamental relation of 
 
84 
 
 DEDUCTIVE LOGIC 
 
 ground and consequent which underlies such necessity. 
 Thus each phase of modality has its own natural form of 
 expression; the assertorical expressing itself in the categori- 
 cal judgment, the problematical in the disjunctive, and the 
 apodeictic in the hypothetical. 
 
CHAPTER X 
 
 THE NATURE OF INFERENCE 
 
 The nature of inference may be unfolded in two ways. 
 We may consider what it is iu its outward aspect ; that 
 is, through its phenomenal manifestation in what it effects ; 
 or it may be more strictly defined in terms of its warrant 
 or ground. From the first point of view we examine infer- 
 ence as regards its psychological significance ; that is, 
 what is inference considered as a psychical experience, its 
 nature, and characteristics ? But we must consider also the 
 second question, — whether there is any necessity limiting 
 and determining the subjective experience, which presents 
 the character of a law having universal validity. What 
 goes on in the mind during the process of inference ? Also, 
 what is the rationale of such a process ? These questions 
 we will examine more closely, in order to show the nature 
 of inference under the two aspects, the one psychological 
 and the other logical. 
 
 It is a well-recognized fact in psychology that, in our 
 simplest as well as the more complex perceptions, the inter- 
 pretation of the data of perception always goes beyond the 
 strict content of the data themselves. We see more than is 
 giveu in the field of vision immediately before us. The mind 
 supplies here and there the necessary parts that are lacking in 
 the actual elements of perception, and yet which are necessi- 
 tated by the known nature of that which is actually given. 
 We form our judgment of distance indirectly, and not through 
 direct observation. So, also, our idea of a third dimension is 
 acquired by a process, marvellously complex, in which the 
 data both indicate and yet are transcended by the results. 
 Whether the nativist or empiricist holds the true position 
 
 85 
 
8G 
 
 DEDUCTIVE LOGIC 
 
 concerning original psychical experience, it still must be 
 conceded according to either theory that the development 
 of our perceptions corresponds to a law of growth based 
 upon accumulated inferences. Inference has been defined 
 as the indirect reference of a content to reality, and as such 
 we see the beginnings of inference in the most simple of our 
 perceptions. Every perception contains a direct reference 
 to reality, but also something which in a greater or less 
 degree is '-eferred indirectly to reality. The fact that our 
 knowledge as given in the complete perception contains 
 more than is actually mediated through the avenues of the 
 senses is due to the apperceptive processes of consciousness. 
 Mind is active in perception, and not a mere passive recep- 
 tacle. That which is given, the raw material of the senses, 
 is elaborated and extended, as it is combined with the 
 wealth of representative and conceptual material, which 
 the mind brings to every new perception. To this extent, 
 at least, the mind possesses a creative function. A certain 
 appearance of sky, combined with peculiar conditions of 
 wind and temperature, leads one to assert, with some de- 
 gree of certitude, that it will rain before morning. The 
 prediction is an inference based upon and growing out of 
 the actual data of perception, and yet far outrunning them. 
 We recognize a friend from his step or voice. The mere 
 perception is only a sound. That it is associated with a 
 person, and not an animal, or a thing, is an inference ; that 
 it is the particular person whom we recognize as a friend 
 and can call by name, even before we turn around to con- 
 firm the opinion by direct testimony of vision, this is a still 
 further inference. And even when we open our eyes in 
 simple vision itself, we fill up many a gap in our minds, 
 and give depth and distance, and interpret the contrasts 
 of light and shade, and the play of colors, through the 
 process of inference, although we may not be aware of the 
 process itself, which is automatically operative through 
 long-continued habit. When we thus regard inference as 
 
THE NATURE OF INFERENCE 
 
 87 
 
 a psychological phenomenon, it may be readily explained 
 by the laws of comparison, association, recognition, generali- 
 zation, etc. And, as such, inference has a subjective force, 
 at least, and leads to the habit of prediction and expecta- 
 tion. The will, influenced by the resulting belief, leads 
 to activities consistent with such expectation. 
 
 Here, however, the question arises which is urged with 
 such force by Hume, Is there objective validity as well as 
 subjective necessity ? This leads to a consideration of 
 inference, from the second point of view, above mentioned. 
 We may be constrained to believe certain things concerning 
 the great world lying beyond the sphere of immediate con- 
 sciousness ; but what warrant have we in so doing, or what 
 assurance that our conclusions are correct ? May we not be 
 deceived, after all, and by some psychological trick be led to 
 regard the phenomena of consciousness as quite otherwise 
 than that which obtains in reality ? We may have a strong 
 aversion to sitting down at a table where the number of per- 
 sons will be thirteen. But has the subjective conviction, 
 that one of the thirteen will die in the course of the year, 
 any value when we come to refer it to reality, and ask our- 
 selves the nature of the ground upon which the conviction 
 is based ? 
 
 On the other hand however it is quite a different kind of 
 necessity which constrains us to judge that if a person jumps 
 off of the roof of a house, he must surely fall to the ground 
 below. Some grossly superstitious and ignorant people may 
 believe the former with as obstinate a conviction as the 
 latter, so that a purely psychological criterion of the 
 strength of conviction is not at all adequate or satisfactory. 
 Is there any other criterion ? In what instances does this 
 subjective constraint proceed from the necessities of reality ? 
 or, in other words, in what cases are we able to discover a 
 logically grounded warrant which compels the inference, in 
 distinction from the mere psychological compulsion which 
 is occasioned by the psychical tendencies of association and 
 generalization ? 
 
88 
 
 DEDUCTIVE LOGIC 
 
 This leads us to consider the logical, in distinction from 
 the psychological nature of inference. Inasmuch as the 
 characteristic feature of inference consists in this, that while 
 depending upon certain data of perception, it nevertheless 
 wholly transcends them, the question naturally suggests 
 itself, whether it is something within the data themselves, 
 cr without, by virtue of which the mind thus goes beyond 
 them in the process of inference. If it lies wholly without 
 the data, it must be something imposed upon them by the 
 mind, and as such can have only a psychological force and 
 value. For instance, the belief that if thirteen sit down 
 together at a table, one will die in the course of the year, 
 can have only a subjective value and significance. This is 
 true in all cases where the necessity of conviction finds its 
 origin in prejudice or in superstition, or it may be in the 
 force of authority. In all such instances we feel the lack 
 of a satisfactory logical ground. However, on the other 
 hand, if the data of consciousness contain within themselves 
 that which enables us to transcend them at the same time 
 that we interpret them, there is external validity for our 
 inference that has a logical worth. This seems at the first 
 glance to be a paradox. How can any content enable us to 
 state concerning it more than is contained within it ? The 
 answer to the seeming paradox is that every concept, and 
 every perception as well, have both an explicit and implicit 
 content. We never attain complete vision or perfect appre- 
 hension. 
 
 There are, moreover, many points of view, each giving 
 additional knowledge concerning any phenomenon present 
 in consciousness. We see, therefore, only in part, and yet 
 that which is seen contains certain necessary implications 
 concerning that which is not seen. In the progress of 
 knowledge, subsequent observations, different points of 
 view, are ever confirming and amplifying our inferences, 
 enabling us to perceive immediately what formerly was only 
 inferred. The process by which the implicit is becoming 
 
THE NATURE OF INFERENCE 
 
 89 
 
 explicit indicates a necessary relation existing between that 
 which is known mediately and that which is known imme- 
 diately. Moreover, consciousness has been represented as a 
 stream, or an intricately interwoven web, — something ex- 
 tremely complex. Every part is related both proximately 
 and remotely. There is no such thing as an isolated per- 
 ception ; every perception has its complex relations and 
 connections. So also every concept which is formed by 
 generalization through comparison and abstraction of our 
 perceptions as interpreted by us, possesses this character- 
 istic of greater or less complexity. In this manner the 
 world of consciousness is constructed, that is, the world as 
 it is for us. This forms a complex whole made up of parts, 
 which in themselves may be regarded as wholes, and yet 
 which may be still further divided and subdivided. 
 
 Such an interrelated whole we may style a system, or, in 
 other words, a complex whole whose parts are congruently 
 arranged. The idea of system finds expression in the “ Law 
 of Totality,” — that our knowledge is capable of arrange- 
 ment in a self-consistent and harmonious system, and which 
 moreover in its content and form faithfully represents 
 objective reality . 1 We find, therefore, that in the focus of 
 consciousness at any one time, whether in the sphere of per- 
 ception or in the region of representative or the conceptual 
 processes, whatever is given carries with it always certain 
 implications, and therefore certain necessary relations. This 
 is specially emphasized in Bosanquet’s definition of system : 
 “ System is a group of relations, or properties, or things, so 
 held together by a common nature that you can judge from 
 some of them what the others must be .” 2 Two facts re- 
 garded as independent and considered separately may give 
 no information beyond their explicit contents ; but when 
 conjoined, they imply more than the sum of their parts. 
 
 1 Ueberweg, A System of Logic and History of Logical Doctrine, pp. 
 540 f. 
 
 2 Bosanquet, The Essentials of Logic, p. 140. 
 
90 
 
 DEDUCTIVE LOGIC 
 
 How often two ideas in separate minds yield no result ; but 
 brought together, they give light. Isolation negatives 
 inference. To unfold whatever is given in all its manifold 
 implications is the process of inference. Its warrant lies in 
 the fundamental postulate of knowledge which we are con- 
 strained to assume ; namely, that our consciousness must be 
 self-consistent throughout. Whatever is admitted as true 
 must find a congruent place in the system to which it is 
 possible to refer it. The necessity of fitting it in its proper 
 place gives rise to certain implications which necessitate 
 corresponding relations and attributes. And if it could not 
 be put into such a place, we would feel that we should have 
 to surrender the idea of self-consistency in the variously 
 related elements of our consciousness. The very integrity 
 of our mental life necessitates this conviction. 
 
 Therefore a part being given, we supply in our minds 
 other parts, or the whole to which the given part must nec- 
 essarily belong. To achieve this, with logical warrant, our 
 knowledge of the part must be adequate to the extent that 
 we know that the element under consideration cannot be 
 complete in itself, but must be supplemented by its appro- 
 priately related elements which with it go to make up the 
 complete system. We infer the nature of the flower not yet 
 in bud by the sprouting leaf. The one necessitates the 
 other by virtue of their common inherence in the same plant 
 system. We know that figs do not come from thorns nor 
 grapes from thistles. Columbus, noting the seaweed, and 
 birds, and the drift of the sea, inferred a shore beyond, to 
 which he was constrained by the necessities of thought to 
 refer them. It is said of Cuvier that he was able to re- 
 construct part for part the entire frame and organism of an 
 animal whose fossil tooth alone formed the original datum. 
 He knew the system to which it must have belonged and to 
 which it alone could possibly be referred. An interesting 
 quotation from Cuvier himself illustrates most appropriately 
 this function of inference. He says, in his Ossemens Fossilen : 
 
THE NATURE OP INFERENCE 
 
 91 
 
 “ I doubt if any one would have divined, if untaught by 
 observation, that all ruminants have the foot cleft, and 
 that they alone have it. I doubt if any one would have 
 divined that there are frontal horns only in this class ; that 
 those among them which have sharp canines for the most 
 part lack horns. However, since these relations are con- 
 stant, they must have some sufficient cause ; but since we 
 are ignorant of it, we must make good the defect of the 
 theory by means of observation : it enables us to establish 
 empirical laws which become almost as certain as rational 
 laws when they rest on sufficiently repeated observations ; 
 so that now whoso sees merely the print of a cleft foot may 
 conclude that the animal that left this impression ruminated, 
 and this conclusion is as certain as any other in physics or 
 morals. This footprint alone, then, yields to him who 
 observes it the form of the teeth, the form of the jaws, the 
 form of the vertebrae, the form of all the bones of the legs, 
 of the thighs, of the shoulders, and of the pelvis of the 
 animal which has passed by.” 1 
 
 In the common conduct of everyday life we infer beyond 
 the immediate present experience to future happenings and 
 in a similar manner. My train is half an hour late. I 
 know I must miss my connections at the station ahead ; for 
 the train I am hoping to catch at that place is scheduled to 
 leave five minutes after the time of arrival of the train I am 
 now on. The time relations here necessitate my missing 
 my connections. This is rendered still more certain if they 
 are rival roads ; on no account will one wait for the other. 
 Moreover, the train I hope to make is made up and leaves 
 the station in question, and so I cannot fall back upon the 
 favoring chance that it also may be detained en route, and 
 so enable me, after all, to reach it in time. Thus, with 
 every additional knowledge of the system which forms the 
 ground of my inference, and the various conditions which 
 affect it, the validity of my inference is thereby increased. 
 
 1 Quoted by Jevons, Principles of Science, 2d ed., p. 683. 
 
92 
 
 DEDUCTIVE LOGIC 
 
 Inference regarded as the analysis of a system of inter- 
 related parts is illustrated in the following paragraph of 
 Professor James : “ The result of reasoning may be hit upon 
 by accident. Cats have been known to open doors by pulling 
 latches, etc. But no cat, if the latch got out of order, could 
 open the door again, unless some new accident at random 
 fumbling taught her to associate some new total movement 
 with the total phenomenon of the closed door. A reasoning 
 man, however, would open the door by first analyzing the 
 hindrance. He would ascertain what particular feature of 
 the door is wrong. The lever, e.g., does not raise the latch 
 sufficiently from its slot — case of insufficient elevation — • 
 raise door bodily on hinges ! Or door sticks at top by fric- 
 tion against lintel — press it bodily down ! I have a 
 student’s lamp of which the flame vibrates most unpleas- 
 antly unless the collar which bears the chimney be raised 
 about a sixteenth of an inch. I learned the remedy after 
 much torment, by accident, and now always keep the collar 
 up with a small wedge. But my procedure is a mere asso- 
 ciation of two totals, diseased object and remedy. One 
 learned in pneumatics could have named the cause of the 
 disease and then inferred the remedy immediately.” 1 
 
 Inference, therefore, may be regarded as a deep penetrat- 
 ing insight. The explicit is that which lies upon the surface, 
 which the mind immediately grasps, for it lies directly in 
 the focus of consciousness. Whereas the implicit is beneath 
 the surface, and is revealed only through a searching analy- 
 sis. This difference may be exhibited through the distinc- 
 tion between the actual and the potential. A child regards 
 gunpowder merely as a pile of coarse-grained sand. The 
 man sees what the child sees, but also the existing possibili- 
 ties under certain conditions of explosive force. He appre- 
 hends the potential as well as the actual ; and his inference 
 as to the possible results is based upon his superior insight. 
 It is therefore the well-furnished mind which sees things 
 1 James, Psychology, Vol. II, pp. 339, 340. 
 
THE NATURE OF INFERENCE 
 
 93 
 
 as most widely related, and discerns the potential as well 
 as the actual manifestation, which will prove the most 
 fertile in accurate inference, in prophetic suggestion, and 
 in inventive resource. 
 
 The whole world of reality, as well as that of knowledge, 
 may be considered as one system, embracing within the 
 unity of its totality all the various systems with their com- 
 plicated parts. From this point of view everything sustains 
 relations to everything else in the universe. The original 
 signification of the term universe is thus emphasized. This 
 thought, no doubt, Tennyson had in mind in the following 
 verse : — 
 
 Flower in the crannied wall, 
 
 I pluck you out of the crannies, 
 
 I hold you here, root and all, in my hand, 
 
 Little flower — but if I could understand 
 What you are, root and all, and all in all, 
 
 I should know what God and man is. 
 
 We can, in this connection, best exhibit the precise nature 
 and function of the universal in inference. The possibility 
 of unfolding the properties or relations of anything in all 
 its implications depends upon our knowledge of the univer- 
 sal concept to which the properties or relations in question 
 are naturally referred. While a singular proposition is the 
 statement of the mere occurrence of a phenomenon, the 
 universal always implies a knowledge of the conditions 
 and relations of the phenomenon . 1 Insight is only possible 
 where there is a wealth of universal concepts. We see an 
 animal which we observe to be cloven-footed. We infer 
 that it also chews its cud. We do not observe this. The 
 assertion does not arise directly from observed reality, but 
 indirectly through the generic concept that has grasped to- 
 gether the two attributes, of chewing the cud and cloven 
 feet as always and necessarily coexisting in one and the 
 same animal. Inference, in this sense, may be regarded 
 1 See Green, Philosophical Works , Yol. II, pp. 284, 285. 
 
94 
 
 DEDUCTIVE LOGIC 
 
 as the indirect reference of knowledge to reality, and this 
 is always mediated through the universal. The universal 
 has this characteristic feature, that it preserves an identity 
 in the midst of manifold differences. The same thought 
 may be expressed by saying that the universal manifests 
 a unity in the midst of diversity. However widely different, 
 in many respects, the animals may appear that chew the 
 cud, — as the cow, deer, sheep, etc., — there is always the 
 constant characteristic that they are cloven-footed. 
 
 Such a point of identity furnishes the constant factor 
 which determines the nature and the validity of the in- 
 ference. Were it not for this conceptual power of the mind, 
 this ability to grasp phenomena in their universal essence, 
 and consider them as interrelated and connected, we could 
 never pass beyond individual and particular experiences 
 which would form a series of wholly disconnected events. 
 Knowledge could not then form a self-consistent system, 
 or inference possess any higher worth than a haphazard 
 guess. As Green says, “ A ‘ mere fact,’ a fact apart from 
 relations which are not sensible, would be no fact, would 
 have no nature, would not admit of anything being known 
 or said about it.” 1 
 
 Moreover, inference is not merely employed to extend 
 the field of consciousness in unfolding supple mentai’y ele- 
 ments lying beyond the sphere of direct cognition; the 
 elements may all be given immediately, and inference em- 
 ployed to discover their connection and interrelations, and by 
 virtue of what bond they belong in one or the same system. 
 Inference here functions as explanation. A man is found 
 dead ; there are many wounds upon his person, and evidences 
 of a struggle in an out-of-the-way place upon a lonely road. 
 Such a combination of facts calls for an explanation which 
 shall be consistent with them. The facts must all be cor- 
 related in a system whose related facts and the unity of 
 the whole will completely satisfy the mind. The mind 
 1 Green, Philosophical Works, Vol. II, p. 301. 
 
THE NATURE OF INFERENCE 
 
 95 
 
 is satisfied only when all hang together in what seems the 
 only possible self-consistent coordinated system. The facts 
 being given, they must be read backward to their origin. 
 The other aspect of inference is the reading of facts for- 
 wards, or unfolding them in their necessary consequences. 
 Inference is the reply to the natural questions of the mind, 
 — whence and whither ? And the process is essentially the 
 same, whether its peculiar mode consists in the evolution or 
 the involution of that which is given in consciousness. 
 
 Moreover, the mere psychological inference, the subjective 
 extension of the data of consciousness without any objec- 
 tive ground or warrant, should ever be corrected, or even 
 at times wholly set aside by means of the truly logical 
 inference. Where the psychological experience, in tran- 
 scending simple presentation, proceeds upon strictly logical 
 grounds, and has objective validity as well as subjective 
 necessity, we possess a warrant of the highest possible 
 worth. 
 
 The relation of the process of inference to that of judg- 
 ment may be expressed in the following definition that in- 
 ference is a judgment plus the reason for it. Whenever the 
 reason for a judgment is obvious, the inferential element 
 falls into the background. The judgment then appears 
 merely as a restatement of a well-known truth which no one 
 would think of gainsaying, or as the result of referring a 
 familiar object of perception to its generally recognized 
 concept. But if the averred truth is challenged, or if the 
 reference of the perceived object is not clear, then in order 
 to make good the judgment, recourse must be had to some 
 phase of the inferential process. We have the accepted 
 judgment that lightning is a form of electrical discharge. 
 Such a statement commands assent without question. But 
 when Franklin proved the identity of these two phenomena, 
 it was by a process of inference in which it was necessary 
 to establish the common ground of these two phenomena. 
 If one should point to a bird circling above a field in 
 
DEDUCTIVE LOGIC 
 
 96 
 
 majestic lines of flight, and say, “That is an eagle,” the 
 observation would probably receive immediate assent. It 
 would pass then as an obvious judgment of perception. 
 
 If, however, the statement should meet with dissent, or an 
 opposed judgment should be urged that it is a crow, then 
 the inferential element revealing the necessary ground of 
 the judgment would at once come to the fore. It would 
 be possible to point out that the flight of the bird is so 
 characteristically the flight of an eagle that it could not be 
 mistaken or confused with that of a crow. It will be readily 
 seen that the inferential element is contained potentially 
 in every judgment. A direct assertion, received without 
 question, is the judgment in its simplest form. An indirect 
 statement, showing that it must be true because of its nec- 
 essary connection with some other judgment, is an inferred 
 judgment. In the light of this distinction the difference 
 between judgment and inference may be defined as fol- 
 lows : — 
 
 The judgment is a direct reference of a concept to reality. 
 
 The inference is an indirect reference of a concept to 
 reality. 
 
 The differentiating line is evidently a variable one. Its 
 variability depends upon the presence or absence of any 
 occasion which demands a fuller explication of the ground 
 of a judgment. As long as the ground is obvious and the 
 judgment unchallenged, it is not necessary to offer any proof 
 of it. If however it is necessary for any reason to give an 
 explicit statement of the ground underlying a judgment, 
 then at once the inferential element passes from its potential 
 stage into its developed form as actually expressed. It is 
 often the opposition of a negative judgment which provokes 
 the inferential process underlying some positive assertion. 
 
 Inference may be deductive or inductive. It is deductive 
 when the process shows that from a universal principle or 
 law there must follow some special case, or some more 
 special phase of that principle or law. It is inductive when 
 
THE NATURE OF INFERENCE 
 
 97 
 
 the process shows that a general principle or law must result 
 from the investigation of special cases. 
 
 When we reason that a man’s conduct under certain given 
 circumstances will be honorable or dishonorable, as the case 
 may be, our inference is based upon our general knowledge 
 of the man’s character, and the inferential process is one 
 of deduction. When however we reason that a man must 
 have a certain kind of character in the light of a number of 
 particular instances which we have observed, our inference 
 is based upon our interpretation of these special cases as re- 
 vealing an underlying universal nature which we call the 
 man’s character. Such a process is one of induction . 1 
 
 1 See Part II, Chapter I, on “ Deduction and Induction.’ 
 
CHAPTER XI 
 
 THE LAWS OF THOUGHT 
 
 In order that we may be able to justify our judgments 
 and relate them to each other and to the main body of our 
 knowledge, we must recognize certain fundamental and 
 universal principles known in logic as the laws of thought. 
 These laws are as follows : — 
 
 1. The Law of Identity. 
 
 2. The Law of Contradiction. 
 
 3. The Law of Excluded Middle. 
 
 4. The Law of Sufficient Reason. 
 
 1. The law of identity requires every concept to repre- 
 sent some phase of reality which remains essentially the 
 same. This does not mean an identity which admits of no 
 variety ; for we have seen that it is of the very nature of 
 the concept to manifest many shades of difference within 
 the variety of special cases which illustrate it. It does 
 mean however that in spite of manifold differences, there 
 is a central core of essential identity which remains con- 
 stant and unaffected by the various unessential changes. 
 This law has been formulated in the simple expression 
 A = A. Such an expression is true but meaningless, and 
 were the law of identity restricted to such an expression of 
 it, there could be no progress in thought, for every judg- 
 ment would be a mere tautology lacking any significance 
 whatever. The law would be more exactly formulated by 
 the expressions A = A! = A" = A"', etc. ; that is, every vari- 
 ety of A is nevertheless A, or every special case of A is the 
 same as every other special case of A in spite of all differ- 
 
 98 
 
THE LAWS OF THOUGHT 
 
 99 
 
 ences. This law therefore is merely the expression of the 
 unity which is the ground of all our judgments. Inasmuch 
 as inference has been defined as the reference of a judgment 
 to its proper ground, then this law, regarded as a law of 
 inference, demands that such ground must be something 
 abiding, no matter what variety of form it may assume. If 
 the ground to which we refer a judgment in the process of 
 inference is uncertain and shifting, then the inference itself 
 is invalidated. Every inference therefore requires as its 
 ground a relation which is constant, that is, identical with 
 itself. 
 
 This abiding ground which gives validity to our infer- 
 ence may be either (1) a single thing or person whose self- 
 identity is obviously preserved, or (2) it may be a universal 
 whose very nature is such that it preserves a unity in spite 
 of the manifold differences in the various instances which 
 illustrate it. As an example of inference wherein the 
 identity is that of a single person there is the story of 
 Thackeray’s of the old Abbe, who, one day conversing with 
 a party of intimate friends, chanced to say, “ A priest has 
 strange experiences; why, my first penitent was a mur- 
 derer.” At this moment, the principal nobleman of the 
 neighborhood enters the room. “ Ah, Abbe ! here you are ; 
 do you know, ladies, I was the Abbe’s first penitent, and 
 I promise you my confession astonished him ! ” The two 
 statements of the Abbe and the nobleman become signifi- 
 cant solely because of their identity of reference to one and 
 the same individual. 1 Again in the case wherein the identi- 
 cal ground is not an individual but is a universal, a state- 
 ment might be made that a certain cloth will fade. When 
 asked for a reason, the reply might be, because that cloth 
 contains a dye which always does fade. It is evident that 
 the validity of such an inference depends upon the constant 
 nature of the peculiar kind of dye in question. The show- 
 ing of a universal property of the dye, such as that of fading, 
 1 This illustration is taken from Bosanquet's Essentials of Logic, p. 140. 
 
100 
 
 DEDUCTIVE LOGIC 
 
 forms in this case the justifying, ground of the inference 
 that the cloth containing the dye will fade. A true uni- 
 versal assures an identical ground, and therefore the pos- 
 sibility of a constant reference as completely as does a 
 single individual. 
 
 2. The law of contradiction is that judgments which are 
 opposed to each other (as this is a, and this is not a ; or a 
 is b, a is not b) cannot both be true. The truth of either 
 one renders the other false. This is essentially the axiom 
 of consistency. It serves to buttress the law of identity. 
 The latter demands the preservation of a unity in spite of 
 differences. The law of contradiction draws a line of limi- 
 tation as a boundary to these differences. Beyond such a 
 line, the differences contradict the underlying unity which 
 must be preserved in accordance with the law of identity. 
 It prevents the reference of incompatible properties to one 
 and the same subject at the same time and in the same sense. 
 
 The law of contradiction applies to judgments which are 
 opposed in a contrary as well as a contradictory manner. 
 The contradictory, it will be remembered, is the general 
 term for the total area of negation lying outside the defin- 
 ing boundary of the positive term to which it is opposed. 
 The contrary is any special case of the contradictory which 
 may be designated by a part of the area of total negation. 
 The judgments a is b, a is not b, are contradictorily opposed. 
 The judgments a is b, a is c, are contrarily opposed when- 
 ever c is any property incompatible with b. To such judg- 
 ments the law of contradiction also applies ; if it is true that 
 a is b, then the statement that a is c must be false. 
 
 We have seen that a bare denial as in contradictory oppo- 
 sition is not significant, and that significant denial rests 
 upon the knowledge of some property or relation which is 
 contrary to the alleged assertion which it opposes. Most 
 of our denials, therefore, are contrary rather than contradic- 
 tory. Inconsistencies arise in thought more often by the 
 endeavor to unite properties slightly contrary than those 
 
THE LAWS OF THOUGHT 
 
 101 
 
 wholly contradictory. Controversies which take the form, 
 It is, It isn’t, and are conducted by continued reiteration 
 of bare assertion and denial, are always meaningless and 
 futile. If a statement is made that a certain ore is gold, 
 we may deny it merely by saying it is not. This is contra- 
 dictory opposition. We may say also, It is iron pyrites, 
 i.e. a special case of that which is not gold. The denial 
 is significant and represents contrary opposition. The law 
 of contradiction applies equally to the two cases. If the 
 statement, It is gold, is true, then both of the following 
 statements are negatived : It is not gold ; also it is iron 
 pyrites. 
 
 3. The law of excluded middle is, that between two 
 judgments contradictorily opposed there is no middle or 
 third judgment which is true. One or the other of the 
 two given judgments must be true. This law, however, 
 does not apply to judgments which express contrary oppo- 
 sition, for it is of the very nature of contraries that there 
 is middle ground between the extremes which they repre- 
 sent. Both statements, x is greater than y, x is less than 
 y, may be false, because of the middle possibility x=y. 
 However, contrary statements in the light of special circum- 
 stances which render them an exhaustive disjunction come 
 under the law of excluded middle, e.g. He had either to 
 jump from the window, or perish in the flames. The cir- 
 cumstances were such as to leave no other course open. A 
 contrary relation within a limited universe of discourse 
 thus ranks as a contradictory relation because the limita- 
 tion of the area of relevant subject-matter cuts out a 
 middle ground which in an unlimited universe of thought 
 might otherwise appear. Much of the loose thinking, 
 especially in untrained and unreflecting minds, arises from 
 the careless assumption of contradictory alternatives, when 
 in reality they are merely contrary. The middle ground 
 is overlooked, and logical confusion inevitably results. 
 The law of excluded middle always secures an exhaustive 
 
102 
 
 Deductive logic 
 
 disjunction, and therefore renders a negative statement 
 significant inasmuch as the other and opposed alternative 
 is then necessarily true. 
 
 4. The law of sufficient reason is that every judgment 
 must be based upon some satisfactory ground which fully 
 justifies it. This law was first formulated by Leibniz 
 (1646), and placed by him side by side with the law of 
 contradiction. It is so intimately associated with the 
 great philosopher that it would be worth while to have 
 his own statement of it. “Our intellectual inferences rest 
 on two great principles: the principle of contradiction, and 
 the principle of sufficient reason, in virtue of which we 
 know that no fact can be found real, no proposition true, 
 without a sufficient reason why it is in this way rather 
 than in another.” This law is essentially the statement of 
 the fundamental logical basis upon which all inference 
 rests, namely, that our knowledge forms a system of inter- 
 related and coordinated parts, and that any single element 
 can be determined only when its relation is known to some 
 other element or elements upon which it depends. It is 
 a law which recognizes a reciprocal dependence of part to 
 part throughout the entire body of knowledge. It is a 
 corollary of this law that every judgment contains a poten- 
 tial inference ; for every judgment is true in so far as it is 
 based upon a sufficient ground, and to render explicit the 
 ground upon which it rests is itself the process of inference. 
 
 In these four laws we find that certain logical demands 
 are made to which all processes of thought must adhere. 
 The law of identity demands a basis of constant reference", 
 the law of contradiction, that of consistent treatment ; the 
 law of excluded middle, that of an exhaustive survey of 
 possibilities ; and the law of sufficient reason, that of ade- 
 quate explanation. There are many rules which are given 
 for guidance in the various processes of inference, which, 
 however, are merely adaptations of some one or other of the 
 several phases of these four fundamental principles. 
 
CHAPTER XII 
 
 IMMEDIATE INFERENCE 
 
 In the traditional logic the distinction is drawn between 
 immediate and mediate inference, the former being the di- 
 rect reference of a judgment to its ground, the latter the 
 indirect reference of a judgment to its ground through the 
 medium of one or more intervening judgments. Such a dis- 
 tinction, however, will not hold. All inference is indirect. 
 Indeed inference is defined as the indirect reference of a 
 concept to reality. The difference between the so-called 
 immediate and mediate inference is rather one of degree. 
 
 In the immediate inference from a given proposition in the 
 form, All x is y, to the derived proposition, Some x is y, the 
 process is not as direct as it seems. It assumes, tacitly at 
 least, another mediating judgment that whatever is true of 
 a class generically is true of every member of the class, — 
 the old Aristotelian dictum. Such a judgment as this, how- 
 ever, is so obvious that it falls into the background, and 
 the inference seems to be immediate. Immediate inference, 
 therefore, may be regarded as an abbreviated form of infer- 
 ence in general. The term “ immediate reference,” however, 
 in the history of logic, is not applied to any inference what- 
 ever which employs an obvious mediating judgment, but it 
 is restricted to certain definite aspects of inference dependent 
 upon general considerations of a self-evident character. 
 These considerations give rise to two well-defined types of 
 immediate inference according as the process is one of 
 implication or transformation. 
 
 1. The process of implication depends upon the funda- 
 mental relations which exist between “all” and “some” and 
 
 103 
 
104 
 
 DEDUCTIVE LOGIC 
 
 between “yes” and “no”; that is, if we have a judgment, for 
 instance, in the form of a universal affirmation, all are, what 
 is implied in reference to the particular affirmation, some 
 are, or the universal negative, none are, or the particular 
 negative, some are not? The possible combinations which 
 we are able to make with the terms, “all,” “some,” “none,” 
 “ some not,” give us four distinct types of judgment which 
 for convenience of reference are designated by the four 
 vowels A, E, I, and 0 as follows : — 
 
 A — The Universal Affirmative ; All x is y. 
 
 E = The Universal Negative ; No x is y. 
 
 I = The Particular Affirmative ; Some x is y. 
 
 0 = The Particular Negative ; Some x is not y. 
 
 Judgments which differ as universal and particular are 
 said to differ in quantity ; those which differ as affirmative 
 and negative are said to differ in quality. It will be seen 
 that the question of the various implications involved in the 
 relations which these several kinds of judgment sustain to 
 one another, is a general question which has to do with the 
 significance of the forms which all our judgments assume, 
 whatever may be their content; for any judgment concern- 
 ing any object of knowledge must be put in one or another 
 of these four forms. 
 
 Now if a judgment in any one of these four forms is given 
 as true, certain necessary implications will follow in refer- 
 ence to the other three. Likewise, if any judgment is given 
 as false, certain necessary implications will follow. 
 
 In order to exhibit these relations in as clear a manner as 
 possible, Aristotle devised the scheme of placing the four 
 kinds of judgment each at a corner of a square, known as the 
 Aristotelian square, or the square of opposition. The latter 
 term is misleading, however, as all the relations are not 
 opposed, but only those obtaining between affirmation and 
 negation. A better term, which covers all the possible rela- 
 tions, is implication. The judgments are arranged about 
 
IMMEDIATE INFERENCE 
 
 105 
 
 the square so that the universals are above, the particulars 
 beneath, the affirmatives at the left, and the negatives at the 
 right. This arrangement will give us the following : — 
 
 THE SQUARE OF ARISTOTLE 
 
 All xisy • No x is y 
 
 A Contrary E 
 
 In the above, the word “ some ” is to be regarded as equiv- 
 alent to “ some at least.” In the proposition, Some x is y, 
 there is no indication, as far as the bare form is concerned, 
 whether it may not also be true that All x is y, or, on the 
 other hand, that Some x is not y. “ Some,” used in this 
 sense, is the “ some ” of preliminary investigation, wherein a 
 connection has been established between x and y, but the in- 
 vestigation is not fully complete. Upon further research, it 
 
106 
 
 DEDUCTIVE LOGIC 
 
 may be that exceptions will be found which might render a 
 generalization impossible, or it may be that the connection 
 can be so firmly established as to admit of a generalization 
 as regards its logical force. “ Some,” in this sense, lies be- 
 tween the terms “ all ” and “ some only,” and is equivalent 
 to “ some at least.” 
 
 Now, as regards the various relations which this diagram 
 illustrates, there are the following : — 
 
 1. The subaltern relation between the universal (either 
 affirmative or negative) and its corresponding particular is 
 so called because the particular is regarded as being subor- 
 dinated to the universal. The relation between universal 
 and particular is such that if the universal is true, the par- 
 ticular is true also ; but if the particular is true, the truth 
 of the universal is left in doubt. The truth of a particular 
 judgment, as based upon the truth of the corresponding uni- 
 versal, follows from our fundamental law of identity, that 
 the universal preserves its essential unity in all the particu- 
 lar forms of its manifestation. The indeterminateness of the 
 universal, when the particular is given as true, is due to 
 the possibility that the connection expressed by the particu- 
 lar judgment in question may be accidental, and therefore 
 not a part of the essential content of the species as a whole. 
 
 Moreover, if the universal is false, the particular is left in 
 doubt. It may be true or false, according to the concrete 
 circumstances in any given case. The reason for this is 
 that the bare denial of a universal is always ambiguous. It 
 may be a total denial by confronting it with the opposite 
 universal, or it may be a partial denial by pointing out 
 exceptions to it ; which, of course, render the affirmed uni- 
 versality false. But the falsity of a particular renders its 
 corresponding universal false; for, if the particular state- 
 ment is not true, much less will be the universal, which 
 embraces the particular under it. 
 
 2. The contrary relation between A and E propositions is 
 such that if either of the related judgments is true, the other 
 
IMMEDIATE INFERENCE 
 
 107 
 
 must be false, but if either is false, the other is indeter- 
 minate. For it is obvious that between “ all ” and “ none ” 
 there is middle ground, and therefore they are related as con- 
 traries ; and it is the nature of the contrary relation that, 
 according to the law of contradiction, the truth of one ren- 
 ders the other false ; and, as there is middle ground between 
 them, the law of excluded middle does not apply, and there- 
 fore the fact that one is false merely leaves the other inde- 
 terminate. 
 
 3. The subcontrary relation between I and 0 is the inverse 
 of the contrary. Here the falsity of either renders the other 
 true, but the truth of either leaves the other indeterminate. 
 This is perhaps more difficult to see. It should be remem- 
 bered that “ some ” = “ some at least.” Now, if it is false that 
 Some x is y, it must be true that Some x (at least) is not y, 
 which latter statement is not incompatible with the fuller 
 statement that No x is y, for it is merely a special case under 
 it. But if it is true that Some x (at least) is y, we have seen 
 that by the very significance of “ some ” thus interpreted, 
 the question as to whether there may be exceptions ex- 
 pressed in the form Some x is not y is left in doubt. 
 
 4. The contradictory relations between A and 0 and 
 between E and / are such that if either is true, the other is 
 false, and if either is false, the other is true. This follows 
 directly from the law of excluded middle. That the propo- 
 sitions, All x is y, and Some x is not y, have no middle 
 ground between them is evident. It may be put in this 
 way : if a judgment is always true, it admits of no excep- 
 tions, and if it has exceptions, it is not always true ; if a 
 judgment is not always true, it must have exceptions, and if 
 it does not have exceptions, it must be always true. 
 
 These relations may be summarized as follows : — 
 
 1. Given A true, then I is true, the others false. 
 
 2. Given E true, then 0 is true, the others false. 
 
 3. Given A false, then 0 is true, the others unknown. 
 
108 
 
 DEDUCTIVE LOGIC 
 
 4. Given E false, then I is true, the others unknown. 
 
 5. Given I true, then E is false, the others unknown. 
 
 6. Given 0 true, then A is false, the others unknown. 
 
 7. Given I false, then A is false, the others true. 
 
 8. Given 0 false, then E is false, the others true. 
 
 These eight statements may be still further condensed as 
 follows : — 
 
 I. Given A or E true, I or 0 false, the corresponding 
 subaltern is the same, the others opposite. 
 
 II. Given A or E false, I or 0 true, the corresponding 
 contradictory is opposite, the others unknown. 
 
 There are two practical suggestions which emerge from 
 these dry symbols, which may prove not only interesting 
 but also of some value. (1) The one is that the trend of 
 logical thought is always from the universal to the particu- 
 lar, from “ all ” to “ some,” and that procedure in the oppo- 
 site direction is one of the most fertile sources of error in 
 thinking. It is the well-known fallacy of hasty generali- 
 zation, namely, the collecting of a few instances of experi- 
 ence and immediately raising them to the rank of a 
 universal. There is no procedure of thought which needs 
 to be so carefully safeguarded as that from “ some ” to 
 “all.” (2) Again there is the principle which I would 
 call, the economy of refutation. It is this : Whenever in 
 discussion or debate a universal judgment is advanced, do 
 not attempt to controvert it by the opposite universal, but 
 rather by the opposite particular. There will be less diffi- 
 culty in proving a particular, and thus a strategic point of 
 advantage will be gained. If a proposition is advanced in 
 the form All x is y, to refute it, it is only necessary to prove 
 essential exceptions in the form of Some x is not y. Thus 
 in the Harvard-Princeton debate in 1896, the question was, 
 Resolved that Congress should take measures to retire all 
 the legal tender notes. Princeton maintained the affirm a- 
 
IMMEDIATE INFERENCE 
 
 109 
 
 tive. Harvard’s attack upon this position was not, as might 
 have been expected, a universal negative, — namely, that no 
 legal tender notes should be retired by Congress, — but a 
 particular negative, that not all but only some should be 
 retired. It is a useful rule to remember in debate, — 
 never attempt to prove more than is necessary to overthrow 
 your opponent’s main contention. 
 
CHAPTER XIII 
 
 ON TRANSFORMATIONS OF JUDGMENT FORMS 
 
 The different forms of judgment may be subjected to 
 various changes, some of which give slightly new shades of 
 meaning, without however altering the logical force of the 
 judgment itself. The original judgment and its transfor- 
 mation must be logically compatible. This is the criterion 
 by which all transformations are to be tested. These trans- 
 formations may be produced in various ways : by an 
 
 interchange of subject and predicate; by a change in the 
 quantity or quality 1 of the judgment; by the change of a 
 term to its contradictory; or by certain complex changes 
 involving all of these. 
 
 The interchange of subject and predicate is called the 
 Conversion of a proposition. 
 
 If it is a proposition of the A form, All x is y, its simple 
 conversion will give All y is x. This, however, alters the 
 logical force of the original proposition ; for, if we have 
 given the form All x is y, it maj^ be that the predicate y is 
 the common mark of a number of species besides x, such as 
 x, z, w, etc. Therefore, y is not a distinctive mark of x at 
 all, and it does not follow that because All x is y, therefore 
 All y is x. In the conversion of an A proposition the uni- 
 versal force is lost, and only a particular is possible. Thus 
 All x is y becomes Some y is x. This is called conversion by 
 limitation, or conversio per accidens. 
 
 With the universal negative, however, No x is y, a simple 
 conversion is possible, because the negative asserts a com- 
 plete incompatibility of x and y, and such being the case, it 
 is a matter of indifference whether we say that x cannot be 
 
 1 See page 104. 
 
 110 
 
TRANSFORMATIONS OF JUDGMENT FORMS 111 
 
 fused into any unity with y, or that y cannot be fused into 
 any unity with a;. Thus No x is y becomes by conversion 
 No y is x. 
 
 With the particular affirmative form, Some x is y, a simple 
 conversion into Some y is a; is also possible, because if 
 some x forms a unity with y, some y at least must be pres- 
 ent with x to constitute that unity. Thus Some x is y 
 becomes, by conversion, Some y is x. 
 
 But with the particular negative, Some x is not y, the 
 simple conversion Some y is not x does not necessarily 
 follow; for the subject y may represent a species and the 
 predicate x its corresponding genus. Obviously, Some y 
 is not x will be false, for the species must fall wholly 
 within its corresponding genus. Thus if we have a judg- 
 ment of this kind such as, Some reptiles are not snakes, 
 and convert it, we get Some snakes are not reptiles, which 
 is obviously false. Thus a particular negative cannot be 
 converted. 
 
 The possibilities of conversion may be summarized as 
 follows : — 
 
 The above are the only transformations which are pos- 
 sible when we regard the form of the propositions merely. 
 If, however, in addition to their mere formal structure, we 
 take into consideration their content, — that is, the meaning 
 of the subject and predicate terms and their relation to each 
 other in any judgment, — then a greater range in conversion 
 is possible. 
 
 Thus, in the universal affirmative, if the subject and 
 predicate are coextensive terms, or if they are coordinate 
 properties of the one and the same concept, then a simple 
 conversion without change is possible. Given, All equian- 
 
 Con verted 
 
 Given 
 
 A All x is y . . . . 
 
 E No x is y . . . . 
 
 I Some x is y . . . . 
 
 0 Some x is not y . . 
 
 I Some y is x 
 E No y is x 
 I Some y is x 
 
 No result 
 
112 
 
 DEDUCTIVE LOGIC 
 
 gular triangles are equilateral. By conversion we have All 
 equilateral triangles are equiangular. 
 
 Or if the universal proposition is in the form of a defini- 
 tion, — i.e. a concept referred to its genus and differentia, — 
 then simple conversion is possible. Democracy is govern- 
 ment by the people. A government by the people is a 
 democracy. It is evident that an indefinite reference of a 
 concept to a class genus merely, or a description of a concept 
 by one or more of its attributes, will give a proposition 
 which admits of conversion only by limitation, i.e. change 
 of “ all ” to “ some ” ; but, on the other hand, a definite refer- 
 ence which serves to differentiate the concept in question 
 admits of simple conversion. 
 
 The same observation applies to the conversion of a 
 hypothetical judgment. Given a judgment of the form, 
 If x is y, z is w, it does not follow that if z is w, x is y ; for 
 there may be other antecedents which will give us z is w, 
 as well as the given one x is y. Thus, given the judgment, 
 If the democrats win, they must carry New York State, 
 it does not follow that if they carry New York State, they 
 will win. 
 
 It is the aim of all exact thinking, of all scientific formu- 
 lation especially, to render thought so definite that a simple 
 conversion is possible. It is not sufficient to refer a species 
 to a genus, which is a class embracing also many other 
 species, but to so refer the species in question by means of 
 its differentiating properties, that the reference will become 
 distinctive. Moreover, while a given consequent may follow 
 from many antecedents, it is the aim of exact thinking to 
 connect certain specific marks which accompany that con- 
 sequent with certain causal conditions present in some one 
 of the many possible antecedents and not present in the 
 others. Simple conversion is then of course possible. 
 
 Logical error arises when judgments expressing inexact 
 references are converted simply by unreflecting persons. 
 As, for instance, when an ignorant foreigner reasons that be- 
 
TRANSFORMATIONS OF JUDGMENT FORMS 113 
 
 cause all travellers who give unusually large tips are Ameri- 
 cans, that therefore all Americans will give unusually large 
 tips. The error is more apt to arise when subject and predi- 
 cate, or antecedent and consequent, approach very near the 
 boundary of simple conversion, but have not quite reached 
 it. The margin is so narrow however that it is overlooked, 
 and error naturally results. Thus, no one would think of 
 converting the proposition, All United States Senators 
 are members of Congress, into All members of Congress 
 are United States Senators, but many might fall into the 
 fallacy of converting the proposition, All the democrats 
 in the Senate voted against the bill, into All Senators who 
 voted against the bill were democrats. 
 
 The wider range of conversion which is rendered possible 
 by the consideration of content in addition to that of form 
 merely, may also be illustrated in the particular affirmative, 
 Given, Some x is y ; then, if it is known in addition that y 
 is a species of x, we may convert the particular into a 
 universal, and get All y is x as the result. Thus, if we 
 have given the judgment that Some birds of prey are vultures, 
 we can convert it so as to obtain All vultures are birds of 
 prey. 
 
 Again, in the particular negative, conversion, which is not 
 possible by consideration of form alone, becomes possible 
 if, on examination of conten t, we know that the predicate 
 is not a species of the subject. Thus, if we have given Some 
 birds of prey are not hawks, we can convert it into Some 
 hawks at least are not birds of prey. But if the predicate is 
 a species of the subject, conversion is impossible, e.g. Some 
 governments are not republics. The relation of form to 
 content is such in general that not merely is it impossible 
 to interpret the full significance of a proposition without 
 knowing its content, but also it is impossible to assent to 
 any formal statement whatsoever unless we know in addition 
 the significance of the terms used. The proposition, All x 
 is y, is a mere skeleton form, but in the actual judgments 
 
114 
 
 DEDUCTIVE LOGIC 
 
 of our thinking x and y are replaced by definite concepts 
 with a real significance. Our first thought, therefore, is 
 whether the real concepts which we substitute for x and y 
 in our symbolic form will admit of a universal affirmative 
 assertion, or of a universal negative, etc. Form without 
 content is meaningless ; content without form is confusion. 
 The one is always a function of the other. 
 
 We come now to a second kind of transformation, known 
 as Obversion. It consists in a change in the quality of a 
 proposition from affirmative to negative, or from negative to 
 affirmative, and at the same time a compensating change of 
 the original predicate to its corresponding contradictory. 
 If the original proposition is true, a single change of 
 quality would render the transformed proposition false, 
 therefore the predicate term is changed by way of com- 
 pensation, because the reference of any predicate to a sub- 
 ject has the same logical force as that of excluding the 
 contradictory of that predicate from the same subject. 
 Given, All such conditions are impossible, by obversion we 
 have No conditions of such a nature are possible. The 
 same process holds in the obversion of the other forms 
 of judgment, and we have the following tabulated sum- 
 mary : — 
 
 Given 
 
 All x is y A 
 
 No a; is y E 
 
 Some x is y I 
 
 . Some x is not y O 
 
 Obverted 
 
 No a; is not-?/ E 
 All x is not -y A 
 Some x is not-?/ 0 
 Some x is not-?/ I 
 
 The term “not-?/” is usually expressed by some form of a 
 negative affix such as impossible, ?«icontrollable, etc. 
 
 There are several complex transformations formed by 
 the combined processes of conversion and obversion. Of 
 these the so-called Contrapositive is formed by subject- 
 ing the given proposition to three transformations, as fol- 
 lows : — 
 
TRANSFORMATIONS OF JUDGMENT FORMS 115 
 
 1. Obversion. 
 
 2. Conversion. 
 
 3. Obversion. 
 
 Given the proposition : All scholarly work is logical, 
 
 1. By obversion, No scholarly work is illogical. 
 
 2. By conversion, No illogical work is scholarly. 
 
 3. By obversion, All illogical work is unscholarly. 
 
 In the final proposition, which is the contrapositive, it 
 will be seen that the subject and predicate of the original 
 proposition have been interchanged and each replaced by 
 its corresponding contradictory. The contrapositive may be 
 defined, therefore, as a transformation which subs titutes 
 for the given terms their corresponding contradictories, 
 and at the same time interchanges the subject and predi- 
 cate positions. The three processes by which the contra- 
 positive is formed may be omitted, and the contrapositive 
 formed directly according to the above definition. The 
 processes, however, form the proof that this direct transfor- 
 mation is admissible. 1 
 
 There is another proof for the contrapositive of a uni- 
 versal affirmative which is as follows : Given, All x is y ; 
 then All not-y is not-x\ For what is not-y must be either 
 x or not-x. But if it is x, it is also y, according to the 
 given proposition. This, however, is impossible, for the same 
 concept cannot be both not-y and y. Therefore, the other 
 alternative must be true, namely, that not-y must be not-x, 
 which was to be proved. 
 
 When an A proposition is given, its contrapositive is also 
 an A proposition. When, however, the given proposition is 
 of the E form, there is a loss of logical force, and the result 
 of the three processes is an 0 proposition. 
 
 1 Some logicians regard the contrapositive as the result merely of the 
 two processes, obversion and conversion. This, however, is merely a mat- 
 ter of definition, and no confusion can result, because the additional process 
 of obversion simply carries the operation one step farther. 
 
116 
 
 DEDUCTIVE LOGIC 
 
 Given, No insane persons are responsible, E. 
 
 (1) By obversion, All insane persons are irresponsible, A. 
 
 (2) By conversion, Some irresponsible persons are in- 
 sane, I. 
 
 (3) By obversion, Some irresponsible persons are not 
 sane, 0. 
 
 In a similar manner it will be readily seen that the 
 contrapositive of an 0 proposition is also an 0 proposition. 
 The I proposition yields no contrapositive, because the first 
 step of obversion gives an 0 proposition ; the second step of 
 conversion cannot be applied to an 0 proposition, and con- 
 sequently the process is blocked at this point. 
 
 It is well to remember that the contrapositive is formed 
 by taking contradictories of the original subject and predi- 
 cate ; for, if contraries are taken, the process is rendered 
 invalid. For instance, if we have given the proposition, 
 All honest acts are moral, the contrapositive, according to 
 rule, would seem to be, All immoral acts are dishonest. 
 This, however, is not true, and the reason is that the terms 
 “honest” and “dishonest” are not contradictory but contrary, 
 for between honest and dishonest acts there is the middle 
 ground corresponding to acts concerning which the ques- 
 tion of honesty is not raised at all. 
 
CHAPTER XIV 
 
 A GENERALIZATION OF IMMEDIATE INFERENCES 
 
 As the various immediate inferences by opposition have 
 been generalized in the ancient logical square, the question 
 suggests itself, cannot a similar method be applied to the 
 other forms of immediate inference ? And the following 
 is the result of the problem thus proposed. 
 
 The possible ti’ansformations of a simple proposition may 
 occur in any of the following ways : by a change of the 
 quality of a proposition, i.e. change from affirmative to 
 negative and vice versa; or, by a change of quantity, i.e. 
 from universal to particular and vice versa; or by a change 
 of either subject or predicate terms by substituting for them 
 their respective contradictory terms ; or, by an interchange 
 of subject and predicate in the proposition. Of these pro- 
 cesses or combinations of them, the ones which are legiti- 
 mate inferences are as follows: — 
 
 Having given, for example, an A proposition, All x is y, 
 it is possible to infer : — 
 
 (1) The converse, Some y is x. 
 
 (2) The obverse, No x is not-,?/. 
 
 (3) Converted obverse, No not-y is x. 
 
 (4) Contrapositive, All not-y is not-x. 
 
 (5) Obverted converse, Some y is not not-x. 
 
 (6) Inverse, Some not-x is not y. 1 
 
 (7) Obverted inverse, Some not-x is not-y. 
 
 1 The inverse of a proposition has the same predicate, but for its sub- 
 ject the contradictory of the original subject. 
 
 117 
 
118 
 
 DEDUCTIVE LOGIC 
 
 These transformations may be comprehended in the fol- 
 lowing logical square : — 
 
 x E not-y 
 
 A or I A or I 
 
 y 0 not-x 
 
 Here I have placed the terms *, y, and their contradic- 
 tions, not-*, not-y, in the corners of the square so that any 
 term and its contradiction will be situated diagonally oppo- 
 site. The letter A, E, I, or O, indicates that the two terms 
 between which the letter is situated may be formed into a 
 proposition of the character represented by that letter, and 
 in every case such a proposition is a legitimate inference 
 from the original proposition, All * is y. Thus, between 
 the two upper terms, * and not-y, there are possible two 
 universal negative propositions, one the converse of the 
 other : — 
 
 No * is not-y, E. 
 
 No not-y is *, E. 
 
 Between the two lower terms, two particular negative 
 propositions : — 
 
 Some y is not not-*, 0. 
 
 Some not-* is not y, 0. 
 
 Between either upper one as subject and corresponding 
 lower one as predicate there is possible a universal affirma- 
 tive. This gives : — 
 
 All * is y, A. 
 
 All not-y is not-*, A. 
 
 Between either lower term and corresponding upper one 
 there is possible a particular affirmative. This gives : — 
 
A GENERALIZATION OF IMMEDIATE INFERENCES 110 
 
 Some y is x, I. 
 
 Some not-x is not -y, I. 
 
 By comparison of these results with the legitimate infer- 
 ences given at the beginning of this discussion, there will 
 be seen an exact correspondence. This square, therefore, 
 summarizes exhaustively all possible legitimate infer- 
 ences. 
 
 I would note in passing that of the two inferences of the 
 0 form, while one is the converse of the other, still it is 
 not derived from the other by conversion, which process 
 is logically inadmissible, but is derived independently : 
 Some y is not not-x, being the obverted converse, and Some 
 not-x is not y being the inverse. 
 
 Again, when E is the original proposition, the possible 
 inferences are : — 
 
 (1) No y is x. 
 
 (2) All x is not-y. 
 
 (3) All y is not-x. 
 
 (4) Some not-y is x. 
 
 (5) Some not-y is not not-x. 
 
 (6) Some not-x is y. 
 
 (7) Some not-x is not not-y. 
 
 All of these are comprehended in the same square as that 
 indicating the inferences from an A proposition, provided 
 the positions of y and not-y are interchanged. This gives 
 the following square for inferences from an A 1 proposition : — 
 
 x 
 
 E y 
 
 A or I 
 
 A or 
 
 not-y o 
 
 not-x 
 
120 
 
 DEDUCTIVE LOGIC 
 
 This agrees with the fact that an A proposition, All x is 
 y, becomes by obversion an E proposition, No x is not-y; 
 in this transformation it is observed that not-?/ has displaced 
 y. Such a substitution will affect all inferences from the 
 original proposition uniformly. With this one change, 
 therefore, the inferences exhibited by the A square and 
 the E square coincide throughout. 
 
 The I square is the same as the A square, with the 
 exceptions that the E and A inferences become 0 and I, 
 respectively, and that the propositions indicated by the two 
 horizontal lines of the square are to be formed by reading from 
 left to right only ; also that no inference is possible between 
 not-x and not-//, i.e. no contrapositive of an I proposition is 
 possible. The I square is as follows : — 
 
 x 0 noUy 
 
 1 
 
 y 0 not-x 
 
 The possible inferences based upon an I proposition are 
 indicated in this square, and are as follows : — 
 
 (1) Some y is x. 
 
 (2) Some x is not not-y. 
 
 (3) Some y is not not-x. 
 
 The 0 square is the same as the I square, provided y and 
 not,-?/ are interchanged as above in the case of the E and A 
 diagrams. The following is the 0 square: — 
 
 x 0 y 
 
 I 
 
 not-y 0 not-X 
 
A GENERALIZATION OF IMMEDIATE INFERENCES 121 
 
 The possible inferences based upon an 0 proposition are 
 indicated in this square, and are as follows : — 
 
 (1) Some x is not -y. 
 
 (2) Some not-?/ is x. 
 
 (3) Some not -y is not not-*. 
 
 There is no relation between y and not-* as a possible form 
 of inference, inasmuch as the inverse of an 0 proposition is 
 impossible. 
 
CHAPTER XV 
 
 MEDIATE INFERENCE — THE SYLLOGISM 
 
 True inference always contains an element of mediation. 
 It is the process of grounding a judgment upon some other 
 judgment essentially related to it, and which stands as the 
 warrant of its truth. The reference of a judgment to an- 
 other judgment as its ground implies a knowledge of a 
 third judgment which expresses a universal and necessary 
 connection between the two. The complete process of me- 
 diate inference, therefore, consists in exhibiting a judgment 
 as the necessary result of the combination of two other 
 judgments. Thus, the judgment that a certain heap of 
 black sand is magnetic is justified when referred to its 
 ground, namely, that it attracts iron filings. To complete 
 the process, however, a third judgment is necessary, which 
 shall express the constant bond of connection between the 
 given judgment and its alleged ground, such as the judg- 
 ment that whatever attracts iron is magnetic. 
 
 This form which mediate inference naturally takes is the 
 syllogism, which is a process of combining two judgments so 
 as to produce a third. The above judgments expressed in 
 syllogistic form would be : — 
 
 Whatever attracts iron is a magnet. 
 
 This black sand attracts iron. 
 
 This black sand is a magnet. 
 
 It will be observed that the two judgments which combine 
 to produce the third have a term in common. This is the 
 middle term of the syllogism. Moreover, the third judg- 
 ment is formed by eliminating the middle term and taking 
 
 122 
 
MEDIATE INFERENCE 
 
 123 
 
 as its subject and predicate respectively the remaining 
 term in each of the two given judgments. The subject of 
 the judgment thus formed is called the minor term of the 
 syllogism, and the predicate the major term. Minor and 
 major are applied to these terms because in any judgment 
 the predicate generally refers to a larger class than the 
 subject. 
 
 Of the two given judgments, the one containing the major 
 term is called the major premise; and the one containing 
 the minor term, the minor premise. The premises take 
 their names from the major and minor terms, and not the 
 terms from the premises. In most syllogisms, the major 
 premise is placed before the minor; but this order is not 
 essential to the structure of the syllogism, or is it by any 
 means an invariable practice. The judgment which is 
 derived from the combination of the two premises is called 
 the conclusion. 
 
 It is the peculiar function of the major premise to ex- 
 hibit some phase of our general knowledge; and of the 
 minor premise, to exhibit some more particular phase of 
 our general knowledge, or, as it more frequently occurs, 
 some special case embodied in a concrete experience. It 
 is the function, therefore, of the two combined, — that is, of 
 the syllogism itself, — to apply universal knowledge to a spe- 
 cial case so as to yield its true interpretation. The process 
 is one which consists essentially in eliminating the middle 
 or common term. It is the same process which we find in 
 algebra. Equations are merely a special case of judgment. 
 The following is in every respect a true syllogism : — 
 
 x = y. 
 
 y = z. 
 
 x = z. 
 
 There is, however, a difference between the algebraical 
 equation and the ordinary logical proposition in this re- 
 spect that in the equation it is a matter of indifference 
 
124 
 
 DEDUCTIVE LOGIC 
 
 whether we say a; = y or y = x ; but the proposition cannot 
 be converted in this manner without impairing its logical 
 significance. 
 
 Compare the following syllogisms : — 
 
 (1) All x is y. (2) All y is a:. (3) Some x is y. 
 
 All z is x. All z is x. All z is a;. 
 
 .\ All z is y. All z is y. All z is y. 
 
 It is obvious that the first of these syllogisms is valid, the 
 other two invalid. Moreover, it is evident that the position 
 of the terms in the syllogism, as well as the kind of proposi- 
 tions employed in its structure, whether A, E, I, or O, 
 have an essential bearing upon its validity. How this 
 comes to pass and what criteria may be formulated for 
 testing the validity of syllogisms will appear in the fol- 
 lowing exposition concerning the so-called distribution of 
 terms. 
 
 A term is said to be distributed when it is used in a uni- 
 versal sense, and undistributed when it is used in a limited 
 or partial sense. The word distributed is regarded as 
 synonymous with universal, because it is of the nature of a 
 universal to distribute or apply the full force of its signifi- 
 cance to every individual case which is subsumed under it. 
 In the proposition, All the schoolmen were logicians, the 
 subject is distributed in the connection in which it is used, 
 so that what is affirmed of the class that they were logicians 
 can be affirmed of every individual of the class. The term 
 logicians in this connection is undistributed, because it is 
 only a part of the class of logicians that can be identified 
 with the schoolmen. 
 
 In respect to the four propositions, A, E, I, 0, the follow- 
 ing are the possibilities as regards distributed and undistrib- 
 uted terms. 
 
 1. The universal affirmative distributes the subject but 
 not the predicate. This will be evident, if the given propo- 
 
MEDIATE INFERENCE 
 
 125 
 
 sition be converted, for while All x is y, by conversion 
 Some y is x. 
 
 x is seen to be distributed, and y undistributed. 
 
 2. The universal negative distributes both subject and 
 predicate. It is a matter of indifference whether we say Ho 
 x is y, or by conversion No y is x. In the one case x is wholly 
 excluded from y, but that is the same as excluding y wholly 
 from x. 
 
 x is distributed, and y is distributed. 
 
 3. The particular affirmative does not distribute either 
 term. For Some * is y gives by conversion Some y is x. 
 
 .*. x is undistributed and y is undistributed. 
 
 4. The particular negative does not distribute the sub- 
 ject but does distribute the predicate. This cannot be 
 shown by converting the given proposition, for the par- 
 ticular negative does not admit of simple conversion. How- 
 ever, given the proposition Some x is not y, it is evident 
 that the subject, some x, is excluded wholly from y, there- 
 fore such exclusion must cut off all of y from that special 
 some x, which is its subject. 
 
 .-. x is undistributed but y is distributed. 
 
 The above results may be tabulated as follows, the dis- 
 tributed terms being marked with a V and the undistributed 
 with a °. 
 
 ✓ . ° 
 
 All x is y A. 
 
 </ v/ 
 
 No x is y E. 
 
 o . o 
 
 Some x is y I. 
 
 o # V/ 
 
 Some x is not y 0. 
 
 In determining whether a term is distributed in any 
 given proposition, the distribution of the subjects will be 
 readily recognized because indicated by the qualifying terms, 
 
126 
 
 DEDUCTIVE LOGIC 
 
 “all,” “some,” “none,” or “some not.” The distribution 
 of the predicates may be recalled by the following gen- 
 eralization which is obvious upon inspection of the above 
 table. 
 
 Affirmative propositions do not distribute their predi- 
 cates. 
 
 Negative propositions do distribute their predicates. 
 
 In reference to the criticism of any syllogism, there 
 are two fundamental rules of distribution which must be 
 observed : — 
 
 1. The middle term must be distributed at least once. 
 
 2. If a term is distributed in the conclusion, it must also 
 be distributed in its premise. 
 
 The middle term must be distributed at least once in 
 order to provide a common point of connection between the 
 two premises. For if the middle term is undistributed in 
 both premises, then the major term is related to a part of 
 the middle term in the major premise, and the minor term 
 is related to a part of the middle term in the minor premise, 
 and there is no assurance whatever that these two parts 
 have anything in common. 
 
 Given the premises (1) All x is y, 
 
 (2) All z is y, 
 
 the following diagrams will represent these relations 
 respectively. 
 
MEDIATE INFERENCE 
 
 127 
 
 There is nothing in the above relations, 
 however, to indicate whether within the 
 common circle y, x and 2 be wholly apart 
 as in the following diagram 
 
 or whether they have some common 
 ground as 
 
 or whether x falls within z as 
 
 or whether z falls within x as 
 
 The relation between x and z is left wholly indeterminate 
 by the given premises. If, however, the middle term is dis- 
 tributed at least once, it serves to bring the two premises 
 into a logically significant relation freed from all ambiguity. 
 It is not necessary, however, that it should be distributed 
 twice ; for the object of its distribution is to connect the 
 two premises. This connection once effected, it is not neces- 
 
128 
 
 DEDUCTIVE LOGIC 
 
 sary to secure it again ; if the middle term should happen 
 to be distributed in both premises, the existing connection 
 is merely confirmed and in no sense invalidated by such 
 twofold distribution. 
 
 The following syllogism will serve as a concrete illustra- 
 tion of the fallacy of an undistributed middle : — 
 
 All agnostics repudiate the methods of metaphysical in- 
 quiry. 
 
 All materialists repudiate the methods of metaphysical 
 inquiry. 
 
 All agnostics are materialists. 
 
 This conclusion does not necessarily follow. The middle 
 term, being in the predicate of an affirmative proposition in 
 each case, is undistributed. 
 
 The second rule that a term distributed in the conclusion 
 must also be distributed in its premise, is directed against 
 that illogical procedure from a term used in a partial sense 
 to the same term used in the universal sense. In the dis- 
 cussion concerning the opposition of propositions, it was 
 seen that the truth of the particular does not imply the 
 truth of the universal. It is the same principle which 
 emerges here. The truth of the universal carries with it, 
 however, the truth of the particular; therefore, it is per- 
 missible to have a term distributed in the premise and 
 undistributed in the conclusion. The beginner in logic is 
 liable to confuse these two modes of procedure ; therefore it 
 should be especially held in mind that the invalid procedure 
 is only from a term undistributed in the premise to the same 
 term distributed in the conclusion, or from the particular 
 to the universal. As a concrete illustration, take the fol- 
 lowing syllogism in which the distribution of terms is 
 marked : — 
 
 V ' O 
 
 All foreigners who are naturalized may vote. 
 
 v V 
 
 No native-born citizens are foreigners who are naturalized. 
 
 v v 
 
 No native-born citizens may vote. 
 
MEDIATE INFEKENCE 
 
 129 
 
 This conclusion is obviously incorrect; the major term 
 is distributed in the conclusion and undistributed in the 
 premise. When such invalid procedure is concerned with 
 the major term, it is called the illicit process of the major 
 term, or simply illicit major; when it is concerned with the 
 minor term, it is the illicit process of the minor term, or 
 illicit minor. 
 
 There are several special cases in which the general rules 
 for distribution must be somewhat modified : — 
 
 1. The predicate of some affirmative propositions is dis- 
 tributed because of a special significance which it may 
 possess. While according to form alone it would be undis- 
 tributed, the sense may afford additional information which 
 justifies its distribution. This is the same principle which 
 was seen to operate in reference to the conversion of a 
 universal affirmative proposition, All x is y to All y is x 
 when x and y are coextensive terms. 
 
 Thus the following syllogism is invalid because of an 
 undistributed middle : — 
 
 All x is y. 
 
 All z is y. 
 
 .-. All z is x. 
 
 Here the form alone serves as the test of its validity. 
 But in the filling up of such a form with significant terms, 
 the meaning may possibly render such a syllogism valid. 
 Thus, 
 
 Every government by the people is a democracy. 
 
 The United States is a democracy. 
 
 .-.The United States is a government by the people. 
 
 The middle term in this syllogism is undistributed as 
 regards its bare form. As regards the meaning of the terms 
 the major premise may be converted simply, every democ- 
 racy is a government by the people. The term democracy is 
 in reality therefore distributed, the subject and predicate 
 terms of the major premise being coextensive. 
 
130 
 
 DEDUCTIVE LOGIC 
 
 2. There are certain qualifying words which, while restrict- 
 ing the subject at the same time, distribute the predicate. 
 In all propositions of this kind the subject is undistributed, 
 and the predicate is distributed. The qualifying words are 
 “only,” “none but,” “alone,” and the like. In the proposi- 
 tion, None but members of the union will be employed, the 
 subject is undistributed, and the predicate distributed ; the 
 logical force of this proposition will be the more readily 
 seen if we convert it. It then becomes, All who are em- 
 ployed must be members of the union; in this form, the 
 subject is distributed, the predicate undistributed, as it is a 
 universal affirmative. 
 
 In the two syllogisms following, the first is valid, the 
 second is invalid, being a case of undistributed middle : — 
 
 (1) None but members of the union will be employed. 
 
 A certain man was employed. 
 
 He must have been a member of the union. 
 
 (2) None but members of the union will be employed. 
 
 A certain man is a member of the union. 
 
 •\ He must be employed. 
 
 In the criticism of the various modes of reasoning atten- 
 tion should be drawn to the fact that we seldom find our 
 thought expressed in the form of a complete syllogism. 
 Usually one of the parts of the syllogism is omitted, not, 
 however, because its force is unessential to the reasoning 
 process, but because it is so obvious that it is unnecessary to 
 state it explicitly. This condensed form of the syllogism is 
 known as the Enthymeme, so called, as its name indicates, 
 because a part of the syllogism is not expressed but in the 
 reasoning process is carried along in the mind. The omitted 
 portion is usually the major premise ; that is, the general 
 principle of which the course of the reasoning in question 
 forms the special case. Both the minor premise, or the 
 conclusion, may also be omitted in the construction of an 
 enthymeme. There are three kinds of enthymeme : — 
 
MEDIATE INFERENCE 
 
 131 
 
 1. With the major premise omitted. 
 
 This enterprise will tend to increase the public wealth, 
 because it will promote the general happiness of the people. 
 
 2. With minor premise omitted. 
 
 That expedition is doomed to failure, because no small 
 body of men insufficiently equipped and cut off from their 
 base of supplies can ever reduce so strongly fortified a 
 garrison. 
 
 3. With conclusion omitted. 
 
 All members of that conference were traitors to their 
 party. And you were a member of that conference. Noth- 
 ing more need be said. 
 
 The enthymeme may be tested as regards its validity by 
 supplying the omitted part, and then applying the usual 
 rules of the syllogism. But, inasmuch as the enthymeme 
 expresses the immediate connection between two judgments, 
 it may be subjected to direct criticism according to the 
 following criteria : — 
 
 If the major premise is omitted, the enthymeme consists 
 of a special case referred to its ground, This is x because 
 it is y. The enthymeme is valid, provided the ground as- 
 signed for the special case applies as well to all other cases 
 of the same kind ; that is, according to the symbols used, 
 if All y is x. 
 
 In the enthymeme, He is a free-trader because he is a 
 democrat, the connection is a valid one provided all demo- 
 crats are free-traders. 
 
 Again, if the enthymeme has the minor premise omitted, 
 it may be expressed in symbols, as follows: — 
 
 A certain thing is x, because All z is x. In such a relation, 
 the special case must be recognized as a special case of the 
 universal ; that is, we must know that the thing in question 
 is z. 
 
 For instance, given the enthymeme as follows : That 
 man is a German, for all the crew are Germans. The 
 inference based upon the assigned ground is valid, provided 
 
132 
 
 DEDUCTIVE LOGIC 
 
 we know that the man in question is a member of the crew ; 
 that is, if the single case falls with the area of the universal 
 which is stated as its ground. 
 
 Syllogisms may be combined in various ways into chains 
 of reasoning. When the conclusion of one syllogism becomes 
 the premise of a second syllogism, the former is called the 
 prosyllogism and the latter the episyllogism. When we 
 combine a number of prosyllogisms and episyllogisms so 
 that all the conclusions except the last are omitted, the 
 chain of reasoning is called the Sorites. There are two 
 forms of the Sorites, known as the Aristotelian and the 
 Goclenian. 1 
 
 These forms may be expressed symbolically as follows : — 
 
 I 
 
 Aristotelian Sorites 
 
 A is B. 
 
 B is a 
 <7 is D. 
 
 D is E. 
 
 A is E. 
 
 II 
 
 Goclenian Sorites 
 
 D is E. 
 
 C is D. 
 
 B is a 
 A is B. 
 
 A is E. 
 
 It will be seen that the middle terms cancel through- 
 out, and the conclusion is formed from the remaining terms 
 in the first and last premises. Thus, it may be reasoned 
 that a certain political boss has caused his chosen man to be 
 made governor of New York ; for he controls the machine, 
 and the machine controls the party, and the party controls 
 the state vote, and the state vote creates the governor. The 
 Sorites is commonly used to indicate the various links of 
 cause and effect which may be interpolated between an 
 effect and a remote cause. 
 
 The Sorites often appears in hypothetical form, for the 
 reason that the causal relation is best expressed by a 
 hypothetical. In the life of Sir James Fitzjames Stephen, 
 
 1 Named from Goclenius, a German logician of the sixteenth century. 
 
MEDIATE INFERENCE 
 
 133 
 
 the following remark of his tutor appears, which illustrates 
 the hypothetical form of the Sorites, and at the same time 
 will serve to show how plausibly a Sorites may express a 
 subtle fallacy : “ If you do not take more pains, how can you 
 ever expect to write good longs and shorts ? If you do not 
 write good longs and shorts, how can you ever be a man 
 of taste ? If you are not a man of taste, how can you ever 
 hope to be of use in the world ? ” 
 
CHAPTER XVI 
 
 MOOD AND FIGUKE 
 
 A syllogism may be constructed by combining in various 
 ways the four propositions, A, E, I, and 0. The particular 
 combination employed in any one syllogism constitutes the 
 mood of that syllogism. Thus, to refer to a syllogism as hav- 
 ing the mood AAA, means that the premises and conclusion 
 are all universal affirmative propositions; the mood EAE 
 means that the major premise is a universal negative, the 
 minor premise a universal affirmative, and the conclusion a 
 universal negative. The three letters designating the mood 
 are to be interpreted in the order of major premise, minor 
 premise, and conclusion. 
 
 The problem which the subject of mood presents is to 
 find which moods are valid ; for there are sixty-four possi- 
 ble permutations of three propositions out of four, repeti- 
 tions such as AAA being allowed. In order to discriminate 
 between the valid and invalid moods, the following rules 
 must be taken to guide us : — 
 
 1. A particular premise gives a particular conclusion. 
 
 2. Two particular premises give no conclusion. 
 
 3. A negative premise gives a negative conclusion, and 
 conversely if the conclusion is negative, one of the premises 
 must be negative. 
 
 4. Two negative premises give no conclusion. 
 
 The first and second rules follow from the rules relating 
 to distribution of terms ; this is obvious upon simple inspec- 
 tion. The third rule as to a negative premise giving a nega- 
 tive conclusion and its converse is based upon the necessary 
 
 134 
 
MOOD AND FIGURE 
 
 135 
 
 relation that if one of the two terms major or minor agrees 
 with the middle term and the other disagrees, then they 
 must necessarily disagree with each other ; that is, the con- 
 clusion expressing this disagreement must be in the negative 
 form. As to the rule that two negatives give no conclusion, 
 it is evident that when the major and minor terms both are 
 excluded from all relation to the middle term, no indication 
 whatever is given as to their relation to each other. Ac- 
 cepting these rules therefore as binding, let us examine their 
 effect upon the sixty -four possible permutations. This prob- 
 lem we will divide into two parts : — 
 
 (1) What pairs of premises are valid? 
 
 (2) What valid conclusions follow from them ? 
 
 First, the major premise may be either A, E, I, or 0, and 
 the minor premise may be either A, E, I, or 0. The per- 
 mutations resulting from combining these letters to form 
 possible pairs of premises are as follows : — 
 
 AA, AE, AI, AO. 
 
 EA, EE, El, EO. 
 
 I A, IE, II, 10. 
 
 OA, OE, 01, 00. 
 
 Of these the following cannot stand as pairs of prem- 
 ises : — 
 
 EE, because there are two negatives. 
 
 EO, because there are two negatives. 
 
 II, because there are two particulars. 
 
 10, because there are two particulars. 
 
 01, because there are two particulars. 
 
 OE, because there are two negatives. 
 
 00, because there are two negatives, and also two par- 
 ticulars. 
 
 Eliminating these tentative forms, there remain the fol- 
 lowing : — 
 
136 
 
 DEDUCTIVE LOGIC 
 
 AA, AE, AI, AO. 
 
 EA, EI. 
 
 I A, IE. 
 
 OA. 
 
 The second question is, given the above premises, what 
 conclusions are possible ? 
 
 AA will give as a conclusion either i or 7; but will not 
 give E or 0, for a negative conclusion requires one of the 
 premises to be negative. By inspection, after the same 
 manner, it will be found that AE will give two conclusions, 
 E and 0 ; so also EA. The remaining, with the exception 
 of IE, have each one conclusion, — All, AOO, EIO, IAI, 
 OAO. 
 
 The premises IE would seem to require the conclusion 0 
 and so form a valid mood IEO. This mood, in fact, squares 
 with all the special rules which we have formed above to 
 guide us in discussing this present problem. However, it is 
 impossible to construct a syllogism in this form which does 
 not contain an illicit major, for the conclusion, being nega- 
 tive, distributes the major term, and the major premise, being 
 7, cannot distribute either subject or predicate term. For 
 example, take the following syllogism : — 
 
 Some x is y I. 
 
 No z is x E. 
 
 Some z is not y 0. 
 
 7 is here distributed in the conclusion, but not in the 
 premise. The syllogism, therefore, in this form is impossible. 
 
 The valid moods which remain after this process of elimi- 
 nation which we have now completed are as follows: — 
 
 AAA AEE EAE All EIO OAO 
 
 (AAI) ( AEO ) (EAO) AOO IAI 
 
 The three in parentheses are called the weak moods of 
 the syllogism, because the conclusion in each case is really 
 
MOOD AND EIGUKE 
 
 137 
 
 implied in the stronger conclusion immediately above it, and 
 therefore they do not constitute distinct types. The truth 
 of A always necessitates the truth of 7, and the truth of E 
 always necessitates the truth of O. 
 
 There remain all together only eight distinct types out 
 of the sixty-four which are valid forms of the syllogism. 
 
 There is still a further problem which remains to be 
 considered, whether all of these moods are valid irrespec- 
 tive of the relative positions of the major, minor, and mid- 
 dle terms in the syllogism. The position of the middle 
 term in reference to the major and minor term constitutes 
 what is known as the figure of the syllogism. If we 
 represent the middle term by 31, the minor term by S, and 
 the major term by P, the four possible figures are as 
 follows : — 
 
 I 
 
 II III IV 
 
 M. P. P. 3f. 31. P. P. 3f. 
 
 S. 31. S. 3f. 31. S. 31. S. 
 
 S. P. .-. S. P. .-. S. P. .-. S. P. 
 
 A change in the relative position of the terms will of 
 course affect the matter of their distribution, and therefore 
 the validity of the various moods in the different figures 
 will turn upon the question of the distribution of terms. 
 The two rules for distribution, it will be remembered, are 
 as follows : — 
 
 (1) The middle term must be distributed at least once. 
 
 (2) If a term is distributed in the conclusion, it must be 
 distributed also in the premise. 
 
 The following are the valid moods in the several figures, 
 the invalid moods being stricken out, and the number 
 appended being the number of the rule violated in each 
 case : — 
 
138 
 
 DEDUCTIVE LOGIC 
 
 Figure I 
 
 Figure II 
 
 Figure III 
 
 Figure IV 
 
 AAA 
 
 AAA 
 
 -AAA 1 (. AAI ) 
 
 -AAA 2 (AAI) 
 
 AEE 2 
 
 AEE 
 
 -AEE 2 
 
 AEE 
 
 EAE 
 
 EAE 
 
 MAE 2 (EAO) 
 
 MAE 2 (EAO) 
 
 All 
 
 AH 1 
 
 All 
 
 -AH 1 
 
 -AAO 1 
 
 AGO 
 
 -ADD 2 
 
 -ADO 1 
 
 EIO 
 
 EIO 
 
 EIO 
 
 EIO 
 
 JAf 1 
 
 AAA' 
 
 IAI 
 
 IAI 
 
 OAO 
 
 -OAA) 2 
 
 OAO 
 
 -OAO 2 
 
 The first figure is called by Aristotle the perfect figure, 
 for it alone, he averred, conforms to the fundamental canon 
 of all reasoning. This canon of Aristotle is called the 
 Dictum de omni et nullo. It has come down to us from the 
 mediaeval logicians and is formulated as follows : — 
 
 Whatever is predicated affirmatively or negatively of a 
 whole class must be predicated affirmatively or negatively 
 of everything contained under that class. The affirmative 
 predication is expressed by the phrase de omni, and the 
 negative by de nullo. 1 
 
 Thus the perfect syllogism is a process of applying 
 our general knowledge (the major premise) to a special 
 case (minor premise), the conclusion being the special case 
 interpreted in the light of our general knowledge. 
 
 It will be readily seen, also, upon inspection, that the first 
 figure is the only one of the four which proves any one of 
 the four propositions, A, E, I, or 0, as its conclusion. 
 
 The second figure proves only negative conclusions. It 
 is used in proving distinctions between things. 
 
 The third figure proves only particular conclusions. The 
 moods with an I conclusion are useful in proving a rule 
 by positive instances ; the moods with an 0 conclusion in 
 proving exceptions to a rule. It will be noticed that in 
 the third figure the strong moods AAA and EAE are 
 
 1 Aristotle stated it, Whatever is said of the predicate is said of the 
 
 subject. 
 
MOOD AND FIGURE 
 
 139 
 
 invalid, but the weakened mood AAI and EAO are 
 valid. 
 
 The fourth figure was regarded by Aristotle as merely 
 an awkward variety of the figure, and therefore he ignored 
 it altogether. His pupils, Theophrastus and Eudemus, 
 however, added its five moods to Figure I, calling them 
 indirect moods. The fourth figure is called the Galenian 
 figure from Claudus Galenus (died about 200 a.d.), who 
 insisted upon ranking it upon the same footing as the other 
 three figures. In the fourth figure, also, the weakened 
 moods take the place of their corresponding stronger 
 moods, the latter being invalid. 
 
 The Latin schoolmen in the thirteenth century invented 
 a system of mnemonic verses for the purpose of assisting 
 the memory as regards the valid moods in each figure. 
 While such a mechanical device is not needed by the student 
 of logic, it is given a place in the text as a curious bit of 
 logical history. It furnishes also an excellent illustration 
 of the scholastic type of mind. The lines are : — 
 
 Barbara , Celarent, Darii, Ferioque prioris ; 0 : 
 
 Cesare, Camestres, Festino, Baroko, secundae, 
 
 Tertia, Darapti, Disamis, Datisi, Felapton, 
 
 Bokardo, Ferison , habet ; quarta insuper addit 
 Bramantip, Camenes, Dimaris, Fesapo, Fresison. 
 
 The words printed in italics are artificial words having no 
 significance whatsoever. Each word represents a mood, its 
 three vowels indicating the propositions which it contains. 
 The words “ prioris,” “ secundae,” etc., refer, of course, to the 
 figure in each case. Thus Barbara signifies AAA of the first 
 figure; Disamis, IAI of the third figure. Some of the 
 consonants in these words are also significant, indicating 
 the method by which the moods in any of the three figures 
 may be reduced to the form of the first figure. Aristotle 
 insisted that a mood in any other figure could be tested 
 as regards its validity only after it had been changed so 
 as to conform to the “ perfect figure.” This process is 
 
140 
 
 REDUCTIVE LOGIC 
 
 called reduction. The significance of the consonants in 
 reference to this process is as follows : — 
 
 In the several words, s indicates that the proposition rep- 
 resented by the preceding vowel is to be converted simply ; 
 p indicates that the proposition represented by the preced- 
 ing vowel is to be converted per accidens, or by limitation, 
 that is, changing all to some ; m ( mutare ) indicates that 
 the propositions which stand as the premises are to be 
 transposed; k means that an indirect proof is necessary 
 in order to reduce the mood to the first figure. Moreover, 
 the initial consonants of the so-called imperfect figures cor- 
 respond with those of the moods in the first figure to which 
 they can be reduced. 
 
 Thus Darapti reduces to Dcirii : — 
 
 The mood expressed by Darapti is AAI as in the 
 following : — 
 
 All B is A. 
 
 All B is C. 
 
 Some C is A. 
 
 The p in Darapti indicates conversion of minor premise 
 per accidens ; this gives the mood All which is the Darii of 
 the first figure : — 
 
 All B is A. 
 
 Some C is B. 
 
 Some C is A. 
 
 So also Disamis becomes Darii : — 
 
 Given the syllogism in the form of Disamis : — 
 
 Some B is A. 
 
 All B is C. 
 
 Some C is A. 
 
 Here the first s indicates a simple conversion of the major 
 premises, the m a transposition of premises, and the final 
 
MOOD AND FIGURE 
 
 141 
 
 s a simple conversion of the conclusion, all of which will 
 result as follows : — 
 
 All B is C. 
 
 Some A is B. 
 
 Some A is C. 
 or Some C is A. 
 
 The process of reduction has no practical value whatso- 
 ever ; as a device to arrange the syllogism in proper form for 
 the testing of its validity, it is wholly unnecessary. Every 
 syllogism, whether of the first or of the other figures, may 
 be tested quietly by the application of the rules concerning 
 the distribution of terms. If the middle term is distributed, 
 and no illicit process either of the major or the minor term 
 is involved, the syllogism needs no further justification. 
 
CHAPTER XYII 
 
 THE HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 
 
 The hypothetical syllogism is a syllogism in which the 
 major premise is a hypothetical proposition, the minor 
 premise a categorical, and the conclusion a categorical propo- 
 sition also. The hypothetical proposition is of the general 
 form, — If a; is y, then z is w. The conditional clause is 
 known as the antecedent, the following clause the conse- 
 quent. 
 
 Let us examine some hypothetical proposition regarding 
 it as a major premise, and putting the question as to how 
 many syllogisms may be constructed by means of introduc- 
 ing various minor premises in connection with it. Let us 
 take the proposition, If the Japanese are to be victorious 
 in the war with Russia, they must take Port Arthur. With 
 this proposition as a major premise, there are four minor 
 premises possible according as we affirm or deny the ante- 
 cedent, or affirm or deny the consequent, as follows : — 
 
 (1) They are victorious. 
 
 (2) They are not victorious. 
 
 (3) They have taken Port Arthur. 
 
 (4) They have not taken Port Arthur. 
 
 It will be observed that the first and fourth statements 
 when taken in connection with the major premise give 
 definite conclusions. 
 
 When we affirm the antecedent, They are victorious, the 
 conclusion follows necessarily, They roust have taken Port 
 Arthur. 
 
 142 
 
THE HYPOTHETICAL SYLLOGISM 
 
 148 
 
 Similiarly, when we deny the antecedent, They have not 
 taken Port Arthur, the conclusion follows, They are not 
 victorious. 
 
 Granting the truth of the major premise, these two con- 
 clusions must necessarily follow from the respective minor 
 premises as above stated. 
 
 But when we come to the other two cases, the denial of 
 the antecedent, or the affirmation of the consequent, the case 
 is very different. If it is stated that they are not victorious, 
 it does not follow that they did not take Port Arthur, for 
 they might take Port Arthur and yet fail of victory for 
 some other reason. And so also, if it is stated that they 
 have taken Port Arthur, it cannot be inferred that they 
 are victorious, for here again some other cause may have 
 operated to prevent victory. 
 
 In general therefore the denial of the antecedent or the 
 affirmation of the consequent leaves the conclusion indeter- 
 minate ; for, as in the special case cited above, there may be 
 some other antecedent which may give rise to the conse- 
 quent as well as the particular antecedent connected with 
 it in the given hypothetical proposition which forms the 
 major premise. This possibility will always render the infer- 
 ence indeterminate. If however it is known that the 
 given antecedent is the sole antecedent of the given conse- 
 quent, and therefore every other possibility is eliminated, 
 then the denial of the antecedent, or the affirmation of the 
 consequent, will also give a determinate conclusion. This 
 special case of the hypothetical syllogism may be recognized 
 by the simple test of conversion. Thus if the hypothetical 
 major premise can be converted simply, then any one of the 
 four possible minor premises will yield a definite conclusion. 
 Thus we have the proposition, If any substance turns blue 
 litmus paper red, it is an acid. Here antecedent and conse- 
 quent are reciprocally related, so that we can also state the 
 proposition conversely, If the substance is an acid, it will 
 turn blue litmus paper red. 
 
144 
 
 DEDUCTIVE LOGIC 
 
 With such a major premise, any one of four conclusions 
 may be possible according as the antecedent is affirmed or 
 denied, or as the consequent is affirmed or denied. 
 
 It is possible, moreover, to transform any hypothetical 
 proposition into a categorical form. Let us take the hypo- 
 thetical, If the patient takes this medicine, he will get well. 
 The two minor premises which give indeterminate conclu- 
 sions are as follows : — 
 
 (1) He does not take the medicine. 
 
 .-. Conclusion is left in doubt. 
 
 (2) He gets well. 
 
 .-. Conclusion is left in doubt. 
 
 Forming these into categorical syllogisms, we have : — 
 
 (1) The taking of this medicine will restore health. 
 
 The patient does not take the medicine. 
 
 .-.He will not be restored. 
 
 (2) The taking of this medicine will restore health. 
 
 The patient’s health is restored. 
 
 .-. He has taken the medicine. 
 
 By examining these two conclusions, obviously invalid, it 
 will be seen that the denial of the antecedent in a hypotheti- 
 cal syllogism is equivalent to the illicit process of the major 
 term in the categorical syllogism, and the affirmation of the 
 consequent is equivalent to the undistributed middle in the 
 same. The inferences which are always possible in the hypo- 
 thetical syllogism, the affirmation of the antecedent, or the 
 denial of the consequent, are designated by the Latin phrases, 
 modus ponens and modus tollens respectively. 
 
 The Disjunctive Syllogism. — In this syllogism we have as 
 major premise a disjunctive proposition of the form, A is 
 either B or C. There are four possible minor premises, — 
 being the affirmation or the denial of either one of the alter- 
 natives. The conclusions which are possible depend upon 
 
THE DISJUNCTIVE SYLLOGISM 
 
 145 
 
 the nature of the disjunctive major premise. There are 
 the following cases : — 
 
 (1) If the disjunction is a strictly logical one, — that is, 
 the terms mutually exclusive and the disjunction complete, 1 
 — then the affirmation of either alternative necessitates as a 
 conclusion the denial of the other, while the denial of either 
 one necessitates the affirmation of the other. The former is 
 called the modus ponendo tollens, i.e. the mood which denies 
 by affirming ; the latter is called modus tollendo ponens, i.e. 
 the mood which affirms by denying. 
 
 (2) If the disjunctive members are not mutually exclu- 
 sive, the affirmation of the one does not necessarily deny the 
 other. Thus we might have the disjunctive proposition, 
 The disease is either pneumonia or typhoid fever. The 
 assertion that it is pneumonia does not necessarily render 
 the typhoid fever an impossibility ; for a patient may have 
 both diseases at the same time. 
 
 (3) If the disjunction is not complete, then the denial of 
 one member of the disjunction does not necessitate the 
 affirmation of the other, for one or more possibilities not 
 expressed in the original disjunctive statement must be 
 reckoned with. For instance, let us take the disjunctive 
 syllogism, The prices of commodities will be either in- 
 creased or lowered by this law. 
 
 They cannot be increased. 
 
 They must be lowered. 
 
 It may be shown that there is a third possibility, namely, the 
 law does not affect the prices one way or the other. 
 
 The Dilemma. — This is a complex syllogism in which 
 both hypothetical and disjunctive propositions are combined. 
 The dilemma in its most complete form is constructed as 
 follows : the major premise consists of two hypothetical 
 propositions, — the minor premise, of a disjunctive ; and the 
 conclusion, of a disjunctive. 
 
 1 See p. 51. 
 
146 
 
 DEDUCTIVE LOGIC 
 
 The minor premise may take either one of two forms. It 
 may affirm disjunctively the two antecedents contained in 
 the double hypothetical of the major premise; or it may 
 deny disjunctively the two consequents contained in the 
 same. If the former, the dilemma is called constructive; 
 if the latter, destructive. The symbolic representation of 
 these two forms may be expressed as follows : — 
 
 (1) The constructive dilemma. 
 
 If A is B, C is D ; if ^7 is F, G is H. 
 
 Either A is B, or E is F. 
 
 C is D, or G is H. 
 
 (2) The destructive dilemma. 
 
 If A is B, C is D ; if E is F, G is H. 
 
 Either C is not D, or G is not H. 
 
 •\ Either A is not B, or E is not F. 
 
 The above being the complete form of the dilemma, there 
 may be certain variations introduced, as, for instance, instead 
 of two consequents there may be only one, or instead of two 
 antecedents there may be only one. The principle of the 
 dilemma is, however, not affected by these changes. This 
 principle is essentially that of presenting two possibilities 
 with definitely determined consequences, so that a choice 
 must be made between them which in either case results in 
 embarrassment, confusion, or contradiction. The following 
 dilemma, which will serve as a type of dilemmas in general, 
 illustrates these various features : — 
 
 If the charges of the Senator from South Carolina are 
 true, I am unfit to remain a member of the Senate ; and if 
 they are untrue, the man who made them is unfit to remain 
 a member of this honorable body. 
 
 But they must be true or untrue. 
 
 Either the Senator from South Carolina is unfit or I 
 am unfit to remain a member of this body. 1 
 
 1 Extract from a speech of Senator McLaurin in answer to Senator 
 Tillman’s charges. 
 
THE DILEMMA 
 
 147 
 
 It will be observed that the minor premise of a dilemma 
 states the possibilities to which a given situation gives rise, 
 and the major premise states the necessary relations which 
 these possibilities respectively sustain. 
 
 There are two parts of a dilemma where a structural 
 weakness is apt to occur, which of course affects seriously 
 the validity of the conclusion. The one weakness is an 
 absence of necessary sequence between antecedent and 
 consequent in either one or both of the hypothetical 
 propositions which form the major premise. The other 
 is the incompleteness of the disjunctive proposition which 
 forms the minor premise. If the alternatives are not 
 mutually exclusive, or if they are not exhaustive, error of 
 course must result. Sometimes a specious argument in 
 the form of a dilemma may be suddenly presented by an 
 opponent in controversy or in debate, and produce a tempo- 
 rary confusion of mind because it is not known just where 
 the fallacy of the dilemma is concealed. It is well to know 
 therefore the exact sources whence errors in the dilemma 
 are apt to proceed. 
 
 When, in the major premise of a dilemma, the conse- 
 quents do not invariably follow from the given antecedents, 
 or when other consequents also may follow which are not 
 mentioned in the premise, then it is possible to form a 
 counter dilemma which, starting from the same premises, 
 reaches an opposite conclusion. Both the original dilemma 
 and the counter dilemma in such cases are at fault, because 
 they both start from an inadequately expressed hypotheti- 
 cal relation. An illustration of this is found in the classi- 
 cal incident of the Athenian mother who advised her son 
 not to enter public life ; “ for,” said she, “ if you act justly, 
 men will hate you, and if you act unjustly, the gods will 
 hate you ; but you must act either justly or unjustly ; there- 
 fore public life will result in your being hated.” The son, 
 however, brought in rebuttal an equally plausible state- 
 ment; “ If I act justly, the gods will love me; and if I 
 
148 
 
 DEDUCTIVE LOGIC 
 
 act unjustly, men will love me ; therefore, entering public 
 life will make me beloved.” 
 
 Trilemma. — There is a still more complex form of the 
 combined hypothetical and disjunctive propositions which 
 is known as the trilemma. As the name indicates, the dis- 
 junction in the minor premise consists of three members. 
 This is illustrated in the following statement regarding the 
 Louisiana Purchase. It is averred that the sale of Louisiana 
 to the United States was invalid ; because, if it were French 
 property, Buonaparte could not constitutionally alienate it 
 without the consent of the Chambers ; if it were Spanish 
 property, he could not alienate it at all ; if Spain had the 
 right of reclamation, the sale was worthless. 
 
CHAPTER XVIII 
 
 EXTRA-SYLLOGISTIC REASONING 
 
 The syllogism, as we have seen, is a form of inference 
 which is essentially the interpretation of a special case in 
 the light of a universal concept to which it can be referred. 
 The function of the major premise is the statement of the 
 universal principle or relation which forms the basis of the 
 inference; that of the minor, the statement of the connec- 
 tion of the special case under consideration to this universal ; 
 that of the conclusion the investiture of the special case 
 with the essential properties which belong to the universal. 
 Now there are certain forms of reasoning which do not ex- 
 plicitly at least conform to this programme of the syllogism, 
 and which judged by the formal rules of the syllogism must 
 be regarded as invalid, but which nevertheless are commonly 
 employed in our everyday inferences and whose validity is 
 indisputable. 
 
 There is in the first place the so-called reasoning from 
 “particulars to particulars.” John Stuart Mill, as is well 
 known, attacks the accepted view of the syllogism insisting 
 that the reasoning process is never based upon a complete 
 universal, but always starts with particulars and concludes 
 with particulars . 1 
 
 In this connection, he gives the following illustrations : — 
 
 “ It is not only the village matron who, when called to a 
 consultation upon the case of a neighbour’s child, pronounces 
 on the evil and its remedy, simply on the recollection and 
 authority of what she accounts the similar case of her Lucy. 
 
 1 Mill’s Logic, Book II, Chap. Ill, § 3. 
 
 149 
 
150 
 
 DEDUCTIVE LOGIC 
 
 We all, when we have no definite maxims to steer by, guide 
 ourselves in the same way; and if we have an extensive 
 experience and retain its impressions strongly, we may 
 acquire in this manner a very considerable power of accu- 
 rate judgment, which we may be utterly incapable of justify- 
 ing or of communicating to others. Among the higher 
 order of practical intellects, there have been many of 
 whom it was remarked how admirably they suited their 
 means to their ends without being able to give any sufficient 
 reasons for what they did ; and applied, or seemed to apply, 
 recondite principles which they were wholly unable to state. 
 This is a natural consequence of having a mind stored with 
 appropriate particulars, and having been long accustomed 
 to reason at once from these to fresh particulars, without 
 practising the habit of stating to oneself or to others the 
 corresponding general propositions. An old warrior, on a 
 rapid glance at the outlines of the ground, is able at once 
 to give the necessary orders for a skilful arrangement of 
 his troops ; though if he has received little theoretical in- 
 struction, and has seldom been called upon to answer to other 
 people for his conduct, he may never have had in his mind 
 a single general theorem respecting the relation between 
 ground and array. But his experience of encampments, 
 under circumstances more or less similar, has left a number 
 of vivid, unexpressed, ungeneralized analogies in his mind, 
 the most appropriate of which, instantly suggesting itself, 
 determines him to a judicious arrangement.” 
 
 Mr. Mill is no doubt quite correct in this outline which 
 he sketches of common procedure in inference. However, 
 it cannot be claimed, and Mr. Mill is the last one to claim 
 it, that every particular instance furnishes sufficient ground 
 for an inference concerning a similar particular instance. 
 On the contrary, it is only the particular instance of a cer- 
 tain well-defined kind which can give to such an inference the 
 proper logical warrant and validity. And this special kind 
 is one in which the particular instance ranks as a typical 
 
EXTRA-SYLLOGISTIC REASONING 
 
 151 
 
 case. It stands in one’s thought as the representative of the 
 universal of which it is a special case. In our reasoning we 
 speak of it in terms of its particularity, but the correspond- 
 ing universal is always in the background of thought, and 
 it invests the particular case with its essential significance. 
 The particular is merely a disguised universal. The partic- 
 ular as mere particular is barren of any inferential result. 
 When however it stands as representative of the universal 
 of which it is a special case, then it serves as a valid ground 
 of inference. When the village matron argues from her 
 own child’s case to that of some other child, she has in mind, 
 dimly it may be, but nevertheless truly, some idea which 
 embraces her child’s case and her neighbor’s in one and the 
 same class. She knows, although it may not be explicit in 
 her thought, that the cure of the child did not depend upon 
 any circumstance peculiar to her constitution or nature, but 
 that the treatment employed possessed some essentially 
 efficacious tendency of a universal nature. 
 
 When the argument is, however, narrowed down to a 
 single special case, and this is made the basis of an infer- 
 ence to another case which closely resembles it, then we 
 have inference by analogy . 1 There is a marked difference 
 between the special case which furnishes ground for infer- 
 ence, because it stands in our minds as a typical case repre- 
 sentative of its appropriate universal, and on the other hand 
 that special case which does not imply a universal at all, 
 but immediately suggests some resemblance to a similar 
 case and thus opens the way for reasoning by analogy. 
 Analogy, as a form of inference, has attached to it an element 
 of uncertainty so long as its basis is merely a particular 
 instance. When that particular instance begins, however, 
 to assume the characteristics of a typical case, and to direct 
 the thought to its corresponding universal, then inference 
 by analogy passes over by insensible degrees to the ordinary 
 syllogistic inference, or inference by subsumption. 
 
 1 See p. 186. 
 
152 
 
 DEDUCTIVE LOGIC 
 
 There is, again, another form of inference, which departs 
 from the syllogistic type but which nevertheless possesses 
 undoubted logical validity, such as the following : — 
 
 A is to the right of B. 
 
 B is to the right of C. 
 
 A is to the right of C. 
 
 Judged strictly by the logical rules of the syllogism, the 
 above conclusion is invalid, because the given syllogism has 
 four terms, A, B, the right of B, and the right of C. There 
 is, therefore, no proper middle term ; for B and to the right 
 of B are different and can give no identical point of refer- 
 ence for the two premises. Nevertheless this syllogism 
 holds. No one would think of denying its validity. How- 
 ever, its form alone does not warrant the conclusion ; for we 
 may construct a syllogism of the same form whose conclu- 
 sion is invalid. For example, in the following syllogism: — 
 
 A is a friend of B. 
 
 B is a friend of C. 
 
 A is a friend of C. 
 
 it is obvious that the conclusion does not follow necessarily 
 from the premises. Again, let us take a concrete example 
 of a line of argument which appeals to many as quite cogent, 
 but is nevertheless evidently fallacious, such as the fol- 
 lowing: — 
 
 Princeton has defeated Yale in base-ball. 
 
 Yale has defeated Harvard. 
 
 .-. Princeton will defeat Harvard. 
 
 We are confronted therefore by this problem : — 
 
 Given the following syllogism, 
 
 A sustains certain relations to B. 
 
 B sustains similar relations to C. 
 
 A must sustain these same relations to C. 
 
EXTRA-SYLLOGISTIC REASONING 
 
 153 
 
 What kind of relations are they which necessitate such a 
 conclusion, and what kind are they which leave the conclu- 
 sion indeterminate ; or, in other words, what are the precise 
 criteria which will differentiate the truly logical ground 
 from the illogical as regards the nature of the relations upon 
 which the inference is based ? The answer is not far to 
 seek. It lies in the very nature of the syllogistic inference 
 itself. We have seen that every valid inference must pro- 
 ceed from premises which have as common ground some 
 identical point of reference . 1 If the premises are not joined 
 at a common point of articulation, their logical force can- 
 not be combined, and without the premises in combination, 
 no conclusion follows. 
 
 Now, in the syllogism expressing relations of a perfectly 
 general character as given above, the form alone does not 
 give this necessary point of common reference. We must 
 look, therefore, for some direct test as regards the nature 
 of the relations as there expressed. If the relation which 
 obtains in the major premise is the same as that which 
 obtains in the minor premise, then evidently this identity 
 of relation secures the desired identical point of reference, 
 and therefore furnishes logical warrant for the derived con- 
 clusion. This identity of the relations obtaining in the major 
 and minor premises can be established indisputably, however, 
 only when these relations appear in a system of coordinated 
 parts, wherein there is such simplicity that the relations 
 of part to part, throughout the whole extent of the system, 
 can be definitely and exhaustively comprehended. It is 
 only simplicity of system that gives necessity of inference. 
 Otherwise in relations which seem to be identical, there 
 may lurk some unknown and essential differences. From 
 the premises that A is a friend of B, and that B is a friend 
 of C, the conclusion that A is a friend of C does not fol- 
 low because the system in which these relations obtain 
 is so exceedingly complex as to allow the possibility of a 
 1 Bosanquet, Essentials of Logic, p. 74 f. 
 
154 
 
 DEDUCTIVE LOGIC 
 
 very wide divergence between phenomena, which upon the 
 surface seem quite similar. Not so, however, with the 
 premises, A is to the right of B and B to the right of C. 
 The conclusion is left in no doubt, for the very reason that 
 the given relations emerge in a system so simple that no 
 new or unknown elements can be conceived as disturbing 
 factors. Think however of introducing a change into this 
 simple system. Regard it no longer as a plane surface, but 
 as the surface of a sphere. The conclusion from the given 
 premises does not follow necessarily. 
 
 Any system, therefore, which is of such simplicity as to 
 assure the identity of given relations, will always furnish 
 a logical ground for inferences of the kind we have been 
 discussing. Such inference is called inference by construc- 
 tion rather than inference by subsumption. It is inference 
 by construction because the mind takes the material fur- 
 nished by the premises, and places it where it belongs in 
 an underlying system which is explicitly or implicitly 
 assumed. The conclusion follows because the construction 
 has been made within that system and according to the 
 possibilities which the nature of that system imposes. 
 With any other system such a construction would not 
 have necessitated the same conclusion. The conclusion that 
 the square on the hypothenuse is equal to the sum of the 
 squares on the other two sides follows only when we con- 
 ceive our right-angled triangle as constructed upon a plane 
 surface and not upon a sphere. If you say to me, “ You 
 must be a friend to my friend because you are a friend to 
 me,” my reply would be: “Not necessarily; for in the vast 
 system of social relations exposed to the many perturba- 
 tions arising from the qualities and the frailties of human 
 nature alike, the relation of friend to friend is too com- 
 plex, too subtle, too profound, to furnish any simple and 
 constant basis of inference. There is here something more 
 than a matter of mere magnitude and position.” 
 
 In addition to the examples already given there are many 
 
EXTRA-SYLLOGISTIC REASONING 
 
 155 
 
 other simple systems, which for the most part grow out of 
 the fundamental categories of thought, and which provide 
 a logical ground upon which one may construct these in- 
 ferences of relation. 
 
 There is the system which expresses solely the relations 
 of degree, in which it is possible to construct inferences 
 such as the following : — 
 
 A is taller than B. 
 
 B is taller than C. 
 
 A is taller than C. 
 
 There is also the simple time system, giving the infer- 
 ence : — 
 
 A is older than B. 
 
 B is older than C. 
 
 A is older than C. 
 
 We may have also somewhat more complicated relations 
 within, however, an exceedingly simple system, as the fol- 
 lowing will show : — 
 
 A and B, two angles of a plane triangle, equal together 95°. 
 
 C, the third angle, must equal 85°. 
 
 These illustrations might be multiplied. They are, how- 
 ever, sufficient to render clear the criteria regarding 
 all inference concerning related elements of one and the 
 same system. Whenever identity of relationship can be 
 established, a valid inference is possible; and identity of 
 relationship can be established only in systems of such 
 simplicity that no unknown elements which might dis- 
 turb the given relations can be conceived. Our thought 
 must command the system ; otherwise we are never justi- 
 fied in using that system as a basis of reasoning. It should 
 be added, however, that the relations given in the premises 
 may be exceedingly complex, provided only the system in 
 which they inhere remains so simple that our knowledge 
 commands it fully. Thus, in geometry, there is the possi- 
 
156 
 
 DEDUCTIVE LOGIC 
 
 bility of indefinitely complex constructions ; there are many 
 steps in the reasoning process from the statement of the 
 theorem to the joyful stage of the Q. E. D. ; nevertheless, 
 there must remain the constant simple system of space and 
 magnitude relations which constitutes the ground of it all. 
 
 There is no limit to the length of a series which may 
 express continued relations. We may have a related to b, 
 b to c, c to d, d to e, and so on. The relations between 
 proximate terms will not insure like relations between more 
 remote terms necessarily. Here again our test comes to the 
 fore. If in such a series the underlying system is so 
 simple as to render the various relations identical in kind, 
 then all terms of the series are brought within a closed cir- 
 cuit, as it were, and we can then pass in thought from the 
 first to the last term as well as from the first to the second. 
 
 There is still another kind of inference which is based 
 upon the nature of certain given relations and partakes of the 
 general characteristics of immediate inference. It is this, 
 that whenever we have given a judgment of the form, a is 
 related to b, the given relation necessitates a converse rela- 
 tion, b is related to a. The converse relation is not identical, 
 however, with the given relation, but has an essentially 
 distinct significance, usually of an opposite nature. For 
 example, we have given A is the father of B, therefore B 
 is the son of A; New York is east of Chicago, therefore 
 Chicago is west of New York. The following may be urged 
 as an exception to the statement that the converse relation 
 differs essentially from the given one: A is a friend of B, 
 therefore B is a friend of A. However, this is only a seeming 
 exception, for even in the relation of the most intimate friend- 
 ship conceivable, the attitude, feeling, or disposition of one 
 party in the friendship is never the same as that of the other. 
 The precise nature of the converse relation will always de- 
 pend upon the nature of the system in which the given 
 relation obtains . 1 
 
 1 See Russell, The Principles of Mathematics, Chap. IX, on “ Relations.” 
 
CHAPTER XIX 
 
 FALLACIES 
 
 Fallacies or errors in reasoning may be formal or mate- 
 rial. The formal fallacy is one which is due to the struc- 
 ture of the reasoning process itself ; the material fallacy is 
 due to the thought which underlies the structure. The 
 formal fallacies have been treated indirectly at least in 
 reference to the various rules of the syllogism, the violation 
 of which of course results in a fallacy of this kind. It will 
 be sufficient at this juncture merely to summarize these 
 fallacies, the most important of which are as follows : — 
 
 1. Undistributed middle. 
 
 2. Illicit process of the major or minor term. 
 
 3. Denying the antecedent, or affirming the consequent 
 of the hypothetical syllogism. 
 
 4. Inadequate disjunction of the several members of the 
 major premise in the disjunctive syllogism ; that is, when 
 these members are not exclusive and therefore overlap. 
 
 5. The incomplete enumeration of possibilities in the 
 major premise of the disjunctive syllogism. 
 
 The material fallacies may be divided, as did Aristotle, 
 into two classes, — those fallacies which are due to language 
 (napa ttjv Ae|iv, or in dictione) ; and those which are due" to 
 certain errors in the content of thought itself rijs \e£ews, 
 or extra dictionem). 
 
 The fallacies which are due to language arise from the 
 fact that both in single words and in syntactical forms there 
 may lurk ambiguities of meaning. Any ambiguity of mean- 
 ing in the course of reasoning violates the fundamental law 
 
 157 
 
158 
 
 DEDUCTIVE LOGIC 
 
 of identity, which demands that a single and constant sig- 
 nificance should attach to all the thought elements which go 
 to make up the data and the processes of our reasoning. 
 
 The fallacies due to language are often referred to as fal- 
 lacies of ambiguity. Their violation of the law of identity 
 will be seen in the several instances which will be given. 
 These fallacies are as follows : — 
 
 1. Equivocation. 4. Division. 
 
 2. Amphiboly. 5. Accent. 
 
 3. Composition. 6. Figure of Speech. 
 
 1. Equivocation. — This fallacy consists in using a word 
 or a phrase which is capable of a double meaning, as, for 
 example : — 
 
 I have the right to publish my opinions concerning the 
 present administration. 
 
 What is right for me to do, I ought to do. 
 
 .-. I ought to publish my opinions concerning the present 
 administration. 
 
 The ambiguity here, of course, lies in the meaning of the 
 word right, which in the one premise is to be taken in a 
 legal sense, and in the other in a moral sense. 
 
 This fallacy is in reality a fallacy of four terms ; that is, 
 in every syllogism there should be only three terms, each 
 term however being repeated. The law of identity de- 
 mands that in this repetition the integrity of significance, 
 as regards the repeated term, must be preserved. To intro- 
 duce a term, therefore, which is ambiguous violates this 
 fundamental principle of thought. The law of identity, 
 however, it must be remembered, allows a certain margin of 
 variation in meaning, provided only that the essential sig- 
 nificance of the thought is not impaired. There is often a 
 difference of opinion as to whether a change in meaning 
 affects the essential significance of a concept or not. For 
 instance, let us consider the following syllogism : — 
 
 Whatever menaces the public interests should be pre- 
 vented by law. 
 
FALLACIES 
 
 159 
 
 The Great Northern Securities Merger menaces the public 
 interests. 
 
 It should be prevented by law. 
 
 Here the question is raised, Does this merger menace the 
 public interests in the sense that it should be punished by 
 law ? And that, of course, is the point upon which the 
 argument turns. 
 
 2. Amphiboly. — This is a fallacy in which the ambiguity 
 lies in the syntax of the proposition rather than in the terms 
 of which it is composed. The following, taken from a notice 
 in the New York Tribune, will illustrate this : — 
 
 “ To-morrow afternoon, at four o’clock, the Kev. J. A. 
 Francis will deliver the third and last address of a series of 
 plain talks to young men about their perils at the East 86th 
 St. branch of the Y. M. C. A.” The conclusion is obvious. 
 
 The following epitaph, also illustrating this same fallacy, 
 I discovered several years ago on a tombstone in the old 
 burying-ground at Concord, Massachusetts : — 
 
 “ Sacred to the memory 
 of 
 
 After living with her husband for fifty-five 
 years, she departed in the hope of a better life.” 
 
 3. Composition. — This is the fallacy due to the supposi- 
 tion that what may be affirmed of individuals separately 
 may also be affirmed of them when taken together. It does 
 not follow, for instance, that because the members of a foot- 
 ball team are all individually excellent players, therefore 
 the team play will show a similar order of excellence. This 
 fallacy is also illustrated in the following quotation from 
 John Stuart Mill: — 
 
 “No reason can be given why the general happiness is 
 desirable except that each person, as far as he believes it 
 to be attainable, desires his own happiness. . . . Each per- 
 son’s happiness is a good to that person, and the general 
 
100 
 
 DEDUCTIVE LOGIC 
 
 happiness therefore a good to the aggregate of persons.” 
 It does not follow, however, that because each desires his 
 own happiness, therefore all desire the happiness of the 
 whole. The root of this fallacy is to be found in the neglect 
 of the distinction between the distributive and the collective 
 use of a term. A term is used distributively when it is ap- 
 plicable to each individual of the class separately; but 
 collectively when it is applicable only to all the individuals 
 which compose the class when taken together. It is the dif- 
 ference between “ all ” meaning each one, and “ all ” meaning 
 all together. 
 
 4. D ivisio n. — This is the converse of composition, and 
 consists in affirming of individuals separately what is true 
 only when they are taken together. It does not follow, for 
 instance, that because a certain board of directors has the 
 reputation of being exceedingly conservative, therefore any 
 individual member of that board is necessarily conservative 
 also. 
 
 5. Accent. — This is a fallacy due to the undue accentua- 
 tion of a word or clause in any statement so as to create an 
 implication which the bare words themselves do not indi- 
 cate, and which, moreover, was not intended by the author 
 of the words. To quote from the text of an author and to 
 italicize certain words will often necessitate an interpreta- 
 tion quite foreign to the author’s mind. This is often done 
 with malice aforethought, and is an eminently unfair and 
 indefensible liberty to take with the thought of others. 
 
 6. Figure of Speech. — This is a fallacy of using different 
 parts of speech having a common root as though they had 
 precisely the same meaning. The fact is, however, that a 
 noun may have a certain meaning, while an adjective derived 
 from the same root will have acquired a twist of meaning or 
 a subsidiary significance which will prevent their being re- 
 garded in the light of interchangeable terms. The following, 
 also from John Stuart Mill, will illustrate this: — 
 
 “ The only proof capable of being given that an object is 
 
FALLACIES 
 
 161 
 
 visible is that people actually see it. The only proof that 
 a sound is audible is that people hear it. . . . In like man- 
 ner, I apprehend, the sole evidence it is possible to produce 
 that anything is desirable is that people do actually desire 
 it.” In this quotation, the relation of the word desirable 
 to desire is not the same as the other two cited, namely, 
 the relation of the word visible to the word see, and of 
 audible to the word hear. Visible means that which can be 
 seen ; audible means that which can be heard ; but desirable 
 does not mean that which can be desired, — rather, that 
 which ought to be desired. 
 
 We come now to the second division of the material 
 fallacies, those which are due to inconsistencies of thought 
 rather than to ambiguities in the expression of the thought. 
 These fallacies are as follows : — 
 
 1. Accident. 5. Petitio Principii. 
 
 2. Converse Accident. 6. Non Causa pro Causa. 
 
 3. Ignoratio Elenchi. 7. Many questions. 
 
 4. Non Sequitur. 
 
 1. Accident. — This is expressed in the Latin phrase, a 
 dicto simpliciter ad dictum secundum quid. 
 
 This is the fallacy of reasoning from what is true as a 
 general statement ( simpliciter ) to the same statement which 
 is restricted or conditioned in some manner ( secundum quid). 
 
 The following is this fallacy of accident : — 
 
 Strychnine is a deadly poison, and therefore it can never 
 be used as a medicine. 
 
 2. Converse Accident. — This is expressed in the Latin 
 phrase, a dicto secundum quid, ad dictum simpliciter. This 
 is the fallacy of reasoning from that which may be true 
 under certain conditions or limitations, to that which how- 
 ever is not true when these conditions or limitations are 
 removed. This is illustrated in the following argument 
 which is very often heard : — 
 
 Certain men have risen to prominent positions who never 
 
162 
 
 DEDUCTIVE LOGIC 
 
 had a college education ; therefore a college education is un- 
 necessary to equip a man for his life’s work. 
 
 In reference to these two fallacies, there is a passage in 
 Lotze which is of interest, and which is well worth quoting 
 here. 
 
 “ Two general modes of fallacious thought are developed 
 by the habitual commission of these fallacies, and illustrate 
 them on a grand scale. The first is doctrinairism, the second 
 narrow-mindedness. The doctrinaire is an idealist who refuses 
 to see that though ideas may be right in the abstract, yet the 
 nature of the circumstances under which and of the objects 
 to which they are to be applied must limit not only their 
 practicability but even their binding force. The narrow- 
 minded, on the other hand, can recognize and esteem no 
 truth and no ideal, even the most universal^ valid, except 
 in that special form to which they have become accustomed 
 within a limited circle of thought and personal observation. 
 Life is a school which corrects these habits of mind. The 
 parochially minded man sees things persist in spite of him- 
 self in taking shapes which he considers unprecedented, but 
 he finds the world somehow survives it, and learns at last 
 that a system of life may be excellent and precious, but that 
 it is rash from that to argue that it is the only proper mode 
 of orderly existence. And the enthusiast for ideals, when 
 he sees the curtailment which every attempt at realization 
 inflicts on them, learns the lesson which the disjunctive 
 theorem might have taught him. Every universal P changes 
 in the act of being applied from something that held sim- 
 pliciter into something that holds secundum quid, — changes 
 from P to p, 1 p, 2 or p 3 ; to refuse to accept it in any one of 
 these, which are its only possible shapes, is to ask that it 
 be realized under a condition which even logic pronounces 
 impossible.” 1 
 
 3. Ignoratio Elenchi. — This is a fallacy which consists 
 primarily in an ignorance of the nature of refutation. To 
 1 Lotze’s Logic, Vol. II, p. 5, Eng. trans. 
 
FALLACIES 
 
 163 
 
 refute an argument, its logical contradiction must be es- 
 tablished. Any proof which falls short of this fails in its 
 end. The nature of this fallacy has been enlarged in scope, 
 so as to comprise any argument whatever which does not 
 squarely meet the point at issue. It is, in many cases, not 
 so much the ignorance of the point at issue, as purposely 
 ignoring the point at issue. It is a natural method of argu- 
 ment when one has a weak case. Any subterfuge which 
 withdraws attention from the point at issue tends, of course, 
 to strengthen the weaker side, at least as regards the plausi- 
 bility of its position. Suppose a student should be urged 
 to spend more time upon his Latin or Greek, and he should 
 excuse his negligence by insisting that in after life he would 
 never find any practical use for his classics, — this would be 
 the fallacy of ignoratio elenchi. 
 
 There are various ways in which this fallacy may be 
 illustrated, as follows : — 
 
 (a) Argumentum ad hominem. — This is the fallacy wherein 
 the argument is diverted from the merits of the case to the 
 character or the position of one’s opponent. 
 
 ( b ) Argumentum ad populum. — This is the fallacy of ap- 
 pealing to the passion or prejudice of an audience, rather 
 than to their reason. It is essentially the argument of the 
 demagogue. 
 
 (c) Argumentum ad ignorantiam. — This fallacy consists in 
 taking advantage of the ignorance of the person or persons 
 addressed who, consequently, lack the power of discrimina- 
 tion between the true and the false, the relevant and the 
 irrelevant. 
 
 (i d ) Argumentum ad verecundiam. — This is an appeal to 
 the sentiment of veneration for authority, instead of an appeal 
 directly to the reason. The weight of great names is with 
 some persons the most convincing of all arguments. Logi- 
 cally it is not an argument at all. It may serve to confirm 
 truth, but it does not establish it. 
 
 (e) Argumentum ad baculum. — This repudiates all argu- 
 
164 
 
 DEDUCTIVE LOGIC 
 
 merit and resorts to force in order to establish, one’s 
 point. 
 
 In distinction from these various kinds of subterfuges to 
 avoid a direct facing of the question, there is the argumen- 
 tum ad rem, or the argumentum ad judicum, i.e. arguing 
 directly to the point at issue. All lines of argument should 
 converge to this central point. 
 
 4. The Fallacy of the Consequent, or Non Sequitur. — This 
 fallacy was defined primarily by Aristotle as the formal error 
 of affirming the consequent. It has received, however, in 
 the course of time, a far wider application, and has come to 
 be applied to any loose argument whatever, in which the 
 conclusion does not seem to follow from the premises. It 
 is very convenient to have the phrase non sequitur where- 
 with to characterize such arguments. 
 
 5. Petitio Principii. — This is the fallacy of begging the 
 question. This is an attempt to assume the conclusion 
 without any attempt whatever to prove it. According to 
 Aristotle this may take place in five ways : — 
 
 (1) To assume the point at issue directly. This, however, 
 cannot be done without resort to some rhetorical device to 
 conceal the absence of any real proof. 
 
 (2) To assume some more general truth which involves 
 the point at issue. 
 
 (3) To assume particular truths which it involves. 
 
 (4) To assume the component parts in detail. 
 
 (5) To assume some necessary consequence of the point in 
 question. 
 
 As an illustration of begging the question, take the fol- 
 lowing extract from a speech of a member of the House of 
 Commons : “ The bill before the House is well calculated 
 to elevate the character of education in this country, for the 
 general standard of instruction in all our schools will be 
 raised by it.” 
 
 Galileo accuses Aristotle of having committed this fallacy 
 in his argument that “ the nature of heavy things is to tend 
 
FALLACIES 
 
 165 
 
 toward the centre of the universe, and of light things to fly 
 from it ; therefore, the centre of the earth is the centre of 
 the universe.” 
 
 There is a special form of this fallacy known as arguing 
 in a circle, circulus in probanda. This is an attempt to 
 prove a conclusion to follow from a premise, when in truth 
 the premise itself depends upon the truth of the conclusion 
 as its ground. This is illustrated in the following statement 
 taken from a letter written to one of our daily journals 
 quite recently : “ The left-handed man lacks will power, 
 for, if not, he wouldn’t be left handed.” 
 
 6. Non Causa pro Causa. — This is the fallacy of regarding 
 as a cause that which is not a cause. It is due to the lack 
 of discrimination between a mere coincidence and a verit- 
 able cause. There is no fallacy, perhaps, which is so subtle 
 as this one, and none which is more common. As an exam- 
 ple of this fallacy, we may cite the exploded hypothesis 
 of a mesmeric fluid to account for the various well-known 
 phenomena of hypnotism ; also the statement that nature 
 abhors a vacuum to account for the rise of water in a 
 pump ; or the belief that any unusual appearance among 
 the heavenly bodies, as that of a comet, is to be interpreted 
 as a portent of disaster. Many of our common superstitions 
 may be traced to this fallacy. Moreover, inasmuch as the 
 causal relation naturally manifests itself in the form of a 
 sequence, there is a special case of this fallacy which con- 
 sists in the confusion of mere sequence with a causal con- 
 nection ; this is called the fallacy of post hoc ergo prop ter hoc. 
 This is illustrated in the belief which many entertain, that 
 when thirteen sit down together at a common board, one 
 of the number will surely die within the year; or in the 
 tendency so often observable to attribute the financial pros- 
 perity or distress of the country to some legislative measure 
 recently enacted. 
 
 7. The Fallacy of Many Questions. — A better name for 
 this would be the Fallacy of a Double Question, for it con- 
 
166 
 
 DEDUCTIVE LOGIC 
 
 sists in asking a question which is in the form of a single 
 question, but which should have been put in the form of two 
 separate questions. The question which is asked assumes 
 that another question has been already asked and answered. 
 This fallacy usually takes the form of asking a question 
 about an assumed fact whereas the fact is itself in dispute. 
 Thus the question, How much do you pay a certain member 
 of your athletic team for his services, presupposes of course 
 that some amount is certainly paid. 
 
 The following anecdote which appeared recently in one of 
 our daily papers also illustrates this fallacy : — 
 
 “ Charles Bradlaugh, the English free-thinker, once en- 
 gaged in a discussion with a dissenting minister. He 
 insisted that the minister should answer a question by a 
 simple ‘Yes’ or ‘No,’ without any circumlocution, assert- 
 ing that every question could be replied to in that manner. 
 
 “The reverend gentleman rose, and- said, ‘Mr. Bradlaugh, 
 will you allow me to ask you a question on those terms ? ’ 
 
 “ ‘ Certainly/ said Bradlaugh. 
 
 “‘Then, may I ask, have you given up beating your 
 wife ? ’ ” 
 
 This completes the table of fallacies usually given in 
 treatises on logic. All the general types of fallacies are 
 comprehended in it. There are fallacies, however, which do 
 not distinctively fall under any one type, but are so subtly 
 complex as to involve the errors of many. There are, again, 
 others which arise out of special circumstances, and cannot 
 be classified under any of the types mentioned. They, how- 
 ever, readily disclose themselves to the open mind which is 
 freed from sophistry and prejudice. 
 
PART II 
 
 INDUCTIVE LOGIC 
 
CHAPTER I 
 
 INDUCTION AND DEDUCTION 
 
 There have been divergent tendencies in the history of 
 logic, to make either deduction or induction alone the whole 
 of logical procedure in the process of inference. The fact 
 that the Aristotelian logic, which is essentially deductive, 
 has been for centuries exclusively associated with logic as 
 a whole, has left the impression upon many minds that it 
 is the beginning and end of the logical encyclopsedia. On 
 the other hand, John Stuart Mill and his followers have 
 attempted to analyze the syllogism so as to prove its es- 
 sentially inductive character; and they maintain that all 
 reasoning is inductive. This is the position in the main of 
 Bacon, Locke, and Bain. Locke, for instance, insists that 
 the syllogism is of less value than external and internal 
 experience, induction, and common sense . 1 
 
 So also, in a similar vein, Schleiermacher says : “ The 
 syllogistic procedure is of no value for the real construc- 
 tion of judgments, for the substituted judgments can only 
 be higher and lower; nothing is expressed in the conclu- 
 sion but the relation of two terms to each other, which 
 have a common member, and are not without, but within, 
 each other. Advance in thinking, a new cognition, cannot 
 originate by the syllogism ; it is merely the reflection upon 
 the way in which we have attained, or could attain, to a 
 judgment, the conclusion ; no new insight is ever reached .” 2 
 The two opposed views thus indicated do not necessitate 
 conflicting or mutually exclusive processes. It is better to 
 
 1 Essay on Human Understanding, Book IV, p. 7. 
 
 2 See Ueberweg, System of Logic, etc., p. 345. 
 
 169 
 
170 
 
 INDUCTIVE LOGIC 
 
 regard them, not as radically different types of inference, 
 but rather as different phases of one and the same inferential 
 process. We have seen that inference consists in interpreting 
 the implications of the system to which the given in con- 
 sciousness belongs. In the light of this definition we can 
 best indicate the relative functions of induction and deduc- 
 tion in the process of inference. When the system can be 
 considered as a whole, and is apprehended in its entirety, 
 then it may become the ground upon which the inference is 
 based, resulting in unfolding the necessary nature or relations 
 of any of the parts considered in themselves, or in reference 
 to the system as a whole. The procedure in such a case 
 is from the nature of the whole system, to the nature of 
 the several parts, and their existent relations, and this is 
 deductive in its essential features. 
 
 On the other hand, when we know the various parts, and 
 proceed from them as data to construct the system which 
 their known nature and relations necessitate, it is induction, 
 or procedure from elementary parts to the whole thus neces- 
 sitated. From a knowledge of the planetary system we 
 can infer the necessary positions of sun, moon, and earth 
 at any required time, as, for instance, in the calculation of 
 an eclipse. This is deduction. But when we begin with 
 investigating the several movements of the different planets, 
 and from them infer the necessary nature of the system of 
 which they are parts, we have the process of induction. 
 Such processes we see must be complementary, and mutu- 
 ally dependent. As Lavater says, “ He only sees well who 
 sees the whole in the parts, and the parts in the whole.’’ 
 
 Moreover, the distinction between deduction and induc- 
 tion may be shown through their respective relations to the 
 universal, which we have seen is the ground of inference. 
 The question whose answer leads to the deductive process 
 in reasoning, is, What does the universal necessitate ? In 
 induction, the question which starts the investigation is, 
 Into what system may the given material properties or 
 
INDUCTION AND DEDUCTION 
 
 171 
 
 relations be constructed so as to reach a universal concept 
 that will be consistent with itself and with the whole of 
 knowledge which forms the world of consciousness ? In 
 this there is an analytical discrimination of the essential 
 from the accidental elements, and the gathering together of 
 the former into the complex whole which is the universal. 
 Induction, therefore, is inference viewed from the side of 
 the differences ; deduction is inference viewed from that 
 of the universal. For instance, we may investigate the 
 characteristic features of a diamond, and find that a certain 
 specific gravity, 3.53 as compared with water, is a con- 
 stant and determining attribute, and as such must be in- 
 corporated as an essential element of the general concept 
 diamond. We can then form the universal judgment, What- 
 ever stones possess this specific gravity are diamonds. Their 
 differences, regarding size, brilliancy, etc., may all be set 
 aside as accidental, but the one constant determining fea- 
 ture indicates a oneness in which they all agree. 
 
 And so with the other essential attributes. After pos- 
 sessing such knowledge gained inductively, we may use it 
 practically in a deductive manner ; and it is so used in 
 discriminating between true and imitation stones, as de- 
 scribed in the following process : “ Diamonds, rubies, and 
 
 sapphires are now tested by floating to prove their genuine- 
 ness. The liquid used has five times the density of water, 
 and is composed of double nitrate of silver and thallium. 
 The tests are rapidly made, as all stones of the same nature 
 have the same specific gravity, while none of the bogus ones 
 have the same weight as those they are made to imitate.” 
 
 Another view of the relation of induction to deduction 
 may be gained by calling attention to the difference of sig- 
 nificance between the terms, a “truth” and a “ fact.” A fact 
 carries with it only the special and individual character of 
 the particular occurrence in which it is manifested. A 
 truth, however, is always universal in its very nature, ad- 
 mitting of universal application, and capable of illustration 
 
172 
 
 INDUCTIVE LOGIC 
 
 in an indefinite number of different facts which embody its 
 essence. In deduction we have given some truth of uni- 
 versal nature that leads to individual facts that may be 
 subsumed under it. In induction, we interpret a fact or a 
 number of facts in the light of their universal implication, 
 on the ground that there can be no such thing as an isolated 
 fact, but every fact must have some relation to a universal 
 to which it must be referred. 
 
 While considering the distinctions between induction and 
 deduction, we must not overlook their mutual dependence. 
 We cannot proceed in deduction irrespective of induction, 
 because the universal upon which the deductive process is 
 based arises in the majority of cases from a previous induc- 
 tion. It is true that the universal term, may be in a propo- 
 sition that is known a priori, as the axioms of geometry and 
 certain space and time postulates ; but a very small propor- 
 tion of major premises can be said to have such an origin, 
 and their resulting conclusions have very slight material 
 significance. Deduction that reaches other than purely ab- 
 stract and formal conclusions must rest upon induction for 
 the material to form its premises. We find this even in 
 the technical construction of the syllogism, where, for in- 
 stance, the question of the distribution of the terms is 
 raised. We may insist that a certain middle term is dis- 
 tributed, as it is the subject of an universal affirmative 
 proposition ; but then the further question naturally sug- 
 gests itself, How do we know that the proposition in ques- 
 tion is really a universal ? Its material significance alone 
 tells us that we may write it as an A or I proposition, as 
 the case may be. The matter is a function of the form, 
 and the form a function of the matter. They cannot be 
 separated, in fact, unless we conceive reasoning as a purely 
 formal process of determining a conclusion, irrespective of 
 the truth or falsity of the premises. If we regard the 
 premises as given, and we accept them with unquestioning 
 credence, the deduction is purely formal ; so, also, if the 
 
INDUCTION AND DEDUCTION 
 
 173 
 
 various terms are expressed by letters A, B, C, etc., and 
 devoid of any material significance. Any process of rea- 
 soning based upon a slavish acceptance of premises can only 
 reach artificial and even false results. In the actual experi- 
 ences of life our premises are not made for us. They must 
 be constructed by us through our interpretation of reality. 
 Disregard of this has brought formal logic into much disre- 
 pute, and it has often degenerated into the barren discussion 
 of logical puzzles and quibbles. Grant a person any prem- 
 ises he may choose to assume, irrespective of an inductive 
 test of their validity, he can prove black white and white 
 black. 
 
 On the other hand, induction is dependent upon deduction ; 
 for we cannot reason from particular instances to a universal 
 proposition, unless we assume as basis of the whole induc- 
 tive process some postulate which has real universal signifi- 
 cance. Otherwise, we reach only a high degree of probability, 
 but not necessity; a rude generalization, but not univer- 
 sality. When we assert some such general statement as 
 this, that arsenic always acts as a poison, we have based 
 the universal character of the proposition upon an under- 
 lying postulate that is understood even though it is not 
 expressed, such as the uniformity of nature, that under 
 identical conditions we always look for identical effects. 
 This will be discussed later more in detail ; it is referred to 
 at this point merely to illustrate the deductive basis of 
 induction. Bradley insists that there can be no such thing 
 as induction, because it always rests upon an implied uni- 
 versal which gives to the process as a whole a deductive 
 character . 1 His criticism has the force only of proving that 
 induction cannot be independent of deduction. This depend- 
 ence does not, however, necessarily vitiate the integrity of 
 induction as a mode of the inferential process. Lotze has 
 placed special emphasis upon this dependemce of induction 
 upon deduction. He says : “ It is the custom in our day to 
 1 Bradley, Principles of Logic, p. 342. 
 
174 
 
 INDUCTIVE LOGIC 
 
 collect into one body the numerous operations which assist 
 us in ascending from particulars to generals, or to call this 
 inductive logic, and to set it against the deductive or demon- 
 strative logic along with much disparagement of the latter. 
 Such disparagement rests on a mistake. The inductive 
 methods, it is certain, are the most effectual helps to the 
 attainment of new truth, but it is no less certain that they 
 rest entirely on the results of deductive logic.” 1 
 
 Moreover, in induction the results obtained and formulated 
 in general propositions may be extended and often modified 
 by a deduction which is based upon them as major premises ; 
 for the deduction thus proceeding from them reveals new 
 instances which conform or perhaps modify the simple 
 inductive results themselves. What is popularly called a 
 hasty generalization, if made a major premise of a syllo- 
 gism, will often lead us astray through the deductions 
 drawn from it. As soon as we are aware of this, we return 
 to question the validity of the generalization, whose weak- 
 ness is not appreciated until thus tested and revealed. Thus 
 deduction serves to extend and correct the results of induc- 
 tion, and at the same time it itself is dependent upon the 
 results of inductive generalization for the material to form 
 its premises. We come to see therefore how intimately 
 associated these two processes are in actual reasoning. For 
 convenience of illustrating their individual characteristics, 
 they may be considered as separate, and each investigated 
 as an independent mode of inference. But they are in reality 
 mutually related and dependent, and are always found mani- 
 festing their functions together. In any course of reasoning 
 concerning the conduct of our everyday affairs, or in sci- 
 entific investigation, — anywhere, indeed, outside of the 
 artificial examples of logical text-books, — we reason both 
 inductively and deductively in one complex process. 
 
 1 Lotze, Logic, p. 288. See also Bosanquet, Logic, Vol. II, p. 119. 
 
CHAPTER II 
 
 THE ESSENTIALS OF INDUCTION 
 
 We now proceed to a more precise determination of the 
 nature of induction. Its point of view in all reasoning has 
 reference to concrete instances. They are the data, and 
 from them general propositions are to result. The pro- 
 cedure is from given facts to laws which are the ground and 
 explanation of these facts. We are here however at once 
 struck with the evident break in the course of our reasoning. 
 Procedure from the particular to the universal cannot be a 
 continuous process. There is a gap somewhere. The con- 
 clusion contains more than the premises. In deduction, we 
 are proceeding from the greater to the less, and we experi- 
 ence no violation of our logical sense ; but at once we 
 appreciate the difficulty which attends the reverse process 
 from the less to the greater . 1 Here we soon reach a point 
 where we pass beyond the sphere of our experience to the 
 generalization which necessarily embraces far more than 
 our experience. This is the so-called inductive leap ; or it 
 is sometimes referred to as the inductive hazard. But is this 
 a leap in the dark — a wild guess concerning all that lies 
 beyond the sensuous sphere of our immediate experience ? 
 This would be the case, were we compelled to use the mere 
 data of experience as sole ground for our inferences. John 
 Stuart Mill insists that nothing whatever is given in con- 
 sciousness but particular sensations, and these are but sub- 
 jective states of feeling, and with no assurance of any 
 definite correspondence with the external world. With such 
 purely empirical data it is impossible to proceed to truths of 
 
 i See p. 107. 
 
 175 
 
176 
 
 INDUCTIVE LOGIC 
 
 universal validity. It is necessary to postulate some uni- 
 versal truth which the mind through strictly a priori con- 
 siderations is constrained to formulate, and which will serve 
 to bridge the gulf between the particular and the universal. 
 
 This postulate has been variously expressed by different 
 authors, yet with substantially the same significance in all. 
 In the older logic, it is put under the convenient formula of 
 the uniformity of nature ; that is, that beyond the sphere 
 of experience, phenomena will behave in the same manner 
 under like conditions, as in the sphere of immediate obser- 
 vation and experiment. In the modern logic this is some- 
 what differently expressed. The phrase “uniformity of 
 nature,” being somewhat indefinite and implying a point 
 of view purely objective, is not used. Modern writers have 
 omitted it largely from their terminology. Lotze says: 
 “The logical idea upon which induction rests is by no 
 means merely probable, but certain and irrefragable. It 
 consists in the conviction based upon the principle of 
 identity, that every determinate phenomenon M can depend 
 upon only one determinate condition, and accordingly that, 
 where under apparently different circumstances or in differ- 
 ent subjects P, S, T, U, the same M occurs, there must 
 inevitably be in them some common element 2 which is the 
 true identical condition of M, or the true subject of M.” 1 
 We have a somewhat similar description of the basis of the 
 inductive process given by Sigwart: “The logical justification 
 of the inductive process rests upon the fact that it is an inevi- 
 table postulate of our effort after knowledge that the given is 
 necessary, and can be known as proceeding from its grounds 
 according to universal laws.” 2 Bosanquet considers as the 
 basis of inductive inference that which he calls the postu- 
 late of knowledge, that “ the universe is a rational system, 
 taking ‘ rational ’ to mean not only of such a nature that it can 
 be known by intelligence, but further of such a nature that 
 it can be known and handled by our intelligence.” 3 
 
 1 Lotze, Logic , p. 102. 2 Sigwart, Logic (Eng. trans.), Vol. II, p. 289. 
 
 8 Bosanquet, The Essentials of Logic, p. 166. 
 
ESSENTIALS OF INDUCTION 
 
 17T 
 
 I have quoted these passages from Lotze, Bosanquet, and 
 Sigwart, that we may appreciate the modern tendency to 
 derive the inductive postulate from an epistemological 
 source; namely, that our knowledge must be consistent 
 throughout with itself, part to part, and parts to whole, and 
 that the world for us is the world as constructed by our 
 knowledge. Whatever is given in consciousness must be- 
 long therefore in the one place where it appropriately and 
 necessarily belongs. Here also there must be a place for 
 everything, and everything in its place. There must be a 
 uniformity of consciousness ; that is, the primary postulate 
 and the uniformity of nature is secondary to this, and 
 implied in it. This postulate may also be expressed as 
 follows: What is once true is always true. Here “true” is 
 used in the sense of the universal significance of a fact. 
 Whenever a concrete instance is present in consciousness, its 
 existence must be considered as necessitated by some ante- 
 cedent which can satisfactorily account for it, and which 
 can at the same time be appropriately adjusted to the whole 
 of our knowledge in interpreting it. Bosanquet says that 
 “ ideally speaking, every concrete real totality can be 
 analyzed into a complex of necessary relations.” 1 These 
 necessary relations of course have a universal significance, 
 and therefore in every concrete instance, if we can rightly 
 interpret it, we may discern the universal element which is 
 contained in it, and gives it a place and meaning in the 
 world as cognized by us. Nature, after all, is only another 
 word for the world as we know it. 
 
 There is a sense in which induction may be regarded as 
 the inverse process of deduction. In deduction the problem 
 is concerned with the question, What does the universal 
 necessitate? In induction, the instance is given, and the 
 problem is, What universal can be discovered which could 
 give rise to the instance in question ? This view of induc- 
 tion is especially associated with the name of Jevons, whose 
 1 Bosanquet, Logic, Vol. II, p. 82. 
 
178 
 
 INDUCTIVE LOGIC 
 
 inductive system is described as the inverse of deduction. 
 He calls it the deciphering of the hidden meaning of natural 
 phenomena . 1 The name commonly used to designate this 
 view of induction is that of “reduction,” originally sug- 
 gested by Duhamel . 2 This process was known to the old 
 logicians, who called it “ Method,” to denote the process of 
 hunting for middle terms by the aid of which a given con- 
 clusion could be proved . 3 Like all inverse processes, it is 
 by itself an indeterminate one. 
 
 Given, All A is B, and 
 All B is C, 
 
 we infer by the direct process of deduction that 
 All A is C. 
 
 But in the indirect or inverse process we have given A is 
 C, and the problem, to find a middle term which necessi- 
 tates such a conclusion, is an indeterminate one. There 
 may be a number of middle terms. This is analogous in 
 one respect to the method of integral calculus ; while dif- 
 ferentiation leads to a definite result, the inverse process of 
 integration leads to an indeterminate result. So also we 
 multiply two numbers, producing one determinate result; 
 but inversely, when we have given a certain number, and 
 ask what factors multiplied together could produce this 
 number, we may reach several different solutions. The 
 answer is indeterminate. Professor Jevons, in his scheme 
 of inductive inference, falls back upon probability to indi- 
 cate which of several possibilities is the most likely one in 
 the given case . 4 But before the inverse operation can result 
 in determinate results, the given terms such as A and C 
 must be subjected to some analysis in order that their 
 material signification may give suggestion as to the nature 
 
 1 Jevons, Principles of Science, p. 124. 
 
 2 Duhamel, Methodes, Vol. I, p. 24. 
 
 3 Venn, Empirical Logic, p. 361. 
 
 4 Jevons, Principles of Science, p. 219. 
 
ESSENTIALS OF INDUCTION 
 
 179 
 
 of the middle term. For instance, a man is found dead, 
 washed ashore by the tide ; the natural supposition would 
 be that he met his death by drowning. And yet it might 
 possibly happen that the man died through injuries inflicted 
 by blows, or by poison, or heart failure. The attendant cir- 
 cumstances and bodily indications must suggest the most 
 probable cause to account for the given effect. Venn criti- 
 cises Jevons’ view of induction, that is, making it the 
 inverse process of deduction, on the ground that it is purely 
 a formal process, and therefore can lead only to indetermi- 
 nate results . 1 
 
 It is always possible, however, to make some analysis of 
 the material significance of the data, as has been above indi- 
 cated, which relieves the purely formal processes from the 
 indefiniteness of the results. Bosanquet criticises Jevons’ 
 theory of inductive inference, in that the hypothesis pro- 
 posed to account for the given in reality can at best be 
 only highly probable . 2 However, Venn, Lotze, Bosanquet, 
 Sigwart, all allow a place to the inverse function of all 
 inductive reasoning ; their contention, however, is this, that 
 it does not funish an adequate account of the whole matter . 3 
 
 It is interesting to note that Whewell’s theory of induc- 
 tion corresponds in the main to this idea of reduction, or 
 inverse process. He finds in induction a twofold operation 
 of the mind, consisting in the colligation of facts and the 
 explication of conceptions. By the colligation of facts he 
 refers to that insight which is able to see the connections 
 and relations which necessarily exist between the different 
 phenomena present in consciousness ; and by explication of 
 conceptions he refers to the appropriate fitting in of these 
 related facts to some conception of the mind which most 
 readily accounts for them . 4 Such a process is merely the 
 
 1 Empirical Logic, p. 359. 2 Bosanquet, Logic, Vol. II, p. 175. 
 
 8 Venn, 361 ; Bosanquet, Vol. II, p. 175 ; Sigwart, Vol. II, p. 203, 289. 
 
 Lotze, Outlines of Logic, p. 93. 
 
 4 Whewell, Philosophy of the Inductive Sciences, pp. 172, 202. 
 
180 
 
 INDUCTIVE LOGIC 
 
 reading of given facts backward to their origin, or substan- 
 tially an inverse process, where the procedure is from the 
 given concrete to the explanation of the same in terms of the 
 universal to which it can be most appropriately referred. 
 So also Mill’s account of procedure by hypothesis presents 
 characteristics similar to this process of reduction. 
 
 The end of induction is to discover a law having objective 
 validity and universal application. There is a distinction 
 which must be noticed and clearly kept in mind; namely, 
 the distinction between a law and a rule. Induction seeks 
 a law, and not a rule. A law expresses the essential and 
 universal relations subsisting between given phenomena, 
 eliminating entirely all accidental and local coloring. A 
 law has objective validity, and preserves a constant nature. 
 There can be only one law in reference to one and the same 
 connection of facts. A rule however is subjective, dealing 
 with the individual’s attitude to phenomena, rather than 
 an explanation of the essential features of the phenomena 
 themselves. It often is determined in the concrete by that 
 which is external, local, and accidental. There may be 
 many rules, varying with many minds and many tastes. 
 Fundamental and universal laws of political economy be- 
 come maxims and rules in different communities. The laws 
 of morality, universal and immutable, become rules of con- 
 duct in individual experience, admitting of wide difference 
 of opinion and diversity of application . 1 In the processes 
 of induction, therefore, the law is the desideratum, and not 
 the rule. 
 
 Law however is used rather loosely in our ordinary ter- 
 minology. Law as used in jurisprudence has a meaning 
 quite different from law as used in physical science. And 
 so, also, the laws of biology, the laws of political economy, 
 the laws of ethics, are referred to with different shades of 
 meaning in each sphere. However ambiguous may be the 
 significance of “ law ” in ordinary thought and usage, never- 
 l Lotze, Logic, p. 335. 
 
ESSENTIALS OF INDUCTION 
 
 181 
 
 theless in induction it lias a constant and a simple signifi- 
 cance, which, if carefully adhered to, will avoid confusion 
 and obscurity as well, in our inferential processes and 
 results. Law in induction is always in the form of an 
 hypothetical universal : — 
 
 If A is, B is. 
 
 It does not assert what has happened, but what should hap- 
 pen under certain conditions. Given the antecedent A, a 
 certain determinate consequent B is always necessitated. 
 The relation is constant and invariable, and therefore has a 
 universal significance. 
 
 Induction holds a peculiar and important place in our 
 everyday life, because it has to do with the analytical 
 treatment of instances as they appear in experience. The 
 large part of our conscious thinking has to do with the con- 
 crete, the raw material of experience ; this, induction alone 
 can handle. Leonardo da Vinci's maxim was “ to begin with 
 experience and by means of it to direct the reason.” 1 Thus 
 the superstructure of knowledge is raised day by day. The 
 given is continually being interpreted and referred to its 
 appropriate place, as the stones of the quarry are hewn and 
 fitted into their proper position in the building for which they 
 have been designed. There are certain individual experi- 
 ences which it is impossible to determine through our syllo- 
 gistic forms. They cannot be judged deductively. There 
 is no general category under which they can be subsumed. 
 They may be formally illogical if thus expressed, and yet 
 admit of direct investigation and experiment in the induc- 
 tive manner, for the purpose of disclosing the law under- 
 lying them and as yet unknown. 
 
 It often happens that through indifference or indolence 
 we are content to refer many phenomena to long-established 
 and convenient categories, which, if investigated indepen- 
 dently, we would find could not possibly be so treated. The 
 1 Ueberweg, Logic, p. 42. 
 
182 
 
 INDUCTIVE LOGIC 
 
 convenient pigeon hole, because near at hand, receives much 
 that does not properly belong there. It is the office of 
 induction to investigate anew the old material, and then 
 to reclassify in accordance with the revised generalizations 
 which such investigations may necessitate. 
 
 The procedure by induction is in keeping with the scien- 
 tific spirit of the day, — to interpret the phenomena of 
 nature as given, and not to anticipate nature through pre- 
 conceptions, and wrest fact in order to fit theory. It comes 
 to the sources in nature with empty vessels, to draw and 
 carry away that which nature alone can give. 
 
CHAPTER III 
 
 TYPES OF INDUCTIVE INFERENCE 
 
 The process of induction, as we have seen, is a procedure 
 from given instances to the discovery of the law which 
 underlies them, and which is the ground of the connection 
 of the various attributes and relations that unite in the one 
 concrete whole. Viewed from the standpoint of the direc- 
 tion of the process, we have found that it is always toward 
 some general expression of individual experiences, and in 
 this respect it is the inverse of deduction, which proceeds 
 from the general to the particulars which are embraced in it. 
 There is however another and important point of view that 
 should not be overlooked. We have to consider the mode 
 of the process as well as its direction ; not merely the result 
 to be attained, but also the peculiar manner of realizing the 
 same must be considered. Difference in method here gives 
 rise to various kinds of inductive inference. The end pro- 
 posed in all is to generalize our experiences as they occur 
 in the concrete and particular. When I find a given phe- 
 nomenon, A, given in consciousness, and characterized by 
 several distinctive features among which I note specially 
 the mark B, the question at once most naturally suggests 
 itself, Is there a reasonable expectation that I shall always 
 find B as an inseparable accompaniment of A, so that I can 
 assert confidently that whenever A is found, B also will be 
 found ? There are three ways of satisfying ourselves as to 
 the existence of any constant rather than coincidental con- 
 nection between antecedent and consequent, as A and B. 
 These give rise to three different methods of inductive 
 research, and they are as follows : — 
 
 183 
 
184 
 
 INDUCTIVE LOGIC 
 
 I. The Method of Enumeration. 
 
 II. The Method of Analogy. 
 
 III. The Method of Scientific Analysis, or search after 
 causal connection. 
 
 Failure to distinguish between the three methods has 
 given rise to confusion in the definition of and correspond- 
 ing reference to inductive inference ; some authors use 
 induction in one, and some in another of these senses. It 
 is necessary to discriminate carefully, and to maintain a 
 strict consistency in the usage of the terms as defined. 
 
 I. The Method of Enumeration. — We observe the various 
 instances in which certain attributes, as A and B, are con- 
 joined in our experience. We count them in the sense of 
 noting to what extent they accumulate without noticing 
 any exception to what seems at least an invariable connection. 
 We do not necessarily count by precise enumeration reaching 
 a numerically definite result. We notice merely to what 
 extent the observed instances of like nature accumulate ; 
 that is, whether a few, a considerable number, or a very 
 large number. The mere number of instances produces a 
 certain psychological impression, whatever may be their 
 logical force. This is brought about through the laws of 
 association, and creates an expectation of a continuous 
 repetition of the experience in question. This arises from 
 a natural tendency of the mind to generalize. We observe 
 that crows are black ; and the increasing number of confirm- 
 ing instances goes far to establish a connection between the 
 crow and its color which seems to have universal validity. 
 The enumeration of instances may lead us to any one of 
 three results : — 
 
 1. We may meet with no exception whatsoever, until the 
 scope of observation completely embraces the sum of all 
 possible instances. This is complete enumeration, and 
 when enumeration reaches this limit, it passes over into 
 deductive reasoning, by virtue of the logical canon that 
 
TYPES OF INDUCTIVE INFERENCE 
 
 185 
 
 whatever is true of the parts is true of the whole distribu- 
 tively ; that is, provided the summation of the parts has 
 been an exhaustive one. We assert that all the sheep of a 
 given flock are white ; for we have observed each separately, 
 and no one has been missed in the count. So, also, the 
 judgment that all planets move around the sun, resulting 
 from an enumeration of the planets one by one. It is 
 possible also to have a perfect induction with an infinite 
 enumeration of parts. This is possible in two cases, as 
 pointed out by Beneke . 1 First, when the parts are con- 
 nected together continuously in space. This occurs in 
 geometrical demonstration when the inference, based upon 
 the simple figure it refers to, is extended to all figures falling 
 under the like definition. And second, when the parts are 
 not continuously connected, if it can be proved syllogistically 
 that what is true of a definite ?ith part, must also be true 
 for the (n -f l)th part. 
 
 Perfect induction also embraces arithmetical method and 
 computation. Here the whole, which is the sum of the 
 facts in each case, is a totality or universal whose differences, 
 which are all separate and distinguishable, are yet homo- 
 geneous and equal . 2 There is no qualitative differentiation 
 of parts, only a quantitative one. The total is the sum of 
 the units, and each unit is like every other one. If we 
 have one hundred units making a totality, the one that may 
 be the twenty -seventh is precisely like the sixty-seventh. 
 It is a case where each one counts for one and no one for 
 more than one, in an absolutely literal sense. 
 
 It has been urged against perfect induction that it affords 
 no new information, and, therefore, its results are not 
 valuable. However, the summation of particulars in abbre- 
 viated forms is always an advantage. It is a labor-saving 
 process to the mind. It enables the mind to retain a large 
 number of facts by throwing them into one and the same 
 
 1 Quoted by Ueberweg, Logic , p. 482. 
 
 2 Bosanquet, Logic, Vol. II, p. 54. 
 
186 
 
 INDUCTIVE LOGIC 
 
 category ; and it facilitates arithmetical processes by conven- 
 ient comprehending of units within a totality. 
 
 2. The second result that is possible, is that, in counting 
 instances, our enumeration should prove incomplete. From 
 the necessities of the case, we are often not able to observe 
 the entire sphere of possible occurrences and cover the whole 
 ground. It may be that beyond the sphere of our expe- 
 rience, the constant connection between certain phenomena 
 may be disturbed by the appearance of some variable factor 
 of which we have been wholly ignorant. It is the possibili- 
 ties beyond the sphere of observation which render uncertain 
 the results of our count. We are sure as far as we have 
 observed ; but we have not gone far enough perhaps. Such 
 results, formulated in general propositions, are termed 
 empirical laws ; that is, generalizations from an experience 
 necessarily limited. 
 
 3. We have still a third case ; where in our enumeration 
 of positive instances we meet with exceptions to a greater 
 or less extent. Here we cannot even sum up the actual 
 experience in terms of a generalization. There are out- 
 standing exceptions which will invalidate it. We must, 
 therefore, fall back upon the theory of probability and the 
 calculation of chances, presuming that, in general, we will 
 meet with the same proportion of exceptions to positive 
 instances in the future, that we have already observed in 
 the past. So we make, in our minds at least, comparative 
 tables of positive cases over against exceptions, and reach a 
 summary of the result in the form of a ratio, whose numera- 
 tor will be the number of positive cases observed, and the 
 denominator the total number of instances including positive 
 instances and the corresponding exceptions. We observe 
 that some cryptogamous plants possess a purely cellular 
 structure ; others, however, do not, being partially vascular. 
 The probability that a new cryptogam will be cellular can 
 be estimated only on the ground of the comparative number 
 of known cryptogams which are cellular, as over against 
 
TYPES OF INDUCTIVE INFERENCE 
 
 187 
 
 the total number of cryptogams, both cellular and vascular, 
 previously observed. 1 
 
 II. The Method of Analogy. — Here, also, we start with 
 the experience that A is characterized by the mark B. 
 But there is additional knowledge of which we may avail 
 ourselves in the generalization of some past experience 
 already effected, such as the following : that A very closely 
 resembles C, in that the two have many properties or attri- 
 butes in common. The inference by analogy is that C also, 
 as well as A, will have the mark B. It may be that we 
 cannot examine C in a number of various instances to see in 
 how many the mark B occurs. Our only resource is the 
 inference which is based upon the known resemblances, or 
 analogies. This kind of inference, for example, was em- 
 ployed by Sir Isaac Newton in a very interesting manner. 
 He had observed that certain “fat, sulphureous, unctious 
 bodies,” such as camphor, oils, spirit of turpentine, amber, 
 etc., have refractive powers two or three times greater than 
 might be anticipated from their densities. He noticed also 
 the unusually high refractive index of diamond, and from 
 this resemblance, based upon similarity in reference to one 
 attribute only, he inferred that diamond also would prove 
 to be combustible. His prediction in this regard was veri- 
 fied by the Florentine Academicians in 1694. 2 Brewster 
 made a striking comment upon Newton’s inference, to the 
 effect that if Newton had drawn a like analogy in refer- 
 ence to greenockite and octahedrite as he did concerning 
 diamond, inasmuch as they, too, have a very high refrac- 
 tive index, he would have been wholly incorrect. This is 
 an indication of the fact that argument by analogy is not 
 conclusive. 
 
 Bosanquet has very strikingly expressed the essence of 
 the analogical method in saying that “in analogy we weigh 
 the instances rather than count them.” 3 The distinction 
 
 1 Jevons, Principles of Science, pp. 146, 147. 2 Ibid. p. 527. 
 
 3 Bosanquet, The Essentials of Logic, p. 155. 
 
188 
 
 INDUCTIVE LOGIC 
 
 between analogy and enumeration of instances lies in tbis, 
 that in the former we count similar attributes in the con- 
 tents of two instances, and balance them against the dis- 
 similar or unknown. In induction by enumeration we count 
 similar instances, considering them in their totality without 
 examination and comparison of their respective attributes. 
 
 III. The Method of Scientific Analysis. — The instance in 
 question, A, which is characterized by the mark B, is sub- 
 jected to a vigorous analytical examination, to show that A 
 and B are related through a causal connection. This analy- 
 sis is effected either through a minute observation or by 
 means of exact experiment. The end to be attained by such 
 analysis is to separate a complex phenomenon into its 
 several elements, by which process a causal connection may 
 be revealed, whose very existence is disguised by the com- 
 plexity of the phenomenon. For instance, the phenomenon 
 of death following the taking of arsenic is an event so com- 
 plex as to evade a precise determination of the causal rela- 
 tion. When analyzed into simpler elements, it is found 
 that the immediate effect of arsenic upon the bodily tissues 
 is to harden them so as to prevent their normal functioning. 
 This is the causal ground of the death due to arsenic. 
 Moreover, this analytic process, which may be appropriately 
 called a material one, is supplemented by a formal process 
 of negation ; that is, an instance in which the suspected 
 causal element is absent in the complex phenomenon under 
 investigation, and the related effect, before observed, now 
 no longer appears. This formal process acts as a check, 
 and as a verification as well, of the material analysis of the 
 phenomenon. For example, an antidote, as sesquioxide of 
 iron, being administered, no death from arsenic occurs ; and 
 it is also observed that no hardening of the tissues has 
 resulted, therefore the former result, hardening of tissues 
 producing death, has been thus corroborated negatively by 
 the fact that where no hardening of tissues has resulted, 
 death does not follow. 
 
TYPES OF INDUCTIVE INFERENCE 
 
 189 
 
 We see at once the advantage of such a method over that 
 of counting all instances where taking of arsenic has caused 
 death. The latter is a phenomenally adjudged result; the 
 former penetrates with analytic insight to the ground of the 
 phenomenon itself. Thus one instance, if its parts and 
 their manifold relations are adequately comprehended, may 
 suffice for a universal conclusion based upon it. It is true, 
 however, as remarked by Bosanquet, that “ number of ob- 
 servations does, as a rule, assist analysis and contribute to 
 eliminating error. Scientific analysis as such, however, 
 does not deal with instances, but only with contents.” 1 
 
 In cases where the phenomenon does not reveal its com- 
 ponent elements under observation, and it is impossible to 
 subject it to experiment, the most likely cause of the effect 
 in question is tentatively judged to be the real cause, until 
 it can be verified in reality. This is procedure by hypothe- 
 sis, and is always resorted to as preliminary to a subsequent 
 experiment which is its test, or else in lieu of such an ex- 
 periment when it is by the nature of the case precluded. 
 It is a form of ideal analysis. The experiment is constructed 
 mentally. The phenomenon is separated into what we would 
 reasonably imagine its simpler elements would be. We are 
 constrained to believe that if the hypothetical antecedent 
 existed, it would be adequate to produce the effect. Al- 
 though rising in the sphere of the imagination, it is that 
 with which the mind is, for the time at least, satisfied as 
 an explanation of the facts which demand some cause to 
 account for them. Kegarding induction as a process of 
 reduction, hypothesis is the assumed universal or middle 
 term, which will necessitate the phenomenon under investi- 
 gation as its logical conclusion. 
 
 We will now proceed to a further examination of these 
 methods, considered both singly and together. 
 
 1. They all proceed upon the supposition that what is 
 given in consciousness has some necessary ground for its 
 1 Bosanquet, Logic , Vol. II, p. 118. 
 
190 
 
 INDUCTIVE LOGIC 
 
 being. In enumerative induction, there is some causal con- 
 nection presupposed, yet in a very general and indefinite 
 manner, and accompanied by no analysis of the various 
 concepts either by a systematic observation or experiment. 
 It is a vague sense of uniformity, which, when observed 
 for many times, we feel will continue indefinitely. That 
 which has happened often and not contradicted carries 
 with it a certain convincing power by dint of bare repeti- 
 tion, especially to persons of narrow experience, and un- 
 accustomed to discriminating observation. Ueberweg has 
 made the following comment in reference to the so-called 
 imperfect induction. “ The conclusion is made universal 
 with more or less probability, and the blank which remains 
 over in the given relations of spheres is legitimately filled 
 up partly on the universal presupposition of a causal-nexus 
 in the objects of knowledge, partly on the particular pre- 
 supposition that in the case presented such a causal-nexus 
 exists as connects the subject and predicate of the conclu- 
 sion. The degree of probability of the inductive inference 
 depends in each case on the admissibility of this last presup- 
 position, and the various inductive operations, the extension 
 of the sphere of observation, the simplification of the ob- 
 served conditions by successive exhaustion of the unessen- 
 tial, etc., all tend to secure its admissibility .” 1 
 
 Analogy likewise proceeds upon the assumption of an 
 underlying cause among the observed phenomena, and this 
 is more definitely in the foreground throughout the process 
 than in that of induction by enumeration. Analogy is based 
 upon the postulate that similar phenomena have similar 
 causes ; the greater the agreement of the various attributes 
 of the different phenomena compared, the greater will be 
 the resultant probability that causes capable of producing 
 them as effects will be similar. The similarity of the light- 
 ning flash to the electric spark suggested to Benjamin Frank- 
 lin the possibility that they were due to a like origin, and 
 1 Ueberweg, Logic, pp. 483 f. 
 
TYPES OF INDUCTIVE INFERENCE 
 
 191 
 
 by experiment his analogical reasoning was actually con- 
 firmed, as is well known. Upon the theory that the world 
 as it exists for us in knowledge forms a system, to some 
 place in which every phenomenon given in experience must 
 be appropriately and necessarily referred, it follows there- 
 fore that a simple experience devoid of any complexity of 
 parts may fit into several possible places in our world of 
 consciousness, and remain so far forth indeterminate. How- 
 ever, a complex phenomenon, with many parts intricately 
 connected, will fit into one unique place only in the system 
 to which it must be referred. It is like a key that will fit 
 into only one lock. The presumption therefore is that any 
 other phenomenon which resembles the first through much 
 of its entire content, part for part, attribute for attribute, 
 will also resemble it further as regards other attributes not 
 yet examined, so that it will likewise fit into the peculiar 
 place in the system of knowledge to which the first has been 
 found to belong. There is always a strong probability that 
 agreement in spheres of great complexity is not a mere 
 coincidence, but the result of a causal relation. One charac- 
 teristic of a system, which we have found to be the ground 
 of inference generally, is the coordination of like things 
 under one concept. Analogy therefore is based upon the 
 view of causal connections within the system which com- 
 prises the world as given in consciousness. 
 
 In the third method, the causal relation is more promi- 
 nent still, and the search for it characterizes the procedure 
 employed. That which in the other methods may exist 
 merely as a vague impression is here formulated and made 
 the direct and sole object of research. 
 
 2. The three methods in the order here presented show 
 an increasing prominence given to the causal connection in 
 the phenomena of experience. And therefore they possess 
 a relatively increasing scientific value. As the first has 
 only indirect reference to the causal connection of its facts, 
 it is the least trustworthy and has no claim as a scientific 
 
192 
 
 INDUCTIVE LOGIC 
 
 method. It breaks down as soon as an exception is noted ; 
 and is even weakened by the fact that it is constantly men- 
 aced by the possibility at least of the appearance of an ex- 
 ception. “ How do we know,” says Green, “ that the instances, 
 with the examination of which we are always dispensing on 
 the strength of the rule (that is, our generalization), might 
 not be just what would invalidate it, if they were exam- 
 ined ? ” 1 We may arrive at the conclusion, based upon our 
 observation and consequent record, that all sheep are white, 
 and yet black sheep do occur, in every flock, as the prov- 
 erb has it. According to Aristotle, the proposition that 
 all swans are white, was a perfectly general one, and yet in 
 recent times black swans have been discovered in Australia. 
 Bacon’s criticism upon this method has become classic : 
 “ Inductio quae procedit per enumerationem simplicem, res 
 puerilis est et precario concludit et periculo exponitur ab 
 instantia con trad ictoria et plerumque secundum pauciora 
 quam par est et exiis tantummodo quae presto sunt pro- 
 nunciat.” 2 
 
 The validity of this method of procedure depends largely 
 upon the probability of our meeting and noticing exceptions 
 were they to occur. As Lotze puts it: “A man who never 
 observes a place of public resort but once in every seven 
 days, and that on a Sunday afternoon, has no right to sup- 
 pose, because it is crowded then, that it is as crowded on a 
 week-day .” 3 He is here in no position to note the excep- 
 tions even should they occur. 
 
 Analogy, unless confirmed by experiment, or upon the 
 ground of resemblance established by a verifiable hypothesis, 
 has no claim to be considered as a scientific method. There 
 may be false analogies depending upon surface resemblances. 
 A child might conclude that oil would put out fire because 
 it so closely resembles water, which he knows can extinguish 
 the flames. The difference between essential and accidental 
 
 1 Green, Philosophical Works, Vol. II, p. 282. 
 
 2 Novum Organum, i. 105. 8 Lotze, Logic, p. 343. 
 
TYPES OF INDUCTIVE INFERENCE 
 
 193 
 
 agreement between phenomena can be revealed only when 
 the underlying cause is ascertained. 
 
 The third method alone has scientific worth. True in- 
 duction must be a continued search to discover a causal 
 relation. 
 
 3. The two first processes fulfil their functions largely 
 as tentative and suggestive methods. In enumeration of 
 instances, we are often led to note resemblances which 
 become the basis of analogy. And analogy suggests, in 
 turn, hypothesis which is capable of verification through 
 subsequent experiment. 
 
 The question may be put, “ Which of the three processes 
 is induction proper ? ” The fact is that it may involve all 
 three, but it is not complete until it reaches the third, — the 
 experimental method. Analogy is especially fertile in sug- 
 gestion. Scientific minds most carefully trained and versed 
 in scientific methods of research are often most keen in 
 noting resemblances, and detecting analogies which become 
 the basis of their experiments. Newton possessed that rare 
 insight which, in spite of the manifest dissimilarity of the 
 two phenomena, could yet discern an essential likeness be- 
 tween the fall of an apple and the gravitating force of the 
 moon toward the earth. 
 
 4. It is also to be observed that the choice of method will 
 depend largely upon mental habit. Some minds naturally 
 or by special training and surroundings are given to experi- 
 ment. They have a testing facility and inventive capacity. 
 Others naturally are susceptible in an unusual degree to 
 contrasts and resemblances. Others again are accustomed 
 to accurate observation that is ever pushing beyond and 
 seeking to extend its sphere. Thus we have a natural divi- 
 sion of these methods according to psychical proclivities. 
 The choice of method is often conditioned by the force of 
 circumstances. Experiment is not always possible. Are all 
 crows black ? There is no connection between the general 
 organism of the crow and its color that has thus far been 
 
194 
 
 INDUCTIVE LOGIC 
 
 revealed through analysis or experiment. The only recourse 
 is to number instances over the widest possible field. We 
 say, moreover, that Mars may be inhabited ; for it has an 
 atmosphere similar to the earth and therefore capable 
 of sustaining life. Analogy is the only guide in such a case, 
 and it is impossible to verify it either by observation or 
 experiment. 
 
 5. All the methods tend to one end, that of effecting a 
 generalization of experience. The generalization may be 
 either a numerically general one, or one expressed in terms 
 of a generic concept. 
 
 (1) The former consists in the extension of several in- 
 stances to their repetition under, like conditions. 
 
 (2) The second consists in the extension of several in- 
 stances to all cognate species under the same genus. 
 
 Examples of these two kinds of generalization are as 
 follows : The general proposition that all sulphur is com- 
 bustible is of the former kind ; all instances are substantially 
 of the same nature, and do not differ as distinguishable 
 species under the same genus, but rather a repetition of 
 like phenomena. The general concept in the above propo- 
 sition is of the nature of an infima species. On the other 
 hand, the proposition that all mammals are vertebrates, has 
 the subject-term in form of a generic concept. Many spe- 
 cies, differing widely among themselves, may be embraced 
 under it. 1 
 
 1 Sigwart, Logic, Vol. II, pp. 310, 311. 
 
CHAPTER IV 
 
 CAUSATION 
 
 We have seen that induction as a truly scientific method 
 consists in the analytical determination of the relations of 
 cause to effect in any complex phenomenon, accompanied 
 by a generalization of the result obtained. The final out- 
 come of such a process is a universal concept which em- 
 bodies a law, expressed in terms of a constant connection 
 between antecedent and consequent. As Green has said, 
 “ The essence of induction consists in the discovery of the 
 causes of phenomena .” 1 A causal view of the universe 
 gives rise to logical concepts, whereas a mythological view 
 of the universe, as in ancient times, resulted in mere empiri- 
 cal concepts, which gave no assurance either of stability or 
 invariability. It will be necessary therefore to determine 
 more precisely the logical significance of the causal idea, 
 which seems to underlie all inductive inference. This is no 
 easy task. According to Clifford, “ cause ” has sixty-four 
 meanings in Plato, and forty-eight in Aristotle . 2 
 
 The causal idea has sometimes found expression in the 
 phrase, the uniformity of nature, or it is often referred to 
 as the doctrine of universal causation. These two phrases 
 are often used interchangeably ; this gives rise to confusion 
 of thought, for their meanings are quite distinct. 
 
 Unif or mity o f nature, strictly interpreted, means that like 
 antecedents, under precisely the same conditions, will be 
 followed by like effects ; this idea expresses one phase of 
 causation, viz. its invariability. 
 
 1 Green, Philosophical Works, Vol. I, p. 284. 
 
 2 Clifford, Lectures and Essays, Vol. I, p. 149. 
 
 195 
 
196 
 
 INDUCTIVE LOGIC 
 
 The doctrine of uni versa l causa tion , however, expresses 
 the impossibility of phenomena rising spontaneously, with- 
 out an antecedent, or antecedents, sufficient rationally to ac- 
 count for them. The two ideas lie at the root of the causal 
 idea. As Tennyson has put it : — 
 
 For nothing is that errs from Law. 
 
 Some confusion has also arisen from the failure to discrimi- 
 nate precisely between the philosophical and the purely 
 logical questions relative to the general subject of causa- 
 tion. Causation may be viewed from three different points 
 of view : — 
 
 1. What it is phenomenally, that is, as regards its physi- 
 cal aspects. 
 
 2. What it is essentially, as regards its real nature. This 
 is a metaphysical question. 
 
 3. What it is in respect to its characteristic attribute of 
 invariability. This is a purely logical question. 
 
 (1) As to the first, what is causation phenomenally ? 
 What is its purely physical significance ? Investigations 
 in this line have led to the doctrine of the conservation of 
 energy. This is substantially the assertion that, in every 
 event, no new energy is called forth which did not exist 
 before potentially at least, nor can any energy be ultimately 
 lost; nothing new is created, — there is only a change or 
 transfer from one state or condition to another. Moreover, 
 the sum total of energy in the universe is a constant quan- 
 tity ; it can neither be added to, nor subtracted from. There 
 is an excellent illustration of this theory in the admirable 
 chapter on “ Conservation of Energy ” by Professor Tait. 
 I give it somewhat in full : “ I allow an electric current to 
 pass through a galvanic battery, and there is for the moment 
 a certain quantity of zinc consumed, or, as we may put it, a 
 certain quantity of potential energy in the battery has been 
 converted into the kinetic energy of a current of electricity. 
 That current of electricity passes round some yards of cop- 
 
CAUSATION 
 
 197 
 
 per wire, coiled round a bar of iron or a number of fine iron 
 wires which are standing vertically inside this apparatus. 
 The moment the current passes, these iron wires are con- 
 verted into magnets, but, in consequence of the conservation 
 of energy, while this is going on they weaken the current. 
 The current of electricity becomes weaker in the act of 
 making the magnet, but the moment the magnet springs 
 into existence, it again is weakened, because, from the 
 necessities of its position, its mere coming into existence 
 necessitates the passage of a new current of electricity in 
 another coil of wire which surrounds this externally, and 
 finally this last current we can use to produce heat, or light, 
 or sound.” 1 In this cycle of changes we see how closely 
 connected even disparate phenomena are, and how the ap- 
 pearance of energy in any one definite state is dependent 
 upon its previous existence in some other state. The 
 doctrine of conservation of energy, we shall see later on, 
 may be suggestive as to the nature of the analytical treat- 
 ment of cause and effect. 
 
 (2) The philosophical question as to the inner nature of 
 causation met with one answer generally until the time of 
 Hume ; namely, that the idea of cause signified that the 
 antecedent was efficient in producing the corresponding 
 consequent, implying the transfer of power sufficient to 
 bring about the effect. Hume , however, contended that in the 
 greatest possible extent of our knowledge, all that we cer- 
 tainly know is this, that one event follows another. We have 
 no ground for an assertion concerning the manner in which 
 the sequence is effected, nor for assuming any real tie be- 
 tween them. Hume insisted that phenomena were conjoined, 
 but never connected. 2 His opponents, as Kan t and others, 
 deny him, however, his fundamental position, — that the 
 origin of the causal concept comes from experience alone. 
 They urged that it has an a priori origin, a concept simple 
 
 1 Tait, Recent Advances in Physical Science, pp. 76, 77. 
 
 2 Hume, Essay on Idea of Necessary Causation. 
 
198 
 
 INDUCTIVE LOGIC 
 
 and unanalyzable, given through intuitive insight; developed 
 in the sphere of experience, but not dependent upon expe- 
 rience for its warrant. It is an interesting fact that the 
 idea of the conservation of energy developed subsequent 
 to Hume’s time. It seems to give evidence which Hume 
 insisted was not and could not be forthcoming ; namely, 
 concerning the idea of the antecedent as an efficient power. 
 Through the modern doctrine, the impression of a transfer 
 of real power is produced, though its mode and manner still 
 remain a mystery. 
 
 (3) The logical aspect concerns not the phenomenal 
 manifestation of cause and effect, nor their inner nature, 
 but rather the element of invariability in causation. Two 
 questions here suggest themselves : First, Is invariability a 
 fact, — a constant element in causation? Second, How do 
 we account for its existence ? The first only has truly 
 logical significance. The invariability of causation, that 
 like antecedents under precisely the same conditions pro- 
 duce like effects, alone makes induction possible. Mill says 
 that it is the belief in the uniformity of nature which stands 
 as the ultimate major premise in every process of induction. 
 Hume accepted it, and based inferences upon it, and never 
 challenged it as a working basis as regards the affairs of 
 everyday life. He acknowledged the element of invaria- 
 bility, and only denied the bond of connection. This ele- 
 ment has peculiar logical significance : without it, it would 
 be impossible to extend our knowledge beyond the seen and 
 the heard, indeed that which is seen and heard would then 
 have no meaning, and no basis for their interpretation and 
 appreciation. Being assumed, however, as a logical postu- 
 late, we have a basis for induction, — a constant to be sought 
 for and to be depended upon, in explanation of the past and 
 in prediction of the future. 
 
 When we come to the second question, which is essen- 
 tially a genetic one, how the belief in the uniformity of 
 nature arose, we find two classes which answer respectively 
 
CAUSATION 
 
 199 
 
 that the belief arose a priori, and on the other hand, from 
 experience simply. The former is the opinion especially 
 associated with the Scottish School of philosophy. Hume 
 holds that it proceeds from a psychological law of custom 
 or habit, — an unbroken line of mental associations induc- 
 ing a belief within, concerning the uniformity of nature 
 without. Mill has also a like empirical basis for a belief 
 in the uniformity of nature ; he holds that having observed 
 uniformity in many experiences, in fact never contradicted, 
 we generalize so as to cover a sphere beyond our experience. 
 Moreover, we possess the consensus of testimony, coexten- 
 sive with the history of humanity, of the indefinitely wide 
 extent of the sphere of causation, and the accompanying 
 characteristic of uniformity. His position is fortified by 
 the fact that in the process of incomplete induction, its 
 probability is strengthened where there has been exception- 
 ally abundant scope for observation, so that there is the 
 overwhelming conviction that if there had been a time or 
 place where the law would prove untrue, it would have been 
 noticed. Instead of universal causation, Mill and his fol- 
 lowers make a more cautious statement, — causation as 
 coextensive with the sum total of human experience. This 
 is abundantly adequate to embrace all possible circum- 
 stances of practical inference. The immensely high degree 
 of probability engenders a subjective certitude which in 
 everyday conduct of affairs, and even in the more exact 
 requirements of scientific investigation, is never questioned. 
 
 Preyer has given an interesting account of the extremely 
 early appearance of the appreciation of the causal relation 
 in the case of his child, “who, at the three hundred nine- 
 teenth day of its life, struck several times with a spoon 
 upon a plate. It happened accidentally, while he was doing 
 this, that he touched the plate with the hand that was free ; 
 the sound was dulled, and the child noticed the difference. 
 He now took the spoon in the other hand, struck with it on 
 the plate and dulled the sound again, and so on. In the 
 
200 
 
 INDUCTIVE LOGIC 
 
 evening the experiment was renewed with a like result. 
 Evidently the function of causality had emerged in some 
 strength, for it prompted the experiment. The cause of the 
 dulling of the sound by the hand — was it in the hand or in 
 the plate ? The other hand had the same dulling effect, so 
 the cause was not lodged with the one hand. Pretty nearly 
 in this fashion the child must have interpreted his sound- 
 impression, and this at a time when he did not know a single 
 word of his later language .” 1 
 
 The theoretical soundness of Mill’s speculations, however, 
 has a flaw, although the practical results may not be thereby 
 invalidated. The inductive process, which is supposed to 
 be a truly scientific method, and superior to induction by 
 simple enumeration must, according to Mill, at the last 
 analysis, rest upon a principle which is itself based upon an 
 incomplete induction. A very fair and searching criticism 
 of Mill is that of Venn’s in his Empirical Logic . 2 Whately 
 insists that the whole question concerning the nature of our 
 belief in uniformity is irrelevant, as it is a purely psycho- 
 logical and not a logical one. Mansel holds a mediating 
 position in insisting that the idea of universal causation is 
 intuitive, while that of uniformity is necessarily empirical. 
 Sigwart has very trenchantly criticised Mill in that “ taking 
 away with one hand what he gives with the other, he shows 
 in the uncertainty of his views the helplessness of pure 
 empiricism, the impossibility of erecting an edifice of uni- 
 versal propositions on the sand-heap of shifting and isolated 
 facts, or, more accurately, sensations; the endeavor to ex- 
 tract any necessity from a mere sum of facts must be fruit- 
 less. The only true point in the whole treatment is one in 
 which Mill as a logician gets the better of Mill as an 
 empiricist; namely, that every inductive inference contains 
 a universal principle ; that if it is to be an inference and 
 not merely an association of only subjective validity, the 
 
 1 Preyer, The Senses and the Will, pp. 87, 88. 
 
 2 Venn, Empirical Logic, p. 130. 
 
CAUSATION 
 
 201 
 
 transition from the empirically universal judgment All 
 known J.’s are B to the unconditionally universal All that 
 is A is B, can only be made by means of a universal major 
 premise, and that only upon condition of this being true 
 are we justified in inferring from the particular known A’s 
 to the still unknown A’ s.” 1 
 
 The whole tendency of the modern logic is to base the 
 causal postulate upon a ground which is epistemological ; 
 namely, inasmuch as our knowledge is one and self-con- 
 sistent throughout all its separate elements, there must be 
 a corresponding invariability in the phenomena themselves, 
 as there is in the system of knowledge which results from 
 the interpretation of these phenomena. This is the general 
 view of Sigwart, Bosanquet, Lotze, and Green. 2 
 
 This view may be considered also as an expression of the 
 Law of Sufficient Reason ; namely, that there is an inherent 
 characteristic of intelligence which demands that every 
 element of consciousness must be referred to some other 
 element for its explanation, and that it is only when the 
 logical connection of ideas corresponds to a real causal con- 
 nection, that the mind discovers a reason for its several 
 experiences which is satisfying. It has been said by Ueber- 
 weg, as giving expression to this view : “ The external in- 
 variable connection among sense phenomena is, with logical 
 correctness, explained by an inner conform ability to law, 
 according to the analogy of the causal connection perceived 
 in ourselves between volition and its actual accomplishment.” 3 
 
 There is a distinction that is of importance to note be- 
 tween the popular and the scientific idea of cause. The 
 former is the outcome of the supposition that whatever 
 immediately precedes the effect has evidently produced it, 
 and that this is sufficient wholly to account for it. Such 
 
 1 Sigwart, Logic, ~V ol. II, p. 303. 
 
 2 Ibid., Vol. II, pp. 119, 120 ; Bosanquet, Logic, Vol. II, pp. 220 , 251: 
 Lotze, Logic, p. 68; Green, Philosophical Works, Vol. II, p. 286. 
 
 3 Ueberweg, Logic, pp. 281, 282. 
 
202 
 
 INDUCTIVE LOGIC 
 
 an idea of causes leads, at the best, but to a loose and super- 
 ficial determination of the relation between any antecedent 
 and its consequent, and there is the danger, moreover, of a 
 hasty inference which results in the fallacy of post hoc ergo 
 propter hoc. In order to attain a true view of causation, we 
 must especially attend to the extreme complexity of the 
 causal connection. There is no such thing as a simple 
 cause followed by a simple effect. The cause is always a 
 combination of several elements, circumstances, and condi- 
 tions ; the effect is always manifold. This characteristic 
 has been admirably presented in Mill’s chapter on the 
 “Plurality of Causes and the Intermixture of Effects .” 1 It 
 is well known that the variation in the height of a barometer 
 is due partly to the variation of the atmospheric pressure, 
 and partly to the variation of the expansion of the mercu- 
 rial column due to heat. In exact determination, some 
 experiment or calculation must precede, before there can be 
 a discrimination between the elements of the joint effect. 
 And so also, a number of circumstances may combine to 
 restore an invalid to health, no one of which alone being 
 capable of effecting his recovery. 
 
 The cause of any phenomenon has been defined by Mill, 
 as also by Brown and Herschel, as the sum total of all its 
 antecedents. This statement has been criticised, inasmuch 
 as the sum total of all antecedents is indeterminate, and 
 that there is no end to the possible ramifications in all 
 directions which an exhaustive analysis of any complex 
 cause will- yield. However, the problem is one of reduction 
 to simplest possible terms within the range of our powers of 
 observation and experiment. There is much in the sum 
 total of all the antecedents of any given effect which is 
 irrelevant. It is the peculiar function of logical analysis to 
 discriminate between the relevant and irrelevant. The 
 temperature of the laboratory will not affect, one way or 
 the other, experiments with falling bodies ; but will essen- 
 1 Mill, Logic, Book III, Chap. X. 
 
CAUSATION 
 
 203 
 
 tially influence certain chemical experiments, and must 
 enter as one of the determining factors in the sum total of 
 antecedents. It may be that certain elements of a complex 
 whole may seem to us ultimate and unanalyzable, and yet be 
 themselves systems of more or less complexity. There is 
 always a limit to analysis, both experimental and mental. 
 The analysis is to extend to the ultimate parts as far as 
 possible. It is not an exact process, but a process which 
 tends to exactness to the extent which the scope of finite 
 intelligence will permit. The reason is not at fault so much 
 as the natural limitations of observation and experimental 
 analysis. The end of our research in causal analysis is to 
 discover an invariable relation that can be expressed in the 
 form of an hypothetical universal, — If A, then B. 
 
 In order to effect this, the complex A must be separated 
 into its parts, a, b, c, etc., and the effective, and necessary, 
 and indispensable element producing B must be determined. 
 Suppose it proves to be a, it may be possible to subject this 
 to further analysis, and to reduce it to simpler elements, such 
 as x, y, z, etc., and x be found as the significant element of 
 the real cause. Each analysis determines a narrower and 
 still narrower sphere within which the cause lies. A man 
 is shot. We say the bullet killed him ; then the driving 
 force behind the bullet; then the explosive power of the 
 gunpowder ; this in turn was occasioned by the combined 
 chemical and mechanical energy of its ingredients whereby 
 a solid is transformed into a gaseous substance many times 
 its original bulk. 
 
 Sooner or later we must reach the end of our analysis, 
 and the investigation be necessarily checked. No explana- 
 tion is ultimate ; we only transfer our point of view from a 
 less to a more familiar sphere of interpretation. We do not 
 feel the need of explaining the very familiar ; though the 
 most familiar is hardest satisfactorily to explain, because 
 there is nothing simpler in whose terms we may paraphrase 
 it. We feel this in giving a definition of terms whose 
 
204 
 
 INDUCTIVE LOGIC 
 
 meaning we best know, and which we most frequently use. 
 Mr. Barrett, a former assistant at the Boyal Institution, 
 said of Faraday : “ I well remember one day when Mr. 
 Faraday was by my side, I happened to be steadying, by 
 means of a magnet, the motion of a magnetic needle under 
 a glass shade. Mr. Faraday suddenly looked most impres- 
 sively and earnestly, as he said : ‘ How wonderful and 
 mysterious is that power you have there ! The more I think 
 over it, the less I seem to know.’ And yet, he who said 
 this knew more of it than any living man.” 1 
 
 Although our knowledge is limited as in all cases of 
 causation however simple, nevertheless, as far as it goes, 
 the several elements are related logically, that is, necessarily 
 and universally. We may only know in part, but still we 
 know, and the world, as interpreted for us in knowledge, is 
 a world of invariable sequences. The process of inductive 
 analysis, therefore, consists in reducing a complex antecedent 
 to its ultimate parts, in order to reveal the element or ele- 
 ments in it which may have caused the given effect. It some- 
 times happens that different elements in an antecedent may 
 be considered severally as the cause, according to the psycho- 
 logical point of view as regards the interests of the investiga- 
 tor. It is not always that a scientific determination of the 
 cause is required ; it may be that all that is desired is a 
 knowledge of that part of the antecedent which is most 
 closely and prominently connected with the event in 
 question. An inquiry may be started in reference to the 
 cause of an epidemic in a community. One may discover 
 the cause in the carelessness of sanitary engineers ; another 
 may say the cause lies in the poor construction of the 
 sewerage ; another says that the cause of the epidemic is a 
 certain kind of bacilli. Each one is looking at the chain of 
 events related as cause and effect ; but they all look at 
 different links of the same chain. One element, therefore, 
 of a complex antecedent may be brought into more or less 
 1 Gladstone, Michael Faraday, p. 180. 
 
CAUSATION 
 
 205 
 
 prominence as the efficient element of the cause, according 
 as the point of view is shifted. If, in the search for the 
 cause of phenomena, the sum total of antecedents were 
 always given exhaustively, the explanation might become 
 so loaded down with details as to burden the mind, and 
 confuse rather than clear the understanding. 
 
CHAPTER V 
 
 THE METHOD OF CAUSAL ANALYSIS AND 
 DETERMINATION 
 
 It will be well to consider the various cases which will 
 confront us in seeking to analyze a complex antecedent for 
 the purpose of discovering its cause. 
 
 1. There are instances where cause and effect a ppear i n 
 evident sequence. There is an antecedent which is fol- 
 lowed by a consequent. If A happens, then B will happen. 
 Instances of this kind most readily yield themselves to the 
 process of analysis, because a change in any given phenom- 
 enon is occasioned by the efficiency of the antecedent which 
 may be observed in connection with the change itself. It 
 is easier to note active than passive relations, the dynamic 
 rather than the static. The attention is attracted and held 
 by change. The bird flying across our path is observed, 
 and the one perched upon the tree near at hand, however 
 conspicuous may be its position, is passed by without any 
 notice taken of it. It is easier to connect the moisture of 
 the grass with falling rain, than when the same is occa- 
 sioned by the dew. In one case, the causal relation is ex- 
 hibited in operation ; in the other, the connection is veiled. 
 We find the grass wet; what preceded it we are not able to 
 see. There are several instances of sequence among ob- 
 served phenomena which must be carefully discriminated 
 in order to avoid confusion of thought. They are as 
 follows : — 
 
 (1) When we have A followed by B, and A ceases wholly 
 while B endures for an appreciable time afterwards, or it 
 may be permanently. A billiard ball strikes another, the 
 
 206 
 
CAUSAL ANALYSIS AND DETERMINATION 207 
 
 second goes on by virtue of the newly acquired energy 
 transferred by impact from the first, which, however, stops 
 altogether. I throw a ball which lodges on the top of a 
 building; the effect produced lasts permanently, for the 
 ball has gained a gravity potential due to the energy im- 
 parted to it by the initial throwing. The old formula, 
 therefore, does not always hold : “ Cessante causa cessat 
 effectus.” 
 
 (2) Cases where A ceases, and thereupon B immediately 
 ceases also. If we cut off the supply of gas which feeds 
 a flame, the flame at once disappears. There are cases, 
 however, when an appreciable time must elapse in order 
 that the transferred energy in the effect may be dissipated. 
 When we shut our eyes the stimulus causing the percep- 
 tion is cut off, and the perception at once is at an end; 
 however, there are cases where the stimulus being very 
 strong, after-images are induced which remain for some 
 time in the dark field after the eyes are closed. 
 
 (3) Cases where the antecedent is wholly inadequate to 
 produce the effect, but whose function is merely to liberate 
 potential energy already stored, and waiting an occasion 
 for its active manifestation. A slight blow upon a piece 
 of dynamite causes an explosion wholly disproportionate 
 to the striking force employed. As is well known, heat is 
 often an exciting cause of chemical action. In such cases 
 the real cause is more or less concealed, while that which 
 is apparent upon the surface is not a cause so much as an 
 occasion of the phenomenon in question. I touch the pen- 
 dulum and a clock starts and so continues for many hours ; 
 the swinging pendulum, however, is only the occasion of 
 liberating the potential energy of the wound-up spring, 
 and thence the power which runs the clock, pendulum, 
 wheels, hands, and all. 
 
 2. We have also instances not so much of sequence as 
 of concurrence. The planets revolve around the central 
 sun; here the cause is constant, attended by constant 
 
208 
 
 INDUCTIVE LOGIC 
 
 effect. The machine never runs down, nor has to be 
 wound up. 
 
 3. Again there are instances of coexistence. These are 
 more difficult to analyze, for the phenomena do not here 
 appear as antecedent and consequent in the midst of chang- 
 ing conditions and circumstances. We have coexistence 
 of two kinds : — 
 
 (1) Coexisting attributes in one and the same organism. 
 They are always found together. They form one generic 
 concept and are called by one name. Cows have horns, 
 cloven feet, are ruminant, etc. Dogs have their distinct 
 and constant characteristics. The orange has its correla- 
 tion of color, taste, smell. And so we have the so-called 
 “ natural kinds,” i.e. organisms presenting an unique and 
 characteristic appearance, differentiated thereby from all 
 others. There are also certain correlations of growth which 
 present a constant relation between certain attributes, as 
 the fact, however we may explain it, that cats with blue 
 eyes are invariably deaf. There are, moreover, illustrations 
 of the same in an inorganic sphere, as the law which con- 
 nects the atomic weight of substances and their specific 
 heat by an inverse proportion; or that other law which 
 obtains between the specific gravity of substances in the 
 gaseous state, and their atomic weights, they being either 
 equal or the one a multiple of the other. In many cases, 
 the bare fact of coexistence must be accepted without being 
 able to explain the causal ground of it. The several ele- 
 ments present a constant association, and that is all that 
 can be said about it. In other cases, however, a cause may 
 be found, for instance, as regards the correlation of warm- 
 blooded animals always possessing lungs ; the connection 
 between respiration and the generation of heat is found to 
 depend upon chemical action as its causal basis. 
 
 (2) A relation of statics rather than dynamics, as, for 
 instance, a pillar supporting a roof or arch is said to be the 
 cause, in the sense of the sustaining cause, of the super- 
 
CAUSAL ANALYSIS AND DETERMINATION 209 
 
 structure. So also the cohesive force which holds together 
 the particles of a stone. In such cases the energy inherent 
 in the cause is of the nature of a stress and strain. 
 
 4. Under this head are embraced the phenomena of vital 
 growth or de velopment, . These are the most difficult of all 
 the causal problems to determine ; for it is required to dis- 
 cover the inner necessity of essence, and how the succeeding 
 stages of development unfold through the play of the cen- 
 tral forces inherent in the very nature and being of the 
 organism itself. Mill is content with classifying organisms 
 as different natural kinds, and he is not concerned with the 
 reason why there should be such and such kinds, nor does 
 he attempt to discover any law concerning these natural 
 correlations and the mode of their growth. In inductive 
 analysis, our concepts must not merely grasp what the natu- 
 ral kinds are, but also what has determined them to be what 
 they are. Darwin puts special emphasis upon the environ- 
 ment as affecting changes in organisms and producing dif- 
 ferentiating modifications among species. This, however, 
 must be considered not as sole factor, but one which is com- 
 bined with inner needs and necessities. Moreover, Darwin 
 has drawn attention to the fact that individual differences 
 need scientific explanation as well as the common attributes, 
 as, for instance, why some sheep are black, and why some 
 pigeons are fantailed and others are not. In all such con- 
 siderations we must not lose sight of the fact that there are 
 two determining factors, — the inner necessity of develop- 
 ment, and the external necessity of causality, as organisms 
 are acted upon by their environment. 1 
 
 5. Cases of collocation where no one element of the cause 
 is efficient, but together they all combine to produce the 
 effect. In searching for the cause, we must not only find a 
 certain amount of energy capable of producing the effect, 
 but we must also discover what peculiar arrangement of the 
 elements concerned must exist before the energy in question 
 
 1 Sigwart, Logic, Vol. II, pp. 322, 330, 331. 
 
210 
 
 INDUCTIVE LOGIC 
 
 can become operative. Chalmers says that “ the existing 
 collocations of the material world are as important as the 
 laws which the objects obey, that many overlook this dis- 
 tinction and forget that mere laws without collocations 
 would have afforded no security against a turbid and dis- 
 orderly chaos. 1 We would naturally say that the sole 
 cause of water boiling at 212° is the enveloping heat ; it has, 
 however, been observed that on top of Mont Blanc, water 
 boils at 180° instead of 212°. This indicates that, in addi- 
 tion to the fire, the atmospheric pressure is an element in 
 the cause, very easily overlooked. Charcoal and diamond 
 are of the same substance ; a difference only in the arrange- 
 ment of the molecules results in such radically different 
 combinations. There are, in the main, three special kinds 
 of collocations, as follows : — 
 
 (1) Cases of modifying circumstance. A strong wind 
 blows down a tree; this would not have occurred had not 
 the tree been hollow. The hollowness of the tree is here a 
 cooperative circumstance that is combined with the efficient 
 cause, — the force of the wind. An instance where arrange- 
 ment of the elements concerned rather than their efficient 
 energies is productive of the effect, is that of capillarity, the 
 rising of liquid in a tube of exceedingly small bore. Here 
 form is more essential to the effect than the expenditure of 
 any visible energy. 
 
 (2) Cases in which certain negative conditions prevent 
 the realization of the effect. The plants and shrubs die in 
 a long drouth, because it does not rain. A train collides 
 with another, because the red signal was not exposed as it 
 should have been. A match will ignite gunpowder gener- 
 ally, but it fails to do so should the powder prove to be 
 wet. 
 
 (3) There are also cases of counteracting causes, where 
 the effect of cause A is not realized, as cause B neutralizes 
 the force of cause A; as when an anchored boat will not 
 
 1 Quoted by Jevons, Principles of Science, p. 740. 
 
CAUSAL ANALYSIS AND DETERMINATION 211 
 
 respond to the pull of the oar. Sometimes the cause is not 
 wholly counteracted, or it may be the counteracting cause 
 more than holds the positive cause in check, and is itself 
 operative. The rise of a balloon in the air is due to the fact 
 that the force of gravity is more than overbalanced by the 
 expansive force of the gas within the balloon ; one force pull- 
 ing downwards, the other bearing up, and the latter pre- 
 vailing. 
 
 Mechanical forces acting in combination admit of a reso- 
 lution of their joint effect according to the theory of the 
 parallelogram of forces. Chemical and vital forces cannot 
 be treated in such a way at all. From the character of the 
 elementary forces in mechanics, one can calculate their com- 
 bination. In chemistry, however, when the elements are 
 given, the resulting compound cannot be thus determined. 
 So, also, in vital and mental phenomena, the necessarily com- 
 plex nature of the elements involved prevents not only 
 prediction of resulting combinations, but even adequate 
 explanation of that which may be immediately given in 
 consciousness. 
 
 It is necessary, in connection with these various instances 
 of causal relations, to understand the different modes of the 
 transfer of energy, which are as follows : — 
 
 (1) Molar or mechanical, as in the case of a billiard-ball 
 transferring its energy to another through impact. 
 
 (2) Molecular, as heat, chemical and electrical and mag- 
 netic forces, light, etc. One passes into another, as chemical 
 force producing electric, electric producing magnetic, or 
 producing heat and light. 
 
 (3) Cases where mechanical force becomes molecular, as 
 friction inducing heat; or cases where molecular becomes 
 mechanical, as heat transferred into the driving power of an 
 engine, or electricity applied as a motor. A precise deter- 
 mination of equivalents can be made between molar and 
 molecular energy; as, for example, it has been found that 
 it takes the same amount of energy to raise 772 pounds a 
 
212 
 
 INDUCTIVE LOGIC 
 
 distance of one foot that it does to raise the temperature of 
 one pound of water 1° F. ; or the heat requisite to boil a 
 gallon of freezing water would lift 1,389,600 pounds through 
 a distance of one foot. 
 
 As a consequence of the doctrine of the transfer of energy, 
 a causal law can be so stated as to express the fact that 
 _ J variations in the antecedents will call for the corresponding 
 variations in the effect, as, for instance, such a law as the 
 following: “Resistance in a wire of constant section and 
 material is directly proportional to the length and inversely 
 proportional to the area of the cross-section.” 1 The neglect 
 of quantitative determination of the proportionate variations 
 of the antecedent and consequent was a glaring defect in the 
 inductive systems both of Mill and of Bacon. 
 
 Through the representation of the various stages of such 
 variation, it is also possible to establish the upper and lower 
 limits beyond which the cause does not produce the corre- 
 sponding effect; as in Weber’s law concerning the relation 
 of stimulus to sensation, that stimulus must increase geo- 
 metrically in order that the sensations increase arithmeti- 
 cally. There is an upper and lower limit beyond which this 
 proportion does not hold. 
 
 The doctrine of conservation of energy creates the im- 
 pression of continuous change in causation, in which the 
 effect unfolds out of the cause. We do not think of phenom- 
 ena under this aspect as discrete events. More than ever, 
 in the light of modern science, does the old saying obtain, 
 “ Natura non facit saitum.” We no longer look for catas- 
 trophic results in nature, but regard causation as a con- 
 tinuous transfer of potential energy into kinetic or actual 
 energy. 
 
 We come now to the consideration of the method by 
 which the causal analysis is mediated. This is effected 
 through observation and experiment. Observation is some- 
 thing more than mere looking at phenomena : it means con- 
 1 Jenkin, Electricity and Magnetism, p. 83. 
 
CAUSAL ANALYSIS AND DETERMINATION 213 
 
 centration of attention for the purpose of research ; it means 
 discriminating insight, an appreciation of likeness and 
 difference ; it means a penetration beneath surface appear- 
 ances, and an apprehension of the essential features of the 
 objects of perception. E xper i m ent consists in modifying 
 the elements which form the complex antecedent in order to 
 observe the resultant effect upon the corresponding conse- 
 quent. Forces may be added or subtracted ; their intensity 
 may be varied, increased, or decreased ; the circumstances 
 or conditions may be altered. Herschel speaks of observa- 
 tion and experiment, as passive and active observation 
 respectively. When we interfere to change the course of 
 nature, or to bring natural forces within the range of our 
 observation, we are experimenting. Observation is prelimi- 
 nary to experiment, and suggests the lines along which 
 experiment should proceed. An observation that sees the 
 parts in the whole and the whole in the parts, is in itself 
 an analysis of a phenomenon, in course of which process 
 causal relations must be disclosed. The scientific spirit 
 demands absolute veracity in observation. One ought not 
 to be blind to facts even though they tend to contradict 
 preconceived theories. Bacon has observed that “ men mark 
 when they hit, never mark when they miss.” We must 
 strive against a natural tendency to see things as we would 
 have them, and not as they strictly are. 
 
 We must also carefully distinguish between observed 
 facts, and inferences which we instinctively draw from 
 these facts. Observation is preliminary to an inductive 
 inference, therefore it must not itself involve an inference, 
 or we should be arguing in a circle. An interesting illus- 
 tration of the difference between observation and inference 
 based upon it, is narrated in the life of Faraday: “An 
 artist was once maintaining that in natural appearances and 
 in pictures, up and down, and high and low, were fixed in- 
 dubitable realities; but Faraday told him that they were 
 merely conventional acceptations, based on standards often 
 
214 
 
 INDUCTIVE LOGIC 
 
 arbitrary. The disputant could not be convinced that ideas 
 which he had hitherto never doubted, had such shifting 
 foundations. ‘ Well,’ said Faraday, ‘ hold a walking-stick 
 between your chin and great toe; look along it and say 
 which is the upper end.’ The experiment was tried, and 
 the artist found his idea of perspective at complete variance 
 with his sense of reality; either end of the stick might be 
 called upper, — pictorially it was one, physically it was the 
 other.” 1 
 
 This indicates how readily our inferences and observations 
 blend, and how difficult it is to separate them in conscious- 
 ness. De Morgan has pointed out that there are four ways 
 of one event seeming to follow another, or to be connected 
 with it, without really being so : — 
 
 (1) Instead of A causing B, our perception of A may 
 cause B. A man dies on a certain day which he has always 
 regarded as his last through his own fears concerning it. 
 
 (2) The event A may make our perception of B follow, 
 which otherwise would happen without being perceived. 
 It was thought that more comets appeared in hot than cold 
 summers ; no account, however, was taken of the fact that 
 hot summers would be comparatively cloudless, and afford 
 better opportunities for the discovery of comets. 
 
 (3) Our perception of A may make our perception of B 
 follow. This is illustrated by the fallacy of the moon’s 
 influence in the dissipation of the clouds. When the sky is 
 densely clouded, the moon would not be visible at all; it 
 would be necessary for us to see the full moon in order that 
 our attention should be strongly drawn to the fact, and this 
 would happen most often on those nights when the sky is 
 cloudless. 
 
 (4) B is really the antecedent event, but our perception 
 of A, which is a consequence of B, may be necessary to 
 bring about our perception of B. Upward and downward 
 currents are continually circulating in the lowest stratum of 
 
 1 Gladstone, Michael Faraday, pp. 165, 166. 
 
CAUSAL ANALYSIS AND DETERMINATION 215 
 
 the atmosphere ; but there is no evidence of this, until we 
 perceive cumulous clouds, which are the consequence of such 
 currents . 1 
 
 There are certain natural limitations to observation, as 
 things too minute to be seen, too swift to be carefully exam- 
 ined; there are sounds which some ears can detect, while 
 others cannot, and shades that some eyes cannot discriminate. 
 There are effects proceeding from certain causes that are so 
 slight that we fail to observe them, and yet erroneously infer 
 that they do not exist. Professor Tyndall has given a strik- 
 ing illustration of the difference of auditory power in two 
 individuals ; he says : “ In crossing the Wengern Alp in com- 
 pany with a friend, the grass at each side of the path swarmed 
 with insects which to me rent the air with their shrill chirrup- 
 ing. My friend heard nothing of this, the insect music lying 
 quite beyond his limit of audition.” 2 Much has been done 
 by inventive skill to increase our powers of observation, and 
 at the same time to render them more accurate, as the tele- 
 scope, microscope, the vernier for precise measurement of 
 minute differences of magnitude, the chronograph for time 
 measurements, self-registering thermometers, the thermopile, 
 galvanometers, etc. One of the chief problems of scientific 
 method is to overcome natural limitations of observation 
 through mechanical devices. 
 
 Observations on a large scale and over a considerable 
 period of time must sometimes be taken in order to disclose 
 tendencies as seen only in the average or the mean of the 
 observed results. Thus meteorological, vital statistics, and 
 others of a like kind, must extend over a large area, and 
 embrace a large number of instances in order to reach 
 results of any value. It is known that Tycho Brahe made 
 an immense number of most exact records of the positions of 
 the heavenly bodies with the aid of the best of astronomical 
 
 1 Quoted by Jevons, Principles of Science, pp. 409-411. 
 
 2 Tyndall, On Sound, pp. 73, 74. 
 
216 
 
 INDUCTIVE LOGIC 
 
 instruments, and these records afterwards became the foun- 
 dation of Kepler’s laws and of modern astronomy . 1 
 
 The faculty for accurate observation can be increased by 
 acquiring the habit of examining carefully everything within 
 the field of vision. We fail to see many things because we 
 .fall into the easy way of passing them by without noting 
 their presence or appreciating their significance. It was 
 said of Charles Darwin by his son that “ he wished to learn 
 as much as possible from every experiment, so that he did not 
 confine himself to observing the single point to which the 
 experiment was directed, and his power of seeing a number 
 of other things was wonderful.” 2 The open-eyed vision is 
 the prime requisite for scientific investigation. 
 
 The limitations of observation naturally lead to experi- 
 ment, whose special function is to so modify phenomena as 
 to bring a suspected causal element more prominently into 
 notice. This can be done by intensifying the force in ques- 
 tion, or by neutralizing all other elements in combination 
 with it, so that the sole effect of this force in actual opera- 
 tion can be observed. When the cause is not a simple ele- 
 ment, but a combination, then the problem is to vary the 
 conditions so that but one possible combination can be opera- 
 tive alone, and note the corresponding effect. Given a 
 certain number of elements, the number of possible com- 
 binations is mathematically determinate, and can be tried 
 seriatim until all possibilities are exhausted. Venn has 
 given a long and interesting illustration of this in his Em- 
 pirical Logic . 3 All combinations need not be tried, how- 
 ever ; for many will be seen to be either impossible or 
 irrelevant. The aim is to obtain an antecedent which shall 
 consist either of a simple element, or a combination such 
 that with its presence the effect in question is present also, 
 but with its disappearance the effect is wanting. 
 
 1 Gore, The Art of Scientific Discovery, p. 316. 
 
 2 Life and Letters of Charles Daruiin, Vol. I. p. 122. 
 
 8 pp. 402 ff. 
 
CAUSAL ANALYSIS AND DETERMINATION 217 
 
 It is not sufficient to note merely the presence of an ante- 
 cedent connected with a corresponding consequent; scien- 
 tific determination consists also in proving the absence of 
 the suspected cause in cases where the given effect is not 
 present. This is called determination by negation. A 
 proposition which is held affirmatively has only a vague 
 significance; it must be determined within definite limits 
 assigned to it by virtue of what it is not. Defining means 
 to set limits to a term ; these limits grow out of the nature 
 of the thing itself. The negative judgment marks a transi- 
 tion always from that which is indefinite and incoherent 
 to that which is definite and coherent . 1 
 
 This may be illustrated in the concrete, when in dissec- 
 tion one is tracing a nerve; it is followed throughout its 
 course by a series of negative judgments though they be 
 unexpressed : This is not a nerve, but an artery ; this is not 
 a nerve, but a vein ; this is not a nerve, but a filament, or 
 shred of muscle, etc. So we rise through negative discrim- 
 ination to a clear apprehension of an object under investi- 
 gation. The original proposition must be readjusted with 
 every new negative determination. It sometimes happens 
 that the original proposition is completely negatived by the 
 negative determination, sometimes again it is confirmed. 
 
 A proposition that has not been worked over through such 
 a process has no real logical worth or scientific value. There- 
 fore in the analysis of phenomena when the suspected cause 
 and effect are combined in a proposition, it can at first be 
 held only tentatively. It must be confirmed negatively, or 
 else readjusted to conform to the negative requirements. 
 Suppose we have given that A is followed by B as far as we 
 have been able to observe. We may proceed by experiment, 
 to multiply instances of A’s connection with B, but still the 
 causal relation is not absolutely proved. We must go on 
 to show that in all cases of not- A there is not-jB, or in all 
 cases of not-U there is not- A. Negative experiment pro- 
 
 1 See p. 74. 
 
218 
 
 INDUCTIVE LOGIC 
 
 duces the contrapositive, or the converse contrapositive, of 
 the proposition under investigation, which deductively neces- 
 sitates the validity of the original proposition. 
 
 This is substantially Mill’s method of difference, that if 
 an instance in which the phenomenon under investigation 
 occurs, and an instance in which it does not occur, have 
 every circumstance save one in common, and that one oc- 
 curring only in the former, the circumstance in which alone 
 the two instances differ is the effect or cause or a necessary 
 part of the cause of the phenomenon. This method will 
 be described later; it is the main inductive method, the 
 others being largely modifications of it. A negative in- 
 stance which is established concerning relations of not-M 
 and not-B is absolutely conclusive, inasmuch as not- A is 
 the contradictory of A, and uot-B is the contradictory of B. 
 They are mutually exclusive. No other possibility can be 
 forthcoming, and the experimental analysis is exhaustive. 
 Professor Tyndall gives the following account of an experi- 
 ment to determine the cause of resonance. “ I hold a vibrat- 
 ing tuning-fork over a glass jar eighteen inches deep ; but 
 you fail to hear the sound of the fork. Preserving the fork 
 in its position, I pour water with the least possible noise 
 into the jar. The column of air underneath the fork be- 
 comes shorter as the water rises. The sound augments in 
 intensity, and when the water reaches a certain level, it 
 bursts forth with extraordinary power. I continue to pour 
 in water, the sound sinks, and becomes finally as inaudible 
 as at first .” 1 
 
 From this it is inferred that a certain column of water of 
 definite height is necessary to the production of the sound, 
 for above and below the limits no sound is heard. This 
 experiment also indicates that which is most important in 
 causal determination, — a variation in cause accompanied by 
 a variation in effect, as also a maximum and minimum as 
 regards the intensity of the sound. Experiment proceeds 
 1 Tyndall, On Sound, p. 172. 
 
CAUSAL ANALYSIS AND DETERMINATION 219 
 
 upon the supposition of the measurableness of phenomena, 
 and seeks numerically expressible results in this regard. 
 For instance, by different experiments, Tyndall proved that 
 the length of the column of air which resounds to the fork 
 in a maximum degree of intensity is equal to one-fourth of 
 the length of the wave produced by the fork . 1 
 
 The negative determination of a suspected connection 
 of cause and effect must be precise in order to establish 
 the causal relation with that degree of accuracy which is 
 demanded in a truly logical and scientific method. Upon 
 this point, Bosanquet has a very suggestive passage : “ The 
 essence of significant negation consists in correcting and 
 confirming our judgment of the nature of a positive phe- 
 nomenon by showing that just when its condition ceases, 
 just then something else begins. The ‘Just-not’ is the im- 
 portant point, and this is only given by a positive negation 
 within a definite system. You want to explain or define the 
 case in which A becomes B. You want observation of not-B, 
 but almost the whole world is formally or barely not-B, 
 so that you are lost in chaos. What you must do is to find 
 the point within A where A x which is B, passes into A 2 
 which is C, and that will give you the just-not-B which is 
 the valuable negative instance .” 2 For example, in Professor 
 Tyndall’s experiment, the significant negative instance was 
 this, — when the water in the tube reached just that height 
 when for the first time during the experiment no sound was 
 audible. The discriminating observation that can mark and 
 measure the precise point of transition from sound to no 
 sound, has determined accurately the conditions necessary 
 to produce the sound, and precisely define their limita- 
 tions. 
 
 In all observation and experiment, the following possi- 
 bilities should be kept before the mind in order to avoid a 
 hasty conclusion in reference to a seeming causal connec- 
 
 1 Tyndall, On Sound, p. 174. 
 
 2 Bosanquet, The Essentials of Logic, p. 134. 
 
220 
 
 INDUCTIVE LOGIC 
 
 tion. We may think that we have discovered the relation 
 that if there is A, then there must be B, and the one there- 
 fore the cause of the other, but it may happen that 
 
 1. Both A and B are effects of another cause and are 
 thereby related coordinately in reference to it. 
 
 2. A may be merely a liberating circumstance, or an inva- 
 riable accompaniment of B. 
 
 3. A may not be the cause of B, but only an element of a 
 complex collocation which is the cause of B. 
 
 4. Each separate instance of B may so differ as to 
 respond to the action of A in a manner different from the 
 others. 
 
 5. A may be related to B in a system of such a nature 
 that the system in continuously developing new effects 
 causes B, as the introduction of medicine into an organism 
 whose forces are themselves effecting a healing process. 
 
 6. It is often very difficult to tell whether A is the cause 
 of B, or B the cause of A, as in districts where drunkenness 
 and poverty are prevalent, or cases of moral and intellectual 
 feebleness. Which is the cause ? and which the effect ? In 
 many cases such as these, the forces react upon each other, 
 the effect tending to increase the intensity of the cause. 
 
 7. The connection of A and B may be one of mere coin- 
 cidence, and not of a causal nature whatsoever. Newton 
 was much impressed with the apparent connection between 
 the seven intervals of the octave, and the fact that the 
 colors of the spectrum divide into a like series of seven 
 intervals. And yet there is no causal connection that can 
 be proved to exist between the two. 
 
 The more we dwell upon these various possibilities, ths 
 more are we impressed with the extreme complexity in 
 which the relation of cause and effect is involved. The 
 investigator must bring to his research the spirit of patience 
 and perseverance, as well as a clear vision and discriminat- 
 ing insight. Sir John Lubbock, in his observations upon 
 the habits of ants, says that at one time he watched an ant 
 
CAUSAL ANALYSIS AND DETERMINATION 221 
 
 from six in the morning until a quarter to ten at night, as 
 she worked without intermission during all that time . 1 It 
 is to such patient investigators that nature reveals her 
 secrets. 
 
 1 Sir John Lubbock, Scientific Lectures, p. 73. 
 
CHAPTER VI 
 
 MILL’S INDUCTIVE METHODS— THE METHOD OF 
 AGREEMENT 
 
 There are certain specific methods by which a supposed 
 relation of cause and effect may be tested. Before applying 
 any method however to concrete instances, there is naturally 
 in mind some suspected causal relation which is the result 
 of one or both of the two preliminary inductive processes. 
 
 As we have seen, these primary processes in inductive in- 
 quiry are induction by simple enumeration, and induction 
 by analogy. By the enumeration of the special cases in 
 which we have found a significant coexistence or sequence, 
 a causal relation is suggested as a possible or probable ex- 
 planation. By analogy also a causal relation is suggested 
 on the basis that a given phenomenon which in essential 
 particulars resembles another phenomenon whose cause or 
 effect is already known will, in all probability, have a like 
 cause or effect. Enumeration and analogy thus suggest a 
 probable explanation which is not as yet proved, but which 
 ranks as a tentative hypothesis. The natural history, there- 
 fore, of the final product of the inductive process recognizes 
 the initial stages of enumeration and analogy leading to 
 some preliminary hypothesis, which is to be tested by one 
 or more of the specific methods of scientific investigation. 
 These methods have been formulated by John Stuart Mill 
 and are especially associated with his name. They are as 
 follows : — 
 
 1. The Method of Agreement. 2. 
 
 2. The Method of Difference. X.3 g 
 
 3. The Joint Method of Agreement and Difference. 3 
 
 222 
 
MILL’S INDUCTIVE METHODS 
 
 223 
 
 4. The Method of Concomitant Variations. 2.5 S 
 
 5. The Method of Residues. 2 ir *J f 
 
 The method of agreement consists in inferring the exist- 
 ence of a causal relation, when in a number of varying 
 instances it is observed that the supposed cause is always 
 accompanied by the phenomenon in question, as correspond- 
 ing effect. 
 
 The method of difference is the comparing of an instance 
 where the supposed cause is present, accompanied by the 
 corresponding effect, with an instance having precisely the 
 same setting, but where the supposed cause is withdrawn, 
 the effect also disappearing ; the inference of a causal rela- 
 tion is then permissible. 
 
 The joint method of agreement and difference is the com- 
 paring of instances where the supposed cause is present, 
 with similar instances where it is absent ; if the correspond- 
 ing effect is present in the former, and absent in the latter, 
 group of instances, a causal relation may be inferred. This 
 differs from the method of difference, that in the latter the 
 same instance, now with, and again without, the presence of 
 the suspected cause, is the subject of observation ; in the 
 joint method it is a number of instances with, compared 
 with a number of similar instances without, the presence of 
 the supposed cause. 
 
 The method of concomitant variations consists in so modi- 
 fying any given phenomenon that the supposed cause will 
 vary in intensity; then a corresponding variation in the 
 accompanying effect is evidence of a causal relation. 
 
 The method of residues consists in the analysis of a given 
 complex phenomenon, in which all elements save one of the 
 antecedent are known to be related severally in a causal 
 manner to all elements save one of the consequent; then 
 the residual element of the one may be regarded as the 
 cause of the residual element of the other. 
 
 These methods, it is true, deal only with, concrete 
 
224 
 
 INDUCTIVE LOGIC 
 
 instances ; but, in so far as these instances discover an 
 underlying causal connection, they thereby furnish sufficient 
 ground for a complete generalization, and warrant the induc- 
 tive procedure from special cases to the universal. 
 
 We will now examine these methods more in detail. The 
 brief outline above is intended merely to give a general idea 
 of the methods, that it may lead to a better understanding of 
 the more exact statement of their nature and characteristics. 
 
 The Method of Agreement. — The more precise statement 
 of this method is given in the first canon of Mill, which is 
 substantially as follows: — 
 
 If two or more instances of the phenomenon under investi- 
 gation have only one circumstance in common, the circum- 
 stance in which alone all the instances agree is the probable 
 cause (or effect) of the given phenomenon, or sustains some 
 causal relation to it. 
 
 The above is based upon the causal axiom that the constant 
 elements which emerge in any given series of similar phe- 
 nomena are to be considered as connected in some manner 
 with the cause of the phenomena; but that the variable 
 elements are not connected with the phenomena in any 
 causal manner whatsoever. 
 
 The method of agreement is illustrated in the investiga- 
 tion of the very common phenomenon of the transformation 
 of substances from the solid to the liquid state. What is 
 the one circumstance which is always present when we con- 
 sider the melting of such widely different substances as 
 butter, ice, lead, iron, etc. ? In all instances, to whatsoever 
 extent they may be multiplied, of the change from solid to 
 liquid states, heat has been observed to be present, and 
 is thereby indicated as the likely cause of the phenomenon 
 in question. The method may be represented through the 
 use of symbols which, according to Mill, are capital letters 
 to denote antecedents, and smaller letters to denote corre- 
 sponding consequents. Let the following be a number 
 of different instances with the antecedents and con- 
 
THE METHOD OF AGREEMENT 
 
 225 
 
 sequents arranged in order, and represented as above in- 
 dicated : — 
 
 ABC abc. 
 
 ADE ade. 
 
 AMN amn. 
 
 etc. etc. 
 
 By inspection of such a table of instances thus analyzed, 
 and symbolically represented, it will be readily seen that A 
 is the only element common to all the antecedents, while 
 a is the only one common to all the consequents. The in- 
 ference, therefore, is that A is the cause of a. It has been 
 objected to this system of representation that it artificially 
 arranges the elements of antecedent and consequent, as 
 though there were a number of distinct cause-elements, each 
 connected with a correspondingly distinct effect-element, and 
 it produces the impression that it is quite an easy matter 
 to see how these causal pairs are thus separately related . 1 
 As nature presents her phenomena to us, however, there is 
 such complexity throughout, that the analysis cannot readily 
 distribute part to part in appropriate causal relations. To 
 avoid such an error in notation, I have adopted the follow- 
 ing symbols, which will be used hereafter to describe the 
 various methods. Let us take C as the letter to represent 
 the supposed causal element, and S, the entire setting of 
 accompanying circumstances; let e denote the corresponding 
 effect, and s the sum total of the attendant consequences. 
 The causal relation will be then indicated, according to the 
 method of agreement, as follows : — 
 
 S + C s+e. 
 
 S' + C s' + e. 
 
 S" + C s" + e. 
 
 Here the setting changes throughout, as indicated by S, 
 S', S", etc., but C remains constant in the antecedents ; also 
 1 Venn, Empirical Logic, p. 411. 
 
226 
 
 INDUCTIVE LOGIC 
 
 the corresponding setting in the consequents changes, as in- 
 dicated by s, s', s", etc., but e remains constant throughout. 
 Such a notation does not attempt to represent just which 
 parts of S cause corresponding parts of s, nor by what ele- 
 ments precisely S differs from S' and S", etc. It does rep- 
 resent, however, the difference between the variable and 
 constant elements of the table of instances which are ar- 
 ranged for comparison, and this is the key to disclose the 
 causal relation. 
 
 As an example of this method, let us take the physical 
 law that different bodies tend at the same time to absorb 
 and to emit the same waves of light. It is known that every 
 substance in burning gives its own lines in the spectrum 
 analysis, sodium, for instance, producing a very bright line 
 in the yellow portion of the spectrum in a definite locality 
 (Line D, of Fraunhofer). If now, instead of burning sodium, 
 we interpose the vapor of sodium in the path of the ray 
 which should give a continuous spectrum, the phenomenon 
 is completely reversed ; at the exact point where there was 
 a bright line in the spectrum, a dark line now appears. 
 Thus the vapor of sodium, acting as a screen, absorbs the 
 rays which it emits when it acts as the luminous source. 
 A similar effect is observed in the case of vapors of iodine, 
 of strontium, of iron, etc. ; it may therefore be regarded as a 
 phenomenon, admitting of generalization by induction . 1 This 
 is according to the method of agreement; and we may make 
 the following representation : — 
 
 Vapor of sodium acting as a screen — S + C 
 Vapor of iodine acting as a screen = S' + C. 
 Vapor of iron acting as a screen = S" -f C. 
 Vapor of strontium acting as a screen = S'" + C. 
 
 etc. etc. 
 
 1 Saigey, The Unity of Natural Phenomena, pp. 94, 95. 
 
THE METHOD OF AGREEMENT 
 
 227 
 
 The corresponding consequents are : — 
 
 Reversing bright sodium line to dark = s + e. 
 
 Reversing bright iodine line to dark = s' -f- e. 
 
 Reversing bright iron line to dark = s" + e. 
 
 Reversing bright strontium line to dark = s'" + e. 
 
 etc. etc. 
 
 Therefore we have : — 
 
 S + C s + e. 
 
 S' + C s' +e. 
 
 S" +C s" +e. 
 
 S'" + C s'" + e. 
 
 etc. etc. 
 
 In this the constant C of the antecedents is the vapor of 
 any substance acting as a screen; the constant e is the 
 reversal in each case of the bright line of the substance in 
 the spectrum to the corresponding dark line of the same. 
 From this it is inferred that the vapor of any substance acting 
 as a screen absorbs exactly those rays which it emits when 
 it acts as the luminous source. 
 
 It is of great importance that the instances selected for 
 observation or experiment be as varied as possible, so that 
 widely differing phenomena may be gathered together. 
 Then if running through them all there is one common 
 element observed among the antecedents, and one common 
 element among the consequents, the greater the variation 
 among the instances the more pronounced will be the signifi- 
 cance of the constant elements. In the illustration given 
 the substances which are so different as iron, strontium, 
 sodium, iodine, etc., preclude the possibility of the resultant 
 phenomenon described being due to the peculiar properties 
 of any one metal, or group of metals. So many phenomena 
 and so different in kind are taken as to eliminate the 
 peculiarities attached to any one in particular. In this re- 
 spect the method is one of elimination. By varying the 
 
228 
 
 INDUCTIVE LOGIC 
 
 instances the non-essential is eliminated, and the essential, 
 which remains as the element common to all, is thereby 
 emphasized, and differentiated from all attendant circum- 
 stances. 
 
 This method also is one of discrimination, of discerning 
 the constant element under the various changing forms 
 which it can assume, and as such it is similar to the logical 
 process of the formation of a concept. The concept is the 
 grasping of the universal element which is present through 
 the particular and concrete manifestations of the same. 
 Through them all there is the like common element which 
 is the basis of the concept itself. So out of many particular 
 instances the mind grasps the elements which are common 
 to all, and considers them as related in a constant and 
 therefore causal manner, which has in itself the character 
 of a universal concept and so admits of being formulated in 
 the form of a law universal, which is the end of all induc- 
 tion. 
 
 This method, moreover, is peculiarly adapted to observa- 
 tion, the collating of a number of instances, rather than to 
 experiment. Instances cannot always be manufactured, and 
 so it may be beyond the power of experiment to reproduce 
 them. They can, however, always be the objects of research, 
 and as such fall naturally into the field of observation. 
 
 The question may properly be asked at this point, 
 How does this method differ from that of induction by 
 simple enumeration ? The latter we have seen is never 
 satisfactory because the enumeration cannot be complete, 
 and may be contradicted by an enlarged experience. This 
 method however is superior in that it provides for more 
 than simple enumeration of instances in which the phenome- 
 non in question has occurred ; there must be a corresponding 
 analysis of the instances, accompanied by a discriminating 
 insight to distinguish the essential from the unessential. 
 Number of instances increases the probability that the 
 variable elements have been eliminated, and enables the 
 
THE METHOD OF AGREEMENT 
 
 229 
 
 mind to concentrate upon tlie constant elements that remain 
 and are thereby disclosed. 
 
 This method primarily admits of application to instances 
 where a sequence is observable ■ that is, where antecedent 
 can be distinguished from consequent by an appreciable 
 time element. It is however possible to apply this method 
 to the investigation of coexistences, where it may show that 
 either the coexisting elements are related as cause and 
 effect, or that in some causal manner they are the correlated 
 effect of some cause sufficient to account for them both. 
 Many instances may be adduced of the prevalence of 
 poverty and crime associated together. This may indicate 
 a causal relation between them, and yet a sequence cannot 
 be observed of sufficient definiteness to indicate which is 
 the cause, and which the effect. The problem is thus left 
 indeterminate, with the suggestion of some other cause 
 which may possibly account for them both. All that the 
 method of agreement can attain, is by collecting a number 
 of instances of diverse nature to indicate that in some way 
 at least poverty and crime are connected by causal ties. The 
 constant coexistence of attributes in one individual admits 
 of a similar treatment and similar results. The fact of the 
 high coloring of male butterflies in a large number of 
 instances, in reference to a variety of species, indicates a 
 constant relation between the fact of its being a male 
 and the possession of brilliant coloring. This inseparable 
 association indicates a causal relation, which, however, 
 cannot be more precisely determined by this method. The 
 full explanation of the phenomenon requires some supple- 
 mentary hypothesis depending upon conditions not disclosed 
 by this method, an hypothesis such that the high coloring has 
 the special function of attracting the female butterfly and 
 has been intensified and developed by natural selection. 
 
 The method of agreement is open to criticism at several 
 points, and yet it must be at the beginning understood that 
 this method does not rank as a final method. We shall 
 
230 
 
 INDUCTIVE LOGIC 
 
 soon see that in many cases it needs to be supplemented by 
 the method of difference, in order either to confirm or to 
 disprove its tentative results. The chief criticisms that have 
 been made of this method may be summed up as follows : — 
 
 1. The cause indicated by the method of agreement is 
 not thereby proved to be the sole cause of the phenomenon 
 in question. We may gather together a number of varied 
 instances where an extensive failure of crops in the summer 
 has caused hard times during the winter following. And 
 yet there may be, and as a fact there are, many other causes 
 which engender periods of industrial depression. We may 
 say, therefore, that this method is capable of establishing, 
 tentatively at least, a universal proposition of the form, 
 All x is y ; it does not, however, attempt to give any indica- 
 tion, one way or the other, regarding the validity of the con- 
 verse, All y is x. Knowing the limitations of a method does 
 not by any means destroy its legitimacy as a method ; it rather 
 increases its efficiency within its proper sphere, by the more 
 exact knowledge as to the precise extent of that sphere itself. 
 
 2. It is urged that while it is possible to recognize in 
 most, if not in all, cases, the common element in the several 
 effects of similar phenomena, it is not so easy a matter to 
 separate the common element in the corresponding antece- 
 dents by the simple method of agreement alone. For 
 instance, in Bacon’s illustration of the investigation of the 
 cause of heat, he cites such disparate phenomena as the 
 sun’s rays, friction, combustion, etc. The element of heat 
 is readily discernible through them all; but what is the 
 common element which operates as cause in each case ? 
 There is the difficulty. Sigwart illustrates this in the case 
 of the phenomenon of death. The effect can be easily de- 
 tected as similar throughout, but in all the antecedents the 
 only property common to them all is life, and, therefore, we 
 are led into the fallacy of attributing to life the cause of 
 death. 1 We must therefore acknowledge that some phe- 
 
 1 Sigwart, Logic, Vol. II, p. 341. 
 
THE METHOD OF AGREEMENT 
 
 231 
 
 nomena may occur in such a variety and such a number of 
 manifestations as to disguise the nature of the cause under 
 the mask of a generality too indefinite to be recognized. In 
 all such instances, the method of agreement must avail itself 
 of suggestions received from some other source, as to the 
 nature of the common element in the antecedents. Or, some 
 minor circumstances attending the effect may indicate more 
 precisely the nature of the cause, as, for instance, the pecul- 
 iar symptoms associated with death by drowning, which dif- 
 ferentiate it from death due to any other cause. 
 
 3. The common element in the antecedents may prove to 
 be an unessential accompaniment of all the instances exam- 
 ined. Its presence, therefore, may have nothing whatso- 
 ever to do with the observed effects. A number of different 
 medicines, for example, may produce a certain effect alike 
 in all instances. The only common element that can be 
 detected in the various medicines examined may be the 
 alcohol which is used as the common vehicle of the different 
 drugs, and yet its effect may be entirely inert as regards the 
 medicinal qualities in question. The common element really 
 efficient may be overlooked, and another common element 
 -which is easily discernible may nevertheless remain wholly 
 inoperative. This difficulty may be overcome by a more 
 thorough analysis of the phenomena observed, which may 
 be attained by a judicious variation of the instances, so as 
 to reveal, in turn, the precise effect of the various simple 
 elements which together constitute the complex whole of 
 the phenomenon in question. The defects of the method 
 in this respect are, in a word, the defects of induction by 
 simple enumeration. 
 
 4. The cause may be present in all the antecedents, and, 
 notwithstanding the corresponding effect not appear, and 
 this, not because the two are not related in a causal manner, 
 but because the cause is neutralized by the associated ele- 
 ments which appear in combination with it in the various 
 antecedents. Tor instance, diphtheria germs are the cause 
 
232 
 
 INDUCTIVE LOGIC 
 
 of diphtheria, and have been found accompanying this 
 disease in all cases which have been observed. And yet 
 their presence is often noted when the disease itself does 
 not develop. The tendency existing is counteracted by the 
 condition of the organism at the time, so that the dread 
 bacilli are inoperative and therefore harmless. As we have 
 seen before, the presence of the effect necessitates the pres- 
 ence of the corresponding cause; but by no means is it 
 always true that the presence of the cause necessitates the 
 effect. The cause always produces the tendency at least, 
 which however may be neutralized. 
 
 5. This method is often applied in a very careless way to 
 the observations of persons who do not possess the power 
 of accurate discrimination, and therefore observed coinci- 
 dences are hastily assumed to be particular instances of an 
 universal law. Such procedure leads to superstition and 
 prejudice. It not only warps the judgment, owing to its 
 illogical nature, but it also affects indirectly the man’s 
 moral view, as it implies a weakness in character as well 
 as in mind. This criticism refers however to the abuse 
 rather than the legitimate use of this method under such 
 restrictions as have been already indicated. 
 
 The chief function of this method is that of suggestion. 
 It indicates often only the possibility of the existence of a 
 causal relation ; in other cases it leads to an inference of 
 high probability. In all cases however it marks merely the 
 preliminary steps of an investigation which should be fol- 
 lowed up by painstaking experiment. As it is the method 
 of observation chiefly, it is natural that it should precede 
 experiment ; for it is only by reflection upon our observa- 
 tions that we discover the nature and relations of phenomena, 
 which serve as data for subsequent experiment. 
 
 I have selected several illustrations to indicate the various 
 fields of research in which this method of agreement has led 
 to satisfactory results. 
 
 The first refers to the relation between the occurrence of 
 
THE METHOD OF AGREEMENT 
 
 233 
 
 financial crises and the prevalence of over-production. Guyot, 
 in his Principles of Social Economy, gives the following in- 
 stances: An enormous consumption of capital in the United 
 States in the seventies, for the construction of railroads, was 
 followed by unusual commercial depression. Then the like 
 outlay in India for railway construction by means of loans 
 and taxes which absorbed the whole circulating capital of 
 the Indian population was followed by a devastating fam- 
 ine and general commercial paralysis. Again in Germany 
 there was an enormous consumption of capital in forts and 
 armaments and general military equipment, bringing on the 
 crisis of 1876-1879. England at the same time was unduly 
 supplying circulating capital to the United States, Egypt, 
 and her colonies, and a financial crisis was the result. 
 Through all these varying instances and others of a like 
 nature which might be added, the constant relation of over- 
 consumption in the antecedents to the industrial depression 
 evident in the effect indicates the one to be the cause of the 
 other, either in whole or in part. 
 
 Again it is narrated in Brewster’s Treatise on Optics that 
 he accidently took an impression from a piece of mother-of- 
 pearl in a cement of resin and beeswax, and, finding the 
 colors repeated upon the surface of the wax, he proceeded 
 to take other impressions in balsam, fusible metal, lead, 
 gum arabic, isinglass, etc., and always found the iridescent 
 colors the same. His inference was that the form of the 
 surface is the real cause of such color effects. 1 The com- 
 mon element which appears in all the antecedents is evidently 
 the same form impressed upon each, which was originally 
 received from the mother-of-pearl. The cause is moreover 
 independent of the nature of the substance in each case 
 which received the impression upon its surface, because 
 such a variety of substances was chosen as to eliminate the 
 individual nature of each as an influencing factor in the 
 result. In this experiment we see the advantage of varying 
 1 Quoted by Jevons, Principles of Science, p. 419. 
 
234 
 
 INDUCTIVE LOGIC 
 
 the instances as far as possible for this very purpose of 
 eliminating all irrelevant elements. Similar experiments 
 have proved like results in reference to the colors exhibited 
 
 thin plates and films. Here the rings and lines of color 
 have been found to be nearly the same whatever may be 
 the nature of the substance. A slight variation in color is 
 due to the refractive index of the intervening substance. 
 With this exception, the nature of the substance is not 
 operative in producing the color effect, but the form alone. 
 
 The celebrated scientist, Pasteur, in the year 1868 was 
 carrying on his investigations as to the cause of the blight 
 then devastating the silkworms of France. One of his ex- 
 periments consisted in selecting thirty perfectly healthy 
 worms from moths that were entirely free from the cor- 
 puscles, which latter are the germs of disease, or at that 
 time suspected to be the germs of disease. Then, rubbing 
 a small corpusculous worm in water, he smeared the mix- 
 ture over the mulberry leaves. Assuring himself that the 
 leaves had been eaten, he watched the consequences day by 
 day. One after the other the worms languished ; all showed 
 evidences of being the prey of the corpusculous matter, and 
 finally, within one month’s time, all died. Pasteur’s infer- 
 ence naturally was that the corpuscles had produced the death. 
 Of course his results were not founded upon this experiment 
 alone, but other experiments, carried on in many different 
 ways, served to corroborate the causal relation which the 
 experiment just described had suggested as at least highly 
 probable. 
 
 In medicine also the method of agreement is often used 
 with effect. Certain drugs are administered in a number of 
 cases and the results noted. A uniform effect consequent 
 upon the administration of a given drug indicates a causal 
 connection capable of generalization. Not only are subjects 
 in disease, but also in health, selected, and the effects upon 
 both the normal and morbid natures compared. Thus a 
 variation in instances is secured. If a number of different 
 
THE METHOD OF AGREEMENT 
 
 235 
 
 drugs produce like effects, the question at once suggests 
 itself, What is the property common to them all ? The 
 method of agreement often gives some indication of this, 
 ■when the elimination of the inert properties can be accom- 
 plished through a sufficient variation of instances. The 
 difficulty lies, however, in this very thing, to so vary the in- 
 stances as to disclose the efficient element present in them all. 
 Various medicines present a complex nature of such a char- 
 acter that it is extremely difficult to discriminate the precise 
 effects which the several component parts individually 
 exercise. 
 
 The method of agreement is also used, perhaps uncon- 
 sciously, in the conduct of the everyday affairs of life. 
 Whenever different phenomena in our experience present 
 certain characteristics of a constant nature, we are at once 
 led to suspect a causal connection, and to start upon a more 
 searching investigation of the same. Too often however 
 the supplementary investigation is omitted, and the mind 
 rests content with a few surface resemblances that lead to 
 a hasty generalization without being more precisely and 
 adequately determined. 
 
CHAPTER VII 
 
 THE METHOD OF DIFFERENCE 
 
 The method of agreement, as we have seen, presents a 
 causal relation as a suggestion, admitting of a high degree 
 of probability it may be, but requiring to be tested by some 
 more scientific method. This is accomplished by the method 
 of difference. Here a phenomenon is observed, in which 
 the supposed cause-element and effect-element appear ; then 
 while all other circumstances and conditions remain unal- 
 tered, the supposed cause-element is withdrawn, or its force 
 adequately eliminated ; the immediate disappearance of the 
 supposed effect-element, consequent upon this, indicates a 
 causal relation between the two. Or the experiment may 
 be made in a different manner, but to the same end, that 
 is, a phenomenon may be characterized by the absence of 
 both cause-element and effect-element; then, if the intro- 
 duction of the cause-element does not disturb the phenomenon 
 in question, except immediately to produce the effect-ele- 
 ment, the inference may be drawn that the one is the 
 veritable cause of the other. 
 
 Canon of the Method of Difference. — If an instance in 
 which the phenomenon under investigation occurs, and an 
 instance in which it does not occur, have every circumstance 
 save one in common, that one occurring only in the former; 
 the circumstance in which alone the two instances differ is 
 the effect, or it may be the cause, or a necessary part of the 
 cause, of the phenomenon. 
 
 This method admits of manifold illustration in our every- 
 day inferences. A person is asleep in the room with us, 
 and we hear the loud noise of a slamming door, and observe 
 
 236 
 
THE METHOD OE DIFFERENCE 
 
 237 
 
 the person at once awakening with a start and exclamation. 
 We have no hesitancy in ascribing the awakening to the 
 noise immediately preceding it. We observe again some 
 one receiving a letter or telegram, and immediately upon 
 opening it the face grows white with anxiety and fear, the 
 hands tremble, and there are shown general symptoms of 
 perturbation. The message received, we say, has caused 
 the mental shock and physical accompaniments. 
 
 Or, taking a simple experiment in quite another sphere, 
 it was observed by Boyle, in 1670, that an extract of litmus 
 was immediately turned red by the introduction of an acid. 
 This subsequently became a test for the presence of acids, 
 the inference being that an acid has this capacity of chang- 
 ing the litmus to a red color from its original blue. 
 
 Professor Tyndall describes an experiment to prove that 
 waves of ether issuing from a strong source, such as the sun 
 or electric light, are competent to shake asunder the atoms 
 of gaseous molecules, such as those of the sulphur and oxy- 
 gen which constitute the molecule of sulphurous acid. He 
 enclosed the substance in a vessel, placing it in a dark room, 
 and sending through it a powerful beam of light. At first 
 nothing was seen ; the vessel containing the gas seemed as 
 empty as a vacuum. Soon, along the track of the beam, a 
 beautiful sky-blue color was observed, due to the liberated 
 particles of sulphur. For a time the blue grew more intense ; 
 it then became whitish ; and from a whitish-blue it passed 
 to a more or less perfect white. Continuing the action, the 
 tube became filled with a dense cloud of sulphur particles 
 which, by the application of proper means, could be rendered 
 visible. 1 In this series of continuous changes, we find the 
 one antecedent giving the causal impulse to be the beam of 
 light. It was the one element introduced which started 
 the several changes leading to the appearance of the sulphur. 
 The one, therefore, is to be regarded as the cause of the 
 other. 
 
 1 Tyndall, Use and Limit of the Imagination in Science, p. 33. 
 
238 
 
 INDUCTIVE LOGIC 
 
 It is possible to represent this method by means of sym- 
 bols in a manner similar to that of the method of agreement. 
 Let C be the supposed cause and e the effect corresponding, 
 while S and s denote the setting of antecedent and conse- 
 quent respectively. We have, therefore, the following : — 
 
 S + C s - f e. 
 
 Then, withdrawing C, we have the absence of e. 
 
 S s. 
 
 The inference then is that C is the cause of e. Or, we may 
 have given 
 
 S s. 
 
 Then if, adding C, we find that e also appears, represented 
 
 by 
 
 S G . . . . . . . . s - f- e, 
 
 we infer that C and e have a causal connection. 
 
 In the method of agreement, a number of instances are 
 taken agreeing only in the possession of two circumstances, 
 — the cause and effect elements common to them all. In 
 this method, only two instances are taken, and they must 
 be precisely alike, -with the one exception, — the presence 
 of two circumstances in one, that is, the cause and the effect 
 elements, and the absence of the same in the other. In the 
 method of agreement, we compare the various phenomena 
 to note wherein they agree; in the method of difference, 
 we compare the two phenomena to note wherein they differ. 
 The logical axiom underlying the two methods is sub- 
 stantially one and the same, differing only in its special 
 adaptation in each case. The former method rests on the 
 assumption, which must be accepted as a fundamental postu- 
 late, that whatever can be eliminated from the various 
 instances is not connected with the phenomenon under in- 
 vestigation in any causal manner ; and the method of differ- 
 
THE METHOD OF DIFFERENCE 
 
 239 
 
 ence is based on the postulate that whatever cannot be elimi- 
 nated is connected with the phenomenon by a causal law. 
 
 The method of difference is evidently the method by 
 negation, which has already been indicated as the truly 
 scientific process in induction. It is also preeminently the 
 method of experiment rather than observation ; for the with- 
 drawal or introduction of forces can only be accomplished 
 at will when we bring the phenomena under experimental 
 control. At times nature herself may perform the experi- 
 ment for us, and we stand simply as observers to note the 
 results. This is especially the case in the catastrophic 
 phenomena, such as volcanic eruption, earthquakes, etc. 
 Generally speaking, however, the method of difference is the 
 process of man’s manipulation to secure purposed results in 
 which a causal relation is disclosed. 
 
 A question naturally suggests itself, What is there to 
 determine the precise mode of experiment ? We may have 
 given a concrete whole of extreme complexity. In our ex- 
 periment, which element shall we proceed to eliminate, in 
 order to note the result ? An answer may be given us 
 through suggestions received from the results of enumera- 
 tion, analogy, or the method of agreement. If it is not 
 possible to avail one’s self of this contribution from another 
 sphere of investigation, then the complex whole must be 
 broken up, as far as possible, into its simplest component 
 parts, and one after another these parts, singly, then in 
 pairs, and all other possible combinations, caused to be 
 withdrawn, or their force neutralized, and the results in 
 each case noted, as to whether the effect under investigation 
 disappears. The exhaustion of all possible combinations 
 must yield some definite result. Suppose, for instance, 
 there is a complex antecedent involving four separable ele- 
 ments, as A, B, C, D. Withdraw severally A, B, C, and D, 
 noting results ; then withdraw, in turn, AB, AC, AD, BC, 
 BD, CD, that is, the possible combinations of four elements 
 taken two at a time ; then withdraw ABC, then BCD, ABD, 
 
240 
 
 INDUCTIVE LOGIC 
 
 and ACD, that is, combinations of four elements taken three 
 at a time. 1 By such a process there will be disclosed 
 whether one element alone or whether a combination of two 
 or more have produced the effect under investigation. The 
 practical difficulty in separating the elements of a complex 
 whole, and withdrawing the several combinations from the 
 whole, renders this process in many cases impossible. The 
 cause, however, is generally suspected. It may be suggested, 
 as Ave have seen, by the method of agreement, by analogy, 
 or by that insight which at once declares certain combina- 
 tions to be impossible and others irrelevant. There is 
 generally a mental experiment in which the judgment 
 rejects unlikely combinations, thus narrowing the field of 
 investigation and furnishing a tentative hypothesis as a 
 preliminary to the experiments proper. 
 
 The method of difference is open to various criticisms ; 
 the most important are the following : — 
 
 1. In applying this method, we may be easily misled, in 
 supposing our two instances are precisely alike Avith the 
 one exception of the presence or absence of the supposed 
 cause, but in reality the instance may differ radically, and 
 yet we may be unable to detect this. A patient may have 
 medicine administered to him, and begin at once rapidly to 
 recover, and yet the very taking of the medicine in itself 
 may have made such a mental impression inducing confi- 
 dence and hope that the real cause of the recovery may be 
 due wholly to this mental reaction. Persons taking pills 
 composed of inert substances have often given evidence of 
 bodily effects wholly impossible to trace to the medicine 
 itself. And yet this criticism is one of caution rather than 
 of censure; for the defects are but difficulties which ex- 
 treme care and insight may overcome. 
 
 2. It has been objected that this method may point out 
 the cause in the concrete instance before the experimenter, 
 
 1 This process has been illustrated and criticised at length in a striking 
 manner by Venn, Empirical Logic, pp. 101 ff. 
 
THE METHOD OF DIFFERENCE 
 
 241 
 
 but that this furnishes no basis whatsoever for a wider 
 generalization that the effect in question is always produced 
 by this cause. Sigwart has illustrated this objection by the 
 instances in which typhus fever has been traced to the 
 drinking of impure water. 1 The causal relation may be 
 fully established in the cases investigated, but the universal 
 proposition does not follow that wherever typhus fever 
 appears, impure water has been drunk. This objection 
 applies especially to cases of extreme complexity, where 
 proximate causes alone can be discovered, and their ultimate 
 nature which may appear in various forms is not revealed ; 
 for instance, the impure water is not in itself the ultimate 
 cause of the typhus fever. It contains the poison germs, 
 the real cause ; they may be introduced into the system in 
 some other way. Care therefore should be taken to reveal 
 the cause in and by itself, and not the cause of the cause. 
 The objection, therefore, may be in a measure overcome. 
 To effect a generalization of logical validity, it is necessary 
 to supplement the method of difference by hypothesis and 
 subsequent verification, which will be described later on. 
 
 3. This method may lead to error in cases where the sup- 
 posed causal element is regarded as the cause in its entirety, 
 when it is in reality but a part of the cause. If one should 
 plant seed in a garden and water only one-half of the plot, 
 and it should follow that only the watered part brought 
 forth the leaf and flower, then an inference according to the 
 method of difference might be drawn that the water caused 
 the sprouting of the young plants. And yet it must be re- 
 garded simply as contributory to the real cause. Such a 
 difficulty may be obviated by a careful discrimination in the 
 analysis of the phenomenon investigated. 
 
 4. Sometimes a liberating cause may be revealed by a 
 strict interpretation of the method of difference, when the 
 real cause is more obscure, and may be overlooked. A stone 
 may strike a can of dynamite, and the explosion which 
 
 1 Sigwart, Logic, Yol. II, p. 120. 
 
242 
 
 INDUCTIVE LOGIC 
 
 occurs may be traced to the impact of the stone. It is the 
 one element of difference introduced in the sphere of the 
 observed phenomena, with the consequent result. The 
 force existing as a potential is naturally obscure, and apt to 
 elude observation. Therefore, whenever a cause disclosed 
 by the method of difference seems to be out of all propor- 
 tion to the effect, it at once suggests the probability that a 
 potential force not discerned by our powers of observation 
 has been the real cause, and the former a conditioning cause 
 merely. Another illustration of this is the experiment of 
 Priestley, which led to his discovery of oxygen in 1774. 
 He placed some oxide of mercury upon the top of quick- 
 silver in an inverted glass tube filled with that metal and 
 standing in mercury ; he then heated the oxide by means of 
 a glass lens and the sun’s rays, and obtained a gas, which 
 he called “ nitrous air,” afterwards designated as oxygen. 
 The heat in this case was the sole element of difference 
 between the two instances, one in which there was no gas, 
 and the second after application of the heat, when the gas 
 was present. Here the heat must be regarded as the liber- 
 ating and not in any sense the producing cause. Again, as 
 Lotze says, “ the fact that with the destruction of a single 
 part of the brain a definite psychical function ceases, is no 
 proof that just this single part was the organ which alone 
 produced that function.” 1 
 
 In addition to the difficulties attending this method, which 
 have been enumerated and which have to do with the logi- 
 cal theory of the method, there are also difficulties of a prac- 
 tical nature which arise in the actual application of this 
 method in experimental inquiry. They are as follows: — 
 
 1. Care must be taken that, in the two phenomena com- 
 pared, with and without the supposed cause, there shall not 
 be an interval of time elapsing, in which period some other 
 cause might be introduced unknown to the investigator, and 
 yet capable of producing the result, or else of neutralizing 
 1 Lotze, Logic, p. 322. 
 
THE METHOD OF DIFFERENCE 
 
 243 
 
 some force that is present and itself capable of producing 
 the result. For instance, if a chemical compound be left 
 for an appreciable time, we may notice certain changes and 
 be able to assert positively that no new element has been 
 introduced, and yet the action of the air may in itself have 
 been sufficient to work these changes. When the two phe- 
 nomena to be compared can be presented for inspection 
 simultaneously, this difficulty is obviated. This is illus- 
 trated in an experiment devised to exhibit the presence of 
 light effects in the spectrum beyond the violet rays ; that is, 
 beyond the place where the spectrum seems to end. A 
 sheet of paper is taken, the lower part of which is moistened 
 with a solution of sulphate of quinine, while the upper part 
 remains dry. Let the image of the solar ray fall upon this 
 sheet ; the spectrum preserves at the top of the sheet in the 
 dry portion of the paper its ordinary appearance, while in 
 the moistened portion a brilliant phosphorescence appears 
 beyond the region of the violet rays. Here the dry and wet 
 portions are simultaneously presented, and there is but one 
 point of difference between the two. The inference, there- 
 fore, is readily drawn that the solution of sulphate of quinine 
 is a substance sensitive to the ultra-violet portion of the sun's 
 rays, the phosphorescence being the effect of these rays upon 
 the solution. 
 
 2. Extreme care must be taken that, in the withdrawing 
 of any element in the course of the experiment, no other 
 element is inadvertently introduced, and that, in adding 
 any element, no existing element or combination of elements 
 is destroyed, or their effect neutralized. Mr. Venn has ad- 
 mirably illustrated this difficulty, and I give the following 
 quotation in full from him: “We suppose that when we 
 have put a weight into one pan of a pair of scales we have 
 done nothing more than this, or can at any rate by due cau- 
 tion succeed in doing nothing more. But if we exact the 
 utmost rigidity of conditions, we easily see that we have 
 done a great deal more. Our bodies are heavy, and there- 
 
244 
 
 INDUCTIVE LOGIC 
 
 fore tlie mere approach to the machine has altered the mag- 
 nitude and direction of the resultant attraction upon the 
 scales. Our bodies are presumably warmer than the sur- 
 rounding air ; accordingly, we warm and therefore lighten 
 the air in which the scales hang, and if the two scales and 
 their contents are not of the same volume, we at once alter 
 their weight as measured in the air. Our breath produces 
 disturbing currents of air. Our approach affects the sur- 
 face of the non-rigid floor or ground on which the scales 
 stand, and produces another source of disturbance, and so 
 on through the whole range of the physical forces.” 1 
 
 In the Report of the British Association, 1881, an account 
 is given of Professor G. H. Darwin’s experiments to meas- 
 ure the lunar disturbance of gravity at the Cavendish Lab- 
 oratory by means of an extremely delicate pendulum. It 
 was found that approaching the pendulum in order to ob- 
 serve its reading, the surface level of the stone floor on 
 which the instrument stood was deflected by the weight of 
 the observer. As he stood to take the reading, the shifting 
 of his weight from one leg to the other was perceptible ; so 
 it became necessary to observe the reading by a telescope 
 from a distance, or to adopt some similar plan. 2 
 
 Faraday was able at will to produce or remove a magnetic 
 force, through the revealed properties of the electromagnet. 
 Many of his experiments would have been impossible if it 
 had been necessary to remove a cumbersome magnet and 
 reinstate it again and again in his experiments. The elec- 
 tromagnet however could produce or destroy the presence 
 of magnetic force without any incidental perturbations. 
 Thus Faraday was enabled to prove the rotation of circu- 
 larly polarized light by the fact that certain light ceased to 
 be visible when the electric current of the magnet was cut 
 off, and instantly reappeared when the current was reestab- 
 lished. Faraday says of the experiment himself : “ These 
 
 1 Venn, Empirical Logic, p. 416. 
 
 2 Quoted by Venn in Empirical Logic , p. 419. 
 
THE METHOD OF DIFFERENCE 
 
 245 
 
 phenomena could be reversed at pleasure, and at any instant 
 of time, and upon any occasion, showing a perfect depend- 
 ence of cause and effect.” 1 
 
 3. In some cases it is impossible to remove an element 
 which is supposed to be the cause of an effect under investi- 
 gation. Its removal might cause the destruction or the im- 
 pairing of the whole phenomenon. The force therefore 
 that cannot be eliminated must be neutralized by an equal 
 and opposing force. For instance, the force of gravity can- 
 not be eliminated ; it must therefore be counterbalanced by 
 some device of the investigator. In chemistry the removal 
 of an element from a compound may be impossible without 
 destroying utterly the compound itself ; in such a case also 
 a neutralizing agent must be introduced. Darwin wished to 
 prove that the odor of flowers is attractive to insects irre- 
 spective of the attraction of color. He therefore covered 
 certain flowers with a muslin net, and still the insects were 
 attracted to the flowers although the color was thus con- 
 cealed. 2 
 
 The following illustrations may serve further to exhibit 
 the various features of the method of difference : — 
 
 Mr. Robert Mallet gives the following interesting account 
 of his visit to Faraday: “It must be now eighteen years 
 ago when I paid him a visit, and brought some slips of 
 flexible and tough Muntz’s yellow metal, to show him the 
 instantaneous change to complete brittleness with rigidity 
 produced by dipping into pernitrate of mercury solution. 
 He got the solution and I showed him the facts ; he 
 obviously did not doubt what he saw me do before and 
 close to him ; but a sort of experimental instinct seemed to 
 require he should try it himself. So he took one of the 
 slips, bent it forward and backward, dipped it, and broke it 
 up into short bits between his own fingers. He had not 
 before spoken. Then he said, ‘ Yes, it is pliable, and it does 
 
 1 Experimental Researches in Electricity , Vol. IH, p. 4. 
 
 2 Darwin, Cross and Self Fertilization, p. 374. 
 
246 
 
 INDUCTIVE LOGIC 
 
 become instantly brittle.’ ” 1 Here the experiment with and 
 without the significant antecedent and consequent indicates 
 the causal relation, especially as the instantaneous effect 
 precludes the possibility of the operation of any other 
 cause. 
 
 Another experiment of Faraday’s is that of his investiga- 
 tion of the behavior of Lycopodium powder on a vibrating 
 plate. It had been observed that the minute particles of 
 the powder collected together at the points of greatest motion, 
 whereas sand and all heavy particles collected at the nodes, 
 where the motion was least. It occurred to Faraday to 
 try the experiment in the exhausted receiver of an air- 
 pump, and it was then found that the light powder behaved 
 exactly like heavy powder. The inference was that the 
 presence of air was the condition of importance, because it 
 was thrown into eddies by the motion of the plate, and 
 carried the Lycopodium powder to the points of greatest 
 agitation. Sand was too heavy to be carried by the air . 2 
 
 Sir John Lubbock gives an account of experiments per- 
 formed upon insects to prove that the sense of smell is in 
 some way connected with their antennae. One experiment 
 was performed by Forel, who removed the wings from some 
 blue-bottle flies and placed them near a decaying mole. 
 They immediately walked to it, and began licking it and 
 laying eggs. He then took them away, and removed the 
 antennae, all other circumstances remaining the same as 
 before, after which, even when placed close to the mole, 
 they did not appear to perceive it. Another experiment 
 similar to this was tried by Plateau, who put some food of 
 which cockroaches are fond on a table and surrounded it 
 with a low circular wall of cardboard. He then put some 
 cockroaches on the table ; they evidently scented the food, 
 and made straight for it. He then removed their antennae, 
 after which, as long as they could not see the food, they 
 
 1 Gladstone, Michael Faraday, p. 175. 
 
 2 Jevons, Principles of Science, p. 419. 
 
THE METHOD OF DIFEEEENCE 
 
 247 
 
 failed to find it, even though they wandered about quite 
 close to it . 1 
 
 Another experiment is that of Graber to prove the sense 
 of hearing in insects. He placed some water-boatmen 
 ( Corixa ) in a deep jar full of water, at the bottom of which 
 was a layer of mud. He dropped a stone on the mud, but 
 the beetles, which were reposing quietly on some weeds, 
 took no notice. He then put a piece of glass on the mud, 
 and dropped a stone on to it, thus making a noise, though 
 the disturbance of the water was the same as when the stone 
 was dropped on the mud. The water-boatmen, however, 
 then at once took flight . 2 
 
 An illustration of the method of difference occurs in the 
 so-called blind experiments, which are often made in chemistry 
 especially. As Professor Jevons has described such an 
 experiment : “ Suppose, for instance, a chemist places a 
 certain suspected substance in Marsh’s test apparatus and 
 finds that it gives a small deposit of metallic arsenic, he 
 cannot be sure that the arsenic really proceeds from the 
 suspected substance; the impurity of the zinc or sulphuric 
 acid may have been the cause of its appearance. It is 
 therefore the practice of chemists to make what they call 
 blind experiments, that is, to try whether arsenic appears 
 in the absence of the suspected substance. The same pre- 
 caution ought to be taken in all important analytical 
 operations. Indeed it is not merely a precaution, it is 
 an essential part of any experiment. If the blind trial be 
 not made, the chemist merely assumes that he knows what 
 would happen .” 3 
 
 1 Lubbock, On the Senses, Instincts , and Intelligence of Animals, p. 45. 
 
 2 Ibid., p. 75. 8 Jevons, Principles of Science, p. 433. 
 
CHAPTER VIII 
 
 THE JOINT METHOD OF AGREEMENT AND DIFFERENCE 
 
 It has already been shown that the method of difference 
 is sometimes not available, inasmuch as it may be neither 
 possible nor practicable to remove from the phenomenon to 
 be investigated the suspected causal element without destroy- 
 ing the phenomenon itself. Sometimes, too, it is impossible 
 even to neutralize the effect of the causal element if it is 
 allowed to remain as an integral part of the phenomenon. 
 This is especially the case in all vital phenomena, and also 
 in many chemical phenomena. Therefore another method 
 is resorted to, which is known as the joint method of agree- 
 ment and difference. Inasmuch as the suspected causal ele- 
 ment cannot be removed, we must select another phenomenon 
 as much like the former as possible, which is however 
 characterized by the absence of the causal element. By the 
 simple method of difference, two instances only need be 
 compared, the one with and the other without the causal 
 element, but agreeing precisely in every other particular. 
 In the joint method, the instances with and without the 
 causal element differ, it may be, in several particulars. A 
 number of varying instances must therefore be selected so 
 as to eliminate the possibility of any of these differing char- 
 acteristics being the cause in question. Therefore two sets 
 of instances are collected and compared. The one set com- 
 prises all the positive instances having the presence of the 
 supposed causal element, and the second set consists of the 
 negative instances having the supposed causal element ab- 
 sent altogether. The validity of the method depends upon 
 the similarity of the two sets of instances. As the similarity 
 
 248 
 
AGREEMENT AND DIFFERENCE 
 
 249 
 
 increases, the method approximates to the simple method 
 of difference. 
 
 The Canon of the Joint Method. — If several instances in 
 which the phenomenon occurs have only one circumstance 
 in common, while several instances in which it does not 
 occur have nothing in common save the absence of that cir- 
 cumstance; the circumstance in which alone the two sets of 
 instances differ, is the effect, or cause, or a necessary part 
 of the cause, of the phenomenon. 
 
 The symbolical representation of this method may be ex- 
 hibited as follows, using a similar notation to that employed 
 in the previous methods : — 
 
 I. Table of positive instances. 
 
 
 
 S + C 
 
 
 + e. 
 
 S' + c 
 
 
 + e. 
 
 S" + c 
 
 . s" 
 
 + e. 
 
 S'" + c 
 
 . s’" 
 
 + e. 
 
 etc. etc. 
 
 II. Table of negative instances 
 
 8 , 
 
 s„ 
 
 
 
 etc. 
 
 In the two sets of instances, the following conditions 
 must be observed in order to render the method valid : — 
 
 1. S + C, S' + C, S" + C, S'" + C, etc., 
 
 must be so varied that they reveal but one constant element, 
 common to them all, as C. It may be that S will resemble 
 S' in more marks than the one, namely C, and this may be 
 true of any two or more instances ; however, taken all to- 
 gether, they must possess but the one common element C. 
 
 2. In the same way S t may resemble S n in more marks 
 than merely the absence of C and so for any two or more 
 
 s r 
 
 s n . 
 
 s nr 
 
 etc. 
 
250 
 
 INDUCTIVE LOGIC 
 
 instances in the series S t , S u , S m , etc. However, the one 
 characteristic common to them all must be the absence of C. 
 
 3. If in the instances chosen an element is common to all 
 in addition to C, or in the second set its absence, then addi- 
 tional instances must be added to the tables both positive 
 and negative in order to secure this all-important condition 
 of elimination through suitable variation. 
 
 4. Moreover, the two series, positive and negative, must 
 have their settings similar. S„ S u , S IIP etc., must resemble 
 S', S", S'", etc. ; otherwise the negative instances would not 
 be significant. 1 They must be chosen from the same sphere 
 as the positive, in order that they may be similar. It is 
 possible to multiply negative instances ad infinitum, which, 
 however, would furnish no ground for any inference, be- 
 cause they would be wholly irrelevant to the problem under 
 investigation. 
 
 5. If S, is so similar to S' as to be identical with it, and 
 also s, passes over into s'; then we have the method of 
 difference in its pure form: — 
 
 S' + G s' + e. 
 
 S' s'. 
 
 Here the setting, instead of being similar in the two cases, 
 is the same in each. 
 
 The following is an experiment of Sir John Lubbock’s 
 concerning the sense of smell in insects, which I have chosen 
 as illustrating this method of inductive research. He took 
 a large ant and tethered her on a board by a thread. When 
 she was quite still, he brought a tuning-fork into close 
 proximity to her antennae, but she was not disturbed in the 
 least. He then approached the feather of a pen very quietly, 
 so as almost to touch first one and then the other of the 
 antennae, which, however, did not move. He then dipped 
 the pen in the essence of musk and did the same; the 
 antenna was slowly retracted and drawn quite back. He 
 
 1 See p. 75. 
 
AGREEMENT AND DIFFERENCE 
 
 251 
 
 then repeated the same with the other antenna, and with 
 like result. Care was taken throughout not to touch the 
 antennae. Lubbock then repeated the experiment with a 
 number of different ants, and using various substances. 
 The results in all cases were the same, and the inference 
 was naturally drawn that the antennae possessed the sense 
 of smell. In these experiments various substances were 
 taken having nothing in common save the odor of musk 
 that had been placed upon them. 
 
 In some cases it is not possible to discover positive in- 
 stances in which the only common element is the suspected 
 cause. In such cases the method is not conclusive in its 
 results, although it may attain a high degree of probability, 
 if all the common elements save the suspected cause-element 
 are known to be irrelevant, or can in any other way be 
 proved to have no influence whatsoever upon the result. 
 Lor instance, an illustration is often given of this method, 
 which fails in the manner just described. A man is attempt- 
 ing to discover whether a particular article of food disagrees 
 with him. He notices several occasions, a large number if 
 you please, when he has eaten this particular kind of food, 
 and has soon after experienced distress. These are the posi- 
 tive instances. This peculiar distress has never been ex- 
 perienced when he has abstained from the food in question. 
 The inference is that this food has caused the distress. In 
 the various instances, however, the sole element in common 
 is not merely the taking or not taking the food. The per- 
 son’s whole bodily organism is common to all the instances. 
 Within it, unforeseen complications, independent of this 
 article of food, might have caused the trouble. In such 
 cases a large number of instances must be resorted to in 
 order to render the possibility of a coincidence out of the 
 question. 
 
 So also in such cases as the treatment of any given disease 
 in a hospital. An experiment may be tried in the treat- 
 ment, say, of typhoid fever. One ward may be subjected 
 
252 
 
 INDUCTIVE LOGIC 
 
 to a particular kind of treatment, and another ward not sub- 
 jected to that treatment. If recovery is hastened in the one 
 and retarded in the other case, an inference may be drawn 
 as to efficacy of this treatment. In these instances again, 
 while they are all different patients, still the nursing, sur- 
 roundings, etc., are common to them all. It must be shown 
 that these are present both in the negative and positive in- 
 stances, and equally capable of accomplishing the effect if 
 they had been real causes. They may therefore be elimi- 
 nated in comparing the two sets of instances, because com- 
 mon both to the negative and positive cases. In this also 
 resort must be had to the number of instances in order to 
 eliminate chance coincidences. The presence of common 
 elements in excess of the common causal element may be 
 represented according to the symbolical notation of the joint 
 method, by the introduction of another symbol x. Let x 
 stand for that which is common to all instances in addition 
 to the common element C. We then have : — 
 
 I. Set of positive instances. 
 
 S + C + x 
 S' + C + x 
 S" + C + x 
 S'" + C +x 
 etc. 
 
 II. Set of negative instances. 
 
 S t + x 
 S u + x 
 S in + x 
 etc. 
 
 We observe x in all instances both positive and negative. 
 Being present when the effect occurs and when it does not, 
 indifferently, we can at once infer that x is not the whole 
 cause of e. However, it may have united with C in the first 
 
 s r 
 
 s ir 
 
 s ur 
 
 etc. 
 
 s + e. 
 s' -f- e. 
 s" + e. 
 s'" + e. 
 etc. 
 
AGREEMENT AND DIFFERENCE 
 
 253 
 
 set of instances to produce the effect e, so that C without x, 
 or some part or parts of x, could not alone produce the effect 
 e. In all such cases the exact force of x must be estimated 
 in some other way. If x is extremely complex, or subject 
 to change from forces emanating from within itself, as in 
 the case of organic phenomena, then it becomes extremely 
 difficult to determine x-, and consequently the method of 
 agreement and difference does not yield as exact results. 
 As long as the force of x remains unknown, it becomes the 
 source of possible disturbance, which may wholly vitiate 
 the results attained. 
 
 Mr. Darwin, in his experiments upon cross and self fer- 
 tilization in the vegetable kingdom, placed a net about one 
 hundred flower heads, thus protecting them from the bees 
 and from any chance of fertilization by means of the pollen 
 conveyed to them by the bees. He at the same time placed 
 one hundred other flower heads of the same variety of plant 
 where they would be exposed to the bees, and, as he observed, 
 were repeatedly visited by them. Here we have the two 
 sets of instances, in one the flowers accessible to the bees, 
 and in the other, not accessible. He obtained the following 
 result. The protected flowers failed to yield a single seed. 
 The others produced 68 grains’ weight of seed, which he 
 estimated as numbering 2720 seeds. Cross-fertilization as 
 the cause in this case is thus proved. The common element 
 in all these instances, however, is not merely the presence 
 in one case and the absence in the other of the bees ; there 
 is also the element of the common plant structure running 
 through all of the two hundred instances. This element is, 
 however, of such an unvarying nature in all the instances, 
 and the number observed so many as to eliminate the possi- 
 bility of any given plant structure possessing unobserved 
 peculiarities sufficient to produce the result in question. It 
 may therefore be considered as an inert element as regards 
 the effects noticed in the one and absent in the other set of 
 instances. 
 
254 
 
 INDUCTIVE LOGIC 
 
 Sir John Lubbock, in his researches concerning the dif- 
 ferent functions of the two kinds of eyes in insects, illus- 
 trates the joint method in its general features. The two 
 kinds of eyes are the large compound eyes, situated one on 
 each side of the head, and the ocelli, or small eyes, of which 
 there are generally three, arranged in a triangle between the 
 other two. He wished to determine the precise function of 
 the small eyes, the ocelli ; and he has gathered together the 
 following facts. Plateau has shown that caterpillars, which 
 possess ocelli, but no compound eyes, are very short-sighted, 
 not seeing above one to two centimetres. He has also 
 proved by experiments that spiders, which have ocelli but 
 no compound eyes, are very short-sighted; they were easily 
 deceived by artificial flies of most inartistic construction, 
 and even hunting spiders could not see beyond ten centi- 
 metres (four inches). Lubbock experimented on this point 
 with a female spider, which, after laying her eggs, had 
 rolled them into a ball, and had enveloped the whole with a 
 silken bag which she carried about with her. Having cap- 
 tured the female and having taken the bag of eggs from her, 
 he placed it on a table about two inches in front of her. 
 She evidently did not see it. He then pushed it gradually 
 towards her, but she took no notice till it nearly touched 
 her, when she eagerly seized it. He then took it away a 
 second time, and put it in the middle of the table, which 
 was two feet four inches by one foot four, and had nothing 
 else on it. The spider wandered about for an hour and 
 fifty minutes before she found it, apparently by accident. 
 He then took it away again and put it down as before, when 
 she wandered about for an hour without finding it. Like 
 experiments were tried with other spiders and with the 
 same results. Plateau also experimented with scorpions 
 which had ocelli and no compound eyes. They appeared 
 scarcely to see beyond their own pincers. Moreover, the 
 ocelli are especially developed in insects, such as ants, bees, 
 aud wasps, which live partly in the open light and partly in 
 
AGREEMENT AND DIFFERENCE 
 
 255 
 
 the dark recesses of nests. Again, the night-flying moths 
 all possess ocelli. On the other hand, however, they are 
 entirely absent in all butterflies, with but one exception, 
 according to Scudder, namely, the genus Pamphila. Forel 
 varnished the compound eyes of various insects which 
 had ocelli as well. The latter however he allowed to 
 remain in their natural state. Inasmuch as their habits 
 of flight required powers of vision in these insects extend- 
 ing to a considerable distance, it happened that when placed 
 on the ground they made no attempt to rise; while, if 
 thrown into the air, they flew first in one direction and then 
 in another, striking against any object that came in their 
 way, and being apparently quite unable to guide themselves. 
 They flew repeatedly against a wall, falling to the ground, 
 and unable to alight against it, as they did so cleverly when 
 they had their compound eyes to guide them. All these 
 instances, taken together in their positive and negative 
 aspects, led Sir John Lubbock to infer that the ocelli were 
 useful in dark places and for near vision, while the com- 
 pound eyes were for the light and more distant vision . 1 
 
 Another illustration of this method may be found in 
 Darwin’s account of the extreme tameness of the birds in 
 the Galapagos and Falkland islands. I quote some extracts 
 from his narrative, in which it will be seen that Darwin’s 
 inferences follow from his comparison of the positive and 
 negative instances before him. He says : “ This tameness 
 of disposition is common to all the terrestrial species of 
 these islands in the Galapagos Archipelago ; namely, to the 
 mocking-thrushes, the finches, wrens, tyrant flycatchers, the 
 dove, and carrion-buzzard. All of them often approached 
 sufficiently near to be killed with a switch, and sometimes, 
 as I myself tried, with a cap or hat. A gun is here almost 
 superfluous ; for, with the muzzle, I pushed a hawk off the 
 branch of a tree. In Charles Island, which had been colo- 
 nized about six years, I saw a boy sitting by a well with a 
 1 Lubbock, On the Senses, Instinct, and Intelligence of Animals, pp. 175 ff. 
 
256 
 
 INDUCTIVE LOGIC 
 
 switch in his hand, with which he killed the doves and 
 finches as they came to drink. He had already procured a 
 little heap of them for his dinner ; and he said that he had 
 constantly been in the habit of waiting by this well for the 
 same purpose. The Falkland Islands offer instances of 
 birds with a similar disposition. The snipe, upland and 
 lowland goose, thrush bunting, and even some true hawks, 
 are more or less tame. The black-necked swan is here wild, 
 and it was impossible to kill it. It however is a bird of 
 passage, which probably brought with it the wisdom learned 
 in foreign countries. 
 
 “ From these several facts, we may, I think, conclude that 
 the wildness of birds with regard to man is a particular 
 instinct directed against him and not dependent on any 
 general degree of caution arising from other sources of 
 danger ; secondly, that it is not acquired by individual birds 
 in a short time, even when much persecuted, but that in the 
 course of successive generations it becomes hereditary. 
 With domesticated animals we are accustomed to see new 
 mental habits or instincts acquired and rendered hereditary, 
 but with animals in a state of nature it must always be 
 most difficult to discover instances of acquired hereditary 
 knowledge. In regard to the wildness of birds towards 
 man, there is no way of accounting for it except as an in- 
 herited habit; comparatively few young birds, in any one 
 year, have been injured by man in England, yet almost all, 
 even nestlings, are afraid of him; many individuals, on the 
 other hand, both at Galapagos and at the Falklands, have 
 been pursued and injured by him, but yet have not learned 
 a salutary dread of him.” 1 
 
 I have given this quotation somewhat at length in order 
 to show the method of a great investigator in the realm of 
 nature ; and that it may be seen how naturally he falls into 
 the method of comparing positive and negative sets of in- 
 stances relative to the object of research. The animal and 
 1 Darwin, Voyage of a Naturalist, Vol. II, pp. 172 f. 
 
AGREEMENT AND DIFFERENCE 
 
 257 
 
 vegetable kingdoms are especially adapted to the applica- 
 tion of this joint method, and therefore it is in biology that 
 it is most frequently employed and where it has yielded the 
 most fertile results. 
 
 The advantage of the joint method over the simple 
 method of agreement is that it largely eliminates the possi- 
 bility of there being any other cause of the given phenome- 
 non than the one disclosed by the operation of this method. 
 The method of agreement, as we have seen, often fails of a 
 definite result owing to the plurality of causes. The joint 
 method tends to indicate the one and only cause, and when 
 the instances are rigorously selected according to the condi- 
 tions of the canon, there is a high degree of probability that 
 the sole cause is discovered. Mr. Mill at this point claims 
 too much for the method in insisting that it gives a certainty 
 regarding the sole cause, when the requirements are perfectly 
 realized. It is impossible to realize the requirements per- 
 fectly. In selecting the negative instances, we are never 
 sure that we have compassed the entire sphere of significant 
 negative instances. We may, however, attain results highly 
 probable in this regard, though they may not reach an abso- 
 lute certainty. Such a statement is more moderate in its 
 expression, and practically it assures as satisfactory results. 
 
CHAPTER IX 
 
 THE METHOD OF CONCOMITANT VARIATIONS 
 
 The method of concomitant variations is a process of 
 determining a causal relation when, as an element in an 
 antecedent varies in intensity greater or less, there is 
 observed a corresponding or concomitant variation in the 
 consequent. 
 
 Canon of the Method of Concomitant Variations. — What- 
 ever phenomenon varies in any manner, whenever another 
 phenomenon varies in some particular, is either a cause or 
 an effect of that phenomenon, or is connected with it through 
 some fact of causation. 
 
 The latter clause of this canon provides for that circum- 
 stance in which the varying elements may both be con- 
 comitant effects of a common cause. When we are assured 
 of the absence of any possible common cause to which we 
 can assign the two phenomena as effects, then they must 
 be related between themselves as cause and effect. A 
 simple illustration of this method is the rise of the mercury 
 in the thermometer owing to the increase of heat ; its fall, 
 whenever there is decrease of heat. One varies as the 
 other concomitantly, and we infer a causal relation that 
 we at once proceed to generalize without hesitation. 
 
 The symbolical representation of this method is as 
 follows : — 
 
 S + C . . . . 
 
 S+C±dC . . 
 
 s + e. 
 s + e ± de. 
 
 etc. 
 
 Then C is the cause of e. 
 
 etc. 
 
 258 
 
CONCOMITANT VARIATIONS 
 
 259 
 
 I have used dC and de to denote the increments or 
 decrements of the cause and effect respectively. This 
 method is used generally when the method of difference is 
 impossible, owing to the fact that the supposed causal 
 element cannot be made to vanish wholly. In all such 
 cases a variation of the element is resorted to, and the 
 corresponding result observed. Heat is relative and not 
 absolute, as also the height of mercury in the tube. The 
 relation is determined, therefore, by variations, greater and 
 less. This method is also used to supplement the results 
 of other methods by which a causal relation has been 
 determined, but not in exact quantitative terms. It may 
 be known that a certain phenomenon C is always the cause 
 of a certain effect e, and the method of concomitant vari- 
 ations will then be of use in determining precisely how 
 much of a variation in C will cause a specified variation 
 in e. A law finds scientific expression only when stated in 
 terms of exact quantitative relation between variations in 
 antecedent and consequent. We may express the law of 
 universal attraction in a vague way that bodies always 
 attract each other, and the greater attraction when the 
 bodies are nearer together, and the larger they are. But 
 this statement needs to be recast in terms exhibiting the 
 precise quantitative variation, — bodies attract each other 
 directly as the product of their masses, and inversely as the 
 square of their distance. It is evident that the special 
 function of this method of concomitant variations consists 
 in just this quantitative determination. In one respect, 
 therefore, it may be regarded as a substitute for the method 
 of difference, and in another way as a supplement to the 
 method of difference in leading to quantitatively determi- 
 nate results. 
 
 The quantitative variation between antecedent and con- 
 sequent may be either direct or inverse variation. The 
 former is when one increases as the other increases, or 
 when one decreases as the other decreases. The inverse is 
 
260 
 
 INDUCTIVE LOGIC 
 
 when one decreases as the other increases, or vice versa. 
 This may be expressed symbolically 
 
 S -f- G i dC . . . . s + e T de. 
 
 We have, for instance, Boyle’s law as regards the variation 
 of volume of gases according to the pressure ; that is, 
 when we double the pressure, we halve the volume. This 
 may be proved experimentally. The method also was 
 used by Ricardo to prove his law that the rate of profits 
 varies in inverse ratio to the rate of wages. We have also 
 the tendency observed in respect to increase of crimes 
 when there is decrease of opportunities for labor. 
 
 The expression of a law in terms of the quantitative 
 relation between antecedent and consequent may be facili- 
 tated by a graphic representation of the same, through 
 corresponding abscissae and ordinates. The varying ante- 
 cedents, for instance, may be laid off on the axis of X, 
 and each several consequent represented by the corre- 
 sponding ordinate. The resulting curve thus obtained 
 will represent the law of their mutual relation. If the 
 equation of the curve can be determined, it will represent 
 the mathematically exact expression of the law in ques- 
 tion. If this is not possible, it may prove at least sug- 
 gestive of the law which otherwise might have remained 
 concealed. This graphical method is especially useful in 
 dealing with physical phenomena. “If the abscissas rep- 
 resent intervals of time, and the ordinates corresponding 
 heights of the barometer, we may construct curves which 
 show at a glance the dependence of barometric pressure 
 upon the time of day. Such curves may be accurately 
 drawn by photographic processes on a sheet of sensitive 
 paper placed behind the mercurial column, and made to 
 move past it with a uniform horizontal velocity by clock- 
 work. A similar process is applied to the temperature and 
 
CONCOMITANT VARIATIONS 
 
 261 
 
 electricity of the atmosphere, and to the components of ter- 
 restrial magnetism.” 1 
 
 The method of concomitant variation has the advantage 
 of the psychological impression which it makes. The 
 mind is more susceptible to the perception of variation in 
 forces where the change is apparent to the senses, than to 
 the perception of a constant force, whose constaut character 
 thereby conceals its nature and function from the senses. 
 Synchronous changes attract the attention, and admit of 
 ready comparison, as we follow out the variations from 
 point to point. We may ring a bell in a vacuum, and detect 
 no sound whatsoever, and then allow the air to enter gradu- 
 ally. We notice that as the air enters more and more freely, 
 the sound grows louder and louder. The relation of cause 
 and effect is thus demonstrated to the senses in the most 
 vivid manner possible. The variations are exhibited side 
 by side, and thus, presented together in their concomitant 
 relation, produce the deeper impression. 
 
 This method is of special advantage in all experiments 
 where the intensity of the forces can be varied at will and 
 the consequent effects exhibited in some palpable manner. 
 The determination of the heat rays in the solar spectrum is 
 accomplished by this method. The spectrum may be 
 received upon a plate pierced with a narrow slit, through 
 which the rays can act upon a thermo-electric pile, which 
 will indicate by deflections of a needle the varying intensity 
 of the heat in the several rays of the spectrum. Now, 
 move the slit through the whole extent of the spectrum, 
 beginning with the violet portion. While in the violet, the 
 indigo, the blue, and even the green, the needle of the ther- 
 moscopic apparatus will be deflected but slightly, it will 
 indicate an amount of heat increasing as the slit crosses the 
 yellow, next the orange, then the red ; and then beyond the 
 red, and entering the dark portion of the spectrum, we find 
 the greatest deflection of all. The maximum of heat is 
 
 1 Thomson and Tait, Elements of Natural Philosophy, Vol. I, p. 119. 
 
262 
 
 INDUCTIVE LOGIC 
 
 therefore in a region beyond the observation of the senses 
 when unaided by experimental device ; and yet revealed 
 conclusively by this method . 1 
 
 Professor Tyndall performed a very interesting experi- 
 ment to prove that the cloud of darkness surrounding flames 
 of great heat was due to the fact that the heat consumed 
 the floating motes in the air which serve to scatter the light 
 which is visible only when thus diffused. The phenomenon 
 which he endeavored to explain was somewhat as follows : 
 Beneath a beam of electric light, a red-hot poker was placed, 
 and from it black wreaths as of smoke were seen to ascend. 
 A large hydrogen flame being employed, it produced whirl- 
 ing masses of darkness far more copiously than the poker. 
 Of this Professor Tyndall remarked : “ Smoke was out of 
 the question ; what then was the blackness ? It was simply 
 that of stellar space ; that is to say, blackness resulting from 
 the absence from the track of the beam of all matter com- 
 petent to scatter its light. When the flame was placed 
 below the beam, the floating matter was destroyed in situ ; 
 and the air freed from this matter rose into the beam, jostled 
 aside the illuminated particles, and substituted for their 
 light the darkness due to its own perfect transparency. 
 Nothing could more forcibly illustrate the invisibility of 
 the agent which renders all things visible. The beam 
 crossed, unseen, the black chasm formed by the transpar- 
 ent air, while at both sides of the gap the thick-strewn par- 
 ticles shone out like a luminous solid under the powerful 
 illumination.” 2 Such being the phenomenon and Professor 
 Tyndall’s explanation, it will be seen that he proceeded 
 according to the method of concomitant variations in the 
 following experiment of many which he performed to sub- 
 stantiate this theory : — 
 
 A platinum tube with its plug of platinum gauze was 
 connected with an experimental tube, through which a pow- 
 
 1 Saigey, The Unity of Natural Phenomena, p. 61. 
 
 1 Tyndall, Fragments of Science, p. 280. 
 
CONCOMITANT VARIATIONS 
 
 263 
 
 erful beam could be sent from an electric lamp placed at its 
 end. The platinum tube was heated till it glowed feebly 
 but distinctly in the dark. The experimental tube was 
 then exhausted, and filled with air that had passed through 
 the red-hot tube. A considerable amount of floating matter 
 which had escaped combustion was revealed by the electric 
 beam. 
 
 Then the tube was raised to a brighter redness and the 
 air permitted to pass slowly through it. Though diminished 
 in quantity, a certain amount of floating matter passed into 
 the exhausted experimental tube. 
 
 The platinum tube was rendered still hotter; a barely 
 perceptible trace of the floating matter now passed through 
 it. The experiment was repeated, with the difference that 
 the air was sent more slowly through the red-hot tube. The 
 floating matter was totally destroyed. The platinum tube 
 was now lowered until it bordered upon a visible red heat. 
 The air, sent through it still more slowly than in the last 
 experiment, carried with it a cloud of floating matter. Pro- 
 fessor Tyndall’s commentary upon this experiment is as 
 follows: “If, then, the suspended matter is destroyed by 
 a bright red heat, much more is it destroyed by a flame 
 whose temperature is vastly higher than any employed 
 in this experiment. So that the blackness introduced 
 into a luminous beam where a flame is placed beneath it 
 is due, as stated, to the destruction of the suspended 
 matter.” 1 
 
 Professor Tyndall also supplemented this experiment by 
 one which was according to the joint method of agreement 
 and difference. He prepared oxygen so as to exclude all 
 floating particles, and found that when blown into the beam, 
 darkness was produced ; also that hydrogen, nitrogen, car- 
 bonic acid, and coal-gas, when prepared in a similar way, 
 each produce darkness when poured or blown into the beam. 
 These instances, combined with various positive instances of 
 1 Tyndall, Fragments of Science , pp. 283, 284. 
 
264 
 
 INDUCTIVE LOGIC 
 
 illumination of mote-strewn currents of air, illustrate the 
 method of agreement and difference. 
 
 An additional experiment, according to the method of 
 difference, w T as as follows : Professor Tyndall placed an 
 ordinary glass shade in the air with its mouth downward. 
 This permitted the track of the beam to be seen crossing it. 
 Letting coal-gas, or hydrogen, enter the shade by a tube 
 reaching to its top, the gas gradually filled the shade from 
 the top downward. As soon as it occupied the space crossed 
 by the beam, the luminous track was instantly abolished. 
 Lifting the shade so as to bring the common boundary of 
 gas and air above the beam, the track flashed forth. After 
 the shade was full, he inverted it ; thereupon the gas passed 
 upward like a black smoke among the illuminated particles . 1 
 
 The method of concomitant variations is not only capable 
 of illustration by laboratory methods and devices ; it finds 
 abundant illustration as well in the realm of nature, where 
 observation alone becomes the instrument of investigation 
 and where experiment is impossible or impracticable. Lyell, 
 in his Principles of Geology, gives a very interesting account 
 of the alternate elevation and subsidence of the temple of 
 Jupiter Serapis, at Pozzuoli, on the Bay of Naples.* It is 
 situated in proximity to several volcanoes, Vesuvius, however, 
 being at some distance. It has been observed that there is 
 a certain connection between each era of upheaval, and a 
 local development of volcanic heat ; and on the other hand, 
 between each era of depression, and the local quiescent con- 
 dition of volcanic phenomena. Before the Christian era, 
 when Ischia was in a state of eruption, and Avernus and 
 other points in the Phlegraean fields were celebrated for their 
 volcanic character, it was observed that at that time the 
 ground on which the temple stood was several feet above 
 water. Vesuvius was then regarded as a spent volcano. 
 After the Christian era, Vesuvius became active and then 
 
 1 Tyndall, Fragments of Science, pp. 284, 285. 
 
 2 Chapter XXX. 
 
CONCOMITANT VARIATIONS 
 
 265 
 
 scarcely a single eruption occurred in Ischia or around the 
 Bay of Bairn. It was observed that at that time the temple 
 was sinking. Vesuvius then became quiet for five centuries 
 preceding the eruption of 1631, and during that period the 
 Solfatara was in eruption in 1198, Ischia in 1302, and Monte 
 Nuovo was formed in 1538. Then the foundations of the 
 temple were observed to be rising again. Vesuvius became 
 active after that, and has continued so ever since, and during 
 this time the temple has been subsiding. The inference is 
 that as the subterranean heat increases, and lava forms 
 without obtaining an easy vent like that afforded by Vesu- 
 vius, the surface is elevated, but when the rocks below are 
 cooling and contracting, the pent-up fire being withdrawn 
 in the eruption of the great Vesuvius, then there is a cor- 
 responding subsidence. 
 
 The observation of concomitant variations is furthermore 
 illustrated in Darwin’s researches concerning the formation 
 of coral reefs, as regards the question which some natural- 
 ists have raised as to which part of the coral reef is most 
 favorable to the growth of coral. 1 He adduces the follow- 
 ing facts, most of which are the direct result of his observa- 
 tions : “ The great mounds of living Porites and of Millepora 
 round Keeling atoll occur exclusively on the extreme verge 
 of the reef, which is washed by a constant succession of 
 breakers. At the Marshall Islands the larger kinds of 
 coral which form rocks measuring several fathoms in thick- 
 ness prefer the most violent surf. The outer margin of the 
 Maldiva atolls consists of living corals, and here the surf is 
 so tremendous that even large ships have been thrown, by 
 a single heave of the sea, high and dry on the reef, all on 
 board thus escaping with their lives. In the Bed Sea the 
 strongest corals live on the outer reefs and appear to love 
 the surf. From these facts it is certain that the strongest 
 and most massive corals flourish where most exposed. The 
 less perfect state of the reef of most atolls on the leeward 
 1 Darwin, Coral Reefs, pp. 87 f. 
 
266 
 
 INDUCTIVE LOGIC 
 
 and less exposed side, compared with its state to the wind- 
 ward, and the analogous case of the greater number of 
 breaches on the rear sides of those atolls in the Maldiva 
 Archipelago, which afford some protection to each other, 
 are obviously explained by this circumstance.” There 
 seems to be here a combination of the method of agreement 
 with that of concomitant variations. And such a combina- 
 tion may be employed to advantage in cases where the phe- 
 nomena under investigation show forces under varying 
 degrees of intensity ; the causal relation is more apparent, 
 and the possibility of fortuitous coincidence is largely elimi- 
 nated if a number of instances can be collected in which the 
 forces manifest themselves in varying degrees. Accumula- 
 tion of instances, showing concomitant variations in the 
 forces observed, corresponds to the actual variations which 
 in an experiment are effected by the investigator himself. 
 In such observed instances, however, we cannot always have 
 before us the variations expressed continuously. There 
 are evident gaps that must be interpolated mentally. In 
 experiment however of whatever nature, the degrees of 
 intensity can be exhibited continuously, one degree merg- 
 ing into another through inappreciable increments. There 
 is thus a gradation which has no gaps to be filled, and the 
 psychological impression is thereby heightened. 
 
 By the method of concomitant variations it is possible also 
 to represent to the mind the magnitude of an unknown force, 
 or unobservable force, by a comparison with the intensity 
 of a known force which lies within the sphere of observa- 
 tion. For instance, Mr. Darwin gives an interesting account 
 in his narrative of the finding near the shores of the Plata 
 a group of vitrified siliceous tubes which had been formed 
 by lightning entering loose sand. The internal surface of 
 such tubes is completely vitrified, glossy, and smooth, and 
 the tubes themselves are generally compressed, and have 
 deep longitudinal furrows so as closely to resemble a 
 shrivelled vegetable stalk, or the bark of an elm or cork 
 
CONCOMITANT VARIATIONS 
 
 267 
 
 tree. Their circumference is about two inches, but in some 
 fragments which are cylindrical and without any furrows, 
 it is as much as four inches. Judging from the uncom- 
 pressed fragments, the measure or bore of the lightning 
 proved to be about one inch and a quarter. In contrast 
 with the force of lightning as thus revealed in its effects, 
 Mr. Darwin cites some experiments performed in Paris by 
 an artificial force of great magnitude indeed and yet with 
 results that seem insignificantly small in comparison. He 
 says : “ At Paris, M. Hatchette and M. Beudant succeeded 
 in making tubes in most respects similar to these fulgurites 
 by passing very strong shocks of galvanism through finely 
 powdered glass : they failed, however, both with powdered 
 felspar and quartz. One tube, formed with pounded glass, 
 was very near an inch long, namely, .982, and had an inter- 
 nal diameter of .019 of an inch. When we hear that the 
 strongest battery in Paris was used, and that its power on 
 a substance of such easy fusibility as glass was to form 
 tubes so diminutive, we must feel greatly astonished at the 
 force of a shock of lightning, which, striking the sand in 
 several places, has formed cylinders in one instance at least 
 thirty feet long, and having an internal bore, where not 
 compressed, of full an inch and a half ; and this in a mate- 
 rial so extraordinarily refractory as quartz ! ” 1 
 
 The method of concomitant variations may be used in 
 regard to phenomena whose nature is such as seemingly to 
 indicate a constant law of variation, and yet inferences 
 based thereupon lead to false results. It is therefore well 
 to note some of these instances by way of general precaution 
 in applying this method. 
 
 1. It does not necessarily follow that having observed 
 two forces varying in a constant ratio through several con- 
 comitant modifications, the same ratio will be preserved 
 indefinitely through all subsequent changes. Water con- 
 tracts as it is cooling. Suppose we begin to note this con- 
 1 Darwin, Voyage of a Naturalist, Vol. I, pp. 76 f. 
 
268 
 
 INDUCTIVE LOGIC 
 
 tinued contracting of water from 100° F. to 90° ; we 
 naturally expect to find it continuing through 90° to 80°. 
 And as we observe, we find our expectations confirmed. 
 And so on through to 40°, we find that water continues to 
 contract. It is, therefore, most natural for us to expect to 
 find water contracting at 39°. But just at this point in the 
 series, there is a break in the continuity of variation; at 
 39° water begins to expand and so continues until it passes 
 into the solid form at the freezing-point. The same also is 
 illustrated in Weber’s law, already mentioned, which ex- 
 presses the quantitative relation between the stimulus and 
 the corresponding sensation. The law is that the force of 
 the stimulus must increase geometrically, in order that the 
 intensity of the sensation should increase arithmetically. 
 This law, however, breaks down towards the upper or 
 lower limits, with a stimulus of slight degree of intensity 
 and with one of extreme intensity. We find also an in- 
 crease of temperature as we proceed towards the centre of the 
 earth of about one degree to every fifty-three feet of descent. 
 This by no means warrants us in inferring that this ratio 
 continues constant to the very centre itself. In certain 
 phenomena, moreover, there are natural limits, as in sound, 
 for example, where the pitch rises as the number of vibra- 
 tions increases. At a certain point, varying according to 
 different individuals, increase of vibrations gives no result- 
 ing sound whatsoever ; and so there is a lower limit, — vibra- 
 tions may decrease to a point beyond which no sound is 
 heard. 
 
 An illustration of this fallacy, though not strictly of the 
 method of concomitant variations, is given by Jevons. He 
 takes the following series of prime numbers : 41, 43, 47, 53, 
 61, 71, 83, 97, 113, 131, etc. It will be seen that they all 
 agree in being values of the general expression x 2 -f- x -f 41, 
 where we put for x the successive values of 0, 1, 2, 3, 4, etc. 
 For instance, let x = 0 in x 2 + x + 41, we get 41 ; let x = 1 
 in the same, we get 43 ; when x = 2, we get 47 ; and so on. 
 
CONCOMITANT VARIATIONS 
 
 269 
 
 It seems as though we could keep this up indefinitely, pro- 
 ducing an increasing series, always of prime numbers. It 
 is found, however, that if we take x = 40, in the formula 
 x 2 -f x + 41, we shall have 40 x 40 + 40 4- 41, which equals 
 1681, and this number is the square of 41 and therefore not 
 a prime number. At this point the law breaks down. 1 
 
 In the sphere of political economy also we might be led 
 into an easy yet false inference. Suppose a certain farm 
 yield 500 bushels of com with a given amount of expendi- 
 ture and labor. We might think that if we double the 
 expenditure and labor, we will also be able to double the 
 results, and obtain a yield of 1000 bushels as over against 
 the 500 of the previous year. Here, however, what is 
 known as the law of decreasing returns obtains ; to double 
 the product it may be necessary to triple or quadruple 
 the labor and expense. “ Thus in the production of any 
 plot of land there is a point of equilibrium, which marks 
 an impassable limit, not of course a limit which could 
 not be passed if it were wished, but one that no one 
 wishes to pass, because there is nothing to be gained by so 
 doing.” 2 
 
 To know that such false inferences are at least possible 
 in the application of this method of concomitant variations 
 to the unknown regions beyond our experience, may serve 
 at least to keep us on guard under similar circumstances. 
 
 2. There are certain phenomena moreover in which an 
 increased intensity of the force in question may give rise to 
 incidental effects which tend to neutralize the chief effect to 
 be attained. For instance, an overdose of arsenic causes 
 violent contractions of the stomach so that its contents are 
 immediately ejected, and thus the system is relieved of the 
 noxious substance. 
 
 3. Two elements in a given phenomenon may vary to- 
 gether constantly and yet they may not be related at all as 
 
 1 Jevons, Principles of Science, p. 230. 
 
 3 Gide, Political Economy, p. 325. 
 
270 
 
 INDUCTIVE LOGIC 
 
 cause and effect, but appear as coincidental effects of one 
 and the same cause. It has been observed that the occur- 
 rence of the aurora borealis has been accompanied by pro- 
 nounced magnetic disturbances. It, however, cannot be 
 inferred that the former has been the cause of the latter ; 
 they are probably the varied effects of some widely operat- 
 ing magnetic force. 
 
 The precaution above mentioned has already been referred 
 to as provided for in the canon of this method which states 
 that the observed concomitant variation may indicate not 
 always a direct causal element between the two varying 
 elements, but that they are at least connected with the phe- 
 nomenon under investigation through some fact of causation. 
 
CHAPTER X 
 
 THE METHOD OF EESIDUES 
 
 The method of residues consists in the analysis of a given 
 phenomenon based upon previous inductions, through which 
 it has been determined that certain elements in the antece- 
 dent have caused certain elements in the consequent ; the 
 inference is then drawn, that the remaining elements of the 
 antecedent are necessarily the cause of the remainder of 
 the consequent. It is a method of elimination of the known 
 relations so as to simplify the complex character of the phe- 
 nomenon and disclose the relations that are unknown in the 
 light of a causal connection which we are constrained to 
 believe must obtain. 
 
 The Canon of the Method of Residues. — Subduct from 
 any phenomenon such part as is known by previous induc- 
 tions to be the effect of certain antecedents, and the residue 
 of the phenomenon is the effect of the remaining antecedents. 
 
 The symbolical representation is as follows : — 
 
 Given S + C s + e. 
 
 If it is known that there exists already the causal relation 
 S s, 
 
 we may then infer that C is the cause of e. In this, C may 
 be simple or complex ; if it is simple, the causal relation 
 established is expressed in its simplest terms and is there- 
 fore a determinate result. If however the residue C is 
 complex, it must be reduced by experimental analysis to its 
 simplest elements, and their relation to the elements into 
 which e can be analyzed further determined. 
 
 271 
 
272 
 
 INDUCTIVE LOGIC 
 
 The most striking illustration of this method, and one 
 of the most brilliant achievements of science as well, is the 
 discovery of the planet Neptune by Adams and Le Verrier, 
 working on the problem independently and reaching the 
 same result. These astronomers had observed certain per- 
 turbations in the planet Uranus. It did not keep in its 
 proper orbit as determined by their mathematical calcula- 
 tions based upon the presence of the known stellar bodies. 
 It behaved as though beyond its orbit was an outer planet, 
 whose presence alone could account for the observed per- 
 turbations. Adams and Le Verrier then proceeded to calcu- 
 late the exact position of such a disturbing body as determined 
 by the nature and magnitude of the perturbations of Uranus. 
 The telescope was then pointed to the exact point in the 
 heavens, as thus indicated, and the planet Neptune was 
 revealed to the eye according to the determination of far- 
 reaching prophecy, which confidently asserted that it must 
 be there. 
 
 The method of residues is really a deductive method 
 based upon the law of sufficient reason ; so many elements 
 on the one hand producing so many elements on the other ; 
 if, then, a part of the former can be checked off as cause of 
 a part of the latter, then the remainder on the one hand 
 must be the cause of the remainder on the other. This is 
 pure deduction. For we ask, Why are we constrained to 
 account for the remainder on one side by the remainder 
 on the other ? The only possible answer is that it must be 
 accounted for within the system to which it is referred ; 
 and but one part therein is left which can possibly account 
 for it, because all the others are specifically determined in 
 the known effects which they have produced. This method, 
 however, has a proper place among the inductive methods, 
 inasmuch as it is based on previous inductions, and leads 
 to investigations that can be prosecuted only by the various 
 inductive processes of experiment. 
 
 When the residue of the antecedent is a simple element, 
 
THE METHOD OF RESIDUES 
 
 273 
 
 and no other possible causal clement can lie concealed from 
 our observation, then the inference is simple and conclusive. 
 A difficulty, however, may present itself, owing to the fact 
 that the residual element is apt to be complex and leave the 
 phenomenon still indeterminate, or there may be a lurking 
 element unnoticed by us which is the real cause in question. 
 The function of this method is, therefore, largely suggestive. 
 It says the effect is not wholly accounted for by the known 
 causal elements ; there is a residue unaccounted for, and its 
 cause is to be sought in the residue of the antecedent, and 
 if it is thought that the whole of the antecedent is compre- 
 hended, the question is started, May there not be unobserved 
 circumstances of the antecedent that further experiment 
 will be calculated to reveal ? In many cases, therefore, this 
 method must be supplemented by some other experimental 
 method in order to secure more precise determination, gen- 
 erally the method of difference. It often happens in inves- 
 tigations in chemistry, astronomy, and physics, that the 
 actual phenomena vary in greater or less degree from their 
 expected behavior according to established theory. This 
 must lead either to a reconstruction of theory, or to a search 
 for some unobserved force sufficient to account for the dis- 
 crepancy. Herschel was the first to point out the signifi- 
 cance of such discrepancies in scientific research, and he 
 called them residual phenomena. 
 
 An illustration of such a situation and the solution of the 
 problem thus presented is that of Sir Humphry Davy’s ex- 
 periments upon the decomposition of water by galvanism. 
 “ He found that besides the two components of water, oxy- 
 gen and hydrogen, an acid and alkali were developed at the 
 two opposite poles of the machine. As the theory of the 
 analysis of water did not give reason to expect these products, 
 they were a residual phenomenon, the cause of which was still 
 to be found. The insight of Davy conjectured that there 
 might be some hidden cause of this portion of the effect ; the 
 glass containing the water might suffer partial decomposition, 
 
274 
 
 INDUCTIVE LOGIC 
 
 or some foreign matter might be mingled with the water, and 
 the acid and alkali be disengaged from it, so that the water 
 would have no share in their production. Assuming this, 
 he proceeded to try whether the total removal of the cause 
 would destroy the effect produced. By the substitution of 
 gold vessels for the glass, without any change in the effect, 
 he at once determined that the glass was not the cause. 
 Employing distilled water, he found a marked diminution 
 of the quantity of acid and alkali evolved ; yet there was 
 enough to show that the cause, whatever it was, was still in 
 operation. The impurity of the water, then, was not the 
 sole, but a concurrent, cause. He now conceived that the 
 perspiration from the hands touching the instruments might 
 affect the case, as it would contain common salt, and an 
 acid and alkali would result from its decomposition under 
 the agency of electricity. By carefully avoiding such con- 
 tact, he reduced the quantity of the products still further, 
 until no more than slight traces of them were perceptible. 
 What remained of the effect might be traceable to impuri- 
 ties of the atmosphere decomposed by contact with the 
 electrical apparatus. An experiment determined this ; the 
 machine was placed under an exhausted receiver, and when 
 thus secured from atmospheric influence, it no longer evolved 
 the acid and alkali.” 1 
 
 By means of the suggestions incident upon this method, 
 Bunsen, in 1860, discovered two new alkaline metals, cae- 
 sium and rubidium. He was examining alkalies produced 
 by the evaporation of mineral water from Durkheim. The 
 flame of these salts was examined by the spectroscope. 
 Bunsen discovered several bright lines which he had never 
 noticed before, and which he knew could not be produced 
 by potash or soda, whose corresponding lines were in close 
 proximity. He then subjected the mixture to a searching 
 analysis and succeeded in obtaining two new alkaline sub- 
 stances. When he had separated them, he then tested them 
 iGore, The Art of Scientific Discovery, pp. 432, 433. 
 
THE METHOD OF RESIDUES 
 
 275 
 
 by the method of difference, by which he found that 
 they were capable of producing the lines at first no- 
 ticed ; but when withdrawn, the lines instantaneously dis- 
 appeared. 
 
 Thomson and Tait, in their Elements of Natural Philoso- 
 phy, have the following reference and illustration of this 
 method. “ When, in an experiment, all known causes being 
 allowed for, there remain unexplained effects (excessively 
 slight it may be), these must be carefully investigated, and 
 every conceivable variation of arrangement of apparatus, 
 etc., tried ; until, if possible, we manage so to exaggerate 
 the residual phenomenon as to be able to detect its cause. 
 It is here perhaps that in the present state of science we 
 may most reasonably look for extensions of our knowledge ; 
 at all events, we are warranted by the recent history of 
 natural philosophy in so doing. Thus, to take only a very 
 few instances, and to say nothing of the discovery of elec- 
 tricity and magnetism by the ancients, the peculiar smell 
 observed in a room in which an electrical machine is kept in 
 action was long ago observed, but called the ‘ smell of elec- 
 tricity,’ and thus left unexplained. The sagacity of Schon- 
 bein led to the discovery that this is due to the formation 
 of ozone, a most extraordinary body, of enormous chemical 
 energies ; whose nature is still uncertain, though the atten- 
 tion of chemists has for years been directed to it.” 1 
 
 Another illustration of this method is seen in the com- 
 parison of the observed and calculated positions of Encke’s 
 comet. It was found that the comet returned a little sooner 
 than it should have done, the period regularly decreasing 
 from 1212.79 days, between 1786 and 1789, to 1210.44 
 between 1855 and 1858. The inference has been that there 
 is a resisting medium, as the ether, filling the space through 
 which the comet passes. What the resisting medium is, 
 and its nature, is of course a matter of conjecture as far as 
 revealed by this method alone. The method merely indi- 
 1 Thomson and Tait, Elements of Natural Philosophy , Vol. I, pp. 113 f. 
 
276 
 
 INDUCTIVE LOGIC 
 
 cates some resisting medium to account for the observed 
 discrepancy. 1 
 
 Herschel has observed that all great astronomical discov- 
 eries have been disclosed in the form of residual differences. 
 The practice was introduced by Halley, when astronomer 
 royal, of comparing systematically the positions of the 
 heavenly bodies as actually observed with what might have 
 been expected theoretically. His reductions of the lunar 
 observations gave a series of residual errors, extending from 
 1722 to 1769. These were carefully tabulated, and formed 
 the basis for certain modifications of the lunar theory. 2 
 
 A discrepancy was observed by Newton between the 
 theoretical and actual velocity of sound; the former being 
 968 feet per second, and the latter 1142. Newton’s experi- 
 ments and calculation were both inaccurate ; nevertheless, 
 a real discrepancy has been proved to exist, the theoretical 
 being 916 and the real velocity 1090 feet per second. In 
 1816 La Place showed this difference to be due to the heat 
 evolved by the sudden compression of the air during the 
 propagation of the sound wave, the heat having the effect 
 of increasing the elasticity of the air, and therefore appre- 
 ciably accelerating the sound impulse. 
 
 It sometimes happens that in repeating an experiment, 
 we are confronted with evidently different results. Then, 
 we may be sure, the experiment has been carelessly or inac- 
 curately performed; or else there are some disturbing causes 
 not observed by us. On the other hand, however, if there 
 is no likelihood of coincidence on repeated trials, yet, never- 
 theless, a marked agreement is noticed in the results of vari- 
 ous trials, the mind should be at once alert to discover the 
 hidden cause of such agreement, and possibly may be led 
 to new truths of great importance. The following illustra- 
 tion is given by Thomson and Tait : “With a very good 
 achromatic telescope a star appears to have a sensible disc. 
 But, as it is observed that the discs of all stars appear to 
 1 Jevons, Principles of Science, p. 570. 2 Ibid., p. 572. 
 
THE METHOD OF RESIDUES 
 
 277 
 
 be of equal angular diameter, we of course suspect some 
 common error. Limiting the aperture of the object-glass 
 increases the appearance in question, which, on full investi- 
 gation, is found to have nothing to do with discs at all. It 
 is, in fact, a phenomenon due to diffraction of light.” 1 
 
 It was said of Darwin that in his researches the residual 
 phenomena were always the special objects of his attention. 
 His son, Francis Darwin, says of him: “There was one 
 quality of mind which seemed to be of special and extreme 
 advantage in leading him to make discoveries. It was the 
 power of never letting exceptions pass unnoticed. Every- 
 body notices a fact as an exception when it is striking or 
 frequent, but he had a special instinct for arresting an ex- 
 ception. A point apparently slight and unconnected with 
 his present work is passed over by many a man almost 
 unconsciously, with some half-considered explanation, which 
 is in fact no explanation. It was just these things that he 
 seized upon to make a start from. In a certain sense there 
 is nothing special in this procedure, many discoveries being 
 made by means of it. I only mention it, because, as I 
 watched him at his work, the value of this power to an 
 experimenter was so strongly impressed upon me .” 2 This 
 is striking testimony as to the practical worth of this 
 method as an instrument of research. 
 
 This method has also been applied to the more practical 
 usage of examining the refuse of manufactured and other 
 products in order to discover some concealed utility. The 
 analysis of coal-tar refuse has led to the discovery of many 
 valuable substances that have proved of use’ in the arts, and 
 in medicine as well. Glauber, the eminent chemist, and a 
 discoverer of several chemical compounds, said he made it 
 a rule to examine what every other chemist threw away. 
 
 1 Thomson and Tait, Elements of Natural Philosophy , Vol. I, p. 114. 
 
 2 F. Darwin, Life and Letters of Charles Darwin, Vol. I, p. 125. 
 
CHAPTER XI 
 
 PREDICTION AND VERIFICATION 
 
 When our inductive methods have finally led us to for- 
 mulate some universal law or principle, we are then able to 
 use the same as a major premise upon which to ground fur- 
 ther deductions, and so to apply the results of inductive 
 research to new fields not as yet investigated. Mr. Mill 
 calls this procedure the deductive method of reasoning. 
 Inasmuch however as it is founded upon some previous 
 induction, it would seem more fitting to designate it as the 
 inducto-deductive method. It is essentially a combined 
 process of induction and deduction. 1 This so-called inducto- 
 deductive method consists of three stages as follows : — 
 
 1. Obtaining by the inductive methods already described, 
 the evidence of some existing causal connection, tentatively 
 expressed in the form of a universal law. 
 
 2. Regarding this universal law as the basis for subse- 
 quent deductions, by which we gain a knowledge of the 
 nature of unknown phenomena, as necessitated by the con- 
 ditions of this law. 
 
 3. Verifying the results thus obtained by their corre- 
 spondence with the phenomena as actually observed. Where 
 this correspondence is wanting, then either the law has 
 not been correctly expressed, or there must have been some 
 error in our deduction based upon it. When we are assured 
 that the latter is not the case, then a discrepancy between 
 the theoretically deduced result and the actual facts as 
 observed, always discredits our original induction. This 
 
 1 See pp. 171 f. 
 
 278 
 
PREDICTION AND VERIFICATION 
 
 279 
 
 method of verification serves as a check upon hasty general- 
 ization, on the one hand ; and on the other, it serves to ex- 
 tend our knowledge into unknown regions, and is valuable 
 as a means of scientific prediction. In the development of 
 scientific knowledge, it has been a potent factor in enlarg- 
 ing the bounds of knowledge beyond the sphere of imme- 
 diate observation. 
 
 This combined process of reasoning is the one commonly 
 employed by us all. Induction and deduction are not sep- 
 arate processes, but, as before remarked, they are comple- 
 mentary factors in the one actual process of reasoning. We 
 are continually using our inductions as a deductive basis, 
 inferring how things should be before they are really seen ; 
 and, when seen, at once instinctively comparing prior in- 
 ference with preseut fact, we are either confirmed in our 
 reasoning process, or compelled to discard our previous in- 
 ference as false or inadequate as the case may be. Our 
 world, the world of knowledge, is built up of the seen, and 
 the unseen as well, because necessitated by inferences grow- 
 ing out of the seen which we are constrained to make; the 
 unseen which we thus are continually building into the 
 seen and regarding it as though the actually known, we are 
 however from time to time compelled to alter, and here and 
 there tear down w'hat we have too rashly builded, as the 
 structure is put to the test of verifying fact. 
 
 This method of prediction and verification was used to 
 decide between inferences drawn by Newton and Huyghens 
 respective^, regarding the nature of light. Newton’s ob- 
 servations led him to infer that light consisted of particles 
 of matter shot out from the sun. Huyghens insisted that 
 light consisted in the propagation of some kind of disturb- 
 ance in the manner of a wave-motion. Newton’s theory 
 being taken as established, it would necessitate that light 
 on entering a denser body of water, being refracted more 
 nearly in a direction perpendicular to the surface, should, 
 accordingly, move faster in the denser body than in the 
 
280 
 
 INDUCTIVE LOGIC 
 
 rarer one outside. On the other hand, according to Huy- 
 ghens’s theory, the opposite effect should take place, — light 
 being refracted towards the vertical at the horizontal sur- 
 face of a dense body such as water, its velocity in the dense 
 body should be less than its velocity in the rare body. The 
 experiments separately made by Fizeau and Foucault, both 
 gave the result that in water light moves slower than in 
 air, and therefore the theory of Huyghens, which was in 
 accord with such a fact, was verified, and the theory of 
 Newton, which was radically out of harmony with such a 
 fact, was discredited. 1 
 
 We cannot theorize concerning nature to any considerable 
 extent without resorting to nature again to correct aberra- 
 tions of reason, and the false fancies of the imagination. 
 Theory, if correctly formulated, will always lead to a 
 representation of facts as they are ; just as facts as they 
 are, if rightly interpreted, will always lead to correct 
 theory. 
 
 The following are illustrations of the value of this method 
 in predicting results before unknown. 
 
 “ Halley had the glory of having first detected a periodic 
 comet in the case of that which has since borne his name. 
 In 1705, Halley explained how the parabolic orbit of a 
 planet may be determined from three observations ; and 
 joining example to precept, himself calculated the positions 
 and orbits of twenty-four comets. He found, as the reward 
 of his industry, that the comets of 1607 and 1531 had the 
 same orbit as that of 1682. And here the intervals are 
 nearly the same, namely, about seventy-five years. Are 
 these three comets then identical ? In looking back into 
 the history of such appearances, he found comets recorded 
 in 1456, in 1380, and 1305; the intervals are still the same, 
 — seventy-five or seventy-six years. It was impossible now 
 to doubt that they were the periods of a revolving body, its 
 orbit a long ellipse, not a parabola. If this were so, the 
 1 Tait, Recent Advances in Physical Science, pp. 65, 66. 
 
PREDICTION AND VERIFICATION 
 
 281 
 
 comet must reappear in 1758 or 1759. Halley began his 
 laborious calculations and predicted that the comet would 
 reach its perihelion April 13, 1759, but claimed the license 
 of a month for the inevitable inaccuracies of a calculation in 
 which, in addition to all other sources of error, was made 
 in haste, that it might appear as a prediction. The comet 
 justified his calculations and his caution together ; for it 
 arrived at its perihelion on March 13, 1759.” 1 
 
 Another illustration of a like nature is the prediction of 
 Faraday, based upon Wheatstone’s experimental proof that 
 the conduction of electricity required time; namely, “that 
 if the conducting wires were connected with the coatings of 
 a large Leyden jar, the rapidity of conduction would be 
 necessarily lessened. This prediction was made in 1838 
 and was not verified until, sixteen years later, a submarine 
 cable was laid beneath the English Channel. A considerable 
 retardation of the electric spark was then detected by 
 Siemens and Latimer Clark. Faraday at once pointed out 
 that the wire surrounded by water resembles a Leyden jar 
 on a large scale: so that each message sent through the 
 cable verified his remark of 1838.” 2 
 
 In Pasteur’s experiments with silkworms already referred 
 to, he made a prediction in 1866, when, having inspected 
 fourteen parcels of eggs intended for incubation, and having 
 examined the moths which produced these eggs, he wrote 
 out the prediction of what would occur in 1867, and placed 
 the prophecy as a sealed letter in the hands of the mayor 
 of St. Hippolyte. In 1867, the cultivators communicated to 
 the mayor their results. The letter of Pasteur was then 
 opened and read, and it was found that in twelve out of 
 fourteen cases there was absolute conformity between his 
 prediction and the observed facts. Many of the groups had 
 perished totally ; the others had perished almost totally ; 
 and such was Pasteur’s prediction. In two out of the 
 
 1 Whewell, History of Inductive Science, 3d ed., Vol. II, p. 182. 
 
 2 Jevons, Principles of Science, p. 543. 
 
282 
 
 INDUCTIVE LOGIC 
 
 fourteen cases, instead of the prophesied destruction, half 
 an average crop was obtained. 1 
 
 Another interesting illustration concerns Darwin’s specula- 
 tions regarding the formation of coral reefs and atolls. 
 Before Darwin wrote on the subject, it was generally be- 
 lieved that the coral atolls were formed by the coral polypes 
 growing upon submerged volcanic craters. Darwin insisted 
 that as the polypes cannot live below a depth of 100 feet, 
 and are killed by exposure to sunshine and air, and could not 
 therefore have grown upward from the vast depths to which 
 the coral masses extend, each atoll must have begun as a 
 fringing-reef about an island almost touching the shore, and 
 with only a narrow and shallow channel of water between ; 
 and then became a barrier reef, that is, one with a wider 
 and deeper channel of water separating from the shore, 
 owing to the slow but progressive subsidence of the island 
 round which the polypes first began to build. Then with 
 the further and complete subsidence of the island beneath 
 the water, there remained a ring of coral with a central 
 lagoon forming the so-called atoll. Darwin says in his 
 Autobiography that the main features of his theory were 
 conceived while on the voyage, and that even previous to 
 seeing a true coral reef. 2 He says : “ No other work of 
 mine was begun in so deductive a spirit as this, for the 
 whole theory was thought out on the west coast of South 
 America, before I had seen a true coral reef. I had only to 
 verify and extend my views by a careful examination of 
 living reefs. But it should be observed that I had during 
 the two previous years been incessantly attending to the 
 effects on the shores of South America of the intermittent 
 elevation of the land, together with denudation and deposi- 
 tion of sediment. This necessarily led me to reflect much 
 on the effects of subsidence, and it was easy to replace in 
 imagination the continued deposition of sediment by the 
 
 1 Tyndall, Fragments of Science, pp. 291, 292. 
 
 2 Life and Letters of Charles Darwin, 1887, Vol. I, p. 58. 
 
PREDICTION AND VERIFICATION 
 
 283 
 
 upward growth of corals. To do this was to form my 
 theory of the formation of barrier reefs and atolls.” 
 
 It will thus be seen that Darwin’s deduction was based 
 upon previous inductions in other spheres, the result of his 
 own observation ; he also tells us in the same connection, 
 that he had, in the preparation of his work on Coral Reefs, 
 spent twenty months of hard labor, reading every work on 
 the island of the Pacific and consulting many charts. He 
 thus made the widely extended observations of other men 
 tributary to his inferences concerning coral-reef formations. 
 Dr. Williams says of Darwin’s insight in this particular : 
 “He saw more clearly than his precursors had done the 
 validity of the dictum of Johannes Muller in this, and 
 indeed all his works, that the most important truths in 
 natural science are to be discovered, neither by the mere 
 analysis of philosophical ideas, nor by simple experience, 
 but by reflective experience, which distinguishes the essential 
 from the accidental in the phenomena observed, and thus 
 finds principles from which many experiences can be 
 derived.” 1 This is a very satisfactory and striking account 
 of what may be styled the combined inducto-deductive 
 temper of mind, and especially as embodied in so eminent 
 a student of nature as Darwin. 
 
 Bacon insists that anticipations of nature are sources 
 of innumerable errors, and that the truly scientific method 
 consists in an interpretation of nature as it is revealed to 
 the perception through direct observation and experiment. 
 It is, however, largely through these “ anticipations ” that 
 progress in science is attained. There may be anticipations 
 which are considered final, and all attempts at verification 
 regarded as unnecessary and even as impertinent. Results 
 deductively attained are then asserted with dogmatic insist- 
 ence, as though possessing the convincing power of facts 
 themselves; and all appeal to controverting or exceptional 
 cases are set aside, without even so much as a respectful 
 1 Darwin, Coral Reefs. Prefatory note by Dr. J. W. Williams, p. ix. 
 
284 
 
 INDUCTIVE LOGIC 
 
 hearing. Such anticipations of nature rightfully fall under 
 the scornful reprehension of a Bacon. But there are other 
 anticipations which serve as a spur to a more penetrating 
 observation, and more painstaking experiment, in order to 
 square theory to facts. Such anticipations are the glory of 
 science ! 
 
 Suppose such anticipations are disproved by subsequent 
 experiment or observation ; they have served a high pur- 
 pose in suggesting investigation along lines which otherwise 
 would have remained unthouglit of. Anticipations alone 
 are barren; anticipations leading to verification are produc- 
 tive of valuable results. To this the history of scientific 
 thought bears abundant testimony. Professor Clifford has 
 made the power of prediction one of the essential character- 
 istics of scientific thought. He says, in his essay on the 
 Aims and Instruments of Scientific Thought, that “ the differ- 
 ence between scientific and merely technical thought is just 
 this : Both of them make use of experience to direct human 
 action ; but while technical thought or skill enables a man to 
 deal with the same circumstances that he has met with 
 before, scientific thought enables him to deal with different 
 circumstances that he has never met with before .” 1 He 
 cites two illustrations, which are admirable examples of 
 scientific prediction. The first relates to the suggestion of 
 Fleeming Jenkin, regarding structural bracing. It had been 
 known before that in an arch every part is compressed or 
 pushed by other parts ; and every part of a chain is in a 
 state of tension, that is, pulled by the other parts. In many 
 cases these forms are united in the common girder, which 
 consists of two main pieces, of which the upper acts as an 
 arch, and is compressed, while the lower one acts as a chain 
 and is pulled. “Now,” says Professor Clifford, “suppose 
 that any good, practical engineer makes a bridge or a roof 
 upon some approved pattern which has been made before. 
 He designs the size and. shape of it to suit the opening 
 1 Clifford, Lectures and Essays, Vol. I, p. 128. 
 
PREDICTION AND VERIFICATION 
 
 285 
 
 which has to be spanned ; selects his material according to 
 the locality ; assigns the strength which must be given to 
 the several parts of the structure, according to the load 
 which it will have to bear. There is a great deal of thought 
 in the making of this design, whose success is predicted by 
 the application of previous experience ; it requires techni- 
 cal skill of a very high order, but it is not scientific thought. 
 On the other hand, Mr. Fleeming Jenkin designs a roof con- 
 sisting of two arches braced together, instead of an arch 
 and a chain braced together; and, although this form is 
 quite different from any known structure, yet before it is 
 built he assigns with accuracy the amount of material that 
 must be put into every part of the structure in order to bear 
 the required load, and this prediction may be trusted with 
 perfect security. What is the natural comment on this ? 
 Why, that Mr. Fleeming Jenkin is a scientific engineer .” 1 
 The second illustration which Professor Clifford gives is 
 as follows: “You know that if you make a dot on a piece 
 of paper, and then hold a piece of Iceland spar over it, you 
 will see not one dot, but two. A mineralogist, by measur- 
 ing the angles of a crystal, can tell you whether or no it 
 possesses this property without looking through it. He re- 
 quires no scientific thought to do that. But Sir William 
 Rowan Hamilton, the late astronomer royal of Ireland, 
 knowing these facts, and also the explanation of them, 
 which Fresnel had given, thought about the subject, and 
 he predicted that by looking through certain crystals in a 
 particular direction we should see not two dots, but a con- 
 tinuous circle of dots. Mr. Lloyd made the experiment and 
 saw the circle, a result which had never been even suspected. 
 This has always been considered one of the most signal 
 instances of scientific thought in the domain of physics. It 
 is most distinctly an application of experience gained under 
 certain circumstances to entirely different circumstances .” 2 
 
 1 Clifford, Lectures and Essays, Vol. I, pp. 127, 128. 
 
 * Ibid., Vol. I, pp, 128, 129. 
 
286 
 
 INDUCTIVE LOGIC 
 
 There is also an indirect method of prediction, varying 
 somewhat from the one already described and yet similar to 
 it. It is called prediction by inversion of cause and effect. 
 There are many cases in which cause and effect are related 
 in a reciprocal manner, so that not only will the cause pro- 
 duce the effect, but the effect, operating as a cause, will 
 bring about the original cause as an effect, it may be in a 
 modified form but clearly recognizable as such. Professor 
 Tyndall said of Faraday that “ the strong tendency of his 
 mind to look upon the reciprocal actions of natural forces 
 gave birth to his greatest discoveries.” 1 For instance, Oer- 
 sted had proved that an electric current will produce mag- 
 netism, and Faraday, taking this as a suggestion, inferred 
 that magnetism might produce an electric current; in the 
 year 1831 he devised a suitable experiment of introducing a 
 bar-magnet into a coil of insulated copper wire, and then 
 withdrawing the magnet whilst the two ends of the wire 
 were connected with a distant galvanometer, which indicated 
 the presence of the electric current. Thus, his inference 
 received substantial verification. 2 
 
 It has, moreover, been found that when a given cause pro- 
 duces a certain effect, then if the effect be produced in some 
 other manner, the process will tend to produce the original 
 cause, but inverted as regards its direction or nature. For 
 instance, it is known that heat will expand gases ; now, if a 
 gas be relieved of the pressure of the vessel enclosing it, it 
 will expand by virtue of its own elastic power, producing, 
 however, cold in the surrounding atmosphere. So also heat 
 will cause a bar of iron to expand. Dr. Joule proved that 
 if iron were expanded by mechanical force, it would be ac- 
 companied by cold. Inasmuch as india-rubber is related to 
 heat in an opposite manner to that of iron, being contracted 
 by heat instead of expanded, we would, according to the 
 law above expressed, naturally expect that a mechanical ex- 
 
 1 Tyndall, Fragments of Science, p. 338. 
 
 2 Gore, The Art of Scientific Discovery, p. 594. 
 
PREDICTION AND VERIFICATION 
 
 287 
 
 pansion of india-rubber would give beat, and a contraction 
 produce cold. An experiment may be tried by suddenly 
 stretching a rubber band while the middle part is in the 
 mouth ; when stretched, it grows warm ; when relaxed, it 
 seems cold . 1 
 
 Again, as heat will melt many substances, if we can re- 
 duce the same substance from the solid to the liquid state, 
 we would expect, as a result, the opposite of heat, namely, 
 cold. This occurs in all freezing mixtures ; as the affinity of 
 salt for water causes it to melt ice, thus producing cold in the 
 surrounding atmosphere, sufficient to freeze cream or other 
 similar substance, inasmuch as, passing from solid to liquid, 
 water absorbs heat from all substances near it ; this absorp- 
 tion producing artificial cold surrounding it. The recipro- 
 cal action of heat and cold is illustrated in an interesting 
 experiment described by Tait . 2 He took a bar of ice, sup- 
 ported horizontally at either end, and over the middle of 
 the bar he put a fine wire, and put equal weights to the two 
 ends of the wire. The wire gradually, by the action of the 
 weights, cut through the bar of ice, and yet it was observed 
 that the path of the wire was instantly replaced by the 
 freezing again of the melted portion produced by the press- 
 ure, and when the wire had wholly traversed the entire 
 thickness of the bar, the bar itself was intact, and even 
 stronger along the line of the cutting than before. The 
 explanation of this experiment is that inasmuch as heat 
 melts ice, then when ice is melted by pressure, as in this 
 case of the weighted wire, cold, the opposite of heat, is in- 
 duced ; thus, as the wire was forced by the weights into the 
 ice, the pressure upon the ice melted it, making it colder, so 
 that the water produced, passing around the chilled wire, 
 and being thus relieved of pressure, froze again. 
 
 Faraday predicted certain magnetic phenomena by this 
 method, which are specially interesting as illustrations of 
 
 1 Jevons, Principles of Science, p. 545. 
 
 2 Tait, Recent Advances in Physical Science, pp. 99, 100. 
 
288 
 
 INDUCTIVE LOGIC 
 
 this kind of prediction. It seems that Arago had observed 
 in 1824 that the number of oscillations which a magnetized 
 needle makes in a given time, under the influence of the 
 earth’s magnetism, is very much lessened by the proximity 
 of certain metallic masses, and especially of copper. Em- 
 ploying the latter substance in an experiment upon a mag- 
 netized needle, he succeeded in reducing the number of its 
 vibrations in a given time from three hundred to four. Tak- 
 ing the experiment as a basis for his inference, Faraday 
 predicted that since the presence of a metal at rest stops the 
 oscillations of a magnetic needle, the neighborhood of a 
 magnet at rest ought to stop the motion of a rotating mass 
 of metal. He therefore proceeded to put his inference to 
 the test of actual experiment, by suspending a cube of cop- 
 per to a twisted thread which was placed between the poles 
 of a powerful electromagnet. When the thread was left 
 to itself, it began to spin round with great velocity, but 
 stopped the moment a powerful current passed through the 
 electromagnet. 1 Again, as heat applied to the junction of 
 two metallic bars, as antimony and bismuth, produced an 
 electric current, it was inferred that if an electric current 
 was made to pass through such a junction, it would pro- 
 duce cold, and such proved to be the case. 2 
 
 In the general process of verification, it often happens 
 that seeming exceptions occur which are direct contradic- 
 tions of the law we are attempting to prove. And it is in 
 dealing with such cases that one’s power of discrimination 
 is most fully taxed. It is necessary to make a most careful 
 distinction between seeming and real exceptions. Professor 
 Jevons has given a very exhaustive classification of the dif- 
 ferent kinds of exceptional phenomena, which it is well to 
 have in mind, in order to know in any investigation the 
 various possible complications that may rise. 3 The excep- 
 tional phenomena, as given by Jevons, are : — 
 
 1 Ganot, Physics, pp. 797, 798. 2 Jevons, Principles of Science, p. 547. 
 
 8 See Jevons, Chapter XXIX, in his Principles of Science , on “ Excep- 
 tional Phenomena.” 
 
PREDICTION AND VERIFICATION 
 
 289 
 
 1. Imaginary, or false exceptions ; that is, facts, objects, 
 or events which are not really what they are supposed to 
 be. 
 
 2. Apparent but congruent exceptions, which, though ap- 
 parently in conflict with a law of nature, are really in agree- 
 ment with it. 
 
 3. Singular exceptions, which really agree with a law of 
 nature, but exhibit remarkable and unique results of it. 
 
 4. Divergent exceptions, which really proceed from the 
 ordinary action of known processes of nature, but which are 
 excessive in amount or monstrous in character. 
 
 5. Accidental exceptions, arising from the interference 
 of some entirely distinct but known law of nature. 
 
 6. Novel and unexplained exceptions, which lead to the 
 discovery of a new series of laws and phenomena, modifying 
 or disguising the effects of previously known laws without 
 being inconsistent with them. 
 
 7. Limiting exceptions, showing the falsity of a supposed 
 law to some cases to which it had been extended, but not 
 affecting its truth in other cases. 
 
 8. Contradictory, or real, exceptions, which lead us to the 
 conclusion that a supposed hypothesis or theory is in oppo- 
 sition to the phenomena of nature, and must therefore be 
 abandoned. 
 
 It will be seen that among so many possibilities of inter- 
 pretation an exception does not necessarily prove the rule, 
 as the old adage would have it ; nor does the exception, on 
 the other hand, necessarily disprove the rule or law. It 
 must be in each case strictly and adequately interpreted, 
 which requires a penetrating sagacity and a thorough 
 knowledge of the phenomena under investigation. 
 
 In the process of verification, the question naturally sug- 
 gests itself : How many verifying instances are sufficient to 
 determine the universal validity of a given law ? This ques- 
 tion will be recognized as an old difficulty, now presented 
 in another form ; but in reality it is the perplexing problem 
 
290 
 
 INDUCTIVE LOGIC 
 
 of determining tire logical ground of induction. What is our 
 warrant for proceeding from known and verified instances 
 to unknown phenomena, of the same kind it is true, but as 
 yet beyond the pale of our experience ? The warrant for 
 our generalization does not lie wholly in the number of veri- 
 fying instances. In addition to the effect which mere num- 
 ber produces in confirming our belief, there is the confidence 
 which we feel in the constancy of the order of nature, and 
 which we are constrained to assume as a fundamental postu- 
 late . 1 Therefore, we say that the verifying facts must be 
 of such a number, and of such a nature as well, that they 
 give evidence of a uniformity which transcends all supposi- 
 tion of mere coincidence, and compels us to attribute it to 
 the uniformity of nature itself, in which we find a warrant 
 for our generalization. As Professor Clifford has remarked : 
 “ The aim of scientific thought is to apply past experiences 
 to new circumstances. The instrument is an observed uni- 
 formity in the course of events. By the use of this instru- 
 ment it gives us information transcending our experience, 
 it enables us to infer things that we have not seen from 
 things that we have seen ; and the evidence for the truth 
 of that information depends on our supposing that the uni- 
 formity holds good beyond our experience .” 2 
 
 In extending knowledge and predicting results beyond 
 the sphere of experience, modern scientific investigation is 
 largely indebted to the principles and methods of mathe- 
 matics. Mathematical laws, applied to the data given in 
 sense-perception, give indications of the necessary relations 
 that must exist in the observed phenomena, and all that 
 they involve. Thus, that which is given directly in con- 
 sciousness is supplemented by that which is given indirectly 
 as mathematically necessitated. The mathematico-experi- 
 mental method in physics has led to very rich and impor- 
 tant results which have proved practically its efficiency as 
 a scientific method. 
 
 1 See Sigwart, Logic, Vol. II, p. 348. 
 
 2 Clifford, Lectures and Essays, Vol. I, pp. 131, 132. 
 
CHAPTER XII 
 
 HYPOTHESIS 
 
 The inductive process cannot proceed to any great extent 
 or attain satisfactory results without the aid of some hy- 
 pothesis. An hypothesis is a supposition regarding the 
 cause of a phenomenon, which we make either as prelimi- 
 nary to an experiment which will prove or disprove the 
 supposition, or in lieu of an experiment or systematic obser- 
 vation, when such are impossible owing to the peculiar 
 conditions of the phenomenon itself. We see therefore 
 that the framing of hypotheses has a double function. First, 
 considered, as preliminary to experiment, — we found that 
 in cases where two, three, or more elements enter into 
 a complex antecedent, it is impossible often, and always 
 impracticable to test the various possible combinations sepa- 
 rately in order to note their different results. The com- 
 binations in complex phenomena are indefinitely great, 
 and the isolation of certain elements in order to estimate 
 the exact result of the combined force of the other combina- 
 tions is extremely difficult and often impossible. Therefore 
 the mind discards some combinations as irrelevant, others 
 as impossible, and selects one perhaps as the most likely 
 cause of the given effect. This selective function of the 
 mind, therefore, indicates the line of experiment in a de- 
 terminate manner and does not leave the phenomena to 
 indeterminate and haphazard investigation. 
 
 Consider, for instance, so eminent an experimenter as 
 Charles Darwin, so fertile in all kinds of experimental re- 
 sources ; yet it is said of him that every experiment was the 
 result of a tentative theory, thought out in advance of all 
 
 291 
 
292 
 
 INDUCTIVE LOGIC 
 
 actual test and by a sagacious insight into the necessary 
 conditions of the interrelated phenomena before him. His 
 son, Francis Darwin, says of him in his Reminiscences : 
 “He often said that no one could be a good observer un- 
 less he was an active theorizer. It was as though he were 
 charged with theorizing power ready to flow into any 
 channel on the slightest disturbance, so that no fact, how- 
 ever small, could avoid releasing a stream of theory, and 
 thus the fact became magnified into importance. In this 
 way, it naturally happened that many untenable theories 
 occurred to him ; but fortunately his richness of imagina- 
 tion was equalled by his power of judging and condemning 
 the thoughts that occurred to him. He was just to his 
 theories, and did not condemn them unheard ; and so it 
 happened that he was willing to test what would seem to 
 most people not at all worth testing. These rather wild 
 trials he called ‘ fool’s experiments,’ and enjoyed extremely. 
 As an example, I may mention that, finding the cotyledons 
 of Biophytum to be highly sensitive to vibrations of the table, 
 he fancied that he might perceive the vibrations of sound, 
 and therefore made me play my bassoon close to a plant. The 
 love of experiment was very strong in him, and I can remem- 
 ber the way he would say, ‘ I shan’t be easy till I have tried 
 it,’ as if an outside force were driving him .” 1 Hypothesis 
 and experiment were in the hand of Darwin like a two- 
 edged sword, which he employed with rare skill and effect. 
 
 An hypothesis is to be regarded not only as the precursor 
 of experiment, but it also functions as a method of explana- 
 tion when actual verification is impossible. We see this 
 constantly in our everyday life. We are compelled again 
 and again to account for situations which occur that are 
 impossible for us to reproduce in the form of an experi- 
 ment, that we are able to observe but once. Some explana- 
 tion is required to satisfy mental demands which are 
 imperative in this regard. The explanation which seems 
 1 Life and Letters of Charles Darwin, Vol. I, p. 126. 
 
HYPOTHESIS 
 
 293 
 
 most in keeping with the sum of facts in our possession, 
 is the hypothesis which we frame ; so also in explaining 
 the conduct of others by conjecture as to the most reason- 
 able motives that will satisfactorily account for the same ; 
 such hypotheses we are constantly compelled to assume. 
 We are not always able to perceive the relations existing 
 between facts as they come into the sphere of our experience, 
 and yet we are constrained to think of them as related ; but 
 in order to systematize them, we must supply mentally the 
 lacunae which appear in the phenomena as perceived. This 
 supposition that is necessary to construct facts into a system 
 is an hypothesis. 
 
 An illustration of an hypothesis suggesting systematic 
 observation and experiment is. found in the history of the 
 discovery of vaccination by Jenner. It seems that while a 
 mere youth, pursuing his studies at Sodbury, he chanced to 
 hear a casual remark made by a country girl who came to 
 his master’s shop for advice. The smallpox was mentioned, 
 when the girl said, “I cannot take that disease, for I have 
 had cowpox.” 1 This observation, expressing the common 
 superstition of the simple country folk, appealed to Jenner’s 
 mind as an inchoate hypothesis. Seizing upon it as a sugges- 
 tion of possible value, he proceeded to make diligent in- 
 quiries and careful observations, which finally led him to 
 the discovery of vaccination. 
 
 An illustration of hypothesis as explanation of phenomena 
 beyond the range of experiment is found in the hypothesis 
 as to the source of the sun’s energy. An enumeration of the 
 different hypotheses advanced upon this subject is given by 
 Tait in his Recent Advances in Physical Science ? “ The old 
 
 notion that the sun is a huge fire, or something of that kind, 
 is one which will only occur to one thinking of the matter 
 for the first time ; but with our modern chemical knowl- 
 edge, we are enabled to say that, massive as the sun is, 
 if its materials had consisted of the very best materials for 
 1 Gore, The Art of Scientific Discovery, p. 495. 1 pp. 151 ff. 
 
294 
 
 INDUCTIVE LOGIC 
 
 giving out heat, that enormous lhass of some 400,000 miles 
 in radius could have supplied us with only about 5000 years 
 of the present radiation. A mass of coal of that size would 
 have produced very much less than that amount of heat. 
 Nor would the most energetic chemicals known to us', com- 
 bined in proportion for giving the greatest amount of heat 
 by actual chemical combination, supply the sun’s present 
 waste for even 5000 years. Therefore as we all know that 
 geological facts, if there were no others, point to at least as 
 high a radiation from the sun as the present, for at all 
 events a few hundreds of thousands of years back, — and 
 perhaps also indicate even a higher rate of radiation from 
 the sun in old time than at present, — it is quite obvious 
 that the heat of the sun cannot possibly be .supplied by any 
 chemical process of which we have the slightest conception. 
 
 “Now, if we can find, oil the other hand, any physical 
 explanation of this consistent with any present knowledge, 
 we are bound to take it and use it as far as we can, rather 
 than say : This question is totally unanswerable unless there 
 be chemical agencies at work in the sun of a far more power- 
 ful order than anything we meet with on the earth’s surface. 
 If we can find a thoroughly intelligible source of heat, which, 
 though depending upon a different physical cause from the 
 usual one, combustion, is amply sufficient to have supplied 
 the sun with such an amount of heat as to enable it to 
 radiate for perhaps the last hundred millions of years at 
 the same rate as it is now radiating, then I say we are bound 
 to try that hypothesis first, and argue upon it until we find 
 it inconsistent with something known. And if we do not 
 find it inconsistent with anything that is known, while we 
 find it completely capable of explaining our difficulty, then 
 it is not only philosophic to say that it is most probably the 
 origin of the sun’s energy, but we feel ourselves constrained 
 to admit it. Newton long ago told us this obligation in his 
 Rules of Philosophizing. Now it is known that if we were to 
 take a mass of the most perfect combustibles which we know, 
 
HYPOTHESIS 
 
 295 
 
 and let it fall upon the sun merely from the earth’s distance, 
 then the work done upon it by the sun’s attraction during 
 its fall would give it so large an amount of kinetic energy 
 when it reached the sun’s surface as to produce an impact 
 which would represent six thousand times the amount of 
 energy which could be produced by its mere burning. 
 
 “ It appears, then, that our natural and only trustworthy 
 mode of explaining the sun’s heat at present, in time past, 
 and for time to come, must be something closely analogous 
 to, but not identical with, what was called the nebular 
 hypothesis of Laplace, — the hypothesis of the falling to- 
 gether (from rudely scattered distribution in space) of the 
 matter which now forms the various suns and planets. We 
 find by calculation in which there is no possibility of large 
 error, that this hypothesis is thoroughly competent to ex- 
 plain one hundred millions of years’ solar radiation at the 
 present rate, perhaps more ; and it is capable of showing us 
 how it is that the sun, for thousands of years together, can 
 part with energy at the enormous rate at which it does still 
 part with it, and yet not apparently cool by perhaps any 
 measurable quantity. 
 
 “ In confirmation of this, not only is the hypothesis itself 
 capable of explaining the amounts of energy which are in 
 question, but also recent investigations, aided by the spec- 
 troscope, have shown us that there are gigantic nebular sys- 
 tems at great distances from our solar system, in the process 
 of physical degradation in that very way, by the falling to- 
 gether of scattered masses, and with numerous consequent 
 developments of heat by impacts. What are called tempo- 
 rary stars form another splendid and still more striking 
 instance of it, as where a star suddenly appears, of the 
 first magnitude, or even brighter than the first, outshining 
 all the planets for a month or two at a time, and then, 
 after a little time, becomes invisible in the most power- 
 ful telescope. Things of that kind are constantly occur- 
 ring on a larger or smaller scale, and they can all be easily 
 
296 
 
 INDUCTIVE LOGIC 
 
 explained on this supposition of the impact of gravitating 
 masses.” 
 
 Such a hypothesis, it will be seen, embraces all the facts 
 observed in one self-consistent system. The other hypotheses 
 are inadequate to account satisfactorily for the phenomena. 
 The validity of this hypothesis lies in its being both ade- 
 quate and congruent as well ; experiment or corroborative 
 observation being out of the question, we are, as Tait says, 
 “ constrained to admit it.” 
 
 Mr. Darwin gives an enumeration and criticism of the 
 different hypotheses which have been suggested to explain 
 the extinction of the gigantic animals known to have existed 
 upon the earth. His account will give an indication of the 
 natural propensity of the mind to frame hypotheses con- 
 cerning phenomena which lie outside the sphere both of 
 observation and experiment. Mr. Darwin says : “ It is im- 
 possible to reflect on the changed state of the American 
 Continent without the deepest astonishment. Formerly it 
 must have swarmed with great monsters ; now we find mere 
 pigmies compared with the antecedent allied races. The 
 greater number, if not all, of these extinct quadrupeds, 
 lived at a late period, and were the contemporaries of most 
 of the existing sea-shells. What, then, has exterminated so 
 many species and whole genera ? The mind at first is irre- 
 sistibly hurried into the belief of some great catastrophe ; 
 but thus to destroy animals, both large and small, in South- 
 ern Patagonia, in Brazil, on the Cordillera of Peru, in North 
 America up to Behring’s Straits, we must shake the entire 
 framework of the globe. 
 
 “ An examination, moreover, of the geology of La Plata 
 and Patagonia leads to the belief that all the features of the 
 land result from slow and gradual changes. It appears from 
 the character of the fossils in Europe, Asia, Australia, and 
 in North and South America, that those conditions which 
 favor the life of the larger quadrupeds were lately coexten- 
 sive with the world. What those conditions were, no one 
 
HYPOTHESIS 
 
 297 
 
 has yet even conjectured. It could hardly have been a 
 change of temperature, which at about the same time de- 
 stroyed the inhabitants of tropical, temperate, and arctic 
 latitudes on both sides of the globe. In North America we 
 positively know from Mr. Lyell that the large quadrupeds 
 lived subsequently to that period when boulders were 
 brought into latitudes at which icebergs now never arrive ; 
 from conclusive but indirect reasons we may feel sure that in 
 the southern hemisphere the Macrauchenia also lived long 
 subsequently to the ice-transporting boulder-period. Did 
 man, after his first inroad into South America, destroy, as 
 has been suggested, the unwieldy Megatherium and the other 
 Edentata? We must look at least to some other cause for 
 the destruction of the little tucutuco at Bahia Blanca, and 
 of the many fossil mice and other small quadrupeds in 
 Brazil. No one will imagine that a drought, even far severer 
 than those which cause such losses in the provinces of La 
 Plata, could destroy every individual of every species from 
 Southern Patagonia to Behring’s Straits. What shall we 
 say of the extinction of the horse ? Did those plains fail 
 of pasture which have since been overrun by thousands and 
 hundreds of thousands of the descendants of the stock in- 
 troduced by the Spaniards ? Have the subsequently intro- 
 duced species consumed the food of the great antecedent 
 races ? Can we believe that the Capybara has taken the 
 food of the Toxodon, the Guanaco of the Macrauchenia, the 
 existing small Edentata of their numerous gigantic proto- 
 types ? Certainly no fact in the long history of the world 
 is so startling as the wide and repeated exterminations of its 
 inhabitants .” 1 Mr, Darwin’s own hypothesis concerning 
 this phenomenon is rather indefinite, but nevertheless as 
 definite as the extreme complexity of the facts will allow. 
 He says that there are certain causes operating in nature, 
 their exact character remaining unknown, such that the too 
 rapid increase of every species, even the most favored, is 
 1 Darwin, Voyage of a Naturalist, Yol. I, p. 223. 
 
298 
 
 INDUCTIVE LOGIC 
 
 steadily checked, producing in some cases rarity and m 
 others extinction, if these causes operate with unusual effi- 
 cacy. His hypothesis marks a tendency whose nature, 
 nevertheless, remains concealed. 
 
 In all these widely differing hypotheses we see a certain 
 mental constraint to offer some explanation, even though it 
 be but a disguised confession of ignorance, as in Mr. Darwin’s 
 hypothesis. 
 
 An illustration of an hypothesis to explain observed phe- 
 nomena that cannot be further tested is that given in the 
 following instance cited by Professor Tyndall : “ At Erith, 
 in 1804, there occurred a tremendous explosion of a powder 
 magazine. The village of Erith was some miles distant 
 from the magazine, but in nearly all cases the windows 
 were shattered ; and it was noticeable that the windows 
 turned away from the origin of the explosion suffered 
 almost as much as those which faced it. Lead sashes were 
 employed in Erith church ; and these, being in some degree 
 flexible, enabled the windows to yield to pressure without 
 much fracture of glass. Every window in the church, front 
 and back, was bent inwards. In fact, as the sound-wave 
 reached the church, it separated right and left, and, for a 
 moment, the edifice was clasped by a girdle of intensely 
 compressed air, which forced all its windows inwards. 
 After compression, the air in the church no doubt dilated, 
 and tended to restore the windows to their first condition. 
 The bending in of the windows, however, produced but a 
 small condensation of the whole mass of air within the 
 church ; the force of the recoil was, therefore, feeble in com- 
 parison with the force of impact, and insufficient to undo 
 what the latter had accomplished.” 1 Here also is a set of 
 conditions that must be satisfied by a correct hypothesis. 
 The phenomenon was not capable of repetition by any 
 experiment. Professor Tyndall, therefore, pictures to his 
 mind what must have happened beyond that which was 
 1 Tyndall, On Sound, p. 23. 
 
HYPOTHESIS 
 
 299 
 
 observed, in order to account for the result which actually- 
 happened. He tills up the unseen from what he knows of 
 the nature of sound-waves, and thus constructs one self- 
 consistent system which includes both the seen and the 
 unseen, the known and the unknown, the observed and the 
 inferred. 
 
 It will be noticed in this and other illustrations of 
 hypothesis, how large a part is played by the imagination. 
 It is the imagination which fills out the vacant spaces in 
 the picture of perception. With some, the function of 
 imagination is associated with fancy rather than fact. 
 It must, in this connection however, be clearly emphasized 
 that the imagination which constructs hypotheses must be 
 throughout in touch with fact. It must represent to the 
 mind, not what fancy suggests, but what the known facts 
 necessitate. The unseen is constructed out of the deter- 
 mining conditions of the seen. It is this deductive func- 
 tion of the imagination that gives to it a strictly logical 
 significance. For instance, Professor Tyndall’s reasoning 
 concerning the Erith church was somewhat as follows: The 
 windows are all bent inward, therefore the pressure must have 
 operated on all sides from without, inward ; such pressure 
 could only occur upon the supposition that the sound-waves, 
 separating right and left, wholly encompassed the church, 
 etc. In each case, that which he pictured to his mind as 
 happening, was regarded by him as actually necessitated 
 by the facts as observed. 
 
 Professor Tyndall has most admirably discussed the 
 Scientific Use of the Imagination; and his lecture under 
 that title every student, both of logic or of science, should 
 read. I quote one passage from it, which has special bear- 
 ing upon what has just been said: “ We are gifted with the 
 power of Imagination, — - combining what the Germans call 
 Anschauungsgabe and Einbildungskraft, — and by this power 
 we can lighten the darkness which surrounds the world of 
 the senses. There are tones in science who regard imagina- 
 
300 
 
 INDUCTIVE LOGIC 
 
 tion as a faculty to be feared and avoided rather than em- 
 ployed. They had observed its action in weak vessels and 
 were unduly impressed by its disasters. But they might 
 with equal justice point to exploded boilers as an argument 
 against the use of steam. Bounded and conditioned by co- 
 operant Reason, imagination becomes the mightiest instru- 
 ment of the scientific discoverer. Newton’s passage from 
 a falling apple to a falling moon was, at the outset, a leap 
 of the imagination. When William Thomson tries to place 
 the ultimate particles of matter between his compass points, 
 and to apply to them a scale of millimetres, he is powerfully 
 aided by this faculty. And in much that has been recently 
 said about protoplasm and life, we have the outgoings of 
 the imagination guided and controlled by the known analo- 
 gies of science. In fact, without this power our knowledge 
 of nature would be a mere tabulation of coexistences and 
 sequences. We should still believe in the succession of day 
 and night, of summer and winter; but the soul of Force 
 would be dislodged from our universe; causal relations 
 would disappear, and with them that science which is now 
 binding the parts of nature to an organic whole .” 1 
 
 In all the illustrations which have been given, and, in 
 fact, in all examples of the framing of hypotheses, it will 
 be seen that the mental functions specially in operation are 
 those of analysis and synthesis, — a separation of the ele- 
 ments as far as possible into their simplest forms of expres- 
 sion, and the building them together into some one system 
 whose unity lies in the assumed hypothesis. Mr. Venn has 
 especially emphasized this aspect of hypothesis, and his 
 chapter on this subject will well repay a careful reading . 2 
 
 Every supposition however is not necessarily an hypoth- 
 esis in the logical or scientific significance of that term. It 
 will be necessary therefore to mention some of the require- 
 ments which a logical hypothesis should satisfy. 
 
 1 Tyndall, Use and Limit of the Imagination in Science, p. 16. 
 
 2 Venn, Empirical Logic, Chapter XVI. 
 
HYPOTHESIS 
 
 301 
 
 1. An hypothesis should be plausible ; that is, it should 
 be no fanciful, or merely conjectural, explanation of the 
 phenomena in question. The suppositions of the interfer- 
 ence of spirits, or in a mythological age of the gods, to ac- 
 count for perplexing situations or obscure happenings, have 
 no rank as hypotheses; so, also, Fate is often referred to as 
 a convenient confession of ignorance in lieu of a satisfactory 
 explanation. Spinoza has remarked upon this as follows : 
 “ They who have desired to find scope for the display of 
 their ingenuity in assigning causes, have had recourse to a 
 new style of argument to help them in their conclusions, 
 namely, by reduction, not to the impossible or absurd, but to 
 ignorance or the unknown, a procedure which shows very 
 plainly that there was no other course open to them.” 
 
 The difference between a scientific hypothesis and a pop- 
 ular explanation concerning the same phenomena may be 
 found in Darwin’s account of “ a strange belief which is gen- 
 eral amongst the inhabitants of the Maldiva atolls, namely, 
 that corals have roots, and therefore that if merely broken 
 down to the surface, they grow up again ; but if rooted out, 
 they are permanently destroyed. By this means the in- 
 habitants keep their harbors clear; and thus the French 
 governor of St. Mary’s in Madagascar ‘cleared out and 
 made a beautiful little port at that place.’” 1 Their expla- 
 nation, however, is purely fanciful, having no basis in fact. 
 In contrast, Darwin’s hypothesis to explain the facts in the 
 case is of a logically scientific nature, and is as follows : 
 Inasmuch as loose sediment is injurious to the living poly- 
 pifers, and as it is probable that sand would accumulate in 
 the hollows formed by tearing out the corals, but not on the 
 broken and projecting stumps, therefore in the former case 
 the fresh growth of coral might be thus prevented by the 
 deposited sediment. 
 
 2. The second requirement is that the hypothesis must be 
 capable of proof or disproof. This does not demand a test 
 
 1 Darwin, Coral Reefs, p. 89. 
 
302 
 
 INDUCTIVE LOGIC 
 
 by experiment necessarily ; for that, as we have seen, may 
 be impossible. It does, however, require that some facts 
 should be forthcoming that will either confirm the hypoth- 
 esis or disprove it. There are cases, however, as Lotze sug- 
 gests, whose very nature precludes the possibility of proving 
 or disproving the hypothesis framed to account .for them. 
 For instance, the very common and simple hypothesis of 
 regarding the stars, which are apparently but small points 
 of light, as bodies of vast size, only very remote from us, 
 is in itself incapable of being either refuted or confirmed 
 by subsequent discovery. Lotze says : “ We must abide 
 content if our hypotheses are thinkable and useful, if they 
 are capable of explaining all interconnected appearances, 
 even such as were still unknown when we constructed them, 
 if, that is to say, they are indirectly confirmed by the agree- 
 ment of all that can be deduced from them in thought with 
 the actual progress of experience. But if we would be so 
 fortunate as to find an hypothesis which will not lack this 
 subsequent confirmation, we must not simply assume any- 
 thing that can be barely conceived as real ; we must only 
 assume that which, besides being thinkable, conforms, so to 
 speak, to the universal customs of reality, or to the special 
 local customs which prevail in that department of phenom- 
 ena to which the object we are investigating belongs.” 1 
 
 It is to be specially observed that while the requirement 
 of proof of an hypothesis may be waived in the sphere 
 of phenomena where proof is manifestly impossible, still, 
 where proof is available, an hypothesis must never be so 
 framed as to render the required test either impossible or 
 impracticable. 
 
 3. The hypothesis must be adequate. It must cover all 
 the facts in the case. An outstanding fact which it cannot 
 explain is sufficient to controvert such an hypothesis. A 
 knowledge of the distinction between postulate and hypoth- 
 esis, and of the relation which nominally exists between 
 1 Lotze, Logic, p. 353. 
 
HYPOTHESIS 
 
 303 
 
 the two, will help us to appreciate more clearly the force of 
 this requirement of adequacy. As defined by Lotze, a pos- 
 tulate “expresses the conditions which must be set up, or 
 the ground of explanation which must be given by some 
 reality, force, or event, before we can think the phenomenon 
 in the form in which it is presented to us ; it thus requires 
 or postulates the presence of something that can account 
 for the given effect. An hypothesis is a conjecture which 
 seeks to fill up the postulate thus abstractly stated by speci- 
 fying the concrete causes, forces, or processes out of which 
 the phenomenon really arose in this particular case, while 
 in other cases maybe the same postulate is to be satisfied 
 by utterly different though equivalent combinations of forces 
 or active elements.” 1 According to this distinction as ap- 
 plied to the problem of the source of the sun’s energy, the 
 postulate would be the sum of conditions which require 
 explanation ; namely, the tremendous radiation of heat ex- 
 tending through thousands and thousands of years. The 
 postulate therefore requires a force adequate to supply for 
 so long a period so great an amount of energy. We found 
 that ordinary combustion of the most highly combustible 
 materials would not, as an hypothesis, satisfy the condi- 
 tions which obtain in the postulate ; nor would the libera- 
 tion of chemical energy stand as an hypothesis adequate to 
 satisfy the postulate; the hypothesis of impact of masses upon 
 the sun’s surface from immense distances presents a force 
 sufficient to meet the requirements of the postulate. More- 
 over we see in this illustration how the hypothesis is a par- 
 ticular and concrete expression of the conditions expressed 
 in general and abstract terms in the postulate. The essential 
 characteristic therefore of the hypothesis is that it shall 
 perfectly satisfy all the conditions expressed in the postu- 
 late. 
 
 The hypothesis that nature abhorred a vacuum, in order 
 to account for the rise of water in a tube or pump, was seen 
 1 Lotze, Logic, pp 349, 350. 
 
304 
 
 INDUCTIVE LOGIC 
 
 to break down utterly when it was found that the water did 
 not rise beyond some thirty-three feet. The demand of the 
 postulate in the case was a force of precisely such magni- 
 tude that it would balance a column of water thirty-three 
 feet in height. This force, precisely satisfying the condi- 
 tions of the postulate, is found in the hypothesis that the 
 atmospheric pressure is such a magnitude as to exert a press- 
 ure equivalent to a column of water some thirty-three feet 
 in height. The strength of the hypothesis lies in its exact 
 and appropriate fitting into the facts of the problem. 
 
 Another illustration of the fitting of hypothesis to postu- 
 late, and one where the conditions of the postulate are ex- 
 tremely complex, I have chosen from Mr. Wallace’s work, 
 On Natural Selection : “ There is a Madagascar orchis — 
 the Angrcecum sesquipedale — with an immensely long and 
 deep nectary. How did such an extraordinary organ come 
 to be developed? Mr. Darwin’s explanation is this. The 
 pollen of this flower can only be removed by the base of the 
 proboscis of some very large moths, when trying to get at 
 the nectar at the bottom of the vessel. The moths with the 
 longest probosces would do this most effectually ; they 
 would be rewarded for their long tongues by getting the 
 most nectar ; whilst, on the other hand, the flowers with the 
 deepest nectaries would be the best fertilized by the largest 
 moths preferring them. Consequently the deepest-nectaried 
 orchids and the longest-tongued moths would each confer on 
 the other an advantage in the battle of life. This would tend 
 to their respective perpetuation, and to the constant length- 
 ening of nectaries and probosces. In the Angrcecum sesqui- 
 pedcde it is necessary that the proboscis should be forced 
 into a particular part of the flower, and this would only be 
 done by a large moth burying its proboscis to the very base, 
 and straining to drain the nectar from the bottom of the 
 long tube, in which it occupies a depth of one or two inches 
 only. Now let us start from the time when the nectary was 
 only half its present length, or about six inches, and was 
 
HYPOTHESIS 
 
 305 
 
 chiefly fertilized by a species of moth which appeared at 
 the time of the plant’s flowering, and whose proboscis was 
 of the same length. Among the millions of flowers of the 
 Angroecum produced every year, some would always be 
 shorter than the average, some longer. The former, owing 
 to the structure of the flower, would not get fertilized, be- 
 cause the moths could get all the nectar without forcing 
 their trunks down to the very base. By this process alone 
 the average length of the nectary would annually increase, 
 because the short-nectaried flowers being sterile, and the 
 long ones having abundant offspring, exactly the same 
 effect would be produced as if a gardener destroyed the 
 short ones, and sowed the seed of the long ones only; and 
 this we know by experience would produce a regular increase 
 of length, since it is this very process which has increased 
 the size and changed the form of our cultivated fruits and 
 flowers. But this would lead in time to such an increased 
 length of the nectary that many of the moths could only 
 just reach to the surface of the nectar, and only the few 
 with exceptionally long trunks be able to snck up a con- 
 siderable portion. This would cause many moths to neglect 
 these flowers, because they could not get a satisfying sup- 
 ply of nectar, and if these were the only moths in the coun- 
 try, the flowers would undoubtedly suffer, and the further 
 growth of the nectary be checked by exactly the same pro- 
 cess which had led to its increase. 
 
 “ But there are an immense variety of moths, of various 
 lengths of proboscis, and as the nectary became longer, 
 other and larger species would become the fertilizers, and 
 would carry on the process till the largest moths became 
 the sole agents. Now, if not before, the moth would also 
 be affected ; for those with the longest probosces would get 
 the most food, would be the strongest and most vigorous, 
 would visit and fertilize the greatest number of flowers, and 
 would leave the largest number of descendants. The flowers 
 most completely fertilized by these moths being those which 
 
306 
 
 INDUCTIVE LOGIC 
 
 had the longest nectaries, there would in each generation 
 be, on the average, an increase in the length of the nectaries, 
 and also an average increase in the length of the probosces 
 of the moths ; and this would be a necessary result from the 
 fact that nature ever fluctuates about a mean, or that in 
 every generation there would be flowers with longer and 
 shorter nectaries, and moths with longer and shorter pro- 
 bosces than the average. I may here mention that some 
 of the large Sphinx moths of the tropics have probosces 
 nearly as long as the nectary of Angrcecum sesquipedale. 
 I have carefully measured the proboscis of a specimen of 
 Macrosila cluentius from South America, in the collection of 
 the British Museum, and find it to be nine inches and a 
 quarter long. One from tropical Africa ( Macrosila morganii ) 
 is seven inches and a half. A species having a proboscis 
 two or three inches longer could reach the nectar in the 
 longest flowers of Angrcecum sesquipedale, whose nectaries 
 vary in length from ten to fourteen inches. That such a 
 moth exists in Madagascar may be safely predicted ; 1 and 
 naturalists who visit that island should search for it 
 with as much confidence as astronomers searched for the 
 planet Neptune, — and I venture to predict they will be 
 equally successful .” 2 
 
 I have given this quotation at length in order to indi- 
 cate not only the fitting of hypothesis to the facts observed, 
 but also the large and important part performed by the 
 imagination in reproducing along parallel lines the natural 
 history of the orchid and motli. The hypothesis reaches 
 back over an indefinitely long past, by virtue of the neces- 
 sities observed in the present, and in accordance with 
 well-established analogies and approved inductions. The 
 function of the imagination especially prominent is that of 
 
 1 It is interesting to note that since Mr. Wallace wrote the above, Kirby, 
 in his European Moths and Butterflies, makes mention'of one of the Sphin- 
 gidx with a proboscis twelve inches long! 
 
 2 Wallace, On, Natural Selection, pp. 271-275. 
 
HYPOTHESIS 
 
 307 
 
 its deductive insight, which is able to picture to the mind 
 the inevitable results of this and that condition as furnished 
 by the postulate, and then to fit such necessitated results 
 into one self-consistent system, with nothing left unex- 
 plained, incongruous, or contradictory. 
 
 Another illustration of an hypothesis covering a large 
 number of complex facts is that of the fertilization of cer- 
 tain flowers by means of the wind. As given by Sir John 
 Lubbock, we have the following facts and the correspond- 
 ing explanation of them: “ Wind- fertilized flowers, as a 
 rule, have no color, emit no scent and produce no honey, 
 and are regular in form. Color, scent, and honey are the 
 three characteristics by which insects are attracted to 
 flowers. Again, as a rule wind-fertilized flowers produce 
 much more pollen than those which are fertilized by insects. 
 This is necessary, because it is obvious that the chances 
 against any given pollen grain reaching the stigma are much 
 greater in the one case than in the other. Every one has 
 observed the showers of yellow pollen produced by the 
 Scotch fir. Again, it is an advantage to wind-fertilized 
 plants to flower early in the spring before the leaves are 
 out, because the latter would catch much of the pollen, and 
 thus interfere with its access to the stigma. Again, in these 
 plants the pollen is less adherent, so that it can be easily 
 blown away by the wind, which would be a disadvantage in 
 most plants which are fertilized by insects. Again, such 
 flowers generally have the stigma more or less branched, or 
 hairy, which evidently must tend to increase their chances 
 of catching the pollen .” 1 There is here a structural adap- 
 tation of these plants to the circumstances designed to 
 explain them, so that the consequent self-consistent system 
 thus formed carries with it the weight of conviction. 
 
 There are some explanations which do not perfectly cor- 
 respond to reality, and yet, when their nature is known, they 
 may be profitably used, not to represent reality, but to assist 
 1 Lubbock, Scientific Lectures , pp. 9, 10. 
 
308 
 
 INDUCTIVE LOGIC 
 
 the mind by an approximate representation to better appreci- 
 ate the facts as they really are related one to another. These 
 so-called “ fictions ” are useful, especially in mathematics. 
 We suppose, for instance, inscribed and circumscribed poly- 
 gons of a circle, with ever-increasing number of sides, gradu- 
 ally approaching and becoming coincident finally with the 
 curve itself. This latter we know to be impossible, and yet 
 we may treat that which happens only approximately as 
 though really happening, merely as an aid to the imagina- 
 tion ; and a fiction, if always so understood, may thus prove 
 helpful in the representation of reality more clearly to our 
 minds. 
 
 4. The hypothesis moreover should involve no contra- 
 diction. This is clearly a requirement that is deductive 
 rather than inductive, depending upon the fundamental 
 principle of contradiction lying at the basis of the deduc- 
 tive system of logic. 
 
 5. The hypothesis should be as simple as possible. No 
 involved explanation that mystifies rather than clears the 
 difficulties presented can rank as a true hypothesis. Sim- 
 plex vert sigillum. This requirement, of course, cannot in 
 all cases be strictly complied with ; for the phenomena to 
 be explained may present such a degree of complexity that 
 a simple hypothesis would be altogether out of the question. 
 For instance, the hypothesis of a substance filling the uni- 
 verse, and pervading all particles of matter, however solid 
 and closely knit together, a substance itself more solid than 
 steel, and more elastic as well, such a supposition seems not 
 only too involved, but also even to belie the ordinary judg- 
 ments of common sense. And yet this undulatory hypothe- 
 sis is more and more confirmed by every advance of science 
 in the knowledge of the phenomena of light and heat. 
 
 It sometimes happens that the very failure of am hy- 
 pothesis forms a substantial contribution to the progress 
 of thought, leading to the readjustment of a received 
 theory, or stimulating research in order to discover the 
 
HYPOTHESIS 
 
 309 
 
 true in place of the false hypothesis. As Mr. Tait says : 
 “We all know that if there had not been a pursuit after 
 the philosopher’s stone, chemistry could not yet have been 
 anything like the gigantic science it now is. In the same 
 way we can say, that modern physics could not yet have 
 covered the ground it now occupies had it not been for this 
 experimental seeking for the so-called perpetual motion, and 
 the consequent establishment of a definite and scientifically 
 useful negative.” 1 The circular theory of the orbits of the 
 planets, while incorrect, yet made the transition easier from 
 the hypothesis of circular motion to that of motion in an 
 elliptical orbit, which is the true theory. It often happens 
 that an hypothesis may not be wholly wrong but may need 
 correction, and this is often provided for, not by a total 
 rejection of the hypothesis in question, but by supplement- 
 ing it by so-called subsidiary hypotheses. 
 
 As to the tests of a correct hypothesis in addition to 
 the fulfilment of the requirements already mentioned, Dr. 
 Whewell has especially emphasized the importance of what 
 he has styled a “ Consilience of Inductions.” An hypothe- 
 sis receives a confirmatory strengthening of its validity, 
 when it enables us to explain and determine cases not 
 only of the same kind as the phenomena out of which the 
 hypothesis itself has developed, but cases which arise in a ' 
 sphere entirely different from that which gave material 
 originally for the formation of the hypothesis. An hypothe- 
 sis that can thus be carried into new territory as an effec- 
 tive instrument of research, is thereby doubly accredited. 
 As Dr. Whewell remarks : “ Accordingly the cases in which 
 inductions from classes of parts altogether different have 
 thus jumped together, belong only to the best established 
 theories which the history of science contains. And as I 
 shall have occasion to refer to this peculiar feature in their 
 evidence, I will take the liberty of describing it by a par- 
 ticular phrase ; and will term it the Consilience of Inductions. 
 
 1 Tait, Recent Advances in Physical Science, p. 69. 
 
BIO 
 
 INDUCTIVE LOGIC 
 
 It is exemplified principally in some of the greatest dis- 
 coveries. Thus it was found by Newton that the doctrine 
 of the attraction of the sun varying according to the inverse 
 square of the distance, which explained Kepler’s Third Law, 
 of the proportionality of the cubes of the distances to the 
 squares of the periodic times of the planets, explained also 
 his First and Second Laws, of the elliptical motion of each 
 planet; although no connection of these laws had been visi- 
 ble before. Again, it appeared that the force of universal 
 gravitation, which had been inferred from the perturbations 
 of the moon and planets by the sun and by each other, also 
 accounted for the fact, apparently altogether dissimilar and 
 remote, of the precession of the equinoxes. Here was a most 
 striking and surprising coincidence which gave to the theory 
 a stamp of truth beyond the power of ingenuity to counter- 
 feit.” 1 
 
 When two rival hypotheses can be submitted to the test 
 of an experiment which negatives one and confirms the 
 other, such a testing is called an experimentum crucis. The 
 name was first given by Bacon, and has met with universal 
 acceptance in scientific phraseology. A crucial test, as 
 decisive between the emission and the undulatory theory of 
 light, is given in an experiment first tried by Father Gri- 
 maldi, a Bolognese monk, in 1665. If a shutter be pierced 
 with a very small hole, and the luminous cone which passes 
 through the orifice be examined, the cone will be found to 
 be much less acute than would be expected, considering 
 only the rectilinear transmission of the rays, as according 
 to the emission theory. If there be interposed in the path 
 of the luminous ray a second shutter, pierced with a hole 
 also, it will be noticed that the rays of the second cone are 
 even more divergent than those of the first. If the image 
 of the orifice be received upon a screen, a white circle is 
 seen surrounded by a dark ring, next a white ring, even 
 more brilliant than the central portion, then a second dark 
 1 Whewell, Novum Organum Renovatum, Book II, Chap. V, Art. 110. 
 
HYPOTHESIS 
 
 311 
 
 ring, and finally another very faint white ring. If in the 
 shutter with which the experiment is made, two very small 
 holes are pierced at a distance from each other of one or 
 two millimetres, and the two images received upon a screen 
 in such a manner that they overlap each other, it is found 
 that in the cuticular segment formed by the overlapping of 
 the images, the circles are more obscure than in the part 
 where they are separated. Thus by adding light to light 
 darkness is produced . 1 These phenomena are now known 
 to be consistent only with the undulatory theory, and directly 
 in contradiction to the emission hypothesis. 
 
 M. Romanes performed several experiments upon bees 
 which had the force of crucial tests of two opposed hypoth- 
 eses : one, that bees possess a general sense of direction, 
 irrespective of any special knowledge of their particular 
 surroundings ; the other, that they are guided in their flight 
 by a knowledge of the localities which they have been wont 
 to frequent. M. Romanes took a score of bees in a box out 
 to sea, where there could be no landmarks to guide the 
 insects home. None of them returned home. Then he 
 liberated a second lot of bees on the seashore, and, none of 
 these returning, he liberated another lot on the lawn between 
 the shore and the house. None of these returned, although 
 the distance from the lawn to the hive was not more than 
 two hundred yards. Lastly, he liberated bees in different 
 parts of the flower-garden on either side of the house, and 
 these at once returned to the hive ; and with repetition of 
 the experiment, a similar result, even arriving at the hive 
 before he himself had time to run from the place where he 
 had liberated them to the hive. As the garden was a large 
 one, many of them had to fly a greater distance, in order 
 to reach the hive, than those liberated on the front lawn. 
 Their uniform success, therefore, in finding their way home 
 so immediately was no doubt due to their special knowledge 
 
 1 Saigey, The Unity of Natural Phenomena, p. 66. 
 
312 
 
 INDUCTIVE LOGIC 
 
 of the flower-garden, and not to any general sense of direc- 
 tion . 1 
 
 The hypothesis that leads to verification by experiment 
 represents true scientific procedure, and that which has 
 actually been the most effective instrument of research in 
 all the various spheres of human investigation. The old 
 controversy between Mill and Whewell admits of a ready 
 adjustment in this regard. Whewell emphasized discovery 
 as the heart of the system of induction, leading to the fram- 
 ing of hypotheses whose chief test was not experimental 
 so much as the capability of accounting for the given phe- 
 nomena. Mill, on the other hand, insisted that logic was 
 essentially proof, and not discovery. He, accordingly, 
 emphasized the experimental testing by means of his several 
 methods, as being the all-important part of the inductive 
 method. He had little concern for the origin of the sug- 
 gestions as to the most likely causal elements in the midst 
 of a complex phenomenon. The primary function of 
 logic, according to him, is merely to prove or disprove. 
 The ideas of Whewell and Mill are not necessarily con- 
 tradictory ; they can be regarded as mutually supplementary, 
 which gives us a true account of the ideal logical method, 
 where hypothesis suggests the line of experiment, and 
 experiment in turn confirms hypothesis. In such a method, 
 as can be seen in the illustration given, there is a blending 
 of deductive and inductive reasoning, which is the general 
 characteristic of all actual processes of thought. As Sigwart 
 has so admirably put it : “ Without quickness of combina- 
 tion, by which we can call up a number of possible analogies 
 and apply them to the unexplained case ; without a happy 
 power of divination which is guided by unanalyzable associa- 
 tions to discover that analogy which embraces most aspects 
 of the event; finally, without imagination to construct con- 
 nections for which the only ground may be a hidden 
 
 1 Lubbock, On the Senses, Instincts, and Intelligence of Animals, pp. 
 269 , 270 . 
 
HYPOTHESIS 
 
 313 
 
 similarity, our thoughts, if compelled to proceed strictly 
 according to method, would frequently be condemned, by 
 the impossibility of discovering in this way a sufficiently 
 grounded connection, to complete stagnation. But the fact 
 is in no way contrary to the nature of induction ; it is a 
 necessary consequence of it. We cannot even begin the 
 process of inference without making general assumptions ; 
 and the general proposition which we get by summing up 
 a number of instances is really a hypothesis, to which, it 
 is true, we are led clearly and certainly in this case. But 
 between these most general presuppositions, upon which all 
 induction is grounded, and the simplest cases to which they 
 can be applied, there is a wide region within which the 
 hypotheses which are always necessary for induction can 
 only be formed tentatively, in order to give some definite 
 direction to investigation, to serve in our analysis of phe- 
 nomena into their elements as a means of breaking up com- 
 plete phenomena on certain lines, and to invent the 
 experiments which will make it possible to confirm or 
 refute an opinion.” 1 
 
 1 Sigwart, Logic, Vol. II, p. 423. 
 
CHAPTER XIII 
 
 ANALOGY 
 
 Analogy as we have seen is a process of inference from 
 a particular case to a particular. 1 Because they agree in 
 certain respects, it is inferred that they will agree in other 
 respects also. Such reasoning admits of various degrees of 
 cogency, and in no case is it ever completely conclusive. It 
 may give rise to an exceedingly high degree of probability, 
 but nothing more. However the conclusion which analogy 
 suggests as extremely probable may be submitted to the 
 tests of one or more of the inductive methods, and thereby 
 be satisfactorily proved. In that case, the particular case 
 which was the starting-point of the analogical inference can 
 then be regarded as the typical case which ranks as repre- 
 sentative of the universal attained by the inductive inves- 
 tigation. One of the most important features of analogy 
 is that while incomplete in itself, it nevertheless leads by 
 suggestion to inductive experimentation which renders it 
 complete or else discloses its points of weakness. As an 
 instrument of discovery, analogy has played a very impor- 
 tant role in scientific research. In 1845 Faraday discovered 
 the magnetic rotary polarization of light; by analogical 
 reasoning, Waitmann in the following year inferred that a 
 similar result would be attained with a beam of heat, which 
 was afterwards experimentally verified. 
 
 The so-called “natural kinds” furnish manifold illustra- 
 tions of analogies. They possess numerous properties, some 
 of them known and others unknown. Through large groups 
 of them are found similar characteristics side by side with 
 1 See p. 150. 
 
 314 
 
ANALOGY 
 
 315 
 
 manifest differences, and yet the similarities are so striking 
 that often, when new properties are discovered in certain 
 members of the group, there seems to be ground for infer- 
 ring their existence in other members of the group also. 
 Certain properties known to exist in potassium and sodium 
 were inferred to be present in rubidium and caesium ; the 
 carbonates of sodium and potassium are not decomposed by 
 a red heat, and it was inferred that the same would prove 
 true of the carbonates of rubidium and caesium ; and such 
 proved to be the case. Some of the statements which are 
 true of chlorine are found to be true of bromine and iodine. 
 Mr. Gore, having found the molecular change in antimony 
 electro-deposited from its chloride, he inferred and discov- 
 ered the same in that deposited from its bromide and iodide. 
 Sir Humphry Davy, having discovered that potassium might 
 be isolated by means of electrolysis, immediately inferred 
 and proceeded to prove by experiment that it would be 
 possible also to isolate sodium and other substances having 
 analogous properties . 1 
 
 The principle of analogy lies at the basis of all classifica- 
 tion, the separating and grouping together in appropriate 
 divisions individuals which possess certain salient attributes 
 in common. 
 
 Professor Jevons’s definition of classification embodies at 
 the same time a full statement of its exact logical signifi- 
 cance as an instrument of research, and therefore I give it 
 in full: “By the classification of any series of objects is 
 meant the actual or ideal arrangement together of those 
 which are alike, and the separation of those which are 
 unlike, the purpose of this arrangement being, primarily, 
 to disclose the correlations or laws of union of proper- 
 ties and circumstances, and secondarily, to facilitate the 
 operations of the mind in clearly conceiving and retaining in 
 the memory the characters of the object in question ."’ 2 In 
 
 1 Gore, The Art of Scientific Discovery, p. 522. 
 
 2 Jevons, Principles of Science, p. 677. 
 
316 
 
 INDUCTIVE LOGIC 
 
 describing the purpose of classification, the latter clause is 
 more a psychological desideratum than logical ; the former 
 specification contains its logical purpose ; namely, to dis- 
 close the correlations or laws of union of properties and 
 circumstances. This may be illustrated in the grouping to- 
 gether of potassium, sodium, caesium, rubidium, and lithium, 
 and calling them the alkaline metals. This was done by 
 virtue of the common characteristics in the midst of their 
 individual peculiarities; namely, they all combine very en- 
 ergetically with oxygen to decompose water at all tempera- 
 tures, and form strongly basic oxides, which are highly 
 soluble in water, yielding powerful caustic and alkaline 
 hydrates from which water cannot be expelled by heat ; their 
 carbonates are also soluble in water, and each metal forms 
 only one chloride. The manifest advantage of classifying 
 these metals together lies in its suggestive capacity, as we 
 have already noted in illustrations above given. So many 
 observed similarities suggest inferences by analogy ; when, 
 for instance, a new property is discovered in any one or two 
 of the metals of this class, the idea immediately suggests 
 itself that the same property may possibly extend over all 
 the metals of the same class. Not only is such an idea 
 suggested, but along with it there exists an antecedent 
 probability that it will be realized actually. 
 
 An excellent illustration of the practical results attained 
 through a scientific use of classification is found in Mr. 
 Lockyer’s researches on the sun . 1 As a guide to the ele- 
 ments to look for in the sun’s photosphere, he prepared a 
 classification of elements according as they had or had not 
 been traced in the sun, together with a detailed statement 
 of the chemical nature of each element. He was then able 
 to observe that the elements found in the sun were, for the 
 most part, those forming stable compounds with oxygen. 
 He then inferred that the other elements which were known 
 to form stable compounds with oxygen would, in all proba- 
 1 Quoted by Jevons in Priticiples of Science, p. C76. 
 
ANALOGY 
 
 317 
 
 bility, be found present in the sun. Starting upon this sug- 
 gested track, he succeeded in discovering five such metals. 
 
 Analogical inference carries special weight when it is based 
 upon the principle of teleology ; that is, when any observed 
 phenomena seem to possess structural contrivances adapted to 
 ends, similar in some degree at least to human contrivances 
 designed to produce certain proposed ends. When this simi- 
 larity is apparent, it suggests the possibility that an observed 
 contrivance in nature may subserve ends beyond the possi- 
 bility of observation, and which, therefore, may be inferred 
 really to exist. We have seen that the ground of all inference 
 lies in the representation of any given phenomena of con- 
 sciousness as cohering in one system, which comprehends the 
 several parts in a common unity of such a nature that, know- 
 ing some of the parts and their relations, we infer the charac- 
 ter and function of other parts not known, and yet which that 
 already known necessitates. And among the many kinds 
 of relation that may obtain between part and part, or part 
 and whole, the teleological is a very common one; and, 
 moreover, by its nature necessitates certain consequences 
 that lie beyond the sphere of observation, and yet, never- 
 theless, may very properly be supplied by inference. In 
 other words, the causal connections in a system are not 
 merely those of an efficient or a formal cause ; they may, 
 with a like force and suggestiveness, be considered in the 
 light of a final cause ; that is, the presence of means adapted 
 to certain ends, or of organs adapted to certain necessary 
 functions, or of contrivances of a mechanical nature as 
 though designed for a specific purpose. 
 
 Janet has specially emphasized the importance and prev- 
 alence of this kind of inference, and, as an illustration of 
 the cogency of inference based upon finality, he urges that 
 the certitude which the belief in the intelligence of our 
 fellow-men gives us is based upon analogical reasoning of 
 this type ; and that, moreover, this belief, resting upon such 
 a basis, is one of the strongest beliefs which we possess. 
 
318 
 
 INDUCTIVE LOGIC 
 
 He says: “Now, if we ask ourselves why we suppose that 
 other men think, we shall see that it is in virtue of the 
 principle of final causes. In effect, what is it that experi- 
 ence shows in the actions of other men, but a certain num- 
 ber of phenomena coordinated in a certain manner, and 
 bound not only together, but also to a future phenomenon 
 more or less remote ? Thus, when we see a man prepare 
 his food by means of fire, we know that this assemblage of 
 phenomena is connected with the act of taking food ; when 
 we see a painter drawing lines on a canvas, we know that 
 these apparently arbitrary acts are connected with the exe- 
 cution of a picture ; when we see a deaf mute making signs 
 which we do not understand, we believe that these gestures 
 are connected with a final effect, which is to be understood 
 by him to whom he makes them; in fine, when men speak, 
 we see that the articulations of which a phrase is composed 
 are coordinated to each other so as to produce a certain final 
 effect, which is to awaken in us a certain thought and senti- 
 ment. Now we cannot see such coordinations, whether actual 
 or future, without supposing a certain cause for them ; and 
 as we know by internal experience that with ourselves such 
 coordinations only take place under the condition that the 
 final effect is previously represented in our consciousness, 
 we suppose the same thing in the case of other men ; in a 
 word, we suppose for them the consciousness of an end, a con- 
 sciousness reflecting more or less, according as the circum- 
 stances more or less resemble those that accompany in 
 ourselves the reflecting consciousness. Thus when we affirm 
 the intelligence of other men, we affirm a truth of indisputa- 
 ble certitude; and yet we only affirm it on the ground of 
 analogy, and of analogy guided by the principle of final 
 causes.” 1 
 
 In this illustration of Janet’s we have the idea of a system 
 of coordinated parts especially prominent ; and for a satis- 
 factory account of the relations obtaining in such a system, 
 1 Janet, Final Causes, pp. 113, 114. 
 
ANALOGY 
 
 319 
 
 it will be seen how indispensable it is to postulate the theory 
 of final cause. This mode of inference finds a striking 
 illustration in the famous discovery of Harvey, concerning 
 the circulation of the blood. In the early part of the 
 seventeenth century, while Harvey was his pupil, the cele- 
 brated anatomist, Fabricius Aquapendente of Padua, ob- 
 served that many veins contain valves which lie open as 
 long as the blood is flowing toward the heart. Harvey, 
 learning of this fact, saw in it the suggestion of an adapta- 
 tion of means to an end ; namely, a contrivance so fashioned 
 by nature as to permit the blood to flow always in one direc- 
 tion only, and to prevent its flow in an opposite direction. 
 Observation of other portions of the circulatory mechanism 
 led to a confirmation of the idea, and to the discovery of the 
 circulation of the blood . 1 
 
 Again, many flint substances have been discovered, as 
 though curiously wrought with sharp edges, and a place 
 as though designed for a handle with which to wield the 
 stone as a weapon or a tool ; it has been inferred from these 
 general characteristics that the stones were so constructed 
 by human effort, and used by human beings for the purposes 
 for which they evidently seem to be adapted. This infer- 
 ence is based upon an analogy between the peculiar shapes 
 of such stones, and known shapes designed and used by 
 man. 
 
 This form of analogy has proved especially suggestive in 
 researches regarding plant and animal life. Sir John Lub- 
 bock gives the following description of the common white 
 dead-nettle with the explanation of its functions that is 
 evidently a teleological inference : “ The flower consists 
 of a narrow tube, somewhat expanded at the upper end, 
 where the lower lobe of the corolla forms a platform, on 
 each side of which is a small projecting lobe. The upper 
 portion of the corolla is an arched hood, under which lie 
 four anthers in pairs, while between them and projecting 
 1 Gore, Art of Scientific Discovery, p. 571. 
 
320 
 
 INDUCTIVE LOGIC 
 
 somewhat downwards is the pointed pistil. At the lower 
 end, the tube contains honey, and above the honey is a row 
 of hairs almost closing the tube. Now, why has the flower 
 this peculiar form ? What regulates the length of the tube ? 
 What is the use of this arch ? What lessons do these lobes 
 teach us ? What advantage is the honey to the flower ? 
 Of what use is the fringe of hairs? Why does the stigma 
 project beyond the anthers ? Why is the corolla white, 
 while the rest of the plant is green ? Similar questions 
 may of course be asked with reference to other flowers. At 
 the close of the last century, Conrad Sprengel published a 
 valuable work, in which he pointed out that the forms and 
 colors, the scent, honey, and general structure of flowers, 
 have reference to the visits of insects, which are of impor- 
 tance in transferring the pollen from the stamens to the 
 pistil. Mr. Darwin developed this theory and proved ex- 
 perimentally that the special service which insects perform 
 to flowers, consists not only in transferring the pollen from, 
 the stamens to the pistil, but in transferring it from the 
 stamens of one flower to the pistil of another.” 1 The line 
 of subsequent observation and experiment was thus origi- 
 nally suggested by the structural appearance of these flowers 
 which seemed formed for some specific end. The questions, 
 once started, — To what end? To what purpose? For 
 what use ? — led to the theory of Sprengel and the corrobo- 
 rative experiments of Darwin. 
 
 This is further illustrated in some very interesting flower 
 structures, also described by Sir John Lubbock, which indi- 
 cate peculiar contrivances for the destruction of insects. 
 The peculiarity of formation first suggested some such 
 end as this, which has since been proved by careful observa- 
 tion to be the case. “ The first observation on insect-eating 
 flowers was made about the year 1868 by Ellis. He ob- 
 served that in Dionvea, a North American plant, the leaves 
 have a joint in the middle, and thus close over, kill, and 
 1 Lubbock, Scientific Lectures, pp. 1, 2. 
 
ANALOGY 
 
 321 
 
 actually digest any insect which may alight on them. An- 
 other case is that of Utricularia, an aquatic species which 
 bears a number of utricles or sacs, which have been sup- 
 posed to act as floats. Branches, however, which bear no 
 bladders float just as well as the others, and there seems no 
 doubt that their real use is to capture small aquatic animals, 
 which they do in considerable numbers. The bladders, in 
 fact, are on the principle of an eel-trap, having an entrance 
 closed with a flap, which permits an easy entrance, but 
 effectually prevents the unfortunate victim from getting 
 out again. In the genus, Sarracenia, some of the leaves are 
 in the form of a pitcher. They secrete a fluid, and are lined 
 internally with hairs pointing downwards. Up the outside 
 of the pitcher there is a line of honey glands which lure the 
 insects to their destruction. Flies and other insects which 
 fall into this pitcher cannot get out again and are actually 
 digested by the plant .” 1 
 
 In the example where the idea of an eel-trap suggested 
 the possible function of the similar structure in the plant, 
 Utricularia, we find one of the most striking illustrations 
 of this mode of analogical inference. It was an easy and 
 natural transition from similarity of structure to similarity 
 of function. To give an idea of the great number of teleo- 
 logical phenomena in the vegetable and animal world, and 
 the wealth of possible suggestion stored away in these 
 various structures, and disclosed by a sagacious analysis, I 
 quote a remark of Sir John Lubbock’s in commenting upon 
 the variation of color and markings of caterpillars : “ I should 
 produce an impression very different from that which I 
 wish to convey, were I to lead you to suppose that all these 
 varieties have been explained or are understood. Far from 
 it ; they still offer a large field for study ; nevertheless, I 
 venture to think the evidence now brought forward, how- 
 ever imperfectly, is at least sufficient to justify the conclu- 
 sion that there is not a hair or a line, not a spot or a color, 
 
 1 Lubbock, Scientific Lectures, pp. 4, 5. 
 
322 
 
 INDUCTIVE LOGIC 
 
 for which there is not a reason, — which has not a purpose 
 or a meaning in the economy of nature.” 1 
 
 An illustration given by Darwin shows this mode of in- 
 ference applied to the sphere of animal life also. He says : 
 “ The great size of the bones of the megatherioid animals 
 was a complete puzzle to naturalists until Professor Owen 
 lately solved the problem with remarkable ingenuity. The 
 teeth indicate, by their simple structure, that these mega- 
 therioid animals lived on vegetable food, and probably on 
 the leaves and small twigs of trees ; their ponderous forms 
 and great, strong, curved claws seem so little adapted for 
 locomotion that some eminent naturalists have actually be- 
 lieved that, like the sloths, to which they are intimately 
 related, they subsisted by climbing back downwards on 
 trees, and feeding on the leaves. It was a bold, not to say 
 preposterous, idea, to conceive even antediluvian trees with 
 branches strong enough to bear animals as large as ele- 
 phants. Professor Owen, with far more probability, be- 
 lieves that, instead of climbing on the trees, they pulled 
 the branches down to them, and tore up the smaller ones by 
 the roots, and so fed on the leaves. The colossal breadth 
 and weight of their hinder quarters, which can hardly be 
 imagined without having been seen, become, on this view, 
 of obvious service, instead of being an encumbrance : their 
 apparent clumsiness disappears. With their great tails and 
 their huge heels firmly fixed like a tripod on the ground, 
 they could freely exert the full force of their most powerful 
 arms and great claws. Strongly rooted, indeed, must have 
 been that tree which could have resisted such force ! The 
 Mylodon, moreover, was furnished with a long extensile 
 tongue like that of the giraffe, which, by one of those beau- 
 tiful provisions of nature, thus reaches, with the aid of its 
 long neck, its leafy food .” 2 Throughout we observe ana- 
 logical inference based upon these teleological marks, and 
 furnishing a basis for a satisfactory hypothesis. 
 
 1 Lubbock, Scientific Lectures, pp. 60, 67. 
 
 2 Darwin, Voyage of a Naturalist, pp. 106, 107. 
 
ANALOGY 
 
 323 
 
 We see what a wide field thus opens in the region of 
 biology alone for the discovery of resemblances leading to 
 the appreciation of the fuller teleological significance of 
 plant and animal life. 
 
 In the illustrations given, both of the teleological and 
 other forms of analogy, we notice that its chief logical func- 
 tion is that of suggestion of some hypothesis which may or 
 may not be afterwards confirmed by subsequent experiment. 
 Some of the most important discoveries of science have 
 arisen from analogical suggestions. Sir John Herschel was 
 led by observed analogies to predict certain phenomena 
 afterwards verified experimentally by Faraday. Herschel 
 had noticed that a screw-like form, known as helicoidal dis- 
 symmetry, was observed in three cases, namely, in electrical 
 helices, plagihedral quartz crystals (that is, crystals having an 
 oblique spiral arrangement of planes), and the rotation of the 
 plane of polarization of light. As Herschel himself said : 
 “ I reasoned thus : Here are three phenomena agreeing in a 
 very strange peculiarity. Probably this peculiarity is a con- 
 necting link, physically speaking, among them. How, in 
 the case of the crystals and the light, this probability has 
 been turned into certainty by my own experiments. There- 
 fore, induction led me to conclude that a similar connection 
 exists, and must turn up, somehow or other, between the 
 electric current and polarized light, and that the plane of 
 polarization would be defected by magneto-electricity.” 
 Herschel thus anticipated Faraday’s experimental discovery 
 of the influence of magnetic strain upon polarized light. 1 
 
 Another important discovery — the germ-theory of epi- 
 demic disease — was first suggested by an analogy. In the 
 theory, as expressed by Kircher, and favored by Linnaeus, 
 and afterwards supported by Sir Henry Holland, its special 
 strength, according to Professor Tyndall, “ consisted in the 
 perfect parallelism of the phenomena of contagious disease 
 with those of life. As a planted acorn gives birth to an 
 1 Jevons, Principles of Science, p. 630. 
 
324 
 
 INDUCTIVE LOGIC 
 
 oak competent to produce a whole crop of acorns, each gifted 
 with the power of reproducing the parent tree, and as thus 
 from a single seedling a whole forest may spring, so, it is 
 contended, these epidemic diseases literally plant their seeds, 
 grow and shake abroad new germs, which, meeting in the 
 human body their proper food and temperature, finally take 
 possession of whole populations .” 1 
 
 The theory of evolution was first suggested to Mr. Darwin 
 by the analogous phenomena observed in artificial selection 
 and breeding. The transition to natural selection was easily 
 made, especially as, on reading Malthus, On Population, he 
 conceived the idea of a struggle for existence as the inevi- 
 table result of the rapid increase of organic beings. This 
 idea necessitated the natural selection, which he needed to 
 account for results similar to the artificial selection, and 
 thus his theory grew out of an analogy as its beginning. 
 Moreover, in the development of the theory in its manifold 
 details, other analogies proved also suggestive. For in- 
 stance, there is the supposed analogy between the growth 
 of a species and the growth of an individual. It supposes, 
 for example, as Professor Clifford has put it, “that the race 
 of crabs has gone through much the same sort of changes as 
 every crab goes through now, in the course of its formation 
 in the egg, — changes represented by its pristine shape 
 utterly unlike what it afterwards attains, and by its gradual 
 metamorphosis and formation of shell and claws .” 2 
 
 The germ-theory of putrefaction, first suggested by 
 Schwann, received confirmation through certain resem- 
 blances noted by Professor Lister between fermentation 
 and putrefaction. In his Introductory Lecture before the 
 University of Edinburgh, Professor Lister called attention 
 to the fact that fermentation and putrefaction present a 
 very striking parallel. In each a stable compound — sugar 
 in one case, albumen in the other — undergoes extraordi- 
 
 1 Tyndall, Fragments of Science, p. 287. 
 
 2 Clifford, Lectures and Essays, p. 86. 
 
ANALOGY 
 
 325 
 
 nary chemical changes under the influence of an excessively 
 minute quantity of a substance which, regarded chemically, 
 would be considered inert. It was pointed out also by 
 Professor Lister in this connection, that, as was well 
 known, one of the chief peculiarities of living organisms 
 is that they possess extraordinary powers of effecting 
 chemical changes in materials in their vicinity out of all 
 proportion to their energy as mere chemical compounds. 
 Such being the facts in the case, and, moreover, the fermen- 
 tation of sugar being generally allowed to be occasioned by 
 the presence of living organisms, Professor Lister’s infer- 
 ence was that putrefaction was due to an analogous 
 agency. 1 
 
 A discovery in quite a different sphere, that of mathe- 
 matics, leading to the branch of analytical geometry, was 
 first suggested to Descartes through observing the resem- 
 blances existing between geometry and algebra. In a sim- 
 ilar manner, Boole was led, by the resemblances noted 
 between algebra and logic, to give expression to the same 
 in a system which he called the laws of thought, and which 
 has become the basis of a general or symbolic logic. 
 
 While there are thus unquestionable evidences of the 
 value of analogy as a form of inference, there are also cases 
 of false analogy unfortunately so numerous as to discredit 
 the process wholly in some quarters. It will be well, there- 
 fore, to indicate some of the requirements of true analogy : — 
 
 1. In the first place the resemblance must be a prepon- 
 derating one ; that is, the phenomena compared must show 
 a more striking agreement than difference. Some writers 
 have balanced agreement against difference upon a purely 
 numerical basis of comparison, forming what may be 
 called an analogical ratio, with points of similarity forming 
 the numerator, and the points both of similarity and dif- 
 ference, plus the unknown, that is, the total number, form- 
 ing the denominator. Such a representation of the force of 
 1 Tyndall, Fragments of Science, pp. 300-302. 
 
326 
 
 INDUCTIVE LOGIC 
 
 an analogy is given by Mill, Bain, and others. I think, 
 however, that this representation is apt to be misleading 
 in producing the impression that the mere number of points 
 of agreement, irrespective of their significance, is the chief 
 feature of analogy. Whereas it is the weight of the agree- 
 ing attributes, and not the number, that counts. As has 
 been before said, in analogy we weigh instances, and 
 do not count them. The analogical ratio expressed nu- 
 merically, as above, is really equivalent to the ratio of 
 probability which will be described in the following chap- 
 ter. I have therefore changed the usual wording of this 
 requirement, so that it reads, the resemblances must be 
 more striking and more significant than the differences. 
 This provides for cases when perhaps a few points of resem- 
 blance will be of such a nature as to outweigh many points 
 of difference in the total estimate. 
 
 This requirement also excludes all fanciful analogies and 
 all resemblances resting upon a figurative rather than a real 
 basis. For instance, the advocates of annual Parliaments 
 in the time of the Commonwealth, urged their case on the 
 analogical ground that a body politic is similar to a living 
 body and that serpents annually cast their skin, which, 
 being no doubt for a beneficial purpose, might well be 
 imitated. 
 
 2. In noting the points of resemblance between two phe- 
 nomena, all circumstances which are known to be effects of 
 one cause must therefore be regarded not as many, but as 
 one. For instance, two chemical oxides may be compared; 
 the effects common to each may be due to the presence of 
 the oxygen which each contains, and therefore must not be 
 regarded in the light of independent marks of similarity. 
 
 3. If we infer by analogy that a substance possesses a 
 certain property which we know is incompatible with some 
 one or other known properties of the substance, the analogy 
 is at once discredited. We may infer that the moon is 
 inhabited, by virtue of the many points of resemblance 
 
ANALOGY 
 
 327 
 
 between the moon and the earth. However, the fact that 
 the moon has no atmosphere necessary to sustain life, at 
 once makes such an argument based upon analogy wholly 
 out of the question. 
 
 4. There are certain special requirements referring to 
 that particular form of analogy which is based upon teleo- 
 logical considerations. They are as follows : — 
 
 a. This principle must never be used as an argument 
 against an observed fact, or an established law of nature. 
 While this precaution is not necessary at the present time, 
 in scientific circles at least, still there was a time when its 
 counsel was sorely needed. When in astronomy it was 
 proved that there were suns gravitating around other suns, 
 without our solar system, this was objected to upon the fol- 
 lowing ground, as given by one Nicholas Fuss, a celebrated 
 astronomer, at the end of the eighteenth century: “ What is 
 the good of some luminous bodies revolving round others ? 
 The sun is the only source whence the planets derive light 
 and heat. Were their entire systems of suns controlled by 
 other suns, their neighborhood and their motions would be 
 objectless, their rays useless. The suns have no need to bor- 
 row from strange bodies what they themselves have received 
 as their own. If the secondary stars are luminous bodies, 
 what is the end of their motives ? ” 
 
 There is, moreover, another abuse of the principle of final 
 causes, which has also historic interest rather than any 
 present pertinence ; namely, opposing certain false teleolog- 
 ical ideas to established discoveries or inventions, with a 
 mistaken zeal, in defence of a Divine Providence. For 
 instance, at the time of Jenner’s great discovery, an English 
 physician, Dr. Rowley, said of smallpox : “ It is a malady 
 imposed by the decree of heaven, and vaccination is an 
 audacious and sacrilegious violation of our holy religion. 
 The designs of these vaccinators appear to defy heaven 
 itself, and the very will of God.” The introduction of 
 winnowing machines into Scotland met with bitter oppo- 
 
328 
 
 INDUCTIVE LOGIC 
 
 sition on the ground that the winds were the work of 
 God, and that the wind thus artificially raised was a ver- 
 itable “ devil’s wind,” as they were wont to call it. Sir 
 Walter Scott, in Old Mortality, has the old Mause say to 
 her mistress : “ Your ladyship and the steward are wishing 
 Cuddie to use a new machine to winnow the corn. This 
 machine opposes the designs of Providence, by furnishing 
 wind for your special use, and by human means, in place of 
 asking it by prayer, and waiting with patience till Provi- 
 dence itself sends it.” 
 
 b. Final causes should never be employed to explain phe- 
 nomena which do not exist. As M. Florens has said: “We 
 must proceed not from final causes to facts, but from facts 
 to final causes ; that is, we should not superimpose final 
 causes upon phenomena. We must see them in phenomena 
 themselves, and we must not arbitrarily project a teleologi- 
 cal idea, purely subjective, upon an objective ground. ' Thus 
 in ancient times, Hippocrates is said to ‘ have admired the 
 skill with which the auricles of the heart have been made 
 to blow the air into the heart.’ ” 
 
 c. We must distinguish accidental from essential marks 
 of finality, and not be led into fanciful or far-fetched anal- 
 ogies. Voltaire has expressed such a defect when in satire 
 he made that famous remark, “Noses are made in order to 
 bear spectacles.” 
 
 Bernardin de Saint-Pierre says : “ Dogs are usually of two 
 opposite colors, the one light, the other dark, in order that 
 whenever they may be in the house, they may be distinguished 
 from the furniture, with the color of which they might be 
 confounded. . . . Wherever fleas are they jump on white 
 colors. This instinct has been given them, that we may the 
 more easily catch them.” And again the same waiter says : 
 “ The melon has been divided into sections by nature, for 
 family eating .” 1 All such grotesque inferences will give 
 
 1 The illustrations upon the abuse of final causes I have taken from 
 Janet’s admirable chapter, — Chapter VIII of Appendix. 
 
ANALOGY 
 
 329 
 
 an idea of how readily the imagination will run riot if 
 allowed to remain uncurbed by the reason. 
 
 5. Analogy should never be regarded as having more 
 weight than that of extremely high probability, even in 
 cases seemingly most conclusive. Its true function as we 
 have seen is suggestive, leading to hypothesis and experi- 
 ment, and it needs this supplementary proof. It was an 
 inference based on analogy, for instance, which suggested 
 the probability that the Binomial Law, having proved to 
 be valid as regards the second, third, and fourth powers, 
 might also be extended to the fifth, and so on to the other 
 powers indefinitely. This suggestion offered no real basis, 
 however, upon which the Binomial Theorem could rest ; it 
 needed mathematical demonstration to confirm and general- 
 ize its expression in the special cases already experimentally 
 tested, so as to cover all possible exponents, both positive 
 and negative, fractional and integral. 
 
 So also the discovery of the circulation of the blood was 
 first suggested to Harvey, as has been said, by analogical 
 considerations upon observed teleological phenomena. Har- 
 vey, however, was not content with this suggestion merely. 
 He was led to experiment upon the veins and arteries ; he 
 tied an artery and vein, and carefully observed the mechani- 
 cal effects upon the two sides of the tied parts. Experi- 
 ments of this nature, with close observation and study, 
 were kept up most diligently, and with rare perseverance, 
 for nineteen years, before he had traced the entire course 
 of the blood through all parts of the human body, and, in 
 a manner wholly satisfactory to himself, verified the first 
 statement of this theory. 
 
CHAPTER XIV 
 
 PROBABILITY 
 
 There are certain phenomena of such a nature that their 
 antecedents, being extremely complex, cannot be adequately 
 comprehended by observation, however searching it may be ; 
 nor can they be subjected to any analysis that will disclose 
 the causal elements to which the effect in question is due. 
 Moreover, with seemingly the same antecedents, the event 
 sometimes happens, and sometimes does not ; and even with 
 antecedents associated with an event as cause and effect 
 respectively, nevertheless the event does not occur as we 
 should naturally expect, while with antecedents associated 
 with the contradiction of the event as cause and effect 
 respectively, we find the occurrence of the event quite 
 contrary to what we should naturally expect. The evi- 
 dence of a constant connection between antecedent and 
 consequent, that we have found in so many cases which we 
 have examined, is here wholly lacking. Regularity has 
 been replaced by irregularity respecting such phenomena. 
 For instance, I throw dice repeatedly; the antecedent 
 shaking of the box, and tossing the dice upon the table, 
 is about the same each time, at least the difference can- 
 not be determined, and yet the results vary with each 
 successive throw. The causal determination in each case is 
 so complex as to be beyond computation; the initial posi- 
 tion of the dice, the force of their ejection from the box, 
 the height of the box above the table when they leave it, 
 the inequalities of the table itself, a variation between the 
 physical and geometrical centres of gravity of the dice, etc., 
 all these make the antecedent so complex that a slight vari- 
 
 330 
 
PROBABILITY 
 
 331 
 
 ation in any one of these conditions will affect the result. 
 We find, therefore, double sixes at one time, a three and 
 four at another, and so on indefinitely. 
 
 Or, again, it sometimes happens that with perfect sanitary 
 conditions a contagious disease will appear, that has always 
 been regarded, and that correctly, as due to imperfect sani- 
 tation ; or, an entire disregard of sanitary requirements and 
 of all the laws of health may yet give rise to no disease of 
 special moment. Certain conditions of temperature, atmos- 
 pheric pressure, velocity and direction of the wind, may one 
 day bring storm and rain, and as far as observation can 
 detect, similar conditions may again bring fair weather. 
 So, also, the rise and fall in stock and money markets is 
 extremely susceptible to the varying conditions of indefi- 
 nitely complex forces wholly beyond all powers of deter- 
 mination or of prediction. Such phenomena present a 
 problem which the methods of inductive inquiry cannot 
 deal with. Observation is not far-reaching enough to pro- 
 vide the data for the solution of the problem, and, even if 
 it were, our methods of computation and determination are 
 not sufficiently adequate to solve problems of so many terms 
 and of so complex a nature. 
 
 The experimental methods are designed to test causes 
 suggested by analogy, or by mental analysis; but in such 
 phenomena as these, the problem is not simply to find a 
 causal connection. The causal connection may be estab- 
 lished beyond all reasonable doubt, and yet the cause ob- 
 tains in the midst of so complex a setting that the problem 
 is really this, — to determine whether a cause, whose exact 
 nature may be known or unknown, will prove operative or 
 inoperative. The cause may be always present and even its 
 exact nature may be known, and yet the complex circum- 
 stances attending it may be of such a character that one 
 alone, or two or more combining, may neutralize the opera- 
 tion of the cause, and on the other hand a slight variation 
 of the combined circumstances may promote and even 
 
832 
 
 INDUCTIVE LOGIC 
 
 accelerate the operation of the cause in question. The 
 problem then is to determine how often the event happens, 
 and how often it fails of happening, the complex and in- 
 determinate antecedent being present in all the instances 
 examined. 
 
 When we begin to count instances, we are reminded that 
 we must be in the near neighborhood of the sphere of 
 enumerative induction. Enumerative induction, it will 
 be remembered, treats instances by noting the number of 
 observed coincident happenings of the antecedent and con- 
 sequent under investigation, no attempt being made to 
 analyze their respective contents, or to determine a causal 
 connection more definitely by means of any one or more of 
 the inductive methods of research and verification. The 
 result of such an investigation may be formulated in a 
 proposition of the form, Every A is B. This, strictly inter- 
 preted, has the force of, Every A that has been observed is 
 B. The enumeration of the kind of instances which we are 
 discussing in this chapter, however, differs from this in 
 that the observation leads to a twofold result, — a set 
 of instances in which it is observed that the _4’s are B’s 
 also, another set however in which the ,4’s are not B’s. 
 These instances are of such a nature that the observed A 
 is an antecedent so extremely complex that the element 
 within it, which is a cause capable of producing B, may 
 either be absent without producing an appreciable change 
 in the general nature of A, or, being present, may be neutral- 
 ized by some other element of A itself. The result gives 
 a basis for a probable inference only ; and the nature of 
 that inference will depend upon the preponderance of the 
 observed happening, or of the failure of the event under 
 investigation. 
 
 The probability attached to such an inference, however, 
 is different from the probability which characterizes the 
 nature of enumerative induction. In the latter, when the 
 observation has been widely extended and no exceptions 
 
PROBABILITY 
 
 333 
 
 noted, it is usual to say the result expressed in the propo- 
 sition, Every A is B, has the force of a high degree of 
 probability. In the instances, however, whose investigation 
 shows the result that some H’s are B’s, and some not, and 
 yet where the former, for instance, far outnumber the latter 
 cases, then it may be inferred that the A’s which in future 
 we may meet with will probably be B’s ; and the degree of 
 probability expressed in such a proposition is commensurate 
 with the preponderance of the number of observed affirm- 
 ative instances over the negative. Here the probability 
 refers to the validity of an inference concerning certain 
 particular instances, be they many or be they few, which 
 lie beyond the sphere of our present knowledge; in enu- 
 merative induction, the probability is attached to the uni- 
 versality of the proposition affirmed as a result of observation 
 that has not so far detected an exception. In the former 
 case, the question of the universality of the result is con- 
 clusively answered, and that in the negative ; there can be 
 no universal proposition possible, as some instances give 
 A and B together, others give A with the absence of _B; 
 and the question of probability that here arises, therefore, 
 refers to individual cases not yet examined, as to whether 
 they severally will more likely correspond to the set of 
 affirmative, or to that of the negative, instances already 
 noted. 
 
 The comparison of the number of happenings with that 
 of the failures of an event affords a basis for three kinds of 
 inference, all of them in the sphere of probability. 
 
 1. We find in such a comparison a basis for the calcula- 
 tion of the probability of a particular event happening, in 
 case there is a repetition of the circumstances which, in 
 former cases, have sometimes produced the event, and some- 
 times have failed to produce it. If, according to former 
 observation, the event has happened, let us say, seven times, 
 and failed three, the probability, expressed numerically, 
 of its happening again is ^ . The rule is, to express the 
 
334 
 
 INDUCTIVE LOGIC 
 
 probability of an event, take as numerator the number of 
 times which the event has been observed to occur, and as 
 denominator the total number observed, both of happening 
 and failure ; the fraction thus expressed will represent the 
 probability of the event happening. The counter-probability 
 may be represented by the number of observed failures of 
 the event divided by the total number of cases observed. 
 The counter-probability, plus the probability, evidently is 
 equal to unity. If, therefore, the probability is unity, the 
 counter-probability will equal zero ; that is, the probability 
 in that case has merged into certainty. Zero, therefore, 
 represents absolute impossibility. All fractions between 
 the limits zero and one represent varying degrees of proba- 
 bility from impossibility at one extreme to certainty at the 
 other. 
 
 Not only may there be this inductive basis for the cal- 
 culation of probability, arising from actually observed in- 
 stances; there may be also a deductive calculation of 
 probability based upon the known structure or nature of 
 the phenomena themselves in advance of any observation as 
 to their actual behavior. For instance, we say the proba- 
 bility of a penny turning up heads is Knowing the 
 form of the penny and that there are but two possibilities, 
 heads or tails, and there being no reason why one should 
 more likely turn up than the other, we say there is one 
 chance favorable to heads as over against the two chances 
 which represent the total number of possibilities under the 
 existing circumstances. With a die, in the form of a per- 
 fect cube, we say there is one chance of its turning up the 
 face marked 1 , as over against the six chances represented 
 by the six faces, the total number ; here the probability is 
 4. Thus the basis for the calculation of probability may be 
 a theoretical as well as an empirical one. 
 
 In the estimate of the probability of an event in the 
 actual conduct of affairs, we seldom express that probabil- 
 ity numerically. I would say that we express a degree of 
 
PROBABILITY 
 
 335 
 
 probability adverbially rather than numerically ; that is, we 
 say an event is quite probable, or it is very probable, or it is 
 extremely probable. The fact is that, as regards most phe- 
 nomena, we do not keep an exact or even approximate memo- 
 randum of the number of happenings compared with that of 
 the failures. We rather classify our observations in terms 
 of more or less. For instance, certain circumstances we 
 observe produce about as many failures as happenings of 
 an event; other circumstances produce far more happenings 
 than failures ; others far less, and so on. Consequently we 
 receive certain psychological impressions of varying degrees 
 of intensity according to the preponderance of happening 
 over failure, or vice versa; this impression becomes the 
 basis for estimating the probability in question, and the 
 degree of that probability is commensurate with the inten- 
 sity of the original psychological impression arising from 
 concepts of more or of less. In such a sphere, however, as 
 that devoted to the interests of betting, gambling, pool-sell- 
 ing, book-making, etc., probabilities are estimated according 
 to statistical observations and theoretical considerations, 
 whose conditions are expressed numerically ; and the amount 
 risked in each case is strictly estimated according to the 
 exact ratio of probability to counter-probability under the 
 existing circumstances. 
 
 The estimation of probability in terms of a greater or 
 less degree is however more usual, and applicable to the 
 conduct of human life generally. It has special force and 
 utility as a mode of inference, when the observed instances 
 so far outnumber the exceptions as to create an impression 
 of such a high degree of probability as to approximate prac- 
 tical if not theoretical certainty. For instance, it has been 
 noted over a wide field of observation, that a second attack 
 of scarlet fever is extremely rare. Exceptions have occurred 
 and therefore by enumerative induction it is impossible to 
 generalize the universal proposition that a second attack 
 will never occur. It is however possible to assert with 
 
336 
 
 INDUCTIVE LOGIC 
 
 somewhat positive assurance that it is highly probable that 
 a person will be exempt from a second attack. 
 
 Or, yon hear that a person, whose name is unknown to 
 you, has met with an accident in the city of New York, 
 resulting fatally. You are not alarmed, and perhaps the 
 possibility does not even suggest itself to you, that the un- 
 known person may prove to be a member of your own family, 
 or a friend who at the time is known to be in New York. 
 The probability against such a suggestion is so large as to 
 preclude even the thought of it. Suppose, however, the 
 accident occurred at one of the suburban stations. Your 
 knowledge that your friend rides on one of the suburban 
 trains each day to and from town, may be the ground of 
 some anxiety, because in this case the range of possibilities is 
 materially narrowed. Suppose, moreover, that the station 
 where the accident occurred is at the village where your 
 friend resides, your anxiety receives an additional increment ; 
 and, again, suppose it is at the hour at which your friend 
 ordinarily reaches this station, there is then increased appre- 
 hension on his account. Thus, as further knowledge limits 
 the number of total possible cases, the denominator of the 
 probability fraction is continually decreasing, and therefore 
 the probability itself continually increases, until it has 
 developed from a fraction of insignificant proportions to 
 one which is suggestive of great anxiety and suspense. 
 
 2. The comparison of failure and happening of events 
 based upon observation, or theoretical considerations of 
 structure and nature, leads also to inferences concerning 
 large numbers of instances considered together. If a 
 memorandum is kept of the number of times an event has 
 happened, and the number of times it has failed, and the 
 total number of instances examined be sufficiently great, 
 then the resulting ratio of favorable instances to the total 
 number will be found approximately repeated, if a second 
 set of an equal number of instances be likewise examined. 
 There is a law of tendency whereby nature seems to repeat 
 
PROBABILITY 
 
 337 
 
 herself even when the attendant circumstances of an event 
 are most complex, and beyond all powers of accurate deter- 
 mination. As the result of observations extending over 
 thousands and thousands of instances, it is affirmed that 
 about one-fourth of .the children born in the world die be- 
 fore the age of six years, and about one-half before the age 
 of sixteen. Take a group of ten children, the ratios would 
 perhaps be deviated from very materially ; in a group of a 
 hundred the deviation is apt to be less; in a group of a 
 thousand, still less ; and in a group of one hundred thou- 
 sand, the ratios as above given would be substantially real- 
 ized. The approximation would be so near that the error 
 would be insignificant as compared with total number of 
 cases. The following law, therefore, expresses this ten- 
 dency, — that while in a small number of instances there is 
 irregularity in the observed ratio between the number of 
 times a given event has happened and its failures, still in a 
 large number of instances this ratio tends toward a constant 
 limit. This is clearly seen in the pitching of a penny ; 10 
 throws might very possibly result in 7 heads and 3 tails ; 
 in 100 throws, however, the ratio expressing the result as 
 to heads and tails observed will be much nearer 1- than in 
 the former case ; while if 1000 or 10,000 throws be observed, 
 the result will approximate the ratio i. The comparison of 
 observed cases with the number given by the calculation of 
 the probabilities in question has been made by Quetelet, 
 also by Jevons, Their results are most significant and in- 
 teresting. Quetelet made 4096 drawings from an urn con- 
 taining 20 black balls and 20 white. Theoretically, he 
 should have drawn as many white as black balls, 2048 each ; 
 the actual drawings resulted in 2066 white balls and 203C 
 black. Jevons made 20,480 throws of a penny; the theo- 
 retical result should have been 10,240 heads ; the actual 
 result was 10,353 heads. 
 
 The tendeucy towards a constant ratio in aggregates con- 
 taining a considerable number of instances is strikingly 
 
338 
 
 INDUCTIVE LOGIC 
 
 illustrated in the record of baptisms taken from an old par- 
 ish register in England. The number of male baptisms 
 registered to every 1000 female ran as follows for the re- 
 spective years from 1821 to 1830 : 1048, 1047, 1047, 1041, 
 1049, 1046, 1047, 1043, 1043, 1034. We see with what sur- 
 prising accuracy the constant ratio was repeated substan- 
 tially, year after year. This tendency to approximate a 
 constant ratio is seen even in such indeterminate events as 
 railroad accidents. Here the causes producing the accidents 
 are so numerous, so diverse, so complex and extending over 
 so large an area, — as, for example, the whole of the United 
 States, — that we should think that the results would ex- 
 hibit so many variations from any definite ratio as abso- 
 lutely to elude all attempts at accurate determination. The 
 figures on pages 339 and 340, however, given by the Inter- 
 state Commerce Commission, indicate results wonderfully 
 corresponding for year after year. 
 
 An examination of these figures will disclose the fact that 
 there is a striking approximation to an accurately propor- 
 tionate distribution of the number of accidents, of the killed 
 and of the injured, throughout these several years. It will 
 be noticed, also, that the distribution among employees, pas- 
 sengers, other persons, etc., tends toward a regularity that 
 is remarkable when we consider the extreme complexity of 
 the circumstances that must combine to produce these re- 
 sults. A like regularity seems to pervade every department 
 of life. The total number of crimes is approximately the 
 same, year after year ; the annual death-rate, the appor- 
 tionment of deaths, moreover, to the several diseases as 
 their evident causes, the number of missent letters that 
 reach the Dead-Letter Office at Washington each year, the 
 annual number of suicides, of divorces, all these diverse 
 events indicate a regularity, in the long run, as regards their 
 numerical estimate. 
 
 The results which are thus attained regarding aggregates 
 cannot be stated as probable results merely. If a sufficiently 
 
RAILROAD ACCIDENTS IN THE UNITED STATES 
 
 PROBABILITY 
 
 339 
 
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340 INDUCTIVE LOGIC 
 
 Average per year for five years. 
 
PROBABILITY 
 
 341 
 
 large number of instances are taken, the result will be cer- 
 tain within a very small, and in many cases an insignificant, 
 margin. In estimating the probability of a single event, 
 the question is whether it will happen or not happen, and 
 the element of uncertainty is therefore prominent. In deal- 
 ing with aggregates, however, no such element of uncer- 
 tainty enters ; the question is not whether or not there will 
 be certain results, the question concerns rather the degree 
 of exactness with which the results will approximate a 
 definite ratio. And the law of tendency is, that the larger 
 the number of instances, the greater will be the approxima- 
 tion to an accurate and definite result. 
 
 This is especially illustrated in the numerous insurance 
 companies, whose business is conducted upon the basis of an 
 approximately constant death-rate. For instance, the gen- 
 eral procedure is somewhat as follows: Suppose 10,000 
 persons insure their lives at $1000 per individual, and the 
 annual death-rate observed over a rude extent of territory, 
 and including a very large number of instances, amounts to 
 200 persons out of 10,000. The losses then to the insurance 
 company will amount annually to $200,000 on such a basis. 
 These losses, distributed among the 10,000 insuring in the 
 company, would amount to $20 apiece. The company, 
 therefore, has a numerical basis for calculating the amount 
 which each person must pay in order to cover the annual 
 losses and provide an assured revenue for the company. 
 
 I have, of course, stated the problem in round numbers, 
 merely to illustrate in general the principle involved ; the 
 actual calculation is more complicated, because, in each 
 particular case, the age of the individual and the varying 
 death-rates for different years must be taken into account. 
 The substantial standing of the innumerable insurance com- 
 panies in our country bears witness to the fact that these 
 enterprises are based upon a practical certainty regarding 
 death-rates when applied to large aggregates. Chance is 
 thus eliminated almost entirely ; that which would be a 
 
342 
 
 inductive logic 
 
 serious risk as regards an individual is substantially void 
 of all risk when large numbers are concerned. 
 
 Moreover, statistics covering different classes are often 
 most valuable in indicating tendencies operative in the 
 classes when compared one with another. According to 
 M. Loua ( Economiste Frangais, 1882, Vol. I, p. 179), the fol- 
 lowing are the figures of the annual mortality in Paris : — 
 
 The rich and well-to-do classes, 156 out of every 10,000 inhabitants. 
 The poor, 285 out of every 10,000 inhabitants. 
 
 So also, in England, the average duration of life among 
 the wealthy classes is from 55 to 56 years ; for the working 
 classes it falls to 28 years, or even lower. 1 Such compari- 
 sons are significant in indicating underlying forces in society 
 that otherwise might be overlooked, or, at least, not ade- 
 quately appreciated, and which a limited observation could 
 not accurately reveal. Mr. Darwin, after observing and ex- 
 perimenting upon a very large number of plants, found the 
 following figures respecting the relative productivity of cross 
 and spontaneously self-fertilized flowers : As regards the 
 number of seeds per pod yielded by cross and self-fertilized 
 flowers, the ratio was 100 to 41 respectively ; the crossed 
 seeds compared with an equal number of the spontaneously 
 self-fertilized seeds were heavier, in the ratio of 100 to 88. 2 
 The ratios thus disclosed in examining a large number of 
 instances could not have been gained by any experimen- 
 tal method adapted for dealing with individual instances. 
 Although the cause is not quantitatively determined, a 
 tendency of a constant nature toward a definite end is 
 clearly indicated. 
 
 Race characteristics are often disclosed by comparative 
 statistics, and the presence or absence of causes possessing 
 moral significance are thus revealed which otherwise could 
 
 1 Gide, Political Economy , p. 405. 
 
 2 Darwin, Cross and Self Fertilization, p. 165. 
 
PROBABILITY 
 
 343 
 
 not be determined with any considerable degree of definite- 
 ness. The following tables will indicate this : — 
 
 Suicides. — In European cities the number of suicides per 
 
 100.000 inhabitants is as follows : Paris, 42 ; Lyons, 29 ; 
 St. Petersburg, 7 ; Moscow, 11 ; Berlin, 36 ; Vienna, 28 ; Lon- 
 don, 23 ; Pome, 8 ; Milan, 6 ; Madrid, 3 ; Genoa, 31 ; Brussels, 
 15 ; Amsterdam, 14 ; Lisbon, 2 ; Christiania, 25 ; Stock- 
 holm, 27 ; Constantinople, 12 ; Geneva, 11 ; Dresden, 51. 
 Madrid and Lisbon show the lowest, Dresden the highest, 
 figure. 
 
 The average annual suicide rate in countries of the world 
 per 100,000 persons living is given by Barker as follows : 
 Saxony, 31.1 ; Denmark, 25.8 ; Schleswig-Holstein, 24.0 ; 
 Austria, 21.2 ; Switzerland, 20.2 ; France, 15.7 ; German 
 Empire, 14.3; Hanover, 14.0; Queensland, 13.5; Prussia, 
 13.3; Victoria, 11.5; Hew South Wales, 9.3; Bavaria, 9.1 ; 
 Hew Zealand, 9.0; South Australia, 8.9; Sweden, 8.1 ; Hor- 
 way, 7.5 ; Belgium, 6.9 ; England and Wales, 6.9 ; Tasmania, 
 5.3; Hungary, 5.2 ; Scotland, 4.0; Italy, 3.7; Hetherlands, 
 3.6 ; United States, 3.5 ; Russia, 2.9 ; Ireland, 1.7 ; Spain, 1.4. 
 
 The causes of suicide in European countries are reported 
 as follows : Of 100 suicides : Madness, delirium, 18 per cent ; 
 alcoholism, 11 ; vice, crime, 19 ; different diseases, 2 ; moral 
 sufferings, 6 ; family matters, 4 ; poverty, want, 4 ; loss of 
 intellect, 14 ; consequence of crimes, 3 ; unknown reasons, 19. 
 
 Homicides. — Italy takes the lead of European nations, 
 with an average annual crop of murders of 2470, a ratio per 
 
 10.000 deaths of 29.4 ; Spain follows, with a ratio of 23.8, 
 and 1200 murders ; Austria, ratio of 8.8, and 600 murders ; 
 France, ratio of 8.0, and 662 murders; England, ratio of 7.1, 
 and 377 murders. The figures, however, represent actual 
 murders, not homicides from all causes, as do those in the 
 United States table. 
 
 Illegitimacy. — Of each 1000 births, the number illegiti- 
 mate, according to statistics published in London, 1892, 
 
344 
 
 INDUCTIVE LOGIC 
 
 were : Russia, 27 ; Ireland, 28 ; Holland, 33 ; England and 
 Wales, 46; Switzerland, 47; Italy, 73; Norway, 74; Scot- 
 land, 79; Prussia, 80; France, 84; Hungary, 85 ; Belgium, 
 88 ; Denmark, 93 ; Sweden, 101 ; Saxony, 125; Bavaria, 141 ; 
 Austria, 147. No accurate statistics for the United States 
 exist. The lowest rate in Europe is that of Connaught, in 
 Western Ireland, 7 per 1000. — Dr. Albert Leffingwell, Sum- 
 mit, N.J. 
 
 3. When phenomena indicate a marked departure from 
 the ratio of frequency as determined by prior observation, 
 or by theoretical considerations, then it is ordinarily inferred 
 that a new cause has become operative, which was not before 
 existent, or, whose effect had been neutralized. For instance, 
 we would naturally expect a die to show the face three, on 
 an average, about once in six throws. But if it repeatedly 
 turns up three in succession, and no other number appears, 
 or appears but rarely, we are warranted in inferring that 
 the die is loaded. The number of homicides in the United 
 States in 1894 far exceeded the annual number observed for 
 the several years preceding. This discrepancy is easily ac- 
 counted for by the fact that the natural number was swollen 
 by the deaths caused by the strikers and rioters in the 
 month of July of that year. So also a marked departure 
 from the annual death-rate of such a city as New York is at 
 once an urgent suggestion to the Board of Health to start 
 investigations that will unearth the hidden cause that one 
 is constrained to believe must be present. Such causes as 
 defective drains, prevalence of epidemics, etc., are again 
 and again found to accompany an increase of the average 
 death-rate. 
 
 Under such circumstances, the method of investigation, 
 when practicable, which should be pursued, is to endeavor 
 to break up the total into smaller groups of a specific nature. 
 Thus, if the death-rate for the year is appreciably increased, 
 examine the death-rate per month. See if any month shows 
 
PROBABILITY 
 
 345 
 
 a marked departure from the average. If so, this will sug- 
 gest a careful investigation of the circumstances and char- 
 acteristics of the month in question. Or it may be possible 
 to make a geographical distribution of the total over differ- 
 ent sections of the city under investigation. Some special 
 locality may indicate an unusually large death-rate. Inves- 
 tigation, therefore, at that point may reveal a lurking cause 
 of disease, otherwise unnoticed. 
 
 By similar considerations, also, it is often possible to dis- 
 tinguish between a chance coincidence, and a determinate 
 cause which may have produced the event in question. For, 
 if the possibility of some one definite cause is considered out 
 of the question, and the origin of the event is found among 
 complex phenomena of such a number and variety that they 
 may form an indefinite number of combinations, only one 
 of which can possibly produce the event in question, then 
 the probability that the event has actually been produced 
 by such a chance combination is extremely small. We are 
 then thrown back upon the other hypothesis, that, instead 
 of one out of many possible combinations, there is some one 
 determinate cause operative in the case. Its nature may 
 not be definitely indicated, but at least the possibility of 
 its presence is suggested. 
 
 This line of reasoning is illustrated in the following ac- 
 count of the discovery of the existence of iron in the sun, 
 in the researches of Bunsen and Kirchhoff : “ On comparing 
 the spectra of sunlight and of the light proceeding from the 
 incandescent vapor of iron, it became apparent that at least 
 sixty bright lines in the spectrum of iron coincided with 
 dark lines in the sun’s spectrum. Such coincidences could 
 never be observed with certainty, because, even if the lines 
 only closely approached, the instrumental imperfections of 
 the spectroscope would make them apparently coincident, and 
 if one line came within half a millimetre of another, on the 
 map of the spectra, they could not be pronounced distinct. 
 Howthe average distance of the solar lines on Kirchhoff’s map 
 
346 
 
 INDUCTIVE LOGIC 
 
 is two millimetres, and if we throw down a line, as it were 
 by pure chance, on such a map, the probability is about i 
 that the new line will fall within one-half millimetre on 
 one side or the other of some one of the solar lines. To 
 put it in another way, we may suppose that each solar line, 
 either on account of its real breadth, or the defects of the 
 instrument, possesses a breadth of one-half millimetre, and 
 that each line in the iron spectrum has a like breadth. The 
 probability, then, is just \ that the centre of each iron line 
 will come by chance within one millimetre of the centre of 
 a solar line, so as to appear to coincide with it. The prob- 
 ability of casual coincidence of each iron line with a solar 
 line is in like manner i. Coincidence in the case of each 
 of the sixty iron lines is a very unlikely event if it arises 
 casually, for it would have a probability of only (^j 60 or 
 less than one in a trillion. The odds, in short, are more 
 than a million million millions to unity against such a cas- 
 ual coincidence. But on the other hypothesis, that iron 
 exists in the sun, it is highly probable that such coincidences 
 would be observed; it is immensely more probable that sixty 
 coincidences would be observed if irop existed in the sun, 
 than that they should arise from chance. Hence, by our 
 principle, it is immensely probable that iron does exist in 
 the sun.” 1 
 
 This principle is also illustrated in instances of circum- 
 stantial evidence. In such cases, the observed combination 
 of so many diverse circumstances, even as regards an indefi- 
 nite number of minor details, precludes the hypothesis of 
 casual coincidence, and suggests some one definite cause 
 that will prove a unifying principle of explanation of all 
 the attendant circumstances. As Mr. Justice Bullen says: 
 “ A presumption which necessarily arises from circum- 
 stances is very often more convincing and more satisfactory 
 than any other kind of evidence. It is not within the 
 reach and compass of human abilities to invent a train of 
 1 Jevons, Principles of Science, pp. 244, 245. 
 
PROBABILITY 
 
 347 
 
 circumstances which shall be so connected together as to 
 amount to a proof of guilt without affording opportunities 
 to contradict a great part, if not all, of these circumstances.” 
 
 The following account, taken from The New York Law 
 Journal, illustrates the probative force of circumstantial 
 evidence : — 
 
 In Nicholas v. Commonwealth (March 1895, 21 S. E. R. 364) the 
 Supreme Court of Appeals of Virginia sustained a conviction of mur- 
 der, the criminal agency being established by circumstantial evidence. 
 The following extract from the opinion presents the main facts which 
 implicated the defendant : — 
 
 “ On the 8th day of December, 1892, Philip Norman Nicholas, the 
 plaintiff in error, one James Mills, and his wife, Anna A. Mills, and 
 their three small children, were living in the upper part of Henrico 
 County, on a farm known as the ‘ Wickham Place,’ about one mile 
 from James River. Nicholas was the renter of this farm, and culti- 
 vated it on shares. He was himself, however, chiefly engaged as a 
 trapper, having a number of traps set along both sides of the river. 
 He employed James Mills, with whom he lived, and one William Jud- 
 son Wilkerson, as sub-tenants, to do the farm work, for a portion of 
 his share of the crops. Wilkerson lived with an aged mother in a 
 small house very near to Mills’s house — near enough to see into the 
 windows of one house from the other. Philip N. Nicholas, the pris- 
 oner, was an unmarried man, and lived in a room of the house occu- 
 pied by James Mills and his family. The evidence shows that on the 
 night before the drowning, the prisoner, James Mills, and William J. 
 Wilkerson were together at the house of Mrs. Wilkerson, the latter’s 
 mother, and there arranged and determined upon a trip across the 
 river the next morning, to take a bee tree. This expedition was sug- 
 gested, planned, and carried out by the prisoner. Wilkerson was very 
 unwilling to go, and finally consented at the suggestion of his mother, 
 who said that, as Mr. Nicholas seemed so anxious for him to go, he 
 had better do so. Mills was unwilling to go unless Wilkerson went. 
 Wilkerson said he would rather plough than go. The prisoner replied, 
 ‘ If you will go, you shall not lose anything.’ In the course of con- 
 versation which resulted in this expedition being agreed upon, both 
 Mills and Wilkerson stated, in the presence of Nicholas, that they 
 could not swim, and were very much afraid of water ; that they did 
 not like water more than knee-deep. The fact that they could not 
 swim was generally known to their friends. It is further shown that 
 
348 
 
 INDUCTIVE LOGIC 
 
 it was the habit of Nicholas to go every morning, early, to the river, 
 to examine his traps. And it appears from the evidence that on the 
 morning of the day the drowning occurred he went to the river about 
 daylight, and returned about breakfast time, and, when questioned 
 about it, said: ‘ I did not go to my traps this morning. I was sick.’ 
 He afterwards told Mrs. Wilkerson he did not catch anything. 
 Everything being in readiness to carry out the plan for the day, 
 these three men started from home about nine o’clock in the morning, 
 equipped with everything necessary for taking the bee tree ; having 
 with them two buckets holding two and one-half to three gallons each for 
 the honey, two axes, one hatchet, and a piece of netting to protect the 
 person from the bees. The boat used belonged to one Joseph Bruin, 
 and on their way to the river an uncle of the owner was asked if they 
 might use the boat, and was told they could get the key which un- 
 locked the boat from its fastening to the bank from Bruin, the owner. 
 The prisoner replied that he had a key of his own, and had often used 
 it before without permission. It appears that they landed on the 
 Chesterfield side of the river, at a point one mile and a half from 
 where any one lived, and proceeded to the bee tree, which was one 
 mile from the point of landing. Investigation showed that there were 
 no tracks about the point of landing but those of the three men going 
 from and returning to the boat. It further appears from the state- 
 ment of the prisoner that after reaching the tree they concluded not 
 to cut it, because it was a large tree, near the main road, and might 
 get them into trouble, and for the farther reason that the hole was 
 small, and it might not have any honey in it anyhow. The tree was 
 afterwards cut by order of the Magistrate and found to be full of 
 honey. It further appears that the boat was a small one, about ten 
 feet long and about two and one-half feet wide, and that both in going 
 over and returning the prisoner sat in the extreme rear of the boat, 
 with his face to the front, and that Wilkerson and Mills sat in front 
 of him, with their faces to the front and their backs to the accused. 
 This position of the parties the prisoner admitted very reluctantly, 
 when questioned about it. When returning, and about fifty yards 
 from the Henrico shore, the boat suddenly filled with water, and Mills 
 and Wilkerson were drowned, and the prisoner swam to shore. The 
 next day the Magistrate of the district was notified of the occurrence, 
 and an investigation was set on foot. The boat was gotten out of the 
 water, and it was found that immediately under the seat where 
 Nicholas sat there were three holes, freshly bored with an inch and a 
 half auger. The evidence of the owner of the boat shows that on 
 Tuesday evening, the 6th of December, he used his boat, and it was 
 
PROBABILITY 
 
 349 
 
 sound. It was taken by Nicholas for this fatal trip Thursday morn- 
 ing, the 8th of December. Further investigation discovered fresh pine 
 shavings corresponding to size of the holes and to the wood the boat 
 was made of, which had been thrown into the water, but had drifted 
 upon the shore near the point where the boat had stood fastened to 
 the Henrico side. There were also found corn-cobs which had been 
 cut to exactly fit the holes in the boat, which had also drifted to the 
 same point. It was shown that the prisoner had in his possession an 
 auger just the size of the holes. This the prisoner at first denied, but 
 afterwards said that it must be about the place somewhere. Diligent 
 search was made for the auger, but it was never found. 
 
 “ Taken together, the case is an interesting illustration of the con- 
 clusive probative force of circumstantial evidence, provided there is 
 enough of it. The old saying that ‘ murder will out ’ is almost unex- 
 ceptional^ true as to murders of elaborate stealth and complexity of 
 detail. Once let a clue be obtained to the chain of causation and 
 motive, and the mystery unravels almost of itself. It is quite natural 
 that most of the elaborately planned murders of recent times should 
 have been by poison. And the Harris, Buchanan, and Meyer cases 
 in New York disclose how comparatively easy detection and convic- 
 tion are in crimes of such class. It is significant that two of the great- 
 est enigmas in American criminal annals during the last quarter of a 
 century have been the Nathan murder and the Borden murder. In 
 both cases the killing was done not by methods calculated to conceal 
 the agency of a murderer, but in the most primitive and brutal man- 
 ner. No traceable physical clue to any particular person was left, and 
 we are inclined to believe that in both cases the connection of the mur- 
 derer with the crime was merely casual or accidental.” 1 
 
 In the various illustrations which have been given we find 
 that the theory of probability provides a method of dealing 
 with phenomena which cannot be subjected to the ordinary 
 inductive methods. The phenomena are so complex that a 
 specific cause cannot be determined, for the real cause in 
 question is a correlation of many diverse forces, and if only 
 a few instances are examined no causal connection will be 
 disclosed; it is necessary, therefore, to deal with large 
 numbers, statistical averages, etc., in order to detect an 
 emerging relation of a causal character, expressed by a 
 
 1 The New York Law Journal, Thursday, May 2, 189o. 
 
350 
 
 INDUCTIVE LOGIC 
 
 constant ratio. This ratio once determined, it becomes a 
 further test, as we have already seen, when the results 
 widely depart from it, to suggest the presence of a new 
 force outside of the combinations to which the effect would 
 be naturally referred according to the indications of the 
 probability-ratio. This latter mode of inference is akin to 
 the method of residues, for the inference in question is 
 based upon the fact that the probability-ratio will account 
 for only a certain frequency of occurrence of the event 
 under investigation ; a marked excess must be accounted 
 for by positing a definitely operative cause. And if an 
 antecedent of such a nature is known to be present, the 
 suggestion at once rises in our thought that this in all 
 probability is the cause producing this excess in the results. 
 
CHAPTER XV 
 
 EMPIRICAL LAWS 
 
 There is a class of laws which are intermediate between 
 a universal, inductively grounded by scientific determina- 
 tion, and a law of tendency which expresses the probability 
 of the happening of an event in spite of recognized excep- 
 tions. These are laws which have been observed to obtain 
 under given conditions of time, place, and circumstance, and 
 yet the causal relation not sufficiently determined to warrant 
 a necessary extension of the same to a sphere beyond that 
 wherein it has been observed to be operative. Such laws 
 are known as Empirical Laws. 
 
 We have three classes of laws possessing varying degrees 
 of probability. (1) The first is where there has been a 
 scientifically determined causal connection between ante- 
 cedent and consequent; and not only have no exceptions 
 been noted, but the possibility of there being an excep- 
 tion has been eliminated by strict experimental methods. 
 (2) The second is where the regularity of sequence has 
 been broken by actual exceptions, and the result of the 
 observations of instances gives an indication only of the 
 relative frequency of occurrence and failure which will 
 probably characterize other events of that nature. (3) The 
 third class and, as has been said, an intermediate class, 
 comprises all expressions of uniform sequence or coexist- 
 ence, where no exception whatsoever has been rioted, and 
 yet there is no ground for necessitating a universal expres- 
 sion of the observed uniformity. There is here always a 
 possibility of an exception appearing, or of an exception 
 
 351 
 
352 
 
 INDUCTIVE LOGIC 
 
 having been overlooked. This produces an element of un- 
 certainty which pervades all phenomena of this sort. 
 
 There are several kinds of empirical laws, as follows: — 
 
 1. Where the causal relation is in process of scientific 
 determination ; a uniform connection between phenomena 
 has been observed, and as yet has not been proved. All 
 laws, finally determined as expressions of causal connec- 
 tion, pass through this empirical stage. Some expressions 
 of uniform relations never pass beyond this stage, be- 
 cause, as we have seen, the nature of the phenomena may 
 be such as to preclude all experiment or even indirect 
 verification. 
 
 Empirical laws may become ultimate laws or derivative 
 laws, as the case may be. Ultimate laws are those wherein 
 the causal relation between a simple antecedent and its 
 corresponding consequent has been scientifically determined 
 in terms of their exact quantitative variation, and expressed 
 in the simplest form possible. The derivative laws how- 
 ever as the name indicates, are more concrete expressions 
 of the ultimate and simpler laws to which they are referred 
 as special cases. An empirical law may be proved directly 
 an ultimate law, or be proved a derivative law directly 
 traceable to an ultimate law, as its basis, or logical ground. 
 We may observe that a glass of ice-water always shows 
 drops of moisture on its outer surface. This uniformity as 
 thus expressed has the force only of an empirical law. No 
 attempt having been made, as yet, to explain the presence 
 of the moisture, its empirical nature is evident. But as 
 soon as the moisture on the glass is traced to the condensa- 
 tion of the moisture in the atmosphere owing to the differ- 
 ence of temperature between the atmosphere and the cold 
 surface of the glass, we have the empirical law becoming 
 a derivative law; that is, the expression of a uniform 
 sequence directly traceable to the more ultimate laws of the 
 saturation and condensation of vapors. The progress of 
 scientific and logically accurate thought is always marked, 
 
EMPIRICAL LAWS 
 
 353 
 
 therefore, by the resolution of empirical generalities into 
 derivative or ultimate laws. 
 
 2. The character of an empirical law is attached to the 
 relation existing between antecedent and consequent, when 
 that relation is a complex one in which a simple causal 
 relation is so involved with other elements entering into 
 combination with it, that its real nature is thus hidden and 
 cannot readily be disclosed. This class includes all causal 
 relations due to collocations of various kinds that are neces- 
 sary to produce the required effect. As Mill has pointed 
 out : “ It is the nature of an empirical law that we do not 
 know whether it results from the different effects of one 
 cause or the effects of different causes. We cannot tell 
 whether it depends wholly upon laws, or partly upon laws 
 and partly upon a collocation. If it depends upon a colloca- 
 tion, it will be true in all the cases in which that particular 
 collocation exists. But since we are entirely ignorant, in 
 case of its depending upon a collocation, what the colloca- 
 tion is, we are not safe in extending the law beyond the 
 limits of time and place in which we have actual experience 
 of its truth. Knowing of no rule or principle to which the 
 collocations themselves conform, we cannot conclude that 
 because a collocation is proved to exist within certain limits 
 of place or time, it will exist beyond those limits.” 1 
 
 There are many illustrations of such observed generalities 
 where the effect is due largely, if not altogether, to colloca- 
 tions. The effect of certain medicines upon the human sys- 
 tem, the opening and shutting of some flowers at certain 
 hours of the day, the local action of tides at various places 
 on the earth’s surface, the adaptation of certain plants to a 
 peculiar kind of soil, the reappearance of some chronic dis- 
 eases, as hay-fever, at the same season each year, even to the 
 very day of the month, — all such generalities have merely 
 an empirical weight, and the effects mentioned are largely 
 due to collocations that cannot be definitely determined. So 
 i Mill, Logic, Book III, Chap. XVI, § 4. 
 
354 
 
 INDUCTIVE LOGIC 
 
 also certain laws or customs may have proved beneficial in 
 the countries in which they have been tried, and yet, in 
 countries where condition and circumstance are radically 
 different, they may fail wholly of beneficial results. 
 There may be also certain industrial circumstances which 
 in one country might be conducive to prosperity, and 
 in another country to adversity. Certain agricultural 
 methods which in one section of the country tend to an 
 increase of productive power, in another might prove a 
 complete failure. A governmental policy may in one coun- 
 try lead to unparalleled success ; in another, however, a like 
 policy might lead to disastrous results. 
 
 The famous formula of Malthus, that population tends to 
 increase in a geometrical progression, whilst the means of 
 subsistence can only increase in an arithmetical progression, 
 can have only an empirical force. Its extension into an 
 indefinite future is unwarrantable. As is known, produc- 
 tion has increased enormously and at a ratio vastly greater 
 than any contemplated by Malthus as at all in the range 
 of possibility. Many causes, on the other hand, may com- 
 bine to check the rapid increase of population. The colloca- 
 tions here are so complex as to defy any definite prediction. 
 This is true of all tendencies which are due to present social 
 conditions ; the conditions themselves may so vary in time 
 to come as to change totally the accepted generalizations of 
 to-day. Their empirical character is therefore most evi- 
 dent. 
 
 3. A third class of empirical laws comprises all those 
 generalizations which represent a correlation of properties 
 in the same individual. In all such cases no causal relation 
 has been specifically determined between the properties 
 themselves, or between the properties and the whole in 
 which they coinhere. Outside of our experience, the prop- 
 erties observed might be materially changed, and yet not 
 affect the integrity of the concept in general. A propo- 
 sition such as, All swans are white, can have only empirical 
 
EMPIRICAL LAWS 
 
 355 
 
 force; for beyond our experience, tbe discovery of black 
 swans would forbid the proposition being regarded in the 
 light of a universal. Many properties of substances are 
 thus referred to the nature of the substance itself as their 
 ground, and yet because the exact causal relation is not 
 determined, the connection can be considered only as an 
 empirical one. In other words, reference to some ground 
 as explanation of a phenomenon, without explaining why 
 or how such reference is made, has always the force of an 
 empirical law only. The following are empirical gen- 
 eralizations of this nature : Copper is ductile ; steel is 
 elastic; glass is brittle and transparent; the compound sili- 
 cates of alkalies and alkaline metals are transparent ; and 
 other instances of like nature that can be multiplied indefi- 
 nitely. 
 
 In the sphere of biology, Mr. Spencer has drawn attention 
 to the fact that “during the era in which uniformity of 
 many quite simple inorganic relations was still unrecog- 
 nized, certain organic relations, intrinsically very complex 
 and special, were generalized. The constant coexistence of 
 feathers and a beak, of four legs with an internal bony 
 framework, are facts which were, and are, familiar to every 
 savage. Did a savage find a bird with teeth, or a mammal 
 clothed with feathers, he would be as much surprised as an 
 instructed naturalist. Now these uniformities of organic 
 structure, thus early perceived, are of exactly the same 
 kind as those more numerous ones later established by 
 biology. The constant coexistence of mammary glands 
 with two occipital condyles to the skull, of vertebrae with 
 teeth lodged in sockets, of frontal horns with the habit 
 of rumination, are generalizations as purely empirical as 
 those known to the original hunter. The botanist cannot 
 in the least understand the complex relation between 
 papilionaceous flowers and seeds borne in flattened pods ; 
 he knows these and like connections simply in the same 
 way that the barbarian knows the connections between 
 
356 
 
 INDUCTIVE LOGIC 
 
 particular leaves and particular kinds of wood.” 1 Such 
 knowledge as Mr. Spencer here describes is a knowledge of 
 the coexistence of two phenomena in their totality which 
 resist all attempts to analyze into their component parts. 
 Moreover, laws which are but general descriptions of 
 correlated events have the same force as the descriptions 
 of coinhering attributes of substances. They, too, rank 
 as empirical generalizations. The successive stages in 
 the growth of a plant from seed to flower and fruit, 
 the embryonic as well as the post-natal developments 
 in animal life, the habits and instincts of animals, — all 
 these are descriptive generalizations without any attempt 
 at causal determination. 
 
 4. All generalizations expressed in terms of probability 
 only, because of known exceptions, rank as empirical laws. 
 Here, even in the time, place, and circumstance of observa- 
 tion, the law has not been found always valid. The signifi- 
 cance of an empirical law, if we allow this latter class to 
 be included under them, is evidently that of the contra- 
 dictory of a law which is the result of a causal determina- 
 tion. Every generalization not causally determined is then 
 to be regarded as an empirical law. There is, however, a 
 narrower usage of the term which does not include this 
 latter class ; namely, a restriction of the term empirical 
 law to signify the expression of a relation which has been 
 found constant throughout the sphere of observation, and 
 yet where there exists no known causal ground by reason 
 of which we would be warranted in inferring the continua- 
 tion of this relation in a sphere beyond that already observed. 
 We might add that with this there is also the expecta- 
 tion, greater or less, according to the circumstances attend- 
 ing the phenomena, that the generalized experience will be 
 further confirmed by subsequent observation in a wider 
 sphere. This restricted meaning of an empirical law is 
 the one generally understood, unless it is implied to the 
 contrary. 
 
 1 Spencer, Classification of the Sciences, p. 53. 
 
EMPIRICAL LAWS 
 
 357 
 
 An empirical uniformity generally results from the method 
 of agreement. Observed instances, even so selected as to 
 vary the antecedents as much as possible, cannot alone 
 establish a law of uniformity that shall have universal 
 validity. The method of agreement, we have seen, needed 
 to be supplemented by the method of difference if possible, 
 or by an hypothesis capable of subsequent verification. An 
 empirical law is, therefore, due either to some deficiency in 
 method, or to the natural limitations of our knowledge. 
 
 The element of uncertainty attached to all inferences 
 depending upon the extension of an empirical law into un- 
 known territory, it has been insisted upon, may apply equally 
 as well to all inferences depending upon the results of the 
 inductive methods even when most scientifically determined. 
 It is contended that even a causal relation, however firmly 
 grounded, and however simple may be its nature, neverthe- 
 less presents an empirical character. It may give assurances 
 of a high degree of probability, but can never produce abso- 
 lute certitude in our minds. Mr. Venn, for instance, has 
 styled his work on induction, Empirical Logic, that by the 
 title he might indicate his point of view in this regard. He 
 says in the preface to his work : “ By the introduction of 
 the term empirical into the title, I wish to emphasize my 
 belief that no ultimate objective certainty, such as Mill, for 
 instance, seemed to attribute to the results of induction, is 
 attainable by any exercise of the human reason.” Regarded 
 in this light, all laws are empirical. 
 
 The distinction, however, between empirical laws in the 
 sense generally understood, and laws expressing causal rela- 
 tions scientifically determined, is a real distinction, and a 
 significant one as well. And this must not be overlooked ; 
 and it cannot be obliterated by any shifting of the point 
 of view. Bor, to doubt the validity of an empirical law 
 when extended to a sphere beyond that which has been 
 observed, casts a reflection merely upon one’s ability ade- 
 quately to determine the connections existing between the 
 
358 
 
 INDUCTIVE LOGIC 
 
 various elements involved in the particular phenomena under 
 investigation. This is, however, no confession of inability 
 to discover the causal connections of phenomena in general, 
 in such a manner as to determine laws of universal validity. 
 To say that all laws have only empirical significance is to 
 reflect upon the basal postulates of knowledge. Our world 
 is the world as we know it, the world of our consciousness. 
 To discredit the uniformities and regularities therein exist- 
 ing, and which find expression in universal laws, is to dis- 
 credit that which we feel obliged to think in order that our 
 world of knowledge regarded as a system may remain con- 
 sistent with itself, part to part, and part to whole. We 
 must, therefore, regard an empirical law not as the final 
 form of knowledge, or the goal of inductive research, but 
 rather as marking a transition stage toward complete causal 
 determination. And even when, owing to the nature of 
 certain phenomena, we are not able to pass beyond this 
 transition stage of empirical determination, nevertheless, 
 such instances by contrast bear unimpeachable testimony to 
 the fact that there are other phenomena of such a nature 
 that it is possible to subject them to an analysis which will 
 disclose causal connections of such a character as to form a 
 basis for the formulation of universal laws. 
 
CHAPTER XVI 
 
 INDUCTIVE FALLACIES 
 
 A consideration of the various kinds of inductive fal- 
 lacies, and their characteristic features, may be regarded as 
 the obverse representation of the general theory of induc- 
 tion. From the one point of view we consider the positive 
 conditions of true inductive inference ; from the obverse 
 point of view we regard the various breaches of these in- 
 ductive conditions. The discussion of fallacies, therefore, 
 indicates no progress in the elucidation of the subject under 
 consideration ; it rather serves to emphasize distinctions and 
 requirements already indicated by presenting them in a new 
 light, and from a different angle. The subject of fallacies 
 is generally treated by exhibiting through various illustra- 
 tions the cases in which the positive conditions of inductive 
 inference have failed of satisfactory fulfilment. Such illus- 
 trations of the infringement of the requirements of valid 
 induction, I have endeavored to incorporate in the body of 
 the text in connection with the exposition of the various con- 
 ditions and requirements themselves. In this chapter I shall 
 attempt to indicate those fallacies especially which are due to 
 the psychological disturbance of our normal logical processes. 
 An enumeration of these tendencies, partly psychological 
 and partly logical, may serve to impress upon us the danger 
 of falling into easy errors, to which the human mind gen- 
 erally is liable. These errors emerge in the various mental 
 processes. They are as follows : — 
 
 I. Errors of Perception. 
 
 II. Errors of Judgment. 
 
 III. Errors of the Imagination. 
 
 IV. Errors of the Conceptual Processes. 
 
 359 
 
360 
 
 INDUCTIVE LOGIC 
 
 I. Errors of Perception. — Observation is the instrument 
 of research preeminently, in all inductive inquiry. Experi- 
 ment is but a method for increased facility and accuracy of 
 observation. We may say therefore that all the data of 
 inductive inference are furnished by this one process, ob- 
 servation. Any derangement of our powers of observation 
 will affect the nature of the data, and therefore the nature 
 of the results of induction. It becomes therefore all 
 important that we should be appraised at least of the 
 various circumstances whose tendency it is to operate in the 
 midst of the perceptive processes as disturbing forces. We 
 have the following possibilities of error in the sphere of 
 perception : — 
 
 1. Errors due to a failure to take in the whole field of 
 vision. There may be portions omitted which possess a 
 determining significance as regards the object of investiga- 
 tion. Thus exceptions may be overlooked that might have 
 an important bearing upon some received hypothesis; ora 
 fact might be passed by which, if known, would prove 
 highly suggestive. Various devices have been employed to 
 enlarge the sphere of observation beyond the natural limits 
 of the senses. As, for instance, sounds which are inaudible 
 to us may be detected by means of a sensitive flame ; the 
 telescope, the microscope, serve to render the distant near, 
 and the small large. It had been noted that there was a 
 sudden elongation of an iron wire at a particular tempera- 
 ture whilst under longitudinal strain during the act of 
 cooling from a red heat ; an additional circumstance was 
 noted by Professor Barrett when performing the experiment 
 in a darkened room, namely, that at the moment of elonga- 
 tion the wire suddenly evolved heat, and exhibited a visible 
 and conspicuous momentary glow of redness. 1 This circum- 
 stance it would be impossible to note unless in a darkened 
 room. Thus, a prominent characteristic of scientific obser- 
 vation is the endeavor to extend continually the sphere of 
 1 Gore, The Art of Scientific Discovery, p. 321. 
 
INDUCTIVE FALLACIES 
 
 361 
 
 observation. Here also much depends upon the mental 
 habit. There are some who naturally see wider and farther 
 than others. And it is absolutely necessary that the true 
 observer should cultivate with all assiduity such a habit 
 vrhen it is not a natural possession. There is a slovenliness 
 in observation which gives to the inferences based upon its 
 results a color of indefiniteness and inaccuracy, and which 
 proves a fertile source of error. 
 
 It also often happens, that, owing to the mind being 
 prepossessed by a certain idea or theory, research will be 
 thereby restricted to a limited region, and neighboring 
 regions be wholly overlooked. An open-eyed vision, in 
 spite of all preconceptions or prejudices, is the prime 
 requisite for securing from all quarters the greatest possible 
 array of facts that may in any way tend to the formation 
 of a clearer and more adequate judgment. 
 
 2. A second error of observation arises from an opposite 
 mental habit, a failure properly to concentrate the attention 
 upon the relevant facts and so to discriminate as to exclude 
 from consciousness, for the time being at least, all irrelevant 
 details. The lack of such a discriminating faculty leads 
 either to error, or to the dearth of all significant results. It 
 is necessary to avoid either extreme, so that there may be a 
 sweeping survey of all the possible facts relevant to the 
 subject under investigation, combined at the same time with 
 a concentration of attention that is the prerequisite of a 
 deep insight into the inner connections and interrelations of 
 these facts. There must be a depth as well as a wideness 
 of vision. 
 
 There are also errors arising from a failure to note 
 significant differences in phenomena that present striking 
 surface resemblances. Here the closest scrutiny is necessary. 
 The older chemists could not distinguish potash from soda ; 
 baryta and strontia were formerly confounded together, so 
 also potash and caesia. Throughout the whole realm of 
 scientific research, it should be ever kept prominently in 
 
362 
 
 INDUCTIVE LOGIC 
 
 mind that surface differences may hide essential resem- 
 blances, and that surface resemblances may hide essential 
 differences. 
 
 3. Errors may arise from apperceptive projection. Here 
 the objective elements of perception combine with the 
 subjective, so that the complete perception may contain 
 elements which do not correspond with reality. The mind 
 thus projects upon the field of vision its own coloring. We 
 see often that which we wish to see, and fail to see that 
 which we do not wish to see. When palladium was origi- 
 nally made known to the public, Cheuevix proceeded to 
 examine it, prepossessed with the idea that it was an alloy 
 of some two known metals. This idea was so projected 
 upon his experiments, that he at last came to the conclusion 
 that it was a compound of platinum and mercury. Chene- 
 vix was led into an error of observation, as was afterwards 
 proved by Dr. Wollaston, who himself had obtained palla- 
 dium from the solution of crude platina in aqua regia. 1 
 This error of observation was due to the fact that he 
 approached the experiments with a fixed idea in his mind 
 as to what they should prove ; and being determined to see 
 evidences of this in the phenomena, he unconsciously read 
 into them that which was not really there. 
 
 II. Errors of Judgment. — These errors occur in the 
 interpretation of the data of perception. For that which is 
 observed must be referred to its appropriate place in the 
 body of knowledge regarded as a system, in which, part 
 must fit to part, and part to whole. Inaccurate reference 
 results in manifest imperfections and incongruities in that 
 part of the system of knowledge to which the reference has 
 been made. And the inferences based thereupon are 
 naturally affected by this fundamental error of judgment. 
 These errors are as follows : — 
 
 1. Errors due to false associations. Here, where artifi- 
 cial or superficial associations are interpreted as though they 
 1 Gore, The Art of Scientific Discovery. 
 
INDUCTIVE FALLACIES 
 
 365 
 
 were real causal connections, the mistake may prove most 
 serious. The most fertile source of such fallacies is the 
 wrong interpretation of space and time associations, regard- 
 ing mere contiguity in space and time as evidence of causal 
 connection. Under this head may be classed the fallacies, 
 non causa pro causa and post hoc ergo propter hoc. Pros- 
 perity, for instance, following the enactment of certain in- 
 dustrial or tariff measures, is often attributed as the effect 
 of the same, merely because they appear in striking sequence. 
 However, it may be that the prosperity has followed in spite 
 of the laws and not on account of them. 
 
 2. Errors of judgment due to emotional perturbations. 
 When the intellect is deflected from its true pointing by 
 passion, or prejudice, or superstition, or any strong emotion, 
 the consequent judgment is the resultant of two forces, 
 rather than the expression of one. As Bacon says : “ The 
 human understanding resembles not a dry light, but admits 
 a tincture of the will, and passions which generate their 
 own systems accordingly; for man always believes more 
 readily that which he prefers ; his feelings imbue and cor- 
 rupt his understanding in innumerable and sometimes im- 
 perceptible ways.” 1 
 
 The necessity of judging in a “ dry light,” as far as pos- 
 sible, is especially emphasized in the ethical positions of 
 Adam Smith, and later of Mr. Sidgwick. Adam Smith con- 
 tends that one’s duty must be estimated from the standpoint 
 of an impartial spectator and critic. That is, man must, as 
 it were, step out of himself, leaving feeling behind, and 
 judge of himself and of his duty from a purely objective 
 point of view. So also Mr. Sidgwdck says that one of the 
 chief difficulties in the utilitarian position, namely, the dis- 
 crepancy between the egoistic and altruistic claims upon our 
 activities, cannot be harmonized satisfactorily, when stated 
 as a problem of mere feeling. Here again man must elimi- 
 nate feeling and judge of himself merely as one among many, 
 1 Bacon, Novum Organum, Book I, Aphorism XLIX. 
 
364 
 
 INDUCTIVE LOGIC 
 
 where each counts for one and no one for more than one. 
 In the light of pure reason he may be able to see that the 
 good of all is his highest good. But when that dry light is 
 colored by feeling, such judgment is impossible. 
 
 Faraday, in his Observations on Mental Education, has 
 borne testimony directly to the necessity of eliminating feel- 
 ing from our judgments. He says: “The tendency to de- 
 ceive ourselves regarding all we wish for should be kept in 
 mind, and the necessity also of resistance to these desires. 
 The force of the temptation which urges us to seek for such 
 evidence and appearances as are in favor of our desires, and 
 to disregard those which oppose them, is wonderfully great. 
 In this respect we are all more or less active promoters of 
 error. I will simply express my strong belief that that 
 point of self-education which consists in teaching the mind 
 to resist its desires and inclinations until they are proved 
 to be right, is the most important of all, not only in things 
 of natural philosophy, but in every department of daily 
 life.” 1 
 
 3. Errors of judgment due to the common frailties of 
 human nature. Such errors Bacon has styled “ Idols.” His 
 enumeration is not only complete, but is classic in its way, 
 and therefore I quote it at this place : “ Four species of idols 
 beset the human mind, to which, for distinction’s sake, we 
 have assigned names, calling the first Idols of the Tribe, 
 the second Idols of the Den, the third Idols of the Market, 
 the fourth Idols of the Theatre. 
 
 “ The formation of notions and axioms on the foundation 
 of true induction is the only fitting remedy by which we 
 can ward off and expel these idols. It is, however, of great 
 service to point them out ; for the doctrine of idols bears 
 the same relation to the interpretation of nature as that of 
 the confutation of sophisms does to common logic. The 
 idols of the tribe are inherent in human nature, and the 
 very tribe or race of man ; for man’s sense is falsely asserted 
 1 Gladstone, Michael Faraday, p. 128. 
 
INDUCTIVE FALLACIES 
 
 365 
 
 to be the standard of things ; on the contrary, all the percep- 
 tions, both of the senses and the mind, bear reference to 
 man and not to the universe, and the human mind is like 
 those uneven mirrors which impart their own properties to 
 different objects from which rays are emitted, and distort 
 and disfigure them. 
 
 “ The idols of the den are those of each individual, for 
 everybody (in addition to the errors common to the race of 
 man) has his own individual den or cavern which intercepts 
 and corrupts the light of nature, either from his own peculiar 
 and singular disposition, or from his education and inter- 
 course with others, or from his reading, and the authority 
 acquired by those whom he reverences and admires, or from 
 the different impressions produced on the mind as it hap- 
 pened to be preoccupied and predisposed, or equable and 
 tranquil, and the like ; so that the spirit of man (according 
 to its several dispositions) is variable, confused, and as it 
 were actuated by chance ; and Heraclitus said well that men 
 search for knowledge in lesser worlds, and not in the greater 
 or common world. 
 
 “ There are also idols formed by the reciprocal intercourse 
 and society of man with man, which we call idols of the 
 market, from the commerce and association of men with 
 each other; for men converse by means of language, but 
 words are formed at the will of the generality, and there 
 arises from a bad and unapt formation of words a wonder- 
 ful obstruction to the mind. Nor can the definitions and 
 explanations with which learned men are wont to guard and 
 protect themselves in some instances, afford a complete 
 remedy, — words still manifestly force the understanding, 
 throw everything into confusion, and lead mankind into vain 
 and innumerable controversies and fallacies. 
 
 “Lastly, there are idols which have crept into men’s 
 minds from the various dogmas of peculiar systems of phi- 
 losophy, and also from the perverted rules of demonstration, 
 and these we denominate idols of the theatre; for we re- 
 
366 
 
 INDUCTIVE LOGIC 
 
 gard all the systems of philosophy hitherto received or im- 
 agined, as so many plays brought out and performed, creating 
 fictions and theatrical worlds. Nor do we allude merely to 
 general systems, but also to many elements and axioms of 
 sciences which have become inveterate by tradition, implicit 
 credence, and neglect.” 1 
 
 All such tendencies, as thus presented by Bacon, clog and 
 hamper the normal functioning of the judgment. The mind 
 must be alert and on guard to eliminate such fatal seeds of 
 error. 
 
 III. Errors due to the Imagination. — Here the imagina- 
 tion supplies inner connections and relations, lying beyond 
 the sphere of observation, in order to explain the nature of 
 the observed phenomena themselves. The danger here is 
 that the elements supplied in order to make the self-con- 
 sistent whole do not correspond to reality. The system, 
 regarded as a mental construction, may be complete in all 
 of its coordinated parts, and nevertheless possess no objec- 
 tive reality. Under this head fall all loosely constructed 
 hypotheses. In the framing of an hypothesis in general, 
 the imagination functions very largely. It is the inner 
 vision that represents to the mind the things not seen. 
 Moreover, the imagination is peculiarly liable to error, and 
 to swing clear of the trammels of fact, and in the region of 
 pure fancy construct systems that rest upon no solid basis 
 of reality. These dangers in detail have been pointed out 
 in the chapter on hypothesis. 
 
 The most fertile source of error, however, arises from 
 that natural elation of mind upon the discovery even of 
 slight confirming evidence of the truth of the assumed 
 hypothesis. This enthusiasm is apt to magnify unduly an 
 inadequate verification, and to rest satisfied in an hypothesis 
 that is grounded upon an insufficient basis. Thus, since the 
 year 1770, more than forty discoveries of new elementary 
 substances have been announced to the world by enthusi- 
 1 Bacon, Novum Organum, Book I, Aphorisms XXXIX, etc. 
 
INDUCTIVE FALLACIES 
 
 367 
 
 astic experimenters, and, in all cases, tlieir discoveries have 
 been proved to be absolutely worthless. For instance, it was 
 confidently announced that Torbern Bergmann, in 1777, bad 
 extracted from diamonds what he considered to be a new 
 earth, and called it “terra nobilis.” Wedgwood, in 1790, 
 discovered “ australia ” in sand obtained from the continent 
 of that name; but Hatchett proved it to be merely a mix- 
 ture of silica, alumina, oxide of iron, and plumbago. In 
 1805 Richter discovered “ niccolanium ” ; it was afterwards 
 proved to be a mixture of iron, cobalt, nickel, and arsenic. 
 These instances are but a few of the many which charac- 
 terize the history of chemical research, and stand as con- 
 spicuous witnesses of the danger of divorcing fancy from 
 fact. 
 
 The imagination however properly constrained is most 
 potent in suggesting possible causal relations, in construct- 
 ing hypotheses, in devising methods of experiment in order 
 to verify them, and in forming universal concepts in which 
 all the particulars of observation must coinhere. Davy and 
 Faraday were both conspicuous in this mental characteristic. 
 And to this source their eminent discoveries may be traced. 
 Dr. Whewell says, for instance, of Faraday : “ In discover- 
 ing the nature of voltaic action, the essential intellectual 
 requisite was to have a distinct conception of that which 
 Faraday expressed by the remarkable phrase, ‘ An axis of 
 power having equal and opposite forces.’ And the distinct- 
 ness of this idea in Faraday’s mind shines forth in every 
 part of his writings. He appears to possess the idea of this 
 kind of force with the same eminent distinctness with which 
 Archimedes in the ancient and Stevinus in the modern his- 
 tory of science possessed the idea of pressure, and were thus 
 able to found the idea of mechanics. And when Faraday 
 cannot obtain these distinct modes of conception, he is dis- 
 satisfied and conscious of defect.” 1 
 
 It is indeed a touch of genius that enables one to grasp 
 1 Whewell, History of Inductive Sciences, Vol. Ill, 3d ed., p. 147. 
 
368 
 
 INDUCTIVE LOGIC 
 
 and formulate a central idea that will unify and also uni- 
 versalize a large body of seemingly disconnected and incon- 
 gruous facts. But such an idea must be the expression of 
 the relations actually obtaining, and no subjective fancy 
 projected upon the phenomena themselves, however clever 
 or ingenious such an imaginative creation may be. If one 
 were asked what is the most efficient instrument of scientific 
 research, the answer must be, “ The Imagination ! ” And if 
 one were asked what is the most fertile source of error, the 
 answer likewise must be, “ The Imagination ! ” It must 
 also be remembered that it is not sufficient merely that an 
 hypothesis should be in harmony with the facts in the case ; 
 it must be proved, also, that the facts are connected with 
 the hypothesis through necessary links. 
 
 And it is well, also, to bear this in mind when arguing 
 against a rival hypothesis that may have been advanced by 
 an opponent who has claimed for it only the possibility of 
 its validity, and who has not affirmed its necessity. It is 
 manifestly unfair, as well as fallacious, to deny the possi- 
 bility of the hypothesis merely by indicating certain un- 
 certainties connected with establishing it. To contradict 
 possibility, one must prove the hypothesis impossible. Re- 
 garding such a conflict between rival hypotheses Ueberweg 
 suggestively comments as follows: “In cases of this kind, 
 it is one of the hardest of scientific and ethical problems to 
 give fair play to one’s opponent. Our own prejudices are 
 sure to influence us. Yet the effect of the influence of an- 
 other’s standpoint, when it is reached, is of immense value in 
 scientific knowledge. Polemic easily leads to exaspera- 
 tion ; it is easy both to abuse it and to let it alone because 
 of dislike to the conflicts which it produces ; but it is 
 difficult to recognize it, and use it in the right sense as 
 the necessary form which the labor of investigation always 
 takes. Man never attains to a scientific knowledge of the 
 truth without a rightly conducted battle of scientifically 
 justifiable hypotheses, the one against the other : the 
 
INDUCTIVE FALLACIES 
 
 369 
 
 scientific guidance of this battle is the true dialectic 
 method .” 1 
 
 IV. Errors of the Conceptual Processes. — This class of 
 errors arises in the formation of general concepts and their 
 expression in universal laws. The natural tendency of the 
 mind to generalize often leads to ill-considered results. The 
 universal unites many differences into an identity, and the 
 mind will readily minimize the differences in order to form 
 a desired universal ; thus disparate attributes may be incor- 
 rectly coordinated in one and the same system. Herschel 
 has remarked that hasty generalization is the bane of science. 
 And Bacon has said our intellects want not wings, but rather 
 weights of lead to moderate their course. 
 
 The method of agreement, when relied upon to the exclu- 
 sion of further experimental determination, is a fertile source 
 of error in this respect. The possibility of a plurality of 
 causes should be ever kept prominently in mind. One 
 readily assigns an effect to a causal element which is only 
 partially its cause ; the consequent generalization is, there- 
 fore, incorrect. For instance, it often happens that activities 
 of young animals are described as instinctive and congenital ; 
 and universal propositions are founded thereupon. And yet 
 it may be that the activities referred solely to instinct are 
 due partially to imitation. In order to avoid this error and 
 eliminate the factor of imitation, investigators in this line 
 are accustomed to study the activities of animals hatched in 
 incubators and purposely kept from all of their kind. This 
 illustration will serve to show the precautions that must be 
 taken in order to eliminate all possible error from the data 
 which the process of generalization constructs into universal 
 forms. So also inaccuracies in any of the other inductive 
 methods lead to gross errors in the consequent generaliza- 
 tions based upon them. 
 
 Under this head, also, are the fallacies resulting from the 
 extension of empirical laws to spheres beyond the experience 
 1 Ueberweg, A System of Logie, etc., p. 509. 
 
370 
 
 INDUCTIVE LOGIC 
 
 which they embody and express. This source of error is 
 especially illustrated in laws expressing some quantitative 
 relation between antecedent and consequent; it is a natural 
 supposition in such cases, and yet a misleading one often- 
 times, that a simple proportional relation will exist between 
 phenomena of the same nature, but with greater or lesser 
 magnitude, as the case may be. Bacon gives the following 
 illustrations of this fallacy : “ Suppose a leaden ball of a 
 pound weight, let fall from a steeple, reaches the earth in 
 ten seconds, will a ball of two pounds, where the power of 
 natural motion, as they call it, should be double, reach it in 
 five ? No, they will fall almost in equal times, and not 
 be accelerated according to quantity. Suppose a drachm of 
 sulphur would liquefy half a pound of steel, will, therefore, 
 an ounce of sulphur liquefy four pounds of steel? It does 
 not follow; for the stubbornness of the matter in the patient 
 is more increased by quantity than the activity of the agent. 
 Besides, too much as well as too little may frustrate the 
 effect, — thus, in smelting and refining of metals it is a 
 common error to increase the heat of the furnace or the 
 quantity of the flux ; but if these exceed a due proportion, 
 they prejudice the operation, because by their force and cor- 
 rosiveness they turn much of the pure metal into fumes, 
 and carry it off, whence there ensues not only a loss in the 
 metal, but the remaining mass becomes more sluggish and 
 intractable. Men should, therefore, remember how iEsop’s 
 housewife was deceived, who expected that by doubling her 
 feed her hen should lay two eggs a day ; but the hen grew 
 fat and laid none. It is absolutely unsafe to rely upon any 
 natural experiment before proof be made of it, both in a less 
 and a larger quantity .” 1 
 
 Another fallacy of the same order often occurs in the 
 inference concerning the interpolated elements of a series 
 whose successive values have not all been observed. The 
 inference extends the nature of the known to the unknown 
 1 Bacon, Advancement of Learning, Book V, Chap. II, p. 190. 
 
INDUCTIVE FALLACIES 
 
 371 
 
 parts, and presumes that the intermediate links between 
 actually observed parts of the series are in accordance with 
 the general nature of the latter. Such inferences very often 
 give correct results, as, in the plotting of a curve, some 
 salient points may be determined according to observed 
 quantitative variations, and the remaining portions sup- 
 plied, as upon the above supposition. This extension to 
 cover intermediate and unobserved instances may, however, 
 be sometimes very fallacious. For a force may be assumed 
 to be such that its effects increase steadily, and it may be 
 that they operate periodically ; interpolation upon one as- 
 sumed basis when the other is the true one would of course 
 introduce grave errors. To eliminate such errors, devices 
 have in many cases been resorted to by which a self-regis- 
 tering apparatus will record all successive values of the 
 phenomena under investigation. 
 
 Under the fallacies of hasty generalization naturally fall 
 all provincialisms which arise from a narrow nature and 
 habit of mind. The local traditions and superstitions, the 
 prevailing winds, the social customs and manners, are taken 
 as types of a universal experience. The inferential widen- 
 ing of the circle of a limited experience is always provocative 
 of false inference and misleading results. 
 
 We have also false analogies which consist in the ex- 
 tension of our experience of certain phenomena that we 
 have observed to be alike in some respects to include other 
 attributes not observed, concerning which we assume a 
 corresponding similarity ; the abuse of final causes may be 
 regarded as a special case of false analogy. Moreover, a 
 tendency to consider causation in the light exclusively of 
 final causes has often retarded the advance of science, 
 in withdrawing the attention and energies of the investi- 
 gator from a search after physical causes, as, for in- 
 stance, among the ancients it was declared that the leaves 
 of the trees are to defend the fruit from the sun and 
 wind. Besting satisfied in such an explanation, the pre- 
 
372 
 
 INDUCTIVE LOGIC 
 
 cise function of the leaves in the economy of the plant’s 
 growth was not further investigated, and thus progress was 
 impossible. 
 
 Again, incorrect classification is a source of error. In 
 grouping together disparate phenomena, we have a basis for 
 forming a generic concept that will include incompatible 
 species, or, in other words, a universal that will have evi- 
 dent exceptions. Moreover, if the classification is partial, 
 the resulting laws based upon it will have only empirical 
 force. 
 
 I have endeavored in this chapter to indicate errors that 
 are mainly psychological in their origin, for two reasons. 
 In the first place, such errors operate as disturbing forces 
 in the midst of purely logical processes. The data of in- 
 ference are psychological as regards their source, and errors 
 thus originating affect the inference based upon them, 
 appearing in the final result as logical fallacies. An error 
 of observation becomes an error in the judgment that is 
 based upon the original perception, and perdures in the 
 hypothesis, classification, etc., founded on that judgment, 
 and finally emerges in the conclusions based upon these 
 processes. In the second place, the fallacies that are purely 
 formal, and in the strict sense logical, are not as apt to 
 deceive and mislead the mind. In the material data espe- 
 cially lurk the germs of fallacy. On the theory that it is 
 wiser and also more logical to stamp out an error in its 
 incipiency, I have placed special emphasis upon the various 
 psychological processes as initial sources of error. More- 
 over, it is more rational to deal with errors of process rather 
 than flaws of product. A machine that turns out imperfect 
 articles could have its imperfections rectified by repairing 
 each article thus produced ; or the machine itself could be 
 readjusted so as to produce the articles without flaw. It is 
 needless to say which method is the more logical, and most 
 satisfactory, as well. 
 
 The desideratum is accurate and comprehensive observa- 
 
INDUCTIVE FALLACIES 
 
 373 
 
 tion; a discriminating judgment formed in the “ dry light” 
 of reason ; an imagination that has deep insight into the 
 heart of surface appearances ; and powers of generalization 
 which transcend observed phenomena by adequately inter- 
 preting them. 
 
CHAPTER XVII 
 
 THE INDUCTIVE METHODS AS APPLIED TO THE VARI- 
 OUS SCIENCES 
 
 The nature of each separate science will determine cer- 
 tain peculiarities of method for that science ; and its pecul- 
 iar method will be largely a matter of growth, as experience 
 accredits or discredits the various results which its opera- 
 tion may attain. It will thus be corrected or supplemented 
 according as it stands the test of achieved results. There 
 are, however, some general features, and especially some 
 natural limitations of the inductive methods, that may be 
 properly indicated. 
 
 I. In the first place, the nature of the method used, and 
 its efficiency, as measured by its results, will be found to 
 vary as the nature of the phenomena themselves. Some 
 phenomena admit of analysis and determination by experi- 
 ment. Instead of attempting to determine the relation of 
 a complex antecedent to a complex consequent, the antece- 
 dent is first separated into its component parts, and each 
 element is tested alone in order to disclose its precise effect. 
 The relation can then be expressed between the simple 
 antecedent and simple consequent, as a causal connection ; 
 and it admits, moreover, of a quantitative determination as 
 well. Such a method of procedure by analytical experiment 
 enables us to rise to laws having universal validity. This 
 method is characteristic, especially, of the physical sciences, 
 because the phenomena readily admit of resolution into 
 component parts, and the isolation of one simple force so 
 as to determine its total effect. The physical forces are 
 most readily adaptable to experiment. They therefore 
 
 374 
 
INDUCTIVE METHODS AND THE SCIENCES 375 
 
 afford the widest field for the application of the experi- 
 mental method of inductive inquiry. Moreover, we may 
 readily predict the results of a combination of simple forces, 
 when we know the laws governing their component elements. 
 The inducto-deductive method, therefore, becomes especially 
 efficient in extending the domain of the physical sciences. 
 Here, also, mathematical analysis and calculation is most 
 valuable as an aid to experimental investigation, and in 
 determining quantitative relations as necessitated by the 
 mathematical laws to which the data gathered inductively 
 must conform. 
 
 There are however sciences which present phenomena 
 of such a high degree of complexity that an analysis of a 
 complex whole into its separate parts or elements of force 
 is impossible. Moreover, the phenomena cannot be ana- 
 lyzed so that a certain part of the complex whole can be 
 indicated as the complete antecedent, and the remaining 
 portion as the entire consequent. The difficulty therefore 
 is twofold; it is impossible to separate the complex whole 
 into two other complex wholes, antecedent and consequent, 
 and still further impossible to separate such antecedent and 
 consequent, even if they could be determined, into their 
 simplest component parts. The phenomena presented are 
 here not in the form of a sequence so often as in that of 
 coexistence, as in the sciences of botany, zoology, and the 
 like. Here the methods of analogy and classification must 
 be resorted to, and we obtain descriptive laws as the result. 
 
 The forces manifested in the processes of vital growth 
 are especially difficult to determine by experiment ; for they 
 not only operate to produce certain effects, but are conserved 
 in the effects so as to produce certain other effects in a pro- 
 cess of continuous construction. Separation by mechanical 
 analysis means instant cessation of the process itself. Dis- 
 section means death. Here then is a natural limitation. 
 Moreover, the laws of development are further modified by 
 external changes. The result of the inner force and the 
 
376 
 
 INDUCTIVE LOGIC 
 
 outer influences working together complicates the prob- 
 lems to such an extent that the pure inductive methods are 
 well-nigh impossible of application. Resort is then had to 
 determination by statistical methods. Large groups of 
 plants and animals are examined for the purpose of noting 
 tendencies disclosed in the aggregate, but hidden as regards 
 their manifestation in the individual. Here of course classi- 
 fication is an aid in disclosing similarities and differences 
 that may suggest hypotheses to explain certain dominant 
 characteristics. 
 
 We may moreover have merely permanent effects pre- 
 sented in perception, the cause having ceased to act long 
 since. Thus in geology we have facts that have been caused, 
 it is true, but the causes can be discerned only as manifested 
 in the effects, and, therefore, they can be determined only by 
 the method of hypothesis, which may lead to verification or 
 not, as the case may be. Again, certain sciences may suggest 
 problems which concern the explanation or significance, not 
 of particular phenomena within the sphere of that science, 
 but rather the interpretation of the whdle body of phenom- 
 ena which the science in question comprehends. The prob- 
 lem is not solved, therefore, by any attempt in the way of 
 analysis by experiment, but rather in the way of synthesis 
 through hypothesis, that is, the ideal construction of a whole 
 which will unify and account for all facts, or, in other words, 
 the disclosing of the system which underlies and coordi- 
 nates the various particular manifestations. This is espe- 
 cially illustrated in the problems which geology and biology 
 present concerning the interpretation of their respective 
 phenomena regarded in the light of their totality. Astron- 
 omy also presents a mass of seemingly chaotic phenomena, 
 and yet the aim of this science is to reduce them all to some 
 one self-consistent system. 
 
 For instance, Mr. Spencer remarks concerning the general 
 nature of biological study : “ In like manner biology is the 
 elaboration of a complete theory of life in each and all of 
 
INDUCTIVE METHODS AND THE SCIENCES 377 
 
 its involved manifestations. If different aspects of its phe- 
 nomena are investigated apart, if one observer busies himself 
 in classing organisms, another in dissecting them, another in 
 ascertaining their chemical compositions, another in study- 
 ing functions, another in tracing laws of modification, — 
 they are all consciously or unconsciously helping to work 
 out a solution of vital phenomena in their entirety, both 
 as displayed by individual organisms and by organisms at 
 large.” 1 
 
 Mr. Spencer, as we have seen in the chapter on division, 
 makes the distinction between investigation of particular 
 causal relations on the one hand, and, on the other, the in- 
 terpretation of the total phenomena of a science, as the basis 
 for his classification of the sciences. 
 
 The division of Herbert Spencer can only be accepted in a 
 general way as indicating predominant characteristics of the 
 two kinds of sciences. It will not do to lay down hard and 
 fast lines here, for every science presents two kinds of prob- 
 lems ; the first, to determine particular causal relations ; the 
 second, to coordinate all such relations into a self-consistent 
 system which will unify all separate and individual instances. 
 For instance, take the phenomena of light in physics ; par- 
 ticular problems as regards intensity, velocity, composition 
 of light, etc., present themselves ; then an underlying prob- 
 lem, How explain all the phenomena of light upon some one 
 single basis regarding the essential nature of light ? Hence 
 arose the emission and undulatory theories of light, and all 
 phenomena bearing upon the theory were marshalled in sup- 
 port of one and of the other, until the conflict was conclu- 
 sively decided. And again, the theory of light, the theory 
 of electricity, the theory of heat, etc., suggest still another 
 problem, How unify all the separate theories in one all- 
 comprehensive theory to which the separate phenomena 
 may be alike referred ? thus every science presents particu- 
 lar problems, and a general problem as well. And herein 
 1 Spencer, Classification of the Sciences, pp. 19, 20. 
 
378 
 
 INDUCTIVE LOGIC 
 
 lies a suggestion that all investigators in any branch of 
 science would do well to bear in mind. Specialization in 
 any one line of particular problems should always lead to a 
 consideration of the relations of these particular problems 
 to the general system of which they are parts. Specializa- 
 tion that does not thus supply its own corrective by the 
 natural insistence of the mind to interpret the particular 
 in the light of more general laws, tends to narrowness of 
 mind and barren results. 
 
 II. In reference to method in the sciences it must be 
 observed also that in certain phenomena the simple theory, 
 which regards the causal connection as a transfer of energy 
 according to the doctrine of the conservation of energy, is 
 further complicated by certain variations and modifications 
 of the energy in the process of transference. When, for 
 instance, a billiard-ball strikes another, and the second ball, 
 by virtue of the impact, receives the energy of the initial 
 moving ball transferred to it, the problem is simplified by 
 the fact that the motion of the first is easily traceable in 
 the second, being a transfer of energy which manifests it- 
 self in the same manner in the two cases. However, the 
 problem is complicated at once when in chemistry, for in- 
 stance, the two combining elements form a third in which 
 the characteristic features of the former are wholly lost in 
 the new form. Here is likewise a transfer of energy, which 
 may have mechanical equivalents, it is true, and yet so 
 radical a change of form accompanies the transfer that it 
 complicates the problems which arise in this science. We 
 have seen how the combined inducto-deductive method often 
 predicts events and the nature of phenomena not yet ob- 
 served. And yet this becomes most difficult whenever 
 transfer of energy is accompanied by a change in the 
 peculiarities of its manifestation as well. Knowledge of 
 the nature of two elements, and all their separate charac- 
 teristics, will not be sufficient data for any prediction as to 
 the nature of the compound. Thus chemistry confronts a 
 
INDUCTIVE METHODS AND THE SCIENCES 379 
 
 natural difficulty as regards method, which does not affect 
 physical science generally. 
 
 Another difficulty appears in psychology, for here stimuli 
 from the outer world, expressed in terms of physical energy 
 and quantitatively determined, produce psychical reactions, 
 that cannot be expressed in physical terms. And, on the 
 other hand, processes of ideation produce muscular activi- 
 ties, that may be estimated in physical terms. It has been 
 urged that here the theory of conservation of energy breaks 
 down, that the transferred energy is wholly accounted for by 
 the nerve and brain modifications, and that the psychical ac- 
 companiments are wholly unaccounted for upon this basis. 
 They stand out as unexplored remainders. 
 
 This objection is met in two ways. One is that the 
 physical and psychical are, as it were, two closed circles, 
 and while simultaneous in their functioning do not mutually 
 interact. This is the theory of the so-called “ psychophysi- 
 cal parallelism.” It necessitates metaphysical explanations 
 and postulates that seem to complicate rather than simplify 
 the difficulties. The second is the more reasonable, that 
 psychical activity may be radically different from physical 
 and yet the two capable of reacting upon each other, so as 
 to liberate the potential activities in either sphere, and thus 
 initiate a series of causally connected phenomena. Such a 
 theory is buttressed by substantial analogies in the physical 
 sphere itself; namely, that in many phenomena the imping- 
 ing force is so modified, by the reaction due to the nature of 
 the substance acted upon, as to lose, to all observation at 
 least, its original characteristic features. For instance, 
 friction passes over into electricity because of the nature of 
 the substance that is rubbed ; thunder sours cream, and thus 
 sound vibrations cause effects wholly incongruous to them. 
 
 These illustrations might be multiplied through all the 
 realm of physical science. They are so many as to prepare 
 us for realizing the possibility, at least, that physical excita- 
 tions may produce psychical phenomena in the sense that 
 
380 
 
 INDUCTIVE LOGIC 
 
 the outer stimulus calls into activity psychical energies, that 
 thus stirred, manifest themselves according to the forms of 
 their own nature, rather than the forms of the physical 
 phenomena exciting them. Upon such a theory we may 
 proceed, by observation and experiment, to measure dura- 
 tion, intensity, etc., of mental reactions responding to 
 external stimuli. As regards the method here employed, 
 the series is considered as one and complete, so that physi- 
 cal excitations are traced, as it were, through an unbroken 
 causal chain to their psychical effects, and vice versa. On 
 the theory of two closed circles, it is difficult to indicate a 
 logical method of experimental inquiry, unless it be further 
 postulated that activities in the one, according to its kind, 
 may induce modifications of the other according to its kind. 
 This reservation is generally insisted upon. 
 
 III. It sometimes happens that the phenomena of one 
 science are to be interpreted in the light of the results of 
 another science. Thus the laws of one science become guid- 
 ing principles in investigating the causal relations existing 
 in another sphere. This can only be done when there is 
 some similarity between the phenomena of the two sciences. 
 This method is especially illustrated in historical explana- 
 tion. The problem presents a mass of events that must be 
 coordinated in a system wherein their several causal rela- 
 tions will be exhibited. And not merely must detached 
 epochs be proved interrelated as regards the events occurring 
 in them, but here, also, the special problems give rise to a 
 general problem, to discover in the whole the underlying 
 philosophy of history, and to determine the several histori- 
 cal tendencies in one system whose characteristic features 
 will reveal the fact that “ through the ages one increasing 
 purpose runs.” 
 
 To solve the special and the general problems of history, 
 recourse is had to an analysis of events on the basis of well- 
 established psychological results. The phenomena of his- 
 tory are substantially the activities of man, both in his 
 
INDUCTIVE METHODS AND THE SCIENCES 381 
 
 individual and collective capacities. Events being given, 
 an hypothesis concerning the motives, and ends which 
 actuated them, is framed upon the supposition that men 
 ordinarily are impelled by similar motives under similar 
 circumstances, in order to achieve similar ends. Here the 
 analogies drawn between men of the present and men of the 
 past, or between men moving in the ordinary routine of 
 everyday life and men whose acts may be epoch-making, 
 furnish a basis for historical interpretation. We say that a 
 series of events, perhaps of a very complicated nature, can 
 be explained only by an hypothesis that a well-defined pur- 
 pose and a strong determined will were fashioning them and 
 moving through them to an end that was in the chief actor’s 
 mind from the beginning. And so the rise of social habits, 
 customs, traditions, laws, the religion, the government, and 
 national institutions of a people have an origin in psychical 
 and not physical elements, a deeper understanding of whose 
 nature and all that it necessitates tends to a clearer elucida- 
 tion of the problems therein presented. The knowledge of 
 man, the microcosm, is a guiding thread amid the bewilder- 
 ing mazes of the macrocosm. It is possible, of course, for 
 the imagination of the historian to lead him to wander far 
 afield, and invent fanciful motives, purposes, public poli- 
 cies, etc., to explain given events. However, here, as in 
 the physical and other sciences, the hypotheses framed must 
 meet the general requirements and conditions of a valid 
 hypothesis. 
 
 IV. There has been a growing tendency in sciences re- 
 garded as solely or largely deductive, to correct and supple- 
 ment the traditional method and results by a more searching 
 inductive inquiry. This is especially true of political 
 economy. The deductive method proceeded to build up a 
 body of doctrine composed of inferences necessitated by a 
 few fundamental premises. The premises were such as the 
 following : The principal motive of action is self-interest ; 
 the earth, as man’s great supply-house, is limited in extent 
 
382 
 
 INDUCTIVE LOGIC 
 
 and productivity ; the physical and psychological tendencies 
 of man lead him to multiply his own species with a rapidity 
 which, if not counteracted by obstacles, would bring about 
 an unlimited increase of population. All economic laws 
 were thus deduced from some such fundamental propositions 
 as these. The results of this deductive method, however, 
 have been brought to the bar of another method for search- 
 ing examination and judicial sentence. In 1848 Hildebrand, 
 and Knies in 1853, with Roscher in 1854, set forth the prin- 
 ciples of the historical school of political economy. They 
 held that an inductive inquiry must be started in order to 
 estimate the physical, ethnical, and historical conditions of 
 a nation and its stage of civilization. These forces, correctly 
 assessed, will give the economic conditions of a particular 
 period of history, or of a particular nation. This is not the 
 place to criticise the tenets of this school, but merely to 
 point out the fact that its influence has been potent in cor- 
 recting and supplementing the results obtained in a purely 
 deductive manner. 
 
 Deduction may give the joint effect of universal psycho- 
 logical impulses, operative under certain natural conditions 
 of environment, etc., provided no disturbing force is present. 
 But the question here is not whether a certain cause, if act- 
 ing alone, will produce a certain effect ; but whether coun- 
 teracting causes will be present, or modifying causes, as the 
 case may be. To estimate the results of collocations and 
 not simple causes becomes, as we have seen, a complex 
 problem. For its solution recourse must be had largely to 
 statistical methods whereby large aggregates reveal ten- 
 dencies that are actual and not theoretical merely. 
 
 In a similar way, the historical school of jurisprudence, 
 associated with Savigny, has influenced the so-called philo- 
 sophical school in demonstrating that results theoretically 
 determined by deduction are constantly modified by the real 
 conditions and limitations of each particular nation’s life. 
 The influence of this school is indicated by a significant 
 
INDUCTIVE METHODS AND THE SCIENCES 383 
 
 fact, that when Hegel wrote his theory of law ( Rechtslehre ) 
 he paid more regard to the historical formation of states 
 than did the earlier theorists of natural law . 1 
 
 Again, another illustration of the growing prevalency of in- 
 ductive method is found in the modern psychological method. 
 The sole method was considered from time immemorial to be 
 that of introspection. Its results, however, were meagre ; 
 the method itself was indefinite and lacked certainty and 
 uniformity. Inductive inquiry therefore proceeded by its 
 own methods to secure and interpret material in other and 
 various fields. As Professor Ladd says: “The method of 
 psychological science is peculiarly introspective and analytic 
 of the envisaged phenomena called states of consciousness. 
 But it is far broader and more effective than it could be if 
 it were merely introspective. It pushes its analysis of the 
 genesis of the phenomena as far back as possible, by the use of 
 experimental methods, and methods of external observation 
 applied to the whole process of mental evolution (study of 
 infants, of primitive man, and of the lower animals, — evo- 
 lutionary and comparative psychology). It interprets the 
 psychological life of the individual mind in the light of knowl- 
 edge gathered concerning the psychical development of the 
 race (the psychological study of literature, society, art, reli- 
 gion, etc.). It lays peculiar emphasis upon abnormal and 
 pathological phenomena of the nervous and mental life 
 (psychiatry, hypnotism, phenomena of insanity and of the 
 criminal classes, etc.). It takes account of the rise and fall 
 of particular forms of psychological theory (the history of 
 psychology). It strives to transcend experience by hypo- 
 thetical principles of explanation. But in the employment 
 of all these methods this science differs in no important 
 respect from the sciences which deal wholly with physical 
 phenomena. It is only the use of introspection for the 
 possession, and, to some extent at least, for the analysis, of 
 
 1 Bluntschli, The Theory of the State, p. 69. 
 
884 
 
 INDUCTIVE LOGIC 
 
 its objects, which makes psychology, as respects its method, 
 different from the other sciences.” 1 
 
 In the above, we see that inductive inquiry lays all pos- 
 sible fields of research under tribute to the one end of ex- 
 plaining and correlating psychical phenomena. The systems 
 of ethics also, which are founded upon an a priori basis, are 
 becoming more indebted to empirical investigations which 
 have given a richer content to the strictly formal ethic. 
 Advanced psychological research, the study of race char- 
 acteristics, tribal customs, habits, law, religion, etc., the 
 indications of moral progress, — all give material which, if 
 interpreted by right hypotheses, will throw light upon the 
 theory of ethical principles regarded merely from a specula- 
 tive point of view. We may conclude, therefore, that the 
 inductive method and the deductive are not mutually exclu- 
 sive processes. They may be so combined as mutually to 
 strengthen one another. What Bluntschli says of jurispru- 
 dence may be applied equally as well to all sciences that 
 claim some a priori basis : “ The old strife between the 
 philosophical and historical schools in Germany has alto- 
 gether ceased. Peace was made as early as 1840. Since 
 then it is recognized on all sides that the experiences and 
 phenomena of history must be illumined with the light of 
 ideas, and that speculation is childish if it does not con- 
 sider the real conditions of the nation’s life.” 2 
 
 It will be seen how important a factor historical data be- 
 come in all the sciences that deal with human volition and 
 activities. Whatever hypothesis may be framed, it must 
 correspond to these data, because they represent actual con- 
 ditions that must be coordinated in a self-consistent system, 
 and their nature and relations must admit of satisfactory 
 interpretation. 
 
 1 Ladd, Introduction to Philosophy , p. 116. 
 
 2 Bluntschli, The Theory of the State, p. 70. 
 
CHAPTER XVIII 
 
 HISTORICAL SKETCH OF INDUCTION 
 
 Socrates (470-399 b.c.). — We find the beginnings of 
 inductive inquiry in the Socratic or maieutic method, that 
 art of mental midwifery by which conceptions were to be 
 delivered from the mass of individual experiences and 
 opinions in which they lie concealed. The Socratic pro- 
 cedure in the formation of conceptions is to question every 
 particular view, and estimate it by bringing together analo- 
 gous cases, and discovering their natural connections, so as 
 to explicate the general notion which it contains, and thus 
 proceed from comparison of particulars to the framing of 
 general propositions. Socrates’s generalizations were many 
 of them hasty, and in his desire to formulate a general con- 
 ception he overlooked exceptions and minimized difficulties, 
 but in his method there were the germs of truly scientific 
 procedure. The sphere of his method was, however, lim- 
 ited, as he applied it only to the illumination of ethical 
 controversies. 
 
 Plato (427-347 b.c.). — Plato enriched the Socratic method 
 of induction by removing its limitation to ethical inquiry. 
 Plato was especially concerned with investigating the rela- 
 tions of his “ ideas ” to each other, and this led to the 
 apprehension of the logical relations between conceptions, 
 especially as regards their subordination and coordination. 
 This forms a basis for classification, — Plato’s division of 
 class-concepts or logical genera into their species is a promi- 
 nent feature of his method. He also suggests the hypotheti- 
 cal method of treating the relations of concepts ; namely, to 
 examine a tentatively proposed conception by developing 
 
 385 
 
386 
 
 INDUCTIVE LOGIC 
 
 all the possible consequences that would follow from its 
 union with known conceptions. This is in keeping with 
 the inducto-deductive method of Mill and the modern 
 logicians. 
 
 Aristotle (384-322 b.c.). — Aristotle’s name is especially, 
 and it may be said almost exclusively, associated with 
 deductive logic and syllogistic reasoning. Although he did 
 not develop fully the inductive logic, he nevertheless did 
 not ignore it, in some of its essential features at least. He 
 acknowledged the necessity of investigating the starting- 
 point of deduction, namely, the ultimate grounds of proof, 
 and of the principles of explanation. This process he called 
 dialectic. It is a double process that proceeds from the 
 particulars given in perception, and from the ideas current 
 in customary opinion, to discover the general, and then 
 from the general to deduce the particular, which is thereby 
 verified in the process. The former procedure is the reverse 
 of the deductive, and is epagogic or inductive. Induction, 
 according to him, is a syllogism in which the inference that 
 the major belongs to the middle, is mediated through the 
 minor directly; and not indirectly through the middle. 
 Thus, to use Aristotle’s illustration, the investigation of the 
 connection between the absence of gall in animals and lon- 
 gevity in a number of instances, as in man, horse, mule, etc., 
 may disclose their coexistence. 1 They are then united 
 directly without mediation of a middle term. If we had 
 given the universal proposition to start with, Whatever 
 animal has no gall is long-lived, and the minor premise that 
 man, horse, mule, etc., are animals having no gall, then the 
 conclusion would follow, therefore they are long-lived. This 
 is the deductive syllogism. The inductive method, on the 
 other hand, starts from particular observation that the horse 
 which has no gall is long-lived, so also the mule, so also 
 man, etc. ; therefore, without any middle term, a coexistence 
 is taken as equivalent to a causal relation between these 
 1 Aristotle, Prior Analytics , II. xxiii. 
 
HISTORICAL SKETCH OF INDUCTION 
 
 387 
 
 attributes, and the inference is drawn that all animals 
 having no gall are long-lived. Such an inference is valid 
 syllogistically, however, only on the assumption that the 
 instances examined comprise the whole class having the 
 attributes under investigation. This inductive syllogism, 
 therefore, expresses inferences only of complete enumeration. 
 
 The form of such a syllogism is as follows : — 
 
 Let S = minor term, 
 
 P = major term, 
 
 M = middle term. 
 
 This, that, and the other S is P. 
 
 This, that, and the other S is all M. 
 
 All M is P. 
 
 Here it will be observed that the particular instances 
 comprising the minor term S, when summed up, equal the 
 middle term. There is no inference in this if we have 
 regard to the strict sense in which the word is used. 
 Aristotle, indeed, considered the only scientific induction 
 to be the so-called perfect induction, and says that to 
 generalize many experiences of the same kind is admissible 
 only when there is no contrary case. The thought that the 
 proof of causal connection enables us to generalize is stated 
 by Aristotle, but, as Ueber weg says, it “does not attain to 
 a fundamental significance in his logical theory.” 1 
 
 The Precursors of Bacon. — The revolt against the scho- 
 lasticism of the Middle Ages and the fetters of the Aristote- 
 lian logic was many-voiced, culminating, however, as regards 
 the emphasis placed upon induction as a scientific method, 
 in the works of Francis Bacon. 
 
 Foremost among the early champions of inductive inquiry 
 we find Boger Bacon, born in 1214, a Franciscan monk, yet 
 devoted heart and mind to the cause of science. His Opus 
 Majus was published first in 1733 by Dr. S. Jebb, princi- 
 pally from a manuscript in the library of Trinity College, 
 1 Ueberweg, Logic, p. 479. 
 
388 
 
 INDUCTIVE LOGIC 
 
 Dublin. This work is characterized by a spirit of protest 
 against authority in general, and that of Aristotle and his 
 logic especially. He recommends mathematics and experi- 
 ment as the two great instruments of scientific investigation. 
 In this particular it is interesting to note his anticipation 
 of the modern mathematico-physical modes of scientific in- 
 quiry. The following quotation will give an indication of 
 his spirit and aims : — 
 
 “ Experimental science, the sole mistress of speculative 
 sciences, has three great prerogatives among other parts of 
 knowledge : First, she tests by experiment the noblest con- 
 clusions of all other sciences ; next, she discovers, respect- 
 ing the notions which other sciences deal with, magnificent 
 truths to which these sciences of themselves can by no 
 means attain ; her third dignity is, that she by her own 
 power, and without respect of other sciences, investigates 
 the secrets of nature.” 1 
 
 Leonardo da Vinci (1452-1519). — Leonardo combined 
 in one personality many brilliant talents, being eminent as 
 sculptor, painter, architect, engineer, astronomer, and natural 
 philosopher. His works, unpublished, exist in manuscripts 
 in the library of the Institute at Paris. He expresses him- 
 self very clearly and emphatically concerning the relation 
 of experience to speculation : “ Theory is the general ; ex- 
 periments are the soldiers. We must consult experience, 
 and vary the circumstances till we have drawn from them 
 general rules ; for it is she who furnishes true rules. But 
 of what use, you ask, are these rules ? I reply, that they 
 direct us in the researches of nature and the operations of 
 art. They prevent our imposing upon ourselves and others, 
 by promising ourselves results which we cannot obtain. 
 But see the absurdity of men ! They turn up their noses 
 at a man who prefers to learn from nature herself rather 
 than from authors who are only her clerks.” 2 This latter 
 
 1 Whewell, Philosophy of the Inductive Sciences, Vol. II, p. 369. 
 
 2 Ibid., Vol. II, p. 369. 
 
HISTORICAL SKETCH OF INDUCTION 
 
 389 
 
 remark is similar in its reference to the epithet of Galileo, 
 applied to men whose knowledge comes wholly from books 
 and not from observation ; namely, “ paper philosophers.” 
 Bernardinus Telesms (1508-1588). — His work, entitled 
 De R erum Natura, anticipated, in some degree at least, the 
 Novum Organum of Bacon. Bacon himself says of him : 
 “We think well concerning Telesins, and acknowledge him 
 as a lover of truth, a useful contributor to science, an 
 amender of some tenets, the first of recent men.” Telesius 
 set for himself a high aim and purpose, but in the applica- 
 tion of his method he was not so fortunate, being dominated 
 in his researches by speculation rather than the results of 
 experimental inquiry. As to his professed method, he an- 
 nounces in the title of his Be Natura that “ the construction 
 of the world, the magnitude and nature of the bodies con- 
 tained in it, are not to be investigated by reasoning, which 
 was done by the ancients, but are to be apprehended by the 
 senses and collected from the things themselves.” And in the 
 Proem of the same work he says in a like strain that “ they 
 who before us have inquired concerning the construction of 
 this world, and of the things which it contains, seem indeed 
 to have prosecuted their examination with protracted vigils 
 and great labor, but never to have looked at it. For, as it 
 were, attempting to rival God in wisdom, and venturing to 
 seek for the principles and causes of the world by the light 
 of their own reason, and thinking they had found what they 
 had only invented, they made an arbitrary world of their 
 own. We then, not relying on ourselves, and of a duller 
 intellect than they, propose to ourselves to turn our regards 
 to the world itself and its parts.” 
 
 Following Telesius, and of his school, was Thomas Cam - 
 panella ( 1568-1639). He was a contemporary of Bacon, 
 and, under the influence of Telesius, early conceived the 
 idea of an inductive method of research. At the age of 
 twenty-two, he published a work whose character may be 
 judged by its title, — “ Thomas Campanella’s Philosophy 
 
390 
 
 INDUCTIVE LOGIC 
 
 demonstrated to the senses, against those who have philos- 
 ophized in an arbitrary and dogmatical manner, not taking 
 nature for their guide ; in which the errors of Aristotle and 
 his followers are refuted from their own assertions and the 
 laws of nature ; and all the imaginations feigned in the 
 place of nature by the Peripatetics are altogether rejected; 
 with a true defence of Bernardin Telesius of Cosenza, the 
 greatest of philosophers; confirmed by the opinions of the 
 ancients, here elucidated and defended, especially those of 
 the Platonists.” 
 
 The ideas of Bacon, with their impetus to the inductive 
 method of research, were not only anticipated by writers of 
 books ; but actual discoveries by zealous investigators were 
 turning the attention of the thinking world to nature and 
 her secrets. There was an illustrious line of pioneers in 
 this undiscovered country. There was Andrew Csesalpinus 
 (1520-1603), the founder of the science of botany; and 
 earlier, Copernicus (1473-1543), advancing his heliocentric 
 theory ; and Gilbert (1540-1603), the court physician of 
 Elizabeth and James, conducting with untiring perseverance 
 his investigations of the nature of magnetism and electricity. 
 Kepler, born ten years after Bacon, 1571, and Galileo, born 
 in 1564, and their contemporary, Tycho Brahe, born in 
 1546, formed a triumvirate of scientific power and brill- 
 iancy, made resplendent by the glory of the heavens 
 itself. It must be remembered, too, that at this time a new 
 world had been discovered across the seas; the recent in- 
 ventions of gunpowder, of the mariner’s compass, and of 
 the art of printing, all tended to stimulate the thought 
 of the world, and usher in a new epoch in the history 
 of civilization. 
 
 Francis Bacon (1561-1626). — Bacon’s inductive system 
 is given, for the most part, in the Novum Organum. The 
 title of this work was in itself a protest against Aristotle 
 and his logic, implying that Aristotle’s Organon was now 
 out of date and was to be superseded by the new. Bacon 
 
HISTORICAL SKETCH OF INDUCTION 
 
 391 
 
 insists that all knowledge of nature has for its end the dis- 
 closing of the causes of things. According to the Aristote- 
 lian scheme, causes are formal, material, efficient, or final. 
 Bacon is only concerned with the formal causes. For, he 
 says, all events have their ground in the “ forms ” of 
 things. By the form of a thing, he meant its essential 
 nature. Where he uses the form we may well supply the 
 word law. To discover the forms of phenomena, it is nec- 
 essary, according to Bacon, to collect as many instances as 
 possible in which the phenomenon under investigation ap- 
 pears ; together they form a tabula prcesentice. In like man- 
 ner, the instances in which the phenomenon is lacking are 
 grouped in a tabula absentice; and a third group must be 
 formed, — a tabula graduum in which the variations of 
 intensity in the phenomena are compared with the varying 
 intensity of other phenomena. The problem is then to be 
 solved by a process of exclusion ( exclusio ) ; that is, the 
 rejection or exclusion of the several qualities which are not 
 found in some instance where the given quality is present, 
 or are found in some instance where the given quality is 
 absent, or are found to increase in some instance where the 
 given quality decreases, or to decrease when the given qual- 
 ity increases. By this process an indication will be given 
 by which an hypothesis may be framed, and finally verified 
 by subsequent observation and experiment. In the sketch 
 of this method it will be seen that his three tables of in- 
 stances closely resemble the methods of agreement, of dif- 
 ference, and of concomitant variations. They, however, 
 lack the precision of the later formulation of these methods. 
 There is no hint at a systematic selection and variation of 
 the instances ; and no requirement, as in the method of dif- 
 ference, that two instances shall be so experimentally de- 
 termined that they will agree in every point save the given 
 phenomenon, which is present in the one and absent from 
 the other. Bacon, however, made a substantial contribu- 
 tion to the method of induction in general, in insisting upon 
 
392 
 
 INDUCTIVE LOGIC 
 
 the examination of instances themselves, and in ascending 
 from them quite gradually the scale of the more general 
 up to the most general, and in this he entered a vigorous 
 protest against hasty generalization. 
 
 As to the manner of certifying the hypothesis formed 
 after the process of collecting and sifting instances, Bacon 
 has no recourse to deduction based upon the hypothesis and 
 consequent verification. He seems to despise mathematical 
 method as an ally of inductive inquiry ; and therefore has 
 no place in his scheme for the prediction of new phenomena 
 by means of calculation. Of his nine divisions of aids to 
 induction, he completed only the first, — Prerogative In- 
 stances. Of the instances which he enumerates, twenty- 
 seven in all, only a few have any bearing directly upon the 
 inductive method proper. Two sets of these instances may 
 be considered as a crude statement of the methods of agree- 
 ment and difference ; the Solitary Instances, which either 
 exhibit a phenomenon without any of its usual accompani- 
 ments or which agree in everything except some particular 
 phenomenon, and Migratory Instances, where qualities are 
 produced in bodies by evident causes, as, for instance, the 
 producing of whiteness by pounding glass, also by stirring 
 water into froth. These instances however as exhibited 
 by Bacon lack precision and the possibilities of accurate 
 determination of causal connections. The only other group 
 of instances having special inductive significance is that of 
 the Instantia Crucis; as before mentioned, such instances are 
 valuable in deciding between rival hypotheses. With all the 
 deficiencies of Bacon’s method, however, his service to the 
 thinking world is indisputable, in emphasizing the need of 
 investigating phenomena themselves as a corrective of fanci- 
 ful speculations, and in his vigorous warnings against preju- 
 dice, against intellectual indolence, against subjection of the 
 mind to the trammels of authority, and against over hasty 
 generalizations. 
 
 Locke (1632-1704). — Locke applied the method of Bacon 
 
HISTORICAL SKETCH OF INDUCTION 
 
 393 
 
 to the objects of inner experience. He declared that the 
 data of all knowledge come from sensation, or sense-percep- 
 tion, and from reflection, and that there are no “innate 
 ideas,” and therefore no starting-point for a priori specula- 
 tions. The method that had been found useful in actual 
 discoveries, such as those of Newton, Kepler, and others, 
 Locke insisted would prove productive also of rich results 
 in the intellectual sphere. 
 
 Isaac Newton (1642-1727). — Scientific method was grad- 
 ually formulating itself in the actual pursuits of scientific 
 investigation, — not thought out as much as worked out, and 
 its efficiency tested and confirmed by results. Newton gives 
 form to that which was a result of many experiments, and 
 of a mass of various experiences, in his Rules of Philoso- 
 phizing (Regulce Philosophandi ) prefixed to the Principia. 
 
 These rules are as follows : — 
 
 1. The first rule is twofold : — 
 
 a. “ Only real causes are to be admitted in explanation of 
 phenomena.” 
 
 b. “No more causes are to be admitted than such as 
 suffice to explain the phenomena.” 
 
 2. “In as far as possible, the same causes are to be 
 assigned for the same kind of natural effects.” 
 
 3. “ Qualities that can neither be increased nor dimin- 
 ished in intensity, and that obtain in all bodies accessible to 
 experiment, must be considered qualities of all bodies what- 
 soever.” 
 
 4. “In philosophical experiment, propositions collected 
 from phenomena by induction are to be held, notwithstand- 
 ing contrary hypotheses, as either exactly or approximately 
 true, until other phenomena occur whereby they are either 
 rendered more exact or are proved liable to exceptions.” 
 
 New'ton’s celebrated saying, “ Hypotheses non fingo,” was 
 originally a protest against the supposition of the existence 
 of occult or imaginary causes to explain phenomena, notably 
 
394 
 
 INDUCTIVE LOGIC 
 
 the Cartesian explanation of the celestial movements by 
 vortices. Hypotheses of a different nature, and rationally 
 grounded, did not fall under Newton’s reprehension. 
 
 Sir John Herschel (1792-1871). — Herschel’s Discourse 
 on the Study of Natural Philosophy was published in 1832. 
 John Stuart Mill reviewed this book in the Examiner, and 
 was evidently impressed and influenced by it. Herschel’s 
 design was to make the methods of science more explicit. 
 These are contained in nine “ propositions readily applicable 
 to particular cases, or rules of philosophizing.” 
 
 Of these propositions, the second, seventh, eighth, and 
 ninth present substantially the experimental methods as 
 afterwards more precisely formulated by Mill. These 
 methods, however, he regards simply as means to discovery, 
 and not methods of proof. Of the remaining propositions, 
 the first is a more precise statement of Bacon’s principle 
 of exclusion, and is the foundation of the joint method of 
 agreement and difference. The third proposition is that 
 “ we are not to deny the existence of a cause in favor of 
 which we have a unanimous agreement of strong analogies, 
 though it may not be apparent how such a cause can pro- 
 duce the effect, or even though it may be difficult to con- 
 ceive its existence under the circumstances of the case.” 
 The fourth is that “contrary or opposing facts are equally 
 instructive for the discovery of causes with favorable ones.” 
 The fifth recommends the “ tabulation of facts in the order 
 of intensity in which some peculiar quality subsists.” 
 The sixth rule insists upon the investigator keeping promi- 
 nently in mind the possibility that “counteracting or modi- 
 fying causes may subsist unperceived,” and that this fact 
 may be the means of explaining many apparent excep- 
 tions. 
 
 Herschel also emphasizes the necessity of combining in- 
 duction and deduction in complicated inquiries ; and, further, 
 he explains the nature of empirical laws, as also the nature 
 and tests of hypotheses. We can now see that the body of 
 
HISTORICAL SKETCH OF INDUCTION 
 
 395 
 
 inductive principles begins at length to assume final form 
 and proportion. 
 
 Whewell (1795-1866). — Dr. Whewell published his Phi- 
 losophy of the Inductive Sciences in 1840, containing his sys- 
 tem of induction. His method involves two principal 
 processes, — the colligation of facts and the explication of 
 conceptions. The investigator is to gather all the facts at 
 his disposal, and upon them he is to superinduce a concep- 
 tion which will unify them, or colligate them. He says 
 these conceptions are supplied by the mind, while facts are 
 supplied by the sense. This however is a distinction that 
 separates so widely the spheres of the particular facts, and 
 the general conceptions, that upon such a basis a union of 
 the two as explaining one by the other would be artificial 
 and with no corresponding bond of reality. The colligating 
 conception does not exist in the mind before or apart from 
 its existence in fact. The attempt to fit facts to ready-made 
 conceptions is of the nature of guesswork. Kepler’s nine- 
 teen guesses regarding planetary orbits is an instance of 
 attempting to superinduce conceptions upon a mass of facts. 
 It is not a truly scientific or logical procedure, and the 
 great danger of applying it lies in the fact that the mind 
 all too readily tends to mould facts into the forms of prior 
 conceptions. 
 
 “The Methods employed in the Formation of Science,” 
 the title of his concluding chapter, are three, as follows: 
 Methods of Observation, Methods of Obtaining Clear Ideas, 
 and Methods of Induction. The last principally concerns 
 our present purposes. The methods of induction are 
 methods of discovery rather than proof ; save the last, which 
 is one of the experimental methods. They are, the method 
 of curves to express graphically the graduated results of sev- 
 eral observations ; the method of means, and the method of 
 least squares, both designed to eliminate accidental accom- 
 paniments of constant causes by striking an average of sev- 
 eral observations ; and the method of residues. Whewell’s 
 
396 
 
 INDUCTIVE LOGIC 
 
 method may be characterized in brief as a method of discov- 
 ery rather than proof. 
 
 John Stuart Mill (1806-1873). — Mill’s Logic, published 
 in 1813, was essentially a method of proof rather than a 
 method of discovery. His aim in formulating the methods 
 in vogue in experimental science, was to discover the pre- 
 cise modes of their operation in order to apply the same in 
 investigating the various mental, moral, social, and political 
 phenomena. Bacon in the Novum Organum had asserted 
 that this inductive method was applicable to the intellectual 
 and moral sciences. This was no doubt suggestive to Mill, 
 as it had been to Locke. Whately’s Logic, published in 
 1827, influenced Mill, and was the means of turning his 
 attention to logical studies. Whately’s book was reviewed 
 by Mill, when only twenty -one, in the Westminster Review. 
 The revival in logical interest at this time and the depar- 
 ture from scholastic traditions have been traced to the influ- 
 ence of Edward Copleston, tutor at Oxford, and afterwards 
 Bishop of Llandaff. Whately’s work represented the first- 
 fruits, and Mill’s the richer and riper product of this revival 
 of logic. It is a matter of more than passing interest to 
 note that one of Whately’s most active collaborators in the 
 work was John Henry Newman, so that, as Professor Minto 
 says, “ the common room of Oriel, which Mr. Froude de- 
 scribes as the centre from which emanated the High Church 
 Movement, may also be said to have been the centre from 
 which emanated the movement that culminated in the revo- 
 lution of logic.” 
 
 Mill’s special office as regards induction consists in his 
 crystallizing the principles and practices of the scientific 
 investigators who had caught and reflected the spirit of 
 modern research. The formulated methods of inductive 
 logic, substantially as given by Mill, have become the 
 recognized methods of all investigation that is actuated by 
 a scholarly spirit and a scientific habit. Mill’s contribu- 
 tions to the inductive logic have been so largely drawn 
 
HISTORICAL SKETCH OF INDUCTION 
 
 397 
 
 from and so frequently referred to in the composition of 
 this book, as to need no further comment here. The works 
 of the more recent writers, as Lotze, Sigwart, Bosanquet, 
 Jevons, Venn, etc., have also been noticed in the body of 
 the text. Their work is largely critical, and no distinct 
 inductive system is especially associated with any of their 
 names. 
 
LOGICAL EXERCISES 
 
LOGICAL EXERCISES 
 
 PART I 
 
 1. (a) All A is B. 
 All B is C. 
 .•. All C is A. 
 
 (Z>) All A is B. 
 
 No A is C. 
 •\ No C is B. 
 
 (c) All A is B. 
 
 (d) Some A is B. 
 
 All C is B. 
 All C is A. 
 
 No A is C. 
 
 Some C is not B. 
 
 2. The atmosphere cannot be a conductor of electricity ; for 
 metals are conductors of electricity, and the atmosphere is of course 
 not a metal. 
 
 3. If there is to be any appreciation of German literature, one 
 must be conversant with the German language. 
 
 A certain man has a knowledge of the German language. 
 
 .-. He appreciates German literature. 
 
 4. Whatever is opposed to our industrial prosperity is to be re- 
 garded as a serious evil. 
 
 All European wars are serious evils. 
 
 .-. They are opposed to our industrial prosperity. 
 
 5. All patrons of the arts and sciences are public benefactors. 
 
 No poor men are patrons of the arts and sciences. 
 
 /. No poor men are public benefactors. 
 
 6. All democrats are hostile to the bill. 
 
 All beet-sugar men are hostile to the bill. 
 
 .•. All beet-sugar men are democrats. 
 
 7. Given A is B, to prove B is A. 
 
 Now B is either A or not A. 
 
 If B is not A, then by -what is given we have the syllogism, 
 
 A is B. 
 
 B is not A. 
 
 A is not A, which is absurd. 
 
 Is this reasoning correct or not ? 
 
 401 
 
 — Professor Jastrow, 
 
402 
 
 LOGICAL EXERCISES 
 
 8. The courageous are confident and the experienced are confi- 
 dent. Therefore the experienced are courageous. 
 
 9. If the door were locked, the horse would not be stolen ; but the 
 horse is not stolen ; therefore the door must have been locked. 
 
 10. Given the major premise, If an engineer sees a danger signal, 
 he will stop the train. What can be inferred from the several minor 
 premises as follows : — 
 
 (a) He saw a danger signal. 
 
 (b) He did not see a danger signal. 
 
 (c) He stopped the train. 
 
 (d) He did not stop the train. 
 
 11. All dishonest men are immoral, and as a certain man is con- 
 fessedly immoral, it follows that he must be dishonest. 
 
 12. All members of the finance committee are members of the 
 executive committee. No members of the library committee are 
 members of the finance committee ; therefore no members of the 
 library committee are members of the executive committee. 
 
 13. Given the major premise, If the game is lost, we lose the cham- 
 pionship. What follows as the result of the several minor premises ? 
 
 (а) The game is lost. 
 
 (б) The game is won. 
 
 (c) The championship is lost. 
 
 (d) The championship is won. 
 
 14. Given, x, y, z, P, Q , R, so that 
 
 (a) Of x, y, z, one and only one is true. 
 
 (5) Of P, Q, R, one and only one is true. 
 
 (c) If x is true, P is true. 
 
 (d) H y is true, Q is true. 
 
 (e) If z is true, R is true. 
 
 Prove, If x is false, P is false. 
 
 If y is false, Q is false. 
 
 If z is false, R is false. 
 
 — Keynes's Logic. 
 
 15. I am sure that he must have known of the plan ; for only 
 members of the committee knew of it, and he was a member of the 
 committee. 
 
 16. A certain man will make an excellent electrical engineer ; for 
 he is a good mathematician. 
 
 17. If he insists upon the present policy, he will fail ; but he is 
 willing to give up this policy and therefore he will succeed. 
 
LOGICAL EXERCISES 
 
 403 
 
 18. Only those messages which are prepaid will be delivered. This 
 message has been prepaid ; and therefore it will be delivered. 
 
 19. If a is b, c is d ; if c is d, e is f; if e is/, g is h. 
 
 What inferences are possible if yon have given that e is d ? 
 
 What inferences, if e is not / ? 
 
 20. A is nearer than B ; B is nearer than C ; therefore A is nearer 
 than C. 
 
 21. All who were pledged voted for him. 
 
 A certain man was not pledged. 
 
 :. He did not vote for him. 
 
 22. Because the poor who have cows are the most industrious, the 
 way to make them industrious is to give them cows. — Malthus. 
 
 23. Governor McKinley charges that the democratic party believes 
 in taxing ourselves. I’m afraid, gentlemen, we must admit this charge. 
 We stand disgraced in the eyes of mankind if we cannot and if we do 
 not support our own government. We can throw that support on other 
 people only by beggary or by force. If we use the one, we are a pau- 
 per nation ; if we use the other, we are a pirate nation. — Congressman 
 William L. Wilson of West Virginia. 
 
 24. If the plate found had been originally on the outside of the ship, 
 I should have judged that there must be green paint on it ; but I couldn’t 
 find green paint on that part of the plate. — Maine Court of Inquiry. 
 
 25. Question : Can you imagine a 10-inch charge bursting inside of 
 a tank ? Would they look like that ? [Showing a split tank.] 
 
 Answer : If a 10-inch charge burst inside of a tank, there would be 
 nothing left of the tank. It would be blown into small pieces. 
 
 26. No one of the crowd would by himself stoop to so mean an act, 
 and, therefore, I am quite sure that as a body they would not do it. 
 
 27. Our rule in the Philippines is unjust ; for it is manifestly unjust 
 to tyrannize over an inferior people. 
 
 28. A few years ago there appeared an unusual number of spots on 
 the sun, and there followed immediately a very severe famine in India. 
 It would seem that such variations in the nature of the sun had some- 
 thing to do with the consequent failure of the crops. 
 
 29. There should be no restriction of debate in the United States 
 Senate, because freedom of speech is one of our most sacred privileges. 
 
 30. Each member of a certain board is liable to err in judgment, 
 therefore as a body the chance of error is multiplied, and consequently 
 is so much the greater. 
 
 31. It would be greatly to our advantage as a people were we to 
 have a silver standard, for the prosperity of the people would be 
 increased. 
 
404 
 
 LOGICAL EXERCISES 
 
 32. The expedition was destined to fail, because it started on 
 Friday. 
 
 33. These men are traitors because they are opposed to the war, 
 and opposition to the war is an opposition to the government, and 
 opposition to the government is traitorous. 
 
 34. The combination which has been formed need not be feared, for 
 all of its members are exceedingly weak and inexperienced. 
 
 35. That writer must be a follower of Plato ; for all followers of 
 Plato are idealists, and he is an idealist. 
 
 36. The philosophy of Naturalism, if regarded from the practical 
 side, is insufficient; if from the speculative side, it is incoherent. 
 Therefore it fails to justify itself. — Mr. Balfour in Foundations of 
 Belief. 
 
 37. It is possible to have in thought the conception of the most per- 
 fect Being. This conception implies the reality of such a Being ; for 
 if the most perfect Being as thus conceived has no real existence, then 
 it would be possible to conceive of a still more perfect Being which 
 should possess reality, and thus the former would not be the most 
 perfect Being possible. — Anselm's Ontological Argument. 
 
 38. Students who are free to choose their studies will, as a rule, 
 select the easiest ; therefore the easiest courses will be largely attended, 
 or, conversely, the much-chosen courses will include all the easiest. 
 
 39. If there had been no portent of the Wilson-Gorman bill, there 
 would have been no panic in 1893, no consequent revenue deficit, no 
 need to issue bonds in time of peace, no addition to the national debt, 
 no resulting 16-to-l free silver craze, and no chance for the ring of 
 silver Senators to bestride the financial legislation of the country. 
 
 40. The following is an excerpt from a letter written to one of our 
 daily journals : — 
 
 I am in favor of free silver. First — Because I believe it to be right. 
 
 Second — Because it is constitutional and democratic, and right here 
 I may say that for thirty-two years I have voted the democratic 
 ticket. 
 
 Washington and Jefferson (the father of Democracy) bequeathed 
 to the American people in 1792 the legacy that the dollar of 371^ grains 
 of pure silver was the unit of value. This legacy was ever kept sacred 
 and preserved until 1873, when Congress destroyed the unit of value 
 that had stood the test for over eighty years of American independence, 
 and substituted a unit that seems to be acceptable to the Rothschilds 
 of England and America. 
 
 From the effects of that outrage, the work, no doubt, of men who 
 did not fully understand what they were doing, the people have never 
 
LOGICAL EXERCISES 
 
 405 
 
 recovered. They can still see its effects by comparing the reduction 
 in value of all property during recent years with the steady increase 
 in value which took place before silver was demonetized. 
 
 The value of nearly everything that a man owned was depreciated 
 by the demonetization of silver, but then there was no depreciation in 
 any debt that he owed ; on the contrary his debts increased because 
 gold appreciated when made the only redemption money of the country, 
 and consequently it took more labor and products to get the gold with 
 which to pay his debts. 
 
 The people can also see the effects of the demonetization of silver 
 by comparing the number of strikes and lockouts we have had since 
 1873 with the number we had for eighty years before. They can see 
 its effect by comparing the number of trusts of the last fifteen years 
 with the number we had before silver was demonetized. Before 1873 
 labor had little cause to organize for protection. America was the 
 asylum for the oppressed of all nations, and American labor was the 
 best paid and the most contented in the world. How is it now, and 
 how has it been, on the average, since the old American policy of 
 “live and let live” was abandoned at the behest of the comparative 
 few who control the gold of the world ? Instead of being those to 
 whom the oppressed of other nations come for “fair play,” we are a 
 part of the world’s great throng which is trying to get “ fair play ” for 
 themselves. 
 
 The masses of our country are little, if any, better off, all things 
 considered, than those of the most favored of the over-populated 
 countries of the old world. It was not always thus, and it will not 
 long continue to be so if the voters will turn a deaf ear to the pluto- 
 crats and their agents, the time-serving politicians, who tell them that 
 silver money would be “dishonest” money unless measured by the 
 gold standard which these same plutocrats have substituted for the old 
 gold and silver standard which we used until 1873. 
 
 41. Luxurious expenditure is a good thing for laborers, as it in- 
 creases the demand for labor, 
 
 42. Payment of interest on a public debt, so far as it is confined 
 to the citizens of one country, neither enriches nor impoverishes the 
 country, but is a payment of money from the right hand to the left. 
 
 43. A great fire tends to increase wages, as it creates employment 
 to replace the devastated district. 
 
 44. A dense population implies a high rate of natural increase ; 
 hence (apart from immigration) the birth-rate in a city is higher than 
 in the country. 
 
 45. As a thing is generally sold for more than it is worth, or for 
 
406 
 
 LOGICAL EXERCISES 
 
 less, one of the parties to an exchange commonly is a loser by the 
 transaction. 
 
 46. An increase in the amount of money tends to lower the rate of 
 interest, for interest is paid for the use of money. 
 
 47. Exchange between two traders in the same community com- 
 monly results in a profit to both. Such exchange is preferable to 
 exchange where one of the parties is an outsider, because only one 
 profit is realized by the community in the latter case. 
 
 48. The two following syllogisms are after the Stoic manner : — 
 
 (a) Nihil est tam contra naturam quam turpitudo. 
 
 Nihil est tam secundum naturam quam utilitas. 
 
 . \ In eadem re utilitas et turpitudo esse non possunt. 
 
 (f>) Quod honestum est, id est aut solum aut summum bonum. 
 
 Quod autem bonum est id certe utile. 
 
 Itaque, quidquid honestum, id utile. 
 
 — Cicero, De Officiis, III. viii , 35. 
 
 49. There is no such thing as innate knowledge. As it is evident 
 that new-born children, idiots, and even the great part of illiterate 
 men have not the least apprehension of the axioms alleged to be innate, 
 the advocates of innate ideas are obliged to assume that the mind can 
 have ideas without being conscious of them. But to say a notion is 
 imprinted on the mind and at the same time to maintain that the 
 mind is ignorant of it, is to make this impression nothing. If the 
 words, to be in the understanding, have any positive meaning, they 
 signify to be perceived and to be understood by the understanding: 
 hence, if any one asserts that a thing is in the understanding and yet 
 not understood by the understanding, and that it is in the mind with- 
 out being perceived by the mind, it amounts to saying that a thing is 
 and is not in the understanding. — Locke, Essay on Human Under- 
 standing. 
 
 50. There are some philosophers who imagine we are every mo- 
 ment intimately conscious of what we call our Self ; that we feel its 
 existence and its continuance in existence ; and are certain, beyond the 
 evidence of a demonstration, both of its perfect identity and simplicity. 
 Now, it is evident that there must be some one impression that gives 
 rise to every real idea. But self or person is not any one impression, 
 but that to which our several impressions and ideas are supposed to 
 have a reference. If any impression gives rise to the idea of self, that 
 impression must continue invariably the same through the whole 
 course of our lives ; since self is supposed to exist after that manner. 
 But there is no impression constant and invariable. Pain and pleasure, 
 
LOGICAL EXERCISES 
 
 407 
 
 grief and joy, passions and sensations succeed each other and never 
 all exist at the same time. It cannot, therefore, be from any of these 
 impressions or from any other that the idea of self is derived ; and 
 consequently there is no such idea. — Hume , A Treatise on Human 
 Nature. 
 
 51. According to the common view external objects — tables, trees, 
 horses, dogs — have an existence quite independent of the mind which 
 perceives them, and our ideas of them are copies or resemblances of 
 these things without us. Berkeley, however, combats this view with the 
 following argument : Either those external objects or originals of our 
 ideas are perceivable or they are not perceivable. If they are, then 
 they are ideas and we have gained our point ; but if you say they are 
 not, I appeal to any one whether it be sense to assert a color is like 
 something which is invisible ; hard or soft like something intangible; 
 and so of the rest. — Principles of Human Knowledge. 
 
 52. Motives are good or bad only on account of their effects ; good 
 on account of their tendency to produce pleasure, or avert pain ; bad 
 on account of their tendency to produce pain or avert pleasure. Let a 
 man’s motive be ill-will, — call it even malice, envy, cruelty, — it is still 
 a kind of pleasure that is his motive ; the pleasure he takes at the 
 thought of the pain which he sees, or expects to see, his adversary 
 undergo. Now even this wretched pleasure, taken by itself, is good : 
 it may be faint ; it may be short ; it must at any rate be impure ; yet 
 while it lasts and before any bad consequences arrive, it is as good as 
 any other that is not more intense. — Bentham, Principles of Morals 
 and Legislation. 
 
 53. It is in accordance with the traditional policy of the United 
 States that we should possess and develop colonies; for the states 
 were themselves originally a group of colonies, and our territories have 
 always been a most important feature of the growing power of the 
 nation, and territory is only another name for colony. 
 
 54. All that we know or conceive are our own ideas. When, there- 
 fore, you say all ideas are occasioned by impressions in the brain, do 
 you conceive this brain or no ? If you do, then you talk of ideas 
 imprinted in an idea causing that same idea, which is absurd. If you 
 do not conceive it, you talk unintelligibly, instead of forming a rea- 
 sonable hypothesis. — Berkeley, Hylas and Pliilonous. 
 
 65. What proves the soul to be matter — exceedingly fine matter, 
 of course — is the influence exercised upon it by the body in fainting, 
 anaesthesia, and delirium, in cases of injury and disease, and, above 
 all, the fact that the advance and the decline of the soul correspond 
 to analogous bodily conditions. The intellectual faculties are weak in 
 
408 
 
 LOGICAL EXERCISES 
 
 the period of childhood ; they grow strong in youth, and gradually 
 decay in old age. Sickness causes a serious reaction upon the soul ; 
 without the body the soul has no power to manifest itself. Nay, more 
 than that, the dying man does not feel his soul gradually withdrawing 
 from one organ to another, and then finally making its escape with its 
 powers unimpaired ; he experiences a gradual diminution of his mental 
 faculties. — Epicurus. 
 
 56. Consequens est : Si orator est, homo est. Inconsequens est : 
 Si homo est, orator est. Repugnans : Si homo est, quadrupes est. 
 
 — Augustine, Be Boot. Christ., II, 34. 
 
 57. The Greeks honored the gods and also the actors who took 
 part in scenic games (often debasing) in honor of the gods. The 
 Romans excluded such actors from citizenship on the ground that 
 their calling was degrading. Augustine reasons as follows : — 
 
 Proponunt Graeci : Si tales dii colendi sunt, tales homines hono- 
 randi. Adsumunt Romani : Sed nullo modo tales homines honorandi 
 sunt. Concludunt Christiani: Nullo modo igitur dii tales colendi 
 sunt. — Be Civ. Bei, II, 13. 
 
 58. Bain, in Senses and Intellect (p. 374), argues that “the con- 
 joint experience of the senses and the movements appears to me to 
 furnish all that we possess in the notion of extended matter. The 
 association between sight and locomotion, or between touch and the 
 movements of the arm, tells us that a given appearance implies the 
 possibility of a certain movement ; that a remote building implies a 
 continuance of our walking exertions to change its appearance into 
 another that we call a near view ; and the power of moving, the scope 
 for moving, exhausts every property in the idea of empty space. We 
 estimate it first by our own movements, and next by other movements 
 measured in the first instance by our own, as, for example, the flight 
 of a bird, the speed of a cannon ball, or the movement of light. The 
 mental conception that we have of empty space is scope for movement.” 
 
 Professor Baldwin, in the Handbook of Psychology (Vol. I, p. 136), 
 criticises the above as follows: “Now, if the idea of space enters 
 through the intensive feeling of muscular contraction, there is more 
 in our conclusion than in our premises, and we have an ignoratio ; if, 
 on the other hand, the sensation is one of movement proper, extension 
 has already entered and we need no association ; this is a petitio." 
 
 59. In mediaeval times it was held that Venus or that Saturn was 
 inhabited, not because any one could devise, with any degree of proba- 
 bility, any organized structure which would be suitable for animal 
 existence on the surfaces of those planets, but because it was conceived 
 that the greatness or goodness of the Creator, or His wisdom, or some 
 
LOGICAL EXERCISES 
 
 409 
 
 other of His attributes, would be manifestly imperfect if these planets 
 were not tenanted by living creatures. — Whewell. 
 
 60. That God is, the Bible affirms. Whatever the Bible affirms is 
 true, because it is from God, and declares it is impossible for God to 
 lie. Therefore the existence of God is surely proved. 
 
 61. No species of agnosticism is unrelated to its genus. No agnos- 
 ticism with a special reference or limited sphere is without reference 
 to the agnostic idea, spirit, and aim. On the contrary, every kind of 
 agnosticism tends towards agnostic completeness. Agnosticism in any 
 form is of the nature of agnosticism in every form. — Flint, Agnos- 
 ticism, p. 311. 
 
 62. The propounders of what are called the “ethics of evolution” 
 adduce a number of more or less interesting facts, and more or less 
 sound arguments in favor of the origin of the moral sentiments in the 
 same way as other natural phenomena, by a process of evolution. I 
 have little doubt, for my own part, that they are on the right track ; 
 but as the immoral sentiments have been no less evolved, there is, so 
 far, as much natural sanction for the one as the other. The thief and 
 the murderer follow nature just as much as the philanthropist. — 
 Huxley, Evolution and Ethics. 
 
 63. There is another fallacy wdiich appears to me to pervade the 
 so-called “ ethics of evolution.” It is the notion that because, on the 
 whole, animals and plants have advanced in perfection of organization 
 by means of the struggle for existence and the consequent survival of 
 the fittest ; therefore men in society, men as ethical beings, must look 
 to the same process to help them towards perfection. - — Huxley. 
 
 64. A profound study of the system of protection has taught us this 
 syllogism, upon which the whole doctrine reposes : — 
 
 The more men work the richer they become ; 
 
 The more difficulties there are to be overcome, the more work ; 
 
 Ergo , The more difficulties there are to be overcome, the richer 
 they become. — Bastiat, Economic Sopthisms. 
 
 65. The shopkeeper thrives only by the irregularities of youth ; the 
 farmer by the high prices of corn ; the architect by the destruction of 
 houses ; the officers of justice by lawsuits and quarrels. Ministers of 
 religion derive their distinction and employment from our vices and 
 our death. No physician rejoices in the health of his friends, nor 
 soldiers in the peace of his country ; and so of the rest. Therefore 
 carelessness, calamity, pestilence, disease, and even death are economic 
 blessings. — Montaigne. 
 
 66. Restrictive laws always land us in this dilemma : Either you 
 admit that they produce scarcity, or you do not. If you admit it, you 
 
410 
 
 LOGICAL EXERCISES 
 
 avow by the admission that you inflict on the people all the injury in 
 your power. If you do not admit it, you deny having restricted the 
 supply and raised prices, and consequently you deny having favored 
 the producer. — Basticit. 
 
 67. When products such as coal, iron, corn, or textile fabrics are 
 sent us from abroad, and we can acquire them with less labor than if 
 we made them ourselves, the difference is a free gift conferred upon 
 us. The gift is more or less considerable in proportion as the differ- 
 ence is more or less great. It amounts to a quarter, a half, or three- 
 quarters of the value of the product when the foreigner only asks us 
 for three-fourths, a half, or a quarter of the price we should otherwise 
 pay. It is as perfect and complete as it can be, when the donor (like 
 the sun in furnishing us with light) asks us for nothing. The question, 
 and we ask it formally, is this : Do you desire for our country the 
 benefit of gratuitous consumption, or the pretended advantages of 
 onerous production ? Make your choice, but be logical ; for as long as 
 you exclude as you do, coal, iron, corn, foreign fabrics in proportion 
 as their price approximates to zero, what inconsistency would it be to 
 admit the light of the sun, the price of which is already at zero during 
 the entire day ? — Bastiat. 
 
 68. To hear the roaring of the sea as one does, one must hear the 
 parts which compose its totality, that is, the sound of each wave, . . . 
 although this noise would not be noticed if the wave were alone. One 
 must be affected a little by the movement of one wave, one must have 
 some perception of each several noise, however small it be. Otherwise 
 one would not hear that of 100,000 waves, for of 100,000 zeros one can 
 never make a quantity. — Leibniz. 
 
 69. Mr. Spencer, in his exposition of the doctrine of evolution, is 
 guilty of the amazing fallacy of supposing that, because the laws of 
 energy are everywhere present, they are everywhere sufficient to ex- 
 plain what we see ; which is much the same as assuming that, because 
 a painter’s palette, like his finished canvas, shows us a mixture of 
 colors laid on with a brush, therefore what sufficed to produce the 
 one would equally suffice to produce the other. — Professor Ward, 
 Naturalism and Agnosticism. 
 
 70. No one can believe what he does not understand ; therefore 
 there are no mysteries in true religion. 
 
 71. Christianity is necessarily modified by the growth of civilization 
 and the exigencies of the times ; therefore the Catholic priesthood, 
 though necessary in the Middle Ages, may be superseded now. 
 
 72. There are rights of conscience such that every one may lawfully 
 advance a claim to profess and teach what is false and wrong in mat- 
 
LOGICAL EXERCISES 
 
 411 
 
 ters religious, social, and moral, provided that it seems absolutely 
 true and right to his private conscience ; therefore individuals have a 
 right to preach and practise polygamy. 
 
 73. There is no such thing as a national or state conscience ; 
 therefore no judgments can fall upon a sinful nation. 
 
 74. The civil power lias no positive duty in a normal state of 
 things to maintain religious truth ; therefore blasphemy and Sabbath- 
 breaking are not rightly punishable by law. 
 
 75. The civil power may dispose of church property without sacri- 
 lege ; therefore Henry VIII committed no sin in his spoliations. 
 
 76. The civil power has the right of ecclesiastical jurisdiction and 
 administration ; therefore parliament may impose articles of faith on 
 the church or suppress dioceses. 
 
 77. The people are the legitimate source of power ; therefore uni- 
 versal suffrage is among the natural rights of man. 
 
 78. Virtue is the child of knowledge and vice of ignorance ; there- 
 fore education, periodical literature, travelling, ventilation, drainage, 
 and the arts of life, when fully carried out, serve to make a population 
 moral and happy. 
 
 79. Unbelievers use the antecedent argument from the order of 
 nature against our belief in miracles. Here, if they only mean that 
 the fact of that system of laws, by which physical nature is governed, 
 makes it antecedently improbable that an exception should occur in it, 
 there is no objection to the argument ; but if, as is not uncommon, 
 they mean that the fact of an established order is fatal to the very 
 notion of an exception, they are using a presumption as if it were a 
 proof. — Newman, Grammar of AsseMf. 
 
 80. Gibbon mentions five causes to account for the establishment of 
 Christianity, — the zeal of the Christians, inherited from the Jews, 
 their doctrine of a future state, their claim to miraculous power, their 
 virtues, and their ecclesiastical organization. He thinks these five 
 causes, when combined, will fairly account for the event ; but he has 
 not thought of accounting for their combination. If they are ever so 
 available for his purpose, still that availableness arises out of their 
 coincidence, and out of what does that coincidence arise ? — Newman. 
 
 81. Bentham was clearly the victim of a common delusion. If a 
 system will work, the minutest details can be exhibited. Therefore, 
 it is inferred, an exhibition of minute detail proves that it will work. 
 Unfortunately, the philosophers of Laputa would have had no more 
 difficulty in filling up details than the legislators of England or the 
 United States. — Leslie Stephen , The English Utilitarians. 
 
 82. The “ rights of man ” doctrine confounds a primary logical canon 
 
412 
 
 LOGICAL EXERCISES 
 
 with a statement of fact. Every political theory must be based upon 
 facts as well as upon logic. Any reasonable theory about politics must 
 no doubt give a reason for inequality and a reason, too, for equality. 
 The maxim that all men were or ought to be “ equal ” asserts correctly 
 that there must not be arbitrary differences. Every inequality should 
 have its justification in a reasonable system. But when this undeni- 
 able logical canon is taken to prove that men actually are equal, there 
 is an obvious begging of the question. —Leslie Stephen. 
 
 83. I shall offer this one mark whereby prejudice may be known. 
 He that is strongly of any opinion must suppose (unless he be self- 
 condemned) that his persuasion is built upon good grounds, and that 
 his assent is no greater than what the evidence of the truth he holds 
 forces him to ; and that they are arguments and not inclinations of 
 fancy that make him so confident and positive in his tenets. Now if, 
 after all his profession, he cannot bear any opposition to his opinion — 
 if he cannot so much as give a patient hearing, much less examine and 
 weigh the arguments on the other side — does he not plainly confess, it 
 is prejudice governs him ? And it is not the evidence of truth, but 
 some lazy anticipation, some beloved presumption that he desires to 
 rest undisturbed in. For, if what he holds be as he gives out, well 
 fenced with evidence, and he sees it to be true, what need he fear to 
 put it to the proof ? — Locke , The Conduct of the Understanding. 
 
 84. When Mill urges us to choose the higher rather than the lower 
 pleasures, then either the so-called “higher” pleasure is actually, as 
 pleasure, so preferable to that called “ lower ” that the smaller amount 
 of the one would be more pleasurable than the largest amount of the 
 other ; or else the higher is called higher and is to be preferred to the 
 lower — even though the latter may be greater as pleasure — because 
 of a quality belonging to it over and above its character as pleasant 
 feeling. The former verdict would be, in the first place, paradoxical, 
 and in the second place would give up Mill’s case by reducing quality 
 to a quantitative standard. According to the latter verdict, the char- 
 acteristic upon which the distinction of quality depends, and not 
 pleasure itself, becomes the ethical standard. — Sorley, Ethics of 
 Naturalism. 
 
 85. Every one desires happiness; virtue is happiness; therefore 
 every one desires virtue. — Aristotle. 
 
 86. The principles of justice are variable ; the appointments of 
 nature are invariable ; therefore the principles of justice are no 
 appointment of nature. — Aristotle. 
 
 87. It is no doubt true that if a law be universal, it will be confirmed 
 by all our experiments ; therefore, when all our experiments fail to 
 detect an exception, we may regard the law as true universally. 
 
LOGICAL EXERCISES 
 
 413 
 
 PART II 
 
 1. When a coin and a feather are dropped simultaneously in the 
 receiver of an air-pump, the air being left in, the feather flutters to 
 the bottom after the coin ; but, when the air is pumped out of the 
 receiver, the coin and the feather, being dropped at the same instant, 
 reach the bottom of the receiver together. 
 
 2. If a beam of the sun’s light is passed through a prism, a colored 
 band nearly five times as long as it is broad results. Newton tried 
 several experiments in which he varied the size of prism, and the 
 quality of the glass ; he also passed the beam through various parts of 
 the same prism, and tried other minor suppositions. But in all these 
 cases there was the same color effect produced. 
 
 3. Nitrogen obtained from various chemical sources is of uniform 
 density ; in 1894, Lord Rayleigh and Professor Ramsay, noting the 
 fact that atmospheric nitrogen is about one-half per cent heavier, were 
 led to the discovery of a hitherto unknown substance which received 
 the name of argon. 
 
 4. If the earth were 9500 miles in diameter instead of 8000, this 
 increase would give two-thirds increase in bulk, and a corresponding 
 increase of density due to the greater gravitative force ; the mass 
 would be about double what it is. But with double the mass, the 
 quantity of gases of all sorts attracted and retained by gravity would 
 probably have been double, and in that case there would have been 
 double the quantity of water produced, as no hydrogen would then 
 escape. But the surface of the globe would be only one-half greater 
 than at present, in which case the water would have sufficed to cover 
 the whole surface several miles deep. 
 
 5. Wherever the winds blow over extensive areas of water on to 
 the land, especially if there are mountains or elevated plateaus which 
 cause the moisture-laden air to rise to heights where the temperature 
 is lower, clouds are formed and rain falls. But where the land is of 
 an arid nature and much heated by the sun, the air becomes capable 
 of holding still more aqueous vapor, and even dense rain-clouds disperse 
 without producing any rainfall. 
 
 6. Very thin sheets of white light proceeding from various incan- 
 descent substances are passed through incandescent hydrogen, and 
 the emergent light is then separated into its constituent elements by a 
 prism. In the spectra thus obtained it is found that there are invariably 
 dark lines occupying precisely the same relative position. But trying 
 similar experiments with any other element than incandescent hydro- 
 
414 
 
 LOGICAL EXERCISES 
 
 gen, the lines obtained never occupy the same positions in the spectrum 
 as the lines in question. 
 
 7. (a) Hawksbee in 1715 first noticed that by striking a bell in the 
 receiver of an air-pump, the bell was heard when the receiver was full 
 of air ; but when the receiver was exhausted, no sound was heard. 
 
 (6) Also, it was found that as the air was gradually admitted into 
 the receiver, the sound of the bell grew louder and louder. 
 
 8. The following are the results of a series of experiments conducted 
 by Dr. Wells in order to discover the cause of dew : — 
 
 (a) Moisture bedews a cold metal or stone when we breathe upon it. 
 The same appears on a glass of ice-water, and on the inside of windows 
 when sudden rain or hail chills the external air ; the inference is that 
 when an object contracts dew, it is colder than the surrounding air. 
 
 (b) No dew is deposited on a piece of metal which has been polished, 
 but on the same metal unpolished dew is deposited copiously. There- 
 fore the deposit of dew is affected by the kind of surface which is 
 exposed. 
 
 (c) With various kinds of polished metals, no dew is deposited ; 
 but with various kinds of glass, having highly polished surfaces, dew 
 is deposited. Therefore, the deposit of dew is affected also by the 
 kind of substances themselves. 
 
 (d) In general, it has been found that those substances are most 
 strongly dewed which conduct heat worst, while those which conduct 
 heat well resist dew most effectively. 
 
 (e) Again, substances of close firm texture, as stones and metals, 
 have less dew, while substances of looser texture, as cloth, wool, velvet, 
 eider-down, cotton, have more dew. But substances of loose texture 
 resist the passage of heat, therefore the more these substances resist 
 the passage of heat the greater the deposit of dew. 
 
 (/) All instances in which much dew is deposited have this feature 
 in common : they either radiate heat rapidly or conduct it slowly. 
 All instances in which no dew or very little is deposited have in com- 
 mon the opposite feature. 
 
 (ff) The property of radiating heat rapidly, or conducting it slowly, 
 signifies that the body in question tends to lose heat more rapidly from 
 the surface than it can be restored from within. And this in turn 
 renders the body colder than the surrounding air. Therefore a body 
 colder than the surrounding air precipitates the dew upon it. 
 
 (fi) It is known by direct experiment that for any given degree of 
 temperature, only a limited quantity of water can remain suspended 
 in the state of vapor, and this quantity grows less and less as the 
 temperature diminishes. Therefore if there is already as much vapor 
 
LOGICAL EXERCISES 
 
 415 
 
 suspended as the air will contain at its existing temperature, any 
 lowering of the temperature will cause necessarily a portion of the 
 vapor to he condensed and become water. 
 
 (i) It is possible by cooling the surface of any body to find some 
 temperature lower than that of the surrounding air, at which the dew 
 begins to appear. 
 
 ( j) It is observed that dew is not deposited on cloudy nights, but 
 if the clouds withdraw and leave a clear opening a deposition of dew 
 immediately begins. Dew formed in clear intervals disappears when 
 the sky becomes thickly overcast. Now a clear sky is nothing but the 
 absence of clouds, and it is a known property of clouds that they keep 
 up the temperature of exposed surfaces by radiating heat to them. 
 We see that the disappearance of clouds will cause these surfaces to 
 cool, and cold surfaces, as has been shown, condense the moisture of 
 the air in the form of dew. 
 
 9. To the Editor of The Tribune. 
 
 Sir: In your issue of Sunday, February 7, is an article entitled 
 “Results of Antitoxin Treatment.” After quoting statistics showing 
 a remarkable decrease in the mortality from diphtheria treated with 
 antitoxin, as compared to diphtheria treated without antitoxin, you 
 say: — 
 
 “ The one point now in doubt, and, it must be confessed, in serious 
 doubt, is the effect of antitoxin itself upon the human system. In 
 many cases this has seemed to be injurious, if not fatal. Patients have 
 been cured of diphtheria, only to suffer from declining vitality and a 
 train of grievous disorders sometimes baffling the physicians’ skill and 
 ending in death. Are they caused by antitoxin ? ” 
 
 Before the antitoxin treatment was dreamed of it was a common 
 occurrence — more common than now — for a patient to be “ cured of 
 diphtheria” and then to “suffer from declining vitality,” etc., all too 
 frequently “ending in death.” 
 
 But no one ascribed these post-diphtheritic fatalities to the treat- 
 ment. They were, very properly, believed to be the result of the 
 action of the poison of diphtheria upon the cells of the body. There 
 can be no doubt that this toxin (poison) has the power seriously to 
 affect, and even to destroy, certain tissues. Therefore it is common 
 for diphtheria to be accompanied or followed by palsies, Bright’s dis- 
 ease, neuritis, anaemia (declining vitality), etc. 
 
 A child who has had diphtheria is liable to suffer from the dele- 
 terious effects for months or even years. That these results are due 
 to the toxin of diphtheria and not to the antitoxin is very clearly shown 
 by the fact that the mortality and the serious after-effects are so much 
 
416 
 
 LOGICAL EXERCISES 
 
 less when the antitoxin is used early in the disease than when it is used 
 in the last stages thereof, i.e. when the antitoxin is administered early 
 the poison is destroyed before it has had time to do extensive injury. 
 
 10. Further explanation is needed of the extraordinary increase in 
 deaths from consumption in this state as shown by the annual report 
 of the State Board of Health. There were 361 more deaths by con- 
 sumption reported in 1899 than in 1898, and the number was 419 more 
 than the average for the preceding twenty-one years. The increase in 
 deaths from acute lung diseases is also noteworthy, and as the same 
 conditions which give rise to the latter are likely to produce fatal ter- 
 mination in chronic cases, the connection between the two is perhaps 
 not difficult to establish. There must, however, have been some special 
 cause for the unusual mortality from diseases of the lungs. 
 
 The hypothesis may be advanced that there was no real increase 
 over past years, but that the apparent increase is due to fuller and 
 more accurate reports. This can hardly be accepted as a plausible 
 explanation, since the system of gathering mortuary statistics last year 
 was the same that had been employed for a number of years previously, 
 and is as complete as can be devised to secure accuracy. The cause 
 must be looked for elsewhere, and it will probably be found by a care- 
 ful study of the atmospheric and climatic conditions existent during 
 the year just ended. The winter was not one of more than ordinary 
 severity, but attended with sudden and sharp variations of tempera- 
 ture, always trying upon persons of weak lungs. There was much 
 snow and slush, filling the air with moisture, and during the late winter 
 and early spring dense fogs were frequent. The spring months were 
 also marked by rapid changes in temperature, while during the summer 
 cool nights following hot days were the rule. 
 
 Considerable light might be thrown on the matter by noting whether 
 the increase in deaths was general throughout the state or confined to 
 certain localities ; whether there was any difference between the region 
 adjacent to the sea-coast and the more remote sections, where the influ- 
 ence of the ocean upon the climate is not so marked. The reports 
 from city and country might also be compared. 
 
 11. To the philosopher the state is a human organism, a human 
 person ; but if so, the human spirit which lives in it must also have a 
 human body, for spirit and body belong to one another, and between 
 them make up the person. In a body which is not organized and 
 human, the spirit of man cannot truly live. The body politic must 
 therefore imitate the body natural of man. The perfect state is, as it 
 were, the visible body of humanity. — Bluntschli, Theory of the State. 
 
 12. In the Yale-Princeton intercollegiate debate in 1895, Yale con- 
 
LOGICAL EXERCISES 
 
 417 
 
 tended that the referendum had failed in Switzerland, and therefore, 
 in all probability, would fail in the United States. On the other hand, 
 Princeton maintained that the referendum had succeeded in Switzer- 
 land, and therefore, in all probability, would succeed in the United 
 States. Supposing the premise true in each case, which position is 
 the stronger ? 
 
 13. We may observe a very great similitude between the earth 
 which we inhabit and the other planets. They all revolve around the 
 sun as the earth does, though at different distances and in different 
 periods. They borrow all their light from the sun as the earth does. 
 Several of them are known to revolve round their axis like the earth, 
 and by that means have a like succession of day and night. Some of 
 them have moons that serve to give them light in the absence of the 
 sun, as our moon does to us. They are all, in their motions, subject 
 to the same law of gravitation as the earth is. From all this simili- 
 tude, it is not unreasonable to think that these planets may, like our 
 earth, be the habitation of various orders of living creatures. — Reid, 
 Intellectual Powers. 
 
 14. Some remarkable observations of the French astronomer, 
 M. Camille Flaminarion, have been recently reported, which go to 
 show that within certain limits the radiations of heat from the sun 
 vary quite regularly during the eleven and a half year sun-spot cycle, 
 and that these variations of solar heat apparently cause some defi- 
 nite changes in the natural phenomena of the earth. For instance, 
 his figures prove that when sun spots are most numerous (as in 
 1893), migratory birds return to any given place earlier in the year than 
 usual ; and, on the contrary, when spots are at a minimum, they do 
 not come back until a much later date. These phenological researches 
 corroborate previous evidence, proving that after the sun has been 
 abnormally agitated — erupting enormous tongues of flame one hun- 
 dred thousand miles high, which frequently form directly over the 
 spots — the earth receives more heat ; and when (as was the case in 
 1898) the sun is comparatively calm and spotless he is less fiery, and 
 hence slightly less influential on our globe. 
 
 Because the well-known periodic changes of solar activity are not 
 followed by corresponding synchronous changes in the earth’s atmos- 
 phere, many scientists deny that there is any connection — forgetting 
 that effects generally lag far behind their causes and that nature seldom 
 accomplishes her work at a leap. Professor Yon Bezold, the German 
 meteorologist, expresses the view generally accepted by astronomers, 
 when he says: — 
 
 “It is not inconceivable if we should find the explanation of that 
 
418 
 
 LOGICAL EXERCISES 
 
 remarkable periodicity in the temperature of whole zones, demon- 
 strated by Koeppen in 1873, which without doubt indicates a close 
 connection with the processes on the sun’s surface, although the 
 irregularities in the times of occurrence of the maximum and minimum 
 temperatures, amounting to years of delay in certain zones, seem at 
 first sight to prove that there is no such connection.” 
 
 15. If a small jet of steam is sent into two large glass receivers, 
 one filled with ordinary air, the other with air which has been filtered 
 by passing through a thick layer of cotton-wool, so as to keep back all 
 particles of solid matter, the first vessel will be instantly filled with 
 condensed, cloudy-looking vapor, while in the other vessel the air and 
 vapor will remain perfectly transparent and invisible. 
 
 16. It is a very suggestive fact that most of the stars belonging to 
 the Milky Way have spectra of the solar type, which indicates that 
 they are of the same general constitution as our sun, and are also at 
 about the same stage of evolution ; and this may well have arisen 
 from their origin in a great nebulous mass situated at or near the 
 centre of the galactic plane, and probably revolving round their com- 
 mon centre of gravity. — Wallace, Man's Place in the Universe. 
 
 17. If the moon had been destined to be merely a lamp to our 
 earth, there was no occasion to variegate its surface with lofty moun- 
 tains and extinct volcanoes, and cover it with large patches of matter 
 that reflect different quantities of light and give its surface the appear- 
 ance of continents and seas. It would have been a better lamp had it 
 been a smooth piece of lime or of chalk. It is therefore prepared for 
 inhabitants, and similarly all other satellites are also inhabited. — Sir 
 David Brewster. 
 
 18. A chemist, as Mill observes, analyzes a substance, and assum- 
 ing the accuracy of his results, we at once infer a general law of 
 nature from “a single instance.” But if any one from the beginning 
 of the world has seen that crows are black, and a single credible wit- 
 ness says that he has seen a gray crow, we abandon at once a conjunc- 
 tion which seemed to rest upon invariable and superabundant evidence. 
 Why is a “single instance” sufficient in one case, and any number of 
 instances insufficient in the other ? 
 
 19. What is the explanation of the following quotation from Scho- 
 penhauer : “False judgments are frequent, false conclusions very 
 rare.” 
 
 20. Stahl, a contemporary of Newton, supposed that all combust- 
 ible substances contain a common element, or fire principle, which he 
 called phlogiston, and which escapes in the process of combustion. 
 But when it was observed that zinc and lead and sundry other sub- 
 
LOGICAL EXERCISES 
 
 419 
 
 stances grow heavier in burning, it seemed hardly correct to suppose 
 that anything had escaped from these substances. To this objection 
 the friends of the fire principle replied that phlogiston might weigh 
 less than nothing, that is, might be endowed with a positive property 
 of levity, so that to subtract it from a body would increase the weight 
 of the body. 
 
 21. In all unhealthy countries the greatest risk of fever is run by 
 sleeping on shore. Is this owing to the state of the body during sleep, 
 or to a greater abundance of miasma at such times ? It appears cer- 
 tain that those who stay on board a vessel, though anchored at only a 
 short distance from the coast, generally suffer less than those actually 
 on shore. — Darwin in Voyage of Naturalist. 
 
 22. That the period of the tide should be accidentally the same as 
 that of the culmination of the moon, that the period of the highest 
 tide should be accidentally the same as that of the syzygies, is possible 
 in abstracto ; but it is in the highest degree improbable ; the far more 
 probable assumption is, either that sun or moon produce the tide, or 
 that their motion is due to the same grounds as the motion of the tide. 
 
 23. In measuring the velocity of sound by experiments conducted at 
 night with cannon, the results at one station were never found to agree 
 exactly with those at the other. Moreover, it was noticed that on the 
 nights when the discordance was greatest, a strong wind was blowing 
 nearly from one station to the other. 
 
 24. M. Melloni, observing that the maximum point of heat is trans- 
 ferred farther and farther towards the red end of the spectrum, accord- 
 ing as the substance of the prism is more and more permeable to heat, 
 inferred that a prism of rock salt, which possesses a greater power 
 of transmitting the calorific rays than any known body, ought to throw 
 the point of greatest heat to a considerable distance beyond the visible 
 part of the spectrum ; and his prediction was verified by subsequent 
 experiment. 
 
 25. During the middle of the eighteenth century Bonnet and Spal- 
 lanzani discovered that the horns, tails, legs, eyes, or even head of 
 some creatures, if cut off, would grow again. The tail and legs of a 
 salamander were removed and reproduced themselves eight times in 
 succession. By means of a number of experiments it has been found 
 that the more simple the structure of an animal is, the more do its 
 several parts possess a power of independent existence, and that in the 
 more complex animals, the derangement of one part much more affects 
 the action of the entire organism. 
 
 26. Professor Jevons has observed that economic crises have occurred 
 at regular intervals of about ten years. This ten-year periodicity, 
 
420 
 
 LOGICAL EXERCISES 
 
 moreover, seems to correspond to a similar periodicity of bad harvests ; 
 and the cause of this seems to be a decennial periodicity in the spots 
 on the sun. 
 
 27. What is the significance of the remark of Chevreul, the French 
 scientist : “ Every fact is an abstraction.” 
 
 28. Also of the following remark of M. Espinas: “If human activity 
 was incompatible with the order of things, the act of boiling an egg 
 would have to be regarded as a miracle.” 
 
 29. It had long been known that grasshoppers and crickets have on 
 their anterior legs two peculiar, glassy, generally more or less oval, 
 drumlike structures ; but these were supposed by the older entomolo- 
 gists to serve as resonators, and to reenforce or intensify the well- 
 known chirping sounds which they produce. Johannes Muller was 
 the first who suggested that these drums or tympana act like the tym- 
 pana of our own ears, and that they are really the external parts of 
 a true auditory apparatus. That any animal should have its ears in 
 its legs sounds, no doubt, a priori, very unlikely, and hence probably 
 the true function of this organ was so long unsuspected. — Sir John 
 Lubbock. 
 
 30. In simple fracture of the ribs, if the lung be punctured by a 
 fragment, the blood effused into the pleural cavity, though freely 
 mixed with air, undergoes no decomposition. Why air introduced 
 into the pleural cavity through a wounded lung should have such 
 wholly different effects from that entering directly through a wound 
 in the chest was to me a complete mystery until I heard of the germ- 
 theory of putrefaction, when it at once occurred to me that it was only 
 natural that air should be filtered of germs by the air-passages, one of 
 whose offices is to arrest inhaled particles of dust and prevent them 
 from entering the air-cells. — Professor Lister. 
 
 31. If the lungs be emptied as perfectly as possible and a handful 
 of cotton-wool be placed against the mouth and nostrils, and you 
 inhale through it, it will be found on expiring this air through a glass 
 tube that its freedom from floating matter is manifest. The applica- 
 tion of this is obvious : if a physician wishes to hold back from the 
 lungs of his patient, or from his own, the germs, or virus, by which 
 contagious disease is propagated, he will employ a cotton-wool respi- 
 rator. — Professor Tyndall. 
 
 32. In the desert of North Africa, where neither trees, brushwood, 
 nor even undulation of the surface afford the slightest protection to 
 its foes, a modification of color in animals which shall be assimilated 
 to that of the surrounding country is absolutely necessary. Hence, 
 without exception, the upper plumage of every bird, whether lark, 
 
LOGICAL EXERCISES 
 
 421 
 
 chat, sylvian, or sand-grouse, and also the fur of all the smaller mam- 
 mals and the skin of all snakes and lizards, is of one uniform isabelline, 
 or sand color. — Wallace. 
 
 33. Darwin, in investigating the difference in weight between cross 
 and self-fertilized plants, found that the six finest crossed plants 
 averaged 108.16 ounces, whilst the six finest self-fertilized plants 
 averaged only 23.7 ounces, or as 100 to 22. 
 
 34. Bees incessantly visit the flowers of the common broom, and 
 these are adapted by a curious mechanism for cross-fertilization. 
 When a bee lights on the wing-petals of a young flower, it is slightly 
 opened, and the short stamens spring out, which rub their pollen 
 against the abdomen of the bee. If a rather older flower is visited 
 for the first time (or if the bee exerts great force on a younger flower), 
 the keel opens along its whole length, and the longer as well as the 
 shorter stamens, together with the much elongated curved pistil, 
 spring forth with violence. The flattened spoonlike extremity of 
 the pistil rests for a time on the back of the bee, and leaves on it the 
 load of pollen with which it is charged. As soon as the bee flies away, 
 the pistil instantly curls round, so that the stiginatic surface is now 
 upturned and occupies a position in which it would be rubbed against 
 the abdomen of another bee visiting the same flower. Thus, when 
 the pistil first escapes from the keel, the stigma is rubbed against the 
 back of the bee, dusted with pollen from the longer stamens, either of 
 the same or another flower ; and afterwards against the lower surface 
 of the bee, dusted with pollen from the shorter stamens, which is often 
 shed a day or two before that from the longer stamens. If the visits 
 of bees are prevented, and if the flowers are not dashed by the wind 
 against any object, the keel never opens, so that the stamens and 
 pistil remain enclosed. Plants thus protected yield very few pods in 
 comparison with those produced by neighboring uncovered bushes, 
 and sometimes none at all. — Darwin. 
 
 35. Baron Zach received a letter from Pons, a successful finder of 
 comets, complaining that for a certain period he had found no comets, 
 though he had sought diligently. Zach, a man of much sly humor, 
 told him that no spots had been seen on the sun for about the same 
 time — which was true — and assured him that when the spots came 
 back, the comets would come with them. Some time after that he got 
 a letter from Pons, who informed him, with great satisfaction, that he 
 was quite right, that very large spots had appeared on the sun, and 
 that he had found a fine comet shortly after. — Be Morgan's Budget 
 of Paradoxes. 
 
LOGICAL EXERCISES 
 
 If Tellus winged be, 
 
 The earth a motion round ; 
 
 Then much deceived are they 
 Who nere before it found. 
 
 Solomon was the wisest, 
 
 His wit nere this attained ; 
 
 Cease, then, Copernicus, 
 
 Thy hypothesis vain ! 
 
 — Sylvanus Morgan , 1652. 
 
 37. Weather Forecaster Dunn has prepared a chart showing the 
 number of deaths from grip in New York City during the period from 
 March 22 to May 16, 1891, establishing the relation between the death- 
 rates and weather conditions during the grip epidemic of that year. 
 Mr. Dunn has made a careful study of records of the disease, and 
 selected the epidemic of 1891 as being the time when the grip was 
 most pronounced. 
 
 He has apparently demonstrated that the weather is an important 
 factor in the mortality of grip cases. He says that humidity or mois- 
 ture in the air seems to be the most important element in causing the 
 disease to spread. There is a corresponding increase of deaths with 
 increasing humidity. 
 
 The fatality is most marked when the humidity is at its maximum 
 and there is a sudden fall of the temperature. This is shown by the 
 record of April 21, when the death-rate from grip was the highest ever 
 known. During the twenty-four hours of that day 250 deaths were 
 reported. On April 1 and April 30 the death-rate was also high. These 
 were days following a sudden fall in temperature. 
 
 All through the epidemic the charts show an increasing death-rate 
 with high or increasing humidity. The higher the humidity and the 
 more sudden the fall in temperature, the greater was the number of 
 deaths. When the temperature and the humidity dropped at the same 
 time, there was a decrease in the death-rate, as Mr. Dunn points out 
 by several examples. He says that the lesson to be learned from his 
 chart is that those suffering from an incipient attack of the grip should 
 be most cautious of the cold, humid days that immediately follow the 
 warm, damp ones. 
 
 38. If in a reservoir, immersed in water, the air be compressed to 
 the extent of ten atmospheres, and supposing that now, when the com- 
 pressed air has acquired the temperature of the water, it be allowed to 
 act upon a piston loaded by a weight, the weight is raised. At the 
 same time the water becomes cooler, showing that a certain quantity 
 
LOGICAL EXERCISES 
 
 423 
 
 of heat had disappeared in producing the mechanical effort of raising 
 the weight. 
 
 39. That the feeling of effort is largely, if not entirely, of peripheral 
 rather than central origin, appears from such experiments as the 
 following : — 
 
 Hold the finger as if to pull the trigger of a pistol. Think vigorously 
 of bending the finger, but do not bend it. An unmistakable feeling of 
 effort results. Repeat the experiment, and notice that the breath is 
 involuntarily held, and that there are tensions in the other muscles. 
 Repeat the experiment again, taking care to keep the breathing regular 
 and the other muscles passive. Little or no feeling of effort will now 
 accompany the imaginary bending of the finger. — Ferrier. 
 
 40. As to the nature of petrified shells, Quirini conceived that as 
 earthy particles united in the sea so as to form the shells of Mollusca, 
 the same crystallizing process might be effected on the land ; and that 
 in the latter case the germs of the animals might have been dissemi- 
 nated through the substance of the rocks, and afterwards developed by 
 virtue of humidity. 
 
 41. Voltaire suggested that the marine shells found on the tops of 
 mountains are Eastern species dropped from the hats of pilgrims as 
 they returned from the Holy Land. 
 
 42. The epicyclical theory of the heavens was confirmed by its pre- 
 dicting eclipses of the sun and moon, configurations of the planets, and 
 other celestial phenomena. 
 
 43. Arfvedson discovered lithia, by perceiving an excess of weight 
 in the sulphate produced from a small portion of what he considered 
 as magnesia present in a mineral he had analyzed. 
 
 44. We see among the nebula? (which are diffused along the Milky 
 Way) instances of all degrees of condensation, from the most loosely 
 diffused fluid to that separation and solidification of parts by which 
 suns and satellites and planets are formed ; and thus we have before 
 us instances of systems in all their stages, as in a forest we see trees 
 in every period of growth. — Laplace. 
 
 45. It had been deductively inferred from the Copernican theory 
 that the planets, Venus and Mercury, ought to pass through phases, 
 like the moon, and the telescope revealed this to be the case. 
 
 46. Werner, says Sir Charles Lyell, had not travelled to distant 
 countries ; he had merely explored a small portion of Germany, and 
 conceived, and persuaded others to believe, that the whole surface of 
 our planet, and all the mountain chains in the world, were made after 
 the model of his own province. 
 
 47. Scheiner was a monk ; and on communicating to the superior 
 
424 
 
 LOGICAL EXERCISES 
 
 of his order the account of the spots on the sun, received the reply : 
 “ I have searched through Aristotle, and can find nothing of the kind 
 mentioned : be assured, therefore, that it is a deception of your senses, 
 or of your glasses.” 
 
 48. When we are told that a man has become deranged from 
 anxiety or grief, we have learned very little if we rest content with 
 that. How does it happen that another man, subjected to an exactly 
 similar cause of grief, does not go mad ? — Maudsley. 
 
 49. It was a general belief at St. Kilda that the arrival of a ship 
 gave all the inhabitants colds. Dr. John Campbell took pains to 
 ascertain the fact and to explain it as the effect of effluvia arising from 
 human bodies ; it was discovered, however, that the situation of St. 
 Kilda renders a northeast wind indispensably necessary before a ship 
 can make the landing. 
 
 60. Chrysippus maintained that cock-fighting was the final cause of 
 cocks, these birds being made by Providence in order to inspire us by 
 the example of their courage. 
 
 61. Touch in succession various objects on the table. A paper- 
 weight, if metallic, is usually cold to the touch ; books, paper, and 
 especially a woollen table-cover, comparatively warm. Test them by 
 means of a thermometer, and there will be little or no difference in 
 their temperatures. Why then do some feel cold, others warm, to the 
 touch ? The sense of touch does not inform us directly of temperature, 
 but of the rate at which our finger gains or loses heat. As a rule, 
 bodies in a room are colder than the hand, and heat always tends to 
 pass from a warmer to a colder body. Of a number of bodies, all 
 equally colder than the hand, that one will seem coldest to the touch, 
 as the metallic, which is able most rapidly to convey away heat from 
 the hand. — Tait. 
 
 52. One of Joule’s experiments concerning the mechanical value of 
 
 light is as follows : He compared the heat evolved in the wire 
 
 conducting a galvanic current when the wire was ignited by the 
 passage of the current with that evolved when with an equal current it 
 was kept cool by immersion in water. These experiments showed a 
 small but unmistakable diminution of the heat when light also was 
 given out. — Tait. 
 
 53. It is an illusion in psychology and a corruption of logic to take 
 the conditions which occasion the logical operations of thought for the 
 operations themselves. There is only one delusion more desperate 
 still, — to imagine that a complete physical theory of the nervous 
 system will explain that which is itself the condition of any theory 
 being possible at all. — Lutze. 
 
LOGICAL EXERCISES 
 
 425 
 
 54. During the retreat of the Ten Thousand a cutting north wind 
 blew in the faces of the soldiers ; sacrifices were offered to Boreas, and 
 the severity of the wind immediately ceased, which seemed a proof of 
 the god’s causation. 
 
 55. It has been shown by observation that over-driven cattle, if 
 killed before recovery from their fatigue, become rigid, and putrefy in 
 a surprisingly short time. A similar fact has been observed in the 
 case of animals hunted to death, cocks killed during a fight, and 
 soldiers slain in battle. The contrary is remarked when the muscular 
 exercise has not been great or excessive. 
 
 56. A correct analysis of lapis lazuli was suspected to he erroneous 
 because there seemed to be nothing in the elements assigned to it, 
 which were silica, alumina, soda, sulphur, and a trace of iron, to 
 account for the brilliant blue color of the stone. 
 
 57. According to the theory that the earth has but a thin crust, it 
 is still substantially a liquid globe, and therefore, under the attractive 
 influence of the sun and moon, it ought to behave like a yielding liquid. 
 According to Hopkins, Thomson, and others, the earth in all its 
 astronomical relations behaves like a rigid solid, — a solid more rigid 
 than a solid globe of glass, — and the difference between the behavior 
 of a liquid globe and a solid globe could easily be detected by astro- 
 nomical phenomena. — Le Conte. 
 
 58. Many years ago I was struck with the fact that humblehees, as 
 a general rule, perforate flowers only when these grow in large num- 
 bers near together. In a garden where there were some very large 
 beds of Stachys coccinea and of Pentstemon argutus, every single 
 flower was perforated ; but I found two plants of the former species 
 growing quite separate with their petals much scratched, showing that 
 they had been frequently visited by bees, and yet not a single flower 
 was perforated. I found also a separate plant of the Pentstemon , and 
 saw bees entering the mouth of the corolla and not a single flower had 
 been perforated. In the following year (1842) I visited the same 
 garden several times: on the 19th of July humblehees were sucking 
 the flowers in the proper manner, and none of the corollas were per- 
 forated. On the 7th of August all the flowers were perforated, even 
 those on some few plants of the salvia, which grew at a little distance 
 from the great bed. On the 21st of August only a few flowers on the 
 summits of the spikes of both species remained fresh, and not one of 
 these was now bored. Again, in my own garden every plant in several 
 rows of the common bean had many flowers perforated; but I found 
 three plants in separate parts of the garden which had sprung up 
 accidentally, and these had not a single flower perforated. General 
 
426 
 
 LOGICAL EXERCISES 
 
 Strachey formerly saw many perforated flowers in a garden in the 
 Himalaya, and he wrote to the owner to inquire whether this relation 
 between the plants growing crowded and their perforation by bees 
 there held good, and was answered in the affirmative. Hence it follows 
 that the red clover and the common bean when cultivated in great 
 masses in fields, Erica tctraliz growing in large numbers on heaths, — 
 rows of the scarlet kidney-bean in the kitchen garden, — and masses 
 of any species in the flower garden are all eminently liable to be per- 
 forated. The explanation of this is not difficult. Flowers growing in 
 large numbers attract crowds of insects. They are thus stimulated to 
 work quickly by rivalry. Also many flowers have their nectaries dry, 
 which is most quickly discovered by biting holes in them. 
 
 — Charles Darwin. 
 
 69. The seat of sensation is in the heart, as it is in the centre of 
 the body ; the brain is cold in order that it may counteract the heat 
 of the heart. In order to temper the coldness of the brain, blood is 
 conveyed to the membrane which envelopes it by means of veins or 
 channels. But, lest the heat so conveyed should injure the brain, the 
 veins, instead of being large and few, are small and many, and the 
 blood conveyed, instead of being copious and thick, is thin and pure. — 
 Aristotle. 
 
 60. The lungs of a fox must be a specific for asthma, because that 
 animal is remarkable for its strong powers of respiration. — Paris' 
 Pharmacologia. 
 
 61. Galileo discovered, by the use of his telescope, the four small 
 satellites which circulate round Jupiter. It was then inferred that 
 what happened on the smaller scale might also be found true of the 
 larger planetary system. 
 
 62. The first step toward the discovery of photography was the 
 knowledge that visual light caused a chemical change in iodide of 
 silver. The second step was to fix in permanent position the portion 
 of the substance changed by the light, while the unchanged portion 
 was removed. 
 
 From what is known of the chemical elements and their compounds, 
 it seems highly probable that numerous compounds may exist which 
 are sensitive in the same way to waves of entirely different lengths 
 from those that produce vision. Even with the salts of silver it has 
 long been known that the range of wave-lengths capable of producing 
 photographic effect is much greater than the visual range ; and that the 
 wave-lengths which produce the maximum physiological effect (light) 
 are not the same as those that produce the maximum photographic 
 effect. 
 
LOGICAL EXERCISES 
 
 427 
 
 It has been shown by Professor S. R. Langley that flint glass is 
 transparent to waves about four times as long as the longest in the 
 visual range ; and that rock-salt is transparent to a range below the 
 red end of the visible spectrum twenty-nine times as long as the entire 
 visual range. Glass is opaque to very short waves, its limit in that 
 direction being nearly coincident with the visual limit. Quartz, on 
 the other hand, is transparent to a range of short waves extending far 
 beyond the visual limit, but is opaque to very short waves. May not 
 these substances prove valuable in this new field of actinography, as 
 quartz trains have proved in photographing the ultra-violet spectrum ? 
 
 Should the report of this discovery (Rontgen’s) be confirmed, we 
 cannot fail to accord the highest praise to this new triumph of science, 
 and to predict a development of the new field of actinography that 
 may prove of greater importance than photography. 
 
 From the analogy between this form of radiant energy and dark 
 heat it might appropriately be called “dark light.” — The Electrical 
 World. 
 
 63. As to the theory of geyser-eruption, the following principles 
 have been established. The boiling-point of water rises as the pressure 
 increases, being 293° for a pressure of four atmospheres. Also, if the 
 pressure be diminished when the water is under very strong pressure, 
 the water will immediately flash into steam. Moreover, if the circula- 
 tion is impeded, as when the water is contained in long, narrow, 
 irregular tubes, and heated with great rapidity, the boiling-point will 
 be reached below while it is far from this point in the upper part of 
 the tube. Therefore at the moment of eruption the boiling-point for 
 the lowest depth is actually reached. The water there being trans- 
 ferred into steam, the expanding steam would lift the whole column of 
 water in the tube, causing an overflow. This would diminish the press- 
 ure in every part of the tube, and consequently a large quantity of 
 water before very near the boiling-point would flash into steam and 
 instantly eject the whole of the water in the pipe, the steam rushing 
 out immediately afterwards. The premonitory cannonading beneath 
 is evidently produced by the collapse of large steam-bubbles rising 
 through the cooler part of the water of the tube. — Bunsen's Theory. 
 
 64. Mackenzie’s theory of geyser-eruption is that the geyser pipe is 
 connected by a narrow conduit with the lower part of a subterranean 
 cave, whose walls are heated by the near vicinity of volcanic fires. 
 The water rising above the opening of the conduit, and changing into 
 steam, and having no way of escape, would, through pressure thus 
 caused, be forced up the pipe, the steam rushing after it. Professor 
 Le Conte says of this theory : If there were but one geyser, this would 
 
428 
 
 LOGICAL EXERCISES 
 
 be considered a very ingenious and probable hypothesis ; for we may 
 conceive of a cave and a conduit so constructed as to account for the 
 phenomena. But there are so many geysers that it is inconceivable 
 that all of them should have caves and conduits so peculiarly con- 
 structed. This theory, therefore, is entirely untenable. 
 
 65. It has been found by experiment that a current moving at the 
 rate of three inches per second will take up and carry along fine clay ; 
 moving six inches per second, will carry fine sand ; eight inches per 
 second, coarse sand the size of linseed ; twelve inches, gravel ; twenty- 
 four inches, pebbles ; three feet, angular stones of the size of a hen’s 
 egg. It will be readily seen that the carrying power increases much 
 more rapidly than the velocity. For instance, a current of twelve 
 inches per second carries gravel, while a current of three feet per 
 second, only three times greater velocity, carries stones many hundred 
 times as large as grains of gravel. 
 
 66. If wood be soaked in a strong solution of sulphate of iron 
 (copperas) and dried, and the same process be repeated until the 
 wood is highly charged with this salt, and then burned, the structure 
 of the wood will be perserved in the peroxide of iron left. Also, it is 
 well known that the smallest fissures and cavities in rocks are speedily 
 filled by infiltrating waters with mineral matters. Now, wood buried 
 in soil soaked with some petrifying material becomes highly charged 
 with the same, and the cells filled with infiltrated matter, and when the 
 wood decays the petrifying material is left, retaining the structure of 
 the wood. In nature also there is an additional process, not illustrated 
 by the experiment or by the example of infiltrated fillings. As each 
 particle of organic matter passes away by decay, a particle of mineral 
 matter takes its place, until finally the whole of the organic matter is 
 replaced. 
 
 67. As to the origin of bitumen, the following observations have 
 been made : Certain organic matters a,t ordinary temperature, in pres- 
 ence of abundant moisture, and out of contact of air, will undergo a 
 species of decomposition or fermentation by which an oily or tarry sub- 
 stance, similar to bitumen is formed. In the interior of heaps of vege- 
 table substance such bituminous matter is often found. Fossil cavities 
 have been found in solid limestone containing bitumen, evidently 
 formed by decomposition of the animal matter. So, also, shales have 
 been found in Scotland, filled with fishes which have changed into 
 bitumen. 
 
 68. Count Rumford in 1798 proved that the common notion that 
 heat was a substance was false, by boring a large piece of brass, 
 under great pressure of the borer, whilst the brass was in a gallon 
 
LOGICAL EXERCISES 
 
 429 
 
 of water ; and at the end of two and one-half hours the water actually 
 boiled. 
 
 69. Kenelm Digby’s treatment of wounds was to apply an ointment, 
 not to the wound itself, but to the sword that had inflicted it, to dress 
 this carefully at regular intervals, and in the meantime, having bound 
 up the wound, to leave it alone for seven days. It was observed that 
 many cures followed upon this treatment. 
 
 70. When Pascal’s barometer was carried to the top of Puy-de- 
 Dome, and the mercury in it fell, it was inferred that the fall of the 
 mercury was due to the change in elevation. Before finally accepting 
 this conclusion, the barometer was placed in exposed positions and in 
 sheltered, when the wind blew and when it was calm, in rain and in 
 fog ; and these varying circumstances did not materially affect the 
 result. 
 
 71. A French experimenter, Pouchet, thought he had obtained 
 indubitable evidence of spontaneous generation. He took infusions 
 of vegetable matter, boiled them to a pitch sufficient to destroy all 
 germs of life, and hermetically sealed the liquid in glass flasks. After 
 an interval, micro-organisms appeared. It seems that at a certain stage 
 in Pouchet’s process, he had occasion to dip the mouths of the flasks 
 in mercury. It occurred to Pasteur, in repeating the experiments, 
 that germs might have found their way in from the atmospheric dust 
 on the surface of this mercury. And when he carefully cleansed the 
 surface of the mercury, no life appeared afterwards in his flasks. 
 
 72. The causes to which the decay of the natives of New Zealand 
 have been assigned are given as follows : drink, disease, European cloth- 
 ing, peace, and wealth. — Journal of the Anthropological Institute. 
 
 73. An eminent judge was in the habit of jocosely propounding, 
 after dinner, a theory that the cause of the prevalence of Jacobinism was 
 the practice of bearing three names. He quoted, on one side, Charles 
 James Fox, Richard Brinsley Sheridan, John Horne Tooke, John 
 Philpot Curran, Samuel Taylor Coleridge, Theobald Wolfe Tone. 
 On the other hand there were William Pitt, John Scott, William 
 Windham, Samuel Horsley, Henry Dundas, Edmund Burke. More- 
 over, the practice of giving children three names has been a growing 
 practice, and Jacobinism has also been growing. The practice of 
 giving children three names is more common in America than in Eng- 
 land. In England, we still have a King and a House of Lords ; but 
 the Americans are Republicans. Burke and Theobald Wolfe Tone 
 are both Irishmen ; therefore the being an Irishman is not the cause 
 of Jacobinism. Horsley and Horne Tooke are both clergymen ; there- 
 fore the being a clergyman is not the cause of Jacobinism. Fox and 
 
430 
 
 LOGICAL EXERCISES 
 
 Windham were, both educated at Oxford ; therefore the being educated 
 at Oxford is not the cause of Jacobinism. Pitt and Horne Tooke 
 were both educated at Cambridge ; therefore the being educated at 
 Cambridge is not the cause of Jacobinism. The cause is, therefore, 
 the having three names. — Macaulay. 
 
 74. The exotic Pelargonia have a peculiar herring-bone structure in 
 the petals ; moreover, the herring-bone structure is conjoined in the 
 Pelargonia with the general characteristics of the Geraniece. Also the 
 flowers with such seed-vessels as our wild geraniums have the char- 
 acters of Geraniece. It is, therefore, exceedingly probable that our 
 wild geraniums should have the peculiar herring-bone structure. 
 
 75. Colonies ought not to rebel against the mother country, since 
 they are its children and children ought not to rebel against their 
 parents. 
 
 76. Finding that the size of towns varies concomitantly with the 
 size of the rivers on which they are built, an observer might infer 
 that the size of the river was due to the size of the town. 
 
 77. An eminent author, writing on the work of the English Church 
 before the Tractarian movement, contrasts the newer state of things 
 unfavorably with the older, because the Church in those former days 
 taught us to use religion as a light by which to see our way along the 
 road of duty. Without the sun our eyes would be of no use to us ; but 
 if we look at the sun, we are simply dazzled and can see neither it nor 
 anything else. It is precisely the same with theological speculations. 
 If the beacon lamp is shining, a man of healthy mind will not discuss 
 the composition of the flame. 
 
 78. Scarlet color prevails among balsamina, euphorbia, pelargo- 
 nium, poppy, salvia, bouvardia, and verbena, yet none of the scarlets 
 are of sweet perfumes. Some of the light-colored balsams and ver- 
 benas are sweet-scented, but none of the scarlets are. The common 
 sage with blue blooms is odoriferous both in flower and foliage ; but 
 the scarlet salvias are devoid of smell. None of the sweet-scented- 
 leaved pelargoniums have scarlet blooms, and none of the scarlet 
 bloomers have sweet scent of leaves nor of blooms. Some of the 
 white-margined poppies have pleasant odors ; but the British scarlets 
 are not sweet-scented. The British white-blooming hawthorn is of 
 the most delightful fragrance ; the scarlet flower has no smell. Some 
 of the honeysuckles are sweetly perfumed, but the scarlet trumpet is 
 scentless. 
 
 79. The productive powers of plants, judging from the increased 
 fertility of the parent plants and from the increased powers of growth 
 in the offspring, are favored by some degree of differentiation in the 
 
LOGICAL EXERCISES 
 
 431 
 
 elements which interact and unite so as to form a new being. Here 
 we have some analogy with chemical affinity or attraction, which 
 comes into play only between atoms or molecules of a different nature. 
 As Professor Miller remarks : “ Generally speaking, the greater the 
 difference in the properties of two bodies, the more intense is their 
 tendency to mutual chemical action. But between bodies of a similar 
 character the tendency to unite is feeble.” 
 
 80. In affirming that the growth of the body is mechanical, and 
 that thought, as exercised by us, has its correlative in the physics of 
 the brain, I think the position of the “materialist” is stated, as far 
 as that position is a tenable one. I think the materialist will be able 
 finally to maintain this position against all attacks ; but I do not 
 think, in the present condition of the human mind, that he can pass 
 beyond this position. I do not think he is entitled to say that his 
 molecular groupings and his molecular motions explain everything. 
 In reality, they explain nothing. The utmost he can affirm is the 
 association of the two classes of phenomena, of whose real bond of 
 union he is in absolute ignorance. The problem of the connection of 
 body and soul is as insoluble in its modern form as it was in the pre- 
 scientific ages. Phosphorus is known to enter into the composition of 
 the human brain, and a trenchant German writer has exclaimed, 
 “Ohne Phosphor, kein Gedanke ! ” That may or may not be the 
 case ; but even if we knew it to be the case, the knowledge would not 
 lighten our darkness. — Tyndall. 
 
 81. Granting that Hegel was more or less successful in constructing, 
 a priori, the leading results of the moral sciences, still it was no proof 
 of the correctness of the hypothesis of identity, with which he started. 
 The facts of nature would have been the crucial test. That in the 
 moral sciences traces of the activity of the human intellect and of the 
 several stages of its development should present themselves, was a 
 matter of course ; but surely, if nature really reflected the result of 
 the thought of a creative mind, the system ought, without difficulty, to 
 find a place for her comparatively simple phenomena and processes. 
 — Helmholtz. 
 
 82. When young Galileo was a student at Pisa, he noticed one day, 
 during the service at the great Cathedral, the chandelier swinging 
 backwards and forwards, and convinced himself, by counting his 
 pulse, that the duration of the oscillations was independent of the arc 
 through which it moved. 
 
 83. Goethe enunciated the existence of a resemblance between the 
 different parts of one and the same organic being. According to 
 Goethe’s own account, the idea first occurred to him while looking at 
 
432 
 
 LOGICAL EXERCISES 
 
 a fan-palm at Padua. He was struck by the immense variety of 
 changes of form which the successively developed stem-leaves exhibit, 
 by the way in which the first simple root leaflets are replaced by a 
 series of more and more divided leaves, till we come to the most com- 
 plicated. He afterwards succeeded in discovering the transformation 
 of stem-leaves into sepals and petals, and of sepals and petals into 
 stamens, nectaries, and ovaries, and thus he was led to the doctrine of 
 the metamorphosis of plants which he published in 1790. 
 
 84. A fortunate glance at a broken sheep’s-skull, which Goethe 
 found by accident on the sand of the Lido at Venice, suggested to him 
 that the skull itself consisted of a series of very much altered vertebrae. 
 At first sight no two things can be more unlike than the broad, uni- 
 form, cranial cavity of the mammalia, enclosed by smooth plates, and 
 the narrow cylindrical tube of the spinal marrow, composed of short, 
 massy, jagged bones. — Helmholtz. 
 
 85. The existence of the so-called blind spot in the eye was first 
 demonstrated by theoretical arguments. While the long controversy 
 whether the perception of light resided in the retina or the choroid 
 was still undecided, Mariotte asked himself what perception there was 
 where the choroid is deficient. He made experiments to discover this 
 point and in the course of them discovered the blind spot. 
 
 86. Haiiy observed that crystals of “heavy spar” from Sicily and 
 those from Derbyshire (which were considered to be the same sub- 
 stance) differed in their angles of cleavage by three and one-lialf 
 degrees, and remarked : “I could not suppose that this difference was 
 the effect of any law of decrement ; for it would have been necessary 
 to suppose so rapid and complex a law, that such a hypothesis might 
 have been justly regarded as an abuse of the theory.” Vauquelin by 
 chemical analysis discovered that the base of the crystals from Sicily 
 was strontia, and that of those from Derbyshire was baryta. These 
 facts, becoming known to Haiiy, enabled him by inference to discover 
 that the angles of crystals might be employed as a test for the presence 
 of different substances which very nearly resemble each other in other 
 respects, 
 
 87. Graebe, a German chemist, in investigating a class of com- 
 pounds, called the quinones, determined incidentally the molecular 
 structure of a body closely resembling alizarine, which had been dis- 
 covered several years before. This body was derived from naphthaline, 
 and, like many similar derivatives, was reduced back to naphthaline 
 when heated with zinc-dust. This circumstance led the chemist to 
 heat also madder alizarine with zinc-dust, when, to his surprise, he 
 obtained anthracene. Of course, the inference was at once drawn that 
 
LOGICAL EXEECISES 
 
 433 
 
 alizarine must have the same relation to anthracene that the allied 
 coloring matter bore to naphthaline ; and, more than this, it was also 
 inferred that the same chemical processes which produced the coloring 
 matter from naphthaline when applied to anthracene would yield aliza- 
 rine. The result fully answered these expectations, and now alizarine 
 is manufactured on a large scale from anthracene obtained from coal- 
 tar. — Coolie , The New Chemistry. 
 
 88. Sir Charles Lyell, by studying the fact that the river Ganges 
 yearly conveys to the ocean as much earth as would form sixty of the 
 great pyramids of Egypt, was enabled to infer that the ordinary slow 
 causes now in operation upon the earth would account for the immense 
 geological changes that have occurred, without having recourse to the 
 less reasonable theory of sudden catastrophes. 
 
 89. Joule’s experiments show that when heat is produced by the 
 consumption of work, a definite quantity of work is required to produce 
 that amount of heat which is known to the physicists as the unit of 
 heat ; the heat, that is to say, which is necessary to raise one gramme 
 of water through one degree centigrade. The quantity of work neces- 
 sary for this is, according to Joule’s best experiments, equal to the 
 work which a gramme would perform in falling through a height of 
 425 metres. 
 
 In order to show how closely concordant are his numbers, I will 
 adduce the results of a few series of experiments which he obtained 
 after introducing the latest improvements in his methods. 
 
 (а) A series of experiments in which water was heated by friction 
 in a brass vessel. In the interior of this vessel a vertical axis provided 
 with sixteen paddles was rotated, the eddies thus produced being broken 
 by a series of projecting barriers, in which parts were cut out large 
 enough for the paddles to pass through. The value of the equivalent 
 was 424.9 metres. 
 
 (б) Two similar experiments, in which mercury in an iron vessel 
 was substituted for water in a brass one, gave 425 and 426.3 metres 
 respectively. 
 
 (c) Two series of experiments, in which a conical ring rubbed 
 against another, both surrounded by mercury, gave 426.7 and 425.6 
 metres respectively. 
 
 Exactly the same relations between heat and work were also found 
 in the reverse process; that is, when work was produced by heat. — 
 Helmholtz. 
 
 90. A gas which is allowed to expand with moderate velocity be- 
 comes cooled. Joule was the first to show the reason of this cooling. 
 Eor the gas has, in expanding, to overcome the resistance which the 
 
434 
 
 LOGICAL EXERCISES 
 
 pressure of the atmosphere and the slowly yielding sides of the vessel 
 opposed to it ; or, if it cannot of itself overcome this resistance, it sup- 
 ports the arm of the observer, which does it. Gas thus performs work, 
 and this work is produced at the cost of its heat. Hence the cooling. 
 If, on the contrary, the gas is suddenly allowed to issue into a perfectly 
 exhausted space where it finds no resistance, it does not become cool, 
 as Joule has shown. — Helmholtz. 
 
 91. The principal feature in the plan of my attempt to penetrate 
 into the North Polar region, or if possible to cross it, is, in brief, to try 
 to make use of the currents of the sea, instead of fighting against them. 
 My opinion is, as I have already explained on several occasions, that 
 there must somewhere run currents into the Polar region, which carry 
 the floe-ice across the Polar Sea, first northward toward the Pole, and 
 then southward again into the Atlantic Ocean. That these currents 
 really exist all Arctic expeditions prove, as most of them have had to 
 fight against the currents and against the ice drifting southward, be- 
 cause they have tried to get northward from the wrong side. I think 
 a very simple conclusion must be drawn from this fact that currents 
 and drifting ice are constantly coming from the unknown north, viz. : 
 Currents and perhaps also ice must pass into this same region, as the 
 water running out must be replaced by water running in. This con- 
 clusion is based upon the simplest of all natural laws ; but there seem 
 to be people who will not even admit the necessity of this. 
 
 That such currents run across the North Polar region is also proved 
 by many facts. I may mention the great quantities of Siberian 
 driftwood which are annually carried to the shores of Spitzbergen and 
 Greenland ; it comes in such abundance and with such regularity that 
 it is quite impossible it should be carried to these shores, so far from 
 the original home, by occasional winds or currents. There must be a 
 regular communication between the coasts of Siberia and those of 
 Spitzbergen and Greenland. By this same communication were several 
 objects from the unfortunate Jeannette carried to the Greenland coast. 
 The Jeannette sank in June, 1881, to the north of the New Siberian 
 Islands, and three years afterward, in June, 1884, a great many objects 
 belonging to her or her crew were found on an ice-floe on the southwest 
 coast of Greenland. This floe can only have been brought there by the 
 same current which carries the driftwood. By this same current an 
 Esquimau implement, a throwing-stick or harpoon-thrower, was also 
 carried the long way from Alaska to the west coast of Greenland. 
 There can, in my opinion, be no doubt of the existence of such a com- 
 munication or current across the North Polar region from the Siberian 
 side to the Greenland side. — Dr. Nansen in The Strand Magazine. 
 
INDEX 
 
 Abstract, 20. 
 
 Abstraction, 15. 
 
 Accent, 160. 
 
 Accident, 391., 161. 
 
 Adams, 272. 
 
 A dicto secundum quid ad dictum 
 simpliciter, 161. 
 
 A dicto simpliciter ad dictum secun- 
 dum quid, 161. 
 
 ^Esthetics and logic, 11. 
 
 Agassiz, 72. 
 
 Agreement, method of, 222 f. 
 
 Algebra and logic, 123. 
 
 Ambiguity, fallacies of, 158 ff . 
 Amphiboly, 159. 
 
 Analogy, 151, 187, 314 f., 371, 375. 
 Analysis, 376. 
 dtpaipems, 15. 
 
 Aquapendente, 319. 
 
 Argumentum ad baculum, 162; 
 hominem, 162; ignorantiam, 162; 
 judicum, 163; populum, 162; rem, 
 163 ; verecundiam, 162. 
 
 Aristotle, 15, 23, 37, 53, 103, 104, 138, 
 139, 157, 164, 169, 192, 195, 386 f., 
 390. 
 
 Bacon, 62 f., 169, 192, 212, 213, 230, 
 310, 326, 363 f., 369, 370, 390 f. 
 
 Bain, 169, 327. 
 
 Barrett, 204, 360. 
 
 Begriff, 5. 
 
 Beneke, 185. 
 
 Bergmann, 367. 
 
 Berkeley, 17. 
 
 Beudant, 267. 
 
 Bluntschli, 383 f. 
 
 Boole, 325. 
 
 Bosanquet, 89, 99, 176, 177, 185, 187, 
 189, 201, 219, 397. 
 
 Boyle, 237. 
 
 Brahe', Tycho, 215, 390. 
 
 Brewster, 187, 233. 
 
 Brown, 202. 
 
 Bullen, 346. 
 
 Bunsen, 345. 
 
 Caesalpinus, 390. 
 
 Campanella, 389. 
 
 Categorical judgment, 78 f. 
 Categories, 37. 
 
 Causal analysis, 188, 206 ff. 
 Causation, 41, 195 ff., 330 f. 
 Chalmers, 210. 
 
 Chemistry, method of, 378. 
 Chenevix, 362. 
 
 Circulus in definiendo, 46; in pro - 
 bando, 165. 
 
 Circumstantial evidence, 346. 
 
 Clark, 281. 
 
 Classification, 55 f., 316, 372, 374; 
 artificial, 56 ; as affected by evolu- 
 tion, 59 f. ; serial, 58 ; natural, 56 f. ; 
 of the sciences, 62 f . 
 
 Clifford, 195, 284 f ., 290, 324. 
 Coexistence, 208. 
 
 Coincidence and cause, 345. 
 Collective use of a term, 160. 
 Collocation, 209 f., 353. 
 
 Composition, 159. 
 
 Comte, 62 f. 
 
 Concept, 5, 7, 10, 13 f., 25 f. 
 Conceptual processes, fallacies of, 
 359. 
 
 Concomitant variations, method of, 
 223, 258 ff . 
 
 Concrete, 21. 
 
 Concurrence, 207. 
 
 Connotation, 42. 
 
 Conservation of energy, 196. 
 Consilience of inductions, 309. 
 Content, 42. 
 
436 
 
 INDEX 
 
 Contradiction, law of, 98 ff. 
 
 Contradictory, 107 ; opposition, 
 100 f. ; terms, 52. 
 
 Contrapositive, 111 f., 116 f. 
 
 Contrary, 106; opposition, 100 f., 
 terms, 52. 
 
 Converse accident, 161. 
 
 Conversion, 110 f., 117 f. 
 
 Copernicus, 390. 
 
 Copleston, 396. 
 
 Copula, 33 f., 73. 
 
 Counter-dilemma, 147. 
 
 Cuvier, 90 f. 
 
 Darwin, Charles, 209, 216, 245, 253, 
 255 f., 265 f., 277, 283 f., 291, 292, 
 296 f., 301, 304, 322, 324, 342. 
 
 Darwin, Francis, 277, 292. 
 
 Darwin, G. H., 244. 
 
 Davy, 273, 315. 
 
 Deduction, 96 f. ; and induction, 
 169 ff. 
 
 Definition, 44 if. ; and determinate 
 reference, 68; by description, 47; 
 for purposes of identification, 48 ; 
 genetic, 47; nominal, 44; real, 
 44. 
 
 Demonstrative judgment, 68. 
 
 De Morgan, 214. 
 
 Denotation, 42. 
 
 Derivative laws, 352. 
 
 Descartes, 325. 
 
 Determinate reference, 68. 
 
 Determination, process of, 74, 81. 
 
 Diagnostic property, 57. 
 
 Dialectic method, 53 f., 369. 
 
 Dichotomy, 51 f. 
 
 Dictum de omni et nullo, 138. 
 
 Difference, method of, 222 f., 
 236 ff. 
 
 Differentia, 39 f. 
 
 Differentiation, 20; of concepts, 79. 
 
 Dilemma, 145 f. 
 
 Disjunctive judgment, 78 ff. 
 
 Distribution of terms, 124 ff. 
 
 Distributive use of a term, 160. 
 
 Diversity, 13. 
 
 Division, 50 f., 160; as in determi- 
 nate reference, 68 ; empirical, 54 ; 
 logical, 54. 
 
 Duhamel, 178. 
 
 Elimination by negation, 83, 102 ; in 
 the syllogism, 123. 
 
 Empirical, 16, 30. 
 
 Empirical laws, 351 if. 
 
 Enthymeme, 130 f. 
 
 Enumeration, 184 f. 
 
 Episyllogism, 132. 
 
 Equivocation, 158 f. 
 
 Ethics and logic, 11. 
 
 Eudemus, 139. 
 
 Exceptional phenomena, 289. 
 Experiment, 212 f. 
 
 Explanation, a form of inference, 
 94. 
 
 Extension, 42. 
 
 Extra-syllogistic reasoning, 149 ff. 
 
 Fact and truth, 171. 
 
 Fallacies, deductive, 157 ff. ; induc- 
 tive, 359 ff. 
 
 Faraday, 204, 213 f., 244, 245 , 246, 
 267, 281, 286, 288, 314, 323, 364. 
 Fichte, 53. 
 
 Figure, 137 f. ; of speech, 160. 
 
 Fizeau, 280. 
 
 Florens, 328. 
 
 Forel, 246, 255. 
 
 Form and matter, 172. 
 
 Foucault, 280. 
 
 Froude, 397. 
 
 Fundamentum divisionis. 50. 
 
 Galenus, 139. 
 
 Galileo, 164, 390. 
 
 Generalization, 107 f. ; hasty, 371. 
 Genetic concept, 22 f. 
 
 Genus, 39 f. 
 
 Gide, 269, 342. 
 
 Gilbert, 390. 
 
 Glauber, 277. 
 
 Gore, 216, 274, 292, 315, 319, 360, 362. 
 Graber, 247. 
 
 Graphic representation of method of 
 concomitant variations, 260. 
 Green, 94, 192, 195, 201. 
 
 Grimaldi, 310. 
 
 Guyot, 233. 
 
 Halley, 276, 281 f. 
 
 Hamilton, Sir Rowan, 285. 
 
 Harvey, 319, 329. 
 
INDEX 
 
 437 
 
 Hatchette, 267, 367. 
 
 Hegel, 53, 54. 
 
 Heraclitus, 365. 
 
 Herschel, 202, 213, 277, 323, 369, 394. 
 
 Hildebrand, 382. 
 
 Holland, 323. 
 
 Hume, 197 f. 
 
 Huyghens, 279 f. 
 
 Hypothesis, 291, 376 f. 
 
 Hypothetical judgment, 78 f. 
 
 Identity, 13 ; in difference, 94 ; law 
 of, 98 ff. 
 
 Idols of Bacon, 364 f. 
 
 Ignoratio elenchi, 162. 
 
 Ignotum per ignotius, 46. 
 
 Illicit process, 129. 
 
 Imagination, 299; fallacies of, 359. 
 
 Immediate inference, a generaliza- 
 tion of, 117 if. 
 
 Impersonal judgment, 67. 
 
 Implication, 104; in immediate in- 
 ference, 103 f . 
 
 Indirect prediction, 286 ff. 
 
 Individual judgment, 69 f. 
 
 Induction, 96 f. ; and deduction, 
 169 ff. ; as reverse process, 177 ; 
 historical sketch of, 385 ; imper- 
 fect and perfect, 185 ; methods of, 
 222 ff . ; types of, 183 ff . 
 
 Inductive hazard, 175. 
 
 Inductive methods and the sciences, 
 374 ff. 
 
 Inducto = deductive method, 278 ff., 
 375, 378. 
 
 Inference, 9 f . ; a generalization of 
 immediate, 117 f. ; immediate, 
 103 ff. ; mediate, 122 ff. ; nature 
 of, 85 ff. ; relation of, to judgment, 
 95. 
 
 Infima species, 40, 
 
 Insurance, 341. 
 
 Intension, 42. 
 
 Interpretation, process of, 6. 
 
 Intuitionalism, 30. 
 
 Inverse, 117 f. 
 
 James, 93. 
 
 Janet, 317, 327. 
 
 Jebb, 387. 
 
 Jenkin, 212 284 f. 
 
 Jenner, 292, 327. 
 
 Jevous, 177, 178, 179, 187, 210, 215, 
 233, 246, 247 , 268 f., 276, 281, 287, 
 288, 316, 323, 397. 
 
 Joint method of agreement and 
 difference, 222 f., 248 ff. 
 
 Joule, 285. 
 
 Judgment, 7 f., 25 f. ; and language, 
 33 ; fallacies of, 359 f . ; of identifi- 
 cation, 8; particular, 40; relation 
 to inference, 95; singular, 67 f. ; 
 universal, 36 f. 
 
 Judgments of elaboration, 8. 
 Jurisprudence, method of, 382. 
 
 Kant, 53, 197. 
 
 Karayopia, 37. 
 
 Kepler, 310, 390, 395. 
 
 Kirby, 306. 
 
 Kircher, 323. 
 
 Kirchoff, 345. 
 
 Knies, 382. 
 
 Ladd, 383 f. 
 
 Language and thought, 23 f. 
 
 La Place, 276, 295. 
 
 Lavater, 170. 
 
 Law. 180. 
 
 Laws of thought, 98 ff . 
 
 Leffingwell, 344. 
 
 Leibniz, 102. 
 
 Leonardo da Vinci, 181, 388. 
 
 Le Verrier, 272. 
 
 Linnaeus, 323. 
 
 Lister, 324. 
 
 Lloyd, 285. 
 
 Locke, 169, 392, 396. 
 
 Lockyer, 316. 
 
 Logical squares : — - A square, 118 ; 
 E square, 119; I square, 120; 
 O square, 120. 
 
 \6yos, 3, 23. 
 
 Lotze, 162, 173, 176, 177, 179, 180, 192, 
 201, 242, 302, 303, 397. 
 
 Loua, 342. 
 
 Lubbock, 220 f., 246, 250, 254 f., 307, 
 312, 319, 320 f . 
 
 Lyell, 264. 
 
 Mallet, 245. 
 
 Malthus, 324, 354. 
 
438 
 
 INDEX 
 
 Mansel, 200. 
 
 Many questions, fallacy of, 165. 
 Mathematico-experimental method, 
 290. 
 
 Matter and form, 172. 
 
 Max Muller, 24. 
 
 Mechanical energy, 211. 
 
 Mental picture and the concept, 19. 
 Method, historical, 380 f. 
 
 Methods of Mill, 222 ff. 
 
 Middle, undistributed, 126 f. 
 
 Mill, 148 f., 160, 169, 175, 180, 198, 199, 
 200, 202, 209, 212, 218, 224, 257, 312, 
 326, 353, 357, 394, 396. 
 
 Minto, 396. 
 
 Mnemonic lines of the syllogism, 139. 
 Modality, 83 f. 
 
 Modus ponens, 144. 
 
 Modus ponendo tollens, 145. 
 
 Modus tollendo ponens, 146. 
 
 Modus tollens, 144. 
 
 Molar energy, 211. 
 
 Mood, 133 If. 
 
 Narrative judgment, 67. 
 
 Natural kind, 57 f., 314. 
 
 Negation, significant and non-sig- 
 nificant, 75, 100, 101; implication 
 of, 76; infinite, 77. 
 
 Negative determination, 217. 
 Negative judgment, 73 ff., 82. 
 Newman, 396. 
 
 Newton, 14, 187, 193, 276, 279 f., 294, 
 310, 393. 
 
 Non causa pro causa, 165, 363. 
 
 Non sequitur, 164. 
 
 Observation, 212 f. 
 
 Obversion, 114 f., 117 f. 
 
 Oersted, 286. 
 
 Owen, 322. 
 
 Particular affirmative, 104. 
 Particular negative, 104. 
 
 Pasteur, 224, 282 f. 
 
 Perception and inference, 86; falla- 
 cies of, 359 ff. 
 
 Perceptive judgment, 68. 
 
 Per genus et differentiam, 45, 47. 
 Petitio Principii, 164. 
 
 Plateau, 246, 254. 
 
 Plato, 53, 195, 385. 
 
 Political economy, method of, 382. 
 Porphyry, 39 ; tree of, 51 f . 
 
 Post hoc ergo propter hoc, 165, 363. 
 Potential in inference, 92. 
 
 Potential properties in concepts, 17. 
 Predicables, 38 f. 
 
 Predicate, grammatical, 33 f. ; logi- 
 cal, 33 f. 
 
 Prediction, 278 ff. 
 
 Preyer, 199. 
 
 Priestley, 242. 
 
 Probability, 330 ff. 
 
 Proper name as subject of a judg- 
 ment, 69; connotation of, 70 f. 
 Property, 39 f. 
 irpbadetris, 15. 
 
 Prosyllogism, 132. 
 
 Psychology, method of, 379, 383. 
 
 Quetelet, 337. 
 
 Railroad accidents, 339 f. 
 
 Reality, 27 f., 94, 96; as logical sub- 
 ject, 33 f. ; metaphysical nature 
 of, 31; in thought, 29. 
 
 Reduction, 178. 
 
 Reference, indeterminate, 68 f. 
 Reflection, 4. 
 
 Refutation, law of economy of, 108. 
 Relations, validity of, in reasoning, 
 152 f. 
 
 Residues, method of, 223, 271 ff. 
 Richter, 367. 
 
 Romanes, 311. 
 
 Roscher, 382. 
 
 Rule, 180. 
 
 Saigey, 226, 262, 311. 
 
 Saint-Pierre, 328. 
 
 Savigny, 382. 
 
 Sclileiermacher, 169. 
 
 Schonbein, 275. 
 
 Schopenhauer, 15. 
 
 Scientific analysis, 188. 
 
 Senses, as source of knowledge, 4 . 
 Sequence, 206 f. 
 
 Sidgwick, 363. 
 
 Siemens, 281. 
 
 Sigwart, 176, 177, 179, 194, 201, 209, 
 230, 241, 290, 312, 397. 
 
lNl)EX 439 
 
 Singular judgment, 27, 67 f., 79. 
 Smith, Adam, 363. 
 
 Social factor in judgment, 31 f. 
 Socrates, 385. 
 
 Socratic method, 74. 
 
 Sorites, 132. 
 
 Species, 39 f. 
 
 Spencer, 62 f., 355, 376 £. 
 
 Spinoza, 301. 
 
 Sprengel, 320. 
 
 Statistical method, 376. 
 
 Subaltern, 105. 
 
 Subcontrary, 106. 
 
 Subject, grammatical, 33 f. ; logical, 
 33 f. 
 
 Sufficient reason, 201 ; law of, 98 ff. 
 Summum genus, 40. 
 
 Syllogism, 122 ff . ; hypothetical, 
 142 ff. ; disjunctive, 144 ff. 
 Synthesis, 15, 376. 
 
 System, 5, 79 f., 89 f., 154 f., 170 ff. 
 
 Tait, 196, 261, 275, 281, 287, 293, 309. 
 Teleology, 317 f. 
 
 Telesius, 389, 390. 
 
 Tennyson, 93. 
 
 Term, 35. 
 
 Thackeray, 99. 
 
 Theophrastus, 139. 
 
 Thomson, 261, 275. 
 
 Thought, the nature of, 3 ff. 
 
 Transformations, 110 ff. 
 
 Trichotomy, 53. 
 
 Trilemma, 148. 
 
 Truth, 11, 171. 
 
 Tyndall, 215, 218 f., 235, 237, 262, 
 263 f., 283, 286, 298 f., 323. 
 
 Ueberweg, 89, 169, 181, 185, 190, 201, 
 368, 387. 
 
 Ultimate laws, 352. 
 
 Uniformity of nature, 173, 176, 196. 
 Universal, 4; in inference, 93; af- 
 firmative, 104 ; judgment, 26, 79 f . ; 
 negative, 104; of discourse, 101. 
 Universe of discourse, 101. 
 
 Variation, limit of, 19. 
 
 Venn, 179, 200, 216, 225, 240, 243, 244, 
 300, 357, 396, 397. 
 
 Verification, 278 ff. 
 
 Voltaire, 328. 
 
 Von Baer’s law, 60. 
 
 Waitmann, 314. 
 
 Wallace, 304 f. 
 
 Warrant of inference, 85 f. 
 Wedgwood, 367. 
 
 Whately, 200, 396. 
 
 Whewell, 179, 281, 312, 367, 388, 395. 
 Williams, 283. 
 
 Wollaston, 362. 
 
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