A TEXT- BOOK OF LOGIC 
 
A TEXT- BOOK OF 
 LOGIC ' 
 
 BY 
 
 ARTHUR ERNEST DA VIES 
 
 PKOFEMOX or PHILOSOPHY IN THE OHIO STATE UNIVERSITY 
 
 R. G. ADAMS AND COMPANY 
 1915 
 
COPYRIGHT. 1915 
 
 BY 
 ARTHUR ERNEST DAVIES 
 
TO 
 MY FATHER 
 
 339514 
 
PREFACE 
 
 The time has not arrived when it is possible or 
 desirable to write a text-book of logic for elementary 
 students which departs very considerably from the 
 course that has been defined by university require- 
 ments in various parts of the world. Both in Eu- 
 rope and in America instruction in this subject has 
 to a large extent been controlled by what may be 
 called the classical tradition of which Aristotle and 
 Mill are the two fountain heads. In some quarters 
 this fact has operated as a hardship, and has led 
 to open, if rather one-sided, criticism of the subject's 
 educational usefulness, on the one hand, and has 
 directed attention to and aroused interest in the 
 real and supposed defects of the traditional logical 
 doctrine, on the other. The position both of those 
 who maintain the conservative attitude, and of those 
 who would substitute for the old some new kind of 
 logic, is capable of defence up to a certain point, 
 and there is no doubt that the stirring of the aca- 
 demic waters on this subject will result at some 
 time in a larger freedom in the choice of the mate- 
 rial and methods of logical instruction, and to that 
 extent will reduce the possibility of attributing to 
 the subject the imperfections of temper and under- 
 standing of those who teach it. 
 
 I hold no brief for traditionalism in logic, and 
 while I sympathise with and, according to my 
 
 vii 
 
Vlii PREFACE 
 
 ability, appreciate the value of much that the advo- 
 cates of the newer logics have contributed to our 
 knowledge of the methods by which the human 
 mind reaches truth, I have never been able to dis- 
 possess myself of the belief that the older logic 
 in some measure had enabled me to understand what 
 the newer logic had to say. Were I an artist, it 
 would be my desire to paint the ocean, just because, 
 I imagine, it is so constantly changing and withal 
 so eternally the sama A similar interest may 
 stimulate one to observe, in all the ways that modern 
 logic is making familiar to us, the wonderful change- 
 fulness and practical resourcefulness of the mind's 
 approach to truth ; but if one were to identify logic 
 with the observation and description of these shift- 
 ing phenomena, he would be in the position of the 
 man for whom the ocean was no more than the 
 waves that rose and fell and broke upon its bosom. 
 The human mind has a determinate structure, and 
 it is with that structure, so far as it is displayed in 
 the field of knowledge, that logic aims to make us 
 acquainted. And I do not believe that it has been 
 reserved for our own times to utter the only true 
 words on this subject, nor that we can afford to neg- 
 lect the teaching of the ancients. Aristotle defined 
 logic and formulated many of its methods in a way 
 that has given life to the subject for over two thou- 
 sand years, and much that is modern takes its point 
 of departure, either by way of criticism or refining, 
 from what he wrote in the beginning of the science's 
 existence. It is not to be understood, of course, 
 
PREFACE IX 
 
 that the traditional doctrine stands in no need of 
 critical examination. The reverse is the fact. The 
 enormous increase of knowledge in the modern era 
 makes it necessary. But how are criticism and 
 revision possible if the subject is, as some seem to 
 think, wholly illusory, or if we remain in absolute 
 ignorance of the doctrine upon which criticism and 
 revision are to be directed? 
 
 It seems, therefore, that for some time to come 
 logic will continue, in the main, to be traditional, 
 and that books of logic will have to conform to the 
 requirements that are determined by that fact. 
 But there are all sorts and degrees of conformity, 
 and I confess to a liking for that kind and degree 
 which is not inconsistent with the exercise of the 
 largest liberty of one's academic conscience. It 
 would not be surprising, consequently, if it were 
 discovered that I had allowed the present situation 
 in logic to sit lightly upon me, and that, where it 
 seemed desirable, I had departed in method and doc- 
 trine from traditional views. It is I believe in some 
 such way as this, rather than in assuming a critical, 
 not to say captious, attitude toward the whole of 
 traditional logic that the best interests both of the 
 subject and of those who study it can be advanced. 
 
 It is hardly necessary to say that the present 
 book as a whole is the product of experience in 
 teaching logic to elementary and advanced students 
 of the subject, No one, I am convinced, should 
 attempt to write a text-book in any subject, and 
 certainly not in logic, who has not learned in the 
 
X PREFACE 
 
 practical way of teaching it where its main difficul- 
 ties are found, and who has not had an oppor- 
 tunity afforded him of devising methods of overcom- 
 ing them. For, in the first place, a text-book must be 
 written for the student, that is, for one who is 
 presumed not to know anything about the subject 
 of which it treats and, for him, the greatest service 
 that it can render is to stimulate an interest in the 
 problems with which it deals. But also it should 
 be an instrument in the hands of the teacher which 
 facilitates the task of teaching, and adapts itself 
 to the purposes that he may hold before himself 
 and the class. However far my book may be from 
 completely fulfilling these objects, I hope it has 
 entirely escaped the capital offence of substituting 
 itself, in the regard and thought of the student, for 
 the teacher, and that it can not be accused of 
 helping to degrade the teaching function to the 
 mere level of hearing a recitation. I trust, there- 
 fore, that there are many sections that will be 
 found to require the generative touch of the teacher, 
 and that what in his hours of preparation may 
 appear to the student as a valley of dry bones will 
 be vitalized by the teacher into living forms in the 
 hours spent in the lecture room. 
 
 I have given to the judgment a prominence in 
 the order of topics which I think is required for a 
 true comprehension of the problem of logic, and 
 have distinguished between it and the proposition 
 for the purpose of indicating the class of questions 
 which any attempt to express our judgments in 
 
PREFACE XI 
 
 words quite naturally suggests. If I am not mis- 
 taken, current controversy in philosophy would 
 sometimes have been simplified, if indeed the occa- 
 sion for it were not entirely removed, if it had been 
 distinctly recognised that the judgment is not the 
 proposition, and that the problems of each are quite 
 distinct. A close relationship must, of course, be 
 recognised between judgments and propositions, but 
 I am not without hope that the separate treatment 
 of these topics will meet with the approval of my 
 colleagues, although it results in placing at the 
 very beginning what must be regarded as one of the 
 difficult chapters of the book. I do not believe that 
 the judgment chapter is insuperably difficult; it is 
 not more difficult, for example, than is the neuro- 
 logical material to which the psychologist introduces 
 his students at the very outset of their studies. And 
 I may say that the effort has been made to present 
 the subject in a manner as simple as is consistent 
 with the real complexity and difficulty of the prob- 
 lem. With a simplification which falsifies a topic in 
 the interests of easing the task of student or teacher 
 I have as little sympathy as I have with the reverse 
 method of creating or magnifying difficulties for the 
 good of the learner's academic soul. But we must 
 cultivate in ourselves and in those we teach the 
 ability to recognise a difficulty when and where it 
 exists, and to face it with determination, and this 
 requires from teacher or pupil neither apology nor 
 praise. 
 
Xli PREFACE 
 
 With respect to other features of the book, I 
 may, perhaps, be expected to say something in justi- 
 fication of the relatively detailed account that has 
 been given of the fallacies. There is, in fact, little 
 to say, and that little I trust will appear quite super- 
 fluous to any one who has read the chapters in 
 question. Both the mode of treatment and the 
 amount of space given to the subject have been 
 determined by the belief that the problem of falla- 
 cies has not received as a rule the recognition that 
 it deserves, and that it has not been correlated to 
 the main logical doctrines in a sufficiently organic 
 way. I do not wish to be understood to mean that 
 the chapters given here are at all adequate in these 
 respects to the importance I conceive the subject 
 to have. I have, however, sought to avoid leaving the 
 impression that the subject has no practical or pos- 
 itive significance, and have endeavoured to keep the 
 whole discussion in close relation to the body of 
 logical doctrine developed in the preceding chapters. 
 To leave the student with some degree of respect 
 for the topic as a whole seems to me to be decidedly 
 worth attempting, especially when the student is 
 one who is making acquaintance with the subject 
 for the first time. It will also be found, I think, 
 that the two chapters in which the fallacies are dis- 
 cussed lend themselves readily to the purposes of a 
 review of the main logical problems, and that the 
 new point of view from which these problems are 
 considered, the point of view, namely, of the sources 
 of error that lurk in the processes of logical thinking, 
 
PREFACE Xlll 
 
 will not only relieve the review from the banalities 
 that usually attach to a twice performed task, but 
 may be found to make the problems themselves more 
 articulate and significant. At any rate, if we begin 
 our logical studies with the object of finding out 
 what is meant by truth, and what are some of the 
 forms in which truth exists, one would think that 
 a discussion of error or at least an examination of 
 some of the forms in which error exists, would 
 serve to emphasise the importance and the character 
 of logical problems. And, I confess, it seems to me 
 that no amount of technical skill in the manipulation 
 of technical formulae can compensate for any failure 
 to perceive that the problems of logic originate in 
 the effort to think and to express ourselves clearly 
 and correctly, and that, therefore, the science that is 
 devoted to the study of the principles of clear and 
 correct thinking is one in which any person that has 
 any pretense to education should have an interest. 
 And in this connection I may add that the questions 
 on the text appended to each chapter are designed 
 as much to stimulate such an interest as to test a 
 student's acquaintance with the details of the dis- 
 cussion; and if any apology for printing them or 
 for making them so numerous is needed, I can only 
 reply that my own students say that they have 
 found them useful. 
 
 I confess to a certain compunction in offering 
 to the public a book on logic which fails to discuss 
 in a systematic way the so-called laws of thought, 
 although I have never felt the necessity of apolo- 
 
Xiv PREFACE 
 
 gising to myself for failing to expound to my ele- 
 mentary students so recondite a subject. I really 
 have never found that any attempt to interest be- 
 ginners in logic in this problem was satisfactory 
 either from my own or from their point of view. 
 The book, therefore, does in this particular conform 
 to my practice, and the justification that may be 
 offered is that it is pedagogically and scientifically 
 preferable for the student to discover some problems 
 for himself in the course of his studies than to force 
 them in a more or less artificial manner upon his 
 attention. There are places in the text where the 
 subject here in question is quite near the surface, 
 and if it happens to break through, the wise teacher 
 will surely not fail to take advantage of his oppor- 
 tunity. 
 
 With respect to the general outcome of such a 
 course in logic as is outlined in this book, it is 
 enough to say that I should be exceedingly disap- 
 pointed if the way had not been prepared for an 
 intelligent study of the larger treatises on the sub- 
 ject, and if the door had not been opened, though 
 only a little way, through which the student might 
 pass to a study of the perennial problems of phil- 
 osophy itself. About the former point, it is only 
 necessary to say that the lists of advanced refer- 
 ences at the end of the chapters, limited as they 
 necessarily had to be, are intended to invite indi- 
 vidual students and whole classes to read more 
 widely and on a more elevated plane discussions of 
 the problems which are considered in the text, and 
 
PREFACE XV 
 
 to which reference is also made in the first lists of 
 books. An experiment on the possibility of profit- 
 ably using books of an advanced character might 
 be made by the student himself in connection with 
 those parts of the text which fail to interest or 
 profit him. I shall not be surprised if very often 
 the presumably .more difficult reference turns out 
 in the end to be the simpler statement. If any 
 one should doubt the value of logic as an introduc- 
 tory approach to the problems of philosophy, which 
 is the second point mentioned above, I can only say 
 that so long as those problems continue to depend, 
 to the extent that they actually do, upon logical 
 construction, there is absolutely no possibility 01 
 understanding what the problems are, much less of 
 contributing to their solution, if one has not ac- 
 quired a mastery of the instruments of logical think- 
 ing. But not only is this true in respect of philos- 
 ophy narrowly interpreted; an acquaintance with 
 logical methods is also important if we who are not 
 philosophers in the techincal sense of the word are 
 to take an intelligent attitude toward our own lives. 
 Toward such an end, I hope some contribution has 
 been made by the mode in which the logical problem 
 has been conceived, and by the manner in which it 
 has been worked out. 
 
 For those who are acquainted with the liter- 
 ature of the subject, it is not necessary for me to 
 name the sources of my chief indebtedness, and for 
 those who are not, such a proceeding would savour 
 of a vain parade. I shall, therefore, content myself 
 
XVI PREFACE 
 
 with the statement that I have learned from the 
 masters of many schools, and have retained a grate- 
 ful affection for them all. As I am not conscious of 
 being a partisan, I presume that even those who 
 have taught me most would hardly recognise me as 
 one of their disciples. The public, consequently, will 
 be in no doubt when it comes to /apportioning praise 
 or blame for what is here set down, although it is 
 evident, so that he who runs may read, that it is 
 not all made up out of my own head. I have quoted 
 when necessary, I have also paraphrased, I have 
 refused neither suggestion nor illustration when any 
 of these methods furthered the object I have can- 
 stantly held before me in writing these pages. I 
 want, therefore, to thank all who by their published 
 writings have rendered themselves liable to this 
 sort of -literary piratage. I am also indebted to col- 
 leagues for particular services which it is a pleasure 
 to acknowledge. Professor Rudolph Pintner has 
 read many of the chapters in the first half of the 
 book, and made suggestions which have improved 
 the form over that in which they were originally 
 cast. Mr. A. P. Weiss made the drawings for all 
 the figures, and also read some of the sections on 
 induction. Professor David R. Major has read all 
 the chapters in manuscript and in proof. I feel that 
 his criticisms and suggestions have been invaluable. 
 It is certainly not for the want of friendly and 
 intelligent advice that I may sometimes have erred 
 in aim and execution. The final stages of the proofs 
 
PREFACE XVll 
 
 have been entirely in Dr. Major's hands. I take 
 this opportunity to acknowledge assistance that has 
 been generously rendered. 
 
 Eltham, Kent. A. E. D. 
 
 Feb. 25, 1915. 
 

CONTENTS 
 CHAPTER I. 
 
 THE PROBLEM OF LOGIC. pAG 
 
 The Starting Point 1 
 
 Each Science has a Different Subject-Matter 1 
 
 The Thought Element in Knowldge 2 
 
 What we Mean by Knowledge 5 
 
 Knowledge is Systematic 6 
 
 Logic and the Knowledges 9 
 
 The Subject-Matter of Logic. 10 
 
 Logic as Scientia Scientiarum 11 
 
 The Humanistic Influence in Logic 12 
 
 Relation of Logic to Psychology 14 
 
 Logic as an Art 16 
 
 What Logic is 18 
 
 References 22 
 
 Questions 22 
 
 Exercises 23 
 
 CHAPTER II. 
 
 THE JUDGMENT. 
 
 The Meaning of Thought 24 
 
 Judgment and Thought 28 
 
 Other Mental Attitudes Akin to Judgment 31 
 
 Judgment and Groundless Statements 33 
 
 Practical and Theoretical Aspects of Thought 35 
 
 Relevant Assertion 36 
 
 The Interest Factor in Knowledge 44 
 
 The Object of Judgment 47 
 
 The Universe of Discourse 50 
 
 xix 
 
XX CONTENTS 
 
 PAGE 
 
 Truth, Probability and Error 58 
 
 References 70 
 
 Questions 70 
 
 Exercises 74 
 
 CHAPTER III. 
 
 THE PROPOSITION. 
 
 Judgment and the Proposition 76 
 
 The Import of Propositions 79 
 
 Formal Analysis of Propositions 84 
 
 Terms 85 
 
 Names and Words 88 
 
 The Copula 91 
 
 The Relational View 92 
 
 The Existential View 95 
 
 Kinds of Propositions 98 
 
 Relations of the Main Types of Propositions 99 
 
 References 104 
 
 Questions 104 
 
 Exercises 105 
 
 CHAPTER IV. 
 
 TERMS. 
 
 Proposition and Terms 107 
 
 Connotative and Denotative Use of Terms 107 
 
 Relation of the Connotative and Denotative Use of 
 
 Terms 110 
 
 Distribution of Terms 114 
 
 Some Other Characteristics of Terms ,- 117 
 
 Concrete Meaning 118 
 
 Individual Meaning: Proper Names and Designa- 
 tions 120 
 
 General Meaning 124 
 
 Collective Meaning: Individual and General 126 
 
CONTENTS XXI 
 
 PAGE 
 
 Abstract Meaning 130 
 
 References 136 
 
 Questions 136 
 
 Exercises 138 
 
 CHAPTER V. 
 TERMS (Continued). 
 
 The Purpose of the Chapter 139 
 
 The Basis of the Distinctions to be Studied 139 
 
 Absolute and Relative Meaning 140 
 
 Positive and Negative Meaning 143 
 
 The Conditions of Negative Meaning 145 
 
 The Logic of Negation 149 
 
 Privative Meaning 153 
 
 Disparate and Contrary Meaning 155 
 
 References 155 
 
 Questions 156 
 
 Exercises 157 
 
 CHAPTER VI. 
 
 DEFINITION AND THE PREDICABLES. 
 
 The Questions of this Chapter 158 
 
 Non-Ambiguity 160 
 
 Ambiguity 162 
 
 Translation 165 
 
 When Translation may be Employed 166 
 
 When Definition is Required 167 
 
 The Method of Definition 168 
 
 Definition per genus et differentiam 170 
 
 Verbal and Real Definition 173 
 
 The Relation of Purpose to Definition 175 
 
 Tests of a Definition 176 
 
 The Problem and Classification of the Predicables 181 
 
 The Commensurable Predicables.. . 183 
 
xxii CONTENTS 
 
 PAGE 
 
 The Non-Commensurable Predicables 185 
 
 References 186 
 
 Questions 187 
 
 Exercises 189 
 
 CHAPTER VII. 
 
 DIVISION AND CLASSIFICATION. 
 
 Relation of Definition and Division 190 
 
 What is Meant by Logical Division 191 
 
 Other Kinds of Division 193 
 
 Fundamentum Divisionis 195 
 
 Questions of Terminology 199 
 
 Rules of Logical Division 200 
 
 Dichotomy 205 
 
 The Tree of Porphyry 210 
 
 Clasification Defined 211 
 
 Classification and Definition 212 
 
 Classification and Division 213 
 
 Kinds of Classification 215 
 
 References 218 
 
 Questions 219 
 
 Exercises 220 
 
 CHAPTER VIII. 
 
 CATEGORICAL PROPOSITIONS. 
 
 Types of Propositions 222 
 
 Classification of Categorical Propositions 223 
 
 Quantity of Propositions 225 
 
 The Singular Proposition 228 
 
 The Universal Proposition 229 
 
 Kinds of Universal Proposition 230 
 
 The Particular Proposition 230 
 
 The Indesignate Proposition 232 
 
CONTENTS xxiii 
 
 PAGE 
 
 Quality of Propositions 234 
 
 The Affirmative Proposition 235 
 
 The Negative Proposition 236 
 
 The Relation of Affirmative and Negative Propo- 
 sitions 238 
 
 Exceptive and Exclusive Propositions 240 
 
 Compound Propositions 244 
 
 Modality of Propositions 246 
 
 The Assertoric Proposition 247 
 
 The Problematic Proposition 248 
 
 The Apodeictic Proposition 250 
 
 References 251 
 
 Questions 252 
 
 Exercises 253 
 
 CHAPTER IX. 
 
 IMPLICATIONS OF CATEGORICAL PROPOSITIONS. 
 
 Relation of Quantity and Quality in Categorical Propo- 
 sitions 255 
 
 Structural Formulae Indicating the Quantity and Qual- 
 ity of Propositions 256 
 
 Distribution of the Terms of the Four Categorical Propo- 
 sitions 259 
 
 Meaning and Classes of Implication 263 
 
 The Opposition of Propositions 265 
 
 Contrariety 266 
 
 Subalternation 269 
 
 Contradiction 272 
 
 Subcontrariety 273 
 
 The Square of Opposition 275 
 
 Nature and Methods of Eduction 278 
 
 Obversion 279 
 
 Conversion 283 
 
 Contraposition 288 
 
 Inversion . . 290 
 
xxiv CONTENTS 
 
 PAGE 
 
 Summary of Eductions 291 
 
 References 293 
 
 Questions 293 
 
 Exercises 296 
 
 CHAPTER X. 
 
 CATEGORICAL ARGUMENTS. 
 
 The Problem of the Chapter 297 
 
 Two Preliminary Questions 298 
 
 Nature of the Syllogism 301 
 
 Structural View of the Syllogism 303 
 
 Rules of the Syllogism 305 
 
 Figures of the Syllogism 310 
 
 Special Rules of the Four Figures 312 
 
 The Moods of the Syllogism 315 
 
 The Valid Moods of the Syllogism ' 316 
 
 Relation of Moods to Figure 318 
 
 References 322 
 
 Questions 323 
 
 Exercises 324 
 
 CHAPTER XI. 
 
 OTHER FORMS OP CATEGORICAL ARGUMENT. 
 
 Their Relation to the Syllogism 326 
 
 Enthymeme 328 
 
 Polysyllogism 329 
 
 Types of Polysyllogism 331 
 
 Sorites 332 
 
 Epicheirema 335 
 
 References 336 
 
 Questions 337 
 
 Exercises . . 338 
 
CONTENTS XXV 
 
 CHAPTER XII. 
 
 DISJUNCTIVE AND HYPOTHETICAL PROPOSITIONS AND 
 
 ARGUMENTS. pAGE 
 
 The Disjunctive Proposition 340 
 
 The Nature and Classes of Disjunctive Syllogism 343 
 
 The Moods of the Disjunctive Syllogism 344 
 
 The Validity of Disjunctive Arguments 345 
 
 The Hypothetical Proposition 347 
 
 The Hypothetical Syllogism 348 
 
 The Moods of the Hypothetical Syllogism 350 
 
 Dilemmas 354 
 
 Classes of Dilemma 357 
 
 The Validity of the Dilemma 359 
 
 References 361 
 
 Questions 362 
 
 Exercises 364 
 
 CHAPTER XIII. 
 
 INDUCTION AND METHODS PRELIMINARY TO INDUCTION. 
 
 General Statement of the Problem 366 
 
 What is Meant by Fact 367 
 
 Nature of Reality 370 
 
 Induction by Simple Enumeration 372 
 
 The Value of Simple Enumeration 375 
 
 Empirical Generalisation 376 
 
 Colligation of Facts 378 
 
 Parity of Reasoning 380 
 
 References 381 
 
 Questions 382 
 
 Exercises 384 
 
 CHAPTER XIV. 
 
 SOME DESCRIPTIVE METHODS OF INDUCTION. 
 
 Relation of Numbers of Instances to an Induction 385 
 
 Logical Significance of Statistical Methods 389 
 
 Qualitative Methods of Observation 393 
 
XXVI CONTENTS 
 
 PAGE 
 
 The Nature of Scientific Observation 395 
 
 Experimental Observation 400 
 
 References 403 
 
 Questions 404 
 
 Exercises 405 
 
 CHAPTER XV. 
 
 SOME EXPLANATORY METHODS OF INDUCTION. 
 
 The Nature of Scientific Explanation 406 
 
 The Meaning of Analogy 409 
 
 The Logical Character of Analogy 411 
 
 The Function of Analogy in Induction 416 
 
 The Nature of Hypothesis 419 
 
 Objections to the Use of Hypothesis 422 
 
 Verification of Hypotheses 427 
 
 Hypothesis and Theory 429 
 
 References 431 
 
 Questions 432 
 
 Exercises 434 
 
 CHAPTER XVI. 
 
 CAUSATION. 
 
 General Statement of the Problem 435 
 
 The Practical Aspect of the Problem 436 
 
 The Theoretical Aspect of the Problem 438 
 
 The Genetic Relation of the Practical and Theoretical 
 
 Views 440 
 
 The Origin and Nature of the Causal Problem 442 
 
 The Course of Our Further Discussion 444 
 
 The Time Relations of Causal Events 445 
 
 The Complex Character of Causal Events 449 
 
 The Necessity of Causal Events 456 
 
 The Plurality of Causes 461 
 
 References 4^7 
 
 Questions 468 
 
 Exercises . 470 
 
CONTENTS XXVii 
 
 CHAPTER XVII. 
 
 MILL'S EXPERIMENTAL METHODS. 
 
 Their Historical Position 471 
 
 The Nature of the Problem to Which These Methods 
 
 Apply 473 
 
 Elimination as a Method of Causal Inquiry 474 
 
 The Method of Agreement 477 
 
 The Method of Difference 482 
 
 The Joint Method of Agreement and Difference 486 
 
 The Method of Concomitant Variations 492 
 
 The Method of Residues 496 
 
 References . 501 
 
 Questions 501 
 
 Exercises 504 
 
 CHAPTER XVIII. 
 
 FALLACIES. 
 
 Fallacy Defined 508 
 
 Classification of Fallacies 511 
 
 Fallacies of Interpretation 514 
 
 Verbal Ambiguity 515 
 
 Equivocation 515 
 
 Accent 517 
 
 Composition 518 
 
 Division 519 
 
 Accident 520 
 
 The Converse Fallacy of Accident 521 
 
 Structural Ambiguity 522 
 
 Amphibole 522 
 
 False Parenthesis 524 
 
 Fallacies of Implication 525 
 
 Fallacies of Opposition 526 
 
 Fallacies of Eduction . . .529 
 
XXV111 CONTENTS 
 
 PAGE 
 
 Fallacies of Inference 531 
 
 The Deductive Fallacies 533 
 
 Categorical Fallacies 533 
 
 Fallacies of Four Terms 534 
 
 Fallacies of Insufficient Premises 537 
 
 Hypothetical Fallacies 539 
 
 Disjunctive Fallacies 544 
 
 References 548 
 
 Questions 548 
 
 Exercises 550 
 
 CHAPTER XIX. 
 FALLACIES (Continued). 
 
 \ 
 
 Inductive Fallacies 552 
 
 Fallacies of Language 553 
 
 Fallacies of Observation 555 
 
 Fallacies of Explanation 563 
 
 Fallacies of the Context 567 
 
 Fallacies of Assumption 569 
 
 Petitio Principii 570 
 
 Complex Questions 572 
 
 Ignoratio Elenchi 573 
 
 Non Sequitur 576 
 
 Fallacies of Interest 578 
 
 References 584 
 
 Questions 585 
 
 Exercises . 587 
 
CHAPTER I 
 
 THE PROBLEM OF LOGIC 
 
 The Starting Point. It is customary to begin the 
 exposition of a branch of knowledge with a state- 
 ment and explanation of its definition. This is a 
 useful mode of procedure when it can be presumed 
 that those for whom one writes have previously 
 acquired an elementary knowledge of the subject to 
 which the definition relates. But since no such pre- 
 sumption is made in regard to those who may be 
 expected to read this book, we shall postpone for 
 the present the task of formulating a definition of 
 logic. Meanwhile, we shall discuss a number of 
 topics, all of which throw light upon some feature 
 of the problem of logic, and each of which will con- 
 tain suggestions as to the nature of the subject to 
 the exposition of which this book is devoted. And 
 we shall find it convenient to begin our discussion of 
 these topics by asking what is the subject-matter 
 of which logic, in all its various stages and branches, 
 is the study. 
 
 Each Science has a Different Subject-Matter. It 
 will, perhaps, help to emphasize the importance of 
 this inquiry if we recall, first, that a science presup- 
 poses the existence of a special kind of material, 
 called its subject-matter; and, second, that each 
 science has a different subject-matter. For example, 
 in geology we learn about the structure of the earth's 
 
 (i) 
 
2 A TEXT-BOOK OF LOGIC 
 
 surface ; in physiology, about the functions of living 
 organisms. Physics is a study of bodies in motion ; 
 and geometry, of figures in space. In these, and in 
 similar cases, the subject-matter of the science is 
 the material which the scientist observes and de- 
 scribes. 
 
 The Thought Element in Knowledge. If we con- 
 sider further how the several sciences are con- 
 stituted, it soon becomes evident that the mate- 
 rial selected for study is only one condition of 
 the existence of a science. The scientist must also 
 think about his material before his knowledge con- 
 cerning it can have the characteristics of scientific 
 knowledge. He must, for one thing, arrange, or, as 
 it is said, classify, the material that he has collected. 
 It is not, however, the purpose of this section to 
 describe the methods that the scientist employs in 
 studying his material. At present, we wish to call 
 the student's attention to the fact that the attainment 
 of any kind of knowledge is impossible without an 
 active exercise of the thinking processes, and to 
 warn him that the passive flow of images and ideas 
 through consciousness must not be mistaken for 
 thinking. It is true that without images and ideas 
 there can be no thought; but thinking consists in 
 comparing objects with one another, in differen- 
 tiating the like from the unlike, in combining them 
 into more complex wholes, in relating in many and 
 diverse ways these wholes to each other, etc. Think- 
 ing, in other words, is a specialised sort of mental 
 activity, an activity that taxes to the utmost, and 
 
THE PROBLEM OF LOGIC 3 
 
 frequently brings into play, all the abilties with 
 which the human mind is endowed. It is the supreme 
 task to which the many have been called; but 
 if we regard it lightly, or presume that it can be 
 accomplished without toil, or if we erect our own 
 incapacity or indolence into a reason for the useless- 
 ness of the endeavor, we must abandon the hope of 
 joining the company of the few who are chosen. It 
 is, therefore, with good reason that logic directs 
 attention to the function of thought in human knowl- 
 edge, for thinking is the one way, the only royal 
 road, to the goal of an educated life. To think about 
 the objects of one's experience is, then, necessary 
 if knowledge is to exist; but thinking, it must also 
 be borne in mind, is "not a passive suffering of some- 
 thing, but a doing of something with" these objects. 
 Or, as Wundt has expressed it, "jedes denken ein 
 Wollen." 
 
 Not only, then, must we think if we are to attain 
 scientific knowledge ; we must also think in order to 
 attain knowledge that, in the strict sense, cannot be 
 described as scientific. Illustrations of the truth of 
 this statement may be found in history, economics, 
 jurisprudence, as, indeed, it may be in all those other 
 studies which, like these, are interested in the ways 
 in which the various needs of men are met in a social 
 organisation. It would seem, then, that wherever 
 we have knowledge, whether it be in the form of the 
 natural or the historical sciences, as these others 
 may be called, we have a witness to the ways in 
 which the demands for thought have been met. In 
 
4 A TEXT-BOOK OF LOGIC 
 
 brief, unless we think about the material that obser- 
 vation brings, knowledge cannot exist ; and, further, 
 it is what we think that converts this material into 
 definite species of knowledge. 
 
 The following illustration may throw additional 
 light upon the statements of this section, and empha- 
 sise the importance of thought for all forms of 
 human knowledge. We all know what a picture puz- 
 zle is, a collection of odd-shaped and variously 
 coloured pieces of cardboard which, when put to- 
 gether in their proper relations, form a complete 
 and consistent whole. All of us, moreover, have 
 experienced difficulty in putting the pieces of card- 
 board together so that the hidden pattern or picture 
 is made evident. If, now, we study a case like this, 
 we may observe that the difficulty we had in bring- 
 ing out the pattern was not due to the lack of any- 
 thing in our material, all the pieces, we shall sup- 
 pose, were before us, and were capable of being 
 fitted to one another in an appropriate way. But 
 the task of putting them together in the proper way 
 was by no means easy. Where was the source of our 
 difficulty ? We cannot attribute it to our material ; 
 and most of us would agree that it was due to our 
 inability to see which parts should come next and 
 next and next. If anyone chanced to observe us at 
 our task, he probably would have heard us exclaim, 
 'How stupid I am!' 'What's the matter with me!' 
 'Why can't I see it!' That is to say, he would have 
 heard us blaming ourselves, and finding fault with 
 the things we were doing to the material with which 
 
THE PROBLEM OF LOGIC 5 
 
 we were working. What bearing, one may ask, does 
 this have upon the question before us? Just this, 
 that if we are to solve the simplest problem, thought 
 must be brought to bear upon the material which 
 constitutes the subject-matter of that problem. 
 When we do not succeed in doing this, and when, 
 for any reason, we are baffled in our endeavour to 
 make out the nature and relations of the material 
 we are studying, a special emphasis is thrown upon 
 the thought factor, the one which, under more favor- 
 able conditions, is liable to be lost sight of entirely. 
 In this we are like children who look about their 
 world delightfully oblivious of the fact that the eyes 
 provide them with the light of all their seeing. It is 
 only when the eyes fail that one becomes conscious 
 of their existence. Similarly, when knowledge fails 
 an unsuspected factor of knowledge gains promi- 
 nence, and to this factor, to which attention is thus 
 drawn, we give the name thought. 
 
 What we mean by Knowledge. The student who 
 has read carefully the foregoing paragraphs will 
 understand what we mean when we say, we are 
 always thinking about something. The italicised 
 words call attention to the two factors in knowledge. 
 There is the object, the million-starred heavens, 
 or the one solitary maiden, on the one side : and, on 
 the other, our thoughts about this object. Both 
 these elements object and thought are neces- 
 sary to knowledge. Objects that no one thinks about 
 are only the materials of knowledge, and thoughts 
 that are not thoughts - about something in par- 
 
6 A TEXT-BOOK OF LOGIC 
 
 ticular can hardly be called thoughts at all. It is 
 only when our thoughts are thoughts-about-objects 
 that we give them the name of knowledge. This 
 statement holds so generally that by knowledge of 
 any sort whatsoever poetry or legend or history 
 or science or just every-day opinion we may be 
 understood to mean our thoughts-about-objects. 
 Accordingly, from the standpoint of our analysis, 
 knowledge=object-f thought. In later sections, we 
 shall have more to say about these two factors of 
 knowledge. 
 
 Knowledge is Systematic. If we consider our 
 thoughts-about objects with some care, we shall ob- 
 serve that they tend constantly to become fixed, 
 orderly, and systematic. This is not an accident ; it 
 is rather of the nature of a demand that we make 
 upon ourselves and our fellows, so much so that we 
 dismiss with a shrug of the shoulders the thoughts 
 of any one who fails to meet it with a fair degree of 
 success. We may say, then, that we are all alike in 
 having ordered thoughts ; we differ only with respect 
 to the degree of success that we attain in intro- 
 ducing that particular kind of order that makes our 
 thoughts most effective. For example, there is a 
 great difference in the coherence of the thoughts of 
 an insane or feeble-minded person and those of the 
 average normal person. In the former case, we 
 observe both a frequent change of the subject of his 
 thought, and an obvious looseness of connection be- 
 tween one thought and another, even when these 
 refer to the same subject. Sometimes the only con- 
 
THE PROBLEM OF LOGIC 7 
 
 nection that can be observed between one thought 
 and another is the similarity in sound of the words 
 in which the thoughts are expressed. On the other 
 hand, we expect to find the average normal person 
 able to think in such a way that the connection be- 
 tween one thought and another follows the line of 
 the essential connections of one part and another of 
 the subject about which he thinks. When this is the 
 case, we call the person's thinking 'systematic', 
 systematic, that is, in the sense that the order of his 
 thoughts is warranted by the nature of the subject 
 to which his thoughts refer. 
 
 Now it may be interesting and profitable to note 
 what are the conditions of systematic thinking. 
 There are three that, from the logical standpoint, 
 require mention. First, there is the difference, 
 native and acquired, in the ability of individuals sys- 
 tematically to develop by thinking any subject in 
 which they may be interested. We recognise the 
 fact that one person is more highly endowed in this 
 respect than another in such every-day expressions 
 as: 'He's just smart'; 'All there is to say is, he's 
 got brains.' But we also recognise the fact that we 
 are all capable of improvement, however excellent 
 or mediocre our native endowment may be. The 
 great national organisations for the education of the 
 young are a recognition of this fact. But, of course, 
 all that we can hope to do by education is to diminish 
 the difference between one individual and another; 
 we do not expect to overcome the advantage that 
 lies on the side of the person who adds to a high 
 
8 A TEXT-BOOK OF LOGIC 
 
 native endowment a careful and industrious train- 
 ing. The second condition of systematic thinking 
 is found in the fact that not all the subjects about 
 which we think seem capable of being systematised 
 with the same degree of completeness. For example, 
 we do not find in the social sciences the same degree 
 of coordination that we find in the natural sciences ; 
 and, in a general way, we may attribute this to the 
 greater complexity of the subject-matter of the for- 
 mer as compared with the latter. 
 
 It may be observed, thirdly, that not every 
 occasion that calls for thought is met best with the 
 strictest and most thorough exercise of our thinking 
 ability. If we compare, for example, the thoughts 
 of the man of business with those of the economist, 
 or the thoughts of the politician with those of the 
 political scientist, we shall see that they differ, not 
 necessarily in proportion to the abilities of the indi- 
 viduals to think, nor directly with respect to the 
 difficulties of the subject-matter about which they 
 think ; but the occasion that sets the thinker his par- 
 ticular task sets also the limits within which the 
 task is to be carried out. The same thing is true up 
 and down the line of our every-day observation and 
 experience. The man, for example, who carried 
 over into social life the passion for precision, accu- 
 racy, and completeness that properly belongs to a 
 scientific publication would be voted a bore, just as 
 surely as the man who worked in his laboratory with 
 the leisurely and lax methods of a man of the world 
 would be pronounced a failure. Circumstances alter 
 
THE PROBLEM OF LOGIC 9 
 
 cases ; and logic observes that in any of the depart- 
 ments of human life where thought is called for, it 
 is only the degree of systematic thinking appro- 
 priate to the circumstances that it is ever necessary 
 to attain. 
 
 Logic and the Knowledges. In our discussion of 
 what knowledge is we have seen that knowledge may 
 exist in many different forms, varieties, depart- 
 ments, or branches. For example, engineering, psy- 
 chology, bacteriology, literature, biology, etc., are so 
 many different forms of the one tiling we call knowl- 
 edge. For this reason, it would be better, simpler, 
 and more concrete if we were to accustom ourselves 
 to speak of these subjects as ^knowledges' whenever 
 we wished to refer to the plurality of the depart- 
 ments of knowledge. We have a precedent for this 
 usage in that we speak more often of the sciences 
 than we do of science. By knowledges, therefore, 
 we mean the several varieties, forms, or kinds into 
 which knowledge has been observed to falL Now 
 we may observe that, historically, most of the other 
 subjects of knowledge existed before logic was for- 
 mulated into a science. Mathematics, astronomy, 
 physics, zoology, political and social philosophy, for 
 example, are must older branches of knowledge than 
 logic. And if to this we add the fact that logic came 
 into existence as a result of a study of the methods 
 of these sciences, we shall see that it was the exist- 
 ence of the knowledges that made logic possible 
 rather than the existence of logic that made them 
 possible. Hence, it would seem to be true that while 
 
10 A TEXT-BOOK OF LOGIC 
 
 every form of knowledge may be cultivated and may 
 flourish independently of logic, logic cannot even 
 begin to be unless some of the forms of knowledge 
 have already established themselves. 
 
 The Subject-Matter of Logic. What, now, we 
 may ask, is the relation of logic to the two factors 
 of which all knowledge is comprised? And, first, 
 what is its relation to the subject-matter of the other 
 sciences? The question needs only to be asked to 
 be answered ; for it is obvious, in the light of what 
 has already been said, that no two departments of 
 knowledge study the same material. Logic, there- 
 fore, cannot study the same subject-matter as any 
 other science without losing its identity by becoming 
 absorbed in that science. For example, if logic were 
 to study the origin, growth, and function of political 
 institutions, the result would be, not a new knowl- 
 edge, but an old one under a new name. Political 
 science and logic would then be the same things. In 
 like manner, if logic were the study of plants it 
 would be identical with botany. Further illustra- 
 tion is not necessary. The subject-matter of logic 
 is not identical with that of any one of the other 
 knowledges. What, secondly, is its relation to the 
 thought factor which, as we have seen, is present 
 in all knowledge? Our answer is that it is this 
 thought factor in the various knowledges that logic 
 makes the direct object of its study. But logic's 
 relation to this thought element is different from 
 that of any of the other sciences. In the several 
 knowledges, thought is the means by which the 
 
THE PROBLEM OF LOGIC 11 
 
 qualities and relations of objects are described and 
 explained. Ordinarily, we are no more aware of its 
 presence, than we are of the pane of glass through 
 which we look out upon the landscape that lies out- 
 side our window. But if, for any reason, we become 
 curious to know how thought does its work, to find 
 out whether it follows any method, we should then 
 set thought before our minds as a distinct object of 
 study, and the resulting knowledge would be called 
 logic. That is to say, logic arises when the thought 
 factor which is present in all knowledge is set before 
 the mind as a subject of investigation. Thought 
 then becomes the material of a special study, and the 
 name of that study is logic. 
 
 Logic as Scientia Scientarium. We have just seen 
 that logic is the science that is interested in the way 
 in which thought does its work in the several fields 
 of knowledge. Now we have previously seen that 
 we are not everywhere equally successful in system- 
 atising our thoughts-about-things. Some branches 
 of knowledge are more loosely, and some are more 
 closely, organised. This fact we may attribute in 
 part to the greater complexity of the subject-matter 
 of some of the knowledges. History, for example, 
 is a less exact science than is physics just in propor- 
 tion to the greater complexity of the material that 
 it studies, and to the difficulty of bringing its mate- 
 rial under controlled observation. Now, in this con- 
 nection, the question arises Do the several depart- 
 ments of knowledge equally well provide guidance 
 for the formulation of logical doctrine? If some 
 
12 A TEXT-BOOK OF LOGIC 
 
 branches of knowledge are better articulated than 
 others, should we not expect that the former would 
 illustrate the methods of thinking more perfectly 
 than those branches that have not taken on the same 
 degree of coordination; and, further, if we can 
 find any group of knowledges that stands pre-emi- 
 nent in this respect, should we not save time and 
 trouble by making it the basis of our study of logical 
 doctrine? Such questions have been asked, and it 
 has been customary to answer them in the affirm- 
 ative. Thus logicians, from the days of Aristotle 
 to the present time, have expounded the subject of 
 logic with their eyes on the methods adopted by the 
 better articulated sciences ; and, by some, the study 
 of logic has been confined to an examination of the 
 methods that have proved useful in reaching the 
 truth in such sciences. From this point of view, 
 logic has been looked upon as a science that lies hid- 
 den in the various sciences, very much as the pattern 
 lies hidden in a picture puzzle. All that needs to be 
 done, according to this view, is to bring logic into 
 the light that it may direct the labors of future 
 workers in the field of the sciences. It is in this 
 sense that logic is spoken of as scientia scientiarum : 
 it is the science of sciences in the sense that it under- 
 lies and gives direction to all the work that science 
 undertakes to do. 
 
 The Humanistic Influence in Logic. That view of 
 logic which identifies it with the study of scientific 
 method has always been considered a little partial 
 and extreme, and it is doubtful if Aristotle, who 
 
THE PROBLEM OF LOGIC 13 
 
 was the first and greatest of the formulators of 
 logical doctrine, and whose authority has been ap- 
 pealed to in support of this position, would subscribe 
 to it. It is probable, as Minto has shown, that in 
 organising his logic, Aristotle had in mind, as much 
 the formulation of the rules of dispute in the social 
 life and court procedure of his times, as the 
 systematisation of the methods of thought in the 
 body of the scientific knowledge of his day. How- 
 ever that may be, it is certain that our own times 
 are witnessing a marked humanistic reaction against 
 a stiff and formal view of logic, and modern logi- 
 cians are looking to the less exact forms of knowl- 
 edge for enlightenment as to the way in which the 
 business of thought is carried on ; indeed, their study 
 now extends to the ways in which difficulties arise 
 and are overcome in our everyday life. This exten- 
 sion of the field within which the logician pursues 
 his studies cannot be taken as an evidence of indif- 
 ference to a strictly logical doctrine ; rather must it 
 be viewed in the light of what is taking place in other 
 departments of knowledge where an investigation 
 of the simpler, more primitive, forms has been found 
 to elucidate much that was obscure in the more com- 
 plex forms of the subject-matter studied by these 
 departments. In zoology, for example, interest in 
 the simpler organisms has flooded with light our 
 understanding of the more complex ones, and in psy- 
 chology the study of the mental processes of young 
 children and of the feeble minded has added to our 
 understanding of the adult, normal mind. Hence it 
 
14 A TEXT-BOOK OF LOGIC 
 
 is felt that if we consider those methods of thought 
 which, in some of the sciences and in the ordinary 
 business of life, have not taken on a strictly rigid 
 form, we shall be able to understand the nature of 
 thinking in a more satisfactory manner than if we 
 confined our observation to those sciences in which 
 the highest degree of precision in methods had been 
 attained. 
 
 Relation of Logic to Psychology. We have used 
 the term 'thought' in the foregoing pages in a some- 
 what broad way. It has meant, in general, the men- 
 tal factor which is never absent from the knowledge 
 experience. Now the question may arise whether in 
 claiming thought, in this sense, as the special sub- 
 ject-matter of logic we have not confused logic with 
 psychology. For what is psychology if it is not a 
 study of mental processes? 
 
 Now there are two ways in which we may dis- 
 tinguish between logic and psychology. In the first 
 place, we may remark that there is a quantitative 
 difference between the two. Grant, for the time 
 being, that the subject-matter of both these sciences 
 falls within the field that we usually designate as 
 mental, it may, nevertheless, be said that not all that 
 is mental is included in the scope of logical inquiry. 
 Logic is interested mainly, if not exclusively, in 
 what are called the cognitive processes; that is, in 
 those processes in and through which we either 
 affirm or deny something. But cognition in the 
 strict sense, cannot claim to be more than a very 
 small part of one's mental life. The latter, and so 
 
THE PROBLEM OF LOGIC 15 
 
 the field of psychological inquiry, includes, in addi- 
 tion to knowledge or cognition, other kinds of men- 
 tal processes, e. g., feelings, emotions, volitions. The 
 whole field of the conscious life lies open to the in- 
 vestigation of psychology; but logic is interested 
 chiefly in that part of it that is called cognition, and 
 in the other parts only so far as they help us to 
 understand what human knowledge is. 
 
 In the second place, we may remark that although 
 logic and psychology both study the cognitive proc- 
 esses, they do not study them from the same point 
 of view. Psychology is satisfied when it has de- 
 scribed and explained the mental changes that take 
 place in a cognitive process. Logic is concerned, not 
 with the natural history of cognition, but with cog- 
 nition as an instrument by means of which the world 
 of reality minds and things is understood. That 
 is, the images and ideas which make up any cognitive 
 process, and which psychology endeavours merely to 
 describe and explain, are, from another point of 
 view, taken to represent objects in the real world; 
 and it seems to be the function of these images and 
 ideas to place those who have them in communica- 
 tion or contact with objects which exist in some sort 
 of independence of these images and ideas. It is this 
 character of images and ideas as affording us a 
 knowledge of a world of objects that is the stand- 
 point of logic, and which enables us to distinguish 
 the logical from the psychological method of dealing 
 with the cognitive processes. Logic is not interested 
 to know what images and ideas are present in con- 
 
16 A TEXT-BOOK OF LOGIC 
 
 sciousness, but whether the images and ideas that 
 we entertain are true, that is, afford us accurate 
 knowledge of the objects which they represent and 
 to which they point. Or, to put it more succinctly, 
 logic studies the conditions of the truth or falsity 
 of our ideas, a problem which, for psychology, is 
 quite indifferent or non-existent. 
 
 Logic as an Art. It is sometimes said that logic is 
 an art as well as a science. The meaning of this 
 statement can be made clear, if we bear in mind 
 that the term 'art' is used in two senses. In the 
 first and most common meaning, it refers to the 
 developed skill that one acquires through practice 
 of a set of more or less mechanised movements. If, 
 for example, you go into a machine shop and watch 
 the workmen at their tasks, you will find them en- 
 gaged in different activities, and displaying varying 
 degrees of skill. It is this ability to do a given task 
 with some degree of proficiency that we call the 
 workman's art. Art is, then, a specialised ability 
 to do. On the other hand, there is an ability, much 
 more specialised than the mechanic's, which con- 
 sists in the perception of how a task should be done, 
 but which does not necessarily carry with it an 
 ability to perform it. The engineer, for example, 
 is able to plan and superintend building enterprises, 
 although he does not have the ability of the work- 
 men upon whom he must rely if these enterprises 
 are to be translated into steel and brick and stone. 
 The skilled workman and the engineer display two 
 different orders of practical ability, and we may 
 
THE PROBLEM OF LOGIC 17 
 
 speak of each one of them as possessing and prac- 
 ticing an art. 
 
 Now, when logic is spoken of as an art, it is well 
 to be clear whether we are using the term art in the 
 first or in the second of the two meanings just dis- 
 tinguished; whether we are thinking of logic as 
 giving to its students the ability to think correctly, 
 or whether we are thinking of it as giving its stu- 
 dents the ability to detect the correctness and incor- 
 rectness of arguments. We are inclined to the 
 opinion that, in the case of logic, these two meanings 
 cannot be separated, and that in learning the regu- 
 lative principles of logic we are at the same time 
 acquiring the ability to order our thoughts in a log- 
 ical manner. The reason for this opinion, briefly 
 stated, is that the study of logic is and must remain 
 unprofitable to anyone who, while he is studying it, 
 does not practice the methods of logical thinking. 
 The meaning of this statement will become clearer 
 as we proceed, but it should be taken by the student 
 as a suggestion that the way to gain a knowledge of 
 this subject is to think each step logically as it is 
 unfolded in the successive chapters. For example, 
 we shall presently be speaking about terms, and we 
 shall call such things as, 'the Sultan of Turkey/ 
 'good,' 'H 2 S0 4 ,' 'man/ terms. Now, it is obviously 
 impossible for anyone to memorise, or even to make, 
 a list of the things that logic calls terms. The only 
 alternative, therefore, is for the student to acquire 
 the ability to think term, to understand what a 
 
 3 
 
18 A TEXT-BOOK OF LOGIC 
 
 term is. When he has done this, he will have to 
 employ this acquired ability in all his subsequent 
 study, so that it never becomes rusty through dis- 
 use. The same remark applies to all the topics of 
 which logic treats. In this sense, therefore, the 
 study of logic is at the same time practice in the 
 methods of logic; and it is because we cannot ac- 
 quire a knowledge of the correct methods of thought 
 without at each step practicing these methods that 
 logic may be said to be an art in both of the senses 
 defined in the beginning of this section. 
 
 What Logic is. We may now, with a summary 
 of the foregoing discussion in mind, undertake a 
 statement of what logic is. We have seen (1) that 
 logic presupposes the existence of knowledge in one 
 or more of its several forms, and that it has sus- 
 tained this relation to the other knowledges from 
 the very beginning. Aristotle, as we said, was 
 prompted to write his treatises on logic from the 
 desire that, along with the improvement in the 
 sciences and arts, there should go the consciousness 
 of the method by which, in these fields, conclusions 
 were being reached. Logic, therefore, was not an 
 invention of new instruments of research and knowl- 
 edge, but the formulation and systematisation of 
 those that in use had already proved their effective- 
 ness. Consequently, we said (2) that when logic 
 sets about its task, it distinguishes between the sub- 
 ject-matter and the thought element in the knowl- 
 edges, and erects the latter into a separate object 
 of study. Logic, therefore, is a study of the relation 
 
THE PROBLEM OF LOGIC 19 
 
 of thought to human knowledge. But, in this con- 
 nection, we had to point out (3) that the interest of 
 logic in thought is different from that which the 
 several knowledges have in it. The knowledges aim 
 to reach conclusions that increase our understanding 
 of the nature of the objects they select for study. 
 It is true that this increased understanding is 
 reached by thinking; but, so long as results are 
 reached, the scientist is no more concerned with 
 thought than is a farmer with the engine that drives 
 the machine that threshes his grain. This is not 
 the case with logic. It studies thought with a view 
 to finding out its methods of work. From this point 
 of view, therefore, we may say that logic is a science 
 of the methods of correct thinking. But (4) if logic 
 is to be guided by the best examples, it will naturally 
 be interested in the methods of the natural sciences. 
 The influence of this interest of logic in the natural 
 sciences has been to restrict unduly the scope of log- 
 ical inquiry, and thereby to give to logic an impor- 
 tance that originally did not belong to it. The 
 restriction is seen in the definition of logic as a study 
 of scientific method, and the new importance it thus 
 assumes is expressed in its claim to be the scientia 
 scientiarum, the science that makes all the other 
 sciences possible and real. In this connection, we 
 pointed out (5) that this view could not claim the 
 support of the earliest writers on the subject, and 
 that in our own times a positive reaction against it 
 has set in. The form that the reaction has taken is 
 to extend the field of logical observation so as to in- 
 
20 A TEXT-BOOK OF LOGIC 
 
 elude not only the more highly specialised sciences, 
 such as physics and chemistry, but also those that 
 are less fully developed, such as the biological, social, 
 and historical sciences. From this standpoint, logic 
 is a study of the methods of human knowledge of 
 whatever kind the knowledge may happen to be. In 
 the section on psychology and logic we saw (6) that 
 thought may be studied in two quite different ways. 
 We may study thought, for example, as a series of 
 consciousnesses made up of various elements and 
 possessing various attributes. This is psychology. 
 If, however, we study the function of thought in 
 affording us a knowledge of the real world, we are 
 led to a very different result, and the kind of knowl- 
 edge thus reached will be logical rather than psycho- 
 logical in character. For logic, that is to say, 
 thought has a meaning over and above what thought 
 is as an item in a stream of consciousness. What 
 thought is or is like is one thing, and what thought 
 means and does it another. It is from the latter 
 point of view that logic studies it. If, therefore, 
 meaning, as one writer says, is a "product of thought 
 in its relation to reality, or of reality in relation to 
 thought," logic may be defined as a science of the 
 development of meaning, or, more briefly, as the 
 science of meaning. 
 
 Only one more point need be raised, namely, in 
 what sense logic is a science at all. In the last sec- 
 tion we saw that logic is an art in the sense that 
 engineering is an art, but we also saw that as such 
 
THE PROBLEM OF LOGIC 21 
 
 it is an art in a somewhat special sense. It is, if 
 we may say so, an intellectual art, an art that con- 
 sists in knowing how certain things should be done. 
 In this respect, logic, to use Minto's illustration of 
 the Aristotelian logic, may be likened to "Cavendish 
 on Whist," a book that states the rules and illus- 
 trates the methods of playing the game. We have 
 done ample justice to this feature of logic, and the 
 student is not likely to lose sight of its importance 
 as we proceed. But we now ask whether it is also, 
 in any sense, a science; in the sense, for example, 
 that physics and chemistry are sciences. Now we 
 ought to be clear that these sciences do not exist for 
 the purpose of providing rules that students may 
 follow in performing laboratory experiments. If 
 this were the whole extent of the scientific character 
 and purpose of these subjects, they would differ in 
 no respect from the practical sciences in which we 
 learn how certain things are done. If, however, we 
 consider these sciences more carefully we shall see 
 that they ^aim to formulate principles or laws, and 
 that it is only as the experiments enable us to ascer- 
 tain these principles that they have their perfect 
 work. So we may say with respect to logic. It has its 
 experimental side, and it formulates rules and states 
 the methods of correct thinking ; but it goes beyond 
 this and tries to express the laws or the principles 
 to which every concrete case of thinking actually 
 conforms. In the light of this fact, we may conve- 
 niently bring this chapter to an end with the state- 
 
22 A TEXT-BOOK OF LOGIC 
 
 ment that logic is a study of the methods of correct 
 thinking and of the principles on which these meth- 
 ods are based. 
 
 REFERENCES 
 
 B. Bosanquet, The Essentials of Logic, Ch. I. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. I. 
 J. G. Hibben, Logic, Inductive and Deductive, Introduction I. 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. I. 
 W. Minto, Logic, Deductive and Inductive, Introduction I. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. I. 
 
 ADVANCED 
 
 J. M. Baldwin, Thought and Things, Vol. I, Ch. I. 
 
 W. R. B. Gibson, The Problem of Logic, Introduction. 
 
 H. W. B. Joseph, An Introduction to Logic, Ch. I. 
 
 H. Lotze, Logic, Vol. I., Introduction. 
 
 F. C. S. Schiller, Formal Logic, Ch. I. 
 
 C. Sigwart, Logic, Vol. I, Introduction. 
 
 J. Welton, Manual of Logic, Vol. I., Ch. I., II. 
 
 QUESTIONS 
 
 1. How do the various sciences differ from one another? 
 Illustrate. 
 
 2. What function has thought in the several sciences, and 
 what reason can you give for your answer? 
 
 3. What do you understand by knowledge, and into what 
 two factors may all knowledge be analysed? 
 
 4. What is meant by calling knowledge systematic? 
 
 5. Upon what three factors does the systematisation of 
 knowledge depend? 
 
 6. Is all knowledge equally systematic? Illustrate. 
 
 7. What is meant by 'knowledges'? 
 
 8. "It is the knowledges that make logic possible." Ex- 
 plain. 
 
THE PROBLEM OF LOGIC 23 
 
 9. What is the subject-matter of logic? What is the rela- 
 tion of this subject-matter to the other sciences? 
 
 10. What is meant by calling logic scientia scientiarum? 
 
 11. Describe the humanistic reaction in logic, and how does 
 it affect our view of the subject? 
 
 12. In what two ways do logic and psychology differ from 
 one another? 
 
 13. What two meanings may be given to the term art? 
 
 14. Is logic an art as well as a science? Explain. 
 
 15. Summarise the various definitions of logic in this chap- 
 ter, and state clearly the points of view from which these 
 definitions are made. 
 
 EXERCISES 
 
 1. Point out the subject-matter in the case of any six 
 subjects with which you may be acquainted. 
 
 2. Show the relation that thought has to each of the sub- 
 jects chosen for your answer to the previous question. 
 
 3. Cite concrete instances of the way that thought be- 
 comes a problem in the pursuit of various kinds of 
 knowledge. 
 
 4. Illustrate how observation of the ordinary modes of 
 conversation may advance our knowledge of the log- 
 ical processes. 
 
 5. Use concrete examples to show the limitations to which 
 logic would be subject if it confined itself to the study 
 of the scientific mind. 
 
 6. Give instances of the practical value that is claimed for 
 an acquaintance with logical doctrine. 
 
CHAPTER II 
 
 THE JUDGMENT 
 
 The Meaning of Thought. Before carrying our 
 study of the logical character of the thought proc- 
 esses, begun in the last chapter, into greater detail, 
 we wish to call attention to two simple and obvious 
 considerations. In the first place, we may observe 
 that the objects that come before us in the course 
 of our experience present a great variety of charac- 
 teristics. The object of which we are aware may 
 be part of the material world, the starry heavens ; 
 it may be part of the common human life that today 
 we share with our fellows, the rush of the ambu- 
 lance in its race with death; it may be part of the 
 inner individual life, the secret and incommuni- 
 cable thing that a man sees when he sits down face 
 to face with himself. In short, the object may be 
 anything from "the choir of heaven to the furniture 
 of earth ;" but whatever it is, it is an object because, 
 and in so far as, we have experience of it. We shall 
 use the term object, then, to denote that of which 
 we have experience, without respect to the kind of 
 object it is, or the kind of experience in and through 
 which it may be said to exist. But this leads to a 
 second remark. There are, as we intimated just 
 now, a variety of ways in which we experience, or 
 react to, or are aware of objects. The terms per- 
 ception, memory, imagination, feeling, volition, are 
 
 (24) 
 
THE JUDGMENT 25 
 
 the names of some of the more familiar ways of 
 reacting to objects. Thus we may perceive an 
 object, or remember it, or imagine it, or be affected 
 pleasantly or unpleasantly by it, or do something 
 because of it. All these are, of course, familiar 
 experiences, and we do not need to be psychologists 
 to be aware of the fact that the object assumes a 
 somewhat different character for the different activ- 
 ities through which it is experienced. That is to 
 say, the object as we perceive it, or remember it, 
 or imagine it, or are pleasantly or unpleasantly 
 affected by it, or do something because of it, has a 
 slightly altered aspect in these several modes of 
 reacting to it. 
 
 Now it will probably help us to understand the 
 problems of this chapter if, at the outset, we observe 
 that the recognition of this implication of objects 
 in all or most of our conscious processes has led to 
 a certain looseness in our use of the term thought. 
 By some, especially among the psychologists, thought 
 is the name that has been employed to denote the 
 various kinds of mental processes, perception, 
 imagination, feeling, desire, emotion, etc. James, 
 for example, speaks of the 'stream of thought/ a 
 phrase in which the term thought, as he tells us, is 
 used for "every form of consciousness indiscrim- 
 inately." In a somewhat more restricted sense, the 
 term thought or cognition is used, in distinction 
 from feeling and conation or striving, with which 
 it is intimately associated, as the name for one of 
 the ultimate modes of consciousness. It appears in 
 
26 A TEXT-BOOK OF LOGIC 
 
 this sense in the writings of Stout and Ladd. When 
 employed with this meaning, it denotes all those 
 mental activities, such as perception, memory, con- 
 ception, etc., in which we are, in one way or another, 
 concerned with the nature of objects. "It covers," 
 as Stout says, "all modes and degrees of being aware 
 of or cognisant of an object." A still more special- 
 ised use of the term is that which limits its appli- 
 cation to those processes whereby we designate 
 objects merely as the objects that are, at the present 
 moment, under consideration. To think, to use 
 James' definition of conception, with which the term 
 thought in this sense is practically synonymous, is 
 to "identify a numerically distinct and permanent 
 subject of discourse;" to mark it off from other 
 objects, and to make it the bearer of whatever attri- 
 butes or relations that our 'thoughts-about' it may 
 show that it actually possesses. 
 
 The three meanings just distinguished of the 
 term thought are doubtless closely connected from 
 the psychological point of view. For if psychology 
 be regarded as "the science of the processes whereby 
 an individual becomes aware of a world of objects 
 and adjusts his actions accordingly," and it is so 
 regarded by Stout, it is perfectly obvious that the 
 several mental processes must be viewed, in them- 
 selves and in their relations to one another, as modes 
 of conscious activity which further, more or less 
 directly, that acquaintance with objects which all 
 the three statements of the meaning of thought 
 alike emphasise. We need not consider whether, 
 
THE JUDGMENT 27 
 
 and, if so, in what sense all the fundamental mental 
 processes serve the purpose of establishing- and im- 
 proving our acquaintance with things; whether, for 
 example, the so-called affective processes are cor- 
 rectly interpreted in this way. It will be enough 
 if we recognise that certain processes can be grouped 
 together, and can be regarded as having for their 
 distinctive function the discriminating and relating 
 of the objects of experience. If we approach the 
 problem of thought from this point of view, we see 
 that the term thought, in the second and third mean- 
 ings distinguished above, have a peculiarly close 
 relation. According to the second meaning, thought 
 is a continuous process which, beginning in percep- 
 tion, culminates in what the psychologist calls judg- 
 ment and reasoning. Without denying that thought 
 is dependent upon the more elementary processes of 
 perception, the third meaning limits the application 
 of the term to the later processes in which, more 
 particularly, we acquire what was described in the 
 previous chapter as 'knowledge-about' objects. For 
 the one, thinking is the name for a process in which 
 perception, memory, imagination, conception and 
 judgment may be found to function; for the other, 
 it is a name by which conception and judgment are 
 specifically signified. In whichever of these two 
 contrasted senses the term is used, each implies, 
 what is undoubtedly the fact, that there is no unique 
 faculty of thought, that thought is a complex process 
 in which a number of mental activities combine to 
 give us a knowledge of objects, and that, while some 
 
28 A TEXT-BOOK OF LOGIC 
 
 of these activities enable us to identify distinct and 
 permanent subjects of discourse, others carry us 
 beyond this to the knowledge of a system of existing 
 things in which numerous terms and relations are 
 discernible. 
 
 Judgment and Thought. Now when we consider 
 the subject of thought from the standpoint of logic, 
 it is in the third of the meanings already distin- 
 guished that, in the main, we shall use the term. 
 Thought will thus signify the processes of judgment 
 and reasoning, those processes in which the cogni- 
 tive process as a whole culminates. Logic, that is 
 to say, is particularly interested in the terminus 
 ad quern of the thought-process, in the goal toward 
 which our desire for knowledge points; and it 
 studies the process of reaching the goal only when 
 a knowledge of such process enables it to determine 
 the nature and grounds of the validity that is 
 claimed for thought. Thinking thus comes to be 
 regarded by logic as having a character which is 
 liable to escape notice so long as we keep strictly to 
 the psychological point of view, the character of 
 assertion. And in order to give prominence to this 
 feature of thought, logicians are more apt to speak 
 of judgment than they are of thought. Thinking, 
 as we have seen, is a mental process in which the 
 psychologist distinguishes a number of constitutive 
 processes, perception, memory, etc. Judgment, 
 as it is used by the logician, regards the thought 
 process as being concerned with the specification 
 of a content, the assertion of which is logically the 
 
THE JUDGMENT 29 
 
 characteristic thing about a judgment. The content 
 of the thought process is taken up by the judgment 
 and constituted the subject-matter of assertion. 
 Thus the experience, say, of red calls from the psy- 
 chologist the statement that, like all sensational 
 experiences red cannot be described, but must be 
 experienced if any one is to know what the word 
 signifies, that it is produced by the action, on the 
 rods and cones of the retina, of ether waves of a 
 certain length, and that these changes are continued, 
 by way of the optic nerve, in a manner that is little 
 understood, to the occipital lobe which is the cortical 
 centre of the visual consciousness. For the logician, 
 the particular patch of colour called red merely 
 exists, and the acknowledgment of it as existing, 
 by the individual who experiences it, is what is 
 meant by assertion or judgment. The red is the 
 content of the processes which are described by the 
 psychologist, and it is this content that is asserted 
 as the subject-matter of the judgment. Whatever, 
 then, exists as content of thought, may become the 
 subject-matter of a judgment; and we may, there- 
 fore, define a judgment, broadly, as an assertion of 
 the qualities and relations of the object of thought. 
 A word or two may be necessary at this point 
 to guard against a possible misunderstanding of 
 what is meant by assertion as the central fact of 
 the logical judgment. In current usage, to assert 
 means to express in words the thoughts and opin- 
 ions that we entertain about things. It is commonly 
 employed as the equivalent of 'to say something.' 
 
30 A TEXT-BOOK OF LOGIC 
 
 In logic, assertion has nothing to do with speech. 
 We may, of course, express what we assert, but 
 we can assert without putting into words, or into 
 any other set of social symbols, the qualities and 
 relations of the object of thought. The question we 
 are now considering, moreover, has nothing to do 
 with the problem whether, as individuals, we can 
 think without words. It is a simpler matter than 
 that; and all that we say is that no one, merely 
 because he judges, is bound, in order to give his 
 judgment the character of assertion, to put into 
 language the truth or fact that his judgment em- 
 bodies. On the contrary, by assertion we mean the 
 attitude of mind in which, for that mind itself, 
 there consciously exists such an acquaintance with 
 an object that, in itself and its relations, it is dis- 
 tinguished from other objects with which it occurs 
 in a common field of knowledge. For example, I 
 may be looking over a collection of curiosities that 
 a friend has accumulated from the four corners of 
 the earth. I look at the objects one after the other, 
 and find that each is a strange and unintelligible 
 thing, and, as I put it back into its place, it is soon 
 lost in the mass of the other strange and unintel- 
 ligible things. If, however, I should find in the col- 
 lection an object that is familiar, there would be, 
 under the circumstances supposed, a mental tang 
 and 'feel' toward it that would make it, as I put 
 it, too, back in its place, stand out from the rest, - 
 its identity would not get lost in the multitude of 
 strange things. What makes the difference in this 
 
THE JUDGMENT 31 
 
 case is my mental attitude toward it, a mental 
 attitude that, in this instance, is called recognitive 
 judgment. In logic, the mental attitude in which 
 we find the characteristic feature of the judgment 
 is described as assertion. Whenever we judge we 
 assert, and whenever we assert we put marks upon 
 the objects that come before us by which they attain 
 unique distinction. 
 
 Other Mental Attitudes Akin to Judgment. It may 
 help to emphasise the assertive character of the 
 judgment if we distinguish certain other attitudes 
 which, like assertion, have received, in the develop- 
 ment of language, definite verbal forms. Judgments, 
 it should be observed, are always expressed in the 
 indicative mood, and what they assert is always true 
 or false. On the other hand, interrogatives, imper- 
 atives, optatives, and exclamations do not assert, 
 and therefore are not judgments, but express either 
 an inquiry, a command, a wish, or an emotion. Of 
 the wishes that optatives express we can say that 
 they are reasonable or unreasonable. The com- 
 mands of imperatives can only be obeyed or dis- 
 obeyed. Our interrogatives formulate inquiries and 
 call for an answer. Exclamations are word ges- 
 tures that express our emotional attitudes toward 
 situations. But while interrogatives, imperatives, 
 optatives, and exclamations are not judgments, they 
 imply attitudes of mind which, if asserted, would 
 be judgments. The rhetorical question, 'Is thy ser- 
 vant a dog?' doubtless implies an assertion, and is 
 equivalent to 'Thy servant is not a dog.' But not 
 
32 A TEXT-BOOK OF LOGIC 
 
 only the rhetorical, but any question may be inter- 
 preted in a similar way. For to ask a question 
 would be meaningless unless we thereby implied 
 that something can be asserted of its subject, and 
 it is to this something that the question, in a general 
 way, points. If, for example, I ask, 'Is that a fire?' 
 I imply that it is a fire, but not in the way that 
 would warrant me in asserting it as a fact. With 
 imperatives the case is different. 'Come,' 'Do this,' 
 cannot be said to be either true or false, and they 
 imply assertion only if imperatives are indicated 
 actions that have reference to a situation which 
 they either help or hinder. Imperatives, that is, get 
 their meaning from a context that exists in the 
 mind of the person issuing the command, a context 
 which must rely for its development upon the action 
 of the person to whom the command is addressed. 
 The implied judgment, therefore, may be thrown 
 into the hypothetical form thus: 'If you do the 
 thing commanded, such and such things will happen.' 
 Commands, that is, are abbreviated antecedents of 
 hypothetical judgments. Optatives express a desire 
 for some state or condition which is thought of as 
 possible, though not, at the moment the wish is 
 entertained, as actual. They imply the assertion 
 of definite objects as the objects of desire. In this 
 way we must interpret, for example, 'Would that I 
 were dead!' It implies that 'to be dead at this 
 moment' is really a desired object. Such exclama- 
 tions as 'Absurd!' 'Impossible!' are predicates of 
 implied judgments, and by them, besides expressing 
 
THE JUDGMENT 33 
 
 our personal attitudes, we are also characterising 
 situations. 
 
 Judgment and Groundless Statements. Before 
 
 proceeding to develop other features of the judg- 
 ment, as this has been defined in the previous sec- 
 tions, there is a class of statements about which we 
 are called upon to say something if only for the 
 sake of clearing our exposition of the subject under 
 discussion from unnecessary ambiguity. We have 
 seen that assertion is the main characteristic of 
 judgment, and that what a judgment asserts is some 
 quality or relation of the objects about which we 
 think. It would seem quite obvious, therefore, that 
 unless we think about some object or other, there 
 can be, for us, no such thing as judgment. Judg- 
 ment implies thought, and thought implies some- 
 thing thought about. 
 
 In contrast to judgment, as thus understood, we 
 are confronted with a class of statements which 
 simulate judgments, but which fall short of being 
 true judgments because they are not based on the 
 thinking of the person who makes them. We may 
 cite in illustration not only the parrot-like state- 
 ments of the class-room recitation, but the ill- 
 informed and often misleading expressions of opin- 
 ion that many of us allow ourselves to make with 
 confidence on all sorts of subjects about which we 
 know relevantly nothing. The certainty that at- 
 taches to such statements has little or nothing to do 
 with their subject-matter; it usually rests upon the 
 
34 A TEXT-BOOK OF LOGIC 
 
 confidence we have in 'authority' of some kind or 
 other. For instance, students rarely call in question 
 the statements they find in their text-books, and 
 consequently they are ready to state as true any- 
 thing they read in them for no better reason than 
 that it is 'in the book.' Indeed, most of us entertain, 
 and express to others, beliefs that are based solely 
 upon statements we have read in some magazine or 
 newspaper, or have heard in a public address or in 
 private conversation. To communicate, in this way, 
 the opinions of others is doubtless a valuable social 
 function, but the statements in which another's 
 views are given currency should not be confused 
 with judgments in the sense in which this term has 
 been defined. We may, for want of a better word, 
 distinguish these statements as groundless asser- 
 tions, for what enables us to distinguish them from 
 true judgments is the fact that, in respect of the 
 latter, we are always more or less conscious of the 
 reasons for what the judgment asserts. Our judg- 
 ments are, as it is said, grounded judgments, and 
 the grounds of the judgment are the reasons that 
 thought can give for the particulars asserted by the 
 judgment. For, as we have seen, the asserted par- 
 ticulars are always what thought reveals as true of 
 the subject thought about. 
 
 The distinction that we have drawn in this sec- 
 tion between groundless statements and judgment 
 corresponds, in a general way, to that which appears 
 in the history of Greek speculation as the distinction 
 between 'opinion' and 'knowledge.' 
 
THE JUDGMENT 35 
 
 Practical and Theoretical Aspects of Thought. 
 Whether we use the term thought in the broadest 
 of the meanings already distinguished, or in one of 
 its more restricted senses, it is undoubtedly true 
 that we cannot fully describe the experience that 
 the term denotes without recognising the fact that, 
 along with those differentiations which the object 
 of thought undergoes, for example, in perception, 
 in ideal representation, and in ideational thought, 
 tendencies of a practical sort are aroused which not 
 only accompany the thinking process, but, in part, 
 give it the character and direction which it undoubt- 
 edly possesses. Thus the psychologists have been 
 accustomed to recognise that instinctive impulses 
 are present in perception which tend to place the 
 percipient subject in relation to external objects; 
 that in ideal representation active tendencies of the 
 kind called desires are directed toward objects 
 which, not being actually present, are held before 
 consciousness as an end to be realised; and that in 
 ideational thought the process of generalisation for- 
 mulates ideals which are sometimes of so complex 
 a character that, while they may become the objects 
 of individual desire, they are attainable only as the 
 result of social cooperation. Whether, therefore, in 
 its simpler or more complex forms, thought seems 
 to have, not only an aspect which is directly con- 
 cerned with the definition of an object, a theoretical 
 aspect, but also a practical aspect, a certain conative 
 tendency whose function it is to direct the process 
 
36 A TEXT-BOOK OF LOGIC 
 
 of thinking and to give its content a definite charac- 
 ter and objective. 
 
 Relevant Assertion. From the point of view we 
 have now reached, we may indicate certain features 
 of the logical judgment which correspond, in a gen- 
 eral way, to this distinction in the nature of think- 
 ing itself. The function of judgment we have said 
 is assertion. We have now to point out that when- 
 ever assertion satisfies the logical conditions of 
 truth, and is not mere or groundless assertion, it is 
 seen to have two characteristics both of which are 
 included under the single term 'relevant.' More 
 explicitly stated, judgments, in the logical sense of 
 that term, are always relevant assertions, and their 
 relevancy is based upon, and is the logical expression 
 of, the theoretical and practical aspects of the 
 though process which were indicated above. Judg- 
 ments, in other words, always refer to some object, 
 and fulfill some need of the person asserting the 
 judgment. Whenever they do either or both of these 
 things, our judgments are said to be relevant asser- 
 tions. Briefly stated, judgments are assertions that 
 are relevant (1) to the motives that operate to 
 produce them, and (2) to the material by which 
 they are called forth and to which they refer. 
 
 To consider the first meaning of relevancy, that 
 which refers to the motives that operate to produce 
 our judgments, we may say that this is concerned 
 with the reasons why any one judges at all. If, 
 then, it were asked why any one judges, the answer 
 would be that one cannot 'get along' without it. In 
 
 
THE JUDGMENT 37 
 
 a broad way, the life of thought is based in and 
 grows out of our practical needs. As an illustration 
 of what this statement means, we may refer to the 
 development of agriculture in the history of civil- 
 isation. Before agriculture had become one of the 
 institutions of human society, men no doubt were 
 confronted with the problem of food supply, and 
 they met this problem in a way that was fairly 
 satisfactory until the accumulation of various forms 
 of wealth made a predatory and wandering life both 
 irksome and unprofitable. When, for instance, the 
 domestication of animals had become an accom- 
 plished fact, this not only made a wandering life 
 more difficult, but it also exposed the primitive com- 
 munity to greater loss through drought, long jour- 
 neys, and marauding attacks from hostile and mer- 
 cenary tribes. But unless fruits and cereals could 
 be domesticated, as animals had been, there was 
 before the primitive community the necessity of 
 seeking food where it grew, whatever the risks and 
 losses that might be incurred. Now it takes but a 
 little imagination to see that the great difficulties 
 that beset tribes advancing from a wandering to a 
 settled mode of life would act as a stimulus to their 
 thought, and would engage their thought in the 
 direction of these difficulties themselves. It may 
 seem to us who have grown up under settled con- 
 ditions of life a simple matter to perceive the prob- 
 lem and the solution of which it was capable. But 
 before the food supply of man and beast could be 
 raised, within a restricted area, by man's efforts 
 
38 A TEXT-BOOK OF LOGIC 
 
 from seeds, there was required exactly that develop- 
 ment of the thought processes which the mainte- 
 nance of the institution of agriculture calls for at 
 the present day. What, therefore, we may say is 
 that the principle of this illustration, namely, that 
 our needs stimulate the judging activity and direct 
 it toward an understanding of whatever threatens 
 the satisfaction of these needs, is capable of indefi- 
 nite extension ; and that the incentives to knowledge 
 become more numerous and diverse as, with the 
 growth in complexity of our social life, obstacles 
 are multiplied, and needs increase in number or 
 change their form. Thus, over the whole course 
 of our experience, thought not only interprets the 
 environment, but determines the particular adjust- 
 ments that, under change of environment, are neces- 
 sary if the varying needs of life are to be met. 
 
 The relevancy of our judgments to the varying 
 needs by which they are called forth may be further 
 illustrated, and, for this purpose, let us suppose 
 that we have a hundred books, and that our problem 
 is what we are going to do with them. It is very 
 probable, first, that we shall want to have them all 
 in one place. Within the space allotted to them, we 
 are likely to arrange them under some scheme of 
 classification, authors, subjects, or what not. 
 Now why do we do this? Is it needless? By no 
 means. We are simply obeying in our manner of 
 dealing with the books a fundamental need for 
 order. But what particular order we impose upon 
 the books will depend upon the particular form that 
 
THE JUDGMENT 39 
 
 the demand assumes. Thus, in the first instance, 
 we bring all the books together in one place; place 
 is the principle of our classification. In the second 
 instance, we have carried the matter further, and 
 have arranged the books, let us say, according to 
 subjects, subject-matter is a more specialised 
 form of the need for order which operates through- 
 out all our classifications. But if it is asked why 
 any order is necessary, we can only say that when 
 classified objects are more easily handled and used. 
 The point of the illustration is that, when we have 
 to deal with a hundred books, we are bound to think 
 about the books in terms of our interest in them. 
 Thus the first classification according to place might 
 be satisfactory to the housekeeper whose interest in 
 the books is aesthetic, as articles of furniture in a 
 room. The classification according to author would 
 satisfy the interests of the man whose manner of 
 speaking about books is, 'Oh, yes, I have Dickens, 
 Eliot, Thackeray, etc.' The scholar's interest is 
 most likely to be met by the arrangement according 
 to subjects. In each case, what we think about the 
 books, whether as articles of furniture, or as the 
 works of such and such authors, or as dealing with 
 given subjects, depends upon the interest we have 
 in them. And what is true in this particular in- 
 stance is true in every case of judgment. Our judg- 
 ments, in a word, are assertions that are relevant 
 to the interests out of which they are born. 
 
 The foregoing statement and illustrations of the 
 conditions under which the judging activity comes 
 
40 A TEXT-BOOK OF LOGIC 
 
 into play indicate clearly enough what is meant by 
 the practical nature of all our thinking. But be- 
 cause the word practical is, in ordinary speech, so 
 intimately associated with the getting of material 
 goods, or with the removal of material hindrances, 
 the exact meaning of the statement that all judgment 
 is conditioned by the presence of practical needs is 
 liable to be given too narrow an interpretation. By 
 a practical need, it is true, we mean one that is con- 
 cerned with getting an anticipated good, or with 
 removing a present hindrance to further goods. 
 But the goods in question need not be material, and 
 in many cases are not material. We have no wish 
 to deny that man is an economic animal, and that 
 what we call property is based in and grows out of 
 his need for 'things/ But it is no less true that 
 man is a social animal, and that the various organ- 
 isations in which he is associated, the family, the 
 shop, the club, etc., have their foundation in the 
 needs which prompt men to associate with their 
 kind. The social is, no less than the economic, a 
 practical need. A similar line of remark applies also 
 to our science, art, and religion. There are, doubt- 
 less, intellectual, emotional, and volitional needs, 
 complex in their nature, and variously combined in 
 the instances just given, which impel men to seek 
 their satisfaction in the formulation of the objects 
 to which these needs point. Over the whole range 
 of life, then, situations are constantly arising in 
 which unsatisfied demands impel us to think, and 
 to think with reference to these demands. Nowhere 
 

 THE JUDGMENT 41 
 
 can this practical aspect of the judging activity find 
 more or more pertinent illustration than in a study 
 of the ways in which the human race has advanced 
 in the arts of civilised life. But to bring the truth 
 of this view home to ourselves, we need only to ask 
 if we, as individuals, ever think when the situations 
 in which we find ourselves are entirely satisfactory. 
 Even a student, very often, will not think until a 
 failure stares him in the face. 
 
 Turning now to the second meaning of relevancy, 
 we may say that judgments are assertions about 
 the material by which they are called forth and to 
 which they refer. In the development of knowledge, 
 our interests never become so one-sided that our 
 judgments are freed from the control of the mate- 
 rial through which these interests are to receive 
 their satisfaction. If, for instance, we were con- 
 scious of nothing but compelling interests, be those 
 interests psychologically never so definite, or if we 
 were moved by a vague catholicity of mind that 
 went out to everything in general, but took hold on 
 nothing in particular, judgment would be impos- 
 sible. There are states of mind that correspond 
 more or less closely to those just described, states 
 that are definite as to interests but indefinite, vague, 
 or empty as to their objects; and others that are 
 vague and indefinite in both respects; but no one 
 would think of calling these states cognition, or the 
 reactions they may involve judgments. What we 
 aim at in the judgment is to characterise an 
 
42 A TEXT-BOOK OF LOGIC 
 
 object in such a way that it becomes better 
 known. The study of the judgment, therefore, is 
 a study of the relation of thought to its object. 
 Now, when one attempts to study the relation in 
 which thought stands to its object, one is partic- 
 ularly prone to two kinds of error. In the first 
 place, he is apt to think of the mind as a passive 
 mirror that reflects indifferently whatever is held 
 up before it. That is to say, he is liable to overlook 
 the presence in all knowledge of the interest factor 
 of which we have already spoken. If, however, he 
 escapes this pitfall, he is prone to go to the other 
 extreme and think of the mind as a magic mirror 
 that transforms out of all likeness to their own 
 nature the objects that pass in front of it. That is 
 to say, he is liable to overlook or underestimate the 
 material factor to which attention is now being 
 directed. Interests, as we have seen, do make our 
 judgments significant; but if they are to reach truth 
 they must also be brought under the control of 
 objective fact. No judgment can be regarded as 
 having reached truth which does not open to us the 
 nature of the object about which it undertakes to 
 inform us. The fact, therefore, about the judgment 
 is that, within the sphere of the interests that 
 stimulate the judging process, the character of 
 our assertions is limited by the nature of the mate- 
 rial or subject with which we are dealing. For 
 example, in writing this section of logic, I am 
 prompted by the desire to write in such a way that 
 the student who reads shall be able, with ordinary 
 
THE JUDGMENT 43 
 
 attention, to understand the doctrine. But what 
 the doctrine is does not depend upon this interest; 
 what I say must be true of the subject we are dis- 
 cussing. However, this must be said, that what I 
 include and what I omit, what form the sentences 
 take, and what illustrations are used, are deter- 
 mined by the purpose and needs the section is in- 
 tended to serve. I cannot say anything I please 
 about the judgment, but I can examine it to see 
 how far it lends itself to the satisfaction of the 
 interests that lead me to write about it. We may 
 take any other illustration we please, and the same 
 thing will be found true. The difference, for ex- 
 ample, between history and romance, other things 
 being equal, is the difference between the way the 
 historian and the novelist feel themselves bound by 
 the character and order of the occurrences which 
 they narrate. The historian's purpose is to describe 
 a complex social situation as it actually existed, and 
 to develop the consequences, in the way of cause and 
 effect, of the situation thus depicted. The novelist's 
 treatment of the same material is much freer from 
 the control of the objective events within which, as 
 in a framework, his romance is made to move. But 
 it is only in the former of these two cases that truth 
 is the aim; the relative unimportance of this aim 
 in the novel accounts for the looser handling of the 
 historical material. We may, therefore, conclude 
 that interest or purpose sustains and directs the 
 whole process in which our judgments are formed, 
 and that what the judgment asserts, since all judg- 
 
44 A TEXT-BOOK OF LOGIC 
 
 ments claim to be true, must derive its character 
 from the material which constitutes the subject- 
 matter of the process of judgment. 
 
 The Interest Factor in Knowledge. In the pre- 
 ceding section, we have seen that judgments are 
 assertions that are relevant to the interests or pur- 
 pose of the person who judges, and also to the 
 material or body of facts which, in the judgment, 
 receive a particular characterisation. Now it will 
 serve to further emphasise this distinction, if we 
 call attention more particularly to the way in which 
 these factors of knowledge are related to one an- 
 other. We may in general distinguish two cases. 
 There is first the case in which our interest in the 
 objects which we are led to observe is extrinsic to 
 the objects themselves, and, secondly, the case in 
 which it is primarily intrinsic. 
 
 To consider the former case, we may remark 
 that we are often led to observe and make asser- 
 tions about objects, not because of any particular 
 interest in the objects themselves, but because of 
 the relation in which these objects stand to other 
 objects in which we are interested. Let us take 
 as an example my observation of the shape, colour, 
 and arrangement of the roses in the vase that stands 
 upon the table at which I write. It is true, of 
 course, that I may be induced to observe them, and 
 to study their particular characteristics by reason 
 of an interest that is rooted in my knowledge of 
 floriculture. But, on the other hand, the attention 
 that I give to the flowers may be due, for example, 
 
THE JUDGMENT 45 
 
 to my interest in the person who picked them and 
 placed them where, as I now write, they become 
 the object of my perception. Or, if this is not the 
 fact, my interest may grow out of my liking for a 
 patch of colour of any kind, or for the particular 
 combination of colours that the flowers present. In 
 the former of these suppositions, the interest is 
 social, and in the latter, it is aesthetic. In in- 
 stances like these, we may say that the object 
 sustains an interest that is extrinsic to itself, and 
 gives to the interest a longer life than it would 
 otherwise have. If, from this point of view, we 
 speak of the flowers at all we should say that they 
 were pretty, a judgment it is true, but one which 
 expresses one's feelings for the flowers rather than 
 one which tells anything about the flowers them- 
 selves. Such judgments are usually called value 
 judgments, judgments which express the value 
 or worth of the objects for the individual expressing 
 the judgment. We express multitudes of such judg- 
 ments in the course of our lives, and of a great deal 
 that is noblest and best in our experience we can 
 speak in no other way. The student will find that 
 most of the judgments that he expresses on morals, 
 art, and religion are what are called value judg- 
 ments ; judgments, that is to say, that are stimulated 
 by interests that are extrinsic to the objects about 
 which he judges. 
 
 If, now, we consider knowledge in the more 
 scientific meaning of the term, we shall find that 
 here the interest factor is intrinsic, that it is 
 
46 A TEXT-BOOK OF LOGIC 
 
 grounded in the object in a way we have seen not 
 to be the fact in the class of cases just studied. 
 Scientific interest, in other words, is an interest in 
 objects for their own sake. Of course, it is some- 
 times said that interest or purpose is altogether 
 absent from our scientific activities, and that it is 
 this fact that distinguishes science from all other 
 kinds of knowledge. If all that has been written 
 about the disinterested nature of scientific study 
 were true, science would have been destroyed, before 
 this, at the hands of its friends. The fact is, how- 
 ever, as our study of the nature of knowledge has 
 shown, there is no knowledge which does not spring 
 from some form of human interest. It is not true, 
 therefore, that what we mean by science, in con- 
 tradistinction to what is not science, can be stated 
 in terms of its freedom from interests which 
 direct the course and prescribe the goal that science 
 aims to reach. What is true, on the negative side, 
 is that certain kinds of interests are detrimental 
 to the existence of science. But to deny the useful- 
 ness of certain kinds of interest, is certainly a very 
 different matter from denying all interest whatever. 
 For science, as was pointed out by Plato and Aris- 
 totle, would have no existence were it not for that 
 curiosity and wonder which is awakened very early 
 in all of us by the changing appearances in the 
 course of nature. It is this curiosity which, when 
 specialised, is the source of scientific interest, and 
 which, in its developed form, is an interest which 
 centres in the objects which it prompts us to study. 
 
THE JUDGMENT 47 
 
 In other words, the interest which is the motive of 
 scientific effort appears in the form of a desire to 
 comprehend the nature and relations of the objects 
 of our experience. The better we understand these 
 objects, the more alive does our interest in them 
 become; and the more alert this interest, the more 
 keen do we become in our study of these objects. 
 The interest and the object of scientific work are 
 thus keyed to each other in a way that makes them 
 mutually supporting; and the further we study 
 their relations, the clearer does it become, as was 
 intimated above, that they are different aspects of 
 a single process. Scientific interest, then, is an 
 interest in objects for their own sake; it is an in- 
 terest that prompts us to ascertain all that can be 
 truly known about these objects. 
 
 The Object of Judgment. If we now pass from 
 the study of the relations of interest and subject- 
 matter upon which we have been dwelling, and 
 regard the judgment as an assertion about its 
 subject-matter, certain other features of the judg- 
 ment come into view. In our previous discussions, 
 we have had occasion to specify what is meant by 
 the subject-matter of the judgment, and this, it will 
 be remembered, was found to be identical with what, 
 from the psychological point of view, is denominated 
 the content of thought. Thought and judgment are 
 thought and judgment about some thing. Without, 
 therefore, the challenge of some thing neither 
 thought nor judgment takes place. But while 
 thought and judgment imply the existence of a 
 
48 A TEXT-BOOK OF LOGIC 
 
 subject, neither, in the strict sense of these terms, 
 is identical with the existence of its subject. There 
 seems to be, therefore, some other feature of the 
 judgment which distinguishes it from mere aware- 
 ness, and it is this feature that we have now to 
 consider. 
 
 We may perhaps bring the question of discussion 
 distinctly forward by the aid of an illustration. 
 Let it, therefore, be supposed that I am gazing out 
 of the window while thinking about the distinction, 
 within the logical judgment, that it is now my desire 
 to state. I turn the subject about which I am 
 thinking this way and that, experimenting with it 
 until my interest in it begins to wane. What I 
 find, under the supposed conditions, is that the 
 more interest in the original subject wanes, the 
 more insistently do factors from other parts of my 
 environment obtrude on consciousness; and by and 
 by I find myself wholly engaged with some of these, 
 -the sloping hill side, the frozen lake, and the 
 lively company of girls and boys skating upon its 
 surface. In such an experience, what one observes 
 is that not only has there been a change from one 
 subject to another, from a logical problem to a 
 physical object, but also that changes of another 
 kind have accompanied those already indicated. The 
 two consecutive contents of the thought processes, 
 that is to say, have been followed by changes in the 
 character of what, in each instance, is asserted. I 
 do not find, in other words, that what I am thinking 
 when engaged with the logical problem fits in with, 
 
THE JUDGMENT 49 
 
 or can be carried over to, the scene in the distance 
 which has now become the content of my thought. 
 Each content has its own appropriate set of asser- 
 tions. To assert of its subject significant qualities 
 and relations is what we understand to be the 
 object of the logical judgment. It will serve to 
 emphasise the distinction between the subject and 
 the object of judgment if we recall that Bradley 
 discriminates in the judgment between what he calls 
 the 'that' and the 'what.' By the 'that' of a judg- 
 ment we may mean the content or material of a 
 thought process, that is, the subject of the judgment 
 as we have used that term. By the 'what' may be 
 understood the complex asserted by the judgment. 
 For instance, the joyful scene upon the frozen lake, 
 of an illustration already used, is the subject-matter 
 of any judgment that I may make about it. In 
 Bradley 's terminology, it is the 'that' of the judg- 
 ment. If, however, I assert that there is danger 
 from the ice because of a thaw, and the children 
 should be warned, this would be the object or the 
 'what' of the judgment, the complex whole that it 
 is the business of the judgment to assert. 
 
 More recently a similar distinction has been 
 drawn by the Austrian psychologist, Meinong. 
 Meinong insists that we must not confuse in any 
 act of judgment that concerning which we judge, 
 and what we judge about it. The distinction that 
 is thus drawn for all judgments is that with which 
 we are familiar in the case particularly of legal 
 
50 , A TEXT-BOOK OF LOGIC 
 
 judgments. Let us say that a person is accused of 
 a crime. In such a case, we may ask, What is it 
 that the judge and jury are expected to judge? In 
 one sense, the object of their judgment is the 
 prisoner, and in another, it is, let us say, that he 
 is not guilty of the offense with which he is charged. 
 There seems, then, to be two objects of judgment, 
 and, as this inevitably leads to confusion, Meinong 
 thinks it important that they should be clearly dis- 
 tinguished. For that purpose, he proposes to use 
 the term 'object' to denote what we have described 
 as the subject-matter of the judgment, that is, in 
 the case supposed, the prisoner; and the term 
 'objective* to denote what we have called the object, 
 that is, in the case supposed, the verdict of the 
 judge and jury. Now Meinong is perfectly right 
 in saying that the object peculiar to the judgment 
 is what he calls the 'objective,' that the judgment 
 exists for the purpose of asserting something about 
 a definitely apprehended subject-matter, and he is 
 also right in calling attention to the importance of 
 fixing this distinction in an appropriate terminology, 
 because, in the absence of such terminology, of the 
 tendency to confuse the two kinds of objects. 
 
 The Universe of Discourse. In view of the course 
 that our discussion has taken up to this point, the 
 logical judgment may be defined as an assertion of, 
 or of something about, the objects of our experience. 
 We may, for example, assert that so and so is the 
 object of which, at the time the assertion is made, 
 we are thinking, or we may assert certain other 
 
THE JUDGMENT 51 
 
 things, besides its existence, of such an object. In 
 each of these cases there is judgment because the 
 object is apprehended as having a particular char- 
 acter, of existence or something else. The judg- 
 ment, consequently, always implies a relational 
 content of some sort, that is, an object qualified in 
 a particular way, and it is such relational contents, 
 as we have seen, that it is the specific aim of the 
 judgment to ascertain and assert. If, for example, 
 the words 'dog,' 'automobile,' 'zeppelin,' are not mere 
 sounds, but significant terms, they must mean some- 
 thing more than they express ; either that something 
 not specified is 'dog,' 'automobile,' 'zeppelin ;' or that 
 the objects denoted by these terms exist ; or that they 
 have characteristics which distinguish them from 
 all other objects ; or that they stand in an indefinite 
 number of relations to each other, and to numerous 
 other objects. Each of these alternatives illustrates 
 the peculiar character of the judgment, since each 
 of them specifies a content of thought in which 
 relations of some sort are involved. The special 
 object of the judgment, as we have seen, is to 
 assert just such relational contents as these. 
 
 The question may now be raised whether this is 
 the whole story of the judgment, whether, that is, 
 the asserted content embodies the whole meaning 
 of an act of judgment. To this a negative reply 
 must be given. Such an answer is necessitated in 
 part by the fact, as we have seen, that our concrete 
 acts of judgment are not satisfied with the assertion 
 of any content, but only with those that are ger- 
 
52 A TEXT-BOOK OF LOGIC 
 
 mane to the motives by which the acts of judgment 
 are controlled. But the negative answer is ren- 
 dered necessary also by the fact that the subject 
 qualified in the judgment, distinguished as the log- 
 ical subject, is only a part of the actual subject, 
 distinguished as the real subject, which the judg- 
 ment, taken as a whole, is understood to qualify. 
 If this is true, a judgment asserts only part of what 
 it means, and we must understand that the unas- 
 serted part of its content is related to the judgment 
 as the judgment's presupposition. On this view, 
 every judgment must be presumed to involve or 
 presuppose, besides and as part of what it asserts, 
 a wider range of fact in the light of which the 
 particulars which form the content of the judg- 
 ment's assertion are to be interpreted. The range 
 of fact presupposed by any of our judgments is 
 described in logic as a universe of discourse. 
 
 The meaning and truth of this statement will be 
 readily seen in a simple illustration. Any proposi- 
 tion which contains, for example, the term 'style' 
 is at once recognised to mean one thing if the topic 
 of conversation is current modes of dress, and that 
 when the topic of conversation is literature it means 
 something quite different. Thus, if we take the fa- 
 miliar saying, Le style c'est I'homme, in abstraction 
 from all contexts, its meaning is certainly ambig- 
 uous ; and the only hope of removing this ambiguity 
 is to restore the saying to a context in relation to 
 which it can be significantly asserted. Or, to borrow 
 an illustration from Major in discussing a closely 
 
THE JUDGMENT 53 
 
 related topic from the psychological point of view, 
 we may say that "if one is engaged with astronom- 
 ical matters, the word 'star' means a heavenly body. 
 . . . But if the general topic of our discourse is 
 theatres or ball games or decorations, the meaning 
 . . . of 'star' will likely be very different." From 
 these and similar illustrations it is evident that the 
 meaning of what is asserted in any judgment is 
 rendered particular as much by virtue of what it 
 presupposes, that is by its universe of discourse, as 
 by what it definitely asserts. We may say, conse- 
 quently, that it is the intention of every judgment 
 to acknowledge the truth of what it asserts in the 
 sphere of what the judgment presupposes, that is, 
 in some definitely implied universe of discourse. 
 To apply this view to another case, we may say that 
 the statement, 'Mr. Wilson was elected by the pop- 
 ular vote of the people,' asserts a fact that qualifies 
 in a unique way the political history of the United 
 States, and not a fact that sets Mr. Wilson, by 
 virtue of his election to the presidential office, apart 
 from his fellow citizens. Mr. Wilson's citizenship 
 is unaffected by his election, and, therefore, it can- 
 not be in respect of this that our judgment is sig- 
 nificant, but the election does determine in a par- 
 ticular way the political history of the Republic, 
 and this, therefore, must, in logical terms, be the 
 universe of discourse within which our judgment 
 of the election must be understood to fall. 
 
 It follows from this view of the j'udgment that 
 the universe of discourse implied by any judgment 
 
54 A TEXT-BOOK OF LOGIC 
 
 exists always in a relatively indeterminate and 
 incomplete form. This statement does not mean, 
 although it is sometimes true, that particular judg- 
 ments indicate only vaguely the universe within 
 which their meaning is asserted. It means rather 
 that, in the particular which the judgment asserts, 
 the universe is found to be either not determined 
 at all, or not to be determined with an explicitness 
 that renders it serviceable for an immediately con- 
 trolling purpose. Whatever degree of determinate- 
 ness the general field or subject presupposed by any 
 of our judgments may have, that field or subject 
 can be used as a universe only if it is thought 
 capable of receiving, through judgment, a more 
 concrete and determined form. But it also follows 
 from the view we are developing that judgments 
 themselves are incomplete and point beyond them- 
 selves. They are, as it were, fragments torn from 
 their contexts; but, even so conceived, they carry 
 with them, as a rule, evidence of their connection 
 with the contexts from which they have been torn. 
 Unless this were so, single judgments would always 
 remain ambiguous. But if this were the case, if, 
 that is, there existed even a considerable number 
 of judgments from which we are unable to remove 
 their ambiguity, because they do not point with 
 sufficient definiteness to an interpreting context, the 
 fact that, apart from such contexts, they remain 
 ambiguous is in itself evidence that they lack some- 
 thing which is characteristic of significant asser- 
 tions. The meaning, therefore, of any judgment is 
 
THE JUDGMENT 55 
 
 the meaning that it comes to have by virtue of its 
 pointing relevantly to something which is not iden- 
 tical with the relational content asserted by it. In 
 so far then as a judgment has to be supplemented 
 by what its context supplies, so far is it incomplete; 
 and if this incompleteness is to be overcome, it must 
 be by what the judgment enables us to add through 
 its presuppositions. 
 
 If, in view of this discussion, we now define the 
 judgment, more fully than we have done hitherto, 
 as an assertion of, or of something about, the reality 
 presupposed by the judgment, we are immediately 
 confronted with a question concerning the kinds of 
 reality presupposed by our various judgments. In 
 respect to this question, it has been maintained, for 
 example by Bradley, that the real subject of which 
 the thought-contents asserted by all our judgments 
 are predicated is the totality of really existing things 
 which we call the universe. Whatever any judg- 
 ment asserts, just that, so it is maintained, is as- 
 serted of reality in the sense of the system of inter- 
 related existences known as the universe. Reality, 
 according to this view, is always that about which 
 we judge, and our particular judgments assign to 
 it, as its subject, the concrete details which such 
 judgments assert. On this view, no question as to 
 what is the universe presupposed by any judgment 
 could arise, or if it did, it would be answered before 
 it was asked. 
 
 Now, in considering this view, we do not need 
 to inquire whether in the end we should be obliged 
 
56 A TEXT-BOOK OF LOGIC 
 
 to take some such position as has just been stated, 
 although there seem to be difficulties in the way 
 of its adoption; what rather is more to our present 
 purpose is to remark that such a statement does not 
 represent the actual circumstances in which many 
 of our concrete acts of judgment are made. For 
 instance, the series of judgments in which the 
 ancient mythologies state the relations of the gods 
 and goddesses to one another, and to natural events 
 and human history, cannot be said to be made of 
 the universe of really existing objects in the sense 
 that the series of judgments which constitute the 
 body of one of the natural sciences can be said to 
 be made of that universe. If, further, we consider 
 the judgments in which we express social, ethical, 
 and aesthetical facts and relations, judgments, as 
 we have seen, which are not descriptive in the sense 
 that scientific judgments are descriptive, but which 
 refer human behaviour and natural phenomena to 
 a norm or standard, it is difficult to maintain that 
 these are made with immediate reference to the 
 universe which sums up in itself all that may be 
 called real. Whether the facts and relations that 
 constitute the subject-matter of mythology, of soci- 
 ology, ethics, and aesthetics can be asserted of the 
 universe of which the facts and relations of the 
 natural sciences are asserted, is not the question 
 that confronts us; the question rather is whether, 
 in the acts of judgment which give definite form 
 to our knowledge of these subjects, they are so 
 asserted, or whether they are asserted of other 
 
THE JUDGMENT 57 
 
 universes than the one which is existentially real. 
 If we admit, as we must, the latter alternative, if, 
 that is, we admit the existence of a number of uni- 
 verses, other than the real, within which judgments 
 may fall, the question whether the real universe 
 includes all these, as is sometimes maintained, is 
 still left open, and we do not need to close it, for 
 the reason, if for no other, that the problem involved 
 belongs to metaphysics rather than to logic. Logic 
 is interested in the question only for the purpose of 
 emphasising the importance of ascertaining the 
 universe in relation to which, as a matter of fact, 
 particular judgments are asserted as the condition 
 of correctly interpreting such judgments. Thus if 
 we were confined to the view we are criticising, the 
 assertion that 'Fishes are animals which get their 
 oxygen from the water in which they live through 
 gill slits/ and The Royal dragon of China has five 
 claws' would have to be taken as qualifying a single 
 universe ; but surely no one not blinded by a theory 
 could fail to observe that in the former case we are 
 asserting in the world of zoological fact, and in the 
 latter in the world of Chinese heraldic design. The 
 view, therefore, that seems most serviceable, and 
 the one which keeps closest to the facts of our ordi- 
 nary experience, is the view that emphasises the 
 importance of bringing particular judgments into 
 relation with their immediate contexts whatever 
 these may be, and warns us against resolving the 
 distinctions by which these contexts are character- 
 ised into a single context about which the only 
 
58 A TEXT-BOOK OF LOGIC 
 
 intelligible thing that can be said is that, in some 
 sense, it is real or exists. In this connection it may 
 be remarked that for logic the important question is 
 in what sense the reality or truth of an assertion 
 is to be understood. 
 
 Truth, Probability and Error. Truth, probability 
 and error, as employed in logic, are terms which 
 describe characteristics that belong to assertions, 
 they are never employed, as they sometimes are in 
 popular speech, to designate qualities of the objects 
 about which the assertions are made. From the 
 standpoint of logic, objects exist, and they are only 
 the assertions which are made about particular 
 existing things that are said to be true, probable, 
 or erroneous. Truth, probability, and error, then, 
 can never be predicated of things, but only of our 
 judgments of, or about, things. 
 
 Now, since all judgments claim to be true, we 
 have to inquire what we mean by truth, and how 
 there can be such things as probability and error. 
 With regard to the meaning of truth, it is pretty 
 generally agreed that the notion is so nearly ulti- 
 mate that we find it difficult, if not impossible, to 
 offer a definition which does not involve the notion 
 itself as one of the terms. But if truth cannot be 
 defined, we can describe, in a more or less satis- 
 factory manner, what we mean when we use the 
 word. We may say, then, that an assertion is 
 true when it assigns a character to the elements 
 and relations of a subject-matter which are found 
 to be verified when this subject-matter is investi- 
 
THE JUDGMENT 59 
 
 gated by appropriate methods. Thus the judgment, 
 'The fire is hot/ is true, if, when I put myself into 
 sufficiently close proximity to the fire referred to, 
 I experience the sensation called heat. Truth, then, 
 is not a quality of judgments merely as such ; it is 
 a quality that belongs to judgments ad hoc, that is, 
 as assertions of definitely specified contents. When, 
 in other words, the ideas conveyed by a judgment 
 are such that, in the universe presupposed by the 
 judgment, there are facts which exist in the manner 
 it asserts, the judgment is said to be true. Truth, 
 that is to say, is always a claim that is set up on 
 behalf of a judgment's object, in behalf, that is, of 
 what Meinong called the judgment's 'objective.' 
 
 In view of this general statement, it may be 
 asked whether any judgment is true, or whether 
 judgments are at best only probable. The answer 
 to this question obviously depends upon whether we 
 ever need to go beyond a judgment's assertion to 
 ascertain whether the facts and relations asserted 
 by it are as they are asserted. When, for example, 
 we assert that The sun is the source of the world's 
 heat,' it is obvious that the verification of the asser- 
 tion must be sought in astronomical physics, that, 
 in other words, the judgment is true conditionally 
 upon our being able to verify, in the appropriate 
 universe, the facts and relations asserted in the 
 judgment. But not all our judgments are, in this 
 sense, assertions about a given subject; judgments 
 are also assertions of a given subject. If, for ex- 
 ample, we say, 'The subject about which we are 
 
60 A TEXT-BOOK OP LOGIC 
 
 thinking is the sun as the source of the world's 
 heat/ it is obvious that, whatever physics may have 
 to say about this particular subject, it can have 
 nothing to say that throws doubt upon the fact that, 
 at the time the assertion is made, we are actually 
 thinking about this particular subject. We select 
 an illustrative example from the world of physical 
 objects because arguments for the absolute contin- 
 gency of truth have sometimes been framed on the 
 supposition that contingency can be removed only 
 when all the factors of the judgment are merely 
 states of one's own mind. It is often said, for instance, 
 that the certainty that belongs to mathematics 
 is rendered possible by the fact that the fundamental 
 notions of mathematics are concepts and not really 
 existing things. Whether this view of mathematics 
 is correct or not, it is certain that the judgments 
 which assert these fundamental notions are no more 
 indubitable than are those judgments which assert 
 some object in the physical world as the object of 
 thought's activity. It would seem to follow, there- 
 fore, that all judgments which are assertions of 
 particular objects as the objects of thought are true 
 in the sense that it is not possible for those who 
 entertain them to be in any doubt that those are 
 the objects with which thought is engaged. 
 
 Judgments which make assertions about, and 
 are not merely assertions of, their subject-matter 
 are in a different position from those just considered. 
 The chief difference is that in their case we have 
 to go outside the judgment's assertion for the veri- 
 
THE JUDGMENT 61 
 
 fication of the truth of what such judgments assert. 
 The grounds, that is to say, on which the truth of 
 these judgments rest are to be found in the universe 
 to which what the judgment asserts is known to 
 belong. The fact to which attention is in this way 
 being directed is that the assertions we make about 
 the objects of our experience do not derive their 
 truth from the fact that they are asserted, but from 
 the fact that there can be shown to exist in a given 
 universe facts and relations of the kind that our 
 judgments assert. This interpretation of the truth 
 of our judgments should not come as a surprise to 
 those who have followed the discussions of this and 
 the preceding chapters, for the demand for a test 
 of truth is after all merely a challenge to refer one's 
 judgments back to the conditions which, in the first 
 place, made them possible. In this way we are 
 enabled to show that, when all the motives that, 
 in the first place, conditioned the judgment are 
 operative, the assertion contained in it is just the 
 assertion that that situation compels us to make. 
 Thus when the chemist's assertion that the liquid 
 contained in a particular bottle is sulphuric acid is 
 called in question, he does not attempt to prove the 
 truth of his judgment by an emphatic restatement 
 of it, nor by any form or number of reiterations; 
 what he does, if he wishes to remove the doubt that 
 the question has raised, is to apply the tests for 
 this substance which, in the first place, convinced 
 him that it was sulphuric acid and not something 
 else. We may conclude, therefore, with reference 
 
62 A TEXT-BOOK OF LOGIC 
 
 to the class of judgments under consideration that 
 their truth is conditional upon our ability to apply 
 tests of a kind suitable to the character of the 
 subject-matter about which the assertions are made, 
 for it is only when tested that we are able to com- 
 pare what is asserted with what happens in situ- 
 ations similar to those in which the judgments in 
 question originated. In the absence of such tests, 
 judgments of this class can only be said to have more 
 or less probability. 
 
 There are situations, however, in which we are 
 either unable or unwilling to verify our judgments, 
 and are thus precluded from determining the par- 
 ticular degree of credibility that properly belongs 
 to them. In these cases, the claim to truth which 
 all judgments maintain on their own behalf can be 
 acquiesced in as little as it can be dissented from. 
 There belongs, consequently, to the judgments in 
 question the probability that attaches to any unver- 
 ified assertion from whatever cause it may arise. 
 
 It is because so large a number of our social 
 judgments are incapable of the strict proof that 
 can be insisted upon when the subject of the judg- 
 ment is some part of the material universe that, 
 as a class, they have generally been regarded as 
 possessing a lower degree of certainty than that 
 which seems to belong to some of the established 
 conclusions of the natural sciences. We cannot 
 revive in the form of actually existing situations, 
 for example, the circumstances which determined 
 our actions of a week ago, and we cannot, therefore, 
 
THE JUDGMENT 63 
 
 verify the judgments of which these actions are 
 the practical expression. That at the time indicated 
 and in relation to the situation then existing we did 
 judge so and so, is as certain as any judgment can 
 be; but that the judgment at which we then arrived 
 was true is, in the nature of the case, beyond the 
 possibility of strict proof. It would certainly be a 
 very gratuitous form of scepticism to repose no 
 confidence whatever in any social judgment, because 
 all such judgments labour under this disadvantage; 
 and to suggest its possibility is sufficient to expose 
 the absurdity of such a course. For it may be 
 affirmed that the disadvantage in question is not 
 confined to the social judgments we are now con- 
 sidering. It may be urged that some of the judg- 
 ments that are made about the material universe 
 are incapable of the experimental proof to which 
 our exposition has pointed as the test of truth. Our 
 belief that the sum total of physical things is a 
 universe, is, that is, a sphere of material existences 
 whose changes are all subject to law, is not beyond 
 question; and when the belief is challenged, as it 
 has been recently, we cannot put the material uni- 
 verse itself in evidence on either side of the ques- 
 tion. Such a belief, and the judgment in which the 
 belief is asserted, can have no other kind of cer- 
 tainty than that which belongs to the social judg- 
 ments of which we have in particular been speaking. 
 Current belief undoubtedly regards the moon as a 
 sphere, but, on account of the particular configura- 
 tion of the solar system, it can never be a practically 
 
64 A TEXT-BOOK OF LOGIC 
 
 demonstrated fact that the side which is always 
 turned away from our earth is not flat. Ether, 
 ions, centres of force, and atoms themselves are all 
 subject to the same kind of doubt, whenever any 
 one, for what seems to him sufficient reasons, is 
 inclined to call them in question. In view of these 
 instances, it is only fair to conclude that judgments 
 about any sort of material must be regarded merely 
 as probable whenever we are unable to show that 
 facts and relations of the kind asserted do exist in 
 the universe that is presupposed by these judgments. 
 Again, judgments must be classed as probable 
 whenever we are unwilling, for a reason that seems 
 sufficient to us, to apply the test of truth. When, 
 for example, one refuses a cup of coffee of one's 
 hostess with, 'No, thank you; coffee always means 
 a sleepless night/ the judgment by which we excuse 
 or explain our refusal has no doubt a certain prob- 
 ability derived from past experience, but it is one 
 that, for prudential reasons, we are unwilling to 
 verify in the particular circumstances which are 
 the occasion of its assertion. Sleepless nights, we 
 may admit, have followed the drinking of coffee in 
 the past, and it is anticipated that a similar result 
 will follow on the present occasion. In a case like 
 this, which is typical of many others that involve 
 future consequences rather than past acts, we should 
 be going beyond the bounds of necessity if we ac- 
 ceded without reservation the certainty that the 
 judgment claims on its own behalf. We feel, per- 
 haps, that the judgment in question has a high 
 
THE JUDGMENT 65 
 
 degree of probability, but whether it deserves the 
 confidence, say, that is commonly reposed in the 
 prediction of a solar eclipse, is a matter upon which 
 it is not necessary to dogmatise. It is more to the 
 point to observe that the class of judgments that 
 we are discussing is conditional, and, consequently, 
 that it is only if we suppose the present situation 
 is in all essential respects similar to those in which 
 the consequence has followed in the past, that we 
 have sufficient reason for believing that a like con- 
 sequence will follow on the present occasion. But 
 it is exactly this supposition of which the judgment 
 itself is unable to give assurance, and which there- 
 fore renders the judgment less, than certain until 
 it is submitted to the process of proof. 
 
 We may now pass to the meaning of error. 
 And, in the first place, error must be distinguished 
 from mere irrelevance. Irrelevance may exist in 
 either of two forms. It may exist, first, as an in- 
 compatibility in the content of what a judgment 
 asserts. If, for example, Shylock's bond had been 
 drawn for a pound of justice, and not for a pound 
 of flesh, there would have been an irrelevance of the 
 kind in question, because the avoirdupois scale can- 
 not in any sense be made the measure of justice. 
 The universe suggested by the assertion, *I will 
 have a pound of justice/ is one in which the content, 
 on account of its internal contradiction, cannot pos- 
 sibly get realised. Irrelevance in this form, then, 
 arises whenever we predicate of a subject qualities 
 5 
 
66 A TEXT-BOOK OF LOGIC 
 
 and relations which cannot be realised in the uni- 
 verse to which the subject is thought to belong. 
 Instances of this occur whenever we attribute to 
 purely natural events moral or aesthetic significance, 
 or when we explain any of our ideals in terms of 
 mechanical causation. Secondly, irrelevance may 
 exist as an incompatibility between what is asserted 
 and the purpose by which the assertion is controlled. 
 What in these instances is asserted may be true, as, 
 for example, 'Mont Blanc is snow-capped all the 
 year round,' but no one would think of making or 
 entertaining the assertion in a discussion on the 
 value of Rotterdam as a Dutch port of entry to the 
 German Rhine. Failure to understand the limita- 
 tions that a guiding purpose or interest imposes on 
 what may and what may not be significantly asserted 
 about a given subject-matter is one of the most 
 fruitful sources of confusion in discussions of all 
 sorts, and it is to this form of irrelevancy that we 
 look for the origin of those half-truths which do 
 more mischief in the world than frank and un- 
 blushing error. The comment is worth while in 
 this connection because it is to the avoidance of 
 such irrelevance that the student may look as one 
 of the means of hastening his academic and prac- 
 tical efficiency. In either of the two forms which 
 we have now distinguished, then, irrelevance is not 
 to be identified with error. 
 
 Error, in contrast with the second of the two 
 forms of irrelevance just distinguished, is an asser- 
 tion which is relevant to a purpose, and, in contrast 
 
THE JUDGMENT 67 
 
 to the first, is an assertion whose contents are com- 
 patible. Unless it possessed both these marks of a 
 true judgment, error could not possibly exist. To 
 emphasise the former contrast, we may say that 
 error is ascribed to any judgment which, if true, 
 would satisfy the purpose for which the judgment 
 is made. There follows from this statement a con- 
 sideration which is important for all our judgments, 
 namely, that the range of assertion about any 
 subject-matter is determined at the outset by the 
 character of the purpose which stimulates and 
 directs the judging process. In other words, to 
 expect our judgments to be true is a perfectly rea- 
 sonable expectation, but to expect that they will 
 assert the whole truth is to convict our expectation 
 of being either unmeaning or false. The latter 
 expectation is indefensible for the same reason that 
 the former is maintained, namely, that we do not 
 as a rule, nor can any reason be advanced why we 
 should, encumber our judgments by asserting non- 
 significant features of the subject-matter to which 
 these judgments refer. And if it is asked, 'What is 
 and what is not significant?' we can only reply that 
 that all depends upon what the judgment* is wanted 
 for. The truth of this statement can be readily 
 seen in what occurs when all interest in a question 
 vanishes. In such a situation nothing whatever 
 can get asserted. But when an assertion is made, 
 it must be made, not merely of something, but for 
 some purpose, and it is the character of the purpose 
 that determines what feature of that 'something' 
 
68 A TEXT-BOOK OF LOGIC 
 
 is selected for assertion. There is, for example, no 
 doubt that the grass is green and, let us say, that 
 it is long, but it is only the latter assertion that is 
 pertinent when one has to decide what instructions 
 to give the gardener about the day's work. What 
 one thinks about any object, say a house, depends 
 upon whether we are considering it architecturally, 
 domestically, or as an investment. These interests, 
 no doubt, overlap, but they are sufficiently distinct 
 to make quite irrelevant certain assertions that 
 might be made from one of these points of view 
 when, as a matter of fact, we are considering it 
 from one of the other points of view. But we do 
 not call judgments false which bear no relation to 
 the interest by which the judging process is initiated. 
 Error as well as truth exist only in those judgments 
 which claim to fulfill the purpose of the individual 
 by whom they are asserted. 
 
 The second contrast stated above calls attention 
 to the fact that the contents of erroneous judgments 
 are, as we said, compatible. That is to say the 
 judgment must assign its content to a sphere in 
 which it is possible for that content to be realised. 
 The absence of incongruity between the elements 
 of what is asserted is a characteristic of error as it 
 is of truth. When, for example, we judge that an 
 object is elliptical when in reality it is round, we 
 are in error, but the error does not consist in 
 assigning it a shape, but in attributing to it the 
 wrong shape. The wrong shape, however, is an 
 antecedently possible shape, and it is upon this ante- 
 
THE JUDGMENT 6$ 
 
 cedent possibility that the erroneous character of 
 the judgment rests. If instead of asserting that the 
 object was elliptical we had asserted that it was 
 blue, we should not regard that as an error; we 
 should regard it either as a misunderstanding of 
 the motive of the judgment or as nonsense. 
 
 We are now in a position to state what error is. 
 The problem of error is greatly simplified when it is 
 observed that no judgment which fails to assert 
 those features of its subject-matter which are perti- 
 nent to the purpose in hand could by any possibility 
 be regarded as true or erroneous. They are, as we 
 saw, merely irrelevant. It is only when judgments 
 offer themselves as the means of satisfying a pur- 
 pose that they are ever entertained. There is, there- 
 fore, from the standpoint of the interest involved, 
 little chance for error. All that we can say about 
 a judgment, from this point of view, is that it does 
 more or less completely fulfil a present purpose. It 
 is, therefore, to the character of what is asserted 
 that we must look finally for the detection of error. 
 And here, as in the coresponding case of truth, we 
 are confronted with a simple question of fact. Is 
 it a fact, we must enquire, that there exist in the 
 universe presupposed by the judgment qualities and 
 relations of the kind asserted in the judgment? If 
 there are, we call the judgment true; if there are 
 not, we call the judgment erroneous. Error, then, 
 may be defined as some discrepancy between asser- 
 tion and fact. 
 
70 A TEXT-BOOK OF LOGIC 
 
 We have been speaking in this section of error 
 as a failure of the judgment to assert the significant 
 qualities and relations of the object upon which 
 thought is directed. The term is also used to denote 
 those mistakes of judgment which depend, for ex- 
 ample, upon inference. In this sense it is preferable 
 to speak of fallacies. A discussion of this subject 
 will be found in the concluding chapters of this 
 book. 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Ch. I., II. 
 B. Bosanquet, The Essentials of Logic, Lect. II., III. 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XXI. 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. III. 
 W. S. Jevons, Lessons in Logic, Lessons VI., VII. 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. I. 
 
 ADVANCED 
 
 J. M. Baldwin, Thought and Things, Vol. I., Ch. XI., 4-8; 
 
 Vol. II., Ch. II., VI., 1-4. 
 B. Bosanquet, Logic, Book I., Ch. I. 
 F. H. Bradley, The Principles of Logic, Book I., Ch. I. 
 W. R. B. Gibson, The Problem of Logic, Ch. IX. 
 H. W. B. Joseph, An Introductory Logic, Ch. VII. 
 H. Lotze, Logic, Book I., Ch. II. 
 J. S. Mill, A System of Logic, Book I., Ch. II. 
 F. C. S. Schiller, Formal Logic, Ch. VIII. 
 J. Welton, A Manual of Logic, Vol. I., Ch. I., II (ii). 
 
 QUESTIONS 
 
 1. What general meaning may be given to the term object? 
 
 2. In what several ways may we be acquainted with 
 objects? 
 
 
THE JUDGMENT 71 
 
 3. Is the character of an object affected by the way in 
 which it is apprehended? 
 
 4. What do you understand by objects being implicated 
 in all mental processes? 
 
 5. Distinguish three senses in which the term 'thought' 
 has been used, and state how they are related to each 
 other. 
 
 6. To which of the meanings already distinguished is 
 thought, from the logical point of view, most closely 
 related? 
 
 7. What particular aspect of thought does logic emphasise 
 in its use of the term judgment? 
 
 8. What is meant by saying that the subject-matter of 
 judgment is the content of a thought process? Illus- 
 trate. 
 
 9. Explain: 'Judgment is an assertion of the qualities and 
 relations of the objects of thought.' 
 
 10. Is language necessary to give thought the character of 
 assertion? Explain. 
 
 11. State clearly what you understand by assertion. Illus- 
 trate. 
 
 12. Show in what ways judgments are implied, but not ex- 
 pressed, in interrogatives, imperatives, optatives, and 
 exclamations. 
 
 13. Describe what is meant by groundless statements, and 
 in what respect do they differ from judgments? 
 
 14. Define and illustrate the practical and theoretical as- 
 pects of thought processes. 
 
 15. 'Judgments may be defined as relevant assertions.' 
 How does this view of the judgment agree with and 
 differ from that stated in Question 9? 
 
 16. In what two respects may all judgments be said to be 
 relevant? 
 
 17. Explain what is meant by saying that judgment is 
 based in and grows out of our practical needs. Illus- 
 trate. 
 
72 A TEXT-BOOK OF LOGIC 
 
 18. Define what you understand by 'practical,' and show 
 how unsatisfied needs of the sort here in question con- 
 dition the formation of judgments. 
 
 19. How is your answer to the preceding question affected 
 by the fact that judgments are assertions about a sub- 
 ject-matter of some sort? 
 
 20. To what two kinds of error is one exposed in trying 
 to show the relation of thought to its object? 
 
 21. Explain and illustrate what is meant by saying that 
 the interest that conditions a judgment may be extrinsic. 
 
 22. What do you understand by a value judgment? 
 
 23. Describe the nature of scientific interest, and explain 
 why it may be called, in contrast to other kinds of 
 interest, intrinsic. 
 
 24. Is judgment to be distinguished from awareness of an 
 object? Explain. 
 
 25. What difference, if any, do you recognise between the 
 subject and the object of judgment, and illustrate by 
 referring to Bradley's distinction between the 'that' and 
 the 'what.' 
 
 26. Explain what Meinong means by the 'object' and the 
 'objective' of logical judgments. 
 
 27. How may Meinong's distinction be correlated with the 
 view taken in the text? 
 
 28. 'Judgment may be defined as an assertion of, or of 
 something about, the objects of our experience.' Explain 
 this statement, and correlate it with the definitions of 
 judgment in Questions 9 and 15. 
 
 29. "Why is the definition of judgment given in the preceding 
 
 question not completely satisfactory? 
 
 30. What do you understand by a universe of discourse? 
 Illustrate. 
 
 31. Why must any universe of discourse have a more or 
 less indeterminate character? 
 
 32. Why must single judgments be regarded as incomplete, 
 and, therefore, as being to some extent ambiguous? 
 
 33. How may this ambiguity be overcome? 
 
THE JUDGMENT 73 
 
 34. 'Judgment may be defined as an assertion of, or of 
 something about, the reality presupposed by the judg- 
 ment/ Explain and compare with other definitions 
 given in Questions 9, 15, 28. 
 
 35. What, according to Bradley, is the universe presup- 
 posed by all our judgments? 
 
 36. What objections can you urge against Bradley's view? 
 
 37. Is there a plurality of universes? Justify your answer 
 and illustrate. 
 
 38. Of what are truth, probability and error predicated in 
 logic? 
 
 39. In what respect does the logical differ from the popular 
 use of these terms? Illustrate. 
 
 40. What is the logical meaning of truth? Illustrate. 
 
 41. Of what class of logical judgments can you say that 
 they are certainly true? Illustrate. 
 
 42. Can the truth of any of our judgments about a given 
 subject-matter be maintained? State reasons for your 
 answer, and illustrate. 
 
 43. What two conditions compel us to regard certain of our 
 judgments as probable, not true? 
 
 44. Why do we generally regard judgments about social 
 material merely as probable? 
 
 45. Do similar reasons apply to any of our judgments about 
 the material world? Explain and illustrate. 
 
 46. How does unwillingness to verify an assertion affect its 
 claim to be true? 
 
 47. In what two forms may irrelevance exist? Explain and 
 illustrate each. 
 
 48. How do you distinguish irrelevance from error? 
 
 49. Why do we not call those judgments which fail to fulfil 
 a purpose erroneous? Illustrate. 
 
 50. What is meant by saying that in order to be erroneous 
 judgments must assert contents that are compatible? 
 Illustrate. 
 
74 A TEXT-BOOK OF LOGIC 
 
 51. Wherein consists the nature of error? 
 
 52. Can you frame a definition of error? 
 
 53. In what respect does error differ from fallacy? 
 
 EXERCISES 
 
 1. In what sense is the word, thinking, used in the follow- 
 ing statements: 
 
 (1) All human beings are thinking beings. 
 
 (2) There is no truth or error but thinking makes it so. 
 
 2. State at least two judgments about each of the follow- 
 ing subjects: 
 
 (1) Mathematics as a required subject for college grad- 
 uation. 
 
 (2) Inter-collegiate football as a desirable form of stu- 
 dent activity. 
 
 3. What are the grammatical forms of the following, and 
 show in what sense they may be said to involve judg- 
 ments : 
 
 (1) O wad some power the giftie gie us 
 To see ourselves as others see us. 
 
 (2) How oft the sight of means to do ill deeds 
 Makes deeds ill done. 
 
 (3) Can one desire too much of a good thing? 
 
 (4) Are things what they seem? 
 Or is visions about? 
 
 (5) Give me that man 
 That is not passion's slave, and I will wear him 
 in my heart's core, ay, in my heart of hearts, 
 As I do thee. 
 
 4. Give six illustrations of what are called groundless 
 statements. 
 
 5. State six judgments on subjects of your own choosing 
 that show the influence of purpose on the judging 
 activity. 
 
 6. Give six illustrations of the way that judgments are 
 controlled by the nature of the subject-matter about 
 which one thinks. 
 
THE JUDGMENT 75 
 
 7. Take three instances of judgment from your answer to 
 Question 5, and the same number from your answer to 
 Question 6, and show in each case the relation of interest 
 to subject-matter. 
 
 8. Take the remaining instances from your answers to 
 Questions 5 and 6, and state what is the subject and 
 the object in each case. 
 
 9. What can you say about 'water' in each of the following 
 universes of discourse: domestic life; chemistry; phys- 
 ics; art; physiology. 
 
 10. Examine the following judgments, and state whether, 
 and under what conditions, you regard them as true, 
 irrelevant, probable, or erroneous: 
 
 (1) Everything comes if a man will only wait. 
 
 (2) For a man's house is his castle. 
 
 (3) The many still must labour for the one. 
 
 (4) Thought is free. 
 
 (5) Virtue is its own reward. 
 
CHAPTER III 
 THE PROPOSITION 
 
 Judgment and the Proposition. In text-books of 
 logic, it is usual to discuss the judgment and the 
 proposition in the same chapter, and to emphasise 
 the points of similarity between them. In the pres- 
 ent chapter, we are to consider the proposition by 
 itself, because in this way we shall be able not only 
 to distinguish between it and the judgment, but to 
 group together certain problems that arise out of 
 the nature of the proposition which are more or less 
 distinct from those of the judgment which were dis- 
 cussed in the previous chapter. 
 
 In its most general meaning, a proposition may 
 be defined as the verbal expression of a judgment. 
 As we proceed, this statement will be made more 
 explicit; but it will suffice for our present purpose 
 if it enables us to understand the importance of put- 
 ting into verbal form the truths that are asserted 
 in our judgments. The necessity of finding a suit- 
 able medium for expressing our judgments is forced 
 upon us when it is realised that explicit statements 
 of our meanings are, sometimes, if not frequently, 
 important factors in our search for truth. We often 
 find, for example, that ideas with which we had sup- 
 posed ourselves perfectly familiar suddenly take on 
 a penumbral haze when we are required to use these 
 ideas in working out new problems, for instance, 
 
 (76) 
 
THE PROPOSITION 77 
 
 in solving an 'original' in geometry or in finding an 
 'unknown' in chemistry ; or when we try to commu- 
 nicate these ideas to other people, for instance, 
 in a class recitation. In both these cases, we have 
 before us the task of setting the ideas in question 
 in a different context, and it is the new context into 
 which they are to be fitted that reveals to us defects 
 in the ideas themselves of which we were hitherto 
 unaware. In order to succeed in the problem that 
 is thus presented, it often becomes necessary to give 
 verbal expression to our ideas, and our search for 
 the suitable form is not infrequently found to re- 
 act upon the ideas themselves to make them more 
 exact. It may also be noticed that when we have 
 once expressed our ideas in accurate verbal forms, 
 we are able to analyse these ideas, and thus to ad- 
 just them to other ideas with which they have 
 various relations. For it must be admitted that our 
 interest in ideas is not merely to know that they are 
 true, but, concurrently with this, to use them in en- 
 larging the boundaries and directions of our knowl- 
 edge. And it contributes to both these objects to 
 secure for our ideas an adequate verbal expression. 
 The statement of our judgments in the form of prop- 
 ositions both clarifies the meaning and renders the 
 application of our ideas possible. 
 
 We may bring out the difference between the 
 judgment and the proposition if we refer to the way 
 that each originates in our ordinary experience. In 
 the foregoing chapter, we have had occasion to indi- 
 cate in a general way the conditions under which our 
 
78 A TEXT-BOOK OF LOGIC 
 
 judgments arise. Judgments were there described 
 as completed solutions of problems set by the situ- 
 ations in which one finds himself from time to time. 
 That is to say, judgments arise out of whatever is 
 problematical, undetermined, baffling, whether this 
 falls in the sphere of perception, or in the sphere 
 of the social, scientific, ethical, sesthetical, or relig- 
 ious life. Whatever sets a barrier to the satisfac- 
 tion of wishes, whatever hinders, arrests, or makes 
 impossible the carrying out of cherished plans, chal- 
 lenges and stimulates the life of thought, and forces 
 us into a judgment. Judgments arise out of our 
 needs for knowledge, and this need is stimulated 
 when the situation which instigates the need is of 
 such a character that our way to the successful con- 
 duct of the theoretical or practical life is blocked. 
 When we have unravelled the tangle, and see the 
 total situation in its bearing upon our arrested pur- 
 suits so that we either modify or change our aims, or 
 they are given an open field, we may be said to have 
 judged. It is another story when we ask what are 
 the conditions that determine the rise of proposi- 
 tions. In the proposition we are not seeking to 
 extricate ourselves from an embarrassment, because 
 no embarrassment is present, and we are not seeking 
 knowledge, because that already exists. A proposi- 
 tion, as we have already said, is the verbal statement 
 of what we already know ; it is a statement in which 
 something is either affirmed or denied of something 
 else. It is, consequently, not an instrument of the 
 search for knowledge, but of its communication. 
 
THE PROPOSITION 79 
 
 When we put our judgments into propositional form, 
 we are making them socially available, and present- 
 ing them for acceptance or rejection. 
 
 The Import of Propositions. A proposition may 
 be interpreted from either or both of two points of 
 view : from the point of view of the person speaking, 
 and from the point of view of the person spoken to. 
 In each of these cases, the proposition has a different 
 import or meaning. In the former, where the person 
 speaking is expressing a judgment concerning a sub- 
 ject about which he has reached a conclusion, the 
 proposition means what the judgment which it ex- 
 presses means, and must be interpreted as a judg- 
 ment. That is to say, the truth of the proposition 
 is also the truth of its corresponding judgment, and 
 vice versa. The meaning of the proposition, inter- 
 preted from the point of view of the speaker, is 
 designated in logic as the truth-import of the propo- 
 sition. In the other case, when we consider the 
 proposition from the standpoint of the hearer of it, 
 the proposition and the judgment which it expresses 
 are not the same, and the truth they express may not 
 be identical. The reason why the proposition may 
 mean one thing to the hearer and another to the 
 speaker must be looked for in the differences of the 
 relations that the hearer and speaker have to the 
 knowledge that the proposition embodies. Or, to 
 put the matter more definitely, the speaker's rela- 
 tions are with the knowledge which the proposition 
 expresses, while the hearer's are with the terms of 
 the proposition itself. When we interpret a propo- 
 
80 A TEXT-BOOK OF LOGIC 
 
 sition from the standpoint of the person spoken to, 
 we have what is called in logic the statement-import 
 of the proposition. The statement-import is, conse- 
 quently, a structural interpretation of the proposi- 
 tion ; it is the meaning that a proposition has when 
 it is considered from the standpoint of its factors 
 or terms. 
 
 We may look at this distinction between the 
 statement-import and the truth-import of proposi- 
 tions a little more in detail. It is obvious that the 
 question before the speaker is one of selecting the 
 words that will adequately convey his meaning. 
 When one wishes to make a judgment socially avail- 
 able, one has to express the judgment in words, or in 
 some other recognised means of communication. 
 When, on the other hand, we listen to what is said, 
 or read what is written, the question before us is to 
 ascertain the meaning that the words were originally 
 intended to convey. This is not always as simple as 
 it may sometimes seem. Because, for example, the 
 words in which we are addressed are familiar, it does 
 not follow that the idea that the words express is at 
 all understood. The common misunderstandings of 
 ordinary life, and the more serious difficulties that 
 we meet with in the course of our studies, are due 
 very often to our failure to interpret aright the 
 meaning, not to our inability to understand the 
 words, of the propositions that are laid before us. 
 In such a case, the proposition means for us some- 
 thing that it does not mean for the speaker; it has 
 
THE PROPOSITION 81 
 
 for us, that is to say, a statement-import but no 
 truth-import. 
 
 It will help our understanding of this statement 
 if we throw the essential factors of our problem into 
 the form of a diagram : 
 
 Speaker Hearer 
 
 f \ f > 
 
 Idea Proposition * Idea 
 
 V J V, J 
 
 ^Y" ~~Y~~" 
 
 Truth-import Statement-import 
 
 If, reading the above diagram, our interpretation of 
 the proposition is made from the standpoint of the 
 speaker, we start with the idea or judgment that has 
 to be expressed in the proposition; the proposition 
 is then the verbal expression of the judgment or 
 idea from which we set out. For the speaker, the 
 proposition does express his judgment, and so inter- 
 preted it embodies the truth of his judgment. If, 
 on the other hand, our interpretation is made from 
 the standpoint of the hearer, we start with the prop- 
 osition, the verbal expression of the speaker's judg- 
 ment, and the words of the proposition have to be 
 interpreted so as to render an idea or judgment pos- 
 sible. But what is the guarantee in such a case that 
 the meaning derived from the proposition will be 
 the meaning expressed by it? The idea in the 
 hearer's mind may be different from the idea in the 
 speaker's mind. It is this idea, the idea or meaning 
 that the hearer of a statement gets from what is said 
 
82 A TEXT-BOOK OF LOGIC 
 
 to him, that we designate the statement-import of 
 the proposition. The truth-import and the state- 
 ment-import of a proposition, therefore, may not be 
 the same. 
 
 But, it may be asked, does not our interpretation 
 of a proposition, even when it is taken from the 
 standpoint of the hearer, aim at an identity of mean- 
 ing between its truth-import and the statement- 
 import? This is doubtless true. But we should 
 miss a great deal in our understanding of the life of 
 thought if we did not see the possibility of the same 
 statement meaning different things for speaker and 
 hearer. It is this fact that we have been emphasis- 
 ing. And it is as desirable to ascertain how this 
 difference may arise as to see how it may be over- 
 come. For if we understand the origin of such dif- 
 ferences, we shall know how to avoid or overcome 
 them. In either case, we are concerned with the 
 context of the idea or judgment that we are trying 
 to understand ; and it is obvious that when the con- 
 text is different for speaker and hearer, the idea 
 the proposition conveys must, in some measure, be 
 different for both. For, as we have seen, the con- 
 texts in which our ideas occur give part of the mean- 
 ing that ideas may have. If, therefore, you change 
 the contexts you change also in part the ideas them- 
 selves. Thus, whenever we fail to get the meaning 
 of what is said to us by reason of our failure to 
 understand the universe of discourse within which 
 the thought of the speaker is moving, we do not 
 naturally ask for a repetition of the sentence or 
 
THE PROPOSITION 83 
 
 proposition, but require, for its comprehension, a 
 larger section of the context, and, in some cases, the 
 revival of the whole universe within which the truth 
 of the judgment is, by the speaker, presumed to 
 exist. In other words, it is the fragmentariness of 
 all our judgments, to which reference has been made, 
 that is the ground of the difference between the 
 truth-import and the statement-import of proposi- 
 tions ; a fragmentariness that can be overcome only 
 if it is supplemented by a larger portion of the inter- 
 preting context than is frequently implied by the 
 single proposition. 
 
 We may further elucidate the important distinc- 
 tion just made between the truth-import and the 
 statement-import of propositions if we consider it 
 as a special instance of the difference, first drawn 
 by the English historian, Grote, and made current 
 by the American psychologist, James, between 
 "knowledge of acquaintance" and "knowledge 
 about." An illustration sometimes used to indicate 
 the contrast between these two kinds of knowledge 
 is the difference between the normal child's expe- 
 rience of light, and the experience of light that a 
 child, blind from birth, has through the reports of 
 seeing adults. The knowledge of the two children, 
 without doubt, is at different removes from the real 
 character of light. That is to say, the contrast be- 
 tween "knowledge of acquaintance" and "knowledge 
 about" calls attention to the fact that the knowledge 
 that any one has is sometimes immediate and direct, 
 and sometimes mediate and indirect. Now, the dis- 
 
84 A TEXT-BOOK OF LOGIC 
 
 tinction between the truth-import and the statement- 
 import of propositions seems to be contingent upon 
 whether propositions express either the one or the 
 other of the above-mentioned kinds of knowledge. 
 We are all aware that much that we ordinarily call 
 knowledge is based upon nothing more certain than 
 our ability to understand the words in which this 
 knowledge has been communicated, while a much 
 smaller fraction of our knowledge rests on direct 
 acquaintance with the facts, and a study of the rea- 
 sons by which such knowledge is supported. In the 
 one case, propositions embody judgments, and are 
 to be interpreted as judgments; in the other case, 
 propositions are statements to be understood, 
 whether they introduce us or not to the facts out of 
 which the judgments which they express have come. 
 To understand what is told us is a first step in knowl- 
 edge; but it is only a first step, and should lead us 
 beyond itself to a more intimate and personal ac- 
 quaintance with the truths and facts that are the 
 material of advancing knowledge. In other words, 
 we must proceed from the statement-import to the 
 truth-import of the propositions which convey to us 
 so large a proportion of the material upon which the 
 educative processes as a whole depend. 
 
 Formal Analysis of the Proposition. The propo- 
 sition was defined above as the verbal expression of 
 a judgment; it is the logical instrument by which 
 what is true for judgment gets a simple and un- 
 equivocal expression. But not every verbal expres- 
 sion of a judgment is a proposition; it may be, for 
 
THE PROPOSITION 85 
 
 example, a sentence. A sentence may be a proposi- 
 tion, as, for example, 'The book is on the table ;' but 
 this is not necessarily the case, as, for example, 'A 
 friend of mine has gone abroad/ From the formal 
 side, the essential difference between the sentence 
 and the proposition lies in the number of the factors 
 present in each. A sentence always requires the 
 presence of a subject and a predicate; the proposi- 
 tion cannot exist without a subject and predicate, 
 which are called terms, and also a copula. If we 
 compare the sentence and the proposition in these 
 respects, we shall see that the predicate of the sen- 
 tence is, by logic, broken up into two parts, the 
 copula and the predicate of the proposition, and that 
 the subject remains the same. The following dia- 
 gram represents these relations to the eye : 
 
 Sentence: Subject Predicate 
 
 A 
 
 Proposition: Subject Copula Predicate 
 
 The doctrine of formal logic depends upon the struc- 
 tural difference between the proposition and the sen- 
 tence as thus outlined. In the following sections, 
 therefore, we shall dwell on the meaning that logic 
 assigns to the several parts of the proposition. 
 
 Terms. The subjects and predicates of proposi- 
 tions are called terms. Now, since the proposition 
 is a statement in which, as we have seen, something 
 is predicated affirmed or denied of something 
 else, we may define the predicate term as that which 
 is predicated, and the subject term as that of which 
 
86 A TEXT-BOOK OF LOGIC 
 
 the predication is made. If, as is usual, we use the 
 symbol S for the subject term, and the symbol P 
 for the predicate term, the structural proposition 
 may be written S P. In such a proposition, P is 
 said to be predicated of S. We may observe that 
 the subject term of a proposition is always written 
 first, and the predicate term last. The reason for 
 this seems to be that since the proposition is deter- 
 mined by the interests of communication, it is im- 
 portant, at first, to call attention to that about which 
 we wish to speak. If the student remembers this 
 he will avoid the difficulty that is sometimes expe- 
 rienced in distinguishing between S and P. For 
 example, if we wished to express in prepositional 
 form the statement, 'Uneasy lies the head that wears 
 a crown,' it would not be accurate to say that 'Un- 
 easy' is the subject. The rule that may be followed, 
 whenever we are in doubt as to what our terms are, 
 is to ask: What am I speaking about? The answer 
 to this question will give us the subject term. The 
 predicate term may be found by asking, What am 
 I saying of this? If we apply these tests to the 
 example just cited, we shall find that we are speak- 
 ing about 'The head that wears a crown/ and this, 
 consequently, is the subject term of the proposition ; 
 and that what we are saying of this is that it is 
 'uneasy,' and this, consequently, is the predicate of 
 the same proposition. 
 
 It should be remarked that we are frequently 
 at a loss to know which is the subject, and which 
 the predicate, term of given statements. The reason 
 
THE PROPOSITION 87 
 
 for this seems to be that in order to know what any 
 statement means we require sometimes to have be- 
 fore us a larger section of the whole context of 
 thought than the particular statement itself pro- 
 vides. This takes us back to what we said above 
 about 'the universe of discourse/ and the function 
 it serves in giving to our particular judgments the 
 meaning they are intended to have. Propositions 
 express judgments which are torn loose from their 
 contexts, and they sometimes do, and sometimes do 
 not, retain sufficient of the original context to make 
 our interpretation of them certain. The example 
 that was quoted above illustrates the former case; 
 we were doubtless talking about 'crowned heads.' 
 A more difficult case, taken from Jevons, is the fol- 
 lowing: 'Life is held dear by every man.' In this 
 statement, are we talking about 'life,' or about 
 'things that are held dear,' or about 'every man'? 
 Grammatically, 'life' is the object of the verb 'holds 
 dear,' and cannot, therefore, be the subject. The 
 meaning of the statement, consequently, is : 'Every 
 man holds life dear.' We are speaking in the uni- 
 verse of values ; and, in the statement, we are nam- 
 ing one of the objects of value. If, however, to take 
 an illustration from Sidgwick, we say that 'Newman 
 wrote the Grammar of Assent,' we have no means 
 of determining whether 'Newman' or The Gram- 
 mar of Assent' is the subject, because, as Sidgwick 
 says, "the statement is regarded in isolation from 
 all context. Regarded in this abstract way, it may 
 equally well be called a statement about Newman, 
 
88 A TEXT-BOOK OF LOGIC 
 
 or about the book, or again about both the man and 
 the book." It would seem, then, that back of all 
 particular statements there lies a universe of fact 
 or idea which flows over into these statements to 
 give them the determinate meaning they may prop- 
 erly have. 
 
 Names and Words. Another question, closely 
 connected with the foregoing, arises when we ask 
 whether terms can exist outside the propositions in 
 which they are found. We may ask, for example, 
 whether The head that wears a crown/ which, as we 
 saw, was the subject term of the proposition which 
 was studied above, is always a term, and in what- 
 ever connection we may meet the phrase. Or, we 
 may inquire, is it a term only when it occurs in a 
 proposition? To this question we reply that terms 
 are terms only in relation to the proposition in 
 which they occur. For example, we may write 
 down the following : 
 
 Silver Conductor of electricity Comets 
 
 Plants Without weight Roses 
 
 But neither this, nor any similar list, is a list of 
 terms. In logical terminology, this is a list of 
 Names. By a name, therefore, we understand a 
 word, or a collection of words, which has a complete 
 meaning, and which may be used as the subject or 
 predicate of a proposition. In the following, 'Silver/ 
 'Without weight/ 'Plants/ etc., names from the 
 above list, are terms : 
 
THE PROPOSITION 89 
 
 Silver is a conductor of electricity. 
 Comets are without weight. 
 Roses are plants. 
 
 Now it may seem that the distinction between 
 terms and names is over-drawn, and that it does not 
 correspond to any real difference. This is not the 
 case. For observe that although the words in the 
 list of names, and the words that appear in the 
 propositions are the same, the meaning in the latter 
 case is much more precise than in the former; it 
 has changed from being vague, general, and loose, 
 to being specific, particular, and fixed. In so far as 
 our propositions express judgments, this is the re- 
 sult that we should expect to find. For the sake 
 of emphasis, the difference between a name and a 
 term may be stated in the following way: 
 
 A Name is a word, or a collection of words, with 
 a complete meaning, which may be thought of as 
 the S or P of a proposition. 
 
 A Term is a word, or collection of words, with 
 a complete meaning, which is thought of as the S 
 or P of a proposition. 
 
 Both terms and names are ordinarily expressed 
 in words, but it is not because they are words, but 
 because they have meaning that they are so called. 
 Terms and names are significant words. We are 
 not confined, however, to the study of words from 
 the standpoint of their significance or meaning. 
 Grammar, for example, studies words with respect 
 to the uses they have in sentences. Substantitives, 
 
90 A TEXT-BOOK OF LOGIC 
 
 verbs, prepositions, adjectives, adverbs, etc., are the 
 names of various classes of words that are recog- 
 nised by grammar when their use is made the basis 
 of classification. Logic also finds it convenient to 
 classify words with respect to their uses as terms 
 in the proposition, disregarding, as does grammar, 
 the meaning that particular words may have. But 
 the logical classification is simpler than the gram- 
 matical, because the logical requirements are nar- 
 rower and more precise than the grammatical. 
 Words, for logic, are arranged in two main groups, 
 according as they are or are not able to stand by 
 themselves as S or P in a proposition. Words which 
 by themselves are capable of being thought of as S 
 or P of a proposition are called Categorematic 
 words. Words, on the other hand, which require the 
 assistance of other words before they can be 
 thought of as the S or P of a proposition are called 
 Syncategorematic words. 'Metal/ 'laws/ 'elements/ 
 'custom/ are categorematic words, since they may 
 stand by themselves as terms in a proposition. For 
 example : 
 
 All metals are elements. 
 Some laws arise from custom. 
 
 The words 'of/ 'the/ 'always/ 'a/ in the following 
 statements, are syncategorematic words, because by 
 themselves they cannot be thought as S or P in a 
 proposition. 
 
THE PROPOSITION 91 
 
 Mistakes are not always a proof of ignorance. 
 Bismarck is the man of iron. 
 A burnt child dreads the fire. 
 
 The only apparent exception to the statement of 
 what should be understood by a syncategorematic 
 word is illustrated by such instances as the follow- 
 ing: 'Good is an adjective,' 'Of is a preposition/ 
 But it should be observed that it is not the use of 
 the word in a logical proposition, but the word as 
 an example of a group of words in grammar that 
 is the subject term of such propositions. They are 
 for logic categorematic words. 
 
 If we examine the logical classification of words, 
 we shall see that the terms of propositions in which 
 categorematic words occur are single-worded terms, 
 while the terms of propositions in which syncatego- 
 rematic words occur must necessarily be many- 
 worded terms. On the basis, therefore, of the 
 kinds of words that enter into them, we may 
 classify terms as either single-worded or many- 
 worded terms. 
 
 The Copula. The most distinctive element of the 
 proposition is the copula. It is always expressed 
 by 'is' or 'is not,' 'are' or 'are not,' depending on 
 whether the subject term of the proposition is sin- 
 gular or plural, and whether the judgment is affirm- 
 ative or negative. From the standpoint of the 
 hearer, the proposition tends to fall apart into its 
 terms; and it is the function of the copula to hold 
 them together in the concrete unity of a single idea, 
 
92 A TEXT-BOOK OF LOGIC 
 
 and thus .to preserve in the proposition a quality 
 that is characteristic of the judgment itself. The 
 copula must not be looked upon as a coupler be- 
 tween the subject and predicate terms, nor is there 
 any separate and distinct element in the judgment 
 corresponding to it, and coming between the idea of 
 the subject and that of the predicate. Its function 
 is to express the act of judgment by which the S 
 and P are really held together in the way that the 
 proposition expresses. 
 
 The copula has been a much debated subject of 
 logic. It will help us to a better understanding of 
 it if we consider some of the views that have been 
 advanced concerning it. We may distinguish two 
 such views, the relational and the existential, and 
 these we shall touch upon briefly in order. 
 
 The Relational View. This view is based upon 
 the assumption that each term of the proposition 
 has a distinct meaning, and it holds that the copula 
 brings these terms together in the unity of a single 
 statement. If we -adopt this view, we are required 
 to admit that our concepts or terms are independent 
 of our judgments, and .that is -to deny that judgment 
 is the starting-point of knowledge. The discussions 
 of the logicians of the Middle Ages over Univer- 
 sals were concerned with this subject, and they were 
 divided in their opinion as to whether concepts ex- 
 isted apart from our knowledge of them. The views 
 developed by the Schoolmen, as the great thinkers 
 of the Middle Ages were called, are three, and these 
 wei may enumerate and describe briefly. The real- 
 
THE PROPOSITION 93 
 
 istic view, held by Anselm and Aquinas r was that 
 universals or concepts have an existence before and 
 independently of the particular objects through 
 which we become aware of them. Briefly expressed, 
 this position was summarised in the Latin state- 
 ment: Universalia ante rem. The view of the 
 Nominalists was that universals or concepts owe 
 their existence to the prior existence of the par- 
 ticular objects of our experience, or, as they said, 
 Universalia post rem. This view was held, among 
 others, by Roscellinus. A conceptualist view, 
 which aimed to embody the truth of each of the for- 
 mer views, was developed by Abelard. This view 
 called attention to the fact that universals or con- 
 cepts have no meaning apart from the particular 
 objects in which they are embodied, and that par- 
 ticular objects have no meaning apart from the uni- 
 versal or concept which gives them their significance. 
 These ideas are expressed in the Latin statement: 
 Universalia in re. Outside the official teaching of 
 the Roman Church, which is realistic, some form of 
 conceptualism quite generally prevails at the present 
 day. At any rate, it would be agreed by most logi- 
 cians that concepts are elements of our knowledge, 
 and that it is our ability to judge, to assert like- 
 nesses and differences of the objects of our expe- 
 rience, that gives existence and life to the things 
 we call concepts. Psychology and logic both teach 
 that the objects of our experience are inextricably 
 connected, and that our knowledge grows by dis- 
 tinguishing now one aspect and now another of the 
 
94 A TEXT-BOOK OF LOGIC 
 
 inter-related world of men and things around us. 
 If this is true, there is no object that is merely 
 itself, or that exists in isolation from everything 
 else. Every object with which we are in any way 
 concerned is always becoming for us something else, 
 showing some new quality or entering into some 
 new relation. This state of affairs is expressed in 
 logic by saying that there are no S's that are not P's, 
 that the P predicated of any S is not a foreign thing 
 that is added to it by the copula, but some quality 
 that it already possesses, or some relation that it 
 actually sustains. In other words, we never start 
 with a bare S, with an S that is an unrelated unit, 
 but with an SP that is a relational unity, and it is 
 this fact that becomes explicit in the judgment, S 
 is P. Unless S were already P, judgment would be 
 impossible, and the proposition could not exist. The 
 proposition makes explicit what is already present 
 in knowledge, and since knowledge, whatever its 
 form, is a qualification of an S by a P, there does 
 not seem to be any separate meaning for the copula 
 when knowledge is expressed in a proposition. That 
 is to say, we do not need the copula for the estab- 
 lishment of the knowledge relation; but it is used 
 in the proposition, as Mill asserts, as "a sign of 
 predication." In other words, the copula must be 
 understood as serving notice upon the person who 
 undertakes to interpret the proposition that S and 
 P are not separate and distinct things, but, for the 
 purposes for which the proposition is expressed, 
 one and inseparable. The proposition, that is, does 
 
THE PROPOSITION 95 
 
 not tell us about any S, but only about the S that 
 is P. 
 
 The Existential View. This view arises out of 
 the fact that 'is,' besides serving as "a sign of pred- 
 ication," has also a meaning of its own, namely, 
 existence. Thus, if we say that, 'Aristotle is the 
 father of formal logic,' it may seem that we are not 
 merely stating the relation of Aristotle to the science 
 of logic, but are also asserting the existence of Aris- 
 totle. For if we do not believe in the reality of Aris- 
 totle, what significance, it may be asked, can belong 
 to the statement that he is the founder of formal 
 logic? To preserve the proposition, therefore, from 
 evaporating into mere nonsense, we seem forced to 
 admit that the reality of the subject term must be 
 secured by the structural character of the proposi- 
 tion itself. Thus, if we consider the structural for- 
 mula, 'S is P,' we must, from this point of view, 
 interpret it as meaning, 'S is, and it is P.' That is 
 to say, the significance of the predication, 'S is P,' 
 depends upon our right to take the copula twice 
 over, and in each case with a different meaning. In 
 the first case, 'S is' is equivalent to 'S exists ;' in the 
 second, 'S is P/ 'is' is "a sign of predication," in 
 the sense already explained. This, in brief, is the 
 existential view of the copula. 
 
 It is evident that we can accept this view only 
 if we take the copula in the same double way in all 
 propositions. But this we can not do. There are 
 some propositions whose terms forbid this interpre- 
 tation of their copula. When, to take Mill's example, 
 
96 A TEXT-BOOK OF LOGIC 
 
 we say that 'A centaur is a fiction of the poets,' 
 existence is explicitly denied, but it is no less ex- 
 cluded when, explaining a name, we say, 'A couch 
 is an article of furniture used for reclining/ Fur- 
 ther, if we say that 'Shakespeare's Henry V is nobly 
 drawn/ we are obviously moving in the sphere of 
 fiction, as we are moving in the realm of mythology 
 when we say that 'Zeus is king of all the gods.' In 
 cases like the foregoing, the existential interpreta- 
 tion of the copula seems to be without meaning; 
 but this is so not because 'is' has lost the meaning 
 of existence, but because the terms of the proposi- 
 tion will not support such an interpretation. Thus 
 we see that the effort to give the copula a distinctive 
 sense, over and above what it has as "a sign of 
 predication," breaks down before the controlling 
 influence of the terms which constitute our proposi- 
 tions. As we have seen, propositions are statements 
 of the relationship of terms, and the relations are 
 determined not by any special meaning carried by 
 the copula, but by the character of the terms that 
 enter into propositional statements. 
 
 To meet these difficulties, it is sometimes pointed 
 out that, for speaker and hearer alike, all motive 
 for judgment is taken away unless we presuppose 
 the reality of the subject-matter of our judgments. 
 We do not express judgments, it is said, about sub- 
 jects which we believe do not exist. This may be 
 readily granted ; but we should remark, at the same 
 time, that it is one thing to admit that existence 
 is presupposed by our judgments, and quite another 
 
THE PROPOSITION 97 
 
 to affirm that reality is asserted by the copula of 
 the propositions in which our judgments are ex- 
 pressed. Judgments may imply reality without as- 
 serting reality. Belief in the reality of Columbus, 
 for example, is implied in the statement that 'Co- 
 lumbus is the discoverer of America ;' but what the 
 statement asserts is that he discovered America. 
 And what is true of this case, is substantially true 
 of every case of the judgment. 
 
 If, then, we must hold that belief in reality is 
 presupposed by every judgment, it is obvious that 
 we cannot mean the same thing by existence in 
 every case of judgment. In the examples, 'Utopia 
 is the ideal commonwealth as depicted by More/ and 
 The sun is the centre of our solar system,' we can 
 not be supposed to imply that 'The sun' and 'Utopia' 
 belong to the same sphere of existence or reality. 
 In other words, we must recognise different spheres 
 of reality, and it is existence within one or other 
 of these spheres that is implied in every judgment 
 that we make. Thus, 'Utopia' belongs to the world 
 of the imagination ; 'The sun' to the world of phys- 
 ical objects. This is a doctrine of logical importance, 
 for we may remark that ambiguity, misunder- 
 standing, and error arise when what a judgment 
 asserts as true within one sphere of reality is taken 
 as true within another with respect to which the 
 judgment has not been determined. If, for example, 
 I say that 'I believe in the reality of Santa Claus,' 
 I am, of course, asserting a belief which falls within 
 
98 A TEXT-BOOK OF LOGIC 
 
 the world of ideas; but if you understand me to 
 imply the corporeal and individual existence of 
 Santa Glaus, you only emphasise your misunder- 
 standing 1 of what I asserted if you challenge me to 
 produce him, or to have him as my guest on Christ- 
 mas Day.. 
 
 We may, then, sum up this discussion in the fol- 
 lowing statements : (1) the copula does not express 
 existence, but is only 'a sign of predication;' (2) 
 reality of their subject-matter is presupposed not 
 expressed by all our judgments; (3) there are 
 different spheres of reality within which the mean- 
 ing of our several judgments is to be determined; 
 and (4) a failure to refer any judgment to its proper 
 or intended sphere of reality leads to ambiguity, 
 misunderstanding, and error. 
 
 Kinds of Propositions. There are three main 
 types of propositions; the categorical, the dis- 
 junctive, and the hypothetical. In this section we 
 shall limit ourselves to the task of characterising 
 each kind of proposition, reserving for other chap- 
 ters the discussion of the logical problems which 
 are connected with these forms of statement. In 
 the first place, however, it should be remembered 
 that we are considering propositions in general, and 
 that, however the categorical, the disjunctive, and 
 the hypothetical propositions differ from each other, 
 they all share the common characteristics of propo- 
 sitions. It is, we have seen, the business of propo- 
 sitions to express the affirmative or negative rela- 
 tions between the objects of our experience when 
 
THE PROPOSITION 99 
 
 these relations have become explicit in judgment. 
 This function of the proposition is called in logic 
 'predication.' In every proposition P is predicated 
 of S, and as we have seen, the copula is the sign 
 of such predication. With respect, therefore, to the 
 three types of proposition we may say that they 
 differ, if they differ at all, by reason of the differ- 
 ence in the forms of their predication. And this is 
 the usual way of distinguishing them. Thus, in the 
 categorical proposition we have simple predication ; 
 in the disjunctive proposition, alternative predica- 
 tion; and in the hypothetical proposition, condi- 
 tional predication. The structural formulae for 
 these three kinds of proposition respectively are: 
 'S is P ;' 'S is either P or Q or M ;' 'If S is P, it is 
 M.' We may also illustrate each kind by the fol- 
 lowing examples : 'The way of the transgressor is 
 hard ;' 'Today is either Monday or Tuesday or Wed- 
 nesday or etc.;' 'If Caesar was ambitious, he de- 
 served to die.' 
 
 Relations of the Main Types of Propositions. Prop- 
 ositions have been distinguished as either categor- 
 ical, disjunctive, or hypothetical. These different 
 forms of proposition correspond to the different de- 
 grees of certainty or explicitness of the judgments 
 they express. Now, since we know more about 
 same subjects than we do about others, and our 
 knowledge of some parts of some subjects is more 
 exact than it is about other parts, we should expect 
 that this fact would be reflected in the propositions 
 in which we express our several judgments. In 
 
100 A TEXT-BOOK OF LOGIC 
 
 other words, the difference in the forms of preposi- 
 tional statements corresponds to a difference in the 
 explicitness of the knowledge asserted by our judg- 
 ments. There is pretty general agreement among 
 logicians as to the foregoing statement. There is 
 not, however, the same harmony among them on the 
 question of the precise order in which the several 
 types of propositions should be arranged. We 
 would suggest that they may be taken, in the order 
 of their increasing exactness, in the following way : 
 the disjunctive, the hypothetical, and the categor- 
 ical. That is to say, the disjunctive and the cate- 
 gorical propositions, respectively, express the least 
 and the most explicit forms of knowledge, and the 
 hypothetical, to which class most of our judgments 
 belong, will appear as a form of statement that ex- 
 presses, in the majority of cases, the maximum at- 
 tainable certainty in our quest for knowledge. 
 
 To consider each case separately, we may say of 
 the disjunctive proposition that it expresses uncer- 
 tainty as to the details of a subject-matter which is 
 explicitly under consideration. For instance, we 
 may not be in doubt that there will be students 
 whose task it will be to read this paragraph, but 
 we may not be certain how far they will understand 
 it. If, in such a case, we tried to make the details 
 of judgment as precise as possible, our proposition 
 would then assume this form: 'The student who 
 reads this paragraph will either understand it, or 
 not understand it, or misunderstand it.' Such a 
 statement, or the judgment presupposed by such a 
 
THE PROPOSITION 101 
 
 statement, does not carry us far on the way to 
 knowledge. It leaves us in doubt at the point where, 
 if we are to have probable knowledge, uncertainty 
 can not exist, namely, in respect to the details of the 
 judgment's content. In other words, the disjunctive 
 proposition starts with a belief in the reality of an 
 S, but is uncertain as to what S is, that is, whether 
 it is one or other of a number of alternatives which 
 are possible of realisation in the sphere of existence 
 or reality covered by S. All that, in such a case, 
 we can say is that 'S is either A, or B, or C, or D.' 
 If now we consider the hypothetical proposition, 
 we find that the defect of the disjunctive propo- 
 sition has been overcome, and we are no longer in 
 doubt as to what we are asked to believe. But we 
 also notice that the greater explicitness of the rela- 
 tions expressed by the proposition has been secured 
 by a corresponding loss. To consider the latter 
 point first, we may observe that the hypothetical 
 proposition does not imply, as does the disjunctive 
 proposition, a definite belief in the existence of the 
 sphere of reality within which the relations ex- 
 pressed by the proposition are understood to fall. 
 In the case cited, for instance, the disjunctive prop- 
 osition started with belief in the existence of The 
 student who reads this paragraph/ In the hypo- 
 thetical proposition the relations involved in this 
 belief are used as a condition of the ensuing judg- 
 ment. Thus, The student who reads this paragraph' 
 becomes, in the hypothetical proposition, 'If a stu- 
 dent reads this paragraph/ a form of statement 
 
102 A TEXT-BOOK OF LOGIC 
 
 which, of course, leaves us uncommitted as to 
 whether there is any such student or not. So far, 
 therefore, as the hypothetical proposition is con- 
 cerned, belief is never definitely implied in the exist- 
 ence of the sphere of reality within which the rela- 
 tions asserted by the judgment find their possible 
 realisation. This, however, is not an uncompen- 
 sated limitation. For, to consider the other point 
 mentioned above, the meaning expressed by the 
 hypothetical proposition is specific; the details with 
 which the judgment is concerned have become de- 
 fined in such a way that the conditions on which 
 belief rests form part of what the judgment asserts. 
 Thus, fully expressed, the hypothetical proposition 
 reads, 'If a student reads this paragraph, he will 
 understand it.' In this case the internal structure, 
 the organic relations, of the elements of thought are 
 more highly specialised than they are in the disjunc- 
 tive proposition, and what we are told is that an 
 understanding of 'this paragraph' is definitely 
 grounded in the sphere of belief implied, although 
 indefinitely, by the proposition itself. If we may 
 hold that knowledge grows by the definition of de- 
 tails, we shall have to say that the hypothetical 
 proposition expresses a higher type of knowledge 
 than the disjunctive proposition. 
 
 The categorical proposition, if it exists, carries 
 us outside the boundaries of probability into the 
 field of certainty. The categorical proposition com- 
 bines certainty as to the existence of the sphere of 
 reality which is characteristic of the disjunctive 
 
THE PROPOSITION 103 
 
 proposition, and certainty as to the detailed rela- 
 tions of the matter of the judgment which is charac- 
 teristic of the hypothetical judgment. Hence our 
 proposition reads, 'The student who reads this par- 
 agraph, will understand it.' But in order to under- 
 stand the categorical proposition, we should observe 
 that our knowledge of any subject-matter is so 
 rarely, if ever, complete, and that, in those cases 
 where it is, the material of judgment is likely to be 
 so insignificant, that, from the logical point of view, 
 the categorical proposition must be held to express 
 either an ideal limit of knowledge, the goal toward 
 which knowledge is constantly advancing but never 
 quite reaches; or that it is the least serviceable, 
 because least significant, form for the expression 
 of truth. We may, perhaps, roughly indicate the 
 meaning of this remark by the commonplace obser- 
 vation that an examination of the forms of state- 
 ment of the poorly educated reveals a predominance 
 of categorical propositions; and, that, as we rise in 
 the scale of educated intelligence, the other forms, 
 and especially the hypothetical form, predominate. 
 Dogmatic statements, in other words, are character- 
 istic of the man who does not know, or of the man 
 who knows things about which no one particularly 
 cares. In either case, we should have to say that 
 such statements, from the logical point of view, are 
 pseudo-categoricals, that they express a belief which 
 either goes beyond or falls below the range of our 
 knowledge of significant reality. But this perver- 
 sion of the categorical proposition by the ignorant, 
 
104 A TEXT-BOOK OF LOGIC 
 
 need not obscure for us its proper logical position. 
 It does express the form into which knowledge, 
 when it is perfect, would naturally fall. The cate- 
 gorical proposition implies belief in the existence 
 of a sphere of reality within which certain ex- 
 pressed relations are fulfilled. It, however, remains 
 an ideal because, our knowledge being finite, we 
 can never get beyond the possibility of doubt as to 
 whether one or other of the conditions of the judg- 
 ment has been completely satisfied. 
 
 REFERENCES 
 
 B. Bosanquet, The Essentials of Logic, Lect. V., VI. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. VI. 
 J. G. Hibben, Logic, Deductive and Inductive, Ch. IX. 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. IV. 
 W. Minto, Logic, Inductive and Deductive, Part III., Ch. I. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. II. 
 
 ADVANCED 
 
 J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. VI. 
 
 W. R. B. Gibson, The Problem of Logic, Chs. IX., XL, XII. 
 
 H. W. B. Joseph, An Introduction to Logic, Ch. VII. 
 
 J. S. Mill, A System of Logic, Book I., Ch. IV., 1, V., VI., 5. 
 
 F. C. S. Schiller, Formal Logic, Ch. IX. 
 
 C. Sigwart, Logic, Vol. I., Part I., 5, Ch. II., 17, VII. 
 
 J. Welton, A Manual of Logic, Vol. I., Book I., Ch. I. 
 
 QUESTIONS 
 
 1. In what respect does the proposition differ from the 
 judgment? 
 
 2. What is meant by the import of a proposition? 
 
THE PROPOSITION 105 
 
 3. Distinguish between the truth-import and the gtatement- 
 import of propositions. 
 
 4. What light does this distinction throw upon the inter- 
 pretation of propositions? 
 
 5. Why do we always write the subject term of a proposi- 
 tion first? 
 
 6. How may we distinguish between the subject and pred- 
 icate terms, and is it always possible to make this dis- 
 tinction? Explain. 
 
 7. What is the logical difference between terms, names, 
 and words? 
 
 8. Give a logical classification of words. 
 
 9. What is meant by single-worded and many-worded 
 terms? 
 
 10. What is meant by saying that the copula is the most 
 distinctive element of the proposition? 
 
 11. State and criticise the relational view of the copula. 
 
 12. What are the realistic, nominalistic, and conceptualistic 
 views of the concept? 
 
 13. What is the existential view of the copula, and what 
 objections can be brought against it? 
 
 12. What do you understand by predication? Characterise 
 the various kinds of predication, and show how these 
 give rise to the several types of logical proposition. 
 
 15. What are the conditions under which we give a disjunc- 
 tive expression to our judgments? 
 
 16. Discuss the nature of hypothetical propositions, and 
 show their relation to disjunctive propositions. 
 
 17. Discuss the nature and limits of categorical proposi- 
 tions. 
 
 EXERCISES 
 
 1. Illustrate, from your own observation preferably, the 
 possibility of confusing the truth-import with the state- 
 ment-import of a proposition. 
 
 2. Write the following sentences in the form of proposi- 
 tions, indicating the subject and predicate terms in 
 each: 
 
106 A TEXT-BOOK OF LOGIC 
 
 (1) Over the mountains poured the barbarian horde. 
 
 (2) The moonlighh plays fitfully upon yonder rippling 
 stream. 
 
 (3) Happy is the man that findeth wisdom. 
 
 (4) All is not misfortune that seems at the moment un- 
 endurable. 
 
 3. Write six sentences in which you think it difficult or im- 
 possible to distinguish the subject and predicate terms. 
 
 4. Make a list of twelve categorematic words. 
 
 5. Write six statements which show the error of an exist- 
 ential interpretation of the copula, and explain the rea- 
 son in each instance. 
 
 6. Write disjunctive propositions about the following sub- 
 jects: 
 
 (1) Your presence at a concert to be given, say, next 
 week. 
 
 (2) The result of a particular political election. 
 
 7. Write hypothetical propositions about the following sub- 
 jects: 
 
 (1) Tomorrow's weather. 
 
 (2) The study of the biological sciences. 
 
CHAPTER IV 
 
 TERMS 
 
 Proposition and Terms. In the last chapter, we 
 defined a proposition as the verbal expression of a 
 judgment in which something (P) is predicated of 
 something else (S). We also analysed the propo- 
 sition into its constituent factors terms and the 
 copula and saw that the relation which these ele- 
 ments sustain to one another is determined by the 
 meaning of the proposition taken as a whole. The 
 proposition, that is to say, was considered as deter- 
 mining the existence and character of its terms, and 
 not the existence and character of terms as deter- 
 mining the existence and character of the proposi- 
 tion. Terms are different aspects of the meaning 
 of the proposition in which they occur. Expressed 
 otherwise, they are functions of their propositions. 
 The further discussion of terms which we begin in 
 this chapter must be carried on in light of these 
 general positions, and it must be considered as a 
 more detailed consideration of certain important 
 features of the proposition. The separate chapter 
 headings are employed merely for pedagogic con- 
 venience. 
 
 Connotative and Denotative use of Terms. We are 
 to consider at the outset a distinction in the use of 
 terms upon which hinge many of the problems that 
 will come before us in the succeeding pages. It is, 
 
 (107) 
 
108 A TEXT-BOOK OF LOGIC 
 
 therefore, important to give special attention to the 
 precise logical significance that the distinction has, 
 and to get clearly before ourselves the scope of its 
 application. The latter point will be discussed in 
 the next section; we shall, therefore, confine our- 
 selves here to a statement and illustration of the 
 uses connotative and denotative to which terms, 
 whatever their character, may logically be put. 
 
 It is part of our common knowledge that words 
 are frequently used as labels by means of which we 
 identify things, and distinguish these things from 
 other things. Many illustrations will come to mind : 
 'the Rocky Mountains,' 'the Amazon River/ 'my old 
 bay horse,' etc. There is hardly any end to the 
 number of words which have this use of pointing 
 to objects, and which put us in contact with par- 
 ticular things, or groups of things. Now it is this 
 fact of our common speech that logic describes when 
 it talks about the denotative use of terms. Terms 
 are used to point out, refer to, or indicate objects. 
 For instance, in the statement, 'When it comes to 
 packing, books are a nuisance,' the term 'books' re- 
 fers to the individuals of a class of objects, and it 
 is, therefore, said to be used denotatively. In the 
 same way, the term 'lion' in the proposition, 'Lions 
 are carnivorous animals,' is used to point out this, 
 that or the other particular lion, and the proposition 
 means that any individual lion will be found to 
 possess the specified characteristics. Since the term 
 'lion* points out the individual objects one has in 
 
TERMS 109 
 
 mind when the term is used it is said to be used 
 denotatively. 
 
 We may also go to our ordinary employment of 
 language to ascertain what logic understands by the 
 connotative use of terms. Words, as we know, not 
 only point out objects, but they also have meanings. 
 When, for example, we hear a strange word spoken, 
 or meet with it in our reading, we ask what the 
 word means. If no one can tell us, we go to the 
 dictionary for the information. Now we do this, 
 because we have been trained to expect that the 
 words we meet will arouse some sort of mental 
 image, and because experience has taught us that, 
 when they do not, we fail to understand what is 
 said to us. That words should have a meaning is 
 just as important as that they should indicate indi- 
 vidual objects. Unless such words as Violin,' 'art/ 
 'mathematics/ 'landscape/ 'ocean' aroused within us 
 quite different images or ideas, we should be at a 
 loss how to use them, or to understand them. Now 
 logic indicates this aspect of words, their meaning 
 aspect, when it speaks of the connotative use of 
 terms. Terms, from this point of view, are used to 
 call up the qualities or attributes of objects. When 
 we use a term connotatively, it must be understood, 
 consequently, that we are speaking about its dic- 
 tionary meaning. But, it should also be observed, 
 the particular dictionary meaning of any term can 
 be determined only from the standpoint of the par- 
 ticular proposition in which the term occurs. For 
 example, in Shakespeare's Coriolanus we read, 'She 
 
110 A TEXT-BOOK OF LOGIC 
 
 will but disease our better mirth/ a passage in 
 which the term 'disease' means 'disturb.' When 
 Locke writes, 'Although great light be insufferable 
 to our eyes, yet the highest degree of darkness does 
 not disease them,' he is using the same word in the 
 sense of 'cause suffering to.' When, further, in 
 Thomson's Summer we read, 
 
 Then wasteful forth 
 Walks the dire power of pestilent disease, 
 
 'disease' is used in the more usual sense of 'a phys- 
 ical or physiological disorder.' This dependence of 
 the meaning of terms on their propositions is of 
 capital importance, and should be kept constantly 
 in mind. 
 
 Relation of the Connotative and Denotative use 
 of Terms. The difficulty that is usually experienced 
 in understanding the doctrine of connotation and 
 denotation is due to the fact that we do not have 
 one group of words whose use is always connota- 
 tive, and another group of words whose use is 
 always denotative. Most, if not all, terms are capa- 
 ble of being used in either the one or other of these 
 ways. But this is not all. The most important 
 fact to remark is that in whichever of the ways 
 mentioned a given term is employed, it is so em- 
 ployed with the other use more or less distinctly 
 in mind. It would be quite a fair statement of the 
 case to say that there is always a reference of the 
 one to the other, and that in any particular instance 
 the one implies the other. It is not difficult to see, 
 
TERMS 111 
 
 for example, that the identification of the individ- 
 uals which are denoted by any term depends upon 
 their possession of the qualities that are connoted 
 by the same term. It is also clear that the qualities 
 that a term connotes are the qualities of the individ- 
 uals which the term denotes. Let us, for example, 
 examine the subject term of the proposition, 'Man 
 is a rational animal.' If the term 'man' is used 
 denotatively, that is, to point out 'Tom, Dick, 
 Harry, etc.,' the proposition must mean that 'Tom, 
 Dick, Harry, etc.,' are the individuals in whom are 
 found realised the qualities expressed by the pred- 
 icate term. If the term 'man' is used connotatively, 
 the proposition must mean that the qualities, 'ra- 
 tional animal,' will be found present in each indi- 
 vidual, that is, in 'Tom, Dick, Harry, etc.' Let us 
 take, as another case, 'Man is a being who volun- 
 tarily sets himself tasks.' If, in this proposition, 
 the term 'man' is used to denote individual men, 
 then our identification of the individuals who set 
 themselves tasks depends upon our knowing what 
 the qualities are which the term 'man' connotes ; and 
 if it is used to connote certain qualities, our under- 
 standing of the proposition depends upon the sup- 
 position that these qualities can be found in a num- 
 ber of discoverable individuals. These illustrations 
 serve to emphasise the general rule that the con- 
 notative use of a term does not break away entirely 
 from its denotative use, or vice versa; and the sole 
 logical distinction between them is that, in the one;, 
 we lay the primary emphasis on the 
 
112 A TEXT-BOOK OF LOGIC 
 
 which possess the qualities, and, in the other, on the 
 qualities possessed by the individuals. 
 
 Another inquiry which conies before us here is 
 whether this relation between the connotative and 
 the denotative use of terms is realised in all terms 
 whatsoever. We can give an answer to this ques- 
 tion only by anticipating certain features of the dis- 
 cussion of terms contained in the following pages. 
 We may, however, at this point call attention to the 
 generally accepted position that no term is ever so 
 exclusively denotative as to lose all connotation 
 whatsoever, and that no term can be said to have 
 developed on the side of meaning, i. e., connotatively, 
 so one-sidedly as to have lost all reference to objects. 
 The discussion of this question has been brought to 
 the study of proper names as to a test case; and it 
 is thought that if the position can be maintained 
 with respect to these terms, it will be possible to 
 maintain it with respect to other kinds of terms. 
 The question is not a theoretical one, and we shall 
 gain nothing by considering it as such. It is a 
 question of fact, and can be determined only by a 
 study of each kind of terms as it comes before us 
 in this and the following chapter. We may express 
 the opinion, however, that it is quite possible that, 
 in the course of time, the employment of particular 
 terms may shift from a predominantly connotative 
 to a predominantly denotative use, and there is no 
 reason, except one of convenience, why all meaning 
 should not drop away from some terms, and that 
 they should stand in our vocabulary merely as sym- 
 
TERMS 113 
 
 bols of the existence of things. Whether there are 
 any such terms cannot be decided now; it is more 
 important to see that the possibility of this being 
 the case does not obscure for us the more general 
 relation which was expounded in the preceding para- 
 graph. 
 
 A subject that is usually discussed in this con- 
 nection relates to the changes that take place in the 
 connotation and denotation of terms when either 
 of these is increased or decreased. Under these 
 conditions, the changes in the connotation and deno- 
 tation of terms are said to vary inversely. More 
 fully stated, when the connotation of a term is in- 
 creased, its denotation is decreased, and vice versa. 
 For example, the denotation of the term 'man' is 'the 
 total population of the earth/ and its connotation, 
 we may say, is 'rationality and the upright position.' 
 If we increase the connotation by specifying 'white 
 man,' the connotation of which term is 'white, ra- 
 tionality and upright position,' we decrease the de- 
 notation which then refers to 'the white population 
 of the earth.' If a further increase in connotation 
 is made by specifying 'European white man,' the 
 denotation is decreased still more, and indicates 'the 
 white population of Europe.' The process thus 
 begun can be carried as far as interest or ingenuity 
 allows. The general truth to which such illustra- 
 tions point is that the denotation of a term is dimin- 
 ished as its connotation is made more definite by the 
 addition of new attributes ; and, conversely, that 
 
114 A TEXT-BOOK OF LOGIC 
 
 when the connotation is decreased by dropping at- 
 tributes the number of individuals to which the 
 term applies is increased. This statement holds 
 good as a general rule, but there is no numerical 
 ratio between the increase or decrease of connota- 
 tion and the accompanying decrease or increase of 
 the denotation. Indeed, the denotation of a term 
 may be increased greatly without any change in its 
 connotation, as actually happened, for example, 
 when the British government annexed some mil- 
 lions of Africans at the close of the Boer war with- 
 out making thereby any change at all in the conno- 
 tation of the term, 'British subject.' 
 
 Distribution of Terms. If we carry our study of 
 the denotative use of terms a step further, we shall 
 find that the purposes which prompt our statements 
 sometimes require us to refer to a determinate num- 
 ber of the individuals denoted by the term, and that 
 sometimes our purpose is satisfied if we indicate 
 an indeterminate number of the individuals included 
 under the term. Let us suppose, for example, that 
 we are discussing the theory of kingship, and that 
 I express the belief, after Hobbes, that the king can 
 do no wrong. If this belief were thrown into a 
 propositional form, it would become clear that I am 
 thinking of all the individuals who have exercised, 
 or at some time may exercise, the functions of king- 
 ship. What I mean is that 'No king can do any 
 wrong/ that is, wrong doing cannot be predicated 
 of any king, of this, that, or of any other indi- 
 vidual who is or may be a king. If such a state- 
 
TERMS 115 
 
 ment does not recommend itself to your judgment, 
 and you express dissent from it, you are not re- 
 quired, by the conditions of the situation which 
 determine your judgment, to concern yourself with 
 each and every king; it will be sufficient, if wrong 
 doing by kings has ever occurred, for you to limit 
 your statement to any of the cases which contradict 
 the theory you oppose. Expressed in a proposition, 
 your judgment will be 'Some kings can do wrong,' 
 or more definitely, 'Some kings have done wrong.' 
 You are obviously speaking of a number of indi- 
 viduals, not definitely specified, who belong to the 
 group denoted by the term 'king.' The distinction, 
 thus indicated, in the denotation, width, or extent of 
 terms, is known in logic as the 'distribution' of 
 terms. By the distribution of terms we mean the 
 consideration of terms from the standpoint of their 
 quantity. Now, in respect of quantity, we are lim- 
 ited in logic by the contrast between a definite and 
 an indefinite number, and the terms which denote 
 these quantities are said to be distributed and un- 
 distributed respectively. A term is 'distributed' 
 when, from the form of the proposition in which it 
 occurs, it is known to refer to a determined number 
 of individuals of the class denoted by the term; it 
 is said to be 'undistributed' when, from the form 
 of the proposition in which it occurs, it is known 
 to refer to an undetermined number of the individ- 
 uals of the class denoted by the term. The tech- 
 nical sign of a distributed term, in an affirmative 
 proposition, is 'All,' and, in a negative proposition, 
 
116 A TEXT-BOOK OF LOGIC 
 
 'No.' The technical sign of an undistributed term, 
 in both affirmative and negative propositions, is 
 'Some.' 
 
 We have just said that the difference between 
 distributed and undistributed terms is that in 
 undistributed terms the exact number of in- 
 dividuals referred to is left indefinite, as, for 
 example, 'Some birds are blue;' while in distributed 
 terms the number is made definite, as for example, 
 'No man is free from the defects of his qualities,' 
 and 'Half my goods I give to feed the poor.' We 
 shall have occasion to discuss this distinction again 
 when we study the interpretation of propositions; 
 but for the present, it is enough to remark that 
 neither in the case of a distributed, nor in that of 
 an undistributed, term can we say, from the form 
 of the proposition, what the arithmetical number 
 of the individuals denoted by the term is. It may, 
 perhaps, help to make the matter clear if we recall 
 that in the study of algebra we are taught to use 
 the first letters of the alphabet, a, b, c, to represent 
 the known quantities of a problem, and the last let- 
 ters of the alphabet, x, y, z, to represent the un- 
 known quantities. The mathematical difference be- 
 tween these two classes of quantity, the known and 
 the unknown, is the difference between the dis- 
 tributed and the undistributed use of terms in logic. 
 In the former case, the known objects are deter- 
 minate; in the latter, the unknown objects are inde- 
 terminate. 
 
 
TERMS 117 
 
 Some other Characteristics of Terms. In the fore- 
 going paragraphs, we have considered mainly those 
 features of terms which are important from the 
 point of view of their denotation. There are cer- 
 tain questions which arise from the standpoint of 
 the connotation of terms to which we shall direct 
 attention in the remainder of this and in the fol- 
 lowing chapter. The questions to which we refer 
 must not be confused with those that will engage 
 us in a later chapter, and which relate particularly 
 to the problem of definition, that is, to the problem 
 of how the meaning of terms receives logical formu- 
 lation. What, rather, we have to consider at pres- 
 ent is the fact that there are certain general charac- 
 teristics of terms which do not depend upon the par- 
 ticular meaning that terms have, but upon the 
 nature of the interest which stimulates our judging 
 activity. The interests under which we are led to 
 judge any subject-matter may require us to express 
 what we wish to say either concretely, abstractly, 
 absolutely, relatively, positively, or negatively. 
 That is to say, our meaning may be either concrete, 
 abstract, absolute, relative, positive, or negative. 
 These distinctions are not coordinate, and they are 
 not at all of equal importance; but the particular 
 relations which they sustain to one another become 
 apparent only when it is clear what each signifies. 
 We shall, therefore, confine ourselves, in the main, 
 to stating how each of these distinctions is to be 
 understood, and we shall begin with the broadest 
 
118 A TEXT-BOOK OF LOGIC 
 
 among them, the distinction between concrete and 
 abstract meaning. 
 
 Concrete Meaning. One of the most familiar 
 facts of our every day life is that we distinguish 
 from one another the various objects that come 
 under our observation. When, for example, we go 
 into the city, we perceive the houses, the shops, the 
 traffic on the streets, and the people on the side- 
 walks as quite different things. We also carry over 
 into our academic studies the endeavor to make dis- 
 tinctions, and to regard different things as different. 
 Thus, the student of zoology learns to discriminate 
 between the blood vessels, the supporting tissue, and 
 the characteristic cells of the specimens he observes 
 under the microscope. Indeed, so general and im- 
 portant is this ability on our part that there is no 
 interest that is not served by it, and no limit to 
 which it may not be carried. For instance, we may 
 mark off in this way not only the objects of the 
 material world, but the qualities and relations of 
 these objects, and set them before us as distinct ob- 
 jects of our thought. Thus, 'green/ 'heavy,' 'but/ 
 'cause/ may become for us objects as distinct as are 
 the chairs and tables of our domestic life. Now 
 whatever we set off as a distinct object of percep- 
 tion or thought is in logic considered as a concrete 
 object, and the term that denotes such an object is 
 called a concrete term. 
 
 It may be observed that the significance for logic 
 of the term concrete depends upon the significance 
 of the word 'thing' in the body of our common 
 
TERMS 119 
 
 knowledge. By a thing we ordinarily mean some 
 part of the physical world which is perceived as dis- 
 tinct from other parts with which it coexists. Thus, 
 the pictures on the walls of our room, the articles 
 on display in the shop widows, the mountains and 
 streams of the landscape, the cattle on a thousand 
 hill, are all called 'things' whenever we think of them 
 as distinct from other objects with which they are 
 associated in the same common environment. But 
 the word 'thing' is not confined to objects of the 
 material world. We also designate as things what- 
 ever can be thought of as having a distinct exist- 
 ence of any kind. Thus, if I am trying to recall 
 something in particular that has been told me, I may 
 express my impatience at not being able to do so by 
 saying, 'Why can't I remember the thing?' What I 
 refer to here as a thing is an idea. A similar usage 
 is found in the commandment against idolatry 
 among the Hebrews when it is forbidden them to 
 make a graven image "in the likeness of any thing 
 in the heavens above," where the word 'heavens' 
 has a quasi-spiritual meaning. Instances might be 
 multiplied of the very wide and varied use to which 
 we put the word thing in popular speech, but those 
 given are enough to emphasise the connection be- 
 tween it and the logical meaning of the term con- 
 crete. 
 
 While, however, there is this general connection 
 between the two words, the meaning of the term 
 concrete is more precise than is the meaning of the 
 word thing. It is true, for instance, that we do not 
 
120 A TEXT-BOOK OF LOGIC 
 
 ordinarily refer to persons as things, but logic 
 would have no hesitation in calling the terms, by 
 which they were denoted, concrete terms. On the 
 other hand, we should describe as a thing any object 
 of which we could say only that it was in our con- 
 sciousness, but unless we knew some of its attri- 
 butes or relations, we should not be warranted log- 
 ically in calling it a concrete object, or the word 
 used to denote it a concrete term. These cases are 
 suggestive of the truth that it is not mere existence, 
 but significant existence that logic, in the main, de- 
 notes by the term concrete. Whenever an object is 
 thought of as having a definite kind of existence, 
 that is, as possessing certain qualities or standing 
 in such and such relations, it is called a concrete 
 object, and the words we use to denote such objects 
 are concrete terms because they are used to connote 
 these qualities and relations. There are, as we shall 
 see, varying degrees of definiteness in the ways in 
 which significant existence is asserted, and there 
 are, consequently, several degrees of explicitness in 
 the meaning of the terms used for denoting such 
 existence. This matter we shall discuss in the fol- 
 lowing sections; it will be sufficient, meanwhile, if 
 the broad meaning of the term concrete has been 
 made clear. 
 
 Individual Meanings: Proper Names and Desig- 
 nations. The first class of concrete terms that we 
 shall consider is that which denotes particular indi- 
 vidual objects. To be able to point out individual 
 objects, we must have in mind, as a general rule, 
 
TERMS 121 
 
 some attribute, or group of attributes, which is 
 thought of as belonging to the one object we desire 
 to single out, and to make the subject of further 
 consideration. The names of such objects, when 
 they are used as terms in a proposition, are definitely 
 denotative and explicitly connotative; they point to 
 their objects by means of the attribute or attributes 
 which the term connotes. Such terms are called 
 individual, or singular, terms. 
 
 Individual concrete terms are of two kinds: 
 proper names and designations. A proper name, to 
 consider that first, is the name given to an object - 
 person, place, or thing as a special means of dis- 
 tinguishing this object from all other objects. We 
 give names to the members of our families, Tom, 
 Dick, Mary, Sue, etc., to continents, mountains, 
 rivers, towns etc. We also give names to the horses 
 in our stables and the cattle in our barns. There 
 is no limit, except its usefulness, to the process of 
 naming the objects of our acquaintance in order to 
 distinguish them from others with which we do not 
 wish them confused. In all such instances the 
 names are proper names, and they serve to individ- 
 ualise the particular objects to which they belong. 
 When such names are made the subject of pred- 
 ication they are singular or individual terms. 
 
 Now, about proper names, as thus defined, we 
 may ask whether their designation of particular 
 objects is made possible because they imply an attri- 
 bute or attributes, that is, because proper names 
 are connotative. In answer to this question, Mill, 
 

 122 A TEXT-BOOK OF LOGIC 
 
 for example, replied that proper names are non- 
 connotative, they can be used only, he said, to sig- 
 nify an subject. This is, in many quarters, consid- 
 ered an extreme position, and it may be due to the 
 failure to see that significance may belong to a sub- 
 ject not only because of the qualities that it pos- 
 sesses, but also because of the relations in which it 
 stands. "The very fact," as Creighton points out, 
 "that a proper name is given to an object implies 
 that is possesses a certain marked individuality," 
 and the intelligent use of the name surely implies a 
 reference to the qualities or relations by which that 
 individuality is defined. However, be that as it may, 
 we may admit that the connotation of proper names 
 is ordinarily quite general and often vague, without 
 thereby refusing to grant them any significance 
 whatever. If the application of such terms is un- 
 ambiguous, it is quite natural that their meaning 
 should drop into the background of consciousness; 
 but if its application should become uncertain or be 
 misunderstood, we should then feel the need of mak- 
 ing the connotation of the term more definite. 
 
 Individual concrete meaning may be expressed, 
 in the second place, by a designation. Logic regards 
 as a designation any phrase that describes an object 
 by its qualities or relations, when such phrase is 
 used for the purpose of definitely pointing out this 
 object. The assassin of Franz Ferdinand of Aus- 
 tria/ 'my winter overcoat/ 'the centre of the mate- 
 rial universe/ 'my partner/ all these are designa- 
 tions in the sense defined. It is clear that a desig- 
 
TERMS 123 
 
 nation depends upon the appropriateness of the de- 
 scription it embodies for the accurate identification 
 of the object to which it points. That is to say, a 
 designation must be explicitly connotative as well as 
 definitely denotative. 
 
 The wide usefulness of this method of express- 
 ing our individual concrete meanings is very evi- 
 dent. It is true that, in ordinary life and in scien- 
 tific pursuits, we need a number of terms which 
 shall have the specialised function of designating 
 particular individual objects, that is, terms that are 
 definitely proper names. But neither in science nor 
 in daily life is it necessary to assign proper names 
 to all the objects that engage attention, and yet 
 some method of referring to these objects is neces- 
 sary if we are to develop the interests that prompt 
 us to take note of them. It is under such circum- 
 stances, as a general thing, that the designation 
 becomes of use. We should be on our guard, how- 
 ever, against supposing that the objects to which 
 proper names are assigned are necessarily of more 
 importance than those to which we refer by means 
 of designations. While it is true that some of the 
 objects which we denote by designations are rela- 
 tively insignificant, this is not always the case. In 
 science, for instance, we speak of 'the law of grav- 
 itation,' 'the law of diminishing returns/ 'cen- 
 trifugal force,' etc.; and in daiy life we use such 
 phrases as 'the President of the United States,' 'the 
 Secretary of State,' etc. These phrases are, accord- 
 ing to the definition, designations; they point out 
 
124 A TEXT-BOOK OF LOGIC 
 
 definite objects by means of a brief description of 
 the objects' characteristics. They have, moreover, 
 a higher importance than some of the objects to 
 which proper names are given. 
 
 General Meaning. The second class of concrete 
 terms, which we have now to consider, is character- 
 ised by the fact that the meaning conveyed by such 
 terms is applicable to more than one object. Now, 
 it is true that, if we were to list all the attributes 
 of all the objects of our acquaintance, it would be 
 found that no one object possessed in every respect 
 precisely the same qualities as any other. Every 
 object, in this sense, is a unique object; and, if there 
 were no other interest in things than that which 
 leads to the observation of their uniqueness, we 
 should have to use, when speaking of such objects, 
 either proper names or designations. It frequently 
 happens, however, that our practical or theoretical 
 interests require us to distinguish among the attri- 
 butes of individual objects those that belong to 
 only one individual, and those that are possessed in 
 common by a number of individuals. On the basis 
 of this distinction, we are able to group together 
 the objects which possess a common set of attri- 
 butes, and, conversely, to make the common attri- 
 butes the basis of our inclusion of other individuals 
 within particular groups. For example, we classify 
 certain animals as quadrupeds, and certain others 
 as bipeds, on the ground that, amid an indefinite 
 number of differences, certain animals are alike in 
 the fact that they walk on four feet, and that cer- 
 
TERMS 125 
 
 tain others are alike in the fact that they walk on 
 two feet. Stated otherwise, in constructing such 
 classes of objects, each of the individuals belonging 
 to any one class is thought of as possessing exactly 
 the same characteristics as any other individual of 
 that class. 
 
 Now the names which embody a meaning that 
 can be applied to any one of an indefinite number of 
 individuals are known in logic as 'general' or 'com- 
 mon' terms. Of such terms we may say, in view of 
 the foregoing discussion, that they are explicitly 
 connotative, but indefinitely denotative. In other 
 words, the attributes that a general term connotes 
 belong equally to each and every individual of a 
 group; but we cannot tell which one or more of 
 these individuals is denoted, merely by knowing the 
 connotation of the term. The characteristic fact 
 about a general term is, then, that while its conno- 
 tation or meaning is concrete, its application is 
 always general; the meaning, that is to say, can be 
 applied to an indefinite number of individuals. It 
 should be observed, however, that the meaning of 
 any such term does not exist apart from some or 
 all of the individuals in which this meaning is con- 
 cretely embodied. That is to say, it is the existence 
 of the individuals which form the group that deter- 
 mines the meaning that any general term may have. 
 Apart from these individuals, indefinitely denoted 
 though they are, the general term would lose all its 
 meaning. One reason for remarking this fact is 
 that the interest, which leads us to observe the com- 
 
126 A TEXT-BOOK OF LOGIC 
 
 mon characteristics of numbers of objects, is an 
 interest that still recognizes the differences that 
 exist among the objects which it groups together. 
 When, therefore, these common characteristics are 
 expressed in general terms, it is not to be supposed 
 that the differences that distinguish one object from 
 another are thereby denied. What our general 
 terms imply is that the presence of individual dif- 
 ferences is not inconsistent with the possession, by 
 a number of objects, of certain characteristics in 
 common. 
 
 Collective Meaning: Individual and General. We 
 have traced the development of meaning from the 
 singular concrete to the general concrete, and we 
 have seen that, in this development, we have been 
 concerned with some feature or features of the indi- 
 vidual or individuals which our interests prompt us 
 to study. For instance, our interest in the differ- 
 ences that exist between one object and another is 
 embodied in the meaning that singular terms have ; 
 our interest in the likenesses which exist along with 
 these individual differences is expressed in the mean- 
 ing that general terms have. That is to say, the de- 
 velopment of meaning which leads from the individ- 
 ual to the general term has been guided by the con- 
 sideration that we must not do violence to the differ- 
 ences that exist between one individual and another 
 while seeking for the common ground of their like- 
 ness. We have now to consider whether, neglecting 
 the differences between individuals, we may start 
 with their common likeness, and carry the develop- 
 
TERMS 127 
 
 ment a step further. Or, to state the inquiry more 
 definitely, we may ask what alteration in our mean- 
 ing is made if and when, in our study of individuals, 
 we ignore their differences, and take note only of 
 their likenesses. We have seen that we may take 
 account of both likenesses and differences, and still 
 be able to define a meaning which applies to each of 
 a number of otherwise dissimilar individuals. What 
 we have now to see is that if we pay attention only 
 to likenesses, or, what amounts to the same thing, 
 consider only similar individuals, we are able to de- 
 fine a meaning which applies to no one of the indi- 
 viduals, but can be intelligently used of all these in- 
 dividuals taken together as a whole. To illustrate, 
 let us suppose that we bring together in one place 
 a number of animals lions, tigers, elephants, 
 jaguars, ibexes, zebras, etc. Such a collec- 
 tion we should call a menagerie. If, again, 
 we were to bring together a number of children 
 for the purpose of educating them we should 
 call such a collection a school. There are many 
 such collective groups of individuals; and we 
 can say that the meaning of the word by which each 
 is indicated applies to none of the individuals which 
 constitute the group, but only to the group which is 
 constituted by the individuals. Thus, 'a menagerie' 
 is the name for a particular group of animals, 'a 
 school' is the name for a particular group of chil- 
 dren under instruction ; 'the United States of Amer- 
 ica' is the name for a particular group of political 
 organisations, etc. 
 
128 A TEXT-BOOK OF LOGIC 
 
 Now a name which embodies a meaning that 
 can be applied to a number of similar individals, 
 taken together and thought of as a whole, is called 
 in logic a collective term. It is obvious, from what 
 has been said, that the connotation or meaning of 
 collective terms is determined for us by the points 
 of observed similarity between the individuals which 
 constitute the groups which these terms denote. 
 Thus, we call a particular group of individuals a 
 nation when we think of all the individuals belong- 
 ing to the group as citizens, citizenship is the one 
 attribute that all have in common. We call another 
 particular group of individuals a legislature when 
 we think of all the individuals belonging to the 
 group as makers of laws, making laws is the one 
 common task in which all its members are engaged. 
 The same thing, mutatis mutandis, will be found 
 true of all collective terms whatever: the connota- 
 tion of such terms embodies certain observed sim- 
 ilarities between the individuals which belong to the 
 groups which the terms denote. 
 
 When, on the other hand, we consider the deno- 
 tation of collective terms, it is evident that the 
 groups which such terms point out constitute a new 
 kind of individual, and must be distinguished from 
 the individuals which are denoted by the general 
 term. The individuals which general terms, as a 
 rule, denote are objects of our ordinary perception 
 and thought; they are the things which, in the 
 course of our daily life, we are accustomed to take 
 as distinct objects; such things, we may say, as 
 
TERMS 129 
 
 each of us has been trained to observe in the course 
 of the education that the community provides. On 
 the other hand, the individuals which collective 
 terms denote are individuals of a higher order, so 
 to speak; they result from a definitely conscious 
 effort on our part to bring together under a single 
 view a number of diverse things, and to regard these 
 things as one object. The objects which collective 
 terms denote are more complex than those denoted 
 by the general term, and should be carefully dis- 
 tinguished from the latter. 
 
 Collective concrete terms may be either individ- 
 ual or general. The individual collective term is 
 used to point out a particular group of objects which 
 we wish to distinguish from all other objects what- 
 ever. The Rough Riders/ 'the Gordon Highlanders,' 
 'the Allies,' (in the present war in Europe) are 
 examples of collective terms used in this way. It 
 may be observed that the individual collective term 
 always contains the definite article, 'the,' as part of 
 its verbal form. Thus, 'the committee,' 'the library,' 
 'the family' are collective terms used to point out 
 particular distinctive groups. The denotation of 
 these terms is definite. The general collective term 
 is used to indicate a particular kind or class of 
 grouped objects, and, therefore, may be applied to 
 any particular group of objects which has the char- 
 acteristics of the class which the term denotes. For 
 example, when the military and naval forces of two 
 or more nations act together for the purpose of de- 
 9 
 
130 A TEXT-BOOK OF LOGIC 
 
 feating a common enemey, these nations are called 
 allies. 'Allies' is a collective term, and, in this case, 
 is general, since we apply the same name to each of 
 the many combinations of this character which his- 
 tory records. Other illustrations of collective terms 
 which have a general application are, 'family,' 'li- 
 brary,' 'committee.' 
 
 It is sometimes said that the individual collective 
 can be changed into a general collective term by 
 substituting the indefinite article, 'a,' for the definite 
 article, 'the ;' or by omitting the article without sub- 
 stitution. Thus, 'the allies,' which is an individual 
 collective term, becomes a general collective term 
 by omitting 'the;' 'the committee,' 'the family,' 'the 
 library' become general by substituting 'a' for 'the' 
 in each instance, 'a committee,' 'a family,' 'a li- 
 brary.' Sometimes, however, the connotation of a 
 collective term has become so highly specialised that 
 it is capable of being applied to only a single object, 
 and in that case it cannot be used, by any change 
 whatever, as a general term. Examples of this are : 
 'the Congressional Library at Washington,' 'the 
 family of King George IV,' 'the Committee on For- 
 eign Relations in the Sixty-third Congress.' 
 
 Abstract Meaning. In the foregoing sections, we 
 have studied how concrete meaning develops, and 
 have seen that such meaning may assume one of 
 three forms, or, as we may say, indicate one of 
 three kinds of objects : individual, general, or 
 collective. We have said that, in these instances, 
 the meaning is concrete because, in each of them, 
 
TERMS 131 
 
 the connection between attribute and object is 
 particularly direct and intimate, although the con- 
 nection is in differing degrees of intimacy. Any 
 meaning is considered concrete which conveys the 
 idea that 'these are the attributes which such or 
 such an object has/ or that 'this is the object which 
 has such or such attributes/ It has been shown 
 that the object, in some instances, is a material ob- 
 ject; in others, it is mental. But so long as the 
 meaning we wish to express is concrete, we always 
 suppose that we can pass from object to attribute, 
 or from attribute to object, without a break, or that 
 the connection between attribute and object is un- 
 equivocal. In other words, whenever we take an 
 object in connection with its attributes, or think of 
 attributes only in connection with their objects, our 
 meaning is concrete. If, however, we were to con- 
 sider attributes apart from objects, we should con- 
 front a new situation, and one which would involve 
 a new set of problems, the consideration of which, 
 in the end, would lead us to define a new kind of 
 meaning which, in contrast to concrete, might ap- 
 propriately be called 'abstract.' For by abstract 
 meaning we commonly understand the idea of an 
 attribute quality or relation thought of inde- 
 pendently of the particular object or objects of 
 which it is the attribute. 
 
 Now, when we look at the possibility of the ex- 
 istence of such meanings as this, we are confronted 
 with the danger of meaning less than we actually 
 say. For instance, some logicians have defined the 
 
132 A TEX r "*' LOGIC 
 
 terms in which jstract meanings are expressed 
 
 'abstract te ,, as they are called as those 
 which apply to objects thought of apart from the 
 whole to which they belong, or to attributes which 
 are thought of apart from the objects of which they 
 are the attributes. Thus, a 'leaf thought of apart 
 from the tree on which it grows is, according to this 
 definition, an abstract term, and 'green/ if it is not 
 thought of as the color of this particular leaf, or of 
 any other particular green object, is likewise an 
 abstract term. In our view, this is a very mislead- 
 ing statement of what abstract meanings and terms 
 are. For instance, in the cases just mentioned, both 
 'leaf* and 'green' are concrete general terms. The 
 one is the name of an object, the other of an attri- 
 bute, and although these terms are not thought of 
 as belonging to any one particular object, still they 
 are thought of as belonging to any one of an in- 
 definite number of particular objects; unless we 
 think of them in this way we cannot think of them 
 at all. But if this is what we are to understand by 
 an abstract term, then abstract are not distinct 
 from general terms, and have to be classed as such. 
 Although the view we have just criticised is apt 
 to be misleading if it is taken as providing a defin- 
 ition of what abstract meaning is, it may neverthe- 
 less serve a useful purpose if it indicates how such 
 a meaning is developed. It is true that in order to 
 make our meanings abstract, we have to take attri- 
 butes and objects apart from their mutual impli- 
 cation of each other; but merely to take objects or 
 
133 
 
 attributes in isolation is not, , if, sufficient to 
 
 secure a new logical product. Tht Difficulty of such 
 a view as we are criticising can be seen if we 
 observe what would follow from its acceptance. 
 For if, according to this view, only a meaning 
 were retained, the thing meant by it being ig- 
 nored, we may ask about this meaning whether 
 it is a detached meaning, a meaning that is not 
 the meaning of any object. If we answer this ques- 
 tion in the affirmative, as we are required to do, we 
 have opened the door to all the absurdities that be- 
 long, in the popular understanding of the word, to 
 'abstract' thought, to thought, that is, that has 
 nothing to do with any definable reality. To illus- 
 trate, if from a student who comes for the first time 
 to the study of philosophy, we were to elicit by care- 
 ful questioning what his uninstructed understand- 
 ing of philosophy is, we should probably find that 
 for him philosophy is a set of ideas more or less 
 connected with one another, but having little or no 
 connection with anything else; and if, by further 
 questioning, we were to get him to state why he had 
 undertaken its study, we should probably find that 
 he looked upon it either as a good mental gymnastic, 
 or as a field in which, since no one can ever be 
 right, he at least can never be wrong, whatever 
 opinions he may hold. Such views are held merely 
 because it is supposed, by those who entertain them, 
 that philosophy is a set of ideas dissociated from all 
 objects whatever, that it is, in the popular under- 
 standing of the word, an 'abstract' subject. But 
 
134 A TEXT-BOOK OF LOGIC 
 
 ideas which do not make some object more intelli- 
 gible cannot be saved from the fate of oblivion by 
 giving them a name ; and we may neglect, as falling 
 below the minimum of what knowledge requires, 
 this understanding of the term abstract. 
 
 Having rejected the popular interpretation of 
 the expression 'abstract idea/ we have to ask 
 whether, in fact, such ideas exist, and if they do, 
 under what conditions their meaning is developed. 
 In answering these questions, we may remark that 
 the situation with respect to abstract ideas is some- 
 what as follows : If, concerning these ideas, we say 
 that they are true of the objects in connection with 
 which they have been formulated already in our 
 experience, then they are not abstract ideas at all ; 
 they are, as we have seen, general ideas ; and if we 
 say that they are ideas which mean nothing, we 
 are talking nonsense. To illustrate, let us suppose 
 that in the spring of the year, we are looking out 
 upon the landscape, and that you remark, 'How 
 green everything is!' Here 'green/ as you use it, 
 is a general idea. If, however, in the midst of a 
 conversation on monometallism, or of an unbroken 
 silence, I were to say 'green/ you would naturally 
 ask, 'Green what?' And if I replied, 'Green nothing, 
 just green/ you would have a right to suspect my 
 sanity. I can only rehabilitate myself in your re- 
 gard by pointing out that 'green' is as possible an 
 object of thought as 'trees' or 'grass;' and this is, 
 without doubt, the course that, under such circum- 
 stances, one would take. Now, in this illustration 
 
TERMS 135 
 
 we have a clue to what happens when a concrete 
 general idea has broken away from its moorings in 
 the world of concrete fact: the meaning conveyed 
 by the general idea becomes at once a new object 
 of thought, which is capable of further considera- 
 tion and characterisation. In brief, it is only when 
 a general idea has, in this way, been dealt with as 
 a subject of predication that we arrive at a true 
 abstract idea. For instance, if we take our former 
 illustration we may observe that although the grass, 
 the oak, maple, sycamore, and elm trees, the wind- 
 ing river, etc., are all 'green,' they are not the same 
 greens; they vary, as the psychologist tells us, in 
 tint and saturation. Now if we ask, with respect 
 to this fact, what we mean by calling things admit- 
 tedly different by the same name, we shall have to 
 say that there is something, whether we can state 
 definitely what it is or not, which is common to all 
 these objects, something which we express by the 
 word 'greenness/ 'Greenness' is the abstract qual- 
 ity by virtue of which any object is called green, it 
 is that which belongs as an attribute to all greens 
 whatsoever. If, to take another illustration, we 
 sort out the skeins of yarn for testing colour blind- 
 ness, and ask what it is that leads us to consider 
 objects which give so many different sensory im- 
 pressions as belonging to a single group, we should 
 doubtless, answer colour. 'Colour' (=colouredness) 
 is the abstract quality by virtue of which objects 
 are classified with regard to the common visual im- 
 pressions that they make. Again, 'triangle' is an 
 
136 A TEXT-BOOK OF LOGIC 
 
 abstract idea, because it implies the quality (tri- 
 angularity) by virtue of which three-sided plane 
 figures are grouped together. These illustrations 
 indicate with sufficient clearness the answer that 
 must be given to the question we are considering. 
 Any idea which denotes certain attributes common 
 to a group of concrete objects is abstract if, at the 
 same time, it connotes the underlying ground of the 
 similarity which exists between these attributes. 
 
 REFERENCES 
 
 SEE THE END OF THE NEXT CHAPTER 
 
 QUESTIONS 
 
 1. What is the relation of terms to propositions? 
 
 2. What is meant by the connotative and denotative use of 
 terms? Illustrate. 
 
 3. Are terms ever used exclusively in a connotative or ex- 
 clusively in a denotative sense? Explain your answer. 
 
 4. In case a term is both connotative and denotative, are 
 the connotation and denotation always equally promi- 
 nent? Explain. 
 
 5. How does any increase in the connotation of a term 
 affect its denotation, and vice versa? 
 
 6. What is the relation of the distribution of terms to the 
 connotative and denotative use of terms? 
 
 7. Explain what is meant by the distribution of terms, 
 being careful to distinguish between distributed and 
 undistributed terms. 
 
 8. What is the relation of the meaning of terms to the 
 connotative and denotative use of terms? 
 
 9. What general characteristics of terms may be mentioned 
 from the standpoint of connotation? 
 
TERMS 137 
 
 10. Upon what do these characterictics particularly depend? 
 
 11. How is the problem of definition distinguished? 
 
 12. Upon what fact of our common experience does concrete 
 meaning depend? 
 
 13. In what respects does the term concrete differ from the 
 word thing? 
 
 14. What do you understand by an individual or singular 
 term? 
 
 15. Name the kinds of individual terms. 
 
 16. Define and illustrate proper names. 
 
 17. Are proper names used connotatively? Explain and 
 illustrate your answer. 
 
 18. Define and illustrate designations. 
 
 19. Are designations used connotatively and denotatively? 
 Explain. 
 
 20. What is the importance of designations? 
 
 21. Explain how meaning becomes general, and show that 
 in doing so it remains concrete. 
 
 22. What is a general, or common, term? Illustrate. 
 
 23. Discuss the connotative and denotative use of general 
 terms. 
 
 24. Explain how meaning becomes collective, and yet re- 
 mains concrete. 
 
 25. What is a collective term? Illustrate. 
 
 26. Discuss the connotative and denotative use of collective 
 terms. 
 
 27. What is an individual collective term? Illustrate. 
 
 28. What is a general collective term? Illustrate. 
 
 29. What is the relation between individual and general 
 collective terms? 
 
 30. Does this relation always hold? Explain. 
 
 31. How does abstract, differ from concrete, meaning? 
 
 32. Distinguish carefully between abstract and general 
 terms. 
 
 33. Discuss the connotative and denotative use of abstract 
 terms. 
 
138 A TEXT-BOOK OF LOGIC 
 
 EXERCISES 
 
 1. What are the connotation and denotation of the follow- 
 ing terms: 
 
 Gentlemen my typewriter logic 
 
 George Washington gratitude the University 
 
 2. Show by an illustration that the denotation of a term 
 may decrease if its connotation is increased. 
 
 3. Classify in a table all the terms discussed in this chap- 
 ter, showing which are coordinate and which are sub- 
 ordinate. 
 
 4. Write a list of twelve concrete individual terms, and 
 indicate which are proper names, and which, if any, 
 are designations. 
 
 5. What kind of term is 'goodness' in each of the following 
 statements? 
 
 (1) Goodness knows what we shall do. 
 
 (2) He did it out of sheer goodness. 
 
 6. Write a list of six general terms. 
 
 7. Derive, if possible, abstract terms from each of those 
 that occur in your answer to the previous question. 
 
CHAPTER V 
 TERMS (CONTINUED) 
 
 The Purpose of the Chapter. In the previous 
 chapter we have traced the development of meaning 
 from its concrete to its abstract form, and in doing 
 so we have touched upon the main principles that 
 control the logical use of terms. There are, how- 
 ever, a number of other interests that lead us to 
 consider objects and their qualities in ways slightly 
 different from those already described, and thus to 
 give our doctrine of meaning, in each case, a slightly 
 different emphasis. In this chapter we shall define 
 and illustrate some of these more common interests, 
 and point out the varying emphasis that our mean- 
 ings come to have under their guidance. 
 
 The Basis of the Distinctions to be Studied. The 
 distinctions in meaning that we are to study in this 
 chapter, like those studied in the last, have a basis 
 in common linguistic usage. The basis of the dis- 
 tinction of concrete and abstract meaning is the 
 fact that we distinguish between an object and its 
 qualities, between the object that is the possessor 
 of qualities, and the qualities possessed by the ob- 
 ject. The distinctions studied in the present chap- 
 ter are based on this broad contrast between objects 
 and their qualities, but are not identical with it. 
 When, for example, we have distinguished between 
 an object and its qualities, so that we can think of 
 the object merely as having existence, and can think 
 of qualities as possible characteristics of objects 
 without at the same time identifying the objects 
 
 (139) 
 
140 A TEXT-BOOK OF LOGIC 
 
 of which they are the qualities, we can take a fur- 
 ther step in regard to objects, and consider whether 
 they do or do not stand in relation to other objects, 
 and, in regard to qualities, whether they do or do 
 not belong to certain objects. In the former case, 
 we ask whether the relation that objects sustain to 
 other objects affects the meaning that such objects 
 have; and, in the latter, we ask whether the pos- 
 session or non-possession of certain qualities by ob- 
 jects in any way modifies the significance that such 
 objects have for us. In the first question, we are 
 concerned with what are known, in logic, as abso- 
 lute and relative terms; and in the second, with 
 what are known as positive and negative terms. 
 
 Absolute and Relative Meaning. This distinction 
 is one that concerns the existential character of 
 objects, that is, objects considered with respect to 
 whether they do or do not depend for the meaning 
 they have upon the relations in which they stand to 
 other objects. Stated otherwise, we are asking 
 whether it is possible and useful to study objects 
 independently of the connections they may have 
 with other objects, and whether the terms we use 
 to denote objects do or do not get part of their 
 meaning from the relations which these objects sus- 
 tain to other objects that fall outside the denotation 
 of these terms themselves. The answer to this 
 inquiry is quite obvious. Objects whose connection 
 with other things is for the time being neglected 
 may certainly be held before the mind as subjects 
 of investigation. These objects may be quite simple, 
 
TERMS 141 
 
 as a chair, or they may be quite complex, as the solar 
 system. But whenever a simple or complex object 
 derives its importance for consciousness from the 
 fact that we ignore the connections it may have with 
 other existential things, it is said to be an inde- 
 pendent object. Now when the names of such objects 
 are used as terms in a proposition, they are called 
 absolute terms. Thus, all individual terms, whether 
 they denote single individuals, or single groups of 
 objects, are, in the sense explained, absolute terms. 
 
 What we should understand by a relative term 
 is more difficult to state. We shall first consider 
 the most general aspect of this question. It is quite 
 clear, in the first place, that since the whole prob- 
 lem of meaning rests, as we have seen, upon the 
 connection between the connotative and denotative 
 use of terms, that there can be no object entirely 
 devoid of qualities, and no quality which is not the 
 quality of some object. There is always a relation 
 between these two aspects of a term's meaning. 
 Further, it is clear that all our meanings, whether 
 concrete or abstract, singular or general, are also 
 relative in the sense that the objects denoted by 
 such terms stand in relation to objects denoted by 
 other terms. Used in the broad way, indicated by 
 these illustrations, the word 'relative' does not point 
 out a particular logical distinction, but describes a 
 common characteristic of all human knowledge 
 whatsoever. 
 
 The term relative is used in logic, in contrast 
 to absolute, to indicate the fact that part of the 
 meaning that a term has is derived from the exist- 
 
142 A TEXT-BOOK OF LOGIC 
 
 ence of an object that the term itself does not denote. 
 Stated another way, a relative term is one that 
 implies the existence of some other object than 
 the one that the term itself denotes. It is obvious 
 that no concrete individual term can be relative in 
 this sense. But some concrete general terms are. 
 For example, the term 'father' is a concrete general 
 term since it is a name which applies to an indefinite 
 number of individuals in whom the relations implied 
 by the name are present; it is also relative because 
 these relations are such that they depend for their 
 application not only upon the existence of the indi- 
 vidual to whom the name is given, but also upon 
 the existence of either a son or a daughter. A sim- 
 ilar double relationship exists in all family connec- 
 tions: uncle, grandfather, niece, etc. We may ob- 
 serve the same thing in other than the family type 
 of social organisation: political, king-subject; 
 economic, debtor-creditor; juridical, -- plaintiff- 
 defendant; commercial, employer-employee; do- 
 mestic, master-servant, etc. Whether this type 
 of relationship is ever found outside of social organ- 
 isations, or if found, whether they are common, has 
 been questioned. We may point out that some logi- 
 cians have been inclined to find the meaning of such 
 a word as 'mountain' in the reference that it is said 
 to contain to the plain from which it rises. There 
 may be other words whose meanings are of this 
 relative sort, such as, right-left, heavy-light, up- 
 down, etc. In deciding whether any term is rela- 
 tive, it should be borne in mind that the only clue 
 
TERMS 143 
 
 that is of logical value, is the sense in which it is 
 actually used in carefully guarded and intelligent 
 speech. And by this test it appears that the words 
 whose meanings are determined by the existence of 
 other objects than those which such words denote 
 are chiefly those that indicate the relations that we, 
 as human beings, have with one another in some 
 type of social organisation. 
 
 One other point remains to be mentioned. It is 
 sometimes found that when one object derives part 
 of its meaning from the existence of another, the 
 latter also derives part of its meaning from the 
 first. Not only, for example, does uncle or aunt 
 imply nephew or niece, but nephew or niece implies 
 uncle or aunt. That is to say, each term of the 
 relation implies, and is implied by, the other. Re- 
 lationships of this kind are called reciprocal. The 
 terms between which such relationship holds are 
 also called correlatives. Thus, when we regard the 
 creditor-debtor relation from the standpoint of 
 creditor, we say that 'debtor' is a correlative term, 
 and when we regard it from the standpoint of debtor, 
 we say that 'creditor' is a correlative term. By a 
 correlative term, therefore, is meant that one of a 
 pair of relative terms which is implied by the other. 
 
 Positive and Negative Meaning. The distinction 
 between positive and negative meaning rests upon 
 the answer we give to the question whether a given 
 object has or has not a certain attribute or set of 
 attributes. In a general way, it is true that every 
 object has or has not the attributes which the word 
 
144 A TEXT-BOOK OF LOGIC 
 
 we use to point it out implies; otherwise, it may 
 be asked, how can we identify any subject of dis- 
 course? It may, however, be said that it is some- 
 times necessary to state emphatically that the ob- 
 jects we are speaking about have or have not cer- 
 tain attributes, and that when this is the case, the 
 meaning of what we express is either positive or 
 negative. A positive meaning, to consider that first, 
 calls special attention to the fact that an object has 
 the attributes which are implied by the term which 
 is used to point it out; and it is necessary some- 
 times to emphasise this fact, because the meaning 
 of what we affirm, without such emphasis, is liable 
 to be misunderstood. Whenever the denotation of 
 a term is unambiguous, or when its popular mean- 
 ing does not render it equivocal, we do not need to 
 call special attention to its precise connotation. For 
 example, the term 'rent' is popularly understood as 
 a fixed sum of money that is paid or received for the 
 occupancy of a house or of land. It is primarily a 
 denotative term, and many judgments may be ex- 
 pressed which are perfectly intelligible about the 
 object, the fixed sum of money which this term 
 denotes. We may say, for example, that 'Rent is a 
 constant drain upon a poor man's wages/ To pay 
 rent all one's life is an indication of improvidence,' 
 etc. In all such instances, the sense of our asser- 
 tions is carried easily by the denotative use of the 
 term 'rent.' However, when what we assert is 
 dependent, not upon the object's existence, but upon 
 its meaning, we are in a different position. In that 
 
TERMS 145 
 
 case, the meaning of the term by which the object 
 is denoted must be made precise if we are to have 
 an intelligent understanding of what a proposition 
 affirms. Thus, for the economist, the term rent is 
 'the remuneration that is derived from the concrete 
 things that have the value of capital,' and this mean- 
 ing of the word must be kept in mind in any discus- 
 sion which involves the idea for which the term 
 stands. In this instance 'rent' is used connotatively, 
 and, so used, it limits whatever can be said intelli- 
 gently on any subject that implies the idea. It is a 
 positive term because it is used to indicate the fact 
 that any object to which it is applied must have the 
 qualities which the term connotes. 
 
 The Conditions of Negative Meaning. In discuss- 
 ing negative meanings, we shall inquire, in the first 
 place, into the conditions under which such mean- 
 ings arise. We call attention to three situations 
 in which knowledge is forced to assume a negative 
 form. First, whenever, for any reason, we fail to 
 reach a positive conclusion on any subject of inquiry, 
 we may map out the progress of the inquiry by a 
 series of negations. For example, let us suppose 
 that a physician is called to see a patient who has 
 a serious illness. As the examination of the patient 
 proceeds, a number of prominent and secondary 
 symptoms are noted and the possibility of typhoid, 
 tuberculosis, scarlet fever, etc., suggest themselves 
 in turn, only to be rejected one after the other; 
 and the physician concludes his visit with a confes- 
 sion, to himself if not to the family of the patient, 
 10 
 
146 A TEXT-BOOK OF LOGIC 
 
 that he has reached no positive knowledge of the 
 disease, or complication of diseases, from which the 
 patient is suffering. The physician's knowledge, in 
 such a case, is made up of a series of negative judg- 
 ments ; not typhoid, not scarlet fever, etc. Through 
 what has been denied, that is, through what the 
 physician calls his differential diagnosis, he has 
 come nearer to, but has not succeded in making, a 
 positive diagnosis. Negations thus mark out the 
 limits within which the positive characteristics of an 
 object are to be found. No doubt, in new and com- 
 plicated situations, business and professional men 
 are often in the position where the only thing that 
 is clear to them is what not to do or think. In such 
 cases, we have negative but not positive meanings ; 
 but the former exist, not as something opposed to 
 the latter, but as stages in our progress toward it. 
 Our subject-matter refuses, one after the other, a 
 number of suggested qualifications, and often we 
 have to stop our investigation of the matter in 
 hand before we have found the particular qualifi- 
 cation which fits. 
 
 Secondly, negative meaning arises when we safe- 
 guard a positive meaning from misunderstanding 
 or falsification. Let us take, as an example, the 
 case where a new truth is presented for the first 
 time for our understanding. We are more often in 
 this relation to truth, as students, than in any other. 
 The teacher, let us say, is expounding the psycho- 
 logical doctrine of perception. We follow him atten- 
 tively as step by step he enumerates and explains 
 
TERMS 147 
 
 the various factors in the problem, and their relation 
 to each other. Now the important question for us 
 as students is whether we have really understood 
 what the teacher has said. Class-room experience 
 shows that a student's reaction to the subjects of 
 his study comes most often in the form of a ques- 
 tion, or a statement, which, from the teacher's stand- 
 point, is the suggestion of a predicate or series of 
 predicates, for the topic of discourse, in the ex- 
 ample, the psychological doctrine of perception ; and 
 the teacher's problem is to determine whether the 
 proposed predicates are compatible with those by 
 means of which his own exposition has been carried 
 on. Now, since our first apprehensions of any new 
 truth are liable to be uncertain, vague, or partial, 
 our proposed predicates not infrequently endanger 
 our grasp of the new truth, and have to be eliminated 
 from the list of those attributes which, when taken 
 together, constitute the positive meaning of the sub- 
 ject under consideration. Now, this elimination of 
 incompatible predicates is performed by the teacher 
 whenever he refuses to accept our statements or 
 questions as elucidations of the subject-matter in 
 hand. And his refusal is given in the form of a 
 negation which means, from his point of view, that 
 he is defending a positive meaning from misunder- 
 standing or falsification. 
 
 Thirdly, negative meaning arises whenever, in 
 carrying forward a special line of work, our prob- 
 lem is to see how far, and in what directions, our 
 subject is capable of development. The starting 
 
148 A TEXT-BOOK OF LOGIC 
 
 point, in a case like this, is the body of knowledge 
 we have already acquired about our subject. We do 
 not become possessed of the truth that lies beyond 
 our grasp by a method that implies disloyalty to 
 the truth that lies within it. The working criterion 
 of the truth of any thing new must be the truth 
 that we already possess. And this means that 
 nothing becomes true which contradicts what is 
 already true. Truth is a system, systematic and 
 coherent, one part of which supports and supple- 
 ments every other. However, this position should 
 not be held in such a way that the limitations of 
 the truth in hand are allowed to make us inhospit- 
 able to the constantly increasing and enlarging body 
 of truth. Truth, it should be borne in mind, grows 
 from less to more; and, in the process, not only do 
 we come into possession of new truths, but the old 
 truths are transformed, and sometimes the entire 
 system of truth changes its character. A familiar 
 instance of this is the change from the Ptolemaic 
 to the Copernican astronomy. The particular use 
 of the statement and illustration in this place is to 
 call attention to the fact that such changes in the 
 character and system of truth is effected by nega- 
 tion working within the field of established truth. 
 For what is the recognition of truth's limitations 
 but the admission that negation not only erects a 
 barrier against outside error, but also against that 
 hardening process in the heart of truth itself which, 
 unchecked, steels it against the recognition of out- 
 side truth? When, therefore, we are endeavouring 
 
TERMS 
 
 to extend the boundaries of a particular subject, or 
 when we have to consider the truth of any subject 
 in its relations to other fields of knowledge with 
 which it may be correlated, we are often forced into 
 the position of either denying all outlying truths, 
 or modifying, in the interest of the systematisation 
 of truth, the knowledge that we already possess. 
 Development of knowledge takes place only when 
 we follow the latter course. But, we should remark, 
 the modification of established truths, which is 
 necessary if what is new is to find a place in the 
 developing field of knowledge, is made possible by 
 the elimination of what is erroneous in it ; or, stated 
 otherwise, the limitations of existent truth are 
 brought to light by negation working within the 
 area of our established beliefs. 
 
 The Logic of Negation. That there is such a 
 thing as negative meaning is not open to serious 
 question, and what the conditions are under which 
 it arises we have already seen. The inquiry that 
 confronts us now is, How are negative meanings to 
 be interpreted? We may approach this question by 
 remarking that negative meanings are developed out 
 of the interests that lead us, in our inquiry into the 
 nature of things, to affirmative conclusions. By 
 this statement we mean that negation must be inter- 
 preted as a form of knowledge, and not merely as 
 an assertion of the absence of knowledge, and that, 
 as such, it satisfies, in the particular instances in 
 which negative meanings arise, the motives that 
 sustain all our cognitive endeavours. Stated other- 
 
150 A TEXT-BOOK OF LOGIC 
 
 wise, we may say that since in all knowledge thought 
 is, as we have seen, in some particular relation to 
 its object, we must hold either that this is true of 
 negative as well as of positive meanings, or that 
 negative meanings fall outside of the field of logical 
 inquiry. The only alternative to this position would 
 be to deny the existence of negation altogether. But 
 this we cannot do. And we cannot do it for the 
 simple reason that if we did succeed in getting rid 
 of negation in one form, it would break out in an- 
 other, a fact that is significant of the distinctive 
 function of negation in our search after the truth 
 of things. An illustration of the fact just referred 
 to may be found in the endeavour to get rid of neg- 
 ative meanings by reducing all propositions to a 
 common affirmative type. Thus, it is contended, the 
 meaning of the statement, 'Some men are not Cau- 
 casians/ is not, 'Some men are-not Caucasians,' 
 a negative proposition, but, 'Some men are 
 not-Caucasians,' an affirmative propostion. But, if 
 this is true, it is obvious that, in the latter case, the 
 predicate term has been burdened with the negative 
 that belonged, in the former case, to the copula. 
 And, what is more important, this way of escape 
 from the difficulties of negative statements seems to 
 have rendered affirmative ones equivocal. For, it 
 will be remembered, in all affirmation we are sup- 
 posed to predicate a positive characteristic, quality, 
 attribute or relation of a subject; but when we 
 affirm by means of negative terms, we seem to be 
 saying that the subject does not possess the attri- 
 
TERMS 151 
 
 butes connoted by the predicate of the proposi- 
 tion which expresses our meaning. So far then 
 from escaping the problem of negation, this attempt 
 to reduce all statements to an affirmative type forces 
 upon us the question of how we are to interpret 
 negative terms. To this question we shall now give 
 attention. 
 
 Let us be perfectly clear what our problem is. 
 When we say 'not-Caucasian/ 'not-typhoid,' etc., it 
 is quite possible, as we have said, that we mean 
 nothing more than that our knowledge is falling 
 short of what knowledge, strictly regarded, requires. 
 This, however, is a different thing from saying that 
 we have attained the full measure of knowledge 
 when all that we can affirm is that a subject has 
 some quality or relation vaguely expressed by neg- 
 ative terms. When, for example, we say of an in- 
 dividual that he is not-Caucasian, or of a disease 
 that it is not-typhoid, what, we should like to know, 
 are the positive attributes, which these terms con- 
 note? And we can ask such a question just because 
 we are dealing with an affirmative statement. 
 Now one way of answering this question has been 
 to say that, by the exclusion of a particular group 
 of attributes, expressed by the negative term, we 
 include within the meaning that the negative term 
 must have all other attributes whatsoever. In other 
 words, the negative term, or, as it is sometimes 
 called, the indefinite, indesignate, or infinite term, 
 is one which divides all existing things into two 
 groups, in one of which there is placed definitely 
 
152 A TEXT-BOOK OF LOGIC 
 
 the excluded meaning, and in the other all other ex- 
 istences and meanings. According to this view, it 
 is the function of the negative term to denote the 
 latter group ; it is the name of a miscellaneous num- 
 ber of things, such as "accidence and adjectives and 
 names of Jewish kings." Thus, as Bosanquet says, 
 "not-Christian literally interpreted includes not only 
 heathen humanity, but the fixed stars, the sea, and 
 indeed, in Aristotle's words, 'every thing whether 
 existent or non-existent' except Christian. It refers 
 to no one sphere in preference to another, and thus 
 says nothing definite enough to be intelligible." It 
 is an example of what we may call bare negation, 
 that is, of negation unlimited by any reference to a 
 positive sphere of reality; and, because it includes 
 so much, succeeds, in the end, in denoting nothing 
 in particular. Now it may be doubted whether, out- 
 side the field of a purely formal logic, there are any 
 such infinite terms as this; that is, whether bare 
 negation, a negation which is not a stage or step in 
 our acquisition or development of positive knowl- 
 edge, is ever rooted in the purposes or motives 
 which, in our relation to things, give birth to rele- 
 vant assertion. But if these infinite terms do not 
 'express meanings that are the outgrowth of the 
 motives that control our knowledge processes, if, 
 that is, they have no relation to the purposes that 
 guide and determine the life of judgment, they lose 
 all interest for logic ; they may have a psychological, 
 but can have no logical, significance. 
 
TERMS 153 
 
 Another way of meeting the question we are 
 considering is to point out that the meaning of any 
 proposition must be sought within the universe of 
 discourse which the proposition implies, and that, 
 consequently, this places a limitation upon the 
 meaning that the proposition's terms can have. If 
 from this point of view we consider the statement, 
 'Some men are not-Caucasian/ it is obvious that we 
 are speaking of men from the standpoint of their 
 racial characteristics, and that the group of men 
 which now interests us, the 'Some men' of the 
 proposition do not have the characteristics of the 
 Caucasian. But if we are making the statement at 
 all intelligently, we mean more than this; we mean 
 that they have the characteristics of either one or 
 other of the remaining divisions of the human fam- 
 ily looked at from the racial point of view. That is 
 to say, the positive meaning of the negative term 
 'not-Caucasian' can be expressed by 'either Negro 
 or Mongolian or American Indian.' Thus, the whole 
 meaning of our statement is, 'Some men are not- 
 Caucasian, but are either Negro or Mongolian or 
 Indian.' Likewise the other statement, 'This dis- 
 ease is not-typhoid,' means that a pathological con- 
 dition is present, but it is not typhoid and it is either 
 scarlet fever or tuberculosis or diphtheria or one 
 or other of an indefinite number of the ills to which 
 the human body is subject. 
 
 Privative Meaning. Closely connected with nega- 
 tive terms are those called privative, terms which 
 indicate the absence of an attribute naturally or 
 
154 A TEXT-BOOK OF LOGIC 
 
 usually belonging to the object which such terms de- 
 note. 'Blind/ 'maimed/ 'orphaned/ 'deaf/ are ex- 
 amples. Because they are so closely connected, it 
 may help us to understand both negative and priva- 
 tive terms if we indicate wherein they seem to differ 
 from each other. The negative term, as we have 
 seen, indicates a number of positive alternatives by 
 means of a negative characterisation of the object 
 which such term is made to qualify. It is, there- 
 fore, not a term that is negative in meaning at all ; 
 it is only its form that has this characteristic. The 
 reverse seems to be true of privative terms, their 
 meaning is negative, and what is negated is defi- 
 nitely the attribute or attributes which such terms 
 connote. Thus, 'The boy is an orphan/ must be 
 understood to mean that he has no parents, 'the 
 absence of parents' being what the term 'orphan' 
 connotes. A further difference between these terms 
 may be indicated. In the case of negative terms, 
 we are able, through what is denied, to affirm cer- 
 tain alternative qualities, that is, to go beyond what 
 is definitely stated by such terms. In the case of 
 privative terms, this is not true. Of the boy who is 
 an orphan, all that we can positively affirm is that 
 he has no parents; we cannot say whether he has 
 either a brother, or sister, or uncle or aunt. If of 
 any one we can say, 'He is deaf/ we do not find in 
 this statement any ground of assertion with respect 
 to the presence, absence, or degree of acuteness of 
 any of his other faculties. In view of these charac- 
 teristics, privation must be interpreted as an ex- 
 
TERMS 155 
 
 treme case of negation ; that is, of a negation which 
 arises under conditions that make defect of quality 
 a differentia of the meaning we intend to convey. 
 
 Disparate and Contrary Meaning. We may touch 
 upon two other related distinctions which have neg- 
 ative significance. Whenever we can divide a class 
 of objects into a number of mutually exclusive 
 classes, as, for example, the class animal into lions, 
 tigers, etc., these subordinate classes are said to be 
 disparate. If, further, we can arrange the exclusive 
 classes of a group of objects with respect to their 
 possessing more or less of some quality, for ex- 
 ample, organisms in a series from amoeba to man, 
 and if we can say of two of these classes that, with 
 respect to the common quality, they differ from 
 each other in a greater degree than either does 
 from any other, the relationship between these two 
 most differing classes is said in logic to be that of 
 contrariety. A contrary relation is one form of 
 negative meaning, and indicates the greatest degree 
 of exclusion, actual or possible, within a single 
 genus. In other words, contraries are the extreme 
 limits of the universe of discourse within which the 
 meaning of any proposition falls. 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Ch. V. 
 
 B. Bosanquet, The Essentials of Logic, Lect. V, 4-7. 
 
 J. E. Creighton, An Elementary Logic, 3d Edition, Part I., 
 Ch. IV. 
 
 W. S. Jevons, Elementary Lessons in Logic, Chs. III-V. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. II. 
 
156 A TEXT-BOOK OF LOGIC 
 
 W. Minto, Logic, Inductive and Deductive, Part I., Ch. I. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. III., 
 
 IV. 
 W. J. Taylor, Elementary Logic, Ch. II-IV. 
 
 ADVANCED 
 
 J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. 
 
 VII. 
 
 B. Bosanquet, Logic, Vol. I., pp. 46-71. 
 F. H. Bradley, The Principles of Logic, pp. 155-173. 
 W. R. B. Gibson, The Problem of Logic, Chs. I., VII., VIII. 
 H. W. B. Joseph, An Introduction to Logic, Chs. II., VI. 
 J. N. Keynes, Studies and Exercises in Formal Logic, 4th 
 
 Edition, Part I., Chs. I., II. 
 H. Lotze, Logic, Vol. I., Ch. I. 
 J. S. Mill, A System of Logic, Book I., Ch. II. 
 J. Venn, Empirical Logic, Ch. VII. 
 J. Welton, A Manual of Logic, Book I., Chs. I., II. 
 
 QUESTIONS. 
 
 1. How are the logical distinctions of absolute and rela- 
 tive, positive and negative terms, related to those dis- 
 cussed in the previous chapter? 
 
 2. Upon the answer to what question does the distinction 
 of absolute and relative depend? 
 
 3. State and illustrate the meaning that belongs to abso- 
 lute terms. 
 
 4. What senses of the term relative are excluded from our 
 discussion of relative terms? 
 
 5. What is meant in logic by a relative term? 
 
 6. What class of experience provides most of our illustra- 
 tions of relative terms? 
 
 7. What are correlative terms? 
 
 8. Upon the answer to what question does the distinction 
 of positive and negative depend? 
 
 9. What is a positive term? 
 
 10. Under what conditions do we express our meaning pos- 
 itively? 
 
TERMS 157 
 
 11. State and explain the conditions under which our knowl- 
 edge has to be expressed negatively. 
 
 12. Are the motives that lead to negative statements differ- 
 ent from those that lead to affirmative ones? Explain. 
 
 13. How have some logicians tried to get rid of negative 
 meaning? 
 
 14. Criticise this effort. 
 
 15. State and illustrate two views of the logical significance 
 of negative terms. 
 
 16. What do you understand by privative meaning? 
 
 17. How are privative related to negative terms? 
 
 18. What do you understand by disparate and contrary 
 meaning? 
 
 EXERCISES 
 
 1. Write three propositions to illustrate the absolute mean- 
 ing of terms. 
 
 2. Discuss each absolute term in your answer to the pre- 
 vious question to show whether it is concrete or abstract. 
 Write new propositions to illustrate your results. 
 
 3. Write new propositions to illustrate concrete and ab- 
 stract terms. 
 
 4. Write three propositions to illustrate the relative mean- 
 ing of terms. 
 
 5. Discuss each relative term in your answer to the pre- 
 vious question to show whether it is concrete, abstract, 
 absolute. Illustrate. 
 
 6. Write three propositions to illustrate the positive mean- 
 ing of terms. 
 
 7. Discuss each positive term in your answer to the pre- 
 vious question to show whether it is concrete, abstract, 
 absolute, relative. Illustrate. 
 
 8. Write three propositions to illustrate the negative mean- 
 ing of terms. 
 
 9. Discuss each negative term in your answer to the pre- 
 vious question to show whether it is concrete, abstract, 
 absolute, relative, positive. Illustrate, 
 
CHAPTER VI 
 
 DEFINITION AND THE PREDICABLES 
 
 The Questions of this Chapter. In our study of 
 terms, in the two preceding chapters, we saw first, 
 that a term may be used either to point out par- 
 ticular existing things or to convey some meaning. 
 When a term is employed to point out particular 
 existing things it is said to be used denotatively; 
 when it is employed to convey some meaning, it is 
 said to be used connotatively. Arising out of this 
 distinction of the denotative and connotative use of 
 terms, certain problems were forced upon us for 
 consideration. For instance, our study of the deno- 
 tative use of terms brought before us the problem 
 of the distribution of terms, and our study of the 
 connotative use of terms brought to our attention 
 certain general characteristics of terms the study 
 of which, as we may now say, involved the problem 
 of the classification of terms. In our statement of 
 this latter problem, we were led to recognize another 
 problem, the (problem of definition, and this 
 problem was said to be concerned with the way in 
 which the particular meaning of terms receives 
 logical formulation. The facts and relations em- 
 bodied in this statement of the logic of terms may 
 be expressed in a tabular form as follows : 
 
 (158) 
 
DEFINITION AND THE PREDICABLES 159 
 
 Standpoint Problem 
 
 Denotation Distribution of terms 
 
 Terms 
 
 f Classification of terms 
 Connotation 
 
 ^Definition of terms 
 
 This table may be read as follows: Terms studied 
 from the standpoint of their denotation give rise 
 to the problem of the distribution of terms ; studied 
 from the standpoint of their connotation, they give 
 rise either to the problem of the classification of 
 terms or to the problem of the definition of terms. 
 
 Of the two problems connected with the conno- 
 tative use of terms, the problem of the classification 
 and of the definition of terms, the former may be 
 said to be concerned with the question, What are 
 the various kinds of terms that form the S and P 
 of logical propositions ? And the latter is concerned 
 with the question, What, irrespective of the kinds 
 that terms may be, are the meanings that terms may 
 have? We have considered the first of these ques- 
 tions in the two previous chapters. The second 
 question we shall study in the first part of the pres- 
 ent chapter. In this part, we shall try to show how 
 to make the particular meanings of the terms we 
 employ definite, how to formulate them in such a 
 way that no doubt remains as to the sense in which 
 they are used. We hope, as the result of our study, 
 to learn how to proceed when we are required to 
 make the meaning of any of our terms explicit. 
 
160 A TEXT-BOOK OF LOGIC 
 
 After we have concluded this study, we shall be in 
 a position to ask and answer the question, What 
 kinds of things can be predicated of a subject? 
 The convenience of discussing this question here 
 is that doubt has been cast upon the possibility of 
 predicating of any subject its own definition. But 
 it is more than a question of convenience; for, as 
 we shall see, our whole view of the nature of defini- 
 tion is involved in the position we take with respect 
 to the predicables. There are, then, two problems 
 to be discussed in this chapter, the problem of defi- 
 nition and the problem of the predicables, and of 
 these the first to be considered is the problem of 
 definition. 
 
 Non-Ambiguity. We may approach the study of 
 this question by calling attention to the fact that in 
 the fields of science, more than anywhere else, our 
 ideas must be accurate, and the language in which 
 these ideas are expressed must definitely convey the 
 meaning intended. That is to say, the natural fluid- 
 ity of language must not be allowed to go in the 
 sciences to the point of ambiguity. Whenever, 
 that is, we wish to express our ideas in words, there 
 is a limit to the indefiniteness that can be allowed 
 to the forms of our speech, and if we really convey 
 the sense of what we mean our words must be 
 definite in what they connote. 
 
 This demand for precision in the use of words 
 may be easily misunderstood, and it may lead to an 
 effort after the impossible or undesirable. The aver- 
 age man's impatience with over-primness of speech 
 
DEFINITION AND THE PREDICABLES 161 
 
 is a healthy protest against pedantry ; but the same 
 man's laxness in the use of words bears witness 
 quite often to the vagueness of his ideas. These are 
 the extremes against which it is desirable to guard : 
 the extreme, on the one hand, of an accuracy of 
 speech out of all proportion to the character and 
 importance of the subject-matter of our thought; 
 and the extreme, on the other hand, of being tyran- 
 nised over by words and of using them as substi- 
 tutes for ideas. There is always an appropriate 
 exactness that we should strive to realise in our use 
 of language, and nothing more than this can be 
 demanded of us by the strictest logic. We must aim 
 to make our speech non-ambiguous, but non-ambi- 
 guity is relative to the purpose of the speaker and 
 to the subject of his thought. Non-ambiguity 
 changes with the change of purpose and subject, 
 and the degree of exactness that is requisite on 
 some occasions and with respect to some subjects 
 might be altogether inadequate if these were differ- 
 ent. There is no one standard of explicitness that 
 we are required to attain ; the most that can be de- 
 manded is that on all occasions, and with respect 
 to all subjects, our language be made a fitting ve- 
 hicle for the expression of the ideas we wish to 
 convey. 
 
 We have called attention to these somewhat 
 obviaus considerations, because, through their neg- 
 lect, the importance of the problems with which we 
 are here concerned has frequently been obscured. 
 11 
 
162 A TEXT-BOOK OF LOGIC 
 
 This, we think, is unfortunate; for whatever can 
 help us to avoid misunderstanding, whatever can 
 strengthen our reputation for saying what we mean 
 and meaning what we say, cannot be of indifference 
 to any one of us, in a world where intellectual integ- 
 rity is coming to play an increasingly important 
 part. 
 
 These considerations may also enable us to see 
 that whenever we are in danger of being misunder- 
 stood, whether in science or literature or business, 
 on account of the indefinite meanings of the words 
 we employ, there is required some method by which 
 the misunderstanding can be avoided, some method 
 by which words can be moulded to the uses of ideas. 
 Life is one, and the occasions when it is necessary 
 to state explicitly the meaning of the words we use 
 arise all along its way, and are not confined to, even 
 if they are more frequent and more urgent in, the 
 various departments into which our human knowl- 
 edge has been organised. In other words, ambiguity 
 may be as undesirable in the drawing-room or 
 counting-house as in the laboratory, and whenever 
 and wherever it is a hindrance, we naturally try 
 to get rid of it. But before we consider how this 
 may be done, a word may be added on ambiguity 
 itself. 
 
 Ambiguity. The traditional doctrine of ambi- 
 guity may be briefly stated. Any term is ambig- 
 uous if it is given a meaning in a proposition which 
 it does not have in the judgment which the prop- 
 osition expresses. For example, 'He was a man who 
 
DEFINITION AND THE PREDICABLES 163 
 
 always chose a mean line of action.' Terms that 
 have more than one meaning, and which, therefore, 
 lead to ambiguity of statement, are called ambig- 
 uous or equivocal; and, in contrast to these, those 
 that have only one meaning are called unambig- 
 uous or univocal. 
 
 There are two respects in which this view of 
 ambiguity does not seem to be satisfactory. First, 
 it implies too formal or mechanical a view of logic. 
 It leaves the impression that words are like counters 
 in a game to be pushed here and there as the exi- 
 gencies of the game demand, that no difference is 
 made to the words themselves by their change of 
 relation in different propositions. Second, it sup- 
 poses that there are certain words which have a 
 fixed meaning, and that the statements in which 
 they occur are, therefore, free from ambiguity. 
 This is difficult to maintain for any class of words, 
 and if it were true of particular words there is no 
 guarantee that it must remain so. The principle 
 that should guide us in a discussion like this is that 
 it is not words that make a language, but language 
 that moulds words and fits them to the uses for 
 which the language exists. For example, the word 
 'Democrat' has a definite historical meaning, as also 
 has the word 'Republican' ; but as names of political 
 parties they no longer mean what they meant origin- 
 ally, and have become vague and indefinite through 
 the growth within each party of sub-classes or 
 varieties of democracy and republicanism, each of 
 which would deny to the other the right to the name. 
 
164 A TEXT-BOOK OF LOGIC 
 
 This process of splitting off from a perfectly clear 
 centre of meaning is going on all the time in the 
 living languages of the world, and is giving rise to 
 conflicting meanings in the uses of words. 
 
 The problem of ambiguity may be viewed in a 
 broader way still. Instead of considering it as hav- 
 ing to do with the indefiniteness that arises from the 
 vague or shifting meaning of words, we may view 
 it as in some sort the central or fundamental prob- 
 lem of the science of logic itself. For logic, as we 
 have seen, is a study of the methods by which mean- 
 ings can get asserted, and how asserted meanings 
 can get expressed in propositions. It is because 
 meaning tends to elude us, and because words are 
 not always, if they are ever, faithful representatives 
 of ideas, because, that is to say, ideas and words 
 are both equivocal, that we are compelled, if the 
 aims of thinking are to be attained, to study the 
 sources of this uncertainty, and to derive guidance 
 from the knowledge that we thus obtain. Ambi- 
 guity, therefore, is a term that describes a natural 
 condition of human thinking, as well as a natural 
 indefiniteness of human speech. But, as we all 
 know, vagueness in an idea and indefiniteness in 
 speech, have many sources ; and it will not be until 
 we have reached the end of our studies that we 
 shall have reviewed even the more important ones. 
 Ambiguity in the meaning and application of words, 
 therefore, is part of a much larger problem ; but in 
 this chapter we shall consider only the ambiguity 
 that arises in connection with our use of words. 
 
DEFINITION AND THE PREDICABLES 165 
 
 Translation. One of the most common means for 
 the removal of ambiguity is translation. Thus, if 
 what we say is not understood, or is in danger of 
 being misunderstood, we often translate the same 
 idea into another set of words in the hope that the 
 ambiguity may be removed. This is a common prac- 
 tice both in literature and in ordinary conversation. 
 When, for example, Shakespeare makes Hamlet say, 
 
 O, that this too too solid flesh would melt, 
 Thaw, and resolve itself into a dew; 
 Or that the Everlasting had not fixed 
 His canon 'gainst self-slaughter! 
 
 he is putting into Hamlet's mouth words that ex- 
 press a single idea twice over, namely, the longing 
 for death as a means of escape from his troubles. 
 If, again, a teacher should ask his class a question 
 which fails to elicit the correct answer, he would 
 probably restate the question in the light of the 
 difficulties that the answers had thrown upon the 
 class's understanding of the question as first stated. 
 If further, to take an illustration already used, we 
 were to say of a given individual, 'He was a man 
 who always chose a mean line action,' and we were 
 misunderstood to say that he was a man 'devoid of 
 a generous disposition', we should probably substi- 
 tute for the word 'mean,' the word 'moderate' in a 
 re-statement of what we had intended, in the first 
 place, to say. There is no doubt that this habit of 
 translating into a variety of forms the ideas we wish 
 to express is so inveterate that most of us talk more 
 
166 A TEXT-BOOK OF LOGIC 
 
 than is necessary for understanding, and many of 
 the books we ordinarily read are much longer than 
 they need be. But the care we exercise in making 
 our meaning clear is grounded in a healthy instinct ; 
 it is the respect we pay to the demand for unambig- 
 uous statements. 
 
 When Translation may be Employed. If we look 
 at the class of cases illustrated in the preceding 
 paragraph, we shall discover that the source of their 
 ambiguity does not lie in the fact that our words 
 have a vague fringe of meaning, but that the centre 
 or core of meaning has been misunderstood. When- 
 ever ambiguity arises from our unfamiliarity with 
 the meaning of the words in which ideas are ex- 
 pressed, what is needed is that the same idea be 
 translated into a set of words with the meaning of 
 which we are familiar. 
 
 In translation, then, ambiguity arises from the 
 fact that the central meaning of a word is not pre- 
 cisely determined, either because the word carries 
 no meaning at all, or because it carries a meaning 
 that renders the whole sentence indefinite. If, for 
 example, you do not know what the word 'com- 
 mandeer' means, you are not likely to understand 
 any statement in which the word occurs, for 
 example, 'My motor has been commandeered.' To 
 meet such a situation it is obvious that some other 
 word or explanatory statement would have to be sub- 
 stituted for the meaningless 'commandeered.' If, 
 to take another case, a class in logic were given the 
 task of stating the meaning of the assertion 'Non 
 
DEFINITION AND THE PREDICABLES 167 
 
 omnis moriar (I shall not all die),' and it proved 
 difficult or impossible, the reason would be that am- 
 biguity spreads over the whole sentence from the 
 indefiniteness of the word 'all/ an indefiniteness 
 that is not due, as in the former illustration, to the 
 absence of meaning, but to the conflict of two mean- 
 ings that are not clearly distinguished. In this ex- 
 ample, the Latin word omnis has a distributed mean- 
 ing, and if the Roman had wished to express the 
 collective meaning of 'all/ he would have written 
 cunctis. We have only, therefore, to point out the 
 distributed use of the word 'all' to enable the student 
 to see that the meaning of the statement is 'some 
 part of me is immortal/ 
 
 When Definition is Required. The conditions un- 
 der which definition is required are different from 
 those under which translation is most effective. 
 Definition is called for when the work-a-day mean- 
 ing of the word that requires defining is already 
 known, but is becoming obscured by the fact that, 
 through the similarity of its meaning to other 
 words, its distinctive characteristics are in danger 
 of being overlooked. For instance, the most obvious 
 common characteristic of the violin, viola, 'cello, 
 and bass viol is their shape, and it is this that 
 leads one to regard all of them, on first ac- 
 quaintance, as, let us say, violins. Our knowledge, 
 that is to say, emphasises the common likeness that 
 exists between the several instruments named, and 
 there is confusion of one thing with another because 
 the differences which give to these objects a distinct 
 place in the universe of musical instruments have 
 
168 A TEXT-BOOK OF LOGIC 
 
 been overlooked. The confusion does not arise from 
 what is included, but from what is omitted, and 
 what is omitted, in this case, lies, outside the centre, 
 at the boundaries of the words' meanings. To state 
 it generally, the meanings of closely related words 
 encroach upon one another when the boundaries 
 that keep their meanings distinct are overlooked or 
 broken down. Now it often happens that the sense 
 of what we say depends to a large extent upon a 
 word's ability to suggest just such differences as, 
 in the illustration used, we persistently ignored. 
 When this happens ambiguity is sure to result, an 
 ambiguity, let it be observed, that is due to the con- 
 fusion of closely related things. In such a case, the 
 practically important problem is to find some 
 method by which ambiguity of the kind here in 
 question can be overcome when it exists, or be 
 avoided when it does not. 
 
 The Method of Definition. In any case of ambi- 
 guity that can be overcome by definition, the indefi- 
 niteness of the word's meaning which occasions the 
 ambiguity is due to our failure to mark off the 
 boundaries of this meaning from those of other re- 
 lated meanings. Indefiniteness of this sort in the 
 meanings of words may be illustrated if we ask our- 
 selves, for example, what we understand by a bal- 
 loon and an air-ship. The conspicuous central mean- 
 ing of the two words is doubtless the fact that they 
 are machines that travel in the air ; but if they mean 
 no more than this, we shall very soon be calling each 
 by the name of the other, or we shall be calling all 
 
DEFINITION AND THE PREDICABLES 169 
 
 machines that travel in the air by the name of the 
 one or the other. It is in cases like this, as we have 
 seen, that the definition of words is necessary. 
 How, then, shall we go about the task of defining? 
 Obviously, by the way of comparison, by the com- 
 parison of the things which our words denote. Thus, 
 if we wish to make our meanings of the words bal- 
 loon and air-ship precise, we compare an air-ship 
 with a balloon, and this comparison will lead to the 
 discovery that they differ from one another in the 
 method of their locomotion: the air-ship is driven 
 by an engine and the balloon is not. We shall, then, 
 call anything an air-ship which travels in the air 
 and is driven by an engine, and the word balloon 
 will be reserved for any air-traveling machine which 
 depends for its locomotion upon the air-currents. 
 This method of definition is for all ordinary purposes 
 the most practical, and it lends itself to the require- 
 ments of the specific occasions which make defini- 
 tion imperative. We get, that is to say, the mean- 
 ing that suits the purpose of the statement. Con- 
 stant practice in the comparison of what words 
 denote will not only render our meanings more pre- 
 cise, but free us from that indefiniteness which 
 comes from an exclusive familiarity with the dic- 
 tionary meanings of words; for what a dictionary 
 cannot do, and what comparison does, is to render 
 the meanings of words appropriate to the particular 
 contexts in which they occur. By the method of 
 comparison we find the relevant meaning, the mean- 
 ing that is required by the universe of discourse 
 
170 A TEXT-BOOK OF LOGIC 
 
 within which our thought is moving, and by the 
 purpose which controls our particular assertions. 
 
 Definition per genus et differentiam. By defini- 
 tion, as we have seen, we aim to substitute definite- 
 ness for indefiniteness in the meaning of our words, 
 and thus to avoid ambiguities of statement. We 
 have seen, also, that not all cases of ambiguity are 
 overcome best by definition, but only, or particularly, 
 those cases in which the vagueness of the boundaries 
 of a word's meaning obscures the sense of what 
 we wish to say. In definition, therefore, we seek 
 to limit the range of a word's meaning, by giving 
 an appropriate degree of definiteness to its fringe 
 or outlying area. 
 
 Now it is quite obvious that we cannot limit 
 the meaning of our words in the way required by 
 definition if these words are used or understood by 
 us with no meaning at all. We cannot talk about 
 limiting the extent of our words' meanings unless 
 these words are used, and are understood, in some, 
 however vague, sense. Hence, as we said above, 
 the central meaning of words is not in question in 
 these cases of ambiguity ; it is only the range of the 
 word's meaning that is in doubt. It would seem, 
 therefore, that the limitations that we put upon 
 our meanings in defining them must have some rela- 
 tion to these meanings themselves, but the particular 
 direction in which the limitation is made depends 
 upon the purpose for which we are seeking the defi- 
 nition. To take a simpler illustration, if the purpose 
 for which we need a definition of 'water' is domes- 
 
DEFINITION AND THE PREDICABLES 171 
 
 tic, we may say that it is a liquid which is useful 
 for cleansing; but if our interests are chemical, we 
 must say that the liquid is composed of two mole- 
 cules of hydrogen and one of oxygen. In both in- 
 stances, we start with the central idea of water as 
 a liquid, and in both we limit the range of this 
 meaning in a direction which is determined by the 
 purpose or interest that the definition is to serve. 
 It would seem, consequently, that every definition 
 has two parts, a central and a peripheral, and that 
 these are different, though related, aspects of a 
 word's explicit meaning. 
 
 Now the two parts of which, as we have seen, 
 the meaning of words is comprised are called in 
 logic the genus and the differentia respectively. By 
 the genus we mean the clear centre, and by the 
 differentia the vague periphery of a word's conno- 
 tation. The connection between the two is obvious 
 if we remember that both are specifications of a 
 single meaning. Since, therefore, in defining a 
 word's meaning we start with the recognition of 
 its genus, the differentia cannot add to that meaning 
 anything inconsistent with what the genus already 
 connotes. That is to say, we must look within the 
 range of meaning broadly marked out already by 
 its genus for the marks that make the meaning of 
 a word distinct. The differentia must lie within the 
 genus, and not outside it, if we are to mark off from 
 encroaching meanings the one that, by definition, 
 we are trying to make distinct. For what lies out- 
 side any genus belongs to another genus, or is that 
 
172 A TEXT-BOOK OF LOGIC 
 
 genus itself, and is not likely to threaten us with 
 ambiguity; but the distinctions that lie within a 
 genus are likely to be overlooked because of the com- 
 mon meaning that pervades all that belongs to the 
 genus. For example, no one is in any danger of 
 confusing a typewriter with the table on which it 
 stands because each belongs, in our common ac- 
 quaintance with it, to a different genus, the one to 
 the genus 'objects for writing with,' and the other to 
 the genus 'objects for placing things upon/ But if, 
 to take another illustration, the poet or philosopher 
 or scientist were to mistake the world of his imagi- 
 nation for the world of his actual experience, this 
 would be because he had failed to observe the marks 
 that keep the two worlds distinct. If, again, the 
 student were to use the words 'university* and 'col- 
 lege' synonymously, this would be because he had 
 failed to notice, within the meaning that both have 
 in common, the specific difference by which the one 
 is distinguished from the other in the same genus. 
 From these statements and illustrations it is obvious 
 not only how genus and differentia are related to 
 each other in a logical definition, but also what the 
 terms themselves signify. Thus, by a genus is meant 
 a group of qualities belonging to a number of par- 
 ticular objects in common. The word is also used to 
 denote any group of objects when these objects are 
 thought of as possessing common qualities. By a 
 differentia, on the other hand, is meant the specific 
 difference by which a distinct place is given to an 
 object within a genus by reason of its possessing a 
 
DEFINITION AND THE PREDICABLES 173 
 
 quality, or group of qualities, that does not belong 
 to any other member of its genus. Hence, in looking 
 for the differentia of an object we must look for some 
 quality, or group of qualities, that does not belong to 
 any other object of the group to which this object 
 belongs. When this quality or group of qualities 
 is not clearly apprehended we are liable to confuse 
 one thing with another. 
 
 Verbal and Real Definition. The distinction be- 
 tween real and verbal definition, or, as it is some- 
 times stated, between scientific and nominal defini- 
 tion, is as old as Aristotle, although in the case of 
 verbal definition modern writers do not seem agreed 
 as to how it should be understood. By a real or 
 scientific definition is meant a definition that is based 
 upon and gives a description of the essential nature 
 of the object which the word to be defined denotes. 
 Far example, a 'liquid' is defined as that form of 
 matter in which the molecules move with perfect 
 freedom without changing their size. Verbal or 
 nominal definitions, on the other hand, have received 
 at least two different interpretations. The first, or 
 Aristotelian, interpretation bids us regard as ver- 
 bal definitions the current or popular meanings of 
 words. For example, the definition of a house as 'a 
 building in which people live' would be, on this in- 
 terpretation, a verbal definition. The second inter- 
 pretation would make any definition verbal when 
 the word in question is used to indicate what any- 
 thing is called. For example, the definition of the 
 word 'dog' is verbal when it fails to convey any 
 
174 A TEXT-BOOK OF LOGIC 
 
 information about the essential qualities of the ob- 
 ject that the word denotes, and connotes only those 
 qualities which make the use of the word appro- 
 priate. 
 
 Now the distinction of real and verbal definition, 
 and the variations of the sense in which verbal defi- 
 nitions are understood, are interesting, from a log- 
 ical point of view, because they raise the question 
 whether in definition we are dealing with thoughts 
 or things, with the nature of objects, or with our 
 interests and purposes in their relation to objects. 
 According to the view of logic which we are ex- 
 pounding, no answer can be given to this question 
 which ignores the intimate connection of thoughts 
 and things. In the pursuit of knowledge, we are not 
 interested exclusively in either thoughts or things; 
 knowledge, as we have shown, exists in the form 
 of thoughts-about-things. If this is borne in mind, 
 it will be evident that in all our efforts to avoid 
 ambiguity we strive to bring our thoughts into rela- 
 tion with things, and things into relation with 
 thoughts; and in definition it is sometimes the one 
 and sometimes the other of these factors of knowl- 
 edge that requires to be made explicit. In the light 
 of this statement, the distinction of verbal and real 
 definition is not an absolute but a relative one, and 
 were it not for the fact that our words need to be 
 wedded to fixed meanings, and meanings to be fixed 
 and made definite by the use of words, the distinc- 
 tion would have no particular logical interest, and 
 might vanish entirely. The distinction, however, 
 
DEFINITION AND THE PREDICABLES 175 
 
 persists and is likely to persist, because our knowl- 
 edge is always in different stages of development, 
 and because with the improvement of knowledge 
 old words receive more precise meanings, and new 
 terms are constantly taking their place in the vocab- 
 ulary of the people. But while this is true, it is 
 quite clear that the goal toward which we move in 
 definition is a truer insight into reality, and the 
 preservation of this insight in terms that adequately 
 express it. 
 
 The Relation of Purpose to Definition. We have 
 said that the aim of every definition is to make our 
 knowledge of things more precise, and to fix this 
 knowledge in words. So far as this is true, we are 
 emphasising the relation of definition to the objects 
 of our knowledge. But what objects and what fea- 
 tures of objects are of importance for knowledge, 
 depends upon the purpose for which the definition 
 of these objects is sought. A change in purpose is 
 liable to produce a corresponding change in the defi- 
 nition. For example, if my purpose is to ascertain 
 the structural character of a circle, my definition 
 will call attention to the fact that a circle is a plane 
 figure bounded in such a way that all straight lines 
 drawn from a fixed point, called the centre, to this 
 bounding line are of equal length. If, on the other 
 hand, my purpose is to enable one to draw a circle, 
 it will then be defined as the plane figure described 
 by a point moving at a given distance around an- 
 other fixed point. This is called, in contrast to the 
 structural, a genetic definition. It should be ob- 
 
176 A TEXT-BOOK OF LOGIC 
 
 served that the distinction between structural and 
 genetic definition is not confined to mathematics; 
 the distinction, that is, does not depend on the sub- 
 ject matter, but upon the purpose for which the 
 definition is sought. But every case of definition 
 whether structural or genetic is per genus et differ- 
 entiam, a form of definition which we must take as 
 typical of all definition whatsoever. 
 
 Tests of a Definition. In text-books of logic, it 
 is customary to enumerate a number of other rules 
 of definition than the one to which our attention has 
 been exclusively directed. There results from this 
 mode of presenting the subject an impression of 
 complexity and difficulty that is really foreign to it, 
 and the student is deprived of the incentive that 
 comes from a simple and unencumbered statement 
 to make a practical use of that rule. We, therefore, 
 emphasise again the fact that all definition is to be 
 sought per genus et differentiam, and that this rule, 
 when properly applied, relieves of ambiguity any 
 statement that is caused by indefiniteness in the 
 meaning of words, and that it is the only one where- 
 by this result can be accomplished. 
 
 The only question remaining on our hands is, 
 then, how we are to know whether the rule has been 
 properly applied. It is as an answer to this ques- 
 tion that the other so-called rules have their value; 
 and because they provide us with an answer to this 
 question they are not rules of definition at all, but 
 tests of the accuracy of definitions reached in some 
 other way. We shall consider them in this light in 
 
DEFINITION AND THE PREDICABLES 177 
 
 the following paragraphs, and thereby make the 
 one rule of definition itself more definite. 
 
 In the first place, let us recall the fact that the 
 object of definition is to limit the extent of a word's 
 meaning, and in limiting it to make it more exact. 
 Omnis determinatio limitatio est: we make our 
 knowledge of objects definite by limiting the range 
 of the object's nature of which our knowledge, at 
 any time, takes account. Nowhere more than in the 
 intellectual life does the proverb 'grasp all lose all' 
 have a more pertinent application. Only if we are 
 willing to let some things go, can we gain anything 
 at all. But in order to gain something, we must 
 systematically eliminate what does not have a bear- 
 ing upon the purpose for which knowledge is being 
 sought. And, as we have shown, definition is a 
 means of systematically eliminating encroaching 
 meanings which are threatening the definiteness of 
 our assertions. It would seem, therefore, that one 
 of the dangers to which our definitions may be ex- 
 posed is to be found in their particular range: our 
 definitions may be either too broad or too narrow. 
 We shall examine each of these cases separately. 
 
 If the genius of a definition is not proximate our 
 definition is likely to be too broad. For example, if 
 we define a square as a quadrilateral figure (genus) 
 whose angles are right-angles (differentia), it is 
 obvious that we are in danger of confusing a square 
 with an oblong which is also a quadrilateral rec- 
 tangular figure. The definition is too wide. To 
 
 12 
 
178 A TEXT-BOOK OF LOGIC 
 
 rectify the definition we shall have to compare the 
 square with an oblong, and then we shall observe 
 that while both are quadrilateral, this is not their 
 nearest genus, that is, it does not contain all the 
 qualities that they have in common. Besides being 
 quadrilateral they are both rectangular. The class, 
 therefore, to which they both belong is quadrilateral 
 rectangle. Now, within this class, the differentia 
 of the square will be equilateral, having all its sides 
 equal. Our finished definition of a square will, 
 therefore, be 'a quadrilateral rectangle having all its 
 sides equal/ 
 
 If the differentia of a definition is not exact our 
 definition is likely to be too narrow. By the differ- 
 entia being exact we mean that it must be such that 
 only the objects denoted by the term we are defining 
 possess the attribute in question. Suppose we were 
 to define man as a civilised animal, the differentia 
 'civilised' would not be exact, and the definition too 
 narrow, because it excluded from the class, man, 
 all individuals who had not reached a certain stage 
 of culture. To test the accuracy of our differentia 
 we may ask ourselves the question : Do all and only 
 the objects denoted by the term we are defining 
 possess the quality connoted by the differentia by 
 means of which we are seeking to mark off the 
 meaning of the term from that of other closely 
 related terms? If not, the definition will be too 
 narrow. 
 
 After we have done the best we can to secure 
 the accuracy of our definition in the ways mentioned, 
 
DEFINITION AND THE PREDICABLES 179 
 
 we may then examine the definition as a whole. We 
 can do this if we remember that a true definition 
 can always be simply converted. If it is true, for 
 example, that 'a house-dog is a domestic animal that 
 barks/ then, if our definition is accurate, it must be 
 true that 'a domestic animal that barks is a house- 
 dog/ That is to say, the object defined (the defini- 
 endum) and the definition must be commensurate. 
 Or, to state the same fact another way, whatever 
 can be relevantly predicated of the object defined 
 must be predicable of the definition, and vice-versa. 
 This rule guards against anything superfluous in 
 definition. 
 
 Further, the terms of the definition must be of 
 the same order as the term defined. If, for example, 
 we defined the body as 'the visible garment of the 
 soul/ it is obvious that the word soul belongs to the 
 order of spiritual facts, and is transferred to the 
 physical order, the order of the term defined. The 
 uselessness of definitions of this kind may be over- 
 come if we take our clue to the order of the terms 
 in which our definition must be stated from the 
 order of the term to be defined. Hence, to satisfy 
 this requirement, we may ask ourselves the ques- 
 tion : Are all the terms of the definition homo- 
 geneous with the term defined? In this way we 
 avoid the indefiniteness that arises from the use of 
 figurative language. 
 
 Another requirement of a good definition is that 
 the terms of the definition should be more ele- 
 mentary than the term defined. The elementariness 
 
180 A TEXT-BOOK OF LOGIC 
 
 of a term is determined with reference to the uni- 
 verse within which the term to be defined belongs. 
 For example, the terms 'rational' and 'animal' are 
 more elementary than the term 'man' of which they 
 are predicated as the definition; and in the same 
 way the terms 'mammal' and 'living in the ocean' 
 are more elementary than the term 'whale.' By ele- 
 mentary, that is, is meant elementary in the field 
 of knowledge to which the term to be defined re- 
 fers, and not to the range of information that may 
 at any time be current. Hence, for one who has no 
 acquaintance with the field of knowledge with which 
 the term is connected, we may remove the ambi- 
 guity that exists in the meaning of the term better 
 by pointing out a specimen of the class or kind of 
 thing that the term denotes than we can by a 
 definition. 
 
 Again, a term must not be defined by the use 
 of the term itself or by one of its synonyms. If 
 this occurs we have what is called a circular defini- 
 tion. For example, if we define a power as 'a force 
 that tends to produce motion,' we are obviously 
 guilty of a breach of this requirement since the word 
 force has the same meaning as the word to be de- 
 fined. 
 
 Finally, the form of our definition must be pos- 
 itive if the term to be defined is positive, and neg- 
 ative if the term to be defined is negative. For 
 example, the term 'gentleman' has a positive mean- 
 ing, and, therefore, it would be a breach of this 
 requirement if we were to define it as 'a man who 
 
DEFINITION AND THE PREDICABLES 181 
 
 has no definite means of support.' But if we were 
 to define an alien as 'a man who is not a citizen of 
 the country with respect to which he is declared an 
 alien,' we should satisfy the requirement, because 
 the term alien carries with it a negative meaning. 
 The Problem and Classification of the Predicables. 
 Whatever can be predicated of a subject is called 
 a predicable. Now if we ask ourselves the ques- 
 tion, What sort of things can be predicables, i. e., 
 can be predicated of a subject? we have definitely 
 placed before ourselves an inquiry that engaged the 
 attention of Aristotle, and again of Porphyry six 
 hundred years after Aristotle's time. The answers 
 that Aristotle and Porphyry gave to this question 
 may be placed in two separate columns thus : 
 
 ARISTOTLE'S LIST OP PORPHYRY'S LIST OF 
 
 PREDICABLES PREDICABLES 
 
 Definition Genus 
 
 Genus Species 
 
 Differentia / Differentia 
 
 Proprium Proprium 
 
 Accident Accident 
 
 The various kinds of things that can form the pred- 
 icates of logical propositions are the kinds of things 
 indicated by the names in these two lists. 
 
 An examination of these lists will show that they 
 differ in the substitution by Porphyry of 'species' 
 for Aristotle's 'definition/ the other four predi- 
 cables being the same. But although apparently 
 only a slight difference, this change indicates a dif- 
 
182 *A TEXT-BOOK OF LOGIC 
 
 ference in the doctrine of definition of sufficient sig- 
 nificance to demand a word or two of explanation. 
 The significance of this difference in the two lists 
 can, perhaps, be seen if we remark that the question, 
 What sorts of thing can be predicated? is not un- 
 connected with the question, What kinds of thing 
 can be defined? We have seen, for example, that 
 in logical propositions we are concerned with both 
 subject and predicate terms, and it has been made 
 clear that our predicate terms must not only be 
 predicable, but predicable of the objects denoted by 
 our subject terms. If, for example, there should be 
 anything indefinable, such a thing would correspond 
 to what is called an individual ; and of such individ- 
 ual it is obvious that we cannot affirm a genus and 
 a differentia. Now, it is the difference between the 
 views of Aristotle and Porphyry as to the kinds of 
 thing that are capable of definition that accounts for 
 the difference in their lists of predicables. Aristotle 
 held that it is only as a universal or species that 
 anything could be defined. Porphyry held that the 
 subject of predication might be not only a species, 
 but also an individual. It was, therefore, reason- 
 able to include species in his list of predicables, for, 
 doubtless, its species can be predicated of an indi- 
 vidual ; but it would have been a mere tautology to 
 predicate species of itself as would have happened 
 if this predicable had been included in Aristotle's 
 list. 
 
 Our exposition of the doctrine of the predicables 
 will follow in the main the Aristotelian view. We 
 
DEFINITION AND THE PREDICABLES 183 
 
 shall assume that the subject terms of logical prop- 
 ositions denote objects, or groups of objects, that 
 are thought of as possessing attributes which ex- 
 press the common nature of all the objects to which 
 the subject term can be applied. Now if it is asked 
 what can be predicated of objects so conceived, the 
 answer is given in the list of Aristotelian predi- 
 cables. Before, however, we consider in detail what 
 each of these predicables means, we may point out 
 that they are not all related to a subject in exactly 
 the same way. Some of the predicables are com- 
 mensurate with their subjects, and some are non- 
 commensurate. To the former class belong defini- 
 tion and proprium; to the latter, genus, differentia, 
 and accident. 
 
 The Commensurable Predicables. By a commen- 
 surate predicable is meant one that is found wher- 
 ever the subject of which it is predicated is found. 
 It is an attribute, or group of attributes, that is 
 always present when the object is present, and ab- 
 sent when the object is absent. This class of pred- 
 icables we shall explain briefly in this section. 
 
 The definition we have considered already. It is, 
 as we have seen, an answer to the question, What 
 is it? and this question may be asked of anything, 
 of an attribute as well as of a substance. For ex- 
 ample, if we ask what acceleration is, and the phy- 
 sicist were to answer, change of velocity per second, 
 he is offering this as a definition, that is, a state- 
 ment of what it is that makes anything the kind 
 of thing called acceleration. Similarly, when an 
 
184 A TEXT-BOOK OF LOGIC 
 
 organism is defined as a material body of which the 
 parts are reciprocally related as ends and means, 
 we should refuse to recognize as an organism any 
 object which did not manifest these particular char- 
 acteristics. The propositions, therefore, in which 
 the predicate terms claim to be definitions are those 
 in which the predicates also claim to be commensu- 
 rate with their subject terms. This is only another 
 way of saying, as we said above, that the state- 
 ments which embody definitions must be capable of 
 simple conversion. The definition states what is 
 essential to the existence of the objects denoted by 
 the term that is defined. 
 
 A proprium or property is an attribute peculiar 
 to or characteristic of an object, and is commen- 
 surate with its existence, but it is not an essential 
 part of its definition. We may state the relation 
 between the proprium and definition by saying that 
 by means of the proprium we develop the meaning 
 of a term from the point at which its definition 
 stopped. From this it will be obvious that whether 
 we go beyond the meaning that is assigned to a 
 term in its definition will depend upon a motive 
 other than that which makes definition necessary. 
 In other words, the propria of terms are those char- 
 acteristic features of an object's nature which re- 
 main after definition has removed any existing am- 
 biguity; and whether these are predicated as part 
 of the term's meaning will depend upon whether 
 special motives operate to make them explicit. For 
 example, an equilateral triangle may be defined as 
 
DEFINITION AND THE PREDICABLES 185 
 
 a three-sided plane figure having all its sides equal. 
 This statement is sufficient for the purpose of dis- 
 tinguishing this kind of triangle from all other 
 kinds. But if we were interested further in equi- 
 lateral triangles, we should find that they are also 
 equiangular, and this fact of being equiangular is 
 called a property of the kind of triangles in ques- 
 tion. Likewise, contractility, irritability, assimilat- 
 ing food, reproduction after its kind, are properties 
 of an organism as this term was defined above. 
 
 The Non-Commensurable Predicables. By a non- 
 commensurate predicable is meant any quality which 
 alone does not exhaust the nature of an object, or 
 which belongs to an object in some only of the ob- 
 ject's relations. In neither case is the nature of 
 the objects denoted by the term made entirely ex- 
 plicit. The following illustrations will make this 
 clear. 
 
 We may, in the first place, predicate of any sub- 
 ject the genus to which it belongs. That is to say, 
 we may affirm the area of clear meaning of a term, 
 and this may be all that is necessary to convey our 
 meaning. It is obvious that we are here dealing with 
 the class of cases that were considered above under 
 the head of translation. But, as we saw there, the 
 genus alone does not tell us all that is necessary 
 for a complete understanding of any object's nature. 
 The genus is, therefore, an incommensurable pred- 
 icable. We may, in the second place, predicate of 
 a subject its differentia, that is, that part of the es- 
 sential nature of the subject which distinguishes it 
 
186 A TEXT-BOOK OF LOGIC 
 
 from other species of the same genus. If, therefore, 
 we are in danger of ambiguity from a tendency to 
 confuse species, we may, to make our meaning clear, 
 resort to the method of calling attention to the 
 specific differences of the objects that we have hith- 
 erto failed to distinguish. But the differentia alone, 
 as we have seen, does not exhaust the nature of any 
 object, and it is not, therefore, a commensurable 
 predicable. In the third place, we may predicate 
 some attribute not included in the definition of a 
 subject, that is to say, an attribute that may or may 
 not belong to the subject. For example, there is 
 nothing in the nature of a pen that it should be 
 made by a particular firm, or that it should belong 
 to a particular person. These are accidental rela- 
 tions, and belong to the pen merely as an individual. 
 All such attributes, not contained in the definition 
 or proprium, are called accidents. 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Ch. II., III. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Pt. I., 
 Ch. V. 
 
 J. G. Hibben, Logic Deductive and Inductive, Chs. IV., V. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lesson XII. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. V. 
 
 W. Minto, Logic Inductive and Deductive, Pt. II., Chs. I., II. 
 
 C. Read, Logic Deductive and Inductive, 3d Edition, Ch. 
 XXII. 
 
 W. J. Taylor, Elementary Logic, Chs. III., VI. 
 
DEFINITION AND THE PREDICABLES 187 
 
 ADVANCED 
 
 R. W. B. Gibson, The Problem of Logic, Chs. II., III. 
 
 H. W. B. Joseph, An Introduction to Logic, Chs. IV., V. 
 
 H. Lotze, Logic, Bk. II., Ch. I. 
 
 J. S. Mill, A System of Logic, Bk. I., Chs. VII., VIII. 
 
 F. C. S. Schiller, Formal Logic, Chs. V., VI. 
 
 C. Sigwart, Logic, Pt. II., 44. 
 
 J. Venn, Empirical Logic, Ch. XI. 
 
 J. Welton, A Manual of Logic, Vol. I., Bk. I., Chs. III., V. 
 
 QUESTIONS 
 
 1. From what two standpoints may the logical discussion 
 of terms be carried on, and to what new problems does 
 such a discussion give rise? 
 
 2. Define each of the problems enumerated in your answer 
 to the previous question. 
 
 3. Define the nature and limits of the demand for non- 
 ambiguous statements. 
 
 4. What is the practical importance of being able to make 
 non-ambiguous statements? 
 
 5. State and criticise the traditional doctrine of ambiguity. 
 
 6. In what sense can ambiguity be said to be the funda- 
 mental problem of logic? 
 
 7. Explain the nature of translation as a method of over- 
 coming .ambiguity. 
 
 8. What conditions call for the employment of translation 
 in the removal of ambiguity? 
 
 9. What conditions call for the employment of definition in 
 the removal of ambiguity? 
 
 10. Explain and illustrate: The method of definition is 
 comparison. 
 
 11. What is meant by: Logical definition is per genus et 
 differentiam? 
 
188 A TEXT-BOOK OF LOGIC 
 
 12. What do you understand by real and verbal definition? 
 In what two senses may verbal definition be understood? 
 
 13. What is the logical significance of the distinction of 
 real and verbal definition? 
 
 14. What is the relation of purpose to logical definition? 
 
 15. In what two ways may our definitions fall short of 
 being strictly accurate? 
 
 16. Explain and illustrate how a definition may be too broad. 
 
 17. Explain and illustrate how a definition may be too nar- 
 row. 
 
 18. How does the simple conversion of a definition guard 
 against introducing anything superfluous into the defi- 
 nition? 
 
 19. How may we guard against figurative language in defi- 
 nitions? 
 
 20. Explain: The terms of a definition should be more 
 elementary than the term to be defined. 
 
 21. What is meant by a circular definition, and how may 
 circular definitions be avoided? 
 
 22. What do you understand by a predicable? 
 
 23. How many predicables are there, and what is the dif- 
 ference between Aristotle's and Porphyry's lists of the 
 predicables? 
 
 24. What is the relation of the problem of the predicables 
 to that of definition? 
 
 25. Explain why Aristotle's and Porphyry's lists of the 
 predicables differ? 
 
 26. What is meant by a commensurable predicable? 
 
 27. Which of the predicables are commensurable? 
 
 28. In what sense is a definition a predicable? 
 
 29. What is a proprium? 
 
 30. What is meant by a non-commensurable predicable? 
 
 31. Explain genus, differentia, and accident as non-com- 
 mensurable predicables. 
 
DEFINITION AND THE PREDICABLES 189 
 
 EXERCISES 
 
 1. Write three ambiguous statements whose ambiguity can 
 be removed by translation. 
 
 2. Write three ambiguous statements whose ambiguity can 
 be removed by definition. 
 
 3. Define, and state, in each case, the purpose that the 
 definition is intended to serve: anger, river, house, em- 
 peror, metal, justice. 
 
 4. Criticise the following definitions, and show what rules, 
 if any, are violated by them: 
 
 (1) Thunderbolts are the winged messengers of the 
 gods. 
 
 (2) Round is a quality that belongs to any rotund 
 object. 
 
 (3) Man is a vertebrate animal. 
 
 (4) An inflammation is some abnormal condition of 
 one of the body tissues. 
 
 (5) An absentee is a person who does not live in his 
 own country, or who does not look after his own 
 property. 
 
 (6) Prudence is the ballast of the moral vessel. 
 
 5. Construct three definitions for the purpose of showing 
 how definition depends upon comparison. 
 
 6. To which of the Predicables does each of the following 
 predicates belong : 
 
 (1) The whale is a mammal. 
 
 (2) The whale is a vertebrate. 
 
 (3) The whale lives in the ocean. 
 
 (4) The whale was caught and brought to land. 
 
 (5) Logic is a good mental discipline. 
 
 (6) The tiger is a predatory animal. 
 
 (7) Englishmen are keen sportsmen. 
 
 (8) Lord Shaftesbury was a great philanthropist. 
 
 7. Give the genus, differentia, proprium, and accidens of 
 (a) peninsula, (b) triangle, (c) affirmative statement, 
 
CHAPTER VII 
 DIVISION AND CLASSIFICATION 
 
 Relation of Definition and Division. Whenever 
 ambiguity threatens any statement on account of 
 the vagueness of the outlying range of a word's 
 meaning, we may remove the ambiguity by defining 
 the word's meaning. The method of definition, as 
 we saw in the last chapter, is comparison. By this 
 method we distinguish a meaning from one or more 
 others with which we are in danger of confusing it, 
 and our result is a division of the genus into two 
 or more species. There is, however, nothing in the 
 nature or conditions of definition that, in principle, 
 assures us that all the distinguishable meanings of 
 a genus have been discovered, and nothing, there- 
 fore, that assures us that we have examined all the 
 species which belong to the genus from which our 
 definition starts. If, therefore, instead of asking 
 how one species differs from another, we wished to 
 know how many species there are in a given genus, 
 we should be confronted with a new problem which 
 it is the business of logical division to consider; for 
 by division we mean, in general, the method that 
 must be employed to develop systematically all the 
 species which belong to a genus. Now, if it is asked 
 why any one should raise such a question as this, we 
 can only say that the demand for non-ambiguous 
 statements may be left unsatisfied after making the 
 
 (190) 
 
DIVISION AND CLASSIFICATION 191 
 
 meaning of our words as clear as possible. Ambi- 
 guity, in other words, may be occasioned not only 
 by uncertainty in the connotation of terms, but also 
 by uncertainty in their denotation; and whenever 
 there is vagueness in either respect there is likely 
 to be a corresponding vagueness in the other. From 
 this point of view, logical definition and division are 
 closely connected problems, and they differ merely 
 as one stage differs from another in a single process. 
 In logical division we carry further the process that 
 begins in logical definition, and the object is to re- 
 move any remaining uncertainty in a word's mean- 
 ing. 
 
 What is Meant by Logical Division. The word 
 'division' is not well chosen to designate the process 
 that we have now to describe. If it should suggest, 
 as it ordinarily must, that it is the method by which 
 we split up a genus into its component parts, in 
 much the same way that a house-wrecker separates 
 the doors, windows, joists, etc., of the building he 
 is dismantling, we should be misled entirely in our 
 understanding of what the term means or the proc- 
 ess implies. If this were the sense in which we were 
 required to understand the word, its application 
 would not give us a clearer apprehension of a term's 
 meaning, but would result in the destruction of the 
 meaning altogether. It will, perhaps, set the mat- 
 ter in a clearer light if we say that logical division, 
 like logical definition, starts with species or con- 
 cepts, and that in both cases we are concerned with 
 the kinds in which the species is found realised. 
 
192 A TEXT-BOOK OF LOGIC 
 
 This being the case, we cannot say that a genus is 
 the sum of its species; we can only say that it is 
 differentiated into its species. 
 
 In logical division, we are concerned with the 
 relation of a genus and its species. But that rela- 
 tion, as we have just seen, cannot be one of a whole 
 to its parts; it is rather a relation in which the 
 species disjunctively enumerate the alternatives 
 which, when taken as an enumeration, denote the 
 range of a term's meaning. That is, by division we 
 analyse the denotation of a term's meaning. For 
 example, if we should divide the genus 'rectangle' 
 into two species, one with its adjacent sides equal, 
 and the other with its adjacent sides unequal, we 
 cannot mean by rectangle, in such a case, the sum 
 of these two species. 'Rectangle' does not mean the 
 square plus the oblong; it means either the square 
 or the oblong. That is to say, the genus is realised 
 in each of its species ; the species of any genus ex- 
 hibit distributively, not collectively, a word's mean- 
 ing. 
 
 If, now, we should seek to derive from these 
 statements about the nature of logical division a 
 rule which, when applied to any case, will serve as 
 a test of the accuracy with which the division has 
 been carried out, we may perhaps say that we must 
 be able to predicate the genus, or whole that is di- 
 vided, of each of the species of a logical division. 
 Thus, in the previous example, we called the oblong 
 a rectangle, and also the square a rectangle. Each 
 js the whole of what a rectangle is. To take another 
 
DIVISION AND CLASSIFICATION 193 
 
 illustration. The genus 'human being' may be log- 
 ically divided into 'man,' 'woman,' etc., and the genus 
 -human being of which they are the species, 
 may be predicated of each one, thus : 'a man is a 
 human being,' 'a woman is a human being,' etc. 
 
 In this discussion of the nature of logical divi- 
 sion we have seen (1) that logical division is the 
 process by which the range of a term's meaning 
 can be exhaustively determined. It follows from 
 this that the process of logical division can be ap- 
 plied only to what is in its nature general, in other 
 words, to a species or concept. The genus, species, 
 or concept to which the process of division is applied 
 is called the totum divisum. We have seen also (2) 
 that the sub-species of the whole that is divided 
 enumerate disjunctively the kinds into which the 
 whole is differentiated, that they are not the parts 
 which when taken together constitute the whole. 
 From this it follows (3) that we must be able to 
 predicate of each kind the qualities connoted by the 
 genus or whole that is divided. When this is not 
 possible logical division has not taken place. 
 
 Other Kinds of Division. It will help to keep the 
 meaning of logical division distinct, if we describe 
 the characteristics of other operations that go by 
 the same general name of division. Of these, there 
 are in particular three : metaphysical, physical, and 
 verbal division. These are, like logical division, 
 mental operations, but each serves a distinct pur- 
 pose. The purpose of logical division, as we have 
 
 13 
 
194 A TEXT-BOOK OF LOGIC 
 
 seen, is to enumerate the kinds or species into 
 which a genus is differentiated, or, what is the same 
 thing, the kinds or species in which the qualities of 
 the genus are realised. The purpose of metaphysical 
 division is to distinguish the several attributes 
 which are capable of being predicated of a genus. 
 This kind of division obviously lies at the founda- 
 tion of the problem of the predicables which was 
 considered in the last chapter. For the problem of 
 the predicables, as we saw, was concerned with the 
 character of the attributes that could be predicated 
 of any species. When, therefore, we divide a spe- 
 cies into its genus, differentia, proprium and acci- 
 dens, we are not employing what is technically 
 known as logical division, but a method that is 
 known as metaphysical division. The difference 
 between these two methods may be brought out in 
 the statement that in metaphysical division we 
 must be able to predicate of the genus the species 
 which our division has been the means of distin- 
 guishing; whereas in logical division the converse 
 statement holds true, that is, it is the genus which 
 must be predicable of the species. For example, if 
 we divide 'organism' into 'animals/ 'birds/ 'fishes' 
 and 'reptiles/ we have a logical division, a divi- 
 sion which makes it possible to predicate of each 
 species the genus which has been divided. If, on 
 the other hand, 'organism' is divided into 'living 
 creature/ 'capable of locomotion/ 'quadruped/ etc., 
 this is called a metaphysical division, a division 
 which makes it possible to predicate of the genus 
 
DIVISION AND CLASSIFICATION 195 
 
 each of the attributes which the division distin- 
 guishes. The purpose of physical division is to anal- 
 yse a whole or aggregate into the parts of which 
 it is composed. Thus, we may divide 'horse' into 
 head, legs, ears, tail, etc. This process is sometimes 
 called physical partition. It is distinguished from 
 the other kinds of division by the fact that neither 
 parts nor wholes can be predicated of each other. 
 For example, it is obvious that 'horse' is neither 
 head, nor legs, nor ears, etc.; nor can we say of 
 any one of these that it is horse. Verbal division is 
 sometimes mentioned as a separate form of division. 
 It is used to denote the act of distinguishing the 
 homonymous meanings of a word. For example, the 
 word 'hand' may mean either 'a labourer' or 'an 
 organ of the human body.' 
 
 Fundamentum Divisionis. We have seen that the 
 motive to logical division is found in the interest 
 we have in determining the whole denotation of a 
 term's meaning. Logical division is, therefore, the 
 method by which we systematically develop the de- 
 notation of terms whose meanings have been fixed 
 by definition. It follows from this that we cannot 
 divide a term whose meaning is unknown to us. 
 This fact is frequently overlooked by the student, 
 and he is apt to make the effort to put the method 
 into operation in a case in which his knowledge of 
 the totum divisum, or term to be divided, makes his 
 failure a foregone conclusion. Logical division pre- 
 supposes that the totum divisum has been given a 
 meaning by logical definition. If, consequently, we 
 
196 A TEXT-BOOK OF LOGIC 
 
 are required to determine the denotation of a term 
 with whose connotation we are unacquainted, we 
 must first determine the meaning of that term by 
 the method of logical definition. While, therefore, 
 logical division and logical definition are, as we 
 have seen, closely related processes, each has a dis- 
 tinctive role to play in the development of meaning. 
 With this caution in mind, we pass to a statement 
 of certain features of the method of logical division 
 which throw light upon the significance of the proc- 
 ess itself. What, we may ask, is the basis of divi- 
 sion? On what principle or principles are we to 
 proceed in any given case? By what are we to be 
 guided in working out a logical division? The 
 answer to such questions as these is usually given in 
 an exposition of what logicians call the fundamen- 
 tum divisionis. By a fundamentum divisionis is 
 meant some characteristic of the totum divisum 
 which, when systematically applied, develops differ- 
 ences among its members. Or, as it is sometimes 
 said, it is that aspect of the genus in respect of 
 which its species are differentiated. If, now, the 
 purpose of logical division is to develop differences 
 in respect of which species may be differentiated, 
 we shall have to seek in our definition of the totum 
 divisum for some indeterminate attribute which 
 can serve as the basis of our division. Now that 
 there should be something indeterminate in a defini- 
 tion will become perfectly clear if we recollect that 
 all that a definition aims to give is a meaning relevant 
 to the situation and purpose which made the defini- 
 
DIVISION AND CLASSIFICATION 197 
 
 tion necessary. There is no such thing as a complete 
 definition in any other sense than a relevant defini- 
 tion. The only other sense in which we can speak 
 of definitions being complete is that we are ac- 
 quainted with all the known meanings of a word. 
 But in that case we should not have a single defini- 
 tion but a series of definitions; and, of course, all 
 that we could say about that is that the series is 
 complete, not that the definition is. If, consequently, 
 our definition of a term enables us to make unam- 
 biguous statements, that is all that we can expect 
 of it; but it does not follow that the definition will 
 be sufficiently determinate for carrying out a logical 
 division. For example, 'man* has been defined as 
 a rational animal, and, as a definition, it serves its 
 purpose well enough. But if we consider the deno- 
 tation of the term's meaning thus defined, we shall 
 find that there is something indeterminate in the 
 word rational, for rationality, as we all know, ad- 
 mits of degrees. When, therefore, we assert of any 
 individual that he is a man, that is, a rational ani- 
 mal, we cannot be understood to imply a definite 
 degree of rationality, but only some degree. If, 
 however, we asked what degrees of rationality exist, 
 we should have to adopt some standard of ration- 
 ality, or state more carefully what we mean by 
 rationality in our definition of man. This standard 
 or statement would be, for the purpose of logical 
 division, our fundamentum divisionis. With respect 
 to this fundamentum divisionis, some individuals 
 will meet the requirements it lays down, and these 
 
198 A TEXT-BOOK OF LOGIC 
 
 we call normal ; others will fail to meet it, and these 
 we call abnormal. In the latter class, we find some 
 who fall below, and some who fall above the stan- 
 dard : the sub-normal and the super-normal respect- 
 ively. The sub-normal, again, may be divided into 
 dements, those in whom mental deficiency appears 
 subsequently to mental development, and aments, 
 those who have never attained normal mental devel- 
 opment. The aments may be divided, according to 
 the degree in which they depart from the normal, 
 into feeble-minded, imbecile, idiot. This division 
 may be shown in tabular form as follows: 
 
 Man 
 
 A 
 
 Nrmal Abnormal 
 
 A 
 
 Sub-normal Super-normal 
 
 Dements Aments Genius 
 
 ^_ A 
 
 f \ 
 
 Feeble-minded Imbecile Idiots 
 
 We may point out in this connection that every 
 division reacts upon the definition from which it 
 starts to make it more exact. For example, we 
 found the definition of man as a rational animal 
 defective because it neither stated what is meant 
 by rationality, nor what degrees of rationality were 
 to be recognised. . Both these deficiencies are made 
 good in logical division. Thus, to make our funda- 
 mentum divisionis clear, we may say that by ration- 
 ality we mean 'a degree of intellectual capacity suffi- 
 
DIVISION AND CLASSIFICATION 199 
 
 cient to enable its possessor to perform his duties 
 as a member of society in that position of life to 
 which he is born/ and the classes of those who ful- 
 fill these standard requirements or depart from 
 them either by way of excess or defect are the 
 normal, dements, feeble-minded, imbecile, idiot, 
 genius. When, therefore, we look back upon the 
 original definition from the standpoint of our 
 completed division, it has taken on a more definite 
 meaning. We now know not only what is specifically 
 meant by calling any man rational, but we also know 
 what are the different degrees in which rationality 
 may in any case be realised. In other words, our 
 division enables us to say that the concept 'man,' 
 when determined with respect to rationality, may 
 be realised in either one or the other of the forms 
 specified in the division. 
 
 Questions of Terminology. We shall postpone 
 further discussion of the problems of logical divi- 
 sion until we have explained the technical terms in 
 which the discussion must be carried on. For the 
 sake of completeness, we may recall that the term 
 totum divisum was used above to denote the whole 
 that is divided; it is the genus with which any 
 division starts. When viewed in relation to all the 
 species to which logical division gives rise, the 
 totum divisum is called the summum genus. The 
 species with which a division ends are called in- 
 firmae species. If, as in the illustration used in 
 the last section, our division is carried through a 
 number of stages, the intermediate species, that 
 
200 A TEXT-BOOK OF LOGIC 
 
 is, those that fall under the summum genus, are 
 spoken of as subaltern genera. When, however, 
 we wish to point out the relation that any one of the 
 subaltern genera has to the next below it in the 
 series, we designate this subaltern genus the prox- 
 imum genus. It will be observed that the totum 
 dioisum is a proximate genus with respect to the 
 next below it in the series, but a summum genus 
 with respect to all, whether one or more, that 
 lie below it in the series. The constituent or co- 
 ordinate species are those which are differentiated 
 at any single stage in the process of logical division. 
 These distinctions, it should be noted, are purely 
 relative, and the student will have no difficulty in 
 mastering the terminology if he observes that they 
 all hinge upon the meaning assigned to genus and 
 species. A genus is anything considered as a sub- 
 ject of division, and a species is always the end- 
 product of a division. The same thing, therefore, 
 may be both a genus and a species, but whenever 
 that is the case, the same thing is being looked at 
 from different points of view. 
 
 Rules of Logical Division. There are other fea- 
 tures of logical division than those that have been 
 already considered with which it is important that 
 the student should become acquainted. These we 
 shall state and illustrate in connection with our 
 enumeration and exposition of the rules of logical 
 division. 
 
 The first rule is that a logical division must pro- 
 ceed in all its stages upon one fundamentum divi- 
 
DIVISION AND CLASSIFICATION 201 
 
 sionis. The reason for this, of course, is found in 
 the nature of the problem that logical division is 
 set to solve. That problem is to develop the mean- 
 ing of a term so as to make determinate whatever 
 may have been left indeterminate in its definition. 
 If we did not keep within that aspect of a term's 
 meaning with which our logical division starts, 
 we should fail to develop this meaning from an in- 
 determinate to a more determinate form. In the 
 example used above, we found that a number of de- 
 grees of rationality exist, and that these must be 
 included in our definition of 'man' if this concept is 
 to be completely determined. If we had found, in 
 our division of the term, species of another kind, 
 let us say red man, yellow man, it would be evi- 
 dent that we had gone outside the fundamentum 
 divisionis, rationality, and that we had consequently 
 failed to determine that aspect of the term's meaning 
 with which we were concerned. Whenever this hap- 
 pens, whenever, that is, we fail to carry the division 
 through on a single principle, we are said to have a 
 cross division. All the species to which a logical 
 division gives rise must be the same in kind; and 
 this is possible only if we retain the same principle 
 of division throughout. Again, in carrying out a 
 principle of division, we aim to make our species 
 exclusive, to include, that is to say, in any one species 
 only that which is definitely excluded by the other 
 co-ordinate species. The constituent species of a 
 genus must not overlap. This requirement is ob- 
 viously related to that feature of a logical definition 
 
202 A TEXT-BOOK OF LOGIC 
 
 which emphasises the difference between two or 
 more conflicting meanings (differentia), as the 
 former requirement connects logical division with 
 the other aspect of definition which emphasises the 
 common likeness of these conflicting meanings 
 (g enus). 
 
 It is not difficult to apply the first rule of divi- 
 sion when the fundamentum divisionis is completed 
 in a single step. For example, if 'man' is defined as 
 'a rational animal possessing a skin-color of some 
 kind/ the latter part of the definition may become 
 for us a principle of division. Dividing man then 
 according to skin-colour we find the denotation of 
 the term to be as follows : 
 
 Man 
 
 ^ A ^ 
 
 f >\ 
 
 White man Black man Yellow man Brown man Red man 
 
 When, however, the division is carried through 
 several stages, as it frequently is, it may not be 
 apparent how a single principle can control the 
 whole series of divisions. If, for example, we were 
 to divide 'human being' into 'male' and 'female,' and 
 were then to divide 'female' into 'brunette' and 
 'blonde,' it is obvious that the fundamentum divi- 
 sionis in the first division is sex difference, and in 
 the second, complexion colour. In cases like this, 
 we cannot look upon the division as a series which 
 develops a single theme; we must regard it rather 
 as a chain of discontinuous divisions which contains 
 as many separate divisions as there are distinct 
 fundamenta. The fact that they can be written 
 
DIVISION AND CLASSIFICATION 203 
 
 consecutively does not have any logical significance ; 
 the reason for giving this form to them is econom- 
 ical; it saves time, when the end product of one 
 division is the starting-point of a new one, to con- 
 tinue in the serial order. If, however, our practice 
 were guided by logical requirements, we should re- 
 write our term whenever we intend to apply to it a 
 new principle of division. 
 
 Let us now consider the case of a division which 
 has the characteristics of a continuous series, that 
 is, a series which develops a single idea through a 
 number of stages. The significance of this case is 
 that it emphasises the importance and illustrates 
 the method of systematically developed knowledge, 
 of knowledge, that is, which proceeds at each step by 
 the smallest possible degrees of relevant difference. 
 Thus, in carrying out a division which develops its 
 meaning in a continuous series, we are counselled to 
 make the steps of the series as small as possible. This 
 is the purport of the Latin injunction, Divisio ne fiat 
 per saltum: you must not make your division go 
 by leaps. A division that is not systematically de- 
 veloped is useless for the purpose that put it in oper- 
 ation. But since, throughout all the stages that we 
 carry our division, we need to be guided by a single 
 principle, it is evident that at each stage of the divi- 
 sion we must use a fundamentum divisionis that is 
 some modification of the principle with which we 
 began the division. That is to say, each subordinate 
 fundamentum must fall within the meaning of the 
 original fundamentum. An illustration, borrowed 
 
204 A TEXT-BOOK OF LOGIC 
 
 from Gibson, will make this evident. Let us take 
 as our fundamentum divisionis, the side-relations of 
 'quadrilateral figures,' understanding by quadrilat- 
 eral figure 'a plane rectilinear quadrilateral figure.' 
 Our purpose is to develop the number of types which 
 belong to this class. According to their side-rela- 
 tions, 'quadrilateral figures' are either 'parallelo- 
 grams/ that is, figures whose opposite sides are 
 parallel and equal, or 'non-parallelograms.' Divid- 
 ing these species further according to the inclination 
 of their sides, a special form of the original funda- 
 mentum, we get, in the case of the parallelograms, 
 rectangle and non-rectangle ; and in the case of the 
 non-parallelograms trapezium, a figure in which 
 there are no parallel sides, and trapezoid, a figure in 
 which two of the sides are parallel but not equal. 
 Another specification of the original fundamentum 
 would be relative side-length. If we apply this to 
 rectangle we get square and oblong; and to non- 
 rectangle, rhombus and rhomboid, oblique figures 
 which correspond to the square and oblong respect- 
 ively. All these relations expressed in the form of 
 a genealogical tree are as follows: 
 
 Quadrilateral Figure 
 
 Parallelogram Non-parallelogram 
 
 Rectangle Non-rectangle Trapezium Trapezoid 
 
 Square Oblong Rhombus Rhomboid 
 
DIVISION AND CLASSIFICATION 205 
 
 The second rule is that a logical division must 
 be exhaustive. The reason for this rule is connected 
 obviously with the purpose that controls such divi- 
 sion, namely, to denote in orderly relation whatever 
 belongs to a certain genus. What the rule states 
 is that a place must be found, when the division has 
 been made, for everything that belongs to the genus 
 in one or other of the constituent species. It is only 
 another way of stating the purport of the rule to 
 say that the constituent species together must be 
 coextensive with the whole genus. The rule is in- 
 tended to guard against too narrow and too broad 
 division. When the division is too narrow some- 
 thing is omitted from, and when the division is too 
 broad something is added to, the genus, and which- 
 ever fault we may fall into, the division is rendered 
 useless. Instances of too narrow division are : 'men' 
 into 'good' and 'bad;' and 'objects' into 'useful' and 
 'ornamental.' Too broad division is likely to occur 
 whenever there is an indistinct apprehension of the 
 connotation of the terms we employ in our divisions. 
 Unless, therefore, a division is exhaustive, that is, 
 neither too narrow nor too broad, we have not really 
 divided at all ; for when the division is too narrow, 
 the constituent species are equivalent to only part of 
 the genus, and when it is too broad, they are equiv- 
 alent to the genus and something else. Whenever a 
 genus has been properly divided, the denotation of 
 genus and species must exactly coincide. 
 
 Dichotomy. Our discussion of logical division 
 has emphasised two things: (1) that our ability to 
 
206 A TEXT-BOOK OF LOGIC 
 
 use the method depends upon our knowledge of the 
 subject to which it is applied, and (2) that to insure 
 against omitting anything that really belongs to a 
 genus we must make our division exhaustive, and 
 that when this requires us to carry the division 
 through several stages, the steps between one sub- 
 division and another must be made as small as pos- 
 sible. Division is not, consequently, an easy method 
 to apply, although it is not difficult to understand; 
 but the difficulty is due primarily to the great com- 
 plexity of the material that nature presents for our 
 study. 
 
 Dichotomy is a traditional method of division 
 which has been supposed to relieve us of the diffi- 
 culties to which we have just referred, and to make 
 it possible, in the absence of any considerable knowl- 
 edge of the subject under investigation, to deter- 
 mine the species which may belong to it. If this 
 were true, we might omit the consideration of it 
 entirely on the ground that it is a merely formal 
 process ; if it is not true, we must consider its value 
 in relation to our effort to make our knowledge of 
 things systematic. That it is not true is the position 
 of modern logicians as it was of Aristotle. We must, 
 therefore, place this method in its relation to our 
 foregoing discussions. 
 
 First, let us inquire how dichotomy differs from 
 the form of division which we have just considered. 
 The characteristic of a dichotomous division is, as 
 the name implies, that it proceeds at each step of 
 the division by dividing a genus into two alternative 
 
DIVISION AND CLASSIFICATION 207 
 
 species. Now, if each step of such a division ex- 
 hausts the genus we are dividing, it is apparent that 
 one of the terms must be an indefinite or so-called 
 negative term. Thus, if we divide 'triangle' accord- 
 ing to the relations of the sides, we shall have at 
 the first division, if we take equality of all the sides 
 as the fundamentum, two species, 'equilateral' and 
 'non-equilateral.' Dividing the 'non-equilateral' 
 term with reference to the equality of two of the 
 sides, we shall have once more two species, 'isosceles' 
 and 'non-isosceles.' If we divide now the 'non- 
 isosceles' term on the basis of the only remaining 
 possibility, namely, the equality of one side with 
 itself, we get also two species, 'scalene' and, if there 
 are any, 'non-scalene.' The arrangement of these 
 divisions in a tree will illustrate the typical form 
 of division by dichotomy. Thus: 
 
 Triangle 
 
 A 
 
 Equilateral Non-equilateral 
 
 Isosceles Non-isosceles 
 
 "N 
 
 Scalene Non-scalene 
 
 From the foregoing statements and illustration, 
 it will be apparent that we cannot begin to divide 
 a term by dichotomy without having before our 
 minds some definition of the genus that we wish to 
 divide. Unless we knew, for example, that a tri- 
 angle was 'a plane figure bounded by three straight 
 lines,' we should not be able to divide it to determine 
 
208 A TEXT-BOOK OF LOGIC 
 
 its species. Dichotomy, as much as any form of divi- 
 sion, presupposes definition. Now, the connection 
 between dichotomy and definition per genus et differ- 
 entiam, may be expressed by saying that every such 
 division suggests a definition of the class we are 
 dividing, and that every definition implies a division 
 by dichotomy. Thus, to take the illustration already 
 used, a 'triangle' may be defined as 'a three-sided 
 plane figure whose sides have a certain relation to 
 each other;' and if we wish to make the indeter- 
 minate part of this definition determinate, we divide 
 by dichotomy in order to bring out the specific rela- 
 tionship of the sides to each other. 
 
 We may observe, further, that, applied to rela- 
 tively simple cases, dichotomy is a rather cumber- 
 some method of doing what can be accomplished 
 more expeditiously at a single step. There is no 
 reason, for example, why we should not divide tri- 
 angle into its constituent species at once ; for, in such 
 a case, it is not by the method of division, but by 
 reason of our acquaintance with the subject-matter, 
 that we know the species that our division is a means 
 of classifying. We may also observe that it is un- 
 avoidable in division by dichotomy that the end- 
 product should be a hypothetical term, 'non- 
 scalene' in the case above on the existence or non- 
 existence of which the division itself can throw abso- 
 lutely no light. 
 
 What now, it may be asked, is the value of a 
 division by dichotomy? It is valuable in the first 
 place as a test of the accuracy and exhaustiveness 
 
DIVISION AND CLASSIFICATION 209 
 
 of our analysis of a term's meaning. To take an 
 illustration from Aristotle, we may classify the 
 Predicables as follows: 
 
 Predicables 
 
 Commensurable Non-commensurable 
 
 f \ r 
 
 Essence Not essence Part of essence Not part of essence 
 (Definition) (Proprium) (Genus or Differentia) (Accidens) 
 
 It will be noticed in this case that the fundamentum 
 divisionis, or, as we may say, the differentia, is the 
 relation of the species according to the degrees of 
 the essential connection that they severally have to 
 the genus, and that the division is throughout dich- 
 otomous. But, of course, the Predicables were al- 
 ready known before they could serve as an illustra- 
 tion of how dichotomy may verify a classification. 
 
 We may also point out that a division by dich- 
 otomy is also valuable if we wish to ascertain the 
 position of a particular species in the class to which 
 it belongs. Thus, to quote Welton, "in the Analytic 
 Key prefixed to Bentham's British Flora, which is 
 intended to enable anyone who has a specimen of a 
 certain plant before him to discover its species and 
 its technical name, the arrangement is nearly en- 
 tirely dichotomous, and, for such a purpose, this 
 form is the most useful. But to adopt dichotomy as 
 a final arrangement would be absurd. A botanist, for 
 example, starts at once with three classes of the sum- 
 mum genus plant, viz., exogens, endogens, and acro- 
 
 H 
 
210 A TEXT-BOOK OF LOGIC 
 
 gens, and each of these is sub-divided into varying 
 numbers of orders, and these again into still further 
 varying number of genera, and so on, with little or 
 no regard to dichotomy, the object being to make the 
 classification agree with the distinctions existing 
 in the plants themselves." 
 
 The Tree of Porphyry. In a typical division by 
 dichotomy, as we saw in the last section, it is the 
 negative or indeterminate term that lends itself to 
 further division. If, now, the division proceeds 
 through all its stages by the dichotomous division 
 of the r^oaitiy^L or determinate term, we have a spe- 
 cies of division which is illustrated by what is tech- 
 nically known as the 'Tree of Porphyry/ An illus- 
 tration will show not only the possibility of such a 
 division, but exhibit the form that is characteristic 
 of it. Thus: 
 
 Substance 
 
 Corporeal Incorporeal 
 
 f \ 
 
 Animate Inanimate 
 
 Sensible Insensible 
 
 Rational Irrational 
 
 In any case of division by dichotomy whether of 
 this type or not, the indeterminate or negative term 
 and the determinate or positive term, in their rela- 
 tion to each other, are sometimes referred to as 
 Contradictory Opposites, Contradictory Relatives, 
 or Contradictories. This designation is apt to be 
 
DIVISION AND CLASSIFICATION 211 
 
 misleading unless it is pointed out that contradic- 
 tion can be logically postulated of terms only when 
 these have a common or underlying basis. There is 
 no contradiction, for example, between virtue and 
 beef-steak, because they do not belong to the same 
 universe of discourse, that is, because they have no 
 common basis. Animate and inanimate are contra- 
 dictories because they are the alternative ways in 
 which corporeal substance is capable of getting itself 
 expressed. The alternative species, therefore, to 
 which a dichotomous division gives rise may be 
 spoken of as contradictory in the sense that they 
 are the definite and exclusive forms in which the 
 genus to which they belong is realised. It would, 
 perhaps, avoid all ambiguity if we spoke of the rela- 
 tion between the determinate and indeterminate 
 terms of a logical division as Complementary* If 
 we did so, we should have to mean that the indeter- 
 minate term included within it all of the denotation 
 of the genus that was not definitely included in the 
 determinate term. Only on this interpretation can 
 these terms be regarded as the names of alternate 
 species. 
 
 It will be observed that in a division of the type 
 illustrated by the Tree of Porphyry the indetermin- 
 ate term is rejected at each of the subordinate steps. 
 This fact is technically known as an abscissio in- 
 finiti. 
 
 Classification Defined. One does not need to go 
 to text-books of logic to become acquainted with the 
 process that is denoted by the term classification. 
 
212 A TEXT-BOOK OF LOGIC 
 
 Before he has entered the university, nay before he 
 has entered the common school, the normal child 
 has learned to arrange the objects with which he is 
 brought daily into contact into groups, and to do 
 this on the basis of their observed likenesses and 
 unlikenesses. Whenever anyone groups objects to- 
 gether on the ground of their likenesses, and dis- 
 tinguishes between groups on the ground of their 
 differences, he is employing the method of classifi- 
 cation. Classification, therefore, may be defined as 
 the process of thinking together a number of objects 
 on the ground of their common attributes, and of 
 thinking apart groups of objects whose attributes 
 are different. 
 
 Classification and Definition. It will be seen that 
 classification, as thus defined, is closely related to 
 definition. Definition completes the process that is 
 begun in classification. Classification underlies the 
 defining process. This relationship will become evi- 
 dent if we recall that definition aims to place the 
 object whose meaning is not clear in a class with 
 other objects which share with it a common set of 
 attributes. When, therefore, we ask how we can 
 find the genus of any term we wish to define, the 
 answer will point us to the method of classification 
 which we are now studying. This is only another 
 way of saying, with a slightly different emphasis, 
 what was said in the last chapter, namely, that the 
 method of definition is based upon the comparison 
 of the object we are defining with other objects that 
 are in danger of being confused with it. Compar- 
 
DIVISION AND CLASSIFICATION 213 
 
 ison is common both to definition and to classifica- 
 tion. But we compare objects with each other in clas- 
 sification for the purpose of ascertaining their com- 
 mon attributes; in definition, we compare the ob- 
 jects of a class for the purpose of discovering the 
 differences which keep the sub-classes distinct. This 
 statement has important practical and philosophical 
 bearings. It enables us to see, for instance, how 
 groups of objects can be considered as a single ob- 
 ject, a fact that gives significance, as we have seen, 
 to the general concrete term. Whenever we over- 
 look the differences between the objects of which 
 a class is composed, and emphasise the points of 
 likeness by which each object retains its place in 
 the class, we have constituted of the class a distinct 
 kind of object. In such a class the individuals are 
 no longer important, there is no discernible differ- 
 ence between one and another ; they are, as Leibnitz 
 would say, identical. But if, for any reason, the 
 statements we make were dependent for their clear- 
 ness upon the differences in the class, we should 
 have to go beyond the method of classification by 
 which our classes are constituted, and we should be 
 forced, as we have pointed out, to adopt the method 
 of definition. In classification, we are interested in 
 the likenesses, in definition, in the differences of 
 objects. 
 
 Classification and Division. Whenever we are in 
 danger of overlooking the distinctions that exist 
 within a genus, whenever, that is, we are in danger 
 of making ambiguous statements through our fail- 
 
214 A TEXT-BOOK OF LOGIC 
 
 ure to keep in mind the whole denotation of a term, 
 there exists a situation that may be relieved by the 
 employment of the method of division. The starting 
 point of a logical division is the genus, the whole 
 which is possessed of a number of common qualities ; 
 and the purpose of division is to mark out within 
 the genus the species which realise, in different 
 ways, these common qualities. The movement of 
 thought is downward from the more general to the 
 less general. If now we consider the characteristics 
 of a classification, we shall find that they are the 
 reverse of this. The situation in which we feel 
 obliged to classify is one in which we are in danger 
 of failing to observe the likenesses of objects on 
 account of the prominence that their individual 
 attributes have come to assume. Popularly ex- 
 pressed, we are exposed to the danger of "missing 
 the wood for the trees." The starting point of all 
 classification, therefore, is the particular, the objects 
 which are kept distinct and apart on account of 
 their differences ; and the purpose that classification 
 is intended to serve is to detect within these differ- 
 ences certain relatively permanent groups of qual- 
 ities. Our most available method for doing this is 
 comparison; but that in respect of which the com- 
 parison is made is determined by the interest that 
 our classification is to promote. For instance, we 
 may classify objects with respect to their use or 
 with respect to their sense-attributes. It is the 
 character of our interest in things that determines 
 which of these principles of classification we choose ; 
 
DIVISION AND CLASSIFICATION 215 
 
 but, in any case, the movement of thought in class- 
 ification is upward from the particular to the gen- 
 eral. Classification is the beginning of a process 
 that we shall study more in detail when we come to 
 the problem of induction. 
 
 Kinds of Classification. It has been customary 
 to distinguish two kinds of classification, the arti- 
 ficial and the natural. By an artificial classification 
 is usually meant one in which the grouping of ob- 
 jects takes place on the ground of their possessing 
 some attribute or group of attributes which does not 
 serve as the basis of any further statement about 
 these objects. We may, for example, classify cer- 
 tain objects of domestic furniture as chairs; but 
 having done so, we are not able, on that basis, to 
 predicate anything further of the objects to which 
 the name chair is given. By a natural classification 
 is generally meant one that groups objects on the 
 ground of their possessing an attribute, or group of 
 attributes, which serves as the basis of further pred- 
 ication. For example, if we classify a group of ani- 
 mals as mammals, we are able to say, by virtue of 
 the fact that they are mammals, that they are also 
 vertebrates. This view has received, among modern 
 writers, a classic expression by Mill. It is based 
 upon the supposition that there exist in nature 
 classes of objects which are distinct from each other, 
 and that if we make the differences of these classes 
 the basis of our classification, we shall thereby mark 
 off the 'natural kinds' from others which by way of 
 contrast may be called artificial kinds. 
 
216 A TEXT-BOOK OF LOGIC 
 
 Since the spread of the doctrine of evolution, it 
 is no longer possible to maintain, in all fields of 
 knowledge, the distinction of natural and artificial 
 kinds. We no longer think of species of animals, 
 for example, as marking fixed and distinct differ- 
 ences between groups of objects; we have to think, 
 according to the doctrine of evolution, of the whole 
 animal series, from amoeba to man, as having 
 sprung from a common ancestor. Species are not, 
 in the meaning of the distinction we are now con- 
 sidering, separate and distinct kinds. 
 
 But while we no longer find it possible to classify 
 objects in the way just considered, the distinction 
 between natural and artificial suggests a truth of 
 which we may take advantage in our discussion of 
 this topic. The fallacy that underlies the separation 
 of classes into natural and artificial seems to be, 
 from the logictl standpoint, that it denies that rele- 
 vancy to purpose is a factor in all classification. The 
 classification of objects, for example, as natural is 
 based on the supposition that the attributes of spe- 
 cies are determined wholly by the nature of the ob- 
 jects themselves, and that they are in no way and to 
 no extent determined by the interest which prompts 
 us to classify; while the classification of objects as 
 artificial is predominantly, if not wholly, determined 
 by the interest that controls the classification. This 
 can not be maintained. For, as we have seen, knowl- 
 edge is always the product of both kinds of factors, 
 of both subjective purpose and objective fact. And 
 it is this analysis of what we mean by knowledge 
 
DIVISION AND CLASSIFICATION 217 
 
 that gives us the clue to the distinction of natural 
 and artificial kinds, and which enables us to under- 
 stand the two main kinds of classification. Our 
 classification does not depend upon the presence or 
 absence of interest, but upon the particular kind of 
 interest which we seek to satisfy. We may be in- 
 terested, for example, in grouping objects according 
 to their essential attributes, that is, according to 
 the attributes which constitute them members of a 
 class. We may also be interested in grouping ob- 
 jects according to their non-essential attributes, 
 that is, according to the attributes which are either 
 implied by their essential attributes, or which are 
 only accidental ones. In view of our discussion of 
 the Predicables, this statement means that we may 
 make the qualities which characterise the genus the 
 principle of classification; or the qualities which 
 characterise the proprium, or the accidens, the basis 
 of classification. 
 
 Classification according to the essential attri- 
 butes of the objects compared gives a theoretical 
 classification; and classification according to the 
 non-essential attributes, a practical classification. 
 In the former case, the theoretical interests which 
 prompt us to study the nature of things are upper- 
 most ; and in the latter, the practical interests wkich 
 are concerned with the uses of things are in control. 
 To take an illustration usually found in text-books 
 of logic, the Swedish botanist, Karl Linnaeus (1707- 
 1778), based his classification of plants upon the 
 comparison of the sexual organs of plants. The 
 
218 A TEXT-BOOK OF LOGIC 
 
 distinct advantage of this method was that it made 
 possible the indexing of plants in a convenient way 
 into genera and species so that their relative posi- 
 tion to each other in a series could be made out. 
 This must be taken not as a theoretical, but as a 
 practical classification, and, in principle, is not differ- 
 ent from the arrangement of words in a dictionary 
 in their alphabetical order. If, on the other hand, 
 we make a classification according to the natural 
 relationships of the species, we shall have an illus- 
 tration of a theoretical classification. It will be 
 obvious that many variations are possible within 
 these two divisions ; but for the details, the student 
 is referred to the larger books on logic and the 
 principles of science. 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Ch. IV. 
 
 J. G. Hibben, Logic, Deductive and Inductive, Ch. VI. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. V. 
 
 W. Minto, Logic, Inductive and Deductive, Ch. IV. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 
 XXI. 
 
 W. J. Taylor, Elementary Logic, Pt. II., Ch. V. 
 
 ADVANCED 
 
 R. W. B. Gibson, The Problem of Logic, Chs. IV., V. 
 
 H. W. B. Joseph, An Introduction to Logic, Chs. III., V. 
 
 F. C. S. Schiller, Formal Logic, Chs. IV., VI., 6-10. 
 
 C. Sigwart, Logic, Pt. II., 42-43. 
 
 J. Venn, Empirical Logic, Chs. XII., XIII. 
 
 J. Welton, A Manual of Logic, Vol. I., Bk. I., Ch. VI. 
 
DIVISION AND CLASSIFICATION 219 
 
 QUESTIONS 
 
 1. In what way is logical division related to logical defini- 
 tion? 
 
 2. Name one way in which logical division may not be in- 
 terpreted. 
 
 3. Explain: By division we analyse the denotation of a 
 term's meaning. 
 
 4. What is meant by saying that the species enumerated 
 in a logical division are to be read disjunctively? 
 
 5. What is the test of a logical division? 
 
 6. What is a metaphysical division, and how does it differ 
 from a logical division? 
 
 7. What do you understand by a physical division? Illus- 
 trate. 
 
 8. What is a verbal division? 
 
 9. Define a fundamentum divisionis. 
 
 10. Explain how one discovers for a particular division an 
 appropriate fundamentum divisionis. 
 
 11. In what respects can a logical definition be improved 
 from the standpoint of logical division? 
 
 12. Explain the following terms: genus, species, totum di- 
 visum, summum genus, infirmae species, subaltern 
 genera, proximate genus, constituent species. 
 
 13. What is the first rule of logical division? 
 
 14. What is a cross division? Explain how it occurs. 
 
 15. What is meant by saying that the species to which a 
 logical division gives rise must be exclusive? 
 
 16. What are the character and importance of a continuous 
 series? 
 
 17. How can we keep within a single fundamentum when 
 our division is carried through a number of stages? 
 
 18. State and explain the second rule of logical division. 
 
 19. What difficulties in the method of logical division are 
 supposed to be met by dichotomy? 
 
 20. What are the characteristics of a dichotomous division? 
 
 21. What is the relation of dichotomy to definition? 
 
220 A TEXT-BOOK OF LOGIC 
 
 22. What advantages are sometimes claimed for a dich- 
 otomous division? 
 
 23. What is the Tree of Porphyry? 
 
 24. What do you understand by contradictory opposites? 
 
 25. Explain absdssio infiniti. 
 
 26. What is classification? 
 
 27. How are classification and definition related? 
 
 26. What is the relation of classification and division? 
 
 29. State Mill's doctrine of classification. 
 
 30. Why has the distinction of natural and artificial kinds 
 broken down? 
 
 31. What is the relation of purpose to classification, and 
 what effect does this have upon the distinction of nat- 
 ural and artificial classification? 
 
 32. What bases of classification may be recognized as im- 
 plicit in Mill's doctrine of classification? 
 
 33. Explain theoretical and practical classification. 
 
 EXERCISES 
 
 1. Divide logically the following terms, stating in each in- 
 stance (a) the definition and (b) the fundamentum di- 
 visionis. 
 
 psychology gun culture 
 
 European student government 
 
 2. Examine the following divisions, and point out which 
 rule of logical division, if any, is broken by them: 
 
 (1) Substances into material and spiritual. 
 
 (2) Books into scientific, philosophical, and literary. 
 
 (3) Religions into true and false. 
 
 (4) Students into those who are diligent, female, and 
 
 athletic. 
 
 3. What is the metaphysical division of the following 
 terms? 
 
 landscape philosophy toy 
 
 capital child amusement 
 
DIVISION AND CLASSIFICATION 221 
 
 4. Divide physically six terms of your own selection. 
 
 5. Give six illustrations of verbal division. 
 
 6. Illustrate a cross division, and explain how it is brought 
 about. 
 
 7. Give two examples of dichotomy. 
 
 8. Illustrate by two examples the Tree of Porphyry. 
 
 9. Give examples which illustrate the characteristics of 
 (a) a theoretical and (b) a practical classification. 
 
CHAPTER VIII 
 
 CATEGORICAL PROPOSITIONS 
 
 Types of Propositions. In a former chapter we 
 saw that predication is the act of affirming or deny- 
 ing something (P) of something else (S). Any 
 statement which rests upon predication, that is, 
 which affirms or denies something of something else, 
 is called in logic a proposition. Predication may be 
 of various degrees of directness or explicitness, ac- 
 cording to the degree of our knowledge of the sub- 
 ject of predication. For example, if my knowledge 
 of natural history is only slight, I shall probably be 
 able to say of a given animal merely that it is either 
 a lion or a tiger or a leopard or something else. If 
 a further study of animals makes me acquainted 
 with the characteristics of the species lion, I shall 
 then be able to say that if a given animal has these 
 characteristics, it is a lion. If, again, the examina- 
 tion of a particular animal showed that it does or 
 does not have these distinguishing qualities, I should 
 then be able to say that it is or is not a lion. The 
 forms of predication illustrated in these instances 
 we have learned already to call alternative, hypo- 
 thetical, and categorically respectively. The state- 
 ments in which these forms of predication are ex- 
 pressed are called disjunctive, hypothetical and cate- 
 gorical propositions. The classification of proposi- 
 tons into disjunctive, hypothetical, and categorical 
 
 (222) 
 
CATEGORICAL PROPOSITIONS 
 
 is said to be made from the standpoint of relation, of 
 the relations, that is, that obtain between the ele- 
 ments that enter into the proposition. It is quite 
 obvious, for instance, that the predicate and subject 
 of each of the above propositions dealing with what, 
 under given conditions, can be predicated of a par- 
 ticular animal, are related in quite distinct ways. 
 The predicate term is asserted differently in each 
 case, and it is this difference in our manner of 
 asserting that lies at the foundation of the distinc- 
 tion we make between disjunctive, hypothetical, and 
 categorical propositions. The form of assertion 
 corresponds to a real element in the knowledge that 
 an assertion claims. We have shown this in detail 
 in the chapter on propositions. Our present task 
 is to study the various kinds of propositions and the 
 logical problems to which they give rise. In the 
 present chapter, we shall consider a number of ques- 
 tions which relate to simple predication and which 
 throw light upon the nature of categorical state- 
 ments ; in the next, we shall consider problems con- 
 nected with the other forms of the proposition. 
 
 Classification of Categorical Propositions. The 
 possibility of a classification of categorical proposi- 
 tions, that is, propositions which predicate P of S 
 simply, rests upon the fact that unconditional state- 
 ments (1) do not always, but sometimes do, apply 
 to a determinate part of the subject-matter of such 
 statements; or (2) do not always, but sometimes do, 
 unite the predicate with the subject of such state- 
 ments; or (3) do not always express the same de- 
 
224 A TEXT-BOOK OF LOGIC 
 
 gree of certainty. We shall illustrate each of these 
 cases in the order in which they have been named. 
 As an illustration of the first case, where the state- 
 ment applies to an indeterminate part of the subject- 
 matter of the statement, let us take 'Not all men are 
 honest who say they are.' This is a proposition in 
 which honesty is predicated of some only of the men 
 who declare their honesty. As an illustration of the 
 second case, where the statement does not unite the 
 predicate with the subject of the proposition, let us 
 take the illustration just used and observe that hon- 
 esty is denied of some of the individuals who assure 
 us that they are honest. As an illustration of the 
 third case, where our statements express different 
 degrees of certainty, let us take the following : 'He 
 may be honest though poor;' 'He is honest but 
 poor;' 'He must be honest.' 
 
 The three characteristics of propositions just 
 mentioned and illustrated are so constant, and they 
 occur in such a wide range of our knowledge, that 
 early in the history of logic it was found necessary 
 to distinguish them by the use of technical terms, 
 that is, by terms which mean, whenever they are 
 used, just these characteristics of propositions. 
 Thus, when we wish to call attention to the fact that 
 our statements do or do not apply to a determinate 
 part of the subject-matter of the proposition, we 
 are said to be dealing with the proposition from the 
 standpoint of its Quantity. When, on the other 
 hand, we wish to emphasise the fact that the pred- 
 icate does or does not belong to the subject, we are 
 
CATEGORICAL PROPOSITIONS 225 
 
 said to be dealing with the proposition from the 
 standpoint of its Quality. When, thirdly, we wish 
 to distinguish the degree of certainty that attaches 
 to our statements, we are said to be dealing with 
 the proposition from the standpoint of its Modality. 
 If to this statement we now add what was said 
 in the first paragraph of the present chapter about 
 the degrees of explicitness in predication being made 
 from the standpoint of Relation, we have before us 
 the four ways in which propositions may be class- 
 ified. We shall now write down, for reference, the 
 classification of propositions when looked at from 
 each of the above-mentioned points of view. 
 
 RELATION 
 
 Categorical 
 
 Hypothetical 
 
 Disjunctive 
 
 QUANTITY QUALITY 
 
 Singular Affirmative 
 
 Universal Negative 
 
 Particular 
 Indesignate 
 
 MODALITY 
 
 Assertoric 
 Necessary 
 Problematical 
 
 Quantity of Propositions. The problem of the 
 quantity of propositions is one which is concerned 
 with the question whether we intend our statements 
 to be true of a determinate or indeterminate part 
 of the subject-matter of such statements. It is, for 
 
 15 
 
226 A TEXT-BOOK OF LOGIC 
 
 example, quite clear that when any one says, 'I have 
 seen Paris/ he is ordinarily understood to mean that 
 he has been to Paris, and visited some of its im- 
 portant boulevards, churches, galleries, etc. No one 
 would understand him to mean that he had become 
 acquainted with the whole of Paris. The truth of 
 the claim to have seen Paris would be that some 
 unspecified parts of Paris had been visited. Again, 
 no one who made the above statement would ordi- 
 narily wish to be understood that he had a thorough 
 acquaintance with those parts of Paris which had 
 come under his observation. The statement is in- 
 tended to claim an acquaintance, such as it is, with 
 certain parts of the French capital. From these 
 considerations, it is quite evident that the statement, 
 'I have seen Paris/ leaves undetermined both the 
 range and the thoroughness of the observation that 
 is claimed by the statement. Now, although a great 
 number of the statements we make about even the 
 most familiar and ordinary events of life are, in the 
 sense of these illustrations, quite undetermined, we 
 sometimes make statements which we intend to be 
 understood with no such limitation. To take a sim- 
 ple illustration, if one were asked, 'What is the most 
 direct route from Chicago to London?' the answer, 
 if one were given, would claim to be determinately 
 true of the subject of the inquiry, either of a speci- 
 fied part of the inquiry or of the whole of it. For 
 instance, the reply might take this form, 'Go by way 
 of the New York Central lines to New York, and 
 then inquire/ or it might take this form, 'Go to 
 
CATEGORICAL PROPOSITIONS 227 
 
 New York, and then take passage with the Cunard 
 Line to London via Liverpool/ Let us take another 
 illustration. A mathematical problem is an inquiry 
 of a definite kind, and we may work the problem 
 up to a certain point quite sure that all the steps 
 we have taken lead us toward the true solution of 
 the whole problem. We may or we may not be able 
 to proceed beyond that point. The fact that we can- 
 not, does not invalidate the claim that we may make 
 of having solved a definite part of the problem. That 
 is to say, if the answers we make to questions, and 
 the statements in which we express our knowledge 
 contain in them a distinct reference to the extent 
 of the subject covered by such answers and state- 
 ments, they are called determinate whether th 
 whole or some definite part of the whole subject has 
 been considered. 
 
 We have seen that statements may be deter- 
 minate or indeterminate in what they assert. Our 
 thought, that is to say, may refer to a definitely 
 specified area of a given subject, or it may refer to 
 an indefinitely specified area. In the former case, 
 the definitely specified area may be either the whole, 
 or an indicated part of the whole. In the latter case, 
 we cannot tell whether the knowledge expressed in 
 the statement is true of the whole or of only a part 
 of the whole. Now these distinctions in the ordinary 
 use of language lie at the foundation of the logical 
 consideration of propositions from the standpoint of 
 quantity. Hence, the question of the quantity of 
 propositions is whether what a statement connotes 
 
228 A TEXT-BOOK OF LOGIC 
 
 is true of a specified or unspecified part of what its 
 subject denotes. When, consequently, we speak 
 about the quantity of a proposition, we must be 
 understood to be interested in the meaning of a state- 
 ment from the standpoint of the number of the ob- 
 jects to which the statement applies. It is obvious 
 that the subject terms of all propositions which ex- 
 press quantity must be read in denotation. 
 
 If now we ask, To how many objects can we in- 
 tend our statements to apply? we may answer to 
 one, to more than one but less than all, and to all. 
 These are all the possible cases, and they afford a 
 clue to the classification of propositions from the 
 standpoint of quantity. 
 
 The Singular Proposition. When a statement is 
 made of one specified individual, that statement, in 
 logic, is said to be a singular proposition. 'Hannibal 
 was a great Carthagenian general' is, in this sense, 
 a singular proposition. It is a proposition that ex- 
 presses what an examination of a single instance of 
 the genus 'general' has led us to affirm. This is not 
 an exceptional case, for we are frequently led, in 
 the course of our experience, to examine single ob- 
 jects and to attempt some classification of them. 
 The child's questions, 'What is this?' 'Who made 
 that?' and the like are illustrations of the impor- 
 tance of this class of judgments in the progress of 
 intelligence and the advancement of knowledge. 
 Singular statements are concrete, or keep us in close 
 connection with what is concrete, and for this reason 
 are of great help in making exact, particular, and 
 
CATEGORICAL PROPOSITIONS 229 
 
 precise the knowledge that, in one way and another, 
 we are daily acquiring. The examination of indi- 
 vidual objects is, also, a large part of the work of 
 any science, and much of the knowledge that science 
 has consists of the singular judgments it is able to 
 assert. We may say in passing that the student's 
 danger is that he will get away from the observation 
 of particular things, and that his education will 
 force him to premature generalisation in which a 
 form of words is substituted for a face to face 
 acquaintance with the facts of his special subjects 
 of study. If such should be the case, it is hardly 
 possible that he will appreciate the importance of 
 this type of proposition. 
 
 The Universal Proposition. Another class of 
 propositions is met with when the subject terms of 
 such propositions are general instead of individual. 
 'All democratic governments tend to issue in despot- 
 ism' is a statement expressing a judgment that pur- 
 ports to be based upon the common character of the 
 individuals that the general term signifies. Greek, 
 French, British, American, etc., are the governments 
 of which such a statement is held to be true, and 
 yet not as Greek, French, etc., but as democratic. 
 Statements of this kind are made because there is 
 conceived to be a necessary connection between what 
 the predicate and subject terms connote, and they 
 apply to all individual or particular instances which 
 possess the attributes of the subject term. In other 
 words, whenever we affirm or deny of each of a total 
 number of instances the meaning that attaches to 
 
230 A TEXT-BOOK OF LOGIC 
 
 the predicate terms of propositions, we have what, 
 in logic, is called a universal proposition. 
 
 Kinds of Universal Proposition. A question may 
 arise as to whether there is any logical difference 
 between a singular and a universal proposition, since 
 in both cases, the subject term must be understood 
 to be distributed, that is, to apply to the whole num- 
 ber of the instances that the connotation of the term 
 implies. There can be no objection to taking these 
 two cases as illustrating the same logical principle, 
 namely, that from the standpoint of their quantity 
 we intend our statements to apply to all the in- 
 stances, whether to a specified one or to all, to which, 
 in the nature of the proposition, the subject term can 
 apply. The singular proposition may thus be taken 
 as a particular form of the universal proposition. 
 Another type of proposition which, like the singular 
 proposition, has a concrete subject term, and which, 
 on account of the definiteness of its denotation, has 
 to be interpreted as a universal proposition may be 
 considered in this connection. For example, in the 
 proposition, 'A part is always less than the whole/ 
 a part is a perfectly determined idea of quantity 
 from the logical point of view, and the proposition 
 in which it serves as a subject term must, therefore, 
 be treated as a universal proposition. 
 
 The Particular Proposition. Whenever the num- 
 ber of instances denoted by the subject term oi; a 
 proposition is, from the logical standpoint, unde- 
 termined, we are said to have a particular proposi- 
 tion. The question for us to bear in mind in decid- 
 
CATEGORICAL PROPOSITIONS 231 
 
 ing the quantity of a proposition is simply whether 
 the number of instances of the kind connoted by the 
 subject term is a determined number or not. For 
 example, if we say that 'Five per cent of all college 
 students fail in their work,' it is clearly not meant 
 that we know the exact number of college students, 
 and therefore that we know the exact number who 
 fail ; the statement, if it is true, must be based upon 
 the examination of large numbers of students work- 
 ing under a great variety of conditions, and, when 
 so based, we feel warranted in saying, even with 
 respect to those students who have not had an oppor- 
 tunity to pass or to fail in any subject, that in the 
 period covered by their college course five per cent 
 of these will fail. Now what we wish to illustrate 
 by this example is that the statement is a universal 
 one because, although arithmetically we have no 
 idea of the number of failing students, we do have 
 in the subject term of our proposition, 'five per cent 
 of all college students,' an idea logically determined 
 from the standpoint of its quantity. 'Five per cent' 
 is just as definite as 'this one* of a given number, 
 and both are as definite as 'all' of the given number. 
 But if, on the contrary, in the absence of all knowl- 
 edge of any such statistical study as we have sup- 
 posed, we were required to express our judgment 
 as to the number of failures likely to be incurred 
 at any given time, we could not logically go beyond 
 the statement that 'Some students will fail in their 
 work.' This statement is true of an undetermined 
 number of students, and 'some,' as a sign of quantity 
 
232 A TEXT-BOOK OF LOGIC 
 
 in propositions, means this. The propositions that 
 express judgments that have not determined the 
 quantity of their subject-matter are called particular 
 propositions. 
 
 The Indesignate Proposition. Whenever we ex- 
 press judgments of quantity, our statements, as a 
 rule, bear upon their face some definite indication 
 of the extent of their subject terms. From the 
 standpoint of quantity, all our statements are offered 
 as true of a number of determined or undetermined 
 individuals, and when a statement is made without 
 specifying which of these two possibilities is meant, 
 we are left in doubt as to how the statement is to 
 be taken. Now sometimes this occurs. The popular 
 wisdom of an age which gets itself hardened into 
 groyerbs is frequently defective in this respect. 
 'Dead men tell no tales,' is an illustration in point. 
 Are we to understand this of all dead men or only 
 of some dead men? Is there, that is, a necessary 
 connection between being dead and being unable to 
 appear as a witness in a trial, for example; or are 
 we to suppose that there is only an accidental con- 
 nection between them, and that in some cases the 
 testimony of dead men is admissible? 'Virtue is to 
 be rewarded/ is a proposition that is defective in 
 the same respect. Are we to understand this of each 
 and all the virtues, of the ordinary virtues of our 
 daily life as well as of the more heroic virtues that 
 are called out in exceptional circumstances; or are 
 we to limit the statement to the latter class of cases ? 
 If the latter, then the same set of questions recurs, 
 
CATEGORICAL PROPOSITIONS 233 
 
 and we should wish to know whether a reward must 
 be attached to all of them or to only some of them. 
 These illustrations are sufficient to indicate a kind 
 of statement we sometimes meet with even in com- 
 mon life, statements that are quantitative by impli- 
 cation but are not explicitly so. How are we to 
 deal with them logically? Our first inclination is to 
 receive all such statements, according to the charac- 
 ter of their subject-matter, as universal or par- 
 ticular propositions. But if it is remembered that 
 all propositions are expressions of the judgments of 
 the person who states the proposition, and that they 
 are, from the standpoint of the person who hears 
 them, proposals for his acceptance or rejection in 
 the sense in which they are made, it will be obvious 
 that we are not allowed to interpret these statements 
 in any sense we wish ; our business is to understand 
 them in the sense they have for the person who 
 makes them. But, as we saw, these propositions 
 create a doubt that is based upon the possibility of 
 understanding the statements in either of two ways. 
 Whenever a statement raises a doubt of this kind, 
 a doubt that may be resolved by accepting either 
 the one or the other of alternative possibilities, 
 without indicating which alternative is to be 
 adopted, it is called an indesignate proposition. An 
 indesignate, or as it is sometimes called, an indefinite 
 proposition is one which implies the existence of a 
 determined or undetermined number of individuals 
 of which the statement is offered as true, but which 
 fails to state explicitly whether it is made of the 
 
234 A TEXT-BOOK OF LOGIC 
 
 number of the determined or of the undetermined 
 instances. 
 
 Quality of Propositions. Our study in a previous 
 chapter has shown that terms always intend more 
 than they express, that they are aspects of a whole 
 meaning which as terms they do not fully bring out. 
 We have also learned that in order to get at the 
 full meaning of any term we must find it functioning 
 in some way in a proposition. It is only in a prop- 
 osition that we discover the full meaning of a term ; 
 the proposition is the express statement of the whole 
 meaning within which the meanings of terms may 
 properly be sought. In other words, it is the way 
 that terms function in propositions that gives the 
 key to the meaning of the proposition and of the 
 terms themselves. That is to say, we have to inter- 
 pret terms from the standpoint of their propositions 
 and proposition from the standpoint of their terms. 
 The reason is that each implies the other, and 
 neither can exist alone. 
 
 Coming now to the particular problem of this 
 section, we may see, in the light of what has just 
 been said, that terms may be related to one another 
 in propositions in one or the other of two ways, in 
 the way of inclusion or of exclusion. The fact that 
 terms are elements of the meaning expressed by the 
 proposition, is indicated, as we have already seen, 
 by the copula. The copula, we said, is the sign of 
 predication, the sign that S and P are to be taken 
 in the way required by the whole meaning expressed 
 in the proposition. One of the ways in which prop- 
 
CATEGORICAL PROPOSITIONS 235 
 
 ositions require us to take their terms is, as we said, 
 with respect to whether they are inclusive or exclu- 
 sive of each other. And this requirement is indi- 
 cated by the copula, which according as it has or 
 has not the negative particle 'not,' distinguishes for 
 us the two kinds of Quality of prepositional state- 
 ments. When the terms are inclusive, this is indi- 
 cated by the copula 'is' or 'are;' when they are ex- 
 clusive, by the copula 'is not' or 'are not.' The 
 propositions that have respectively these two kinds 
 of copula are called affirmative and negative prop- 
 ositions. Affirmative and negative propositions, 
 therefore, are statements that give expression to 
 the inclusive and exclusive relationship of the terms 
 through which our meanings are expressed. 
 
 The Affirmative Proposition. Affirmative propo- 
 sitions, formally considered, are those in which the 
 copula is either 'is' or 'are.' From the standpoint 
 of the character of the thought expressed in them, 
 affirmative propositions may be defined as the ex- 
 pression of our positive meanings. By a positive 
 meaning we understand one which combines in a 
 whole content of thought two or more features of 
 the object thought about. Stated differently, a pos- 
 itive meaning is one that may be analysed into ele- 
 ments each of which expresses some feature of the 
 meaning which the proposition as a whole expresses. 
 For example, the meaning of the proposition, 'All 
 mammals are vertebrates' is, that there is a genus 
 which, when looked at from the standpoint of an- 
 atomy, must be described as a vertebrate, but which 
 
236 A TEXT-BOOK OF LOGIC 
 
 if looked at from the standpoint of physiology must 
 be described as a mammal. Let us call the genus, 
 or the whole meaning of any proposition, SP. Then 
 our positive meaning, SP, may be analysed into S 
 and P, and these terms may be used to express the 
 intended meaning in the proposition 'S is P.' To 
 develop the significance of affirmative predication 
 further, we may say that in any statement of the 
 form 'S is P/ S and P are not isolated or independent 
 terms ; S is not merely S, nor is P merely P. What 
 the proposition affirms is that the S that is P is an 
 SP, and only because it is SP can we say that it is 
 P. But P can be predicated of S only if it also is 
 SP. SP underlies both terms, and gives to the mean- 
 ing that the proposition 'S is P' expresses its posi- 
 tive character. 
 
 The Negative Proposition. Negative proposi- 
 tions, formally considered, are those in which the 
 copula is either 'is not' or 'are not.' Materially, that 
 is, from the standpoint of the character of the 
 thought expressed in them, negative propositions 
 may be defined as the expression of our exclusive 
 meanings. By a negative meaning, therefore, we 
 understand one which excludes from a whole con- 
 tent of thought one or more attributes of the object 
 thought about, either because it does not at all, or 
 because it does not now, form part of the connotation 
 of the whole content of thought. Stated otherwise, a 
 negative meaning is one which may be analysed into 
 elements one or more of which is incompatible with 
 some fact or truth which we have already accepted. 
 
CATEGORICAL PROPOSITIONS 237 
 
 In the chapter on terms we discussed negative 
 meaning, and the conditions under which such mean- 
 ings arise were explained. These conditions can be 
 reviewed profitably in the present connection, and 
 they will be found to throw light upon the general 
 statement in the present parapragh of what we 
 understand a negative meaning to be. 
 
 We shall pass on to other aspects of the same 
 problem. We may call attention then to the fact 
 that the predicate terms of negative propositions 
 are to be read in connotation. The reason for this 
 is that logical negation expresses incompatibility in 
 the meanings of terms. For example, 'Apples are- 
 not pears/ does not express merely the perceptual 
 differences of the things we call apples and the things 
 we call pears ; what the proposition means is that if 
 we know what attributes pears have, they will be 
 found not to be the attributes which apples have. 
 Now, as we see by this illustration, the difficulty 
 about negative statements is that they seem to break 
 the connection that, as we said, must bind S and P 
 together in logical propositions. For example, we 
 have shown that, in order to make any statement of 
 the kind S-P, we have to suppose that P is predi- 
 cated of S on the ground of the common likeness that 
 underlies the differences of S and P. It is, in other 
 words, because S and P make a reference to the same 
 subject, although to different aspects of it, that pred- 
 ication can take place at all. Can we say that in neg- 
 ative propositions there is the same identity in dif- 
 ference that is the ground of every logical state- 
 
238 A TEXT-BOOK OF LOGIC 
 
 ment? It would seem that we can; only the differ- 
 ences, in this case, have come in our thought to be a 
 special motive for the judgment we assert. In other 
 words, in affirmative propositions we express like- 
 nesses amid differences, while in negative proposi- 
 tions we express differences amid likenesses. The 
 negative proposition has this characteristic because, 
 by making difference the motive of our assertions, 
 we can sometimes best conserve the unity of idea 
 that every prepositional statement requires. 
 
 The Relation of Affirmative and Negative Prop- 
 ositions. A study of the relation of affirmative and 
 negative statements will throw still further light 
 upon the meaning of negation. In affirmative state- 
 ments, thought moves between two extremes, the 
 extreme of tautology on the one hand, and the ex- 
 treme of nonsense on the other. If we take affirma- 
 tion in one extreme way, we can only express iden- 
 tical meanings, 'A boy is a boy/ and this is taut- 
 ology. If we take affirmation in another extreme 
 way, we can only express incompatible meanings, 
 'A stove is a gold mine/ and this is nonsense. Now 
 it is the function of negation to save us from mean- 
 ingless tautological or nonsensical assertions. 
 For instance, the case of tautology, when taken 
 absolutely, is a denial of the minimum of difference 
 which must exist if we are to make our assertions 
 significant. Merely to predicate an object's exist- 
 ence of itself, or to affirm a meaning of itself, is 
 nothing but trifling. If we should mean by the 
 
CATEGORICAL PROPOSITIONS 239 
 
 predicate only what we mean by the subject of a 
 proposition, we should state in the whole proposi- 
 tion no more than we stated in either of its terms. 
 Thus, 'A is A' has exactly the meaning of A, whether 
 A is read denotatively in both terms, or connota- 
 tively in both terms. If A is A is a significant state- 
 ment, we must at least read A denotatively in one 
 term, and connotatively in the other. In other 
 words, the identity which unites the subject and 
 predicate of logical propositions must not go to the 
 extreme of eliminating all differences from the 
 meaning which logical propositions state. The 
 affirmative proposition, because its chief interest 
 is in identity, is particularly open to the danger of 
 overlooking the differences that make the subject 
 and predicate of such propositions distinct terms. 
 Now, when this happens, when identity usurps the 
 whole functions of assertion, we can be saved from 
 the fatuity of tautology by resorting to negation as 
 the only means at our disposal for opening the way 
 to some significant statement. Thus, if we oppose 
 any tautology with a denial, the burden of the proof 
 of what we assert is thrust upon us, and this con- 
 sists in showing the grounds on which our negation 
 rests. For example, if we deny that 'A boy is a boy/ 
 we may do so because, as we may point out, he is 
 also a son, and that this relationship is compatible 
 with the fact of boyhood from which, in the tauto- 
 logical statement, we were unable to get away. 
 Negation serves, in such a case, to prevent us from 
 
240 A TEXT-BOOK OF LOGIC 
 
 standing intellectually stock-still; and, as we often 
 find, the denial of truism may sometimes be the 
 open way to the truth. 
 
 The other extreme to which affirmative judg- 
 ments may lead us consists in the development of 
 differences to such an extent that the unity of the 
 judgment is threatened or completely destroyed. 
 This may occur, for example, when the material of 
 the judgment is forced to render so many predicates 
 that the universe of discourse, which in all logical 
 judgment sets the limit to which differences can be 
 carried, is in danger of being superseded, and the 
 qualities which the material may have in other uni- 
 verses of discourse are brought in to satisfy the 
 demand for differences which has, so to say, got out 
 of hand. When, for example, the student of psy- 
 chology speaks of auditory sensations being brought 
 in over the auditory nerve, and when the text-books 
 of physiology speak about the striated muscles being 
 under the control of the will, there is a confusion 
 of universes of discourse, and we can only force the 
 statements within their respective bounds again by 
 a refusal to accept them as significant assertions. 
 The statements are incompatible with the body of 
 knowledge of their respective sciences, and the nega- 
 tion is in each case in the interests of this body of 
 accepted knowledge. 
 
 Exceptive and Exclusive Propositions. Whenever 
 a subject of discourse is qualified by such words as 
 except, only, but, unless, alone, none but, etc., it 
 immediately becomes uncertain to what, in such 
 
CATEGORICAL PROPOSITIONS 241 
 
 cases, the predicate applies. For example, if we say, 
 'All free persons know how to obey,' it is quite ob- 
 vious that we are predicating 'the knowledge of how 
 to obey' of 'the persons who are free.' If, however, 
 we were to say 'None but the free know how to obey,' 
 we should be saying something quite different, al- 
 though most persons would understand that we were 
 still predicating 'the knowledge of how to obey' of 
 'the persons who are free.' If, again, we said, 'Only 
 the free know how to obey,' it might be asked 
 whether we had said something identical with one of 
 the other statements, or something different from 
 both. And, further, if we said, 'No one unless he is 
 free knows how to obey,' the problem would become 
 still more complicated. 
 
 In view of the difficulties of interpretation occa- 
 sioned by such statements as those to which atten- 
 tion has just been called, it is customary for logic 
 to point out that all propositions whose subject 
 terms are qualified by such words as except, only, 
 but, are either exceptive or exclusive propositions. 
 In the exceptive and the exclusive proposition the 
 subject term is an infinite or non-S term, because all 
 the qualifying words, except, but, only, etc., are 
 understood as carrying a negative signification. 
 Examples are : 'All except honor' = 'All that is not 
 honour;' 'None but the free' = 'No one who is not 
 free ;' 'Only natives' = 'No one who is not a native.' 
 It should be observed, moreover, that exceptive and 
 exclusive propositions are always universal, there 
 are no particular propositions of either kind. That 
 
 16 
 
242 A TEXT-BOOK OF LOGIC 
 
 is to say, the subject terms of these propositions 
 denote always a determinate number of individuals. 
 But while the exceptive and exclusive propositions 
 distribute their non-S terms, they differ from each 
 other in quality. That is to say, all propositions 
 which qualify their subjects in the manner indicated 
 are either affirmative or negative. In the light of 
 these statements we may consider these classes of 
 propositions separately. 
 
 The exceptive proposition is affirmative. It ha& 
 
 the genera] form, SaP. Examples are : 'All planets 
 except Venus and Mercury are beyond the earth's 
 orbit' = 'Any planet that is not Venus or Mercury 
 is beyond the earth's orbit;' 'All members but the 
 Irish voted for the measure' = 'All the members 
 who do not belong to the Irish party voted for the 
 measure/ 
 
 In an exceptive proposition the individuals de- 
 noted by the subject term are determined by taking 
 out of a class a certain number of individuals to 
 which the predicate term is meant not to apply. It 
 will be seen that if the part of the class to which 
 the predicate term does apply is to be distributed, 
 the part taken out must be distributed also. What 
 an exceptive proposition says, therefore, is that a 
 statement is true of that part of a class which re- 
 mains when stated exceptions to it are definitely re- 
 moved. The truth of such a statement is maintained 
 of everything that cannot be brought under the ex- 
 ception, that is, of everything that is not the speci- 
 fied exception. Consequently, what we are talking 
 
CATEGORICAL PROPOSITIONS 243 
 
 about, in an exceptive proposition, is anything, 
 within the universe of discourse, that is definitely 
 non-S. Thus, if a circle represents a universe of 
 discourse, and any shaded portion of it the excepted 
 part, which may be called S, the unshaded part will 
 then represent the denotation of the subject of 
 predication, that is, non-S. The exceptive proposi- 
 tion may in these terms be represented thus : 
 
 SaP 
 
 The exclusive proposition is negative. It has the 
 general form, SeP. Examples are : 'None but the 
 brave deserve the fair' = 'No one who is not brave 
 deserves the fair;' 'Only graduates are eligible' = 
 'No one who is not a graduate is eligible.' 
 
 The exclusive proposition determines its subject 
 term in the same way as the exceptive proposition, 
 that is, by taking out of a class some determinate 
 number of individuals, and making all other indi- 
 viduals of the class the subject of predication. Thus, 
 if S be the excluded individuals, non-S will be the 
 subject of which predication takes place. But since 
 exclusive propositions are negative, the individuals 
 denoted by non-S will necessarily have qualities 
 which are incompatible with their possessing those 
 connoted by the predicate term; incompatibility of 
 qualities is what we mean by negation. Hence, the 
 
244 A TEXT-BOOK OF LOGIC 
 
 exclusive proposition definitely denies P of every 
 individual which does not have the qualities also of 
 S ; nothing that is not S is P. If, now, we represent 
 any excluded part of a class by the shaded portion 
 of a circle, the exclusive proposition may be shown 
 as follows: 
 
 SeP 
 
 Compound Propositions. We have said that ex- 
 ceptive and exclusive propositions are always uni- 
 versal. This is not because particular propositions 
 do not qualify their subject terms by such words as 
 only, except, etc., but because when they do, they 
 must be treated as compound propositions. By a 
 compound proposition, or, as the older logicians 
 called them, exponible propositions, is understood 
 one whose meaning requires a number of distinct 
 propositions for its complete expression. 'Milton 
 and Dante -wrote religious poetry of the highest 
 merit,' is a simple example. The meaning of the 
 statement obviously is, (a) 'Milton wrote religious 
 poetry of the highest merit,' and (b) 'Dante wrote 
 religious poetry of the highest merit.' A more com- 
 plex example is, 'Men who are honest though poor 
 will be respected and helped.' The whole sense of 
 this can be expressed in the two statements (a) 
 'Poor men who are honest will be respected,' and 
 (b) 'Poor men who are honest will be helped.' From 
 
CATEGORICAL PROPOSITIONS 245 
 
 these examples we can see that a separate expres- 
 sion must be given to each significant idea of any 
 complex of ideas. 
 
 Bearing in mind what a compound proposition 
 is, let us turn to the particular propositions which 
 qualify their subject terms by the use of exclusive 
 words or phrases. These propositions, we have said, 
 are compound. An example is, 'Some only who en- 
 list will find their way to the firing line/ This 
 obviously cannot mean, 'Some who do not enlist will 
 find their way to the firing line;' that is, it cannot 
 be treated as a particular exclusive proposition. 
 What the statement means is (a) 'Some who enlist 
 will find their way to the firing line/ and (b) 'Some 
 who enlist will not find their way to the firing line.' 
 The following must also be treated as a compound 
 proposition, 'Excepting a few, all these answers are 
 wrong.' What the proposition states is (a) 'Some 
 of these answers are wrong,' and (b) 'Some of these 
 answers are not wrong.' From these examples it 
 seems obvious that whenever we qualify, in the way 
 indicated, the subject terms of particular proposi- 
 tions, that is, whenever 'some' is used in its exclusive 
 sense, the proposition must be resolved into two 
 independent particular propositions, the one affirm- 
 ative and the other negative. In the light of these 
 cases, we may also understand why the particular 
 proposition which has no such exclusive significance 
 must be interpreted as either affirmative or nega- 
 tive, and not as both. For instance, 'Not all for- 
 eigners are to be mistrusted' means 'Some foreigners 
 
246 A TEXT-BOOK OF LOGIC 
 
 are not to be mistrusted;' and if any one were to 
 add to this interpretation, 'Some foreigners are to 
 be mistrusted/ he would be going beyond what is 
 said to a secondary implication of what is said. The 
 latter statement is doubtless implied in the original 
 statement, but it is not what that statement asserts. 
 Modality of Propositions. The knowledge we 
 have of different subjects, as we are all aware, varies 
 not only with respect to the nature of these subjects 
 themselves, so that one kind of knowledge we call 
 history, and another science, and another phil- 
 osophy, but also with respect to the degrees of our 
 attainments in any of these departments of knowl- 
 edge, so that we speak about these several subjects 
 with differing degrees of confidence. If, for ex- 
 ample, the student has diligently pursued the study 
 of bacteriology for a number of years he will not 
 only know a great deal about the nature and condi- 
 tions of the changes that microscopic organisms 
 produce in their hosts, but he will have developed, 
 with his increasing knowledge of the subject, a cer- 
 tain degree of confidence in his ability to describe 
 these changes, to prepare cultures, and to do many 
 things besides. If the same student has not given 
 a good deal of time to the study of history, he will 
 not feel the same degree of confidence that we ob- 
 served in the former case, if he were asked to name, 
 for instance, the causes that produced the French 
 Revolution. There are, then, different degrees of 
 knowledge, and these get reflected in the degrees of 
 confidence with which we express what we know. It 
 
CATEGORICAL PROPOSITIONS 247 
 
 is this fact that logic refers to under the term Mo- 
 dality. The meaning of this statement may become 
 clearer if it is pointed out that the term modality 
 does not refer to any uncertainty that may exist 
 as to the nature and relations of the object of judg- 
 ment, but only to the degrees of certainty of our 
 knowledge of the object. Modality, that is to say, is 
 a logical distinction; it characterises our thoughts 
 about things, and not the things themselves. Whether 
 there is any uncertainty in things themselves can- 
 not be discussed in an elementary logic, but that 
 varying degrees of certainty and uncertainty attach 
 to our knowledge of things is a fact well known to 
 all. 
 
 It is usual, in logic, to distinguish three degrees 
 of certainty, and to throw these into typical preposi- 
 tional forms when we wish to express the modality 
 of our thought. The propositions which set forth 
 the modality of our judgments are called assertoric, 
 problematic and apodeictic. We may state what is 
 to be understood by each of these in order. 
 
 The Assertoric Proposition. An assertoric prop- 
 osition has the same form as the affirmative cate- 
 gorical proposition, and yet is not to be understood 
 in the same way. The categorical proposition ex- 
 presses the way that S and P are related in the uni- 
 verse of discourse that defines the limits of the judg- 
 ing activity, and, therefore, relates to the matter of 
 the judgment. The assertoric judgment, on the 
 other hand, expresses one of the degrees of certainty 
 of our knowledge about the subject-matter. For 
 
248 A TEXT-BOOK OF LOGIC 
 
 example, if we were to say, 'All men are biped/ we 
 should most likely be understood to express a judg- 
 ment founded upon common observation, and that 
 is what the categorical proposition of the form, 
 *S is P,' usually does. If, however, with respect to 
 this judgment, we were asked, 'What makes you 
 think so?' we should possibly hunt around the var- 
 ious corners of our knowledge for a reason for think- 
 ing that walking on two feet is characteristic of all 
 men. If from such an excursion and search we 
 were to return without anything that threw light 
 upon the question, we should probably reply, 'I don't 
 know, but he is a biped.' We should, that is, assert 
 with emphasis our original statement, and thereby 
 express our confidence in the correctness of the 
 original statement. What, therefore, an assertoric 
 proposition does is to assert that S is actually P, or, 
 stated another way, that 'S is P' is actual, whether 
 any reason, other than perception or memory sup- 
 plies, can be given or not. 
 
 The Problematic Proposition. A problematic 
 proposition states that 'S is possibly P,' or the fact 
 expressed by 'S is P' is possible. The possibility 
 does not imply any uncertainty in the fact expressed, 
 but only an uncertainty in the state of our knowl- 
 edge about the fact, an uncertainty that makes it 
 impossible for us to state with any higher degree 
 of confidence the correctness of what we say. For 
 example, the student who is reading this section of 
 logic may say, 'My understanding of the subject is 
 possibly correct.' What he means by this is not 
 
CATEGORICAL PROPOSITIONS 249 
 
 that his understanding may be described as possibly 
 correct, for there is no such thing as 'possibly cor- 
 rect,' but that the statement, 'My understanding of 
 this subject is correct' is a possibility in his own 
 case. If we take a simpler case this will become 
 clear. 'The rose is possibly white' does not mean 
 that 'possibly white' is the colour that the rose has, 
 for there is no such colour. We are to understand 
 the adverb to qualify not any part of the statement, 
 but the whole assertion 'The rose is white,' and 
 then, as in the other case, this statement expresses 
 a possibility. 
 
 If this is the view that we must adopt of prob- 
 lematic propositions, what, we may ask, is the 
 ground of the implied uncertainty? The uncertainty 
 is not due, as in assertoric propositions, to the fact 
 that there are no discoverable reasons for the state- 
 ment, but that the discovered grounds of the state- 
 ment are of such a nature that we can never be sure 
 that we have all the elements necessary to give our 
 statement any higher degree of certainty. To illus- 
 trate : the student's understanding of this paragraph 
 must, as we know, be correct or incorrect, just as the 
 rose must have any one or other of the colours that 
 belong to the species rose. If we have not seen the 
 rose in question, we know only that it is either red 
 or pink or white or yellow, and because it may be 
 something else than what we assert, we merely say 
 that it is possibly white. So in the case of the stu- 
 dent: his understanding is either correct or incor- 
 rect, but because the alternatives have not been de- 
 
250 A TEXT-BOOK OF LOGIC 
 
 termined with respect to the case in hand, he can 
 only say that his understanding of the paragraph 
 is possibly correct. A possibility, therefore, means 
 the presence of alternatives between which no 
 ground of decision has as yet been found. 
 
 Judgments which involve human volition as one 
 of their factors, even when these judgments involve 
 no alternatives, are said to be problematic. For 
 example, 'I may go tomorrow,' means that 'I will 
 go tomorrow' is the statement of a fact that is pos- 
 sible. Here we have not a series of alternatives as 
 the ground of the uncertainty of the judgment, but 
 the absence of some of the factors that are neces- 
 sary for a more positive statement. All actions that 
 depend on human volition are said to be contingent, 
 and therefore a judgment that involves volition as 
 one of its factors must always be problematic. 
 
 The Apodeictic Proposition. Apodeictic judg- 
 ments are necessary : 'S must be P.' There exists, 
 in this case, necessary grounds for the matter of 
 fact judged. 'S is P' is necessary. Necessity is a 
 word that must be used carefully. This is obvious 
 if we call attention to the different kinds of neces- 
 sity upon which our apodeictic statements depend. 
 Mathematical statements, although not expressed in 
 the form of apodeictic propositions, are necessary. 
 For example, 'A straight line is the shortest dis- 
 tance between two points.' What the mathematician 
 understands by this statement is that the shortest 
 distance between two points must be what we mean 
 by a straight line. The idea of a straight line 
 
CATEGORICAL PROPOSITIONS 251 
 
 carries that meaning necessarily. Here, then, we 
 have necessity ' resting upon the clearness with 
 which an idea itself is conceived or apprehended, 
 and not on anything else. Another class of neces- 
 sity is met with when our judgments rest upon 
 other judgments which may or may not be neces- 
 sary. For example, the equality of triangles on 
 equal bases and between the same parallels is a 
 case of necessity resting upon grounds that are 
 themselves necessary. In all truly apodeictic judg- 
 ments there is presumed to be an inter-connection 
 of fact that makes the fact asserted by the judg- 
 ment necessary. 
 
 REFERENCES 
 
 B. Bosanquet, The Essentials of Logic, Lect. VII. 
 
 J. G. Hibben, Logic, Deductive and Inductive, Chs. VII., VIII. 
 W. S. Jevons, Lessons in Logic, Lesson VIII. 
 J. N. Keynes, Formal Logic, 2d Edition, Part II., Ch. I. 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. III., Part I. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. V. 
 
 ADVANCED 
 
 J. M. Baldwin, Thought and Things, Vol. II., Part II., Ch. 
 
 VIII. 
 
 B. Bosanquet, Logic, Vol. I., Book I., Chs. II-IX. 
 F. H. Bradley, The Principles of Logic, Book I., Chs. VI- 
 
 VIII. 
 
 R. W. B. Gibson, The Problem of Logic, Ch. VII. 
 H. W. B. Joseph, An Introduction to Logic, Ch. VIII. 
 H. Lotze, Logic, Vol. I., Ch., II. 
 J. S. Mill, A System of Logic, Book L, Ch. IV. 
 F. C. S. Schiller, Formal Logic, Ch. XI. 
 
252 A TEXT-BOOK OF LOGIC 
 
 C. Sigwart, Logic, Chs. IV-VI. 
 
 J. Welton, A Manual of Logic, Book II., Ch. I. 
 
 QUESTIONS 
 
 1. What is the ground of the difference between the three 
 types of propositions? 
 
 2. Describe* the four main classes of categorical proposi- 
 tions. 
 
 3. Explain and illustrate what you understand by the 
 quantity of propositions. 
 
 4. What is a singular proposition? Illustrate and state 
 its importance. 
 
 5. What is a universal proposition? 
 
 6. What is the relation of the singular and universal prop- 
 osition? 
 
 7. What is a particular proposition, and with what form 
 of universal proposition is it most likely to be confused? 
 
 8. Describe and illustrate the indesignate proposition. 
 
 9. What do you understand by the quality of propositions? 
 
 10. What are the characteristics of affirmative propositions? 
 
 11. Describe and illustrate a negative proposition. 
 
 12. Why must the predicate of negative propositions be read 
 connotatively? 
 
 13. What is the relation of tautology to affirmative state- 
 ments? 
 
 14. In what way can tautological statements be overcome? 
 
 15. What is the logical status of nonsense? 
 
 16. In what respects are exceptive and exclusive proposi- 
 tions alike? 
 
 17. State and illustrate the characteristics of exceptive 
 propositions. 
 
 18. What is an exclusive proposition? Illustrate. 
 
 19. Why are there no particular exceptive or exclusive 
 propositions? 
 
 20. What is a compound proposition? By what other name 
 is it known? Illustrate. 
 
 21. Explain what is meant by the modality of propositions. 
 
CATEGORICAL PROPOSITIONS 253 
 
 22. What is an assertoric proposition, and how does it 
 differ from the categorical proposition? 
 
 23. Explain and illustrate the problematic proposition. 
 
 24. How will you classify judgments which involve human 
 volition as one of its factors? 
 
 25. Describe and illustrate the apodeictic proposition. 
 
 EXERCISES. 
 
 1. Write in parallel columns a list of six singular and six 
 general propositions, and be ready to defend the as- 
 signed character of these propositions. 
 
 2. What kind of proposition is, 'Water is a liquid composed 
 of one part oxygen and two parts hydrogen.' Give rea- 
 sons for your answer. 
 
 3. What is the distribution of the predicate term of the 
 proposition in the preceding question? 
 
 4. Give three illustrations of indesignate propositions. 
 
 5. What kind of proposition is, 'Oxygen is necessary for 
 the maintenance of life'? 
 
 6. Without using the sign of quantity 'some,' give three 
 illustrations of particular propositions. 
 
 7. Classify the following propositions from the standpoint 
 of quantity, and in each case state the reason for your 
 classification : 
 
 (1) Each of the hunters shot a bird. 
 
 (2) Rivers generally run into the sea. 
 
 (3) Blood is thicker than water. 
 
 (4) Afflictions are often salutary. 
 
 (5) Can the leopard change his spots? 
 
 (6) Veteran soldiers are the steadiest in battle. 
 
 (7) Suspicion ever haunts the guilty mind. 
 
 (8) Knowledge is power. 
 
 (9) The longest road has an end. 
 
 (10) Almost any Turk hates a Greek. 
 
 (11) Philosophy and Psychology are necesary to a well- 
 rounded education. 
 
 (12) Only those who know are in the end to be trusted. 
 
254 A TEXT-BOOK OF LOGIC 
 
 8. Illustrate how affirmative statements can be made either 
 tautological or nonsensical. 
 
 9. Write a complete account of how one negative state- 
 ment of your own selection may conceivably have come 
 to be made. 
 
 10. Write a list of three assertoric propositions, and show 
 how they differ from affirmative categorical proposi- 
 tions. 
 
 11. Explain the problematic nature of six propositions of 
 your own selection. 
 
 12. Write a list of three apodeictic propositions. 
 
CHAPTER IX 
 
 IMPLICATIONS OF CATEGORICAL PROPOSITIONS 
 
 Relation of Quantity and Quality in Categorical 
 Propositions. When the subject term of a proposi- 
 tion is read in denotation, it refers to a determined 
 or undetermined number of individuals, and when 
 the predicate term of a proposition is read in conno- 
 tation, it either affirms or denies the meaning of the 
 predicate term of the individuals denoted by the 
 subject term. Now, since every proposition under- 
 takes to set forth both these relations of its subject- 
 matter, there are no propositions which do not pos- 
 sess both quantity and quality. 
 
 From the standpoint of their quantity, categor- 
 ical propositions, as we have seen, are either univer- 
 sal or particular; that is, logical statements are 
 always about a determinate or indeterminate part 
 of the subject-matter of such statements. From the 
 standpoint of their quality, categorical propositions 
 are either affirmative or negative; that is, logical 
 statements either affirm or deny an attribute of 
 some determinate or indeterminate part of their 
 subject. Combined in a single statement, these 
 facts and relations may be expressed thus : Propo- 
 sitions with distributed, as also those with undis- 
 tributed, subject terms are either affirmative or 
 negative in quality. There are thus four proposi- 
 tions, the universal affirmative, the universal neg- 
 
 (255) 
 
256 A TEXT-BOOK OF LOGIC 
 
 ative, the particular affirmative, the particular neg- 
 ative, whose relations may be shown in a table 
 as follows: 
 
 QUANTIT\ QUALITY 
 
 {a. Affirmative 
 
 b. Negative 
 Propositions , 
 
 f a. Affirmative 
 Particular 
 
 [ b. Negative 
 
 This table may be read: Propositions may be 
 universal in quantity and either affirmative or neg- 
 ative in quality ; or they may be particular in quan- 
 tity and either affirmative or negative in quality. 
 
 Structural Formulae indicating the Quantity and 
 Quality of Propositions. The problems that we are 
 to study in this chapter arise out of the fact that 
 propositions involve the relations both of quantity 
 and quality. Whatever else the student can or can- 
 not do with a proposition, it is of fundamental im- 
 portance that he should be able to determine it both 
 with respect to its quantity, and also with respect to 
 its quality. The student will find ic entirely possible 
 to acquire a considerable degree of facility in thus 
 determining the propositions that come before him 
 for study ; and, moreover, a little additional industry 
 in this matter will carry him a long way toward 
 overcoming some of the difficulties that he will meet 
 farther along the road. When he has become prac- 
 tically familiar with these distinctions, it will be a 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 257 
 
 great convenience if, for the propositions that em- 
 body these distinctions, he write formulae which 
 indicate their quantity and quality. The value of 
 such formulae is that they enable one to deal only 
 with the essential aspects of assertions, and they 
 shorten the method of referring to these essential 
 aspects. Like any other formulae, those used in 
 logic are more or less arbitrary devices, and are to 
 be justified by their usefulness. They are in no 
 sense a substitute for the logical facts and relations 
 which they are merely the means of expressing. 
 
 Our first aim then will be to distinguish by a 
 convenient symbol the four typical propositions 
 mentioned above. This is usually done by taking 
 the first vowel of the Latin word for affirmation 
 (affirmo), and the first vowel of the Latin word 
 for negation (nego) to denote the universal propo- 
 sition of the quality indicated by the word, and the 
 second vowel of each word in like manner to indi- 
 cate the respective particular propositions. Thus, 
 A and E, the first vowels in the words affirmo and 
 nego, are used to indicate the universal affirmative 
 and universal negative propositions respectively. 
 The second vowels in the same Latin words are I 
 and 0, and these are used to indicate respectively 
 the particular affirmative and particular negative 
 propositions. If, now, we add these facts to the 
 table printed above, we have the following result : 
 
 17 
 
258 A TEXT-BOOK OF LOGIC 
 
 QUANTITY QUALITY SYMBOL 
 
 f a. Affirmative A 
 1. Universal 
 
 [ b. Negative E 
 Propositions - 
 
 {a. Affirmative I 
 
 b. Negative O 
 
 Whenever, in the foregoing pages, we have had 
 occasion to refer to the structure of a proposition 
 without respect to its quantity, we have written 'S 
 is P,' or 'S is-not P.' Whenever we have wished to 
 indicate the quantity as well as the quality of prop- 
 ositions, we have written 'All S is P,' 'No S is P,' 
 'Some S is P,' 'Some S is-not P.' This, however, is 
 too cumbersome a method when a simpler one is 
 possible. And, therefore, logicians have adopted 
 the device of substituting for the copula in proposi- 
 tions of the general form S-P, one or other of the 
 four vowels by which the four kinds of categorical 
 propositions are distinguished. In this way we get 
 the following structural formulae: SaP, SeP, SiP, 
 SoP, which are read 'All S is P/ 'No S is P,' 'Some 
 S is P/ 'Some S is-not P.' 
 
 The following table summarises the important 
 facts : 
 
 QUANTITY AND STRUCTURAL 
 
 QUALITY FORMULA READ 
 
 f 1. Universal Affirmative SaP All S is P 
 
 2. Universal Negative SeP No S is P 
 Propositions <j 
 
 13. Particulare Affirmative S&P Some S is,P 
 
 4. Particular Affirmative S$P Some 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 259 
 
 This table should be read : Propositions as to their 
 quantity and quality may be either universal affirm- 
 ative, with the structural formula SaP which 
 is read 'All S is P;' or universal negative, with 
 the structural formula SeP which is read 'No S is 
 P;' or particular affirmative, with the structural 
 formula SiP which is read 'Some S is P;' or par- 
 ticular negative with the structural formula SoP 
 which is read 'Some S is-not P.' 
 
 Distribution of the Terms of the Four Categorical 
 Propositions. The logical meaning of distribution has 
 been discussed in the chapter on terms, and we met 
 the same question again when considering the quan- 
 tity of propositions. We need, therefore, only repeat 
 what was shown more at length above, that by dis- 
 tribution is meant the width or extent of the mean- 
 ing expressed in a proposition. We have seen, for 
 example, that from the standpoint of quantity the 
 subject terms of universal propositions are dis- 
 tributed ; they denote a determinate number of indi- 
 viduals, each of which possesses, or does not possess, 
 in addition to the qualities connoted by the term 
 itself, those qualities also that are connoted by the 
 predicate term of such propositions. From the same 
 standpoint, the subject terms of particular proposi- 
 tions, on the other hand, are undistributed; they 
 refer to an indeterminate number of denoted indi- 
 viduals. 
 
 We have now to ask what influence the quality 
 of propositions has upon the distribution of pred- 
 icate terms. And first let us consider affirmative 
 
260 A TEXT-BOOK OF LOGIC 
 
 propositions. In affirmative propositions we pred- 
 icate the attribute connoted by P of the object or 
 objects denoted by S. So far as they are affirmative, 
 propositions do not enable us to say whether there 
 are any objects, other than those denoted by the 
 subject term, to which the attributes of the pred- 
 icate term apply. Sometimes there are such objects ; 
 as, for example, The cat is a domesticated animal/ 
 for, as we know, there are other domesticated ani- 
 mals than cats. Sometimes there are not, as, for 
 example, Terception is the consciousness of par- 
 ticular material objects present to sense/ for there 
 are no other objects to which such a description can 
 apply except perception. In view of these facts, it 
 is obvious that, from the form of the proposition, it 
 is quite impossible to determine whether universal 
 affirmative statements are to be understood in the 
 one or the other of the ways just indicated ; whether, 
 that is to say, they may be said to have distributed 
 or undistributed predicate terms. On account of 
 this uncertainty, it is customary, in the absence of 
 any reason connected with the subject matter to the 
 contrary, to regard the predicate terms of such 
 propositions as undistributed. 
 
 The predicate terms of negative propositions, on 
 the other hand, are distributed. The reason for this 
 is that it is only when every object which can be 
 included in the denotation of the predicate term is 
 excluded from the subject that the proposition can 
 have a negative force at all. For if all P's were 
 not definitely separated from the S, some P's might 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 261 
 
 be included in it, and this would not express the 
 meaning of negation. Negation, as we have seen, 
 has always a definitely exclusive force. And this is 
 true of negative propositions irrespective of their 
 quantity ; it is true of the particular as well as of the 
 universal negative proposition. Of the universal 
 proposition, SeP, this is easily seen to hold. For 
 if 'No S's are P's' has any meaning at all, it must 
 surely mean that not any of the S's are any of the 
 P's. That is to say, of none of the objects that have 
 the qualities connoted by S can we affirm that they 
 have also the qualities connoted by P. If that is 
 true, no P's are any of the S's. But the same thing 
 can be shown also of the particular proposition, SoP. 
 'Some S's are-not P's' must mean that none of the 
 objects denoted by S has the qualities connoted by 
 P ; and that is equivalent to saying that none of these 
 S's are at the same time P's. The objects denoted 
 by P, if there are any, are entirely excluded from 
 the number of objects referred to by S. If, in this 
 case, any difficulty arises on account of the un- 
 distributed nature of the subject term, we can only 
 say that the meaning of the proposition is that there 
 are at least some unspecified instances of S's that do 
 not have the characteristics of P; and that if, as 
 may or may not happen, you discover any S's that 
 do have these characteristics, then they are not the 
 S's to which the proposition refers. It follows, 
 from these considerations, that the predicate terms 
 of all negative propositions are distributed. 
 
262 
 
 A TEXT-BOOK OF LOGIC 
 
 We may summarise the foregoing discussion in 
 the four following statements: 
 
 1. The subject terms of propositions that are 
 universal in quantity are distributed. 
 
 2. The subject terms of propositions that are 
 particular in quantity are undistributed. 
 
 3. The predicate terms of propositions that are 
 affirmative in quality are undistributed. 
 
 4. The predicate terms of propositions that are 
 negative in quality are distributed. 
 
 Thorough familiarity with the distribution of 
 the terms of categorical propositions is so essential 
 to the student's understanding of what follows that 
 he is urged to master the subject at this point of his 
 studies. Because of the importance of the subject, 
 and as a further aid to its mastery, we add the fol- 
 lowing tables each of which represents the facts 
 contained in the foregoing summary. The letters 
 D and U stand for distributed and undistributed 
 respectively : 
 
 PROPOSITION 
 
 STANDPOINT 
 
 Quantity 
 
 f 
 SUBJECT 
 
 D 
 
 a 
 
 > 
 
 PREDICATE 
 
 U 
 
 D 
 
 e 
 
 D 
 
 U 
 
 i 
 
 U 
 
 U 
 
 
 
 D 
 
 STANDPOINT 
 
 Quality 
 
 This table may be read as follows : From the stand- 
 point of quantity, the subject term of an A or uni- 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 263 
 
 versal affirmative proposition is distributed; from 
 the standpoint of quality, the predicate term of an 
 A or universal affirmative proposition is undistrib- 
 uted, etc. 
 
 Another way of stating the same set of facts is 
 to say that the subject terms of propositions that 
 are universal in quantity are distributed, and those 
 that are particular in quantity are undistributed; 
 that the predicate terms of propositions that are 
 affirmative in quality are undistributed, and those 
 that are negative in quality are distributed. The 
 following table represents these facts : 
 
 QUANTITY DISTRIBUTION 
 
 (Universal D 
 
 Subject terms J 
 
 [Particular ^U 
 
 QUALITY DISTRIBUTION 
 
 f Affirmative U 
 
 Predicate terms 1 
 
 [Negative D 
 
 Meaning and Classes of Implication. The group 
 of topics that are now to be discussed, and to which 
 the preceding pages are an introduction, is by some 
 writers brought together under the title of 'imme- 
 diate inferences/ and by others under the title 'in- 
 terpretation of propositions/ The objection that is 
 usually urged against 'immediate inferences' is that 
 an inference always involves the use of a middle 
 term, and is therefore mediate; and, consequently, 
 
264 A TEXT-BOOK OF LOGIC 
 
 that it is a contradiction to speak of 'immediate' in- 
 ferences. The objection that may be brought 
 against 'interpretation of propositions' is that it 
 tends to confuse two different things, namely, the 
 import or meaning of propositions, and the question 
 of what other statements we are committed to in 
 making any statement whatever. We shall speak 
 of the 'implications of propositions,' since the ques- 
 tions that are to be considered in this chapter relate 
 to the various methods of determining the relations 
 that exist between our formally expressed proposi- 
 tions, and other unexpressed propositions with 
 which they are immediately connected. Implication 
 etymologically means 'folded-in,' so that the idea 
 the topic suggests is that folded within any state- 
 ment we make there are other statements that may 
 be brought to light by the use of appropriate meth- 
 ods. The practical value of this chapter consists in 
 the opportunity it affords of finding out that our 
 statements ordinarily mean much more than we 
 actually express in them. 
 
 We have to consider two main classes of impli- 
 cations : 
 
 (1) The Opposition of Propositions. By op- 
 position of propositions is meant the relation that 
 the truth or falsity of one proposition has to the 
 truth or falsity of other propositions dealing with 
 the same subject-matter, that is, having the same 
 subject and predicate. 
 
 (2) Eductions. By eductions is meant the 
 relation that one proposition accepted as true has 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 265 
 
 to other propositions dealing with the same subject- 
 matter from other points of view. 
 
 The Opposition of Propositions. The term oppo- 
 sition applied to propositions would strictly mean 
 that propositions could stand in this relation only 
 when the truth of the one involved the falsity of 
 the other, and vice versa. This was the original 
 meaning and use of the term in logic. But it was 
 found convenient to include under the same title a 
 consideration of propositions that are not incompat- 
 ible with one another. Opposition, as it is now used, 
 embraces, therefore, a study of the relations of any 
 two propositions referring to the same subject- 
 matter whether the truth expressed by one is or is 
 not compatible with that expressed by the other. 
 Thus, propositions relating to the same subject, but 
 differing in quantity, or quality, or both, are said 
 to be opposed to each other. 
 
 Since there are only four categorical proposi- 
 tions, it is evident that each stands in relation to 
 three others. Thus: 
 
 SaP is related to SeP, SiP, SoP. 
 
 SeP is related to SaP, SiP, SoP. 
 
 SiP is related to SaP, SeP, SoP. 
 
 SoP is related to SaP, SeP, SiP. 
 
 If we examine this list of possible oppositions, 
 we shall see that each proposition is related to (1) 
 a universal proposition, (2) a particular proposi- 
 tion, (3) an affirmative proposition, (4) a negative 
 proposition. In other words, all propositions are 
 related to others (1) of the same and (2) different 
 
266 A TEXT-BOOK OF LOGIC 
 
 quantity, and (3) of the same and (4) different 
 quality. There are, consequently, four kinds of 
 opposition in which any proposition may stand. 
 Thus, the relation between 
 
 1. Universal propositions of different quality 
 is said to be one of contrariety : SaP, SeP. 
 
 2. Universal and particular propositions of the 
 same quality is said to be one of subalternation : 
 SaP, SiP; SeP, SoP. 
 
 3. Universal and particular propositions of dif- 
 ferent quality is said to be one of contradiction: 
 SaP, SoP; SeP, SiP. 
 
 4. Particular propositions is said to be one of 
 subcontrariety : SiP, SoP. 
 
 We shall consider each of these kinds of opposi- 
 tion in the order in which they have been named; 
 and since any statement we make may be either true 
 or false, we shall have to examine the propositions 
 that stand in opposition on the supposition both of 
 their truth and falsity. 
 
 Contrariety. Contrary opposition exists between 
 universal propositions of a different quality; that 
 is, between SaP and SeP. Thus, contrary proposi- 
 tions differ in quality only. 
 
 If what any universal proposition states is true, 
 what its contrary states must be false. For example, 
 if it is true that 'All men die/ it is false that 'No 
 men die.' If it is true that 'No men are angels,' it 
 is false that 'All men are angels.' If, therefore, we 
 accept the truth of what either SaP or SeP states, 
 the falsity of what its contrary states follows as a 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 267 
 
 matter of course, for the reason that the same pred- 
 icates or qualities cannot belong, and not belong, to 
 the same subject. On the other hand, if what any 
 universal proposition states is false, what its con- 
 trary states is left in doubt. If, for example, it is 
 false that 'All men are six feet tall,' we are left in 
 doubt as to whether 'No men are six feet tall,' be- 
 cause some men may be. 
 
 Let us connect these facts with what we have 
 already learned. We saw, in the chapter on terms, 
 that if two species of a genus differ from one an- 
 other more than they do from any of the other co- 
 ordinate species, the relation in which they stand is 
 one of contrariety. If, for example, within the genus 
 G the species S have the characteristic P, then how- 
 ever great and numerous the increasing differences 
 between one species and another, they cannot be so 
 great and numerous that, within the genus, P can 
 be denied of any of the species. Based upon the 
 degree of their variation from the genus, all the 
 species, as we have seen, have a recognised place 
 within the genus. But whatever the variations that 
 occur, the species are held together by their common 
 likeness, and so long as predication is concerned 
 with this common likeness, so long can we not en- 
 tertain any proposition which denies it of any or of 
 all the species of the genus. If SaP is true, the 
 proposition that denies that S is P, SeP, must be 
 false, and vice versa. 
 
 Let us look at the other case where something 
 is falsely predicated of all the species. Now what is 
 
268 A TEXT-BOOK OF LOGIC 
 
 thus predicated cannot be the genus, for the genus 
 can only be predicated truly. If anything is falsely 
 predicated, it must be something that is either an- 
 other genus, when the statement would be abso- 
 lutely false, or something that is or may be a differ- 
 entia, when the statement will be partially false. 
 If, for example, 'All flesh is grass' were to be inter- 
 preted literally, the statement would be false, be- 
 cause it predicates a genus that is wholly mislead- 
 ing; and if one were to say that 'All vertebrates 
 live in the water,' that would be false, because it 
 predicates what is or may be a differentia, some- 
 thing that belongs to one of the species though not 
 to all of them. In order to detect the falsity in these 
 instances, we must know that what is predicated is 
 either a wrong genus or a differentia, and this is not 
 possible without going beyond what is given in a false 
 statement. Hence, if all we know is that P is 
 wrongly predicated of S, we cannot say whether P 
 belongs in part or not at all to S, and, therefore, can- 
 not infer the truth of the contrary of the original 
 proposition. The contrary of a false universal, that 
 is to say, is involved in doubt. 
 
 Again, the relations of contrary propositions 
 may be studied from the side of the denotation 
 of their terms. Thus, it cannot be true that 'All' 
 and 'None' of the objects denoted by the subject 
 term of a proposition have the qualities connoted 
 by the predicate term ; the truth of the one excludes 
 the truth of the other. That the falsity of one prop- 
 osition involves its contrary in doubt may be shown 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 269 
 
 as follows: If some of the objects denoted by the 
 predicate term of an affirmative proposition, and 
 none of the objects denoted by the same term in a 
 negative proposition, belong to the group of objects 
 denoted alike by the subject terms of these proposi- 
 tions, then it is obvious that in the one case P falls 
 partly within, and in the other wholly without, the 
 group of objects denoted by the subject terms of 
 the two propositions. If, now, we make the state- 
 ment falsely that 'All S falls within P without ex- 
 hausting it/ we connot affirm truly the contrary of 
 this statement, 'No S falls within P/ because there 
 is another alternative to the one offered by the con- 
 trary, namely, the case where S falls partly within 
 and partly without the class of objects denoted by 
 P; and which of these two cases is true cannot be 
 determined without examining the cases themselves. 
 Representing these facts diagrammatically thus : 
 
 we must say that if SaP is false, SeP cannot be 
 true without disposing of the alternative case SiP. 
 But this cannot be done formally, but only by an 
 examination of the subject-matter of these propo- 
 sitions. 
 
 Subalternation. Subaltern opposition exists be- 
 tween a universal and a particular proposition of 
 the same quality; that is, between SaP and SiP; 
 
270 A TEXT-BOOK OF LOGIC 
 
 SeP and SoP. Thus, subaltern propositions differ 
 in quantity only. 
 
 If what the universal proposition states is true, 
 what its subaltern states is also true. This follows 
 from the fact that universal propositions distribute 
 their subject terms. Thus, if something is true or 
 false, as the universal states, of each of a class of 
 objects, it is true or false of any number of them, 
 since these must be identical with some of the for- 
 mer. The truth, therefore, of the particular is in- 
 volved in the truth of the universal proposition. 
 Hence, as may be seen by studying the accompany- 
 ing diagram, if any part of the S that falls wholly 
 
 SaP SiP SeP SoP 
 
 within P, (SaP), or wholly without P, (SeP), were 
 to fall partly without or partly within P, some part 
 of S would, in the one case, fall partly within (SiP) , 
 and, in the other, partly without (SoP) P, and it is 
 of these parts that the statements of the respective 
 subaltern propositions is made. 
 
 On the other hand, if what the universal proposi- 
 tion states is false, what its subaltern states is left 
 in doubt. The truth of the particular is not involved 
 in the falsity of the universal, and cannot, there- 
 fore, be the ground of the latter's falsity. But, as 
 we shall see, it may be. We have studied already 
 one ground of falsity of universal statements. We 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 271 
 
 have seen, for example, that when the contrary of 
 any proposition is true, that proposition is abso- 
 lutely false. But we have also seen that if we start 
 with the falsity of a universal statement, nothing 
 can be affirmed as to the truth or falsity of its con- 
 trary. Now, in contrast to the falsity involved in 
 the contrary relation, that involved in the subaltern 
 relation is only relative, that is, the falsity may be 
 due not to the fact that S-P asserts something con- 
 trary to fact, but that it is asserted without regard 
 to existing limitations. In other words, since there 
 are degrees of error, as well as of truth, SaP and 
 SeP may owe their falsity to the fact that only SiP 
 and SoP are true respectively. But, here again, if 
 we start with the falsity of the universal, we cannot 
 say that its subaltern is true or false; truth or 
 falsity, in this case, simply remain possible alter- 
 natives between which we can decide only by going 
 outside wha't is given in the original proposition. 
 And this is equivalent to saying that the subaltern 
 is always involved in doubt when all that we know 
 is that the universal or subalternans is false. 
 
 What we have seen is that the truth of a univer- 
 sal involves the truth of its subaltern ; but that the 
 falsity of a universal involves its subaltern in doubt. 
 
 Let us now consider how the universal is affected 
 by the truth or falsity of its particular, subaltern, 
 proposition. And, first, let us take the case where 
 the subaltern is true. If the only thing we know 
 about a group of objects is that some of them are 
 in a particular place, it is obvious that we cannot 
 
272 A TEXT-BOOK OF LOGIC 
 
 say that they are all in that place; and the reason 
 is not that some are in another place, for that ex- 
 ceeds the knowledge contained in the original prop- 
 osition, but that some may be. For a similar reason, 
 we cannot affirm that 'No trees are in leaf/ if all 
 that we know is that 'Some trees are-not in leaf/ 
 From the truth of a particular proposition, there- 
 fore, we can only conclude that its subalternans the 
 universal of the same quality is doubtful. Let 
 us take, secondly, the case where the subaltern is 
 false. Here the falsity of the subaltern involves 
 the falsity of the subalternans. Thus, if 'Some apples 
 are blue' is false, it is likewise false that 'All apples 
 are blue/ and if 'Some apples are-not red' is false, 
 it is likewise false that 'No apples are red/ The 
 reason for this case is found in the fact that par- 
 ticular propositions affirm or deny a predicate of 
 certain unspecified objects of a class, and not of the 
 class as a whole. If, therefore, we know that a 
 statement is false in some case, we know that it 
 cannot be true of all cases, since all cases must in- 
 clude the case in which it is known to be false. 
 Falsus in uno, falsus in omnibus. We are dealing 
 here with the exception under which a rule breaks 
 down. 
 
 Contradiction. Contradictory opposition exists 
 between a universal and a particular proposition 
 that differ from each other in quality; that is, be- 
 tween SaP and SoP, SeP and SiP. Thus, contradic- 
 tory propositions differ both in quantity and quality. 
 
 If what any universal proposition states is true, 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 273 
 
 what its contradictory states must be false. If it 
 be true that 'All men are willing to give their lives 
 for a cause/ it is false that 'Some men are-not will- 
 ing to give their lives for a cause.' If it is true that 
 'No men are utterly selfish/ it is false that 'Some 
 men are utterly selfish/ If, on the other hand, what 
 a universal proposition states is false, what the con- 
 tradictory opposite states must be true. For ex- 
 ample, if it is false that 'Every man has his price/ 
 it is true that 'Some men cannot be bought/ and if 
 it is false that 'None of the candidates were suc- 
 cessful/ it is true that some were. Further, the 
 truth or falsity of particular propositions involves 
 the falsity or truth of their contradictories. If 
 'Some one is going to get hurt/ is true, it is false 
 that 'No one is going to get hurt/ but if the state- 
 ment is false, then 'No one is going to get hurt* is 
 true. If 'Some people are short sighted' is true, it 
 is false that 'No people are short sighted / but if it 
 is false that 'Some kinds of ignorance promote vir- 
 tue/ it is true that 'No kinds of ignorance promote 
 virtue/ 
 
 We may express these results in the single state- 
 ment that the truth of one of the propositions in 
 contradictory opposition involves the falsity of the 
 other ; and the falsity of one, the truth of the other. 
 Of any pair of contradictory propositions, one must 
 be false, and the other true. Contradiction is, there- 
 fore, the most complete form of logical opposition. 
 
 Subcontrariety. Subcontrary opposition exists 
 between particular propositions of different quality ; 
 
 18 
 
274 A TEXT-BOOK OF LOGIC 
 
 that is, between SiP and SoP. Thus, subcontrary 
 propositions differ in quality only. 
 
 If we make the two statements that 'Some men 
 are blue-eyed' and 'Some men are-not blue-eyed,' 
 each of these statements is true, and they are in 
 subcontrary relation to each other. But the truth 
 of either one of them is not sufficient to establish 
 the truth of the other. If, for example, we repre- 
 sent our two propositions thus : 
 
 SiP SoP 
 
 it will be evident that in each case P, in part or 
 whole, is predicated of a different part of S. 
 If, consequently, we know that 'Some indeterminate 
 number of men are blue-eyed,' (SiP), this is not a 
 sufficient ground for saying that the rest are, or are 
 not, blue-eyed. The fact that we are dealing with 
 particular propositions which have undistributed 
 subject terms, that is, terms that do not take into 
 account a determinate number of instances of the 
 class, but only more or less of them, prevents us 
 from saying anything definite of the rest of the class 
 with respect to their being or not being blue-eyed. 
 Of the propositions, therefore, that exist in subcon- 
 trary opposition, we may say that the truth of 
 the one leaves the truth of the other in doubt. 
 
 Propositions in the subcontrary relation cannot 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 275 
 
 both be false. In other words, the falsity of one in- 
 volves the truth of the other. For example, if it is 
 false that 'Some men are four-footed,' it is true that 
 'Some men are-not four-footed.' That is, it is only 
 on condition that some men are not four-footed that 
 we can deny the truth of the statement that 'Some 
 men are four-footed.' This view of subcontrary 
 opposition is required by the fact that if both par- 
 ticular propositions were false, their contradictories 
 would both be true; but, as we have seen, SaP and 
 SeP cannot both be true, for if one is true the other 
 is proved to be false. But if, as we have seen, the 
 falsity of the universal 'All men are four-footed/ 
 for example involves its contrary in doubt, we 
 can at least say that its contradictory 'Some men 
 are-not four-footed' is true. 
 
 The Square of Opposition. The accompanying 
 diagram, called the Square of Opposition, is a me- 
 chanical devise which has long been traditional in 
 logic, and is intended as an aid to the better under- 
 standing of the doctrine of opposition. The univer- 
 sal propositions are placed at the top, the particular 
 propositions at the bottom of the diagram; the 
 affirmative propositions are placed on the left, and 
 the negative ones on the right. The lines connecting 
 any two propositions indicate the kind of opposition 
 that exists between them. The top and bottom lines 
 which are horizontal and parallel to each other con- 
 nect propositions of the same quantity ; the side lines 
 which are perpendicular and parallel connect prop- 
 ositions of the same quality. The long diagonal lines 
 
276 
 
 A TEXT-BOOK OF LOGIC 
 
 connect propositions that are different in both quan- 
 tity and quality. 
 
 Let us now see how it may be used to throw 
 light on the doctrine of opposition. It will be ob- 
 served at once that every proposition has its con- 
 tradictory, and in contradiction, it will be remem- 
 bered, we have the most complete form of logical 
 opposition. To work the relations of opposition out 
 under the control of the contradictory relation seems 
 to simplify the whole matter for most students. We 
 summarise the doctrine of opposition below, and the 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 277 
 
 student is required to follow the statements out on 
 the Square of Opposition. Thus, if 
 
 SaP is true, its contradictory and its contrary 
 are false, and its subaltern is true. 
 
 SaP is false, its contradictory is true, and its 
 contrary and its subaltern are doubtful. 
 
 SeP is true, its contradictory and its contrary 
 are false, and its subaltern is true. 
 
 SeP is false, its contradictory is true, and its 
 contrary and its subaltern are doubtful. 
 
 SiP is true, its contradictory is false, and its 
 subcontrary and subalternans are doubtful. 
 
 SiP is false, its contradictory and sub-contrary 
 are true, and its subalternans is false. 
 
 SoP is true, its contradictory is false, and its 
 subcontrary and subalternans are doubtful. 
 
 SoP is false, its contradictory and sub-contrary 
 are true, and its subalternans is false. 
 
 It may be helpful to represent these facts and 
 relations diagrammatically. This we may do by 
 drawing only so much of the Square of Opposition 
 as embodies the relations in which a given proposi- 
 tion stands, utilising the arrow head to indicate the 
 direction in which given relations are to be read. 
 For example, the lines _^J diverge from a common 
 point and indicate, according to their direction, the 
 propositions we are considering and the relations in 
 which they stand. It is obvious that the example 
 chosen is the proposition. Since, then, the direc- 
 tion of the lines tells us what propositions we are 
 
278 
 
 A TEXT-BOOK OF LOGIC 
 
 
 dealing with, and in what relations of opposition 
 they stand, we may indicate at the ends of the lines 
 whether, in those relations, the proposition is true 
 (T) , false (F) , or doubtful (D) . Further, we may 
 indicate the original proposition by writing its given 
 truth or falsity in a circle. Following these direc- 
 tions, we have the accompanying result : 
 
 A summary of the doctrine of opposition is given 
 in the table on page 279. 
 
 Nature and Methods of Eduction. In the course 
 of our study, we have seen that all our judgments 
 are related to other judgments referring to the same 
 subject-matter, and, consequently, that every judg- 
 ment implies more than it asserts. Put more 
 directly, every judgment commits us not only to 
 what we assert, but also to the acceptance of all 
 the other judgments which are implied in what we 
 assert. Now when these implied judgments involve 
 a change in the point of view from which the sub- 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 279 
 
 ject-matter of the original judgment is viewed, they 
 are called eductions. 
 
 We may classify the methods of eduction as ob- 
 version, conversion, contraposition, and inversion. 
 But only two of these methods, obversion and con- 
 version, are fundamental. In the following sections, 
 we shall study the fundamental methods first, and 
 follow this with a consideration of the derived 
 methods, contraposition and inversion. 
 
 Given 
 
 SaP 
 
 SeP 
 
 SiP 
 
 SoP 
 
 
 
 F 
 
 T 
 
 F 
 
 ""I F 
 
 
 D 
 
 D 
 
 T 
 
 ScP ? 
 
 F 
 
 
 F 
 
 T 
 
 f F 
 
 D 
 
 
 T 
 
 D 
 
 
 D 
 
 F 
 
 
 D 
 
 { F 
 
 F 
 
 T 
 
 
 T 
 
 RnP ) 
 
 F 
 
 D 
 
 D 
 
 
 I F 
 
 T 
 
 F 
 
 T 
 
 
 TABLE OF OPPOSITIONS 
 
 Obversion. Other terms by which this method 
 is sometimes known are Permutation, Aequipollence, 
 Immediate inference by Private Conception. Obver- 
 sion is the logical form of the double negative with 
 which we have all become acquainted in the study 
 
280 A TEXT-BOOK OF LOGIC 
 
 of grammar. Like the double negative, it has the 
 force of changing an affirmative statement into a 
 negative one, and a negative statement into an 
 affirmative one. Obversion_effects no change in the 
 meaning of what is assertednbuT~onTy in its em- 
 phasis. For example, 'Barkis jgL.willin* ' by obver- 
 sion becomes 'Barkis is-not unwillin';' 'To do this 
 is-not unnecessary' becomes by obversion To do this 
 is necessary.' 
 
 In obversion only the quality of the original 
 proposition, called the obvertend, undergoes change ; 
 the quantity and the meaning remain the same. But 
 if the quality changes, the predicate term of the 
 obvertend must also undergo modification if the 
 meaning is to remain unaffected. What exactly is 
 this modification? It cannot be enough to say that 
 the characteristic of the obverse of a proposition is 
 that it has for its predicate term the negative of 
 the predicate of the proposition from which it is de- 
 rived, although, of course, this is, from the formal 
 point of view, true. Nor can we say that the con- 
 notation of the obvertend is affected, for that is the 
 question we are raising. If we are to understand 
 the particular significance of obversion, we shall 
 have to interpret it as a method that affects the 
 meaning of a proposition by a change in what the 
 proposition denotes. That is to say, the particular 
 range of the objects signified by the obvertend is 
 different from that of its obverse. For example, in 
 the illustrations used above, it is obvious that 
 Barkis' attitude must be one of willingness or un- 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 281 
 
 willingness; and of any action we may say that it 
 is necessary or unnecessary. Now, since obversion 
 is, in part, a matter of negation, we carry over into 
 that process all the characteristics that make nega- 
 tion significant. We have seen that negation is very 
 largely a matter of the emphasis that we give to 
 our knowledge, and of the definiteness or indefinite- 
 ness of our acquaintance with what we assert. 
 Thus, if we are not sure of the degree of Barkis' 
 willingness, we may express the actual state of our 
 information or opinion by saying that he is not- 
 unwilling. If we wish to suggest, but not to state 
 explicitly, the degree of necessity of the things we 
 do, we may say that they are not-unnecessary. A 
 guarded statement of the latter kind, it will be ob- 
 served, becomes more emphatic by obversion, for 
 we are thereby led to assert without qualification the 
 necessity of our actions. 
 
 There are two steps in the process of obversion ; 
 the first consists in changing the quality of the 
 original proposition without changing its quantity; 
 the second consists in negating the predicate term 
 of the original proposition. To consider the first 
 step we should observe, with respect to quantity, 
 that if the original proposition is universal the de- 
 rived proposition is universal, and if the original 
 proposition is particular the derived proposition is 
 particular; and, with respect to quality, that if the 
 original proposition is affirmative the derived prop- 
 osition is negative, and that if the original proposi- 
 tion is negative the derived proposition is affirm- 
 
282 
 
 A TEXT-BOOK OF LOGIC 
 
 ative. Combining these two considerations, we find 
 that, in obversion, an A proposition always changes 
 to an E, an E to an A, an I to an O, and an to an 
 I. With regard to negating the predicate term of 
 the original proposition, the second step in obver- 
 sion, we may observe that if we use a short horizon- 
 tal stroke over the symbol of an affirmative predicate 
 term to indicate that that term has been negated, 
 it will be obvious that obverted propositions are 
 characterised generally by having for their predicate 
 terms the so-called infinite or non-P term. It fol- 
 lows that if the predicate term is already a negative 
 or infinite term, the effect of negating it will be to 
 remove the sign of negation. The method of indi- 
 cating negation by the short horizontal stroke over 
 the symbol of an affirmative term is used throughout 
 this book, and this fact should be noted; a horizon- 
 tal stroke over any term, whether predicate or sub- 
 ject term, will have the meaning of negation. Thus, 
 U will mean non-S, M will mean non-M, just as P* 
 means non-P. With these explanations the method 
 of obversion should be sufficiently clear. In the fol- 
 lowing table we illustrate the method of obversion in 
 each of the four categorical propositions : 
 
 Obvertend 
 
 SaP 
 
 SeP 
 
 SiP 
 
 SoP 
 
 First Step 
 
 Second Step 
 Obverse 
 
 SeP 
 
 SaP 
 
 SoP 
 
 SiP 
 
 SeP 
 
 SaP 
 
 SoP 
 
 SiP 
 
 TABLE OF OBVERSIONS 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 283 
 
 Conversion. This is a process by which we affirm 
 or deny of the predicate term of an original prop- 
 osition, called in this relation the con vertend, what 
 was asserted by the subject term of the same prop- 
 osition. If, for example, we know that 'JMlocarpin 
 when taken internally is followed by a slowing of 
 the heart beat,' we are able, by conversion, to place 
 pilocarpin among the agents which have the effect 
 of slowing the heart beat in any investigation we 
 may make about the conditions under which the 
 heart beat is slowed. In other words, the terms by 
 which in one proposition we qualify a subject, may 
 themselves become of direct interest to us, and in 
 looking about for predicates which shall qualify 
 them, we find in the original' proposition something 
 that is serviceable for this purpose. To state gen- 
 erally the fact that conversion denotes, we may say 
 that if we make any statement in the S-P form, 
 conversion is the answer to the question whether we 
 are able, because we have made this statement, to 
 make another which will have the form P-S. Hav- 
 ing said something about S, can we, therefore, say 
 something about P? 
 
 That this is a very reasonable inquiry will ap- 
 pear if we recall what was said about the possibility 
 of predicating of any term S another P. We saw 
 that this possibility rests upon the fact that S is not 
 merely S, and that P is not merely P. In any judg- 
 ment we are dealing with a complex phenomenon, 
 and our statements reflect this fact. We, therefore, 
 said that the S that in any proposition is P is an 
 
284 A TEXT-BOOK OF LOGIC 
 
 SP, and, as we also saw, the P that is predicated 
 of S has its roots running down into, and derives 
 its character from, the same ground that makes of 
 S a significant term. In other words, the P of any 
 proposition is also an SP. It is this fact that under- 
 lies the process and problem of conversion. If S is 
 P at all, then the conditions of its being P are those 
 that will enable us to reverse the relation, and to 
 declare that P is S. This is the general statement 
 of the fact of conversion, but what the limitations 
 are under which conversion may legitimately take 
 place must be ascertained from the study of con- 
 crete cases. In other words, conversion is not a 
 wholly formal process, it is not a mere manipulation 
 of symbols; but a study of the formal relations of 
 the terms of the proposition brings to light some 
 of the limits of this type of thinking. 
 
 Formally considered, conversion is the method 
 by which the predicate term of one proposition, 
 called the convertend, becomes the subject term of 
 another, called the converse, and the subject term 
 of the former proposition becomes the predicate 
 term of the latter. It will be seen, then, that the 
 terms of the converse must be the same as the terms 
 of the convertend. Stated simply, the terms of the 
 converse are derived from the convertend by the 
 transposition of its terms : S-P becomes P-S. Again, 
 we should observe that in conversion there is no 
 change in the quality of the proposition : an affirm- 
 ative proposition remains affirmative, and a neg- 
 ative proposition remains negative. And, further, 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 285 
 
 the quantity of propositions sometimes is, and some- 
 times is not affected by their conversion. This will 
 be shown in our examination of the four categor- 
 ical propositions, and the reason for it will then be- 
 come clear. But before we examine each kind of 
 proposition to ascertain whether and in what form 
 it is capable of conversion, we wish to call attention 
 to the rule which governs all cases of conversion, 
 namely: If a term is distributed in the converse 
 it must have been distributed in the convertend. 
 Practical direction for applying this rule may be 
 laid down thus : Quantify the predicate, and trans- 
 pose terms. 
 
 The simplest cases of conversion are met with 
 in the universal negative and the particular affirm- 
 ative propositions: SeP and SiP. The universal 
 negative proposition has two distributed terms, and 
 the particular affirmative proposition has two un- 
 distributed terms. It follows from these facts that 
 if we transpose the terms of each proposition, with- 
 out changing the quality, no term in the converse 
 is distributed that was not distributed in the con- 
 vertend. If, for example, the whole of P, in the 
 universal negative proposition, lies outside the whole 
 of S, then the whole of S falls outside the whole of 
 P. In the case of the particular affirmative prop- 
 osition, some of S is identical with some of P, and, 
 therefore, it follows that the same part of P is 
 identical with the same part of S. Under these 
 conditions, it is possible not only to say that 'S is 
 P,' but also that T is S.' When, as in these two 
 
286 A TEXT-BOOK OF LOGIC 
 
 cases, we convert a proposition without changing 
 its quantity, we are said to convert simply, or, as 
 the Latin word has it, simpliciter. 
 
 Conversion by limitation, or per accidens, that 
 is, conversion that involves a change in the quantity 
 of a proposition, is necessary in the case of the uni- 
 versal affirmative proposition, SaP. The reason for 
 this is that, being an affirmative statement, the 
 predicate term is undistributed, and when this be- 
 comes the subject term of a new proposition, it does 
 not present a determinate number of objects for the 
 predicate to qualify. For example, 'All the books 
 are on that shelf cannot imply that 'All the things 
 on that shelf are books ;' there may be other things 
 on the shelf than books. All, therefore, that we are 
 warranted in saying is that 'Some of the things on 
 that shelf are books,' a statement that differs in 
 quantity from the original proposition. The stu- 
 dent may find examples of universal affirmative 
 propositions which, on account of the nature of 
 their subject-matter, admit of simple conversion; 
 but the form of the proposition does not show this. 
 'A straight line is the shortest distance between two 
 points/ that is to say, definitions, may serve to show 
 what is meant. So long, however, as we confine 
 attention to the form of the proposition, SaP con- 
 verts by limitation to PiS. 
 
 A particular negative proposition cannot be con- 
 verted at all. In such a proposition the subject 
 term is undistributed, and the predicate term is dis- 
 tributed. If, therefore, we transpose the terms, we 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 287 
 
 have a proposition with a distributed subject and 
 an undistributed predicate, that is a proposition of 
 the form 'All S some P.' Now the only proposi- 
 tion that we have of this form is the universal 
 affirmative, and we should be required to take this 
 as such a proposition. But this we cannot do, be- 
 cause the converse of a proposition must be of the 
 same quality as the convertend, and, moreover, no 
 negative proposition has an undistributed predicate 
 term. But if, in order to overcome this difficulty, 
 we were to distribute this term, we infringe the 
 rule of conversion which states that if a term is 
 distributed in the converse it must have been dis- 
 tributed in the convertend. In no way, therefore, 
 can we convert a particular negative proposition. 
 It may sometimes be true that SoP and PoS are 
 both true, but we must go outside the formal rela- 
 tions of S and P in the propositions to see this. For 
 example, 'Some anarchists are-not Italians/ and 
 'Some Italians are-not anarchists' are both true. 
 But we do not always get a like satisfactory result 
 merely by transposing the terms of particular nega- 
 tive statements. For example, 'Some men are-not 
 professors' is true, but 'Some professors are-not 
 men' is false, so long, that is, as we only mean by 
 men membership in the human race. These cases 
 depend upon a knowledge of more than the original 
 proposition states, and there is no possibility of 
 ascertaining the precise nature of that knowledge 
 from a study of the formal relations of S and P in 
 a particular negative proposition. 
 
288 A TEXT-BOOK OF LOGIC 
 
 We add below a table of all possible conversions : 
 
 Convertend 
 
 SaP 
 
 SeP 
 
 SiP 
 
 SoP 
 
 Converse 
 
 PiS 
 
 PeS 
 
 PiS 
 
 
 TABLE OF CONVERSIONS 
 
 Contraposition. Sometimes called Conversion by 
 Negation, and Contrapositive Conversion. The con- 
 trapositive of a given proposition may be described, 
 according to the method by which we arrive at it, 
 as the converted obverse. The rule, consequently, 
 that we should follow to reach the contrapositive 
 of any proposition is: First obvert the original 
 proposition, and then convert the proposition thus 
 obtained. If we follow this rule, the contrapositive 
 will be seen to be a proposition that has for its 
 subject term the negative of the predicate of the 
 original proposition, called in this case the obver- 
 tend. S-P becomes P-S- Now, since obversion is 
 involved in the process of reaching a contrapositive, 
 and conversion does not change it back again, the 
 contrapositive differs in quality from the original 
 proposition. And since the quantity of a proposi- 
 tion, as we have seen, is sometimes affected by con- 
 version, namely, when the proposition is a univer- 
 sal affirmative proposition, the quantity of the con- 
 trapositive will, in that case, be changed, but in all 
 other cases it will be unaffected. 
 
 The contrapositive of any proposition may be 
 obverted, and the proposition thus obtained will 
 have the characteristics that we have enumerated 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 289 
 
 in the section on obversion. Such a proposition is 
 called the obverted contrapositive. In this case 
 P^-S, the contrapositive of S-P, becomes by obver- 
 sion P-& 
 
 The results of the above statements, expressed 
 symbolically, are given in the following table of 
 contrapositives : 
 
 Original Proposition 
 
 SaP 
 
 SeP 
 
 SiP 
 
 SoP 
 
 Obverse 
 
 SeP 
 
 SaP 
 
 SoP 
 
 SiP 
 
 Contrapositive 
 
 PeS 
 
 PiS 
 
 
 PiS 
 
 Obverted Contra 
 positive 
 
 PaS 
 
 PoS 
 
 
 PoS 
 
 TABLE OF CONTRAPOSITION 
 
 Not many examples of contraposition are neces- 
 sary if the student has mastered the fundamental 
 processes of obversion and conversion. We confine 
 ourselves to one: 
 
 Original 
 Proposition 
 
 SaP 
 
 All acids are substances that turn 
 blue litmus paper red 
 
 Obverse 
 
 SeP 
 
 No acids are substances that do 
 not turn blue litmus paper red 
 
 Contrapositive 
 
 PeS 
 
 No substances that do not turn 
 blue litmus paper red are acids 
 
 Obverted 
 Contrapositive 
 
 PaS 
 
 All substances that do not turn 
 blue litmus paper red are non-acid 
 
 19 
 
 EXAMPLE OF CONTRAPOSITION 
 
290 A TEXT-BOOK OF LOGIC 
 
 Inversion. The inverse of a proposition has for 
 its subject the contradictory of the subject of the 
 
 original proposition (invertend). S-P becomes "S-P. 
 Like contraposition, inversion is arrived at indi- 
 rectly through the use of the two fundamental 
 forms of eduction. And since we can obtain by 
 obversion the contradictory of a term only when 
 that term forms the predicate of a proposition, S 
 must be made the predicate of a proposition before 
 its contradictory can be ascertained, that is, con- 
 version must have taken place at some stage in the 
 process of inversion. In other words, S must have 
 been made the predicate of a proposition, and then 
 that proposition must have been obverted if we are 
 to get a non-S term. Inversion can apply only to 
 the two universal propositions, SaP and SeP, and in 
 each case we get a particular proposition of the gen- 
 eral form ST-P. We must follow a separate rule in 
 each of these cases. To invert a universal affirmative 
 proposition, the rule reads: Obvert and convert 
 alternately until a proposition of the required form 
 is found. The rule for the universal negative prop- 
 osition reads : Convert and obvert alternately until 
 a proposition of the required form is found. We 
 show the necessary steps in each of these cases in 
 the following table : 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 291 
 
 Original 
 Proposition 
 
 SaP 
 
 Obverse 
 
 SeP 
 
 Converse 
 
 PeS 
 
 Obverse 
 
 PaS 
 
 Converse 
 
 SiP 
 
 Inverse 
 
 SoP 
 
 Original 
 Proposition 
 
 SeP 
 
 Converse 
 
 PeS 
 
 Obverse 
 
 PaS 
 
 Inverse 
 
 SiP 
 
 TABLES OF INVERSION 
 
 , We may obvert these inverses, and thus obtain 
 the obverted inverses. Thus, SoP will give SiP, and 
 5iP will give ~SoP. It will be "observed that from 
 the universal affirmative proposition we get, by in- 
 version, a particular negative proposition, and from 
 the universal negative proposition a particular 
 affirmative proposition, and that by obversion these 
 inverses are given the same quality as their re- 
 spective original propositions. 
 
 Summary of Eduction. In this section we give 
 first an outline schema of the characteristics of the 
 propositions arrived at by eduction, that is, we show 
 the character and relations of the terms of all the 
 eductive propositions. Thus: 
 
292 
 
 A TEXT-BOOK OF LOGIC 
 
 Original Proposition 
 
 S-P 
 
 Obverse 
 
 S-P 
 
 Converse 
 
 P-S 
 
 Contrapositive 
 
 P-S 
 
 Obverted Contra 
 positive 
 
 P-S 
 
 Inverse 
 
 S-P 
 
 Obverted Inverse 
 
 S-P 
 
 SCHEMA OF EDUCTIVE PROPOSITIONS 
 In the following table we show, secondly, all the 
 eductions of each of the four categorical proposi- 
 tions in a form which indicates throughout the 
 quantity and quality of the propositions : 
 
 Original Proposition 
 
 SaP 
 
 SeP 
 
 SiP 
 
 SoP 
 
 Obverse 
 
 SeP 
 
 SaP 
 
 SoP 
 
 SiP 
 
 Converse 
 
 PiS 
 
 PeS 
 
 PiS 
 
 
 Obverted Converse 
 
 PoS 
 
 PaS 
 
 PoS 
 
 
 Contrapositive 
 
 PeS 
 
 PiS 
 
 
 PiS 
 
 Obverted Contra 
 positive 
 
 PaS 
 
 PoS 
 
 
 PoS 
 
 Inverse 
 
 SoP 
 
 SiP 
 
 
 
 Obverted Inverse 
 
 SiP 
 
 SoP 
 
 
 
 TABLE OF EDUCTIONS 
 
IMPLICATIONS OF CATEGORICAL PROPOSITIONS 293 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Chs. IX., XI. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. VII. 
 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Chs. 
 XII., XIII., XIV. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lessons IX., X. 
 
 J. N. Keynes, Formal Logic, 2d Edition, Part II., Chs. II., 
 III., IV., V. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. III., Parts ii., iii. 
 
 W. Minto, Logic, Inductive and Deductive, Part III., Ghs. II., 
 III. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. VI., 
 VII. 
 
 W. J. Taylor, Elementary Logic, Ch. VIII. 
 
 ADVANCED 
 
 B. Bosanquet, Logic, Ch. VII. 
 
 W. R. B. Gibson, The Problem of Logic, Chs. XIX, XX. 
 H. W. B. Joseph, An Introduction to Logic, Chs. IX., X. 
 H. Lotze, Logic, Vol. I., Ch. II., 75 to 82. 
 F. C. S. Schiller, Formal Logic, Chs. XII., XIII. 
 J. Welton, A Manual of Logic, Vol. I., Book III., Chs. II., 
 III., 102, 103. 
 
 QUESTIONS. 
 
 1. Classify categorical propositions from the standpoint 
 (1) of their quantity and (2) quality. 
 
 2. What are the quantitative and qualitative characteris- 
 tics of logical statements. 
 
 3. What symbols are used to distinguish the four categor- 
 ical propositions, how are they derived, and what exactly 
 do they represent? 
 
 4 Explain what is meant by a structural formula.. What 
 is the general structural formula of a categorical prop- 
 osition? 
 
294 A TEXT-BOOK OF LOGIC 
 
 6. Write the structural formulae of all the categorical prop- 
 ositions, and explain how they are derived. 
 
 6. What do you understand by the distribution of terms? 
 
 7. What determines the distribution of the subject terms 
 of propositions? 
 
 8. From what standpoint is the distribution of the pred- 
 icate terms of propositions determined? 
 
 9. What is the distribution of each of the terms in each 
 of the four categorical propositions? 
 
 10. Explain why the predicate terms of affirmative propo- 
 sitions are undistributed. 
 
 XI. Explain why the predicate terms in SeP and SoP are 
 distributed. 
 
 12. Classify in any suitable way the distribution of all the 
 terms of all the categorical propositions. 
 
 13. What is meant by the implication of propositions? 
 
 14. What other terms have been used to describe the fact 
 of implication, and why are these not suitable? 
 
 15. What are the main classes of implication? 
 
 16. What do you understand by the Opposition of Proposi- 
 tions? 
 
 17. Name all the relations of opposition of categorical 
 propositions. 
 
 18. Between what propositions can the relation of con- 
 trariety exist? 
 
 19. How do contrary propositions differ from, and in what 
 respects do they argee with, each other? 
 
 20. If one of the propositions existing in a contrary rela- 
 tion is true, what can you say of the other? 
 
 21. Explain why a proposition is doubtful if its contrary 
 is false. 
 
 22. Between what propositions can the subaltern relation 
 exist? 
 
 23. How do subaltern propositions differ from, and in what 
 respects do they argee with, each other? 
 
 24. Why does the truth of the subalternans involve the truth 
 of the subaltern? 
 
IMPLICATIONS OP CATEGORICAL PROPOSITIONS 295 
 
 25. Explain why a proposition is doubtful if its subaltern 
 is true. 
 
 26. Why is a proposition false if its subaltern is false? 
 
 27. Between what propositions can the contradictory rela- 
 tion exist? 
 
 28. How do contradictory propositions differ from, and in 
 what respects do they argee with, each other? 
 
 29. Explain why the truth or falsity of a proposition in- 
 volves the falsity or truth of its contradictory. 
 
 30. Between what propositions can the subcontrary relation 
 exist? 
 
 31. How do subcontrary propositions differ from, and in 
 what respects do they argee with, each other? 
 
 32. Why is a proposition doubtful if its subcontrary is true? 
 
 33. Explain why a proposition is true if its subcontrary is 
 false. 
 
 34. What is the Square of Opposition? 
 
 35. What are Eductions? 
 
 36. Classify the Eductions. 
 
 37. Explain and illustrate the method of obversion. 
 
 38. Upon what characteristics of propositions does the 
 method of conversion rest? 
 
 39. Explain and illustrate the method of conversion. 
 
 40. What is the rule of conversion? 
 
 41. Name and illustrate the classes of conversion. 
 
 42. Why cannot SoP be converted? 
 
 43. Are there any particular negative propositions that 
 can be converted? Illustrate. 
 
 44. If your answer to the previous question is in the affirm- 
 ative, explain why logic says that SoP cannot be con- 
 verted. 
 
 45. What is contraposition? 
 
 46. What steps must be taken to securj the contrapositive 
 of a proposition? 
 
 47. Why is the contrapositive of a proposition sometimes 
 called the converted obverse? 
 
 48. What is inversion? 
 
296 A TEXT-BOOK OF LOGIC 
 
 49. What is the method of finding the inverse of SaP? 
 
 50. How do you proceed to find the inverse of a universal 
 negative proposition? 
 
 EXERCISES 
 
 NOTE State propositions in logical form when answer- 
 ing a question, and write the formula for each proposition 
 involved in your answers. 
 
 1. Write all the relations of Opposition of: 
 
 (1) We are not all college professors. 
 
 (2) Few books in logic are easy reading. 
 
 (3) The old paths are best. 
 
 (4) Improbable events happen almost every day. 
 
 (5) The longest road comes to an end. 
 
 (6) Unasked advice is seldom acceptable. 
 
 (7) Only ignorant persons hold such opinions. 
 
 (8) Infallibility is a myth. 
 
 2. Give the converse of: 
 
 (1) Mercy but murders, pardoning ( = if it pardons) 
 those that kill. 
 
 (2) We cannot all command success. 
 
 3. Give the obverse of: 
 
 (1) Not every advice is a safe one. 
 
 (2) Rivers generally run into the sea. 
 
 4. Give the contrapositive of: 
 
 (1) No one is altogether reliable. 
 
 (2) Every mistake is not a proof of ignorance. 
 
 5. Give the inverse of: 
 
 (1) He that bridleth his tongue is greater than he that 
 taketh a city. 
 
 (2) Natives alone can stand the climates of Africa. 
 
CHAPTER X 
 
 CATEGORICAL ARGUMENTS. 
 
 The Problem of the Chapter. In the previous 
 cnapters we have studied mainly the three following 
 problems: (1) the nature of simple assertion or 
 the judgment, (2) the logical expression of these 
 judgments or the proposition, and (3) the problem 
 of logical implication. In the next two chapters, 
 we shall still be occupied with judgments and their 
 propositions; and, although the new problems that 
 are to come before us are more complex than those 
 we have studied, they will appear simpler, because 
 everyone may be presumed to have already some 
 acquaintance with them. The fact of common ex- 
 perience that underlies the topics of these chapters 
 is, that we connect statements of various kinds with 
 one another in numerous ways, and that we do 
 this with a view to making other assertions that, it 
 seems to us, could not be made as surely in any other 
 way. Often the actual statements we make are not 
 debatable, they are readily accepted by the person to 
 whom we are speaking, and may, therefore, be re- 
 garded merely as reminding him of certain points 
 of common agreement; and if, beyond this simple 
 function, they have any use, this must be found m 
 what they suggest, and not in what they actually 
 state. In other words, we are accustomed to use 
 certain significant statements for the purpose of 
 
 (297) 
 
298 A TEXT-BOOK OF LOGIC 
 
 making them the bases of certain other significant 
 statements which we wish the person to whom we 
 are speaking also to accept. Now it is quite obvious 
 that about such a general fact as this we may ask 
 whether there are any rules of procedure that may 
 be followed, if the suggested truth is to be accepted. 
 We may ask, that is, whether there are any service- 
 able ways of connecting statements when these are 
 used as the basis of others the truthfulness of which 
 we wish particularly to recommend. This is the 
 question we are to consider in this and the following 
 chapters, a question that is technically known as the 
 problem of the syllogism. To state the problem 
 somewhat technically, we are now to enter upon a 
 study of the combination of propositions, and of the 
 laws of their inter-connection. 
 
 Two Preliminary Questions. Before taking up 
 the specific topics to which the present chapter is 
 devoted, there are two questions to which some at- 
 tention must in the first place be given, a ques- 
 tion about the syllogism, and a question about the 
 particular kind of syllogism that we are immediately 
 concerned with. About the syllogism we may ask 
 whether it is a problem that is set by the judgment, 
 by the nature and limitations of human thought, 
 and one, therefore, that reveals the structure of the 
 thinking or knowing mind ; or, if this is not the case, 
 whether it is a problem that grows out of our effort 
 to communicate what we know. In the latter case, 
 the syllogism is not a problem that is set directly 
 by the judgment, but one that arises out of the 
 
CATEGORICAL ARGUMENTS 299 
 
 nature of the proposition. Now it is not possible, 
 nor perhaps is it necessary or desirable, to enter 
 into a full discussion of the question thus suggested ; 
 but, because of its bearing upon our understanding 
 of the nature and function of the syllogism, we may 
 point out more specifically that the question really 
 asks whether the syllogism is a method by which the 
 human mind thinks when it is seeking to gain knowl- 
 edge; or whether it is a method by which we lay 
 bare, for ourselves and others, the grounds on which 
 our knowledge is supposed to rest. That is, we 
 are asking whether the syllogism is, as in the one 
 case, an instrument for acquiring knowledge; or, 
 as in the other, an instrument for the exposition of 
 knowledge. In making this statement disjunctive, 
 we are not to be understood to mean that the syllo- 
 gism may not serve both functions, nor to deny 
 that the two functions may be inter-dependent. In- 
 deed, what we have seen to be true of the relation 
 of the proposition to the judgment, namely, that the 
 former, being the expression in words of the latter, 
 is controlled by motives that grow out of our desire 
 to communicate what we know, may be expected to 
 be true also of the syllogism a series of inter- 
 connected propositions in its relation to the more 
 complex process of reasoning. The view that the 
 syllogism is a method by which we expound and 
 communicate the knowledge that is acquired by 
 reasoning seems to have a high degree of probability, 
 and it may be allowed, in the main, to determine 
 our discussions in the following sections. From this 
 
300 A TEXT-BOOK OP LOGIC 
 
 point of view, the syllogism will come before us as a 
 series of problems connected with the nature and 
 connection of propositions, and we must consider 
 the present chapter as a continuation of those imme- 
 diately preceding it in which we were developing the 
 character of prepositional statements. 
 
 Turning now to the second inquiry, we may 
 raise the question whether we are to study in this 
 chapter the connection between any kinds of state- 
 ment, and any kinds of connection between state- 
 ments. The answer to both parts of the question 
 must be, No. There are forms of statement that, 
 so long as these forms are retained, do not belong 
 to logic at all. We pointed this out above when we 
 were studying imperatives, inter rogatives, optatives, 
 and exclamations. There are also, as we have seen, 
 forms of logical statement that are not categorical, 
 and which, as we shall see later, present problems 
 quite distinct from those that are. Such, for ex- 
 ample, are the hypothetical and disjunctive prop- 
 ositions. We exclude from the scope of this chap- 
 ter both classes of statement, and consider only 
 the relationships that hold between categorical 
 propositions. There are also kinds of connection 
 between categorical statements that are not logical 
 in the restricted sense in which we are using the 
 word here. Such, for instance, are the connections 
 between ideas that the psychologist discusses under 
 the head of association. Such, also, are the con- 
 nections between ideas based upon the mathematical 
 principle of proportion: A is greater than B, B is 
 
CATEGORICAL ARGUMENTS 301 
 
 greater than C, therefore, A is greater than C. 
 Whatever the logical character of these cases may 
 be, they do not, on any strict interpretation, belong 
 to the present chapter which is confined to a study 
 of the connection of categorical propositions which 
 is illustrated in the Aristotelian syllogism. 
 
 Nature of the Syllogism. We may describe a 
 syllogism as a series of three propositions which are 
 related to each other in such a way that the truth 
 expressed in one of them, called the conclusion, de- 
 pends upon the truth expressed in the other two, 
 called the premises, taken together. Let us -illus- 
 trate this statement in the following simple case: 
 
 All insects are arthropods. 
 All bees are insects. 
 All bees are arthropods. 
 
 In this syllogism, there are three inter-related prop- 
 ositions, each one of which has been written sepa- 
 rately. It is obvious to first inspection that the 
 truth of the last written statement, 'All bees are 
 arthropods/ avowedly rests upon the truth of the 
 other two taken together. That is to say, the truth 
 of every conclusion is a truth that rests upon a con- 
 nection of facts that it requires two propositions, 
 at least, completely to express. 
 
 Our understanding of this type of argument will 
 be facilitated if we learn to think about the syllo- 
 gism from the standpoint of the conclusion it states, 
 and not from the standpoint of the premises it ex- 
 presses. The reason for doing so is found in the 
 
302 A TEXT-BOOK OF LOGIC 
 
 nature of the thought processes themselves. In 
 these processes, as we saw when studying the judg- 
 ment, emphasis is laid primarily upon the answer 
 to the cognitive question, What is it? and only sub- 
 ordinate importance is attached to the method by 
 which the answer is reached. Whether the process 
 of thought is relatively simple or complex, sub- 
 stantive emphasis is laid upon the solutions that 
 are found to the problematic situations that stim- 
 ulate the judging activity, and it is the function 
 of the conclusions of syllogisms to express such 
 solutions. From this point of view, the premises 
 must be looked upon as expressing the grounds of 
 the fact or truth stated in the conclusion of the 
 syllogism. Indeed, it is only as stating the grounds 
 of what is expressed in the conclusion that the prem- 
 ises are premises at all. In like manner, a con- 
 clusion can be a conclusion only if it is regarded as 
 the statement of a grounded assertion. The grounds 
 of assertion may be relatively simple as in our judg- 
 ments of perception; they may be relatively com- 
 plex, as in the syllogism; but every judgment is a 
 grounded assertion, and when such assertions are 
 referred to their grounds, when, that is, the reason 
 for holding the assertions is in any way appealed to, 
 such assertions are properly called conclusions. 
 Premises and conclusions are thus correlative terms, 
 and can be understood only from the standpoint of 
 their mutual implication. 
 
 Further light is thrown upon the nature of the 
 syllogism if we recall that the mental process under- 
 
CATEGORICAL ARGUMENTS 303 
 
 lying the syllogism is a process of reasoning. The 
 mental process underlying the proposition, as we 
 have seen, is called a judgment. When, for example, 
 we discern the aspects in which objects differ from, 
 and are like, each other, directly, that is, by having 
 the objects before us and comparing the one with 
 the other, this mental process, involving discrim- 
 ination, abstraction, and synthesis, is called judg- 
 ing, and the mental attitude in which the results of 
 such a process is asserted is called a judgment. Now 
 the mental process underlying the syllogism is not 
 essentially different from that underlying the judg- 
 ment. Like the judgment, reasoning rests upon com- 
 parison, but unlike it, there is no means of direct 
 comparison of one object with another. In this 
 case, we compare each of the objects we are trying 
 to relate with a third object in order to detect 
 whether they have anything in common with it. 
 That is, we compare objects, through the observed 
 likeness or difference that each has to a third. This 
 is called indirect comparison, and the process of 
 reasoning in which this is carried out is called me- 
 diate reasoning. In contrast to the so-called imme- 
 diate reasoning or judgment, mediate reasoning is 
 a process underlying the Aristotelian syllogism, and 
 we may call the stated results of such a process an 
 argument. It is such an argument that gets ex- 
 pressed in the syllogism. 
 
 Structural View of the Syllogism. We may, now, 
 point out certain characteristics of the syllogism 
 that are conditioned by the fact that it is composed 
 
304 A TEXT-BOOK OF LOGIC 
 
 of a series of interrelated propositions. Proposi^ 
 tions, for instance, may be said to bear the same 
 relation to the syllogism that terms do to the prop- 
 osition, that is, they may be regarded as its con- 
 stituent elements. But as terms do not form prop- 
 ositions by being brought together by the copula, 
 so, we may say, the syllogism is not built up by 
 the union of propositions. The propositions of a 
 syllogism express distinguishable features of a 
 complex process of thinking, and it is the purpose 
 of the syllogism to make clear the inter-connection 
 between the several aspects of our thoughts-about- 
 things. In other words, the movement of thought 
 in syllogistic reasoning turns upon a common ele- 
 ment represented in the syllogism by the middle- 
 term, and it is only through this common element 
 that there exist grounds for the truth of any medi- 
 ated judgment. From this point of view, the middle 
 term is as characteristic a feature of the syllogism 
 as the copula is of the proposition. 
 
 Certain other features of the syllogism come into 
 prominence when we consider it from the stand- 
 point of its structure. For instance, every syllo- 
 gism has three and only three propositions, the 
 conclusion, and two premises. The conclusion is a 
 statement of the relation between two terms which 
 are named, from the place they occupy in the syllo- 
 gism, the major and minor terms. The subject 
 1 (S) of the conclusion is the minor term of the syl- 
 llogism, and the predicate (P) of the conclusion is 
 jthe major term of the syllogism. Since now the 
 
CATEGORICAL ARGUMENTS 305 
 
 premises of a syllogism are propositions, they also 
 state a relationship between terms, but not a rela- 
 tionship between any terms. Their function is to 
 state the relationship that the major and minor 
 terms have respectively to a common or middle 
 term (M). The proposition that states the rela- 
 tionship between the major and middle terms is 
 known as the major premise. The proposition thall 
 states the relationship between the minor and the! 
 middle terms is known as the minor premise. Ill 
 should be observed that the nature and validity of 
 categorical arguments do not depend upon the order 
 in which the propositions are named, but upon the 
 connection between the propositions of which they 
 are comprised. It is usual, however, to write the 
 major premise first, the minor premise second, and 
 the conclusion last. 
 
 With these facts in mind, it is possible to give a 
 definition of the syllogism that emphasises the con- 
 nection of the elements that are always present in 
 these kinds of arguments. From this point of view, 
 the syllogism is a method by which we relate two 
 terms (S and P) through the relation that each has 
 to a common or middle term (M). 
 
 Rules of the Syllogism. In the previous section, 
 we pointed out that the syllogism has a definite 
 structure which is determined by the fact that its 
 three constituent propositions are related to each 
 other through a middle term. The rules of the syl- 
 logism may be classified with respect to these facts, 
 
 20 
 
306 A TEXT-BOOK OF LOGIC 
 
 -with respect to the terms, and with respect to 
 the propositions of the syllogism. With respect to 
 its terms, the rules are definitely rules of distribu- 
 tion. With respect to its propositions, the rules 
 refer to the quantity and quality of the propositions. 
 
 RULES OF DISTRIBUTION 
 
 I. The middle term must be distributed in one, 
 at least, of the premises. 
 
 II. If a term is distributed in the conclusion, it 
 must have been distributed in one of the premises. 
 
 The reason for the first rule is, that the validity 
 of the syllogism depends upon the reference of the 
 major and minor terms unambiguously to the same 
 common term, and this is done with certainty only 
 if the middle term is distributed, at least, once. If 
 the middle term is undistributed in each premise, 
 the major term might be related to one part in the 
 major premise, and the minor term to another part 
 in the minor premise. Whenever this is the case, 
 we have four and not three terms in the two prop- 
 ositions, and thus the syllogistic character of the 
 argument is destroyed. For example, from the 
 statements that 'All rash men are confident,' and 
 'All brave men are confident/ we cannot conclude 
 that 'All brave men are rash/ for the reason that 
 the confidence that each has is or might be a differ- 
 ent kind of confidence; there is, in other words, no 
 middle term or common factor to serve as a basis 
 of comparison. If, however, the middle term is dis- 
 tributed in one, at least, of the premises, the part 
 
CATEGORICAL ARGUMENTS 307 
 
 of the term denoted by the undistributed middle in 
 the other premise is included in this distribution, 
 and there is thus a common basis of comparison for 
 the major and minor terms. Thus, we can affirm 
 that 'No Americans are Englishmen' on the ground 
 that 'All Englishmen are Europeans/ and 'No Amer- 
 icans are/ The fallacy involved in breaking the 
 rule for the distribution of the middle term is called 
 the fallacy of Undistributed Middle. 
 
 The reason for the second rule is, that we must 
 not make a statement, in the conclusion, about a 
 determinate number of the objects denoted by a 
 term when, in the premises, our statement has been 
 about an indeterminate number of these objects. In 
 other words, we must not go beyond our accepted 
 facts. Stated conversely, to support a conclusion 
 which denotes, in either of its terms, a determinate 
 number of the objects to which the term applies 
 requires that all these objects shall have been denoted 
 in one of the premises. When this rule is not ob- 
 served by the major term, the fallacy that results is 
 an Illicit Process of the Major, and when it is not 
 observed by the minor term an Illicit Process of the 
 Minor Term. 
 
 RULES OF QUALITY 
 
 I. If the conclusion is affirmative, both prem- 
 ises are affirmative ; and conversely. 
 
 II. If the conclusion is negative, one premise, 
 and only one, is negative; and conversely. 
 
 In discussing these rules, which refer to the 
 relation of identity, or of non-identity, of two 
 classes, on the ground of their identity or non- 
 
308 A TEXT-BOOK OF LOGIC 
 
 identity with a third, it is important to observe that 
 we can argue a relation of identity only on the basis 
 of an identity of relation, and a relation of non- 
 identity only on the basis of a non-identity of rela- 
 tion. In other words, the relation of S and P to M 
 must be either so far identical as to warrant the 
 statement of the complete or partial identity of S 
 and P; or so far non-identical as to warrant the 
 statement of the complete or partial non-identity 
 of S and P. If the conclusion is a statement of 
 identity, the grounds for such a statement cannot 
 be found in a relation of non-identity; nor can we 
 find grounds for a statement of non-identity in a 
 relation of identity. Hence, if the conclusion is 
 affirmative both the premises must be of the same 
 quality ; and if the conclusion is negative, one of the 
 premises must be of that quality. 
 
 Why can we not ground any statement upon two 
 negative propositions? Because, in that case, there 
 is no identity of relation between S and M and P and 
 M, on which to base such a statement. From the ex- 
 clusion of both S and P from M, we cannot argue 
 to the identity of S and P, nor can we argue to the 
 non-identity of S and P. Two negative premises 
 cannot, therefore, support any conclusion, nor can 
 any conclusion be inferred from them. 
 
 RULES OF QUANTITY 
 
 I. A particular conclusion cannot be supported 
 by two particular premises. 
 
 II. If a conclusion is particular, one, and only 
 one, of the premises supporting it can be particular. 
 
CATEGORICAL ARGUMENTS 309 
 
 With regard to the first rule, let us suppose that 
 the particular affirmative, and the particular neg- 
 ative, conclusions, SiP and SoP, can be supported by 
 two particular propositions. In the former case, the 
 premises must be both particular affirmative, and 
 then the middle term is undistributed whichever 
 place it occupied in the premises. This would give 
 the fallacy of the undistributed middle. In the sec- 
 ond case, one premise must be particular affirmative, 
 and the other particular negative, and then there 
 can be only one distributed term, namely, the pred- 
 icate of the negative premise. If this is the middle 
 term, the major term will be of wider extent in the 
 conclusion, which is a negative proposition, than in 
 the major premise, the fallacy of illicit process of 
 the major. If, on the other hand, the middle term 
 is not the predicate term of the negative premise, 
 the argument fails on account of the fallacy of undis- 
 tributed middle. 
 
 With regard to the second rule, the particular 
 conclusion must be either affirmative or negative. 
 If it is affirmative, the premises will both be par- 
 ticular affirmative, II., that is, propositions whose 
 terms are all undistributed. A syllogism whose 
 premises were both particular affirmative would be 
 fallacious on account of undistributed middle. If, 
 on the other hand, the conclusion were particular 
 negative, one of the premises would have to be par- 
 ticular negative, 01, 10, that is, propositions only 
 one of whose terms is distributed. If this were the 
 middle term, then, all the other terms being undis- 
 tributed, the conclusion being negative would involve 
 
310 A TEXT-BOOK OF LOGIC 
 
 the syllogism in an illicit process of the major; and 
 if that term were not the middle term, the syllogism 
 would involve an undistributed middle. Only one 
 premise, therefore, of a particular conclusion can 
 be particular. 
 
 Figures of the Syllogism, The propositions that 
 together constitute the premises or grounds of a 
 syllogism are characterised, as we have seen, by the 
 fact that they have a common or middle term. Now 
 since each premise has two terms, a subject term 
 and a predicate term, and one of these is the middle- 
 term of the syllogism, it is obvious that the middle 
 term may be either the subject term or the pred- 
 icate term of the major premise, and either the 
 subject term or the predicate term of the minor 
 premise. That is to say, the middle term of a syl- 
 logism may occupy four different positions in the 
 propositions which, when taken together, are the 
 premises of the argument which the syllogism is 
 the means of stating. Now the fact that the middle 
 term of a syllogism may occupy different positions 
 in the premises of different arguments is referred 
 to by the term Figure. The Figure of a syllogism, 
 in brief, is determined by the position of the middle 
 term in its major and minor premises. 
 
 The number of Figures depends upon the num- 
 ber of different positions that the middle term may 
 occupy alternately in the premises of a syllogism. 
 Theoretically, there are four. Thus : 
 
 1. The middle term may be the subject term 
 of the major, and the predicate term of the minor 
 premise. 
 
CATEGORICAL ARGUMENTS 
 
 311 
 
 2. The middle term may be the predicate term 
 of each premise. 
 
 3. The middle term may be the subject term 
 of each premise. 
 
 4. The middle term may be the predicate term 
 of the major, and the subject term of the minor 
 premise. 
 
 In the order named, the syllogisms whose form 
 corresponds to the alternative possibilities just 
 named are said to be in the First Figure, the Second 
 Figure, the Third Figure, and the Fourth Figure re- 
 spectively. Written in outline, syllogisms in these 
 Figures will present the following appearance: 
 
 First 
 Figure 
 
 S P 
 
 Second 
 Figure 
 
 P-# 
 
 S $, 
 
 S P 
 
 Third 
 Figure 
 
 M P 
 
 M S 
 
 S P 
 
 Fourth 
 Figure 
 
 P M 
 
 M S- 
 
 S P 
 
 As an aid to the retention of the positions of 
 the middle terms in each of the Four Figures, we 
 may add the following suggestion. If we connect 
 by a line the middle terms of the premises in the 
 Four Figures as just shown in outline, we shall 
 get this result: 
 
 II 
 
 M 
 
 M 
 
 III 
 
 M 
 
 M 
 
312 
 
 A TEXT-BOOK OF LOGIC 
 
 The upper point of these lines is the position occu- 
 pied by the middle term of the major premise, and 
 the lower point of the lines is the position occupied 
 by the middle term of the minor premise in the 
 Four Figures respectively. If now to these lines 
 we add dotted lines to represent the major and 
 minor premises, our diagram will assume this as- 
 pect: 
 
 M 
 
 III 
 
 M 
 
 M/ 
 
 A diagram like this, of course, may mean something 
 or nothing according as the student can bring to it 
 an interpreting idea. A student informed me that, 
 for a number of a class in logic, the two end figures 
 were thought of as snakes fighting or hissing at 
 each other. The two middle figures were thought 
 of as people sitting back to back because they were 
 cross with each other. As this information came 
 to me two years after the course was taken, it may 
 be presumed to have, for one at least, some mne- 
 monic value. 
 
 Special Rules of the Four Figures, Each of the 
 Four Figures has its own special rules, which are 
 applications of the general rules of the syllogism to 
 the specific form that categorical arguments as- 
 sume in these Figures. We shall state and prove 
 the rules for each Figure in order. 
 
CATEGORICAL ARGUMENTS 313 
 
 FIRST FIGURE 
 
 RULE 1. The minor premise must be affirmative. 
 
 Let us suppose the minor is negative. Then, 
 
 M P the major must be affirmative, and the 
 
 S M conclusion negative. Therefore, the major 
 
 term will be undistributed in the major 
 
 S P premise, and distributed in the conclusion ; 
 
 illicit process of the major. Hence, the 
 minor premise cannot be negative, and must be 
 affirmative. 
 RULE 2. The major premise must be universal. 
 
 If the minor premise is affirmative, the 
 middle term is undistributed, and must, 
 therefore, be distributed in the major 
 premise. And since the middle term is 
 subject of this premise, the proposition 
 must be universal. 
 
 SECOND FIGURE 
 
 RULE 1. One premise must be negative. 
 
 Since the middle term is the predicate of 
 P M each premise, one of the premises must be 
 S M a negative proposition to avoid the fallacy 
 
 of undistributed middle. 
 
 S P 
 
 RULE 2. The major premise must be universal. 
 
 The major term being the predicate of a 
 negative proposition in the conclusion, is 
 distributed. It must, therefore, be dis- 
 tributed in the major premise. But since 
 
314 A TEXT-BOOK OF LOGIC 
 
 there it is the subject of the proposition, 
 the major premise must be universal. 
 
 THIRD FIGURE 
 
 RULE 1. The minor premise must be affirmative. 
 Let us suppose that the minor is negative. 
 Then, the major premise must be affirm- 
 ative, and the conclusion negative. There- 
 fore, the major term will be undistributed 
 S P in the major premise, being the predicate 
 of an affirmative proposition, and distrib- 
 uted in the conclusion, being the predicate of a neg- 
 ative proposition. This involves illicit major. 
 Hence, the minor premise must be affirmative. 
 
 RULE 2. The conclusion must be particular. 
 
 Since the minor premise is affirmative, the 
 minor term, being predicate, is undistrib- 
 uted, and must, therefore, be undistributed 
 in the conclusion also. But the minor term 
 is the subject of the, conclusion which, 
 therefore, must be particular. 
 
 FOURTH FIGURE 
 
 RULE 1. If either premise is negative, the major 
 
 is universal. 
 
 P M If either premise is negative, the conclu- 
 M S sion is negative, and the major term of the 
 
 conclusion must be distributed. It must, 
 
 S P therefore, be distributed in the major 
 
 premise. But since there it is the subject, 
 the premise must be universal. 
 
CATEGORICAL ARGUMENTS 315 
 
 RULE 2. If the major premise is affirmative, the 
 minor must be universal. 
 If the major premise is affirmative, its 
 middle term is undistributed. It must, 
 therefore, be distributed in the minor 
 premise. And since there the middle term 
 is the subject, the premise must be uni- 
 versal. 
 
 RULE 3. If the minor premise is affirmative, the 
 conclusion is particular. 
 If the minor premise is affirmative, the 
 minor term is undistributed. In the con- 
 clusion, therefore, this term must be un- 
 distributed. The conclusion, therefore, is 
 particular. 
 
 RULE 4. If the minor premise is negative, both 
 premises are universal. 
 If the minor premise is negative, the minor 
 term is distributed. It must, therefore, 
 be distributed in the conclusion which will 
 then be universal. But a universal con- 
 clusion requires two universal premises. 
 The Moods of the Syllogism. If now we con- 
 sider the structure of the syllogism from the point 
 of view of the quantity and quality of the proposi- 
 tions which enter into it, we meet with the facts 
 which are denoted by the term the Moods of the 
 syllogism. By the Moods of the syllogism is meant 
 the character of a syllogism as determined by the 
 quantity and quality of its constituent propositions. 
 There are, as we have seen, four categorical prop- 
 
316 A TEXT-BOOK OF LOGIC 
 
 ositions, SaP, SeP, SiP, SoP, and any combination 
 of three of these, theoretically, may form the con- 
 stituent propositions of a syllogism. For example, 
 a syllogism may have in its premises and conclusion 
 only universal affirmative propositions. But it may 
 have in its major premise a universal affirmative, in 
 its minor premise a universal negative, and in its 
 conclusion a universal negative proposition. Every 
 syllogism must express itself by the use of the four 
 categorical propositions three at a time, and, there- 
 fore, no syllogism can fail to have a Mood. That is 
 to say, each of the constituent propositions of a syl- 
 logism has both a quantity and a quality, and when 
 we have named the quantity and quality of each 
 proposition, in the order of major premise, minor 
 premise, and conclusion, we have named the Mood 
 of the syllogism. Thus, in the examples just used, 
 the mood of the first is said to be AAA, that of the 
 second, AEE. 
 
 The Valid Moods of the Syllogism. The Mood of 
 a syllogism, we have said, is determined by the 
 quantity and quality of its constituent propositions. 
 The question that now comes before us is, How many 
 of the possible combinations of three out of the four 
 categorical propositions, taken as major and minor 
 premise and conclusion, will give us valid moods, 
 that is, syllogisms whose conclusions logically de- 
 pend upon the premises on which they are said to 
 rest? In answering this question, it will simplify 
 our task if, leaving the conclusions out of consider- 
 ation, we ascertain the combinations of propositions 
 
CATEGORICAL ARGUMENTS 317 
 
 which are possible as premises. Since, as we have 
 seen, there are four categorical propositions, each 
 of these may serve successively as the major prem- 
 ise of a syllogism, and each may serve successively 
 as the minor premise of the same syllogism. Thus, 
 writing the major premise first and the minor sec- 
 ond, we shall get the following sixteen combina- 
 tions : 
 
 AA EA IA OA 
 
 AE EE IE OE 
 
 AI El II 01 
 
 AO EO IO OO 
 
 If, now, we examine this list of possible prem- 
 ises, it is apparent that some must be rejected by 
 the rules of the syllogism that we have stated in 
 another section. Certain combinations are disqual- 
 ified because they violate the rule against negative 
 premises, for example, EE, EO, OE, and 00; cer- 
 tain others must be eliminated because they offend 
 against the rule about particular premises, for ex- 
 ample, II, 10, and 01. There remain, after the dis- 
 qualified members have been eliminated, the follow- 
 ing combinations : 
 
 AA EA IA OA 
 
 AE IE 
 
 AI El 
 
 AO 
 
 These we must consider as the only premises that 
 can be appealed to in support of any conclusion 
 which we may be concerned to maintain. 
 
318 A TEXT-BOOK OF LOGIC 
 
 Relation of Moods to Figure. There is, however, 
 a further question that requires an answer, namely, 
 whether we can throw the defence of a conclusion 
 upon any of the above-mentioned premises in any 
 of the Figures without affecting the validity of the 
 argument. Or, to state the same question con- 
 versely, Is each of the above pairs of premises ca- 
 pable of rendering a valid conclusion in each of the 
 Four Figures? We are asking, what effect, if any, 
 the statement of a syllogism in either of the Four 
 Figures has upon the validity of the argument. 
 
 There are two methods that may be adopted in 
 seeking an answer to this question. And first we 
 shall examine each of the above combinations of 
 premises in the light of the special rules of each 
 Figure, accepting those that conform, and rejecting 
 those that do not conform to the requirements of the 
 particular Figure. 
 
 In the First Figure, the major premise must be 
 universal, and the minor affirmative. The only com- 
 binations of premises that stand these tests are, AA, 
 AI, EA, and El. If we draw the proper conclusion 
 in each case, we may write the four valid moods 
 for this figure as follows : 
 
 AAA All EAE EIO 
 
 It will be observed that in this figure we are able 
 to support by premises a conclusion stated in any 
 one of the four propositions A, E, I, and O. 
 
 In the Second Figure, the major premise must 
 be universal, and one premise negative. The only 
 
I 
 
 CATEGORICAL ARGUMENTS 319 
 
 combinations of premises that satisfy these require- 
 ments are AE, AO, EA, and EL With their respect- 
 ive conclusions, these premises give the following 
 Moods : 
 
 AEE AGO EAE EIO 
 
 The conclusions in the Second Figure, it will be ob- 
 served, are negative propositions, either E or 0. 
 
 In the Third Figure, the minor premise must be 
 affirmative, and the conclusion particular. The fol- 
 lowing are the combinations of premises in which 
 the minor is affirmative : AA, AI, EA, El, IA, and 
 OA. From each of these we may draw, as required, 
 particular conclusions, and the valid Moods will be 
 as follows: 
 
 AAI All EAO EIO IAI OAO 
 
 In the Fourth Figure, if either premise is neg- 
 ative, the major is universal; if the major premise 
 is affirmative, the minor is universal; if the minor 
 premise is affirmative, the concluson is particular, 
 and if the minor is negative, both premises are uni- 
 versal. The only combinations of propositions 
 which satisfy these conditions are: AA, AE, EA, 
 El, IA. To draw conclusions from these premises, 
 we must remember that when, in this figure, the 
 minor premise is affirmative, the conclusion must be 
 particular. The valid moods are : 
 I 
 
 AAI AEE EAO EIO IAI 
 
320 A TEXT-BOOK OF LOGIC 
 
 In this figure, we may support conclusions stated in 
 each of the four propositions, excepting the univer- 
 sal affirmative. 
 
 The second method of determining the valid 
 Moods is to examine each of the combinations of 
 premises in each Figure, and observe whether it 
 satisfies the requirements of a valid argument. 
 Since we have eliminated those combinations of 
 premises which do not meet the rules of quantity 
 and quality as stated above, the validity of the argu- 
 ment will depend upon its satisfying the rules of 
 distribution. We shall give examples below foryall 
 the Figures, and the student is urged to work out 
 the entire list. This will be a review exercise, and 
 it will help him to fix definitely the .essentials con- 
 nected with the Figure and Mood of syllogisms, and 
 the distrbution of terms. 
 
 To begin, we may write the structural formulae 
 for the Figures in which we are to examine the given 
 combination of premises. Thus: 
 
 I II III IV 
 
 M-^-P P M * M P P M 
 
 S M S M ' M S M S 
 
 S P S P S P S P 
 
 In the vacant spaces of each premise may be written 
 the combination of premises we are wishing to ex- 
 amine, and in the vacant space of the conclusion, 
 the conclusion that these premises support. 
 
 When this has been done, our first question will 
 be : Is the middle term distributed in one, at least, 
 
CATEGORICAL ARGUMENTS 321 
 
 of the premises? The second question will be: Is 
 each distributed term of the conclusion, when there 
 is one, distributed also in one of the premises? 
 
 We give the following examples chiefly as a 
 guide to the student in working out the entire list. 
 AE in all the Figures. 
 
 I II III IV 
 
 MaP PaM MaP PaM 
 
 SeM SeM MeS MeS 
 
 SeP SeP SeP SeP 
 
 In the First Figure, this argument is invalid be- 
 cause the major term is distrbuted in the conclusion 
 and is not distributed in the major premise: Illicit 
 process of the major. 
 
 In the Second Figure the argument is valid. 
 
 In the Third Figure the argument is invalid be- 
 cause the major term is distributed in the conclusion 
 and is not distributed in the major premise : Illicit 
 process of the major. 
 
 In the Fourth Figure, the argument is valid. 
 AI in all the Figures. 
 
 I n III IV 
 
 MaP PaM MaP PaM 
 
 SIM SdM I MiS MiS 
 
 SiP ^Sf SiP Si 3 
 
 In the First Figure, the argument is valid. 
 
 In the Second Figure, the argument is invalid 
 because the middle term is not distributed in either 
 premise : Undistributed middle. 
 21 
 
322 A TEXT-BOOK OF LOGIC 
 
 In the Third Figure, the argument is valid. 
 
 In the Fourth Figure, the argument is invalid 
 because the middle term is not distributed in either 
 premise: Undistributed middle. 
 
 REFERENCES 
 H. A. Aikins, The Principles of Logic, Chs. XII., XIII., XIV., 
 
 XV., XVI. 
 J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
 
 VIII., IX. 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Chs. 
 
 XV., XVI. 
 W. S. Jevons, Elementary Lessons in Logic, Lessons XV., 
 
 XVI. 
 J. N. Keyes, Formal Logic, 2d Edition, Part III., Chs. I., III., 
 
 V. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. VI. 
 W. Minto, Logic, Inductive and Deductive, Part IV., Chs. I., 
 
 II., III., IV. 
 
 C. Read, Logic, Deductive and Inductive, Chs. IX., X. 
 W. J. Taylor, Elementary Logic, Chs. IX., XI. 
 
 ADVANCED 
 
 F. H. Bradley, The Principles of Logic, Book I., Chs. III., 
 
 VII., VIII. 
 W. R. B. Gibson, The Problem of Logic, Chs. XXL, XXII., 
 
 XXIIL, XXIV., XXV. 
 H. W. B. Joseph, An Introduction to Logic, Chs. XII., XIII., 
 
 XIV. 
 
 H. Lotze, Logic, Vol. I., Book I., Ch. III. 
 J. S. Mill, A System of Logic, Book II., Chs. II., III. 
 P. C. S. Schiller, Formal Logic, Chs. XIV., XV., XVI. 
 C. Sigwart, Logic, Vol. I., Part II., Ch. III., 54, 55, 59. 
 J. Venn, Empirical Logic, Ch. XV. 
 J. Welton, A Manual of Logic, Vol. I., Book IV., Chs. I., II., 
 
 III. 
 
CATEGORICAL ARGUMENTS 323 
 
 QUESTIONS 
 
 1. In what respects are the problems of this and the im- 
 mediately following chapters related to those of the pre- 
 ceding chapters? 
 
 2. What general view of the syllogism is assumed in the 
 discussions of this chapter? 
 
 3. What particular forms of statement are and what are 
 not studied in this chapter? 
 
 4. Discuss the advantages and disadvantages of viewing 
 the syllogism from the standpoint (1) of its premises 
 and (2) of its conclusion? 
 
 5. What mental process underlies the syllogism, and how 
 does it differ from that which underlies the judgment? 
 
 6. What do you understand by the major, minor and mid- 
 dle terms of the syllogism? 
 
 7. Define the syllogism from the standpoint of its con- 
 tained terms. 
 
 8. Define and illustrate the following: Premise, Conclu- 
 sion, Major premise, Minor premise, Undistributed mid- 
 dle, Illicit process. 
 
 9. With respect to what aspects of its contained proposi- 
 tions are the rules of the syllogism determined? 
 
 10. Explain why the middle term of a syllogism must be 
 distributed in at least one of the premises. 
 
 11. Why is there no separate rule relating to a term in the 
 conclusion that is undistributed? 
 
 12. Why must the premises of an affirmative conclusion be 
 affirmative? 
 
 13. Explain why a negative conclusion can be supported 
 only if but one of its premises is negative. 
 
 14. Why cannot a particular conclusion be supported by two 
 particular premises? 
 
 15. What is meant by the Figure of a syllogism? 
 
 16. Describe the formal characteristics of each of the Fig- 
 ures. 
 
 17. What do you understand by the Special Rules of the 
 Four Figures? 
 
324 A TEXT-BOOK OF LOGIC 
 
 18. What is meant by the Moods of the syllogism? 
 
 19. How do you determine all the theoretically valid Moods 
 of the syllogisms? 
 
 20. What is the relation of the Moods to the Figures of the 
 syllogism? 
 
 21. What two methods may be adopted to determine whether 
 a particular argument is valid in a given Figure? 
 
 EXERCISES 
 
 NOTE Write the formula for each proposition and syl- 
 logism in your answers to the following questions. 
 
 1. Point out (1) the conclusion, (2) the middle term, (3) 
 the major term, (4) the minor term, (5) the major pre- 
 mise, (6) the minor premise in the following argu- 
 ments : 
 
 (1) The receiver of stolen property should be punished; 
 you have received stolen property, and, therefore, 
 should be punished. 
 
 (2) Theft is crime; theft was encouraged by the laws 
 of Sparta, therefore, the laws of Sparta encouraged 
 crime. 
 
 (3) Only those messages which have been prepaid will 
 be delivered; this message has been prepaid, and, 
 therefore, will be delivered. 
 
 2. Name all the rules of the syllogism which are broken 
 by each of the following Moods: 
 
 AIA, EEI, IEA, 101, IIA, AEI. 
 
 3. Prove from the rules alone, irrespective of Figure, that 
 IE can yield no valid conclusion. 
 
 4. In what Figures do the following premises yield a valid 
 conclusion : 
 
 AA, AI, EA, OA. 
 
 5. Why cannot a particular negative proposition stand (1) 
 as a premise in the First, (2) as a major in the Second, 
 (3) as a minor in the Third, or (4) as a premise in the 
 Fourth Figure? 
 
CATEGORICAL ARGUMENTS 325 
 
 6. Arrange the following arguments in the order of major 
 and minor premise, and conclusion, and determine their 
 Figure, Mood, and validity: 
 
 (1) All colours are physical phenomena, but no sounds 
 are colours, and therefore no sound is a physical 
 phenomenon. 
 
 (2) Whatever is given on the evidence of sense may be 
 taken as a fact; the existence of God, therefore, is 
 not a fact, for it is not evident to sense. 
 
 (3) Every candid man acknowledges merit in a rival; 
 every learned man does not do so; therefore, every 
 learned man is not candid. 
 
 7. What can be determined respecting a syllogism under 
 each of the following conditions: 
 
 (1) That only one term is distributed, and that only 
 once. 
 
 (2) That only one term is distributed, and that twice. 
 
 (3) That two terms only are distributed, each only once. 
 
 (4) That two terms are distributed, each twice. 
 
CHAPTER XI 
 OTHER FORMS OF CATEGORICAL ARGUMENT 
 
 Their Relation to the Syllogism. The syllogism 
 may be considered from either of two points of view, 
 from the point of view of its premises, or from the 
 point of view of its conclusion. If we attend par- 
 ticularly to the premises, we shall think of the syllo- 
 gism as a method by which from given data we 
 arrive at a conclusion; if we attend particularly to 
 the conclusion, we shall think of the syllogism as a 
 method by which we state the grounds on which 
 a position already arrived at is held to rest. These 
 two ways of regarding the syllogism are not con- 
 tradictory, nor is our view of the nature of the syl- 
 logism affected by the possibility of this two-fold 
 approach to its problems. There results only a 
 slightly different emphasis in one's exposition; in 
 the one case, the conclusion, in the other, the prem- 
 ises, come to be the focus of our logical interest. 
 
 The reason why we may alter, in the way just 
 indicated, our exposition of the syllogism is that the 
 syllogism does not express a series of consecutive 
 steps by which the judgment actually proceeds for- 
 ward from data to conclusion, or backward from 
 conclusion to grounds; but it represents, in a con- 
 ventional form and order, the simplest inter-connec- 
 tions of a complex process of reasoning. It is some- 
 times brought forward as an objection to syllogistic 
 
 (326) 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 327 
 
 reasoning that it is not an instrument of the dis- 
 covery of truth ; but the objection rests upon a mis- 
 understanding. The truth about any subject-matter 
 is discovered by thinking, and the syllogism is not, 
 and does not affect to be, a substitute for thinking. 
 We may even say that unless truth already exists, 
 unless some kind and degree of thinking has taken 
 place, the syllogism has no function to perform. 
 The syllogism presupposes the existence of truth, 
 and is not the condition of its existence. It repre- 
 sents the results of our reflection upon the truth 
 that is already in our possession, a reflection that 
 is directed towards finding out the reasons why 
 truth assumes a demonstrative character. Now this 
 is not a small nor an easy thing. It is, however, an 
 eminently practical thing. For when thought takes 
 itself to task, and, by reflection upon its own proc- 
 esses, demands that the conditions of truth be 
 erected into principles of demonstration, we may be 
 led to see how far from being demonstrative are 
 many of the beliefs that we hold most confidently. 
 
 These remarks have a practical bearing upon 
 the subjects of this chapter, and may prepare us to 
 understand why our thoughts-about-things can be 
 thrown into a variety of forms which conform in 
 principle only to the Aristotelian syllogism. The 
 discussion of these arguments should lead us to see 
 that even in logic we are not bound in the state- 
 ment of our thought to the formal primness of the 
 three-term syllogism. 
 
328 A TEXT-BOOK OF LOGIC 
 
 Enthymeme. This is the name of a categorical 
 argument which omits, in statement, one of the con- 
 stituent factors of the syllogism. Now since there 
 are three propositions, two premises and a con- 
 clusion, in a categorical syllogism, the omission of 
 either one of these from the syllogism results in an 
 enthymeme. But it must not be supposed that the 
 omission of one member of a syllogism destroys the 
 syllogistic character of the reasoning, for, as the 
 term itself implies, the omitted member still func- 
 tions in the mind of the person who states his 
 thought in this particular form. The enthymeme, 
 consequently, is a particular way of stating a cat- 
 egorical argument, it is not a new form of categor- 
 ical syllogism. 
 
 According as the omitted member of the syllo- 
 gism is the major premise, the minor premise, or 
 the conclusion, the resulting enthymeme is said to 
 be of the First Order, the Second Order, and the 
 Third Order respectively. An enthymeme of the 
 First Order, consequently, is a syllogism which is 
 abbreviated by the omission of the major premise. 
 For example, Those who have no occupation have 
 nothing in which to interest themselves, and are, 
 therefore, unhappy.' An enthymeme of the Second 
 Order is a syllogism which is abbreviated by the 
 omission of the minor premise. For example, Those 
 who have no occupation are unhappy, because they 
 have nothing in which to interest themselves.' An 
 enthymeme of the Third Order is a syllogism which 
 is abbreviated by the omission of the conclusion. 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 329 
 
 For example, 'Those who have nothing in which to 
 interest themselves are unhappy, and those who 
 have no occupation have nothing in which to interest 
 themselves/ 
 
 In the enthymeme, as in the fully expressed 
 syllogism, the order in which the propositions are 
 stated is wholly a matter of convenience, and does 
 not affect the nature or validity of the argument. In 
 case of the enthymeme, however, it must be made 
 obvious by the use of such words as 'and,' 'because/ 
 and 'therefore,' which members of the syllogism we 
 are undertaking to express. 
 
 It may be questioned whether the enthymeme 
 has both Mood and Figure. Perhaps the best 
 answer to this inquiry would be that a syllogism in 
 any Figure and Mood may be stated as an enthy- 
 meme by the omission of one of its constituent prop- 
 ositions. But since Mood and Figure are character- 
 istics of arguments only when fully expressed in the 
 three-term syllogism, the most that we can say is 
 that an enthymeme implies a Figure and Mood, and 
 not that it has either. 
 
 Polysyllogism. In the enthymeme, we have an 
 example of the elliptical character of thought. Think- 
 ing, indeed, is ordinarily carried on by means of the 
 smallest number of factors necessary to its success 
 definitely present to consciousness. When the 
 thought is a simple one, and the inter-connection of 
 its parts consists of a relation of three terms, any 
 one of the relations may fall into the background 
 without invalidating or making doubtful its truth. 
 
330 A TEXT-BOOK OF LOGIC 
 
 This is, as we have seen, the case of the enthymeme. 
 When, however, thinking becomes complex, and the 
 inter-connection of its parts involves relations of 
 many terms, it is much more necessary to simplify 
 our methods, if thinking is not to break down under 
 the weight of the terms into which the subject- 
 matter of thought is analysed. In this case, what 
 we do is to build up a series of enthymemes or 
 abbreviated syllogisms, and such a series is called 
 a polysyllogism. A polysyllogism is, therefore, a 
 series of inter-connected enthymemes representing a 
 continuous chain of reasoning. 
 
 It is customary to denote the syllogisms into 
 which a polysyllogism may be analysed by the terms 
 prosyllogism and episyllogism. The application of 
 these terms depends entirely upon whether we are 
 thinking of the constituent syllogisms in the for- 
 ward direction, that is, of the first syllogism as 
 being connected with the second, and the second 
 with the third, etc. ; or whether we are thinking of 
 them in the reverse order, that is, of the second 
 syllogism as being connected with the first, the 
 third with the second, etc. When we think of the 
 constituent syllogisms in the former way, each syl- 
 logism is called a prosyllogism; and when we think 
 of them in the latter way, each syllogism is called 
 an episyllogism. The terms prosyllogism and epi- 
 syllogism, consequently, are used relatively, and any 
 syllogism in a train of reasoning may be both a pro- 
 and an episyllogism. It is obvious that the first 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 331 
 
 syllogism in such a series can be only a prosyllogism, 
 and the last only an episyllogism. 
 
 Types of Polysyllogism Trains of reasoning 
 of the type just described fall into two main classes, 
 progressive and regressive. We shall describe each 
 of these briefly, and merely for the purpose of show- 
 ing their logical structure. 
 
 A progressive, synthetic, or episyllogistic train 
 of reasoning proceeds from the premises of a pro- 
 syllogism to the conclusion of an episyllogism. A 
 polysyllogism of this character develops progress- 
 ively the consequences of the premises which form 
 its starting point. Stated otherwise, the progressive 
 polysyllogism advances from the conditions to what 
 is conditioned, from causes to effects. Probably 
 the most familiar illustrations of this class of poly- 
 syllogism for the student are to be found in the 
 direct proofs of geometrical propositions. A re- 
 gressive, analytic, or prosyllogistic train of reason- 
 ing proceeds from the conclusion of an episyllogism 
 to the premises of a prosyllogism. In such cases 
 we go back from a conclusion to show the grounds 
 upon which it rests. Stated otherwise, we are said 
 to reason from the conditioned to its necessary con- 
 ditions, from effects to causes. 
 
 Illustrations of these two classes of polysyllo- 
 gisms will be found in the following sections in which 
 we consider the various forms that such trains of 
 reasoning may assume. In this and the preceding 
 section we have been considering the general charac- 
 teristics of a group of syllogisms; in the sections 
 
332 A TEXT-BOOK OF LOGIC 
 
 that follow we are to study the cases that fall under 
 one or other of the two main classes of the group. 
 
 Sorites. This is a polysyllogism whose constitu- 
 ent syllogisms are all in the First Figure, and from 
 which all the conclusions, except the last, are omit- 
 ted. Or, since a syllogism which omits one of its 
 propositions is an enthymeme, we may regard a 
 sorites as a series of enthymemes from each of 
 which, except the first, one premise is omitted, and 
 from each of which, except the last, the conclusion 
 is omitted. 
 
 There are two forms of sorites, progressive and 
 regressive, which are usually distinguished as the 
 Aristotelian and the Goclenian respectively. An ex- 
 amination of each of these will serve to set the 
 nature of this class of arguments more clearly in 
 the light. 
 
 An Aristotelian sorites is a progressive series of 
 enthymemes in which the omitted conclusion of each 
 prosyllogism forms the minor premise of the suc- 
 ceeding episyllogism. A familiar example may be 
 taken from Rom. VIII., 29, 30 : 'For whom he fore- 
 knew, he also foreordained to be conformed to the 
 image of his Son, . . . and whom he foreordained, 
 them he also called; and whom he called, them he 
 also justified: and whom he justified, them he also 
 glorified/ A Goclenian sorites so called from Pro- 
 fessor Goclenius of Marburg (1547-1628) its dis- 
 coverer is a regressive series of enthymemes in 
 which the omitted conclusion of each prosyllogism 
 forms the major premise of the succeeding episyl- 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 333 
 
 logism. For example: 'One must take pains if he 
 is to be a successful man; industry is necessary to 
 taking pains ; health is necessary to industry ; a reg- 
 ulated diet and sufficient recreation and rest are 
 necessary to health ; and, therefore, a regulated diet 
 and sufficient recreation and rest are necessary if 
 one is to become a successful man/ 
 
 The symbolic expression and analysis of each 
 of these forms of sorites may be given thus : 
 
 ARISTOTELIAN SORITES GOCLENIAN SORITES 
 
 S is A Z is P 
 
 A is B Y is Z 
 
 B is C X is Y 
 
 C is P S is X 
 
 S is P S is P 
 
 Analysis : 
 
 S is A ) Z is P ^| 
 
 A is B C Y is ^ I 
 
 f (S is B) ) ('(Y is P)J 
 
 j B is C J Z is Y 
 
 ( (S is C) -) ( (X is P;"| 
 
 C is P C S is X V 
 
 S is P ) S is P J 
 
 Each of these forms is subject to special rules 
 which we shall proceed to state and prove, 
 l 
 
 THE SPECIAL RULES OF THE ARISTOTELIAN SORITES 
 
 RULE 1. Only one premise, and that the last, 
 can be negative. 
 
 Let us suppose that two of the premises are neg- 
 ative. Then the conclusion of the syllogism in 
 
334 A TEXT-BOOK OF LOGIC 
 
 which the first negative premise occurs will be neg- 
 ative. But since this negative conclusion is neces- 
 sarily a premise of the next succeeding syllogism, 
 its concluson will be negative, and so on, until a 
 negative conclusion enters as a premise into a syl- 
 logism which has the second negative premise. But 
 as we have seen, from two negative premises no 
 conclusion can be inferred. Only one premise, there- 
 fore, can be negative. 
 
 This negative premise must be the last. Let us 
 suppose that some other premise is negative. In 
 that case, the conclusion of the syllogism into which 
 it entered would be negative. This conclusion, serv- 
 ing as the minor premise of the following episyllo- 
 gism, would give a conclusion that is negative, that 
 is, one in which the major term is distributed. But 
 since the major term in the affirmative major prem- 
 ise is undistributed, the argument would fail on ac- 
 count of an illicit process of the major. No premise, 
 therefore, except the last can be negative. 
 
 RULE 2. Only one premise, and that the first, 
 can be particular. 
 
 Since every premise, except the last, must be 
 affirmative, it is evident that the conclusions of the 
 constituent syllogisms, except the last, must be 
 affirmative. If now the first premise is particular, 
 the conclusion of the first prosyllogism will be par- 
 ticular. And if any other premise, except the first, 
 were particular, there would occur somewhere in the 
 series two particular affirmative premises, and this, 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 335 
 
 in the First Figure, involves the fallacy of undis- 
 tributed middle. 
 
 THE SPECIAL RULES OF THE GOCLENIAN SORITES 
 
 RULE 1. Only one premise, and that the first, 
 can be negative. 
 
 If more than one premise were negative, one of 
 the constituent syllogisms would be involved in the 
 fallacy of negative premises. And since, if any 
 premise is negative, the conclusion must be negative, 
 that premise must be the one which contains the 
 predicate term of the conclusion, that is, the first 
 premise in this particular case. 
 
 RULE 2. Only one premise, and that the last, 
 can be particular. 
 
 If any premise is particular, the conclusion of 
 the syllogism in which it occurs would be particular ; 
 and if this conclusion became a premise of another 
 syllogism whose premise was already particular, 
 there would be involved, in the First Figure, the fal- 
 lacy of undistributed middle. Only the last premise, 
 therefore, can be particular. 
 
 Epicheirema. This is a regressive chain of 
 
 reasoning in which one, or both, of the premises is 
 expanded by the addition of a reason. In other 
 words, it is an argument in which one of the prem- 
 ises is an enthymeme, but in which both may be. 
 If only one of the premises is supported by a reason, 
 the epicheirema is called single, and when both are 
 so supported, double. A single epicheirema, there- 
 
336 A TEXT-BOOK OF LOGIC 
 
 fore, is a regressive chain of reasoning in which 
 one of the premises is supported by a reason. For 
 example : 
 
 All rational beings are to be treated with respect, inas- 
 much as they are made in the image of God. 
 Slaves are rational beings. 
 Therefore, slaves are to be treated with respect. 
 
 Father Clarke. 
 
 A double epicheirema is a regressive chain of 
 reasoning in which both premises are supported by 
 a reason. For example : 
 
 All Malays are cruel, because all savages are. 
 
 All the aboriginal inhabitants of Singapore are Malays, 
 
 because all the natives of that part of Asia are. 
 Therefore, all natives of Singapore are cruel. 
 
 Welton. 
 
 The formulae for these two kinds of epicheirema 
 may be written as follows : 
 
 SINGLE DOUBLE 
 
 Every M is P, because it is X Every M is P, because it is X 
 
 Every S is M Every S is M, because it is Y 
 
 Every S is P Every S is P 
 
 REFERENCES 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. X. 
 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 
 XVIII. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lesson XVIII. 
 
 J. N. Keynes, Formal Logic, 2d Edition, Part III., Ch. VI. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. VI., 11-13. 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 337 
 
 W. Minto, Logic, Inductive and Deductive, Book I., Part IV., 
 
 Ch. V. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XI. 
 W. J. Taylor, Elementary Logic, Ch. XIII. 
 
 ADVANCED 
 
 W. R. B. Gibson, The Problem of Logic, Ch. XXIX. 
 H. W. B. Joseph, An Introduction to Logic, Ch. XVI. 
 J. Welton, A Manual of Logic, Vol. I., Book IV., Ch. VI. 
 
 QUESTIONS 
 
 1. What characteristic of human thinking underlies the 
 forms of argument studied in this chapter? 
 
 2. What is an Enthymeme? 
 
 3. Name and illustrate the distinct types of Enthymeme. 
 
 4. How do we know whether any expressed proposition of 
 an Enthymeme is major or minor premise or conclusion? 
 
 5. Do Enthymemes have Figure and Mood? Explain. 
 
 6. What is a Polysyllogism? 
 
 7. Under what conditions does human thinking assume a 
 polysyllogistic form? 
 
 8. Explain and illustrate the meaning of the terms Pro- 
 syllogism and Episyllogism. 
 
 9. Describe and illustrate the general characteristics of a 
 Progressive Polysyllogism. By what other names is it 
 known? 
 
 10. Describe and illustrate the general characteristics of a 
 Regressive Polysyllogism. By what other names is it 
 known? 
 
 11. What is a Sorites? 
 
 12. Describe and illustrate the character of an Aristotelian 
 Sorites. Write also its structural formula. 
 
 13. Describe and illustrate the character of a Goclenian So- 
 rites. Write its structural formula, 
 
 22 
 
338 A TEXT-BOOK OF LOGIC 
 
 14. What is an Epicheirema? 
 
 15. Explain and illustrate each type of Epicheirema, and 
 write the formula. 
 
 EXERCISES 
 
 NOTE Write the formula for each of the propositions 
 and syllogisms contained in your answers to the following 
 questions. 
 
 1. What is the logical character of the following argu- 
 ments : 
 
 ( 1 ) He must have committed the murder, for he was the 
 only person present with the deceased at the time. 
 
 (2) Nations are justified in revolting when badly gov- 
 erned, for every people has a right to good govern- 
 ment. 
 
 (3) Death cannot be an evil, for it is universal. 
 
 (4) The planet Mars resembles the earth in possessing 
 atmosphere, water, and moderate temperatures, 
 and these conditions on the earth are necessary to 
 its being inhabited. 
 
 (5) He must be mad to do such a thing. 
 
 2. What is the logical character of the following argu- 
 ments : 
 
 (1) Misfortunes sometimes are circumstances tending to 
 improve character, circumstances tending to im- 
 prove character are promoters of happiness, what 
 tends to promote happiness is for the general well- 
 being, therefore, misfortunes sometimes promote 
 general well-being. 
 
 (2) A wise man is one who seeks to gain knowledge, the 
 man who seeks to gain knowledge must be indus- 
 trious, the industrious man has to make sacrifices, 
 to make sacrifices is always a hardship, and, there- 
 fore, a wise man always lives a life of hardship. 
 
 3. Prove that in an Aristotelian Sorites only the last prem- 
 ise can be negative, and only the first particular. 
 
OTHER FORMS OF CATEGORICAL ARGUMENT 339 
 
 4. Construct an Aristotelian Sorites with a particular 
 negative conclusion. 
 
 5. Prove that in a Goclenian Sorites only the last premise 
 can be particular and only the first negative. 
 
 6. Construct a Goclenian Sorites with a particular negative 
 conclusion. 
 
 7. Give one example of each class of Epicheirema. 
 
CHAPTER XII 
 
 DISJUNCTIVE AND HYPOTHETICAL PROPOSITIONS AND 
 ARGUMENTS 
 
 The Disjunctive Proposition. We have already 
 distinguished the various types of logical proposi- 
 tion, and discussed their relation to each other. We 
 have seen that in the categorical proposition P is 
 affirmed or denied of S simply. The disjunctive 
 proposition, on the other hand, is the expression of 
 an alternative predication. In the disjunctive prop- 
 osition, the character of S seems to waver between 
 a number of alternative possibilities, P or Q or M, 
 and we are not able to determine which of these 
 really, or for our purpose, belongs to S. 'S is either 
 P, or Q, or M,' is a typical disjunctive proposition. 
 
 Before proceedings to the discussion of the dis- 
 junctive syllogism, there are several questions about 
 the disjunctive proposition which require attention. 
 And, first, we may note that the alternatives which 
 form the predicates of such a proposition, are not 
 any alternatives, but are usually alternatives that 
 have something in common. We have met the con- 
 verse of this statement in the chapter on division, 
 where we saw that the species of a genus were to be 
 understood as a series of alternatives which had a 
 common nature. What we mean to express in our 
 disjunctive propositions, is, therefore, not unfa- 
 miliar; and the formal statement 'S is either P or Q 
 
 (340) 
 
PROPOSITIONS AND ARGUMENTS 341 
 
 or M' may be interpreted to mean that P and Q and 
 M are predicates which are, or may be, contained 
 under the wider predicate R which can be asserted 
 of S. For example, 'He is either a lawyer, a doctor, 
 a teacher, or a clergyman,' may be expressed in the 
 simpler statement, 'He is a member of a learned pro- 
 fession/ The alternatives of disjunctive proposi- 
 tions are usually of this class, and fall within a 
 single domain or universe of discourse. They con- 
 form, as do all other statements, to the limitations 
 of relevant assertion. But whether every instance 
 of alternative predication is actually thought of in 
 its relation to a limiting universe is what we cannot 
 affirm. All we hold is that logical alternatives imply 
 a common basis, and that it is this common basis 
 that gives to disjunction its distinctive meaning. 
 
 Second, the question whether the alternatives of 
 a disjunction should be treated as mutually exclusive 
 or not has aroused a good deal of discussion, and 
 there seems to be no simple answer to it. The 
 meaning of the question may be made plain if we 
 give it a formal expression. When it is said that 
 'S is either P or Q or M,' is it necessarily implied 
 that S cannot be both P and Q and M? There can 
 be no doubt that in a great many instances the alter- 
 native predicates do, as a matter of fact, exclude 
 each other. For example, we may say that 'Plato 
 was born in either 429 or 427 B. C.' About the in- 
 surrection in Mexico we may say, 'It will either suc- 
 ceed or be crushed.' Some logicians maintain that 
 this is the only sense in which disjunctive predica- 
 
342 A TEXT-BOOK OF LOGIC 
 
 tion can be understood in logic, and that the in- 
 stances in which this does not occur are due, as 
 Bradley says, to "our slovenly habits of expression 
 and thought," and are "no real evidence against the 
 exclusive character of disjunction." On the other 
 hand, attention may be called to the fact that we 
 do express our meanings in disjunctive forms which 
 cannot or need not be interpreted in this exclusive 
 manner. For example, ' He is either a fool or a 
 knave' may mean that he is the one or the other, 
 but it is quite possible for a knave to be a fool, and 
 a fool, a knave. In such cases as this, where the 
 truth-import and the statement-import are not neces- 
 sarily the same, we are following the line of least 
 error if we choose the less determinate meaning, in 
 the absence of any indication that the more deter- 
 minate meaning is the one intended. What the 
 statement *S is either P or Q or M/ therefore, means 
 is that S cannot be neither P nor Q nor M ; it must 
 be one, and, unless otherwise indicated, it may be 
 more than one. We must be guided in our interpre- 
 tation, not by the form of the proposition, but by the 
 nature of its subject-matter. 
 
 Third, the series of alternatives that constitute 
 the predicates of disjunctive propositions must be 
 exhaustive. That is, they must determine com- 
 pletely the alternative possibilities in the given in- 
 stance. If we say The water is either hot or cold/ 
 the statement is misleading, if we assume that 
 all the alternatives of the disjunction are ex- 
 plicitly stated. But if we say The water is either 
 
PROPOSITIONS AND ARGUMENTS 343 
 
 hot or cold or of some mean temperature/ the state- 
 ment is true, and, in principle, exhaustive. It would 
 seem, therefore, that to secure an exhaustive enu- 
 meration of alternatives were more fundamentally 
 important than to make them exclusive ; and in any 
 case we can say that the latter is sometimes im- 
 possible where the former presents no particular 
 difficulty. 
 
 The Nature and Classes of the Disjunctive Syllo- 
 gism. The syllogism whose major premise is a dis- 
 junctive proposition is called a disjunctive syllo- 
 gism. The significance of such a syllogism consists 
 in the fact that conclusions may be inferred from 
 premises that are indeterminate in content; or, 
 that the truth of any proposition may rest upon a 
 number of conditions, one or more of which may be 
 undetermined in character. 
 
 We may distinguish two classes of disjunctive 
 argument, according as the nature of the subject 
 of the disjunctive major premise requires two, or 
 more than two, terms to state exhaustively the alter- 
 native possibilities. If the major premise of a dis- 
 junctive argument has two alternatives in its pred- 
 icate, the argument is called a simple disjunctive 
 syllogism; if the predicate term of such an argu- 
 ment presents more than two alternatives, the argu- 
 ment is called mixed. The reason for this distinc- 
 tion is that the character of the other two proposi- 
 tions of the syllogism is affected by the consider- 
 ations to which we have adverted. For in such 
 arguments as we are at present concerned with, it 
 
344 A TEXT-BOOK OF LOGIC 
 
 is evident that we can only affirm or deny one or 
 more of the alternatives presented by the major 
 premise, such affirmation or denial giving us the 
 minor premise; and deny or affirm the remaining 
 alternative, or alternatives, such denial or affirma- 
 tion giving us the conclusion of the syllogism. Thus, 
 the general rule to which disjunctive arguments 
 must conform is that to affirm or deny one or more 
 of the members of a series of alternatives is to deny 
 or affirm the remaining member or members. Now 
 if the disjunctive major premise presents only a 
 pair of alternatives, the minor premise and con- 
 clusion of the syllogism are both categorical prop- 
 ositions; there is, in other words, only one disjunc- 
 tive premise, and that the major. Such an argu- 
 ment is called a simple disjunctive syllogism. If, 
 on the other hand, there are more than two alter- 
 natives in the disjunctive major premise, one, or 
 both, of the other propositions of the syllogism must 
 be disjunctive also. In such a case, we call the argu- 
 ment a mixed disjunctive syllogism. 
 
 The Moods of the Disjunctive Syllogism. Each 
 class of disjunctive argument has two moods, de- 
 pending upon whether the minor premise affirms or 
 denies one or more of the alternatives presented by 
 the major premise. The names of these moods, 
 like those that we shall meet with in our study of the 
 hypothetical syllogism, are derived from the Latin 
 words which denote the quality of the propositions 
 which constitute the minor premise and conclusion 
 respectively. For example, if the minor premise is 
 
PROPOSITIONS AND ARGUMENTS 
 
 345 
 
 negative, and the conclusion is affirmative, the mood 
 of the syllogism is called the Modus Tollendo Ponens, 
 that is, the mood which by denying affirms. If, on 
 the other hand, the minor premise is affirmative, 
 and the conclusion is negative, the mood is called 
 the Modus Ponendo Tollens, that is, the mood which 
 by affirming denies. These statements will be 
 understood if read in connection with the formulae 
 for the two classes of disjunctive syllogism in each 
 of these moods which follow : 
 
 DISJUNCTIVE SYLLOGISM 
 
 MOOD 
 
 Ponendo Tollens 
 
 Modus 
 Tollendo Ponens 
 
 SIMPLE 
 
 A is either B or C. 
 A is B. 
 
 A is either B or C. 
 A is not B. 
 A is C. 
 
 MIXED 
 
 A is either B or C or D. 
 
 A is B. 
 
 A is not either C or D. 
 
 A is either B or C or D 
 
 A is not B. 
 
 A is either C or D. 
 
 The Validity of Disjunctive Arguments. A fur- 
 ther question relates to the validity of these moods. 
 We have seen that disjunctive propositions are 
 required to state their alternatives exhaustively, 
 that is, to enumerate alternately all the possibilities 
 presented by the subject-matter under consideration. 
 We have also seen that in some cases the alternatives 
 are at the same time exclusive, that is, incompat- 
 ible. Thus, 'A is either B or C' may mean (1) 'A 
 is either B or C, but not statedly both;' or it may 
 mean (2) 'A is either B or C, but statedly not both/ 
 
346 A TEXT-BOOK OF LOGIC 
 
 that is, the equivalent of 'A is either B or else C.' 
 Now in whichever way we understand the disjunc- 
 tive proposition, an argument based upon it is valid 
 in Modus Tollendo Ponens, because all disjunctive 
 arguments imply the presence in the subject of one 
 or more of the alternatives specified in the predicate 
 of the major premise. That is to say, the subject 
 cannot be neither of the predicated alternatives. 
 The meaning of the subject professedly is to be 
 found within the number of enumerated predicates. 
 Hence, whether the predicates are exclusive or not, 
 to deny one or more of a subject is to bring the 
 subject nearer to one or more of the remaining 
 predicates. That is, the Modus Tollendo Ponens em- 
 phasises the exhaustive character of the disjunctive 
 major. On the other hand, the Modus Ponendo Tol- 
 lens is valid only when an exclusive reading of the 
 major is understood. For example, when we say 
 of any one that 'He is a fool or a knave/ we cannot 
 infer that because 'He is a fool/ that 'He is not a 
 knave/ unless it is distinctly understood that the 
 individual case precludes the possibility of him being 
 both. Thus, if we wish to state this meaning unam- 
 biguously, we should have to say 'He is either a fool 
 or else a knave/ thereby implying that he is not 
 both together. When, therefore, the disjunctive 
 major takes the form of 'statedly not both or all the 
 predicates/ the Modus Ponendo Tollens is a valid 
 mood for disjunctive arguments. This mood empha- 
 sises the exclusive character of the disjunctive 
 major. 
 
PROPOSITIONS AND ARGUMENTS 347 
 
 The Hypothetical Proposition. Any proposition 
 which states a connection between two possibilities 
 is hpyothetical. For example, 'If water is heated at 
 standard pressure, it will boil at 100 C.' There are 
 two characteristics of a hypothetical proposition to 
 which attention should be given. _JThe firat_is_that 
 it isjhe form of statement in which w_a express our 
 judgments when the material of these judgments is 
 possible^ not actual. This does not mean that the 
 material dealt with may not be actual, it means only 
 that we are not concerned with it as existing, but 
 with the situations in which it is possible for it to 
 exist. Thus, to take the judgment which is ex- 
 pressed in the proposition 'If eggs are scarce, they 
 will be dear.' In this proposition we are not assert- 
 ing that 'eggs are scarce,' nor are we affirming that 
 'they are dear;' we are merely stating that 'when- 
 ever eggs are scarce, they_ are_ &t_:the same time 
 dear.' In other words, we are stating a connection 
 between 'it is possible for eggs to be scarce,' and 
 'it is possible for them to be dear.' 
 
 The second characteristic of hypothetical prop- 
 ositions relates to the kind of connection that they 
 affirm. This may be brought out if we regard the 
 judgments underlying hypothetical statements to be 
 concerned with the development of the consequences 
 that follow from a supposition. What leads to the 
 erection of a supposition is, doubtless, some feature 
 of an actually existing situation which cannot be 
 brought under direct observation; but the supposi- 
 tion itself is not part of the situation in the same 
 
348 A TEXT-BOOK OF LOGIC 
 
 sense that the feature itself is. Any supposition is a 
 suggestion which is based upon a wider range of ex- 
 perience than the circumstances which calls it forth, 
 and we fall back upon this broader experience to 
 guide us in dealing with a situation that is proble- 
 matical. Now problematic situations can be de- 
 veloped only in a series of possibilities, and possi- 
 bilities are expressed in hypothetical propositions: 
 'If A is B, it is C.' The part of the hypothetical 
 proposition which states the supposition or condition 
 is called the antecedent, the part which states the 
 result of the supposition is called the consequent. 
 
 is thus affirmed by hypothet- 
 
 ical propositions is a relation of dependence between 
 antecedent and consequent, such Jhflt the truth ?* 
 
 lishment of the_ antecedent. The hypothetical 
 proposition thus states a rule under which we may 
 bring for testing any fact or situation about which 
 we are at all doubtful. It should be observed that 
 it is the nature of the thought expressed, and not 
 the form of the expression that constitutes any 
 proposition hypothetical. While usually we intro- 
 duce hypothetical statements with 'if,' they may be 
 prefaced by 'granted that/ 'suppose that,' 'allowing 
 that,' 'whenever,' 'wherever;' and sometimes there 
 is no verbal sign to indicate that our thought is 
 hypothetical, as, for example, 'Trespassers will be 
 prosecuted/ 'Deserters will be shot on sight/ etc. 
 
 The Hypothetical Syllogism. Any syllogism in 
 which the major premise is a hypothetical proposi- 
 
PROPOSITIONS AND ARGUMENTS 349 
 
 a hypothetical syllogism. In hypothet- 
 
 ical arguments the minor premise and the conclusion 
 are both categorical propositions. Now since the 
 major premise states a connection between two 
 possibilities, the. ^jnin^r^premise must state some- 
 thing about one or other of these possibilities cate- 
 ^gorically if there is to be an inference. The only 
 things that can be stated are that either of the pos- 
 sibilities has or has not been verified. Theoretically, 
 this would give four kinds of hypothetical syllo- 
 gism, the minor premises of which would affirm and 
 deny separately the antecedent and consequent of 
 the major premise. Two of these, however, fail to 
 give the proper basis for an Inference, .namely, when 
 minor premise HpmVfl thfii<U^ p( V^ PT1 ' < 'i and when 
 consequent. The reason for the fail- 
 
 ure is that we are in each case required to go be- 
 yond what is contained in the major premise. For 
 example, when we say 'If A is B, it is C,' we are not 
 to be understood to mean that the only condition of 
 'A being C' is that 'A is B.' We said above, for in- 
 stance, that 'If eggs are scarce, they are dear;' but, 
 of course, they may be dear for other reasons as 
 well, a corner on the market by the cold storage 
 interests, for example. Hence, if we were to deny 
 the antecedent of this proposition, 'Eggs are not 
 scarce/ and use this as a minor premise, we could 
 not infer that 'they are not dear.' . The antecedent 
 of a hypothetical proposition states a condition, but 
 3bes not offer itself as the sole condition of the 
 truth of the consequent. If, on the other hand, 
 
350 A TEXT-BOOK OF LOGIC 
 
 we were to affirm the consequent, 'Eggs are dear/ 
 we cannot infer that 'they are scarce/ and the rea- 
 son is the same. The forms of the syllogism are 
 reduced, therefore, to two, in one of which the 
 minor premise affirms the antecedent of the major, 
 and in the other the minor premise denies the con- 
 sequent of the major. In reference to these forms 
 of the syllogism, we may state the general rule of 
 hypothetical arguments as follows : When two pos- 
 sibilities are related as antecedent and consequent, 
 the truth of the consequent follows from the truth 
 of the antecedent, and the falsity of the antecedent 
 follows from the falsity of the consequent. 
 
 The Moods of the Hypothetical Syllogism. Corre- 
 sponding to these two forms of hypothetical argu- 
 ment we may distinguish two moods of the syllo- 
 gism. There is first the argument in which the 
 minor premise affirms the antecedent of the major 
 premise, the Modus Ponens ; and, second, the 
 argument in which the minor premise denies the 
 consequent of the major premise, the Modus Tol- 
 lens. 
 
 The antecedent and consequent of the major 
 premise of any hypothetical syllogism may be either 
 affirmative or negative. In each of the two moods, 
 therefore, we may distinguish four forms of hypo- 
 thetical argument as follows: (1) the antecedent 
 and consequent of the major premise may both be 
 affirmative; (2) the antecedent may be affirma- 
 tive, and the consequent negative; (3) the antece- 
 dent may be negative, and the consequent affirm- 
 
PROPOSITIONS AND ARGUMENTS 351 
 
 ative; (4) both antecedent and consequent may be 
 negative. It will be evident that arguments in these 
 moods will have sometimes an affirmative and some- 
 times a negative proposition in the minor premise, 
 and the same will be true of the conclusion. The 
 names of the several forms of the moods of hypo- 
 thetical syllogisms, like those of the disjunctive syl- 
 logism, are derived from the Latin words which de- 
 scribe the quality of the propositions which consti- 
 tute the minor premise and the conclusion. We 
 shall briefly characterise each mood and give exam- 
 ples and formula for the different forms of the two 
 moods. 
 
 i. Modus Ponens, the mood in which the minor 
 premise affirms the antecedent of the major premise, 
 and the conclusion affirms the consequent. Argu- 
 ments in this mood are said to be Constructive. 
 The validity of arguments in this mood is based 
 upon the fact that we are bound to accept whatever 
 follows from any data we have accepted. If, for 
 example, we accept as a possibility a fall in temper- 
 ature, we are bound to accept whatever is condi- 
 tioned upon this possibility, say, colder weather. 
 We may, therefore, construct a hypothetical argu- 
 ment in this mood as follows : 
 
 A fall in temperature means colder weather. 
 The temperature is falling. 
 Therefore, the weather will be colder, 
 
352 A TEXT-BOOK OF LOGIC 
 
 The different forms of the Modus Ponens are 
 given here with illustrations of each form. 
 
 1 i ) Modus Ponendo Ponens, the mood which by 
 
 affirming affirms. 
 
 If A is B, it is C. If any county increases in wealth, 
 it increases in power; 
 
 A is B, The United States is increasing in 
 
 wealth, 
 
 A is C, Therefore, the United States is in- 
 
 creasing in power. 
 
 (2) Modus Ponendo Tollens, the mood which by 
 
 affirming denies. 
 
 If A is B, it is-not C. If any import duty is imposed 
 simply for revenue purposes, that 
 duty is not protective; 
 
 A is B. The English import duties are im- 
 
 posed simply for revenue purposes; 
 
 A is-not C. Therefore, they are not protective. 
 
 (3) Modus Tollendo Ponens, the mood which by 
 
 denying affirms. 
 If A is not B, it is C. If any swan is not white, it is 
 
 black ; 
 
 A is-not B. Australian swans are not white, 
 A is C. Therefore, they are black. 
 
 (4) Modus Tollendo Tollens, the mood which by 
 
 denying denies. 
 
 If A is-not B, it is-not C. If any war is not defensive, 
 it is not just; 
 
PROPOSITIONS AND ARGUMENTS 353 
 
 A is-not B. The wars waged by Napoleon the 
 
 Great were not defensive, 
 A is-not C. Therefore, they were not just. 
 
 2. Modus Tollens, the mood in which the minor 
 premise denies the consequent of the major premise, 
 and the conclusion denies f f h^ antPppHpnt Argu- 
 ments in this mood are said to be Destructive. The 
 validity of arguments in this mood follows from the 
 relations expressed by the major premise. For if 
 B follows of necessity from the existence of A, 
 'If A then B,' the failure of B to appear must mean 
 the absence or non-existence of /L An illustration 
 of an argument in this mood is : 
 
 If no men were mad, asylumsjwould be useless, 
 Asylums are-not useless, 
 Therefore, s_ome men are mad. 
 The different forms of the Modus Tollens are 
 given here with illustrations of each form.^ 
 
 ( i ) Modus Tollendo Tollens, the mood which by 
 denying denies. 
 
 If A is B, it is C. If any country is civilised, it has 
 a population amongst whom educa- 
 tion is general; 
 
 A is-notjC^ The people of Russia are not gener- 
 ally educated; 
 
 A is-not B. Therefore, Russia is not a civilised 
 country. 
 
 V 
 
 23 
 
354 A TEXT-BOOK OF LOGIC 
 
 (2) Modus Ponendo Tollens, The mood which by 
 
 affirming denies. 
 If A is B, it is not C. If any social institution is 
 
 justifiable, it oppresses no class of 
 
 the community; 
 A is C. Slavery does oppress a class of the 
 
 community, 
 A is-not B. Therefore, it is not justifiable. 
 
 (3) Modus Tollendo Ponens, the mood which by 
 
 denying affirms. 
 If A is-not B, it is C. If any railroad is not required 
 
 in the district through which it runs, 
 
 it is a financial failure; 
 A is-not C. The great American lines are not 
 
 financial failures, 
 A is B. Therefore, they are required in the 
 
 districts through which they run. 
 
 (4) Modus Ponendo Ponens, the mood which by 
 
 affirming affirms. 
 
 If A is-not B, it is-not C. If any country has no 
 capital invested abroad, its imports 
 will not exceed its exports; 
 
 A is C. England's imports do exceed her ex- 
 
 ports, 
 
 A is B. Therefore, England has capital in- 
 
 vested abroad. 
 
 Dilemmas. We come now to the study of dilem- 
 mas, a class of arguments which combines in various 
 ways characteristics of the three kinds of proposi- 
 
PROPOSITIONS AND ARGUMENTS 355 
 
 tion already studied, the categorical, the disjunctive, 
 and the hypothetical. The peculiar feature of a 
 dilemmatic argument is that it presents a choice 
 between two alternatives. When used for rhetor- 
 ical purposes these alternatives are of such a kind 
 that, whilst one of them must be accepted, both lead 
 to disagreeable results. To force by argument the 
 acceptance of one or other of a pair of alternatives 
 is the chief function of the dilemma, and as the re- 
 sult of such an argument an opponent is said 'to be 
 on the horns of a dilemma/ Arguments in which 
 the choice rests among three alternatives are not 
 dilemmas in the strict definition of the term, but 
 trilemmas, just as those which force a choice among 
 four alternatives are tetralemmas. The principle? 
 of all these arguments, however, are the same, and 
 it will be sufficient to study them in connection with 
 the simplest forms, the dilemmas. 
 
 The dilemma may be defined as a syllogism with 
 a compound hypothetical major premise and a dis- 
 junctive minor. By a compound hypothetical prop- 
 osition is meant one in which there is a plurality 
 of terms in either the antecedent or consequent, or 
 in both. The simplest form of hypothetical prop- 
 osition, we have seen, is 'If A is B, it is C.' Such 
 a proposition may become compound by adding 
 terms to antecedent and consequent. 'If A is B, it 
 is C or D,' is a compound hypothetical proposition, 
 and we must understand it to mean 'If A is B, it is 
 C* and 'If A is B, it is also D.' That is to say, there 
 is no true disjunction in this case, but only an ab- 
 
356 A TEXT-BOOK OF LOGIC 
 
 breviated expression of two simple hypothetical 
 propositions. The same remarks hold good also of 
 the other forms that compound hypothetical prop- 
 ositions may assume; for example of, 'If. _A is B or 
 C^iLisJ) ;' 'If A is B or C, it is D or E.' Proposi- 
 tions of this type form the major premises of dilem- 
 matic arguments. The reason why propositions of 
 this type constitute the major premise of dilemmatic 
 arguments is quite clear. For if the dilemma is 
 thought of as an argument which leads to a con- 
 clusion through the affirmation or denial of alter- 
 natives in the minor premise, the major premise of 
 such an argument must provide the basis for the 
 alternatives affirmed or denied in the minor premise, 
 and this it can do only when there is a plurality of 
 terms in the antecedent, consequent, or both, of 
 the major premise. In view of these more general 
 statements, the structure of the dilemma will be 
 evident from the following analysis : 
 
 1. The major premise is a compound hypothet- 
 ical proposition 
 
 a. with a one-term antecedent and a two- 
 term consequent, 
 
 with a two-term antecedent and a one- 
 term consequent, 
 
 c. or with a two-term antecedent and a two- 
 term consequent. 
 
 2. The minor premise is a disjunctive proposi- 
 tion, 
 
PROPOSITIONS AND ARGUMENTS 357 
 
 3. The conclusion is 
 
 a. either a categorical proposition, when the 
 major premise has a one-term antecedent 
 or consequent. 
 
 b. or a disjunctive proposition, when the 
 major premise has a two-term antecedent 
 and consequent. 
 
 Classes of Dilemma. Dilemmas, which are gov- 
 erned by the laws of the hypothetical syllogism, are 
 of two kinds, Cojosiructive and Destructive. ^A 
 dilemma is said to be constructive when the minor 
 premise affirms the antecedent of the major, and to 
 be destructive when it denies the consequent of the 
 major disjunctively. Within each of these kinds, 
 there are two forms, Simple and Complex. A 
 dilemma is said to be simple when its major premise 
 has a single antecedent or consequent, and it is said 
 to be complex when both the antecedent and conse- 
 quent of the major premise contain two terms. We 
 proceed now to the study of each of these kinds of 
 dilemma, and to an examination of the forms that 
 they may assume. 
 
 i. Constructive Dilemma, an argument which 
 proceeds from the acceptance of the antecedent to 
 the acceptance of the consequent of the major 
 premise. 
 
 (i) Simple Constructive Dilemma, an argument 
 whose minor premise affirms disjunctively the ante- 
 cedent of the major, and whose conclusion categor- 
 ically affirms the consequent. 
 
358 A TEXT-BOOK OF LOGIC 
 
 If either A or B, then C., If a science furnishes use- 
 ful facts, or if the study of it exer- 
 cises the reasoning powers, it is 
 worthy of being cultivated; 
 
 Either A or B. But either a science furnishes useful 
 facts, or its study exercises the rea- 
 soning powers; 
 
 Therefore, C. Therefore, it is worthy of being cul- 
 tivated. 
 
 (2) Complex Constructive Dilemma, an a r g u- 
 ment whose minor premise disjunctively affirms the 
 antecedent, and whose conclusion disjunctively 
 affirms the consequent. 
 
 If A then C, and if B then D. If Aeschines joined 
 in the public rejoicings, he is incon- 
 sistent; if he did not he is unpa- 
 triotic ; 
 
 Either A or B. But either he did or did not; 
 Therefore, either C or D. Therefore, he is either 
 
 inconsistent or unpatriotic. 
 
 2. Destructive Dilemma, an argument which 
 proceeds from the denial of the consequent to the 
 denial of the antecedent. 
 
 (i) Simple Destructive Dilemma, an argument 
 whose minor premise denies disjunctively the conse- 
 quent of the major, and whose conclusion categor- 
 ically denies the antecedent. 
 
 If A, then both B and C. If table-rappers are to be 
 trusted, the departed are spirits, and 
 they also exert mechanical energy ; 
 
PROPOSITIONS AND ARGUMENTS 359 
 
 Either not B or not C. But either the departed are 
 not spirits or they do not exert me- 
 chanical energy; 
 
 Therefore, not A. Therefore, table-rappers are not 
 to be trusted. 
 
 (2) Complex Destructive Dilemma, a n a r g u- 
 ment whose minor premise disjunctively denies the 
 consequent of the major, and whose conclusion dis- 
 junctively denies the antecedent. 
 If A then C, and if B then D. If the industry of the 
 United States is well organised, there 
 is work for every efficient labourer 
 who seeks it, and if all labourers are 
 industrious, they will seek work. 
 Either not C or not D. But either some labourers 
 cannot get work, or they will not 
 seek it; 
 
 Therefore, either not A or not B. Therefore, either 
 the industry of the United States is 
 not well organised, or some labourers 
 are not industrious. 
 
 The Validity of the Dilemma. The logical value 
 of dilemmatic arguments has frequently been called 
 in question. Thus Jevons says, "Dilemmatic argu- 
 ments are more often fallacious than not." It may, 
 therefore, serve to emphasise the character of these 
 arguments if we indicate where their use may in- 
 volve us in error. The fallacious character of a 
 dilemma must be sought either in the major or in 
 the minor premise. In the major premise, the ante- 
 
860 A TEXT-BOOK OF LOGIC 
 
 cedent or consequent may not express possibilities, 
 in which case the error will be easily detected; or 
 the asserted connection between them may be false, 
 in which case the error is likely to be obvious. For 
 example, if we do not admit that 'A is B' and 'A is C' 
 are possibilities, then we are not likely to admit that 
 'If A is B, it is C' is a possible premise of an argu- 
 ment. But if we admit both as possibilities, we may 
 not admit that the one follows as a consequence from 
 the other, and this will preclude 'If A is B, it is C' 
 from figuring as the major premise of an argument. 
 We thus see that before we can accept a compound 
 hypothetical proposition as the major premise of a 
 syllogism, we are required to admit that both ante- 
 cedent and consequence are possibilities, and that 
 they are related to each other as condition and con- 
 ditioned. For example, it is possible for a triangle 
 to be equilateral, it is also possible for a triangle to 
 be equiangular, but in this case wherever one of 
 these possibilities is realised the other is also found, 
 the one is conditioned by the other. These are the 
 facts that we express in the statement, 'If a triangle 
 is equilateral, it is equiangular/ 
 
 Error arises most frequently, however, in the 
 minor premise. The reason for this is that the 
 alternatives may not be either exhaustive or ex- 
 clusive. The difficulty of getting a dichotomous 
 alternative which is exhaustive is due partly to the 
 complex nature of the subjects of discourse, and 
 partly to the fact that the major premise of these 
 arguments is concerned only with the relation of 
 
PROPOSITIONS AND ARGUMENTS 361 
 
 antecedents and consequence, and not with disjunc- 
 tive relations. The proposition 'If A is B, it is C 
 or D' means, as we have seen, that 'A is B' is the 
 condition of both 'A is C' and 'A is D/ When, 
 therefore, we affirm these two disjunctively in 
 the minor premise of an argument, we must do so 
 on other grounds than that they are antecedents or 
 consequent of a compound hypothetical major pre- 
 mise. Hence, to quote Jevons, "if we were to argue 
 that 'if a pupil is fond of learning, he needs no 
 stimulus, and that if he dislikes learning, no stimulus 
 will be of any avail; but as he _is_ either fond of 
 learning or dislikes it, a stimulus is either^ needless 
 or of no avail,' we evidently assume improperly the 
 disjunctive minor premise. Fondness and dislike 
 are not the only two possible alternatives, for there 
 may be some who are neither fond of learning nor 
 dislike it, and to these a stimulus in the shape of 
 rewards may be desirable. Almost anything can be 
 proved if we are allowed to pick out two of the 
 possible alternatives which are in our favor, and 
 argue from these alone." 
 
 REFERENCES. 
 
 H. A. Aikins, The Principles of Logic, Ch. XVII. 
 B. Bosanquet, The Essentials of Logic, Lecture VI. 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XI. 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 
 
 XVI. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lesson XIX. 
 J. N. Keynes, Formal Logic, 2d Edition, Part III., Chs. VII., 
 
 VIII. 
 
362 A TEXT-BOOK OF LOGIC 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. VII. 
 
 W. Minto, Logic, Inductive and Deductive, Book I., Part IV., 
 Ch. VII. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XII. 
 
 W. J. Taylor, Elementary Logic, Ch. XII. 
 
 ADVANCED 
 
 B. Bosanquet, Logic, Chs. VI., VIII. 
 
 F. H. Bradley, The Principles of Logic, Book I., Chs. II., IV. 
 W. R. B. Gibson, The Problem of Logic, Chs. XXX., XXXI., 
 
 XXXII. 
 
 H. W. B. Joseph, An Introduction to Logic, Ch. XV. 
 H. Lotze, Logic, Book I., Ch. II., B, C. 
 F. C. S. Schiller, Formal Logic, Ch. XVII. 
 
 C. Sigwart, Logic, Vol. I., Part I., Ch. VII. 
 J. Venn, Empirical Logic, Ch. X. 
 
 J. Welton, A Manual of Logic, Vol. L, Book IV., Ch. V. 
 
 QUESTIONS 
 
 1. What kind of predication underlies the disjunctive prop- 
 osition? 
 
 2. What relation has disjunctive assertion to the universe 
 of discourse? 
 
 3. Discuss the question whether the alternatives of a log- 
 ical disjunction are exclusive. 
 
 4. "The alternatives of a disjunctive proposition must be 
 exhaustive." Explain. 
 
 5. What are the characteristics and significance of a dis- 
 tinctive syllogism? 
 
 6. Discuss and illustrate the main classes of disjunctive 
 syllogism. 
 
 7. Why do we distinguish classes of disjunctive argument? 
 
 8. What are the functions of the minor premise and con- 
 clusion of a disjunctive syllogism? 
 
 9. In what Moods may a disjunctive syllogism be stated? 
 
PROPOSITIONS AND ARGUMENTS 363 
 
 10. How will your interpretation of 'A is either B or C' be 
 affected, if the alternatives are understood to be ex- 
 clusive, and if they are understood to be not necessarily 
 exclusive? 
 
 11. Why is the disjunctive syllogism in Modus Tollendo 
 Ponens valid whichever view of alternation we take? 
 
 12. Why is a disjunctive syllogism in Modus Ponendo Tol- 
 lens valid only if we give an exclusive reading of the 
 major premise? 
 
 13. What is a hypothetical proposition? 
 
 14. Name and state the difference between the main classes 
 of hypothetical proposition. 
 
 15. What is meant by saying that the material of the judg- 
 ments which are expressed in hypothetical propositions 
 is possible not actual? 
 
 16. "Hypothetical propositions state the connection of a sup- 
 position and what follows from it." Explain. 
 
 17. Into what two parts may a hypothetical proposition be 
 analysed? 
 
 18. What are the characteristics of a hypothetical syllogism? 
 
 19. Why does the denial of the antecedents, and the affir- 
 mation of the consequents of the major premise of a 
 hypothetical syllogism make it impossible to state any 
 valid conclusion? 
 
 20. What are the rules of valid inference for hypothetical 
 arguments? 
 
 21. In what Moods may a hypothetical argument be stated 
 validly? 
 
 22. In what Mood is a hypothetical argument constructive? 
 
 23. Describe and illustrate the Modus Ponens, and state 
 why hypothetical arguments in this Mood are valid. 
 
 24. State and illustrate the different forms of the Modus 
 Ponens. 
 
 25. In what Mood is a hypothetical argument destructive? 
 
 26. Describe and illustrate the Modus Tollens, and state 
 why hypothetical arguments in this Mood are valid. 
 
364 A TEXT-BOOK OF LOGIC 
 
 27. State and illustrate the different forms of the Modus 
 Tollens. 
 
 28. What is it to be 'on the horns of dilemma'? 
 
 29. How do dilemmas, trilemmas and tetralemmas differ 
 from one another? 
 
 30. Define a dilemma. 
 
 31. What are the various theoretically possible forms of 
 dilemma? 
 
 32. What is a constructive dilemma? 
 
 33. Describe and illustrate the various forms of constructive 
 dilemma. 
 
 34. What is a constructive dilemma? 
 
 35. Describe and illustrate the various forms of destructive 
 dilemma. 
 
 36. What must we admit with respect to the major premise 
 of a dilemma before it can serve as the basis of a valid 
 conclusion? 
 
 37. What sources of possible error are found in the minor 
 premise of a dilemmatic argument? 
 
 EXERCISES. 
 
 1. Write three disjunctive propositions in which the alter- 
 natives are exhaustive and exclusive. 
 
 2. Construct on the basis of your answer to the previous 
 question three arguments in Modus Ponens. 
 
 3. Construct three disjunctive syllogisms in Modus Tollens. 
 
 4. Write three hypothetical propositions, only one of which 
 may be introduced by 'if.' 
 
 5. State the nature and Mood of the following arguments, 
 and examine their validity: 
 
 (1) If the study of logic furnishes the mind with a mul- 
 titude of useful facts, like other sciences, it would 
 deserve to be cultivated ; but it does not furnish the 
 mind with a multitude of useful facts; therefore, 
 it does not deserve cultivation. 
 
PROPOSITIONS AND ARGUMENTS 365 
 
 (2) Mars must have warmth sufficient for protoplasmis 
 metabolism, if life exists there; but life is not pos- 
 sible there, since the planet has not sufficient 
 warmth for the purpose named. 
 
 6. What are the nature and validity of the following argu- 
 ments : 
 
 (1) If you say what is just, men will hate you; and if 
 you say what is unjust, the gods will hate you. 
 you must say one or the other. Therefore, you 
 you will in either case be hated. 
 
 (2) If he were clever, he would see his mistake; and if 
 he were candid he would acknowledge it. But either 
 he does not see his mistake, or will not acknowl- 
 edge it. Therefore, he is either not clever or not 
 candid. 
 
CHAPTER XIII 
 INDUCTION AND METHODS PRELIMINARY TO INDUCTION 
 
 General Statement of the Problem. In the fore- 
 going chapters, knowledge was said to have two 
 sides, from one of which it is seen to be almost 
 wholly identified with what we call truth, and from 
 the other it appears to be almost wholly concerned 
 with what are called facts. On whichever of these 
 two sides of knowledge we may chance to look, we 
 are exposed to the danger of neglecting the other, 
 and thus of forgetting that the distinction of truth 
 and fact is only relative. If we say that the dis- 
 tinction is one that concerns the contrast that is 
 ordinarily made between our thoughts-about-objects 
 (truth) and the objects-thought-about (facts), it 
 will not require a great deal of analysis to show that 
 truth and fact are not two separate things, but two 
 ways of looking at the same thing; and conse- 
 quently, that if we try to separate them, in order 
 to give exclusive existence to either, we can get rid 
 of the one only by losing our grasp also upon the 
 other. Thoughts without things are empty, and 
 things without thoughts are meaningless. 
 
 Our previous discussions have led us to lay em- 
 phasis mainly upon the various ways in which our 
 thoughts-about-things are capable of constant im- 
 provement and expansion. We may be said to have 
 taken for granted the existence of truth, and our 
 
 (366) 
 
INDUCTION AND METHODS 367 
 
 problem was to study the methods by which one 
 truth is or may be connected with another; to ex- 
 pound in an elementary way the systematic char- 
 acter of truth. From this point of view, the syllo- 
 gism appeared as an instrument for bringing par- 
 ticular truths under general rules; it enabled us to 
 see what were the conditions of the connection of 
 one truth with another. In definition and classifi- 
 cation we were studying how to make truth more 
 explicit, to rid it of ambiguity, and to bring out 
 other important features. In brief, we have been 
 studying the judgment as the- distinctive element 
 in knowledge, and expounding the relations that 
 judgments may sustain to each other. 
 
 In the present chapter, we turn to another group 
 of problems that is suggested when attention is 
 given to facts rather than, truths. Now about 
 facts, the logical consideration of which is commonly 
 referred to as induction, we are primarily interested 
 to know how facts are constituted; what we mean 
 by fact, and what conditions fact must satisfy if 
 the world of fact, like the world of truth, is to be- 
 come systematic. Broadly stated, the problem of 
 induction is an inquiry into the process by which, 
 when we start with particular facts, universally 
 valid statements about reality can be established. 
 
 What is Meant by Fact. There are several fea- 
 tures of this statement of the problem of induction 
 that need elucidation. And first, what precisely do 
 we mean by fact? The word is used in a narrower 
 and a broader way. It is used in a narrow sense 
 
368 A TEXT-BOOK OF LOGIC 
 
 to indicate the objects of our knowledge of the mate- 
 rial world, such as trees, mountains, railroads, 
 streets, houses, etc. In the broader sense, it is used 
 to indicate any object of knowledge, whether mate- 
 rial or not, of which we may be said to have knowl- 
 edge. Used in this latter way, a sensation, an idea, 
 a purpose, an emotion, when they are made the 
 objects of knowledge, would also be facts. If we 
 compare these two uses of the word, we shall see 
 that a single meaning underlies both; they differ 
 only in the range of its application. For both, a 
 fact is any object of which we are said to possess 
 knowledge. 
 
 We may observe further that by knowledge as a 
 conscious process is meant a judging process ; hence, 
 we may say that whatever is the object of a judging 
 process is a fact, and nothing else is. What a judg- 
 ing process is has been explained in earlier chapters, 
 and it is important here merely to remark that 
 it is only when objects are made the subjects of 
 judgments, and are qualified in distinctive ways, 
 that they can be spoken of as facts. Facts, then, 
 are objects that have been qualified by our thoughts 
 about them. Now there are a number of ways in 
 which facts are qualified by our thoughts about 
 them ; for instance, we think about them as possess- 
 ing certain qualities, as being in a certain place, as 
 continuing to exist for a certain length of time, as 
 related to other objects in numerous ways. The 
 important words in these instances are quality, 
 
INDUCTION AND METHODS 369 
 
 place, time, relation. In logic these are called cate- 
 gories. 
 
 The problem of the categories is much too diffi- 
 cult a subject for discussion in an elementary book 
 of logic, but the student is required to understand 
 at least what the word means and how it is used. 
 We may say, then, that the categories are names 
 for the differences in the forms of our thought about 
 things; and, because thoughts and things imply 
 each other, they indicate also a distinction in the 
 nature of the things about which we think. If we 
 remember that etymologically category means pred- 
 icate, the categories may be looked upon as a list of 
 the classes of attributes that can be predicated of a 
 subject in a logical proposition. Thus, if we say 
 that 'Man is an animal,' the term animal tells us 
 what kind of a substance man is; we are thinking 
 about man under the category of substance. If, 
 again, we say that The violets have a sweet odour/ 
 we are thinking about violets under the category of 
 quality. How many categories or generic differences 
 in the forms of our thought about things there are 
 is a matter that does not concern us here; the list 
 varies with different writers, but Aristotle names 
 ten. The point to emphasise is that the predicates 
 of logical propositions can be classified under a 
 number of main heads which denote the general 
 forms of our thinking about things, and these forms 
 of thought are called categories. Until we have 
 thought the objects of consciousness under one or 
 24 
 
370 A TEXT-BOOK OF LOGIC 
 
 more of the categories in an act of judgment, they 
 are not properly called facts; a fact is, from this 
 point of view, any object of consciousness which 
 has been thought under one or more of the cate- 
 gories. 
 
 Nature of Reality. Our statement of the induc- 
 tive problem contains, secondly, the word reality. It 
 is, we said, about reality that we seek universally 
 valid judgments. What is reality? The answer to 
 this question, like that of the categories, is too diffi- 
 cult for an elementary discussion, and besides the 
 subject itself belongs to another department of phil- 
 osophy, namely, to metaphysics. But we may under- 
 stand the term well enough for our present pur- 
 poses, if we utilise the results of our examination 
 of the meaning of fact. Broadly stated, by reality 
 is meant the 'world of fact.' What such a phrase as 
 that just employed is ordinarily understood to 
 emphasise is that facts are not isolated, unrelated 
 things ; that they are, on the contrary, connected in 
 numerous ways with other facts. This is a matter 
 of our ordinary every day observation and expe- 
 rience. We put our hand in the fire and it is burned. 
 We eat too much or eat the wrong things, and our 
 bodies suffer. In the social world, we have a dis- 
 agreement with one person, and the behaviour of a 
 number of others toward us is affected thereby. 
 The movements of the planetary bodies regulate our 
 seasons, the rain fall determines the size of our 
 crops. These instances are sufficient to suggest, 
 what is true throughout our experience, that facts 
 
INDUCTION AND METHODS 371 
 
 do not exist apart from each other, but are, so to 
 speak, bound up in bundles together. Such bundles 
 or groups of fact we speak of as worlds of fact. 
 If we carry our observation further, it will appear 
 that as individual facts are related to each other so 
 these bundles of facts are connected in numerous 
 ways. The combinations of these more complex 
 groups we may also call worlds of fact. Thus we 
 have the world of commerce, the world of conduct, 
 the world of religion, the world of science. Within 
 each of these worlds, the facts, although diverse, 
 are generically related, they are facts of a given 
 kind. Looked at in one way, it seems as if these 
 several worlds had little if anything in common, and 
 that there were consequently a pluralism of such 
 worlds. A little closer study has convinced some 
 men, however, that we can detect a likeness between 
 some of these worlds on the ground that they are 
 concerned with material things, and that a likeness 
 exists between still others on the ground that they 
 are concerned with mental things. If this is true, 
 the many worlds are reduced to two, each of which 
 is very complex, and between which there is said 
 to exist no similarity at all. Whether this is true 
 or not we need not discuss ; it is a question that be- 
 longs to the philosopher, and there does not seem to 
 be any general agreement about it. The point to 
 emphasise is that whether there be one or many 
 worlds of fact, every one is agreed that when we 
 speak about reality we are speaking about those 
 worlds and the facts therein contained. When, 
 
372 A TEXT-BOOK OF LOGIC 
 
 therefore, we say that the problem of induction is 
 an inquiry into the processes by which, starting 
 with particular facts, universally valid statements 
 about reality can be established, we mean that we 
 are interested in finding out the truth about these 
 worlds, what are the relations between the facts 
 which give these worlds their characteristic fea- 
 tures, and make them the permanent realities they 
 appear to be. 
 
 Our study of this problem falls into two parts. 
 In the first part, we shall consider a number of 
 processes preliminary to induction, and with which 
 induction frequently has been confused; in the sec- 
 ond part, we shall expound the inductive process 
 strictly so-called, a process, however, which we shall 
 see emerging into a clearer and clearer light in our 
 exposition of the first part. The present chapter is 
 devoted to the former task; the next four to the 
 latter. 
 
 Induction by Simple Enumeration. A prevalent 
 notion identifies induction with an examination of 
 a number of instances of a given phenomenon. 
 Whenever we are comparing a number of particular 
 facts for the purpose of discovering in what re- 
 spects they are alike, we are supposed, by those who 
 hold this view, to be engaged in an inductive pro- 
 cedure. In agreement with this supposition, the dis- 
 tinction has been drawn between perfect and imper- 
 fect induction. In the case of perfect induction, we 
 are dealing with a group of facts all the members 
 of which are known. Thus, we may make state- 
 
INDUCTION AND METHODS 373 
 
 ments about the days of the week or the months of 
 the year, and be quite sure that no instances, other 
 than those we have examined, will occur to make a 
 revision of our judgment necessary. We may say, 
 for example, that 'All the months of the year have 
 less than thirty-two days,' and 'The week consists 
 of seven days.' Whenever the group of facts we are 
 examining is known to be limited, we may collect 
 all the instances and observe each before making 
 the general statement. The enrollment of students 
 in a college class is such a definitely limited group, 
 and about it we may, for example, make the state- 
 ment that 'None of the students in this class is over 
 six feet tall.' Imperfect induction is based upon 
 the same principle of counting and comparing in- 
 stances, but we have no assurance that all the cases 
 that have been examined are all the cases that exist, 
 and, therefore, a lower degree of certainty is sup- 
 posed to belong to the statements that, under these 
 circumstances, we are able to make. This was the 
 view of induction commonly held during the Middle 
 Ages. It consists in stating that all the known in- 
 stances of a given kind possess a certain attribute, 
 and, therefore, that all instances of this kind will 
 be found to possess the same attribute. For ex- 
 ample, the Negroes of Africa for centuries had seen 
 no human beings who were not black; they would, 
 therefore, suppose that all human beings were black. 
 For many centuries each and every crow that had 
 been observed by Europeans was black; it was, 
 therefore, supposed that all crows were black. In 
 
374 A TEXT-BOOK OF LOGIC 
 
 both these instances the induction has been found 
 to be erroneous. The fault to which every imperfect 
 induction is liable is that experience is likely at some 
 time to prove it wrong. 
 
 Both of these kinds of induction have been re- 
 jected by writers in the modern era, and especially 
 by Bacon and Mill. Perfect induction, Mill says, is 
 of no scientific value ; the conclusion is only a state- 
 ment in a different form of the premises. The con- 
 clusion, in other words, is merely an enumerative 
 judgment, a judgment which summarises the 
 data and does not lead beyond them. In induction 
 proper, we are said to go beyond what is con- 
 tained in our data ; we proceed from the known par- 
 ticulars to the unknown universal, from what is 
 true of a given case or number of cases to what is 
 true always and everywhere of all cases whatsoever. 
 Jevons, on the other hand, defends perfect induc- 
 tion, and in doing so states very well the value that 
 we may attach to this process. He says: "If Per- 
 fect Induction were no more than a process of abbre- 
 viation, it is yet of great importance, and requires 
 to be continually used in science and common life. 
 Without it we could never make comprehensive 
 statements, but should be obliged to enumerate 
 every particular. . . . The fact is, that the power 
 of expressing a great number of particular facts in 
 a very brief space is essential to the progress of 
 science. Just as the whole art of arithmetic con- 
 sists in nothing but a series of processes for abbre- 
 viating addition and subtraction, and enabling us to 
 
INDUCTION AND METHODS 375 
 
 deal with a great number of units in a very short 
 time, so Perfect Induction is absolutely necessary 
 to enable us to deal with a great number of par- 
 ticular facts in a very brief space." 
 
 The case of imperfect induction is not in prin- 
 ciple different. Imperfect induction, says Bacon, 
 "proceeds by merely citing instances and is a child- 
 ish affair (res puerilis) , and being without any cer- 
 tain principle of inference it may be overthrown by 
 a single negative instance." By a negative instance, 
 Bacon means an instance which contradicts all the 
 instances that previously have been examined. For 
 example, a single instance of a grey crow over- 
 throws the inference that all crows are black. Mill, 
 referring to imperfect induction, says that "it con- 
 sists in ascribing the character of general truths to 
 all propositions which are true in every instance 
 that we happen to know of. ... In science it 
 carries us but a little way. We are forced to begin 
 with it; we must often rely on it provisionally, in 
 the absence of means of more searching investiga- 
 tion. But, for the accurate study of nature, we re- 
 quire a surer and a more potent instrument." This 
 more potent instrument is "to be found in interro- 
 gating nature" by experiment, so as to discover the 
 conditions under which the phenomena occur. 
 
 The Value of Simple Enumeration. In the pre- 
 ceding section, we have examined the two forms of 
 induction by simple enumeration, and we have seen 
 that in perfect induction all the positive instances, 
 and in imperfect induction a larger or smaller num- 
 
376 A TEXT-BOOK OF LOGIC 
 
 ber of the positive instances of a phenomenon are 
 available for observation. The conclusion that is 
 based upon a complete enumeration of the instances 
 does not go beyond these instances themselves, 
 whereas the conclusion that is based upon an in- 
 complete enumeration is understood to apply also 
 to instances that have not been examined and that 
 may not be known to exist. In the former case, the 
 conclusion may be described as an empirical general- 
 isation ; in the latter, the conclusion has the charac- 
 ter of an hypothesis which is held subject to revision 
 or rejection in view of our examination of other 
 instances that may come to light. These descrip- 
 tions serve to distinguish the scientific value of these 
 two forms of simple enumeration. Perfect induc- 
 tion belongs to the stage preliminary to induction, 
 whilst imperfect induction must be classed among 
 the steps of induction properly so-called. The lat- 
 ter, we shall reserve for future consideration, and 
 turn our attention immediately to the former. 
 
 Empirical Generalisation. Induction by complete 
 enumeration, which, as we said, leads to an em- 
 pirical generalisation, is not entirely a simple proc- 
 ess, and it suggests certain questions of importance 
 for the study of induction. These questions we shall 
 consider in this section. And first we should ob- 
 serve that if we ask why there is any such process 
 of combining in single statements a number of facts, 
 why we classify at all, we may perhaps say with 
 Mill, who in this follows Hume, that there is a ten- 
 dency of the mind "to generalise its experience, pro- 
 
INDUCTION AND METHODS 377 
 
 vided this points all in one direction." This abbre- 
 viation and summation of numerous facts and expe- 
 riences takes place as a measure of protection 
 against being overwhelmed with the diversity of the 
 events which life daily presents to each of us. It is 
 not a method that is peculiar to science; it is used 
 by all of us in common life. It has a practical 
 value; it does, as Mill points out, facilitate our 
 handling a great number of data. But because we 
 cannot escape using it, and because its employment 
 is so general, the method is not, therefore, altogether 
 simple. It presupposes the existence of ideas, of 
 the idea, at any rate, that all the instances we ex- 
 amine may possibly constitute a single class. When, 
 however, we ask by virtue of what particular idea 
 a number of facts constitute a class, we must re- 
 member that classes, as we saw in the chapter on 
 classification, are not ready made things ; there are, 
 as we said, no 'natural kinds/ nor, on the other 
 hand, are there any ready made ideas, except as 
 those have been acquired in the course of experience, 
 that can serve as principles of classification. The 
 fact is that we classify on the basis of observed like- 
 nesses, and the members of a class are determined 
 by the kind of likenesses with respect to which 
 each instance is examined. In science, the principle 
 of classification is consciously entertained; in com- 
 mon life, it is not brought into clear definition. In 
 the latter case, we are guided by the accidental at- 
 tributes of phenomena, and our generalisations 
 have, as a rule, the value merely of shorthand mem- 
 
378 A TEXT-BOOK OF LOGIC 
 
 oranda ; by them we are able to get back to the facts 
 at any time we wish, but our understanding of the 
 facts is not thereby advanced. The process is not 
 for this reason without value, but its particular 
 worth is likely to be obscured if we fail to observe 
 its limitations. We may, therefore, repeat that 
 empirical generalisations do not make any group of 
 facts, for science or for common life, more intel- 
 ligible; they merely group together a number of 
 data, and thereby suggest that the observed mate- 
 rial may be connected in some more fundamental 
 way. It is because they hint at some underlying 
 principle of connection that empirical generalisa- 
 tions have a place in the method of scientific inves- 
 tigation. 
 
 Colligation of Facts. A method of dealing with 
 facts which emphasises more directly the impor- 
 tance of ideas in the development of knowledge is 
 that which is called by Whewell the "colligation of 
 facts by means of an exact and appropriate concep- 
 tion." Whewell states his view, and defends it 
 against the objections of Mill, by calling attention 
 to the presence of ideas in all our perceptions. He 
 says, "All perception of external objects and occur- 
 rences involves an active as well as passive process 
 of mind ; includes not only Sensations, but also 
 Ideas by which Sensations are bound together, and 
 have a unity given to them. From this it follows, 
 that there is a difficulty in separating in our per- 
 ceptions what we receive from without, and what 
 we ourselves contribute from within." He, there- 
 
INDUCTION AND METHODS 379 
 
 fore holds that, "we cannot obtain a sure basis 
 of Facts, by rejecting all inferences and judgments 
 of our own, for such inferences and judgments form 
 an unavoidable element in all Facts. . . . We 
 are not able, nor need we endeavour, to exclude 
 Ideas from our Facts; but we may be able to dis- 
 cern, with perfect distinctness, the Ideas which 
 we include." In agreement with this position, 
 what Whewell means by colligation is quite clear; 
 it consists in bringing together a number of ob- 
 served facts under a common description, as, to 
 use one of his own illustrations, when Kepler, hav- 
 ing made a number of observations on the suc- 
 cessive positions of Mars, brought them together 
 under the one conception of an ellipse. Mill con- 
 tends that the method of colligation does not differ 
 from an empirical generalisation, and since it 
 involves no inference, it is not an induction. We 
 do not need to go into the dispute between Whewell 
 and Mill on these points ; it is clear, from the state- 
 ments of what colligation means for Whewell, that 
 ideas are essential to the existence of facts, and that 
 a conception of the mind operates as a principle of 
 connection between facts. The relation between 
 fact and idea, however, is not always stated clearly 
 by Whewell, for he sometimes speaks as if the in- 
 ductive act consisted of a superinduction of concep- 
 tions upon facts, that is, as if facts and ideas were 
 external to each other. Green, in making the same 
 point, says that "Whewell . . . spoils his own 
 case (against Mill) by often writing as if the antith- 
 
380 A TEXT-BOOK OF LOGIC 
 
 esis between ideas and facts were a valid one; as 
 if the 'superinduction of ideas' upon facts were 
 merely an operation that had to be performed ex 
 parte nostra in order to give science." The value 
 of WhewelPs insistence upon colligation lies in this : 
 it asserts that all our knowledge of the world of 
 fact depends upon a more or less conscious exercise 
 of the judging activity which carries us beyond a 
 merely empirical generalisation, and enables us to 
 regard the facts of observation under a new point 
 of view. These points of view, our author contends, 
 are supplied by, but are not necessarily derived 
 from, the mind itself. As we shall see later, the 
 point of view under which a group of facts becomes 
 intelligible is sometimes ascertained by a stroke of 
 genius, sometimes as the result of a laborious and 
 diligent search. But however it may have been dis- 
 covered, ideas and the facts that they make intelli- 
 gible are not two discrete and mutually exclusive 
 things; they are, as we have seen, only the reverse 
 sides of a single experience. It is only by an act 
 of analysis, as Whewell himself believes, that they 
 can be distinguished. 
 
 Parity of Reasoning. We often entertain beliefs 
 about new facts on the ground of the similarity of 
 these facts to other facts with which we are ac- 
 quainted. For instance, if the bull dogs that we 
 have known are unfriendly toward strangers, we 
 shall shape our conduct toward any dog that has 
 the general appearance of this breed in accordance 
 with the belief that no bull dog likes strangers. 
 
INDUCTION AND METHODS 381 
 
 This is an example of an empirical generalisation. 
 From it may be distinguished another type of rea- 
 soning which, while dealing with numbers of in- 
 stances, affirms that we may entertain a belief about 
 new facts, not because we have reason to entertain 
 it about similar facts, but because we may apply 
 to the new facts tests similar to those that were 
 used on the old. That is, if we have shown that X 
 is true of A, we may argue that it is true also of B, 
 not because it is true of A, but for the same reason 
 that it is true of A. This method of argument is 
 called parity of reasoning. Mill's illustration is 
 this: "Having shown that the three angles of the 
 triangle ABC are together equal to two right angles, 
 we conclude that this is true of every other triangle, 
 not because it is true of ABC, but for the same rea- 
 son which proved it to be true of ABC." Mill objects 
 to calling this an induction on the ground that it 
 "is not believed on the evidence of particular in- 
 stances," that is, it is not proved in each of the in- 
 stances, and, therefore, there exists no ground of 
 inference from the known to the unknown cases. 
 The importance of this type of reasoning at our 
 present stage of inquiry is that it raises definitely 
 the question whether numbers of instances are 
 necessary for an inductive conclusion. 
 
 REFERENCES. 
 
 H. A. Aikins, The Principles of Logic, Ch. XXIV. 
 
 B. Bosanquet, The Essentials of Logic, Lecture XI., a-d. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Ch. XIII. 
 
382 A TEXT-BOOK OF LOGIC 
 
 J. G. Hibben, Logic, Deductive and Inductive, Part II., Chs. 
 II., III., a,b. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lessons XXIV., 
 XXV. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. VIII., 1, 2. 
 
 W, Minto, Logic, Inductive and Deductive, Book II., Chs. I, II. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. XV., 
 1-4. 
 
 ADVANCED 
 
 B. Bosanquet, Logic, Vol. II., Book II., Chs. II., V, 3, 4. 
 F. H. Bradley, The Principles of Logic, Book II., Part II., 
 
 Ch. II. 
 W. R. B. Gibson, The Problem of Logic, Chs. XXXVII., 
 
 XXXIX., XL., XLI. 
 H. W. B. Joseph, An Introduction to Logic, Chs. XVIII., 
 
 XXIV. 
 
 H. Lotze, Logic, Vol. II., Book II., Ch. VII. 
 J. S. Mill, A System of Logic, Book III., Chs. I., II., III. 
 F. C. S. Schiller, Formal Logic, Ch. XVIII. 
 J. Venn, Empirical Logic, Ch. XIV., XXIV. 
 J. Welton, A Manual of Logic, Vol. II., Book V., Chs. II., 
 
 146, III., 148. 
 
 QUESTIONS 
 
 1. What do you assign to the distinction of truth and fact? 
 
 2. In what two ways may the word fact be used, and what 
 common element is present in both uses? 
 
 3. 'Facts are objects that have been qualified by our 
 thoughts about them.' Discuss. 
 
 4. What is a category, and what is the relation of cate- 
 gories to the judgment? 
 
 5. What is a fact from the standpoint of the categories? 
 
 6. What is meant by saying that reality is the world of 
 fact? 
 
INDUCTION AND METHODS 383 
 
 7. What light does the study of the worlds of fact throw 
 upon the problem of monism and pluralism? 
 
 8. How must we interpret the inductive problem, if by 
 reality is meant the world of fact? 
 
 9. What view of induction is implied in so-called perfect 
 and imperfect induction? 
 
 10. State and illustrate what is meant by perfect induction. 
 
 11. State and illustrate what is meant by imperfect induc- 
 tion. 
 
 12. What is Mill's criticism of perfect induction? 
 
 13. What is Bacon's estimate of imperfect induction? 
 
 14. What is Bacon's estimate of perfect induction? 
 
 15. What, according to Mill, is the value of imperfect in- 
 duction? 
 
 16. What is the value of perfect and imperfect induction as 
 instances of simple enumeration? 
 
 17. What is an empirical generalisation? 
 
 18. Why, according to Mill, do we generalise our experience? 
 
 19. 'Generalisation presupposes the existence of ideas.' Ex- 
 plain. 
 
 20. What is the value of empirical generalisation for 
 science and for common life? 
 
 21. State WhewelFs conception and explanation of the col- 
 ligation of facts. 
 
 22. State Mill's objections to colligation. 
 
 23. What is Green's criticism of Whewell's position? 
 
 24. What is the essential truth of the doctrine of colliga- 
 tion? 
 
 25. What is parity of reasoning, and how does it differ 
 from empirical generalisation? 
 
 26. Why does Mill refuse to regard colligation as a truly 
 inductive method? 
 
 27. What is the importance of Mill's objection? 
 
384 A TEXT-BOOK OF LOGIC 
 
 EXERCISES. 
 
 1. Give at least six examples of what are known as facts, 
 and distinguish the factual and truth elements in- 
 volved in these examples. 
 
 2. Make six statements of fact, and determine under what 
 category each statement is made. 
 
 3. Give three illustrations of what is known as reality as 
 distinguished from fact. 
 
 4. Give three illustrations each of perfect and imperfect 
 induction. 
 
 5. Write out two examples from common life and two 
 from science of an empirical generalisation. 
 
 6. Illustrate, by a carefully considered example, the mean- 
 ing of a colligation of facts. 
 
 7. Give three illustrations of parity of reasoning. 
 
CHAPTER XIV 
 
 SOME DESCRIPTIVE METHODS OF INDUCTION 
 
 Relation of Numbers of Instances to an Induction. 
 The question with which we closed the last chapter, 
 namely, whether numbers of instances are necessary 
 for an induction, may be made the starting point 
 of the present one. When induction is thought of 
 as an inference based upon the examination of nu- 
 merous instances of a phenomenon, it assumes, as 
 we have seen, two forms : one, when we have assur- 
 ance that all the instances are known; the other, 
 when no such assurance can possibly be entertained. 
 The former, we have considered, and it was said to 
 be an illustration of a method of organising expe- 
 rience that is not confined to any special kinds of 
 fact, but is used over the whole extent of our life. 
 The name that we gave to this method was empirical 
 generalisation. The value of empirical generalisa- 
 tions lies in the fact that they enable us to deal 
 with large numbers of data in a simple way; we 
 can deal with collections of fact as single facts 
 whenever we ignore the differences and are inter- 
 ested in the likenesses between the facts which enter 
 into such collections. The assurance that every one 
 feels in organising his experience in this manner is 
 due to the limits within which it is consciously car- 
 ried out. Empirical generalisations are held to 
 apply only to the instances that have been examined. 
 
 25 (385) 
 
386 A TEXT-BOOK OF LOGIC 
 
 Numerous instances are necessary for an empirical 
 generalisation, but such generalisations, since they 
 do not carry us beyond the instances we have ex- 
 amined, cannot be regarded as inductive inferences. 
 
 The other form of induction by simple enumer- 
 ation differs from the one just considered in the fact 
 that not all the instances of the phenomenon have 
 been observed, and the conclusion which the known 
 instances are found to warrant is extended to other 
 instances that have not come under observation. 
 The question we are concerned with in such a case 
 is whether, as Mill seems to hold, the validity of our 
 inference is in proportion to the number of the in- 
 stances examined, that is, whether the ground of the 
 certainty of such an induction is found in the num- 
 ber of the instances on which it is based ; or whether 
 it is due to some other characteristic of the in- 
 stances, for example, to the nature of the instances 
 themselves. 
 
 In attempting to answer this question, we may 
 observe, in the first place, that the position held by 
 Mill emphasises only one of the factors of an enu- 
 merative induction, and that, even if we hold, with 
 him, that it is an essential factor, it nevertheless 
 depends for its effectiveness on the co-operation 
 of another factor of which no special mention 
 has as yet been made. For no one is prepared 
 to maintain that the mere fact of numbers, irre- 
 spective of the other qualities of the instances that 
 an induction brings under review, can be the ground 
 of an inference to other unknown instances. Mill's 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 387 
 
 position, therefore, must be understood to be that, 
 although a greater degree of certainty attaches to 
 any conclusion we reach respecting certain observed 
 facts if the number of such observed facts is very 
 great, and a lower degree of certainty if the number 
 of such observed facts is relatively few, all the facts 
 that enter into an induction must exhibit the qual- 
 ities or relations with respect to which the induction 
 is made; and that, if we extend to other instances 
 the conclusion reached with respect to any one 
 group of instances, this is possible because the new 
 instances resemble the old ones in their essential 
 nature. Whether, therefore, we are interested in 
 arriving at an induction or in extending to new 
 cases the conclusion of an induction already made, 
 the fact of the common nature of all the instances 
 must be established or assumed if the induction 
 itself is sound, or if it is to make an inference pos- 
 sible. In either case, the instances in question must 
 all resemble one another in essential respects. 
 
 We may remark, in the second place, that, in the 
 light of what has now been shown, the question of 
 the relation of numbers of instances to the validity 
 of an induction is an interesting rather than the 
 most important aspect of the inductive problem. 
 There is no doubt, for example, that, within limits, 
 our confidence in the conclusion of an induction is 
 increased by the number of instances by which it is 
 known to be supported. But we must distinguish 
 between our confidence in a conclusion and the 
 
388 A TEXT-BOOK OF LOGIC 
 
 ground on which the truth of that conclusion is 
 supposed to rest; and, we must remember, it is 
 with this latter question that we are here concerned. 
 But we may say, even with respect to our confidence 
 in the truth of inductive conclusions, that, beyond 
 certain limits which vary for different phenomena, 
 this is not affected in an appreciable manner by any 
 considerable increase in the number of instances of 
 a given phenomenon that may be brought to our 
 attention. For example, should we not feel a jus- 
 tifiable impatience with any one who, during the 
 hours of only a single day, counted the number of 
 objects within his observation that fell to the 
 ground, and who informed us that that additional 
 number of observed cases should be regarded as an 
 additional reason for our confidence in the law of 
 gravitation? And with respect to the truth of an 
 inductive process, we may observe that the number 
 of instances that need to be observed before a con- 
 clusion is reached varies according to the nature of 
 the instances themselves, and the ability of the par- 
 ticular individuals who examine them. If this is 
 true, the number of instances is a somewhat un- 
 certain factor in the establishment of an induction, 
 and there seems to be no reason why, if the nature 
 and conditions of the observation are sufficiently 
 unambiguous, the truth about a whole class of cases 
 may not be reached as the result of the study of a 
 single example. Indeed, in the history of science 
 there have been instances in which some striking 
 event has arrested attention, and set the problem 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 389 
 
 for the scientist, and in which the study of other 
 examples of the same phenomenon has been under- 
 taken mainly for the purpose of verifying the con- 
 clusions reached with respect to the single instance. 
 And, further, it may be said that, whether the truth 
 of an induction has been reached as the result of 
 an examination of one or many instances of a phe- 
 nomenon, we may infer certain facts of other in- 
 stances only when we assume that these also re- 
 semble the old one or ones in essential respects. In- 
 deed, this is only to state the significance that be- 
 longs to all scientific statements whatever, and it 
 gives the reason why all such statements are essen- 
 tially hypothetical. Thus, if we suppose that P is 
 a phenomenon under examination, and that X is 
 the characteristic with respect to which it is finally 
 determined, then we may say of any new example 
 M that 'If M is P, it is X ;' that is to say, X is pred- 
 icated of M, because it is P. We may, therefore con- 
 clude, both with respect to the establishment of an 
 induction and with respect to the possibility of ex- 
 tending an induction to further instances of a phe- 
 nomenon, that "the strength of an induction is not 
 proportional to the number of instances cited. The 
 generalisations that lead to the most trustworthy 
 hypotheses are based, not on the counting of the 
 number of instances, but on the weighing of their 
 quality and character. One crucial instance may be 
 worth a hundred others." 
 
 Logical Significance of Statistical Methods. The 
 progress of modern science has been associated so 
 
390 A TEXT-BOOK OF LOGIC 
 
 intimately with the application of mathematical con- 
 ceptions to concrete phenomena that the conclusion 
 of the preceding paragraph may appear to be one- 
 sided, if not erroneous. To meet this objection, we 
 shall examine the logical character of the statistical 
 methods, and ascertain their place in an inductive 
 process. And, at the outset, we should observe that 
 whenever statistical methods are employed, the data 
 under observation can most often be given only in 
 the form of aggregates and averages. These meth- 
 ods, as a rule, are applied distinctly for the purpose 
 of ascertaining the numerical distribution of cer- 
 tain characteristics which have come under obser- 
 vation in a limited number of cases. Sometimes all 
 that it is necessary or possible to do is to ascertain 
 the total number of the recorded instances of the 
 phenomenon. Usually, however, the interests we 
 hope to satisfy by the use of the statistical methods 
 are more specialised than this. For instance, we 
 may wish to know what is the average occurrence 
 of some irregular group character, as, for example, 
 the average number of insane persons born per 
 generation in a particular family. Or we may wish 
 to ascertain the average amount of a constant group 
 character, as, for example, the average amount of 
 butter fat given per head by a particular breed of 
 cattle. And even when these methods are applied 
 to individuals, we still have in view the discovery 
 of group characteristics. On this point Thorndike 
 writes: "The sciences of human nature commonly 
 use measures of individuals only in order to get 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 391 
 
 measures of groups. Not John Smith's spelling 
 ability, but that of all fifth grade boys taught by a 
 certain method; not A's delicacy of discrimination 
 of weights, but that of all men; not B's wage, but 
 that of all railroad engineers during a certain 
 period ; not C's children, but the productivity of the 
 English race as a whole ; not individuals, but groups, 
 are commonly measured, compared and argued 
 about." An examination of the individuals enu- 
 merated in the census returns as to age, sex, married, 
 unmarried, etc., also illustrates that interest in the 
 characteristics of groups which prompts the use of 
 distinctly statistical methods of inquiry. Sociological 
 and insurance tables, as well as those of the phys- 
 ical, biological and psychological sciences, are based 
 upon the same interest. The particular service, 
 therefore, that the employment of statistical meth- 
 ods is able to render is to bind together diverse 
 numbers of fact of a particular kind, and thus to 
 provide a basis for the comparison of otherwise 
 incomparable aggregates. "The method of count- 
 ing . . . agreements and comparing results," 
 says Gibson, "constitutes the Method of Statistics." 
 The conclusions to which statistical inquiries 
 lead are generalisations, but they are to be distin- 
 guished from the empirical generalisations spoken 
 of above in two respects. In the first place, statis- 
 tical conclusions may be taken as a type of scientific 
 as contrasted with empirical generalisation on the 
 ground that they are the products of a systematic 
 investigation of numbers of fact. By systematic in 
 
392 A TEXT-BOOK OF LOGIC 
 
 this connection we mean that the basis of the class- 
 ification of data is in each case consciously chosen, 
 and that it is applied as a test of what can and what 
 cannot be included in the numeration. For example, 
 in an enumeration of houses in India, as Scripture 
 points out, great difficulty was experienced on 
 account of the indefiniteness of what was meant by 
 a house. Similarly, the Weather Bureau would find 
 it impossible to classify the hot, temperate, and cold 
 days during a single year because of the indefinite- 
 ness of the connotation of these terms. But if hot 
 is defined as a shade temperature above 75, cold 
 as a shade temperature below 35, and temperate 
 any degree between these two, it is readily seen that 
 there will be no difficulty in applying to the days 
 of the year these tests, and generalising the results. 
 In the second place, statistical conclusions are ex- 
 pressed always in quantitative terms. This is, of 
 course, not an accident; it is a result directly aimed 
 at. In this way, certain features of the objects of 
 our experience come to have a value and significance 
 which, under any other method of observation, 
 would be in danger of being overlooked altogether. 
 For example, isolated events, and events that occur 
 but rarely in our experience, unless they are very 
 striking, are liable to receive but a passing notice, 
 and to present but a small part of their meaning to 
 such casual observation. It is also true that we are 
 prone to overlook the import of those occurrences 
 which are brought regularly to our notice. Famil- 
 iarity breeds neglect as surely as do entire novelty 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 393 
 
 and strangeness. The average person seems to 
 dwell in safety between these two extremes, with 
 the result that the world presents him with few 
 problems, and stimulates him but rarely to sus- 
 tained intellectual effort. It is, however, a charac- 
 teristic of the scientific mind that there is nothing 
 so common that it does not deserve comprehension, 
 and nothing so rare that it is beyond consideration. 
 Out of this temper have been born those efforts to 
 reduce the passing show of our daily experience to 
 a definite system and order; and it has seemed, to 
 those engaged in it, not the leas worthy task, as it 
 has been not the least profitable, to count the num- 
 ber of times a given fact occurs, and to make num- 
 ber a part of the facts themselves. Among the 
 Greeks, Pythagoras interpreted the world in this 
 mathematical way ; and all our modern sciences, the 
 physical, biological and social, are employing statis- 
 tics in the belief that when the relative frequency 
 of the occurrences of a phenomenon is known, the 
 phenomenon itself has been more accurately ob- 
 served, and can be more exactly described. 
 
 Qualitative Methods of Observation. Statistics, 
 however, do not provide the only methods by which 
 the observation of phenomena is carried on. There 
 are classes of phenomena to which it cannot be 
 fruitfully applied. We have said that whenever 
 our material can be presented most advantageously 
 in the form of aggregates and averages, statistics 
 lend themselves as a means of bringing out features 
 of this material that in no other way receives ade- 
 
394 A TEXT-BOOK OF LOGIC 
 
 quate recognition. But we are not always or only 
 interested in collective groups of objects. We are 
 also interested in objects as instances of a genus, as 
 instances in which the characteristics of a genus 
 are given concrete expression. For instance, when- 
 ever we call a certain flower a primrose, we are- not 
 describing the flower as an individual thing; rather 
 are we neglecting altogether what is peculiar to the 
 flower as an individual, what makes it this primrose 
 rather than that ; and are recounting the character- 
 istics which this object shares with an indefinite 
 number of other specimens of the same species. The 
 difference between this case and those that are 
 amenable to statistical observation is that in the 
 latter we need to collect together numbers of indi- 
 viduals before the important characteristics are 
 open to observation, whereas in the former, the indi- 
 vidual instance displays all the attributes that are 
 distinctive of the genus to which it belongs. Field 
 botany, as our illustration suggests, is a descriptive 
 science in the sense we are now indicating. Natural 
 history and descriptive geology also belong to the 
 same class. In these sciences, individual objects dis- 
 play universal characteristics, that is, those which 
 in our experience are found to belong to an indefi- 
 nite number of other objects of the same kind or 
 class. These common features of objects have their 
 interest, and they set for us problems which tax our 
 industry and challenge our efforts to solve. It is 
 obvious, in the light of these statements, that the 
 accurate knowledge which is the goal of our intel- 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 395 
 
 lectual life is not all of a single type, and that the 
 methods of observation which we adopt or devise 
 must be appropriate to the nature of the objects 
 which are the material of our study. Sometimes 
 we must avail ourselves of the quantitative methods 
 of statistical observation, sometimes of the quali- 
 tative methods of immediate perception. 
 
 The Nature of Scientific Observation. Whatever 
 the methods of observation may be, and however 
 numerous, they are determined by the nature and 
 purpose of observation itself. Now, in order to gain 
 a clear understanding of the nature and purpose of 
 observation, we may distinguish scientific observa- 
 tion from the attitude we are accustomed to main- 
 tain toward the ordinary events and circumstances 
 of our every day life. Those adjustments with our 
 environments which, during the course of our early 
 years, we have succeeded in acquiring have been 
 determined almost exclusively by practical consider- 
 ations, and they have been maintained as the habits 
 of our lives very largely on account of their value 
 as instruments of physical and social survival. The 
 earliest task that devolves upon the infant is to 
 come into relations with the world around him, and 
 his primary concern is with the world of material 
 things from which he may receive either benefit or 
 harm. It is only so far as it contributes to this end 
 that, in its earliest beginning, the mind of the child 
 is stimulated into activity, and his interest is 
 aroused in the things and persons which constitute 
 his world. Intelligence, that is to say, is a later 
 
396 A TEXT-BOOK OP LOGIC 
 
 development than are those motor responses to 
 environment through which the well-being of the 
 individual is secured, and comes at first upon the 
 scene of the individual's life, not in order to intro- 
 duce any new interest or to initiate a new set of 
 aims, but as the guide and servant of the practical 
 which, through its means, is enlarged and rendered 
 more efficient. These relations of the practical and 
 intellectual in the order of their development throw 
 an interesting light upon the function that intelli- 
 gence plays in the maintenance of human existence ; 
 for, as it was in the beginning, so does it remain for 
 the greater part of each individual's life, there 
 is no independent intellectual interest, and the func- 
 tions of human understanding are determined 
 throughout by the practical purpose which they 
 instrumentally advance. If, in view of these con- 
 siderations, we observe the characteristics of our 
 ordinary life, we shall understand why, instead of 
 displaying a careful attention to details, the per- 
 ceptual consciousness has a conspective range which 
 enables it to take in a large amount of detail with- 
 out losing its practical effectiveness. What is not 
 of practical importance fails to be noticed; only 
 those features of the environment which are prac- 
 tically important are gathered up and made objects 
 of attention. 
 
 How far perception, as it is ordinarily employed, 
 is from giving accurate knowledge of the common- 
 place facts and events of life is well known. As an 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 397 
 
 example of the unreliability of everyday observa- 
 tion, we may cite the contradictory accounts of eye- 
 witnesess of a common street accident. But, fur- 
 ther, the conclusions and inferences that we base on 
 such observations are, as a rule, no more trust- 
 worthy than the observations themselves. In our 
 daily life we exhibit constantly, what Whewell calls, 
 " a vague and loose mode of looking at facts/' As 
 a result, to quote from the author just referred to, 
 we remain "for a long time under the belief that a 
 body, ten times as heavy as another, falls ten times 
 as fast; that objects immersed in water are always 
 magnified, without regard to the form of the sur- 
 face; that the magnet exerts an irresistible force; 
 that crystal is always found associated with ice; 
 and the like. These and many others are examples 
 of how blind and careless men can be, even in obser- 
 vation of the plainest and commonest appearances; 
 and they show that the mere faculties of perception, 
 although constantly exercised upon innumerable 
 objects, may fail in leading to any exact knowl- 
 edge." 
 
 If now we consider what may properly be called 
 scientific observation, we shall see that this differs 
 from immediate perception in important respects. 
 Scientific observation, in the first place, has not the 
 conspective range of immediate perception, but is 
 characterised by a close attention to detail within a 
 limited field. This difference is conditioned by the 
 difference in the purpose for which each exists. 
 The purpose that controls the character and direc- 
 
398 A TEXT-BOOK OF LOGIC 
 
 tion of our perceptions was seen to have its origin 
 in the interests of our practical life. There is not, 
 on the other hand, any such thing as observation in 
 the strict meaning of the term, until our interest in 
 the world of the practical life has failed to be satis- 
 fied, either because the environment is too complex 
 for perception to cope with, or because the relevant 
 features of the environment have been hastily over- 
 looked. In either case, importance comes to be at- 
 tached to the details of a situation, and the condi- 
 tions are favourable for the development of an in- 
 terest in details quite apart from the regulation of 
 our ordinary practical activities. Scientific obser- 
 vation does not differ from immediate perception in 
 the fact that the former is, and the latter is not, 
 purposive, but in the character of the purpose which 
 prescribes the goal and directs the course of each. 
 In the case of scientific observation, the purpose 
 that renders the details of an event or situation im- 
 portant is theoretical; it springs from the interest 
 we have in gaining an intimate acquaintance with 
 these situations and events. That is to say, scien- 
 tific observation must needs be used when we are 
 launched upon a search for truth; it is an instru- 
 ment of our acquisition of knowledge. What things 
 are, and how they come to be what they are, are 
 the questions which emphasise the necessity of accu- 
 rate observation. 
 
 In contrast with immediate perception, scientific 
 observation is, in the second place, analytic ; it seeks 
 in the environment for those features which are 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 399 
 
 relevant to the theoretical purpose by which it is 
 guided. The difficulty that one experiences in his 
 earliest scientific efforts is due to this selective 
 character of observation. If, for example, we placed 
 an histological preparation under the microscope, 
 and, without any previous acquaintance with the 
 subject to which it relates, we were to attempt to 
 observe the character of the tissue, we should very 
 likely fail; and our failure would be due probably 
 to the fact that we had no defined purpose to guide 
 our selection of the relevant detail. The beginner 
 in any science is subjected to much loss of time and 
 unnecessary discouragement if the instructor does 
 not understand that scientific observation does not 
 consist in looking at a mass of detail, but in looking 
 for certain relevant aspects in a mass of detail. But 
 to look for something relevant implies that a pur- 
 pose is functioning in our examination of objects, 
 and it is this purpose or idea which the capable 
 instructor provides as the guide to his pupil's obser- 
 vation. We observe only what we are prepared to 
 observe, and mere collections of fact are useless 
 until an idea illuminates and makes them intel- 
 ligible. This view of scientific observation is illus- 
 trated in the work of all the great scientists. It 
 was conspicuously true, for example, of Darwin, 
 of whom his son writes : "He often said that no one 
 could be a good observer unless he was an active 
 theoriser. This brings me back to what I said 
 about his instinct for arresting exceptions, it was 
 as though he were charged with theorising power 
 
400 A TEXT-BOOK OF LOGIC 
 
 ready to flow into any channel on the slightest dis- 
 turbance, so that no fact, however small, could avoid 
 releasing a stream of theory, and thus the fact be- 
 came magnified into importance." In other words, 
 we observe not with our senses but with our intel- 
 ligence. Or, as Huxley put it, what one sees when 
 he looks through a microscope depends as much 
 upon what is behind the eye-piece as upon what is 
 under the objective. 
 
 Experimental Observation. If we reduce the idea 
 of a scientific experiment to its lowest terms, we 
 may say that it consists in the interposition of an 
 instrument of precision between our sense organs 
 and the material we are studying. From this point 
 of view, a scientific experiment secures an extension 
 of the range of our perceptive organs, and, in so far 
 as it does this, brings out more of the detail of the 
 material under examination. The balances of the 
 physicist, the microscope of the biologist, the tele- 
 scope of the astronomer are devices for thus extend- 
 ing the field of scientific observation. But there are 
 limitations to experimental observation, as thus 
 understood, which often would hinder the progress 
 of truth if they were not offset by observation under 
 normal conditions. Hence, as Lotze says, "Observa- 
 tion often acquaints us with broad characteristics 
 of phenomena, which in experiment would have 
 been obscured by special conditions." The fact is 
 that observation and experiment supplement each 
 other, and there are cases when neither alone could 
 lead us as far as when both are used in conjunction. 
 
SOME DESCRIPTIVE METHODS OF INDUCTION, 401 
 
 There are also some phenomena to which experi- 
 mental observation cannot be applied at all, and for 
 our examination of these we must rely upon other 
 means of observation. In this connection, it may be 
 recalled that Darwin's great work was achieved by 
 the method of observation, in the broad sense just 
 described, rather than by the methods of experi- 
 mental observation. 
 
 A further consideration affecting our view of 
 the range of scientific observation is that, however 
 successful we may be in improving our present 
 apparatus, and in devising and constructing new 
 apparatus, there is, in all probability, a limit beyond 
 which our sense organs are not capable of being 
 supplemented in that way, and a point, consequently, 
 at which the observations we make by the use of 
 instruments of precision must stop. What the 
 scientist does when he has reached his actual per- 
 ceptual limits, and what he would attempt to do if 
 he reached the theoretically possible limits of per- 
 ception, is to supplement his actual observations 
 by guesses as to what, if perception were possible, 
 further observation would, in all probability, make 
 known. In some such way as this have the lumin- 
 iferous ether, atoms, ions, etc., become parts of the 
 actual working data of science, data, be it remarked, 
 that are regarded, by science, as truly material sub- 
 stances as are the grosser bodies that are now within 
 the range of present perception. This kind of obser- 
 
 2$ 
 
402 A TEXT-BOOK OF LOGIC 
 
 vation we may call, for the sake of convenience of 
 reference, theorising, or theoretical observation. 
 
 Another characteristic of experimental observa- 
 tion is that, like all observation, it must be used in 
 the service of the purpose which directs the obser- 
 vation. Hence the impossibility of any one being 
 an experimental scientist who is not thoroughly 
 acquainted with the mechanical structure of the 
 apparatus which he either uses or designs. There 
 is a quite prevalent notion, especially among stu- 
 dents and inexperienced instructors, that one is 
 necessarily an experimentalist if he works in a 
 laboratory and manipulates apparatus. To these, 
 no question could come with more pertinence than 
 this: Tor what purpose are you using this par- 
 ticular piece of apparatus, and precisely in what 
 way does it enable you to realise this purpose?' It 
 is not apparatus that lends significance to our ideas, 
 but ideas that make our apparatus intelligible in- 
 struments of observation. To lose sight of this 
 truth is to miss entirely the true meaning of experi- 
 mental science; for we may be as passively assimil- 
 ative when looking through a microscope as we 
 might be actively observant when using our natural 
 organs of perception. But when our apparatus 
 "passes into the service of an idea, and we proceed 
 to put our object under such conditions as the idea 
 requires for testing and verifying itself, our obser- 
 vation is no longer merely passive, but experi- 
 mental. A definite, purposive interference of some 
 sort with the production of the phenomenon to be 
 
SOME DESCRIPTIVE METHODS OF INDUCTION 403 
 
 noted is the desideratum" of experimental observa- 
 tion. 
 
 At precisely what point can this interference 
 with the phenomenon be introduced most advanta- 
 geously? The answer to this question is given 
 unanimously by all the workers in the field of 
 science. Science seeks to control, not the nature, 
 but the conditions of the occurrence of phenomena. 
 "To observe with accuracy and convenience," says 
 Jevons, "we must have agents under control, so as 
 to raise or lower their intensity, to stop or set them 
 in action at will." Welton writes: "Appeal to ex- 
 periment is, then, necessary whenever simple obser- 
 vation alone will not make plain all the essentials 
 of a phenomenon; and its object is to eliminate all 
 the conditions which are not specially operative in 
 the particular case under observation." In like 
 strain Gibson says: "Control over the conditions 
 under which the object shall present itself for study 
 is the great desideratum and the factor in experi- 
 mental observation which most influences the pre- 
 cision and certainty of the results obtained. Such 
 control enables us to vary the circumstances, and to 
 repeat the observation as often as we please by 
 simply reproducing the concurrence of conditions 
 requisite for bringing into play the desired effect." 
 
 REFERENCES 
 
 SEE THE END OF THE NEXT CHAPTER 
 
404 A TEXT-BOOK OF LOGIC 
 
 QUESTIONS 
 
 1. What are nature, extent and value of empirical general- 
 isations? 
 
 2. Does an empirical generalisation involve an inductive 
 inference? What is your reason? 
 
 3. Are numerous instances of a phenomenon necessary for 
 an empirical generalisation? Why? 
 
 4. Can imperfect induction be regarded as an example of 
 an inductive inference? State reasons for your answer. 
 
 5. What problem is involved in the fact that the con- 
 clusions of imperfect induction are extended to unex- 
 amined instances of the phenomenon in question? 
 
 6. What is Mill's position on the validity of imperfect in- 
 duction? 
 
 7. What influence does the fact that a large number of in- 
 stances of a phenomenon have been examined have on 
 the validity of an inductive inference? 
 
 8. What value may we give to number of instances in an 
 inductive process? 
 
 9. What fact with respect to the nature of induction is in- 
 volved in the hypothetical character of scientific state- 
 ments? 
 
 10. What particular interest determines the use of statis- 
 tical methods? 
 
 11. State and illustrate some of the questions that statis- 
 tical methods enable us to answer? 
 
 12. What purpose does the application of statistical methods 
 to individuals commonly serve? 
 
 13. In what respects do statistical conclusions differ from 
 empirical generalisations? 
 
 14. Describe the particular method of observation employed 
 by field botany, natural history and descriptive geology. 
 
 15. What are the characteristics of perception, and in what 
 relation does perception stand to intelligence? 
 

 SOME DESCRIPTIVE METHODS OF INDUCTION 405 
 
 16. In the light of your answer to the previous question, 
 what view must be taken of the logical function of per- 
 ception? 
 
 17. In what respects does scientific observation differ from 
 ordinary perception? 
 
 18. What do you understand by experimental observation? 
 
 19. What are the limits of experimental observation? 
 
 20. Explain the nature of theoretical observation. 
 
 21. Illustrate by reference to the relation of the scientist to 
 his apparatus the place of purpose in experimental ob- 
 servation. 
 
 22. 'Experimental observation involves a purposive inter- 
 ference with the production of phenomena.' Explain. 
 
 23. State what a scientist may and may not do in inter- 
 fering with the phenomenon he wishes to observe. 
 
 EXERCISES 
 
 1. Give at least six examples of empirical generalisation. 
 
 2. Give six illustrations of imperfect induction, and show 
 how each may be used as the basis of an inference. 
 
 3. Illustrate from each of the sciences you have studied 
 the hypothetical character of inductive inference. 
 
 4. Show, by a carefully worked out example, the nature 
 and method of statistical observation. 
 
 5. Give one example of experimental observation. 
 
 6. Illustrate what is meant by theoretical observation. 
 
CHAPTER XV 
 
 SOME EXPLANATORY METHODS OF INDUCTION 
 
 The Nature of Scientific Explanation. The meth- 
 ods that were examined in the last chapter may be 
 classified roughly as methods of observation, and 
 those that are to be examined in the present chapter 
 may be classified approximately as methods of ex- 
 planation. It will, perhaps, help us to understand 
 these latter methods if in this section we inquire into 
 the meaning of the term explanation. This is the 
 more necessary because some confusion on this sub- 
 ject has been occasioned by the way in which scien- 
 tists have sometimes expressed themselves with 
 respect to the aims of science. For example, one 
 declares that science consists of a complete descrip- 
 tion of the phenomena that are brought under 
 observation, while another declares as emphatically 
 that description is only a preliminary step in the 
 work of the scientist, and that the goal of all science 
 is explanation. If we were to take such statements 
 absolutely, we should be led to suppose that there 
 is between the scientists an irreconcilable differ- 
 ence of opinion as to the nature of the work in 
 which they are engaged, and we might presume 
 that, until they arrived at a settlement of these 
 differences, it were useless for us to discuss the 
 matter further. This, however, would be a false 
 view to take; for not only must logic examine the 
 
 (406) 
 
SOME EXPLANATORY METHODS OF INDUCTION 407 
 
 aims and methods of the sciences, but the differ- 
 ences already referred to are verbal rather than 
 real, and are due in a large measure to the ways in 
 which what is after all a substantial agreement has 
 happened to get itself expressed. 
 
 Let us first get before ourselves what is meant 
 ordinarily by a scientific explanation, and then, in 
 the light of this information, we may consider the 
 distinction between it and scientific observation. 
 All scientific explanation conforms to a very simple 
 type; it consists in stating what other things occur 
 when the particular thing we are observing occurs. 
 If, for example, I hold a book in my hand and, re- 
 leasing my grasp upon it, it falls to the ground, we 
 should ordinarily explain the falling of the book to 
 the ground by saying that I had released my hold 
 upon it. The book fell because I released my hold. 
 If, now, experimenting with other objects than 
 books, I find that pencils, stones, silverware, china- 
 ware, etc., fall to the ground when the hand that 
 held them releases its grasp, I may put the results 
 of these observations into the statement that 'all 
 objects fall to the ground when their support is re- 
 moved/ If, further, the fall not only of the book 
 but of all objects whatsoever is connected with the 
 force of gravity, the process of explanation has been 
 carried a step farther. But however far such a 
 process is carried, it consists essentially in describ- 
 ing events that occur along with the event which, at 
 the beginning, was the object of our observation. 
 This occurs when that occurs' is the universal for- 
 
408 A TEXT-BOOK OF LOGIC 
 
 mula which reveals the nature of scientific explan- 
 ation. 
 
 The same view is sometimes expressed more pre- 
 cisely in the statement that scientific explanation 
 is concerned with the discovery of the conditions of 
 the occurrence of any object of observation. Let 
 P be the phenomenon or object observed, then the 
 question of explanation relates to the conditions, C, 
 under which it occurs. When these conditions have 
 been discovered and recorded, we are said to have 
 explained the phenomenon. Out of the innumerable 
 circumstances that accompany an event, the prob- 
 lem of scientific explanation is to select those which 
 must be present whenever the event is present, and 
 which when they are absent the event itself does not 
 occur. The factors of explanation are always 
 found among the concomitant circumstances of the 
 phenomenon which comes before us for explanation. 
 An examination and description of these is what is 
 meant by a scientific explanation. 
 
 With these statements in mind, we may now 
 make clearer the distinction between scientific ob- 
 servation and explanation. It is obvious, in the 
 first place, that the phenomena which we include 
 under each of these terms are continuous with each 
 other. For instance, the falling of an object is con- 
 tinuous with the release of the hand's grasp upon it. 
 Stated generally, a phenomenon and its conditions 
 form an inter-connected series of events, no one of 
 which is unnecessary to the series, and each of which 
 is important if the series is to maintain its essential 
 
SOME EXPLANATORY METHODS OF INDUCTION 409 
 
 character. From this point of view, the distinction 
 between a phenomenon and its conditions is more 
 or less accidental and artificial ; and if we take such 
 series as scientific units, regarding the objects 
 which are the starting points of our observations 
 as fragments which through scientific methods we 
 are to supplement by their necessary concomitants, 
 we shall see that the whole aim of science has been 
 fulfilled when such a series has received a full and 
 complete description. If, in the second place, we 
 do not regard the object which provides us with 
 the starting point of our observation as a fragment, 
 but as a phenomenon which has a quasi-independent 
 existence, we shall be inclined to consider the search 
 for conditions as a distinct step in scientific investi- 
 gation, and, laying emphasis upon this, the problem 
 of explanation will assume larger proportions than 
 it did in the other view. But whichever of these 
 two ways of looking at the scientific problem we 
 may take, the factors of each are the same, and be- 
 tween these views there is only a verbal difference. 
 On either view, we have to supplement what is 
 given the phenomenon, with what is not given 
 the conditions; and to determine the conditions of 
 a phenomenon is what we understand as the prob- 
 lem of scientific explanation. 
 
 The Meaning of Analogy. The word analogy is 
 used in different senses, and these we shall proceed 
 to distinguish. It is used, in the first place, to indi- 
 cate an identity of relation. This is the meaning 
 that it had for Aristotle with whom it corresponded 
 
410 A TEXT-BOOK OF LOGIC 
 
 to mathematical proportion. In this sense, it as- 
 sumes the form of 2 : 4 : : 3 : 6, where the relation 
 between 2 : 4 is identical with the relation between 
 3 : 6, and the factors between which the relation 
 obtains are homogenous. We may state the charac- 
 teristics of this first meaning of analogy generally 
 by saying that whenever a is related to b in the same 
 way that c is related to d, then whatever follows 
 from a : b follows also from c : d, if the inference 
 is based upon nothing but the identity of the rela- 
 tion between the two pairs of factors or terms. 
 
 The word analogy is used, in the second place, 
 to indicate a similarity of relation. The difference 
 between this and the preceding use of the term is 
 not due to the absence of proportion, but to the dif- 
 ference in the character of the terms between which 
 the proportion obtains. Although the relation be- 
 tween two pairs of terms is similar, the terms be- 
 tween which the relation holds may be heterogene- 
 ous. For example, the number of vibrations per sec- 
 ond of the sound which is recognised by our musical 
 sense as middle C (c') is 261, that of its octave (c") 
 is 522 (2x261). The similarity of relations in- 
 volved in these facts is expressed in the proportion 
 261 : 522 : : c' : c". But since the octave of any 
 musical note always has twice as many vibrations 
 as the note itself, we may express the law of octaves 
 in the proportion : x vibrations of air : 2 x vibra- 
 tions of air : : a note : its octave. The analogy may 
 be interpreted to mean that the relation between 
 the series of physical stimuli is connected in our 
 
SOME EXPLANATORY METHODS OF INDUCTION 411 
 
 knowledge with their corresponding impressions 
 in such a way that given the former we can infer 
 the latter. 
 
 The word analogy is used, in the third place, to 
 indicate any resemblance between things. Here the 
 idea of proportion which was present in the preced- 
 ing uses has dropped out, and resemblance of any 
 kind between objects is made the basis of analogical 
 inference. For example, certain resemblances were 
 early known to exist between sound light : that both 
 were capable of being reflected, that the direction 
 of reflection of each obeyed the same law, that the 
 angle of reflection is equal, in each case, to the angle 
 of incidence. It was further known that sound 
 travelled in waves. From these data it was inferred 
 analogically that light also travelled in waves. If 
 it had been known that the equality of the angles 
 of reflection and incidence in the case of sound were 
 due to its traveling in waves, the inference to a like 
 mode of propagation in the case of light would have 
 been more certain. The more important the re- 
 semblances, that is to say, the more certain the in- 
 ference. From the example just used, the analogy 
 between things may be expressed generally in the 
 following manner: If a resembles b in certain re- 
 spects, x, and a exhibits the character y, it is in- 
 ferred that b will resemble a in possessing the char- 
 acter y also. 
 
 The Logical Character of Analogy. We have 
 shown that analogy is a method of inferring cer- 
 tain possible events on the ground of a resemblance 
 
412 A TEXT-BOOK OF LOGIC 
 
 between certain ascertained events. "In the syllo- 
 gism of Analogy," says Hegel, "we conclude from 
 the fact that some things of a certain kind possess 
 a certain quality, that the same quality is possessed 
 by other things of the same kind." In every argu- 
 ment from analogy an identity of some sort is as- 
 sumed, and it is upon the character of the assumed 
 identity that the validity of the inference is in every 
 case said to depend. Let us look at the soundness 
 of such arguments in the light of this statement. 
 
 In the first place, it is obvious that not any kind 
 or degree of resemblance is a safe principle of in- 
 ference. In common life, we meet with analogical 
 arguments that are very superficial. For instance, 
 the loyalty of college students to the university from 
 which they were graduated may often lead to a 
 mistaken estimate of a man who is a graduate of 
 the same university. "It would be a very bad anal- 
 ogy," as Hegel remarks, "to argue that since the 
 man Caius is a scholar, and Titus also is a man, 
 Titus will probably be a scholar too; and it would 
 be bad because a man's learning is not an uncondi- 
 tional consequence of his manhood." In public ad- 
 dresses on political and social questions we may 
 often detect arguments of this sort. In the period 
 of the Commonwealth in England, the demand for 
 annual Parliaments is said to have been urged on 
 the ground that the serpent which is the wisest 
 of beasts sheds his skin every year. We also find 
 analogical reasoning in the works of men of science, 
 and sometimes the conclusion which these argu- 
 
SOME EXPLANATORY METHODS OF INDUCTION 413 
 
 ments are intended to support rest upon a very 
 weak and even false resemblance. Take, for in- 
 stance, the conception of the human body as a 
 machine. "When we desire to set machinery in 
 operation," as Chittenden, commenting on this view, 
 says, "we must get up steam, and so a fire is started 
 under the boiler and steam is generated in propor- 
 tion as fuel is burned. The source of the energy 
 made use of in moving the machinery is the extra- 
 neous combustible material introduced into the fire- 
 box, but the energy of muscular contraction, for 
 example, comes not from the oxidizable food mate- 
 rial in the stomach, but from the material of the 
 muscle itself. In other words, in the animal body it 
 is part of the tissue framework, or material that is 
 closely incorporated with the framework, that is 
 burned up, and the ability to endure continued mus- 
 cular strain depends upon the nutritive condition of 
 the muscles involved, and not upon the amount of 
 food contained in, or introduced into, the stomach." 
 In the second place, the resemblances upon which 
 analogical arguments are made to rest must be im- 
 portant resemblances. Accidental resemblances and 
 superficial likenesses are at the basis of all falla- 
 cious reasoning by analogy. With this class of anal- 
 ogies in mind Heine was led to exclaim, "Heaven 
 defend us from the Evil One and from metaphors." 
 But if the resemblance is essential and important, 
 there is no need to avoid the use of this method of 
 reasoning. Now when we speak of a resemblance 
 being essential, we mean that the characteristics 
 
414 A TEXT-BOOK OF LOGIC 
 
 with respect to which objects are compared must be 
 essential either to the existence of the objects or to 
 the purpose which these objects realise. If, to illus- 
 trate the former case, we infer that certain things 
 are true of diamonds because they are true of 
 graphite, we, no doubt, do so with the thought in 
 mind that these substances are different forms of 
 carbon. To illustrate the latter, we may argue from 
 the similarity in shape of certain flints found in the 
 ground and those used by certain savage tribes of 
 the present day that the former were used as 
 weapons since this is the use that the latter are 
 known to have. 
 
 In the third place, analogical arguments must 
 take into account not only the importance of the 
 resemblances but the non-importance of the differ- 
 ences between the objects compared. An interest- 
 ing example is the following, borrowed from Gib- 
 son. He says, "we might enumerate many points 
 of external resemblance between the Whale and the 
 Shark, and found upon them an analogical argu- 
 ment to the effect that the respiration-processes in 
 the two animals must be similar. The whale, we 
 might say, resembles the shark not only in all the 
 common characters of Vertebrates, but also in its 
 submarine habitat and in being (as regard species) 
 one of the very largest of marine animals. Like the 
 shark, it is fish-like in external form, its fusiform 
 body being well fitted for cleaving the water. An- 
 teriorly its body passes into the head without any 
 distinct neck, and posteriorly it is furnished with a 
 
SOME EXPLANATORY METHODS OF INDUCTION 415 
 
 swimming-tail into which the body gradually tapers. 
 It has no hairy covering. Like the shark, again, 
 it has a wide mouth, and it is of predaceous habit, 
 feeding only on living animal nutriment. There- 
 fore we may with great probability conclude that 
 its method of respiration is like that of the shark 
 i. e., that it breathes the oxygen dissolved in the 
 water, and has no need to be supplied with atmos- 
 pheric air. 
 
 "But this argument would be unsound. The points 
 that we ought to have observed are the characters 
 connected with the function of respiration. The 
 presence of gill-slits in the shark and their absence 
 in the whale is a difference so essential to the in- 
 quiry that its observation would at once have been 
 sufficient to make our analogy fall to the ground. 
 And among the still more obvious external differ- 
 ences there is a single character which also should 
 alone outweigh all the above mentioned resem- 
 blances. The extremity of the shark's tail is ex- 
 panded vertically ; in the whale the flukes of the tail 
 are placed horizontally. From many points of view 
 this difference might be regarded as unimportant; 
 but from the point of view of our analogical argu- 
 ment it is very important indeed, for it is intimately 
 connected with the problematic point of resemblance 
 that we are endeavouring to establish. For sea- 
 creatures which, like the whale and the shark, spend 
 their life in swimming freely through the water, 
 the direction of movement is chiefly determined by 
 the presence or absence of the air-breathing habit. 
 
416 A TEXT-BOOK OF LOGIC 
 
 Those creatures that have no need of atmospheric 
 air move usually in straight-forward and lateral 
 directions, and for effecting such movements a ver- 
 tically expanded caudal fin is admirably fitted. But 
 creatures that need to rise frequently to the surface 
 of the water for the purpose of respiration are con- 
 stantly moving upward and downward. To move- 
 ments of this kind a tail with horizontally expanded 
 fluxes is precisely adapted. Thus the whale's hori- 
 zontally expanded tail affords a strong presumption 
 in favour of the presence of the air-breathing habit ; 
 and this apparently trifling difference between the 
 two creatures must be regarded as fatal to the 
 cogency of the analogical argument." 
 
 The Function of Analogy in Induction. We have 
 been considering analogy as a special kind of argu- 
 ment, the way in which Aristotle understood it. We 
 proceed now to discuss the value that analogies have 
 for advancing our knowledge of the world about us, 
 the assistance they may give in the problem of ex- 
 planation. Analogy, as our exposition has shown, 
 is an argument from similar instances. It is, to 
 quote Mellone, "any resemblance between things 
 which enables us to believe of one what we know 
 of the other." We advance from one instance to 
 another on the basis of a perceived or imagined sim- 
 ilarity between the instances. The necessity of ad- 
 vancing in an analogical argument from particular 
 to particular, has led to the saying that analogy 
 "sticks in the particular instances." Although this 
 is true, it is not on that account worthless as an in- 
 
SOME EXPLANATORY METHODS OF INDUCTION 417 
 
 strument or means of arriving at the law of the 
 connection between resembling instances. For if 
 there is a resemblance, or a group of resemblances, 
 between P and P', such that we feel warranted in 
 affirming of P' what we know positively only of P, 
 we may look upon the similarity, not merely as a 
 bridge from the one instance (P) to the other (P')> 
 but as a suggestion of a specific connection between 
 the two instances which is not brought out ex- 
 plicitly by the analogy. It is this characteristic of 
 suggesting more than it can possibly make clear, 
 that renders analogy of service in an inductive proc- 
 ess. The following remarks are intended to make 
 this point clear. 
 
 Two things are characteristic of analogy. In the 
 first place, the comparison of instances, as we have 
 seen, rests upon what are called their essential 
 attributes, but, in the second, the degree of the 
 resemblance always remains more or less undeter- 
 mined. When we have assured ourselves that the 
 resemblance depends upon essential features of the 
 compared phenomena, we are, however, still in 
 doubt about the precise factor or factors in the re- 
 semblance upon which the inferred characteristic 
 really depends. Thus any two phenomena, P and 
 P', may resemble each other in possessing the 
 attribute x, a resemblance which seems to warrant 
 us in expecting that if P also shows the character- 
 istic y, P' will likewise show the same characteristic. 
 To take a concrete example. The chemist classifies 
 
 27 
 
418 A TEXT-BOOK OF LOGIC 
 
 a number of elements together under the head of 
 alkaline metals because all these elements potas- 
 sium, sodium, caesium, rubidium, and lithium, - 
 possess certain characteristics in common; for in- 
 stance, their active combination with oxygen to de- 
 compose water at all temperatures; their forming 
 strongly basic oxides, highly soluble in water, yield- 
 ing powerful caustic and alkaline hydrates from 
 which water can not be expelled by heat; the solu- 
 bility of their carbonates in water; and the forma- 
 tion by each metal of only one chloride. Now, if in 
 the progress of the chemistry of any one of these 
 metals a new property is discovered, it is natural 
 to infer by analogy that the other members of the 
 group will display under appropriate conditions the 
 same property. But beyond the suggestion of a 
 connection of the new property with the character- 
 istics of the alkaline group analogy cannot go; it 
 cannot point out on which attribute, or combination 
 of essential attributes, the new property really de- 
 pends. Thus an argument by analogy presumes a 
 connection between x and y, but it cannot show that 
 y depends on x rather than on some other property 
 in P which may not belong to what we have called 
 its essential attributes. However strong the pre- 
 sumption may be that x and y are causally related, 
 there always remains the possibility that y is condi- 
 tioned in some other way. Analogical arguments 
 for this reason are never conclusive, and in an in- 
 ductive process they are valuable only because they 
 suggest lines of further observation which may 
 
SOME EXPLANATORY METHODS OF INDUCTION 419 
 
 either verify or discredit the analogical inference. 
 Mill, therefore, is right when he regards an analogy 
 as "a mere guide post, pointing out the direction 
 in which more vigorous investigations should be 
 prosecuted. It is in this last respect," says Mill, 
 "that considerations of analogy have the highest 
 scientific value. The cases in which analogical evi- 
 dence affords in itself any very high degree of prob- 
 ability are, as we have observed, only those in 
 which the resemblance is very close and extensive; 
 but there is no analogy, however faint, which may 
 not be of the utmost value in suggesting experi- 
 ments or observations that may lead to more posi- 
 tive conclusions." With this view, to which Mill 
 does not consistently adhere, Jevons is in agree- 
 ment, and he has made it the foundation of his chap- 
 ter on analogy in the Principles of Science. 
 
 Nature of Hypothesis. An hypothesis is an at- 
 tempted explanation of an occurrence, a supposition 
 about the connection of particular phenomena. To 
 get the meaning of this general statement before us, 
 let us consider a particular case. Malaria is a dis- 
 ease which has a set of characteristic symptoms, 
 the chief of which are chills and fever occurring at 
 more or less definite intervals of time. When the 
 physician has become familiar with the character- 
 istic symptom complex of the disease, he is able to 
 diagnose the new cases that come under his obser- 
 vation by means of the similarity that they bear to 
 this complex ; all the cases that show the diagnostic 
 marks of the disease he calls malaria. The logical 
 
420 A TEXT-BOOK OF LOGIC 
 
 procedure in this instance is analogical. If, how- 
 ever, instead of taking the physician's attitude which 
 requires him to diagnose only for the purpose of 
 selecting the proper remedies, we approach the dis- 
 ease from the standpoint of the scientist who wants 
 to know what malaria is, we shall have to go beyond 
 the similarities which figure in the physician's diag- 
 nosis, and, by a series of suppositions or hypotheses, 
 work our way among the antecedents and concomi- 
 tants of the cases of the disease for some clue to the 
 agent which is responsible for the production of the 
 disease. It is not enough to say that similar symp- 
 toms mean the same disease, the question we are now 
 asking is what produces the similar symptoms in all 
 the cases that occur. We are looking for something 
 more than similarity, we are searching for an iden- 
 tity among the conditions under which the disease 
 is contracted. Thus, for example, night air, damp 
 places, exhalations from marshy ground have been 
 proposed as the antecedent condition which is 
 capable of producing malarial fever. It is only 
 within comparatively recent times that, for these 
 hypotheses, another has been substituted which con- 
 nects the disease with the bite of the Anopheles 
 mosquito, and this is the view that is held at the 
 present day. The bite of the Anopheles mosquito* 
 is our hypothesis for the occurrence of malaria. 
 
 In the light of this illustration, we may observe 
 that not any supposition about phenomena is an 
 hypothesis. It is only when the supposition points 
 us to phenomena of the same order as the event 
 
SOME EXPLANATORY METHODS OF INDUCTION 421 
 
 that we are trying to explain that it satisfies the 
 conditions of a tenable hypothesis. In medicine, 
 for example, we no longer entertain theological ex- 
 planations of disease, and for devils we are substi- 
 tuting bacteria and their toxins, and in those dis- 
 eases which cannot be shown to be of bacterial 
 origin, as for example many of the occupational 
 diseases, we assign either a chemical cause, as in 
 lead poisoning, or a mechanical one, as in the dis- 
 ease characteristic of the Sheffield steel grinders. 
 When made with regard to the requirement we are 
 now considering, namely, that the supposition 
 should be stated in terms of the same order as the 
 phenomenon to be explained, hypotheses differ from 
 one another only in the degree of their probability; 
 and it seems to us to be quite misleading to speak of 
 them as guesses, as is done by some logicians, as if 
 they were altogether uncontrolled by the nature of 
 the phenomena for which an explanation is being 
 sought. The truth of this statement is apparent 
 when we recognise that the demand for an hypoth- 
 esis is only a particular form of the demand for a 
 careful analysis of the phenomena under observa- 
 tion. Our acquaintance with objects becomes more 
 minute as well as more accurate under the stimulus 
 that comes from the call for explanation ; and if one 
 step in the process of explanation is hypothetical, 
 that step must still be controlled by the nature of 
 the observed material if we are to safeguard the in- 
 ductive process against useless and irresponsible 
 guesses. The satisfaction of this requirement by 
 
422 A TEXT-BOOK OF LOGIC 
 
 science may be briefly illustrated. To account for 
 the phenomena of sound, the physicist, starting with 
 the sound experience, connects this with the undu- 
 lations of the air which occasion it, and these undu- 
 lations, again, he connects with a vibrating body, 
 a stretched string, the vocal cords, an organ pipe. 
 When the scientist asks what is the source of the 
 phenomena of light which occasion the sensation of 
 vision, although he cannot point definitely to the 
 material bodies which produce the undulations in 
 the ether, he forms his hypothesis in terms of the 
 same order as the phenomena that he has under in- 
 vestigation; and he does so because the "scientific 
 imagination," to quote Tyndall, "demands, as the 
 origin and cause of a series of ether-waves, a par- 
 ticular vibrating matter quite as definite, though it 
 may be excessively minute, as that which gives 
 origin to a musical sound. Such a particle we name 
 an atom or a molecule. I think the intellect, when 
 focussed so as to give definition without penumbral 
 haze, is sure to realize this image at last." 
 
 Objections to the Use of Hypothesis. Although 
 the history of modern science furnishes so many 
 illustrations of the value of hypotheses, and al- 
 though the methods in use at the present day for 
 the advancement of scientific knowledge depend 
 also upon their employment, there is, nevertheless, 
 among scientific men either only a half-hearted 
 recognition of their services, or a misleading rejec- 
 tion of their claims to a place in scientific procedure. 
 This interesting fact is not difficult to understand, 
 
SOME EXPLANATORY METHODS OF INDUCTION 423 
 
 and we refer to it here because it enables us to 
 explain some aspects of the formation of hypoth- 
 eses which as yet have not been mentioned. The 
 hesitancy of men of science to recognise that the 
 advancement of scientific knowledge is, in any re- 
 spect, dependent upon hypotheses, may be attrib- 
 uted to their effort to exclude from all parts of their 
 work influences and additions that are derived from 
 the nature of the mental processes through which 
 that work is carried on. The aim of science is 
 throughout objective in the sense that its task is to 
 describe and explain the facts of observation, to 
 arrive at judgments about these facts that are inde- 
 pendent of the idiosyncrasies of the individual mind. 
 "The scientific man," as Karl Pearson says, "has 
 above all things to strive at self-elimination in his 
 judgments, to provide an argument which is as true 
 for each individual mind as for his own." The 
 life of science depends upon loyalty to this aim. 
 The intellectual integrity of every scientific man is 
 involved in his efforts to maintain this aim. All 
 this may be granted; it may even be admired and 
 praised. And yet we cannot avoid the impression 
 that if the spirit of loyalty to professional ideals 
 which is displayed by workers in the fields of the 
 particular sciences were supplemented by an ac- 
 quaintance with the history of scientific achieve- 
 ments, the objections to hypothesis would be miti- 
 gated, and in time might entirely disappear. For 
 the admission of hypothesis in no way interferes 
 with keeping the work of science objective, and 
 
424 A TEXT-BOOK OF LOGIC 
 
 their practical rejection may often render impos- 
 sible of realisation the aims which stimulate scien- 
 tific effort. 
 
 The situation that has just been described may 
 be made more explicit by saying that without an 
 active and fertile imagination, it is impossible to 
 formulate a satisfactory hypothesis. It is, in part, 
 because the scientist does not take the pains to 
 ascertain what are the nature, conditions, and limits 
 of the imagination that he looks askance upon the 
 formation of hypotheses. This is not the place to 
 state and develop a doctrine of the imagination; it 
 is enough for our purpose to call attention to the 
 fact that many of the leading men of science have 
 borne eloquent testimony to the value of the imagi- 
 nation in advancing the interests of scientific truth. 
 In his address on 'Scientific Use of the Imagination/ 
 Tyndall writes: "Bounded and conditioned by co- 
 operant reason, imagination becomes the mightiest 
 instrument of the physical discoverer. Newton's 
 passage from a falling apple to a falling moon was, 
 at the outset, a leap of the imagination." Tyndall 
 prefixed to his essay the following passage from an 
 address to the Royal Society by Sir Benjamin Brodie. 
 "Lastly, physical investigation, more than anything 
 besides, helps to teach us the actual value and right 
 use of the Imagination of that wonderful faculty 
 which, left to ramble uncontrolled leads us astray 
 into a wilderness of perplexities and errors, a land of 
 mists and shadows; but which, properly controlled 
 
SOME EXPLANATORY METHODS OF INDUCTION 425 
 
 by experience and reflection, becomes the noblest 
 attribute of man; the source of poetic genius, the 
 instrument of discovery in Science, without the aid 
 of which Newton would never have invented flux- 
 ions, nor Davy have decomposed the earths and 
 alkalies, nor would Columbus have found another 
 continent." In his Methods and Results, Huxley 
 writes : "It is a favourite popular delusion that the 
 scientific inquirer is under a sort of moral obliga- 
 tion to abstain from going beyond that generalisa- 
 tion of observed facts which is absurdly called 
 'Baconian' induction. But any one who is practically 
 acquainted with scientific work is aware that those 
 who refuse to go beyond fact rarely gets as far as 
 fact; and any one who has studied the history of 
 science knows that almost every great step therein 
 has been made by 'anticipation of nature/ that is, 
 by the invention of hypotheses which, though veri- 
 fiable, often had little foundation to start with, and 
 not infrequently, in spite of a long career of useful- 
 ness, turned out to be wholly erroneous in the long 
 run." 
 
 These quotations are sufficient to illustrate the 
 importance of the imagination in the construction 
 of scientific hypotheses, and to indicate the reason 
 why many men of science look with suspicion upon 
 the use of hypotheses. "Scientific men fight shy of 
 the word (imagination) because of its ultra-scien- 
 tific connotations," because its use is often uncon- 
 trolled, and because under the best conditions it 
 sometimes leads us astray. But to reject an instru- 
 
426 A TEXT-BOOK OF LOGIC 
 
 ment of research because of its limitations is no 
 more reasonable than would be a physician's refusal 
 to employ strychnine in the cure of a patient, be- 
 cause that drug is on the commercial market in the 
 form of 'Rough on Rats.' We are not advocating an 
 indiscriminate exercise of the imagination, nor the 
 substitution of it for the careful and painstaking 
 observation of phenomena. What we are pointing 
 out is that there are conditions of physical investi- 
 gation which render all known instruments of pre- 
 cision inadequate and clumsy tools, and that if 
 observation is not to be hindered its range must be 
 extended as far beyond that of our instrumental 
 world as this is beyond the world made known by 
 our natural organs of perception. We cannot, for 
 example, bring under observation by the most 
 powerful microscope the particles of matter which 
 are the media in our atmosphere of reflected light. 
 By what means has the existence of such particles 
 scattered throughout our space come to be believed 
 in? Tyndall cites this example as an illustration 
 of the use that science may make of the imagina- 
 tion, as he does also Darwin's hypothesis of a pri- 
 mordial germ as the source of all the variety of 
 organisms now upon the earth's surface. These in- 
 stances, and many others that are among the most 
 brilliant achievements of science, lead us to look 
 upon the imagination as itself an instrument of 
 observation, and in the form of carefully stated 
 hypothesis, it leads to an explanation of many ob- 
 
SOME EXPLANATORY METHODS OF INDUCTION 427 
 
 served facts which without its aid would postpone 
 indefinitely important lines of research. 
 
 Verification of Hypotheses. If we are to carry 
 our explanations of events to a successful termina- 
 tion, the hypotheses by means of which the rela- 
 tions of particular phenomena are brought under an 
 intelligible view need to be tested and not merely 
 stated, to be verified, not merely formulated. There 
 are two steps in the process of verification to which 
 we may give attention. "To prove or disprove (an) 
 induction we must have resort," says Tyndall, "to 
 deduction and experiment." Mill's definition of an 
 hypothesis, that it is "any supposition which we 
 make (either without actual evidence, or on evidence 
 avowedly insufficient) in order to endeavour to 
 deduce from it conclusions in accordance with facts 
 known to be real," points to the same two require- 
 ments. An hypothesis which is not capable of be- 
 ing verified would serve no immediate purpose, and 
 whether it serves any purpose at all need not con- 
 cern us. We are now studying living hypotheses, 
 those which answer questions, and render intelli- 
 gible the particular facts of observation. And it is 
 about these that we are warned that it is not their 
 intelligibility merely, and not the fact that they 
 answer questions, which recommends them finally to 
 our acceptance. It is only if our hypotheses are 
 true, if they make us acquainted with the actual 
 relations which objects sustain to one another, that 
 they are received as part of our scientific knowledge. 
 The formation of hypotheses takes us beyond what 
 
428 A TEXT-BOOK OF LOGIC 
 
 is actually known and observed, and for this reason 
 there is in every hypothesis an element of risk ; but 
 they must at the same time make it possible for us 
 to return to fact and the observation of fact, and it 
 is this that renders them useful in the advancement 
 of human knowledge. The return to fact is made 
 in the two steps of deduction and experiment. 
 
 Let us take as an illustration of these two stages 
 in the process of verification the well-known fact 
 that water rises to a certain height in a pump, and 
 the explanation of this fact on the ground that 
 "Nature abhors a vacuum." The story goes that in 
 trying to raise water to a great elevation, some 
 Florentine gardeners found that the column of 
 water ceased at the height of thirty-two feet. The 
 matter was referred to Galileo who, embittered by 
 the reception that had been accorded to his science, 
 said that he supposed that Nature abhorred a 
 vacuum only at the height of thirty-two feet. It 
 was left for Toricelli, Galileo's pupil, to provide an 
 answer to the inquiry. He supposed that water 
 might be forced into a tube by pressure on the sur- 
 face of the liquid outside. After much thought, it 
 occurred to Toricelli that the atmosphere might 
 exert such pressure, and that the column of water 
 thirty-two feet in height might be the exact weight 
 necessary to equalise this atmospheric pressure. 
 This supposition was Toricelli's hypothesis. Was it 
 true? This was the next question that the physicist 
 confronted, and it is exceedingly instructive to ob- 
 serve the way he went to work to verify his hypoth- 
 
SOME EXPLANATORY METHODS OF INDUCTION 429 
 
 esis. He deduced certain consequences from the 
 hypothesis. He argued that if thirty-two feet of 
 water will hold the atmospheric pressure in equili- 
 brium, a shorter column of a heavier liquid should do 
 the same. According to his calculations, mercury, 
 which is thirteen times heavier than water, should 
 be able to balance the pressure of the atmosphere 
 at thirty inches. The next step in the process of 
 verifying the original hypothesis was an experi- 
 ment. Toricelli filled a glass tube a yard or so in 
 length, open at one end and closed at the other, 
 with mercury. Placing his thumb over the open 
 end, he inverted it in a bath filled with the same 
 metal. When he removed his thumb, the mercury 
 began to sink, and continued to sink until the height 
 of thirty inches had been reached. The proof of the 
 hypothesis was complete. 
 
 Hypothesis and Theory. The difference between 
 an hypothesis and a theory is a relative one merely. 
 To bring out this feature of the terms' meanings, 
 we may say that a theory is a completely verified 
 hypothesis, and that an hypothesis is an incom- 
 pletely verified theory. This statement will have 
 served its purpose if it remind us that hypothesis and 
 theory both spring out of the demand for explana- 
 tion, that they both involve the use of the creative 
 imagination for their formation, and call for verifi- 
 cation in the way that has been described. It is these 
 similarities which justifies the popular use of the 
 terms as synonymous. It will be useful for us, how- 
 ever, to look at the matter a little more closely. We 
 
430 A TEXT-BOOK OF LOGIC 
 
 may observe, for instance, that we advance from 
 hypothesis to theory, not by leaving our hypothesis 
 behind, but by developing it in the light of further 
 experiences so as to make it accord with facts hith- 
 erto not known or not understood. In this sense, the 
 hypothesis becomes a theory. To illustrate, when ice- 
 cold water is poured into a glass on a hot summer 
 day, little drops of water collect and trickle down on 
 the outside of the glass. How do we account for this 
 phenomenon ? The sudden cooling of the glass takes 
 place by radiation of its heat, and the water-vapour 
 of the atmosphere condenses on the cooled surface 
 of the glass. The same hypothesis may be extended 
 to account for the formation of dew, and a number 
 of other phenomena. An hypothesis that can be 
 used to explain a variety of facts which were not 
 thought of when the hypothesis was formulated, can 
 justly be regarded with greater confidence than one 
 which explains only a single phenomenon. Every 
 new fact which fits into an hypothesis strengthens 
 it. At first, an hypothesis has an explanatory value 
 only for the particular phenomenon with respect to 
 which it is framed. But if an hypothesis is ca- 
 pable of growth, both in respect to the number and 
 variety of the facts which it is capable of explain- 
 ing, and in the simplicity of the form which it as- 
 sumes, the conditions are present for the develop- 
 ment of the hypothesis into what is known as a 
 theory. We speak, for example, of the Darwinian 
 hypothesis, because the supposition it states is still 
 in a condition of growth, and because the modifica- 
 tions which are being introduced into Darwin's 
 
SOME EXPLANATORY METHODS OF INDUCTION 431 
 
 statement are intended to make his view harmonise 
 more fully with progressive experience and recent 
 discovery. When, however, we regard the idea of 
 growth throughout the known world as a confirmed 
 doctrine of science, we no longer speak of the Dar- 
 winian hypothesis, but of the theory of evolution. 
 In the same way, and for similar reasons, we speak 
 of the theory of gravitation, the Copernican theory, 
 the theory of the conservation of energy. What 
 we mean by such designations is that the evidence 
 for the particular hypotheses which lies back of 
 them is ample and varied, that the exceptions within 
 the fields of their application are either insignficant 
 or are absent altogether, that newer experiences 
 and discoveries tend to confirm these views. When 
 lines of evidence tend to converge and to be f ocussed 
 on an hypothesis, that hypothesis has no longer the 
 tentative position of a supposition, but the firmer 
 and surer foundation of a confirmed belief. The 
 formulation of such a confirmed belief is called a 
 theory. 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Ch. XXV. 
 
 B. Bosanquet, The Essentials of Logic, Lecture X., Ch. I., 
 
 e-b, 3. 
 J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
 
 XIV., XV., XVIII., XIX. 
 J. G. Hibben, Logic Deductive and Inductive, Part II., Chs. 
 
 IIIc, XL, XII., XIII., XIV. 
 W. S. Jevons, Elementary Lessons in Logic, Lessons XXVI., 
 
 XXVII. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. VIII., 4-8. 
 
432 A TEXT-BOOK OF LOGIC 
 
 W. Minto, Logic, Inductive and Deductive, Chs. IX., X. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. 
 
 XV., 5-7, XVIIL, XIX., XX. 
 W. J. Taylor, Elementary Logic, Chs. XV., XVI. 
 
 ADVANCED 
 
 B. Bosanquet, Logic, Vol. II., Book II., Chs. II., III., IV., V. 
 W. R. B. Gibson, The Problem of Logic, Chs. XXXVIII., 
 
 XLII. 
 W. S. Jevons, The Principles, of Science, Chs. XVIIL, XIX., 
 
 XXIII., XXIV., XXVI., XXVII., XVIIL 
 H. W. B. Joseph, An Introduction to Logic, Ch. XXI. 
 H. Lotze, Logic, Vol. II., Book II., Chs. VIII., IX. 
 J. S. Mill, A System of Logic, Book III., Chs. VII., XIV., 
 
 XX., XXIII. 
 
 F. C. S. Schiller, Formal Logic, Chs. XIX., XXII. 
 J. Venn, Empirical Logic, Chs. XVI., XXI. 
 J. Welton, A Manual of Logic, Vol. II., Book V., Chs. III., 
 
 147, 149, IV., V., 153, 154, VII. 
 
 QUESTIONS 
 
 1. Is there necessarily any irreconcilable opposition be- 
 tween the view that the aim of science is complete ob- 
 servation, and that it is explanation? Explain. 
 
 2. To what simple type does all scientific explanation con- 
 form? Illustrate. 
 
 3. What is meant by saying that explanation consists in 
 discovering the conditions of the occurrence of phe- 
 nomena? 
 
 4. Are all the circumstances attending the occurrence of 
 an event conditions of its occurrence? 
 
 5. What is meant by saying that the phenomena of ob- 
 servation and those of explanation are continuous with 
 each other? 
 
 6. What bearing, if any, do the facts included in your 
 answer to the previous question have upon the dis- 
 tinction between a phenomenon and its conditions? 
 
SOME EXPLANATORY METHODS OF INDUCTION 433 
 
 7. In what sense can it be said that scientific explanation 
 is a process by which what is given in observation is 
 supplemented by what is not so given? 
 
 8. Can you connect the conception of scientific explanation 
 implied in the previous question with the conception of 
 knowledge stated in Chapter I? 
 
 9. State and illustrate three senses in which the word 
 analogy is used. 
 
 10. Why is not any kind or degree of resemblance a safe 
 principle of inference? 
 
 11. What is meant when it is said that analogical reasoning 
 depends upon important resemblances? . 
 
 12. In what way does the validity of reasoning by analogy 
 depend upon the attitude one takes toward differences? 
 
 13. What light does the saying that analogy 'sticks in the 
 particular instances' throw upon the character of ana- 
 logical argument? 
 
 14. In what sense can analogy be regarded as a method of 
 explanation ? 
 
 15. What are the limits of analogical argument? 
 
 16. What does Mill mean by calling analogy 'a mere sign 
 post'? 
 
 17. State and illustrate what you understand by an hypoth- 
 esis. 
 
 18. Why must hypotheses be stated in terms of the same 
 order as the phenomena they attempt to explain? 
 
 19. Is there any objection against calling hypotheses 
 'guesses,' and, if so, what is the ground on which it 
 rests? 
 
 20. What reason may be given for the scientists' objection 
 to the use of hypotheses? 
 
 21. What is the relation of imagination to the task of for- 
 mulating scientific hypotheses? 
 
 22. What are some of the 'facts' which we owe to the 
 exercise of imagination in the field of the natural 
 sciences? 
 
 38 
 
434 A TEXT-BOOK OF LOGIC 
 
 23. State and explain the two steps involved in the veri- 
 fication of hypotheses? 
 
 24. Illustrate by the use of concrete example the process 
 of verifying an hypothesis. 
 
 25. How do hypothesis and theory agree with and differ 
 from each other? Illustrate. 
 
 EXERCISES 
 
 1. Examine the explanations of three simple events with 
 which you are acquainted, and state whether they con- 
 form or not to the fundamental form of explanation 
 as stated in the text. 
 
 2. Give three instances in which explanation consists in the 
 statement of the conditions of a phenomenon's occur- 
 rence. 
 
 3. Give two llustrations, one from literature and one from 
 science, of analogy. Examine each with a view to show- 
 ing to which meaning of the word it conforms, and 
 whether it satisfies the conditions of a valid inference. 
 
 4. Upon what logical principle does each of the following 
 statements depend, and what can you say as to their 
 validity as arguments: 
 
 (1) It is said that a general resemblance of the hills 
 near Ballarat in Australia to the California hills 
 
 where gold had been found suggested the idea of 
 digging for gold at Ballarat. 
 
 (2) There are no great nations of antiquity but have 
 fallen to the hand of time; and England must join 
 them to complete the analogy of the ages. Like 
 them she has grown from a birth-time of weakness 
 tutelage to a day of manhood and supremacy, but 
 she has to face her setting. Everything that 
 grows must also decay. 
 
 5. Construct an hypothesis to explain some fact of your 
 experience, and explain how it may be verified or over- 
 thrown. 
 
CHAPTER XVI 
 
 CAUSATION 
 
 General Statement of the Problem. The fact that 
 underlies the problem of causation is the observed 
 regularity in the order of the particular phenomena 
 which occur in the course of our ordinary expe- 
 rience, and in the fields of the several sciences. 
 That our ordinary and scientific experience is char- 
 acterised, within ascertainable limits, by some kinds 
 and degrees of regularity is a fact about which 
 there is universal agreement. Indeed, this is a fea- 
 ture of experience so generally recognised that it 
 constitutes the starting point not only of the theo- 
 retical interest which leads us to the more accurate 
 forms of human knowledge, but also of the practical 
 interests which lie at the foundation of the political, 
 commercial, and social relations by which human 
 individuals are held together in a community. A 
 world from which all order were absent would be a 
 world in which all thought and action would be im- 
 possible, and to which all thinking and active agents 
 would ultimately succumb. The institutions of 
 society and the organisation of the sciences pre- 
 supposes that some sort of unity and order belong 
 to the world ; and it is the business of all our sciences 
 to study the regularities of the phenomena and 
 events of the world for the purpose of endowing 
 our notion of such regularities with greater pre- 
 
 (435) 
 
436 A TEXT-BOOK OF LOGIC 
 
 cision. The problem, then, that confronts us in view 
 of this regularity of the world's order is : How shall 
 we conceive this regularity so as to make intelligible 
 to ourselves the principles or laws by which it is 
 maintained and upon which it depends? 
 
 The Practical Aspect of the Question. There is 
 no doubt that this is not a theoretical question 
 merely, a question only of the sciences, and unim- 
 portant or superfluous in the absence of theoretical 
 interests. The way in which the world in which 
 we live may be expected to behave is a broadly 
 practical interest; and the man who in the morning 
 starts off to his office, as well as the one who goes to 
 his laboratory, begins the day's work with the ex- 
 pectation that the uniformities upon which he has 
 relied in the past will be maintained in the present. 
 Indeed, we may say that, in the history of the indi- 
 vidual and of the race, interest in the regularity 
 of the course of observed events was practical before 
 it was theoretical; and it would not be difficult to 
 show that the practical motive has never been 
 divorced from the theoretical when, in the progress 
 of the sciences, these uniformities have become 
 the subject of very specialised study. No one, 
 for instance, who has the least knowledge of 
 primitive peoples can fail to be impressed with the 
 fact that the origin and development of their insti- 
 tutions is closely interwoven with their struggle 
 with the forces of nature. Upon his understanding 
 of the physical world has depended the primitive 
 man's ability to maintain himself in existence. We 
 
CAUSATION 437 
 
 see the relationship thus indicated between the 
 growth of intelligence and the economic struggle 
 illustrated in a broad way if we contrast, for ex- 
 ample, the peoples of the northern and southern 
 latitudes. Whenever, as in the latter case, the food 
 supply is plentiful and relatively independent of the 
 cultivation of the domestic arts, intelligence is com- 
 paratively low ; but when, as in the former case, the 
 food supply is scanty or precarious, it becomes 
 increasingly important to understand the physical 
 environment from which has to be won the means 
 of physical support, and, if the community is to 
 perpetuate itself, to socialise this knowledge in the 
 domestic arts. 
 
 There are many concrete illustrations of the 
 way in which, at the present time, observation 
 of natural occurrences, and inferences drawn from 
 such observation, are allowed to affect our prac- 
 tical life. From the character of the sunset 
 we infer that it will be a fair or stormy day to- 
 morrow, and, therefore, that it will, or will not, be 
 possible to take a day's outing in the country. What 
 the farmer calls 'good growing weather' is an infer- 
 ence, based upon observed connections in the past, 
 of the same practical sort. Now about the facts that 
 underlie such practical inferences as these, we may 
 observe that they are selected, often by the cooper- 
 ative labours of many generations of observant men, 
 from a very complex mass of details, and that no 
 effort is made, as a rule, either to determine the pre- 
 cise nature and connection of the facts themselves, 
 
438 A TEXT-BOOK OF LOGIC 
 
 or to enumerate exhaustively the other factors with 
 which, in our experience, they are associated. For 
 example, what constitutes 'good growing weather' 
 may be for one man a matter of temperature, for 
 another a matter of humidity, and for a third a 
 matter of both ; but neither of these factors, nor both 
 together, can be regarded as a sufficient explanation 
 of the term, and many other elements of the situ- 
 ation in which it is relevant to talk about growing 
 weather must be taken account of such, for in- 
 stance, as the nature of the particular crop, the 
 particular stage of its growth, its condition at that 
 stage, the nature of the soil, the location of the field 
 in which the crop is growing, etc. if the phrase 
 is to have for us any practical significance. When, 
 therefore, we examine the character of those uni- 
 formities which our practical interests lead us to 
 observe, we find that they are made up of certain 
 striking or important features of a complex situ- 
 ation, which are connected together in such a way 
 that, on their recurrence in our experience, we are 
 led to expect the recurrence of other features of the 
 situation with which they have been associated in 
 our past experience. In other words, one part of 
 an experience is taken as a sign of the recurrence 
 of another part with which it is usually connected. 
 Beyond such empirical connections as are found in 
 experience, the practical view of causation does not 
 enable us to advance. 
 
 The Theoretical Aspect of the Question. If we 
 compare the theoretical with the practical way of 
 
CAUSATION 439 
 
 dealing with the observed regularities in the occur- 
 rence of natural events, we shall see that it differs 
 from the latter in two respects. In the first place, 
 the theoretical view, in Venn's suggestive phrase, 
 'screws up' the antecedent or cause and the conse- 
 quent or effect of an event into close juxtaposition, 
 so that they come to be regarded as nearly as pos- 
 sible concurrent. The possibility of doing this, it is 
 obvious, depends upon our ability to eliminate from 
 the phenomenon we are examining all the disturb- 
 ing or irrelevant elements. If, therefore, it is re- 
 membered that no two natural events are exactly 
 alike in all their details, that some of the attendant 
 circumstances are peculiar to the instance of the 
 phenomenon we are examining, and form no part of 
 the phenomenon itself, it is evident that the omission 
 of these, by whatever means it is brought about, 
 can serve only to give greater precision to the fac- 
 tors that are involved in the orderly sequence, and 
 to make it possible to determine with greater accu- 
 racy the details which are involved in the causal 
 relation. We pass from the practical to the more 
 theoretical view of causation, that is to say, when 
 we devise means of eliminating from our observa- 
 tion of natural events what is irrelevant to our. 
 search for the conditions of the occurrence of such 
 events. 
 
 In the second place, the theoretical view insists 
 upon the importance of a careful analysis of the 
 antecedents of an event as a condition of establish- 
 ing a causal relation. Mill insisted on this point 
 
440 A TEXT-BOOK OF LOGIC 
 
 with some emphasis, and he criticised the practical 
 view for the unregulated way in which it picks out 
 some one event or circumstance, and calls it the 
 cause. There is just ground for Mill's contention, 
 if our study of the observed regularities in the 
 occurrences of natural phenomena is made from 
 the point of view of the requirements of accu- 
 rate knowledge; but if we admit the legitimacy of 
 the practical point of view, if, that is, the order of 
 nature's changes are taken as a clue to the kinds of 
 conduct that are likely to be efficient, we may say 
 that the more refined analysis that Mill had in mind, 
 and which is required by science, would in large 
 measure defeat this latter purpose. It is because 
 the interests of science are so intimately bound up 
 with a detailed knowledge of the conditions of phe- 
 nominal occurrences that, in contrast with those of 
 the practical life, its requirements are satisfied only 
 by the minute analysis of the phenomena with which 
 it is particularly concerned. In emphasising this 
 point Mill has directed attention to an important 
 difference between the practical and theoretical 
 views of the causal relation. 
 
 The Genetic Relation of the Practical and Theo- 
 retical Views. While the theoretical view of caus- 
 ation differs, as we have said, from the practical in 
 important respects, we should be departing from 
 the truth if we supposed that the differences between 
 these views expressed the whole truth about them. 
 There is between the two views no such opposition 
 in fact as an examination of their differences alone 
 
CAUSATION 441 
 
 would lead one to think. We must regard them, 
 rather, as earlier and later stages in the progressive 
 efforts of the race to make clear to itself the rela- 
 tion in which it stands to the changing environment 
 under which its life has to be lived. It was doubt- 
 less useful for the theoretical view that practical 
 interests had led to the observation of large numbers 
 of uniformity in the occurrence of natural events. 
 In this way, material was already prepared for it, 
 and to this material it could apply the stricter 
 methods which a change in interests was the means 
 of defining. But in developing and applying these 
 methods the sciences have not freed themselves alto- 
 gether from practical considerations and, moreover, 
 have themselves contributed very largely toward a 
 new and broader conception of the practical itself. 
 By this statement we do not merely mean that, in its 
 history, scientific progress frequently has been 
 determined by difficulties encountered in a narrowly 
 practical way, nor merely that scientific truth has 
 so often been found capable of a like practical 
 application; the more important fact is that, as 
 scientific aims and methods have become established, 
 our conception of what is practical has been broad- 
 ened to include any kind of activity that is directed 
 toward the attainment of an end. In the sense in 
 which nowadays we use the word, any regulated or 
 consciously controlled process is practical, and it 
 would seem that science has not only contributed to 
 this conception but is itself, in this meaning of the 
 term, preeminently a practical affair. And just be- 
 
442 A TEXT-BOOK OF LOGIC 
 
 cause the scientific man approaches his problems 
 with definite questions in his mind, because, as 
 Bacon said, he interrogates nature, there is a limit 
 set, by the nature of the questions themselves, to 
 the amount of analysis that is necessary in arriving 
 at the solution of particular problems. It is not, 
 therefore, in the amount of analysis performed that 
 we can find the distinguishing mark of a theoretical 
 view of the causal question. For if we insist that 
 our analysis in any field whatever must be relevant, 
 in kind and amount, to the purpose for which it is 
 undertaken, it becomes at once obvious that the 
 practical and theoretical views are brought together 
 under a single view, and that the differences enu- 
 merated above must be understood, not as placing 
 the views in question in different classes, but as indi- 
 cating different species of activity which belong to a 
 single class. 
 
 The Origin and Nature of the Causal Problem. 
 In view of the foregoing considerations, two facts 
 may be said to be fairly well established. In the 
 first place, there is good reason for believing that 
 the causal problem arises from the importance that 
 the presence of order in human experience has for 
 the practical no less than for the theoretical life. 
 The problem of causation is of such general interest, 
 as we have seen, not because the world in which 
 we live is unregulated and disordered, but because, 
 being regulated and- ordered, we can adjust our- 
 selves to it better if we know the principles and 
 laws according to which, in the future as in the 
 
CAUSATION 443 
 
 past, things and events may be expected to happen. 
 It is well to be perfectly clear on this point, because 
 frequently its neglect has led to a somewhat one- 
 sided, if not misleading, view of the problem itself. 
 We have called attention to the impossibility of 
 considering the causal problem as in any essential 
 respect different for the scientist than for the prac- 
 tical man. For both, it is the fact that experience 
 presents us with certain regularities in the order 
 of our experience that directs attention to the prob- 
 lem, and that leads to a study of these regularities. 
 We do not study the causal problem, that is to say, 
 to escape from a world of chaos to a world of order, 
 but, starting with the world of order, we seek to 
 understand its laws, and to ascertain how far these 
 laws are capable of being extended to new and 
 larger areas of life. 
 
 In the second place, it is clear that the problem 
 of causation has nothing whatever to do with the 
 question why things happen as they do, if by that 
 question is meant an inquiry into the reasons why 
 our experience has the distinctive characteristics 
 that it is known to have. Science, and the same 
 thing is equally true of philosophy, starts with the 
 acceptance of the world as it is known in human 
 experience, a world, as we have seen, that has a cer- 
 tain determinate character. Now about such a world, 
 it would be futile to ask ourselves why it has this 
 rather than some other character, since the very 
 problems which confront us in our everyday life, and 
 in our sciences and philosophy as well, arise out 
 
444 A TEXT-BOOK OF LOGIC 
 
 of the world's character as made known by human 
 observation. The facts about the world in which 
 we live, as these are observed and reported in in- 
 creasing numbers and with improving accuracy, 
 constitute the material of all human knowledge, and 
 if there are any further questions that arise, these 
 must concern the way in which such facts are con- 
 nected in the unity of an ordered system. Instead, 
 therefore, of conceiving the causal problem as an 
 inquiry into the reason why facts are what they 
 are, we must view it rather as demanding of us an 
 exposition of the nature of the connection that binds 
 the various parts of human experience together. 
 Put simply, the causal problem is concerned, not 
 with the question why things are what they are, 
 but with the question how things happen as they 
 do. 
 
 The Course of Our Further Discussion. Our fur- 
 ther study of the causal problem will bring before 
 us particularly three closely related questions. We 
 shall examine, in the first place, the time relations 
 of causal events; in the second place, the complex 
 character of such events will demand attention; 
 and in the third place, we must try to make clear 
 what is meant by the necessity that is always recog- 
 nised as belonging to such events. In our discussion 
 of each of these topics, we shall make Mill's 'treat- 
 ment, in Book III., Chapter V., of the Logic, our 
 point of departure. It will be advantageous, there- 
 fore, for the student to read the whole of Mill's 
 
CAUSATION 445 
 
 chapter in connection with the following para- 
 graphs. 
 
 The Time Relations of Causal Events. The first 
 characteristic of a causal relation that Mill enu- 
 merates is the 'invariable antecedence' of certain of 
 the factors involved in the causal relation. He says 
 that "invariability of succession is found by observa- 
 tion to obtain between every fact in nature and 
 some other fact which preceded it. ... The 
 invariable antecedent is termed the cause; the in- 
 variable consequent, the effect. And the universal 
 law of causation consists in this, that every conse- 
 quent is connected in this manner with some ante- 
 cedent or set of antecedents. . . . For every event 
 there exists some combination of objects or events, 
 some given concurrence of circumstances, positive 
 and negative, the occurrence of which is always 
 followed by that phenomenon." He points out that 
 we may not have discovered what the particular 
 concurrence of circumstances may be in a given 
 case, "but," he adds, "we never doubt that there is 
 such a one, and that it never occurs without having 
 the phenomenon in question as its effect or conse- 
 quence." 
 
 In this passage, Mill definitely raises the ques- 
 tion of the time relations of causal events. In lay- 
 ing emphasis on the antecedence of the cause, Mill 
 takes the view that for any event to be considered 
 as a cause at all, it must exist in time before the 
 event which is, or may be regarded as, its effect. 
 This, doubtless, is the conception of the time rela- 
 
446 A TEXT-BOOK OF LOGIC 
 
 tions of cause and effect that prevails generally at 
 the present day, and it may be worth while to ask 
 how far it is an accurate description of the facts 
 that are involved in causal events. There are, 
 without question, many examples of the causal rela- 
 tion that lend themselves quite naturally and easily 
 to this interpretation, examples, that is to say, in 
 which the fact that we call the cause and the fact 
 that we call the effect appear to be temporally dis- 
 tinct events. A blow on the head, for instance, may 
 be followed by the loss of consciousness, and 
 may be said to be the cause of the loss of con- 
 sciousness. The explosion of a powder magazine 
 may follow the application of a lighted match or 
 fuse to the powder. Diphtheria makes its appear- 
 ance ten days after the ingestion of the Klebs- 
 Loeffler bacillus which, the physicians tell us, is the 
 cause of the disease. In all these cases we have, or 
 seem to have, undoubted examples of the necessary 
 temporal priority of the cause, and the necessary 
 posteriority of the effect, in causally related phe- 
 nomena. It may be doubted, however, whether all 
 causally related events can be made to fall so easily 
 and naturally within this scheme or view. It would 
 be difficult, for example, to detect in the explanation 
 offered by the chemist of the formation of rust the 
 temporal discontinuity of cause and effect which is 
 an essential part of Mill's doctrine of causation. 
 Rust formation, so we are told, is due to the combi- 
 nation of iron with the free oxygen of the air; but, 
 if that is so, it is quite obvious that the chemical 
 
CAUSATION 447 
 
 combination of oxygen and iron does not precede, 
 but is contemporaneous with, the formation of rust 
 itself. There are innumerable instances of a similar 
 character, and we may even say that the example 
 chosen is typical of most of the chemical processes 
 with which we are at all familiar. The case is im- 
 portant because of the large field of application of 
 chemical laws, not only in the inorganic, but in the 
 organic world as well. To take only one such 
 example, we now know that bacterial action is 
 largely, if not wholly, due to the toxins generated 
 by microscopic organisms; and, if that is true, the 
 final explanation of their action and results is, as 
 is coming to be seen, a highly specialised branch of 
 the science of chemistry. If, as seems probable, the 
 results of bacterial action are not separable in time 
 from the production of their toxins, an overwhelm- 
 ing list of examples can be appealed to to throw 
 doubt on the necessary temporal antecedence and 
 consequence of the events involved in the causal 
 relation. 
 
 It is owing to some such considerations as these 
 that the position has sometimes been taken that 
 there is no distinction whatever between the cause 
 and the effect of a phenomenon, in other words, 
 that the cause and effect are identical. There seems 
 no sufficient reason in the nature of causal phe- 
 nomena why we should adopt so paradoxical a view. 
 Cause and effect do stand for distinct things in our 
 experience of causal events, and if, as we have said, 
 this distinction is not necessarily one of temporal 
 
448 A TEXT-BOOK OF LOGIC 
 
 discontinuity, we need to inquire further what the 
 distinction is. 
 
 When we say that the relation of cause and 
 effect is not necessarily one of antecedence and 
 consequence in time, we must not be understood to 
 affirm that causal phenomena have no relation at 
 all to time. That would be not only a paradox, but 
 exceedingly difficult to maintain. It is no doubt 
 true that all causal phenomena are events in time, 
 that they are constituted by a number of facts 
 which come before and after one another in a series. 
 That the whole number of facts in a causal phe- 
 nomenon have a definite sequence and order in time 
 there is no need to deny, and that the order and 
 sequence can be determined is the permanent ex- 
 pectation and belief of science. From this fact, 
 however, it does not follow that, within the series, 
 the cause and effect are separated by a necessary tem- 
 poral interval. What rather we seem warranted 
 in saying with respect to the causal series is that 
 their factors are continuous, temporal continuity, 
 not temporal discontinuity, seems to be the charac- 
 teristic of all such events. But whether within the 
 causal series the cause antedates the effect, or is 
 contemporaneous, at least in part, with it, as it 
 must be, for example, in the circular reactions of 
 chemistry, is a fact to be determined in the par- 
 ticular instance. But whatever may be true of any 
 particular instance, temporal discontinunity cannot 
 be regarded as an essential feature of the causal 
 relation. The utmost that we can say, from the 
 
CAUSATION 449 
 
 standpoint of their temporal relations, is that the 
 cause and effect are continuous with one another. 
 
 The Complex Character of Causal Events. It is 
 seldom, if ever, according to Mill, that an invariable 
 sequence subsists between a consequent and a single 
 antecedent. Usually, the causal relation exists 
 between "a consequent and the sum of several ante- 
 cedents ; the concurrence of all of them being requi- 
 site to produce, that is, to be certain of being fol- 
 lowed by, the consequent." If, for example, "a per- 
 son eats of a particular dish and dies in consequence, 
 that is, would not have died if he had not eaten of 
 it," the death is usually attributed to eating of the 
 dish although, as Mill points out, there were other 
 factors contributing to the result, such as the bodily 
 constitution of the individual, the particular state 
 of his health, and, perhaps, a certain state of the 
 atmosphere. These taken in conjunction with eat- 
 ing of the dish are, according to Mill's view, the 
 'invariable antecedent/ When we select one among 
 the antecedents of a phenomenon and call this the 
 cause, our selection, Mill says, falls generally on 
 the one which came last into existence. But, he also 
 points out, there is hardly any one among the num- 
 ber of antecedents that may not serve in this special 
 sense as the cause "according to the purpose of our 
 immediate discourse." This tendency "to associate 
 the idea of causation with the proximate antece- 
 dent event, rather than with any of the antecedent 
 states, or permanent facts, which may happen also 
 
450 A TEXT-BOOK OF LOGIC 
 
 
 to be conditions of the phenomenon," Mill regards 
 as not at all necessary to the common notion of 
 cause. The conclusion, then, at which he arrives 
 is that by a cause is meant "the sum total of the 
 conditions, positive and negative, taken together; 
 the whole of the contingencies of every description 
 which being realised, the consequent invariably fol- 
 lows. The negative conditions . . . may be all 
 summed up under one head, namely, the absence 
 of preventing or counteracting causes." 
 
 The essential contentions of Mill in this passage 
 are, first, that the antecedent of any fact is a com- 
 plex group of facts, and, second, that the cause, 
 popularly considered, is taken to be some one fact 
 among the antecedents selected arbitrarily or for 
 some special purpose. With regard to the first 
 point we may quote Jevons. He says : "By an ante- 
 cedent we mean any thing, condition, or circum- 
 stance which exists before or, it may be, at the same 
 time with an event or phenomenon. By a conse- 
 quent we mean any thing, circumstance, event, or 
 phenomenon, which is different from any of the 
 antecedents and follows after their conjunction or 
 putting together. It does not follow that an ante- 
 cedent is a cause, for the effect might have hap- 
 pened without it. Thus the sun's light may be an 
 antecedent to the burning of a house, but not the 
 cause, because the house would burn equally well 
 in the night; but a necessary or indispensable ante- 
 cedent is identical with a cause, being that without 
 which the event would not take place. . . . There 
 
CAUSATION 451 
 
 are usually many different things, conditions, or 
 circumstances necessary to the production of an 
 effect, and all of them must be considered causes 
 or necessary parts of the cause. Thus the cause 
 of the loud explosion in a gun is not simply the 
 pulling of the trigger, which is only the last appar- 
 ent cause or occasion of the explosion ; the qualities 
 of the powder, the proper form of the barrel, the 
 proper arrangement of the percussion-cap and pow- 
 der, the existence of the surrounding atmosphere, 
 are among the circumstances necessary to the loud 
 report of a gun ; any of them being absent it would 
 not have occurred." In this passage it may be 
 observed that what is popularly regarded as the 
 cause, the second point mentioned by Mill, Jevons 
 calls the occasion of the event, that is, that which, 
 in connection with the other necessary antecedent 
 or coexisting conditions, is effective in bringing 
 these latter into active operation. What Jevons 
 here speaks of as the occasion is sometimes called 
 the immediate cause, the other necessary attendant 
 circumstances being referred to as the conditions 
 or causal conditions of the event in question. 
 
 That the cause of any event is some complex 
 group of facts or circumstances is undoubtedly true. 
 Indeed, this seems to follow as a matter of necessity 
 from the general character of human experience. 
 As we have pointed out frequently, objects and 
 events are experienced by us, not as separate and 
 individual things, but as subsisting with other ob- 
 jects and events with which they are connected in 
 
452 A TEXT-BOOK OF LOGIC 
 
 a variety of ways. It is this feature of experience 
 that was said above to be the starting point of the 
 casual problem. Now it is no doubt true that within 
 any experienced complex we can, and in fact do, 
 isolate, by an act of discriminative attention, a 
 given fact or event which we regard, for reasons 
 special to the case, as the effect or result of other 
 perceived or discoverable facts, and that, in this 
 way, a certain uniqueness, a certain independence, 
 comes to be regarded as the distinguishing mark of 
 all effects whatever. But while no objection can be 
 brought against thus isolating an effect, since in this 
 way it is rendered more capable of exact descrip- 
 tion, and the particular causal relation that has to 
 be determined is made more capable of exact defi- 
 nition, a similar line of remark does not apply to 
 what we understand as a cause. For, in the first 
 place, it is only because what we call the effect 
 has a definite character that the search for a cause 
 becomes a problem at all. Unless the fact or event 
 of which we wished an explanation were made 
 definite, there would be no point of starting for the 
 establishment of a causal relation. It is owing to 
 the fact that some part of the experience of which 
 the effect is only a fragment remains indefinite that 
 the cause is characterised at first by an indeter- 
 minateness that would be quite fatal if it attached 
 to the effect. 
 
 But, not to press this point, we cannot be 
 sure, in the second place, that, in any particular 
 case, all the conditions which will make the oc- 
 
 
CAUSATION 453 
 
 currence of an effect intelligible fall within our 
 experience of that case. As we have seen above, 
 experimental and theoretical observation are val- 
 uable chiefly because they bring within experience 
 factors, material to our understanding of a phe- 
 nomenon, that are not included in our ordinary 
 perception of it. An example, usually cited, is the 
 discovery of the planet Neptune by Galileo in 1846. 
 The observed fact which led to its discovery was the 
 deviation of the planet Uranus from the course 
 determined for it by the attractive forces of the 
 sun, Jupiter, and Saturn. It was suggested, first 
 by Adams and later by LeVerrier, that this devia- 
 tion could be accounted for if we supposed that 
 some hitherto unknown body, situated external to 
 it in a particular position and at a given distance, 
 were affecting the movement of the planet. Such 
 a body, situated where Adams and LeVerrier had 
 suggested, was later discovered by Galileo, and 
 exists in our solar system as the planet Neptune. 
 In the third place, we may observe that, whether 
 all the factors necessary to a causal relation are or 
 are not parts of our ordinary perception of it, as 
 indeed the illustration just used is sufficient to show, 
 the effectiveness of any given fact, the planet 
 Neptune, for example, seems to depend as much 
 on its relations to other facts, the sun, Jupiter 
 and Saturn, as it does on its own existence. It 
 is no doubt true that if the fact, the planet Nep- 
 tune, did not exist, it could be neither a cause 
 nor any part of a cause ; but if it is a cause or part 
 
454 A TEXT-BOOK OF LOGIC 
 
 of a cause at all, it owes this character, not merely 
 to its existence, but also to the way it acts and is 
 acted upon by other facts in the system of facts in 
 which the effect, the course of Uranus, is in- 
 cluded as an important, and, indeed, a necessary ele- 
 ment. To take another illustration, we cannot re- 
 gard death as the result of a gun shot, poison, or 
 any other single fact, but as the result of a net- 
 work of facts which includes the gun shot or what 
 not in a system which extends to and embraces the 
 stated effect. From this point of view, it is evident 
 that the problem of causation is one in which, start- 
 ing with some fact or event, we endeavour to build 
 up by observation and experiment a system of facts 
 within which the fact or event with which we 
 started is necessarily included. Causes, conse- 
 quently, must always be complex, and the difficulty 
 of determining causes is the difficulty of including 
 within the system only those factors that are mate- 
 rial to it. 
 
 Few words are necessary to make our position 
 clear on the second point raised by Mill, namely, the 
 importance usually given to one of the conditions 
 of an event and naming this the cause. Prac- 
 tically, as Mill pointed out, the fact selected is 
 usually the one which is nearest in time to the effect. 
 But, as we have seen, the immediate temporal ante- 
 cedence of the cause is not necessarily an essential 
 feature of the causal relation. What rather, even for 
 the practical view, is needed is the selection of an 
 agent on which reliance can be placed to bring about 
 
CAUSATION 455 
 
 the desired result. Certainty as to the cause seems 
 to be the desideratum, whether the causal factor is 
 the immediate temporal antecedent of the effect or 
 not. When, for example, we wish to rid the prem- 
 ises of rats, to borrow an illustration, we may 
 choose either traps, strychnine, phosphorus, or ter- 
 riers, and doubtless the one selected will be the one 
 that, under the circumstances, is regarded as most 
 efficient. And by efficient, in this connection, we 
 mean the one that, with due regard to the circum- 
 stances of the case, realises best the purpose for 
 which it is chosen. Now when the purposes, for 
 the satisfaction of which causal relations are sought, 
 become specialised as they do in science, when, 
 that is, they are directed toward the attainment of 
 knowledge, and not toward the improvement of the 
 material conditions of life, the situation, so far as 
 the causal relation is concerned, is not greatly dif- 
 ferent, for in science the search for a cause is 
 determined by a purpose which the ascertainment 
 of the cause itself is expected to satisfy. In the 
 field of science, as was pointed out before, the pur- 
 pose that directs an inquiry does not lie outside of, 
 but is one with, the attainment of scientific truth. 
 In this the chief difference between the theoretical 
 and practical life is to be found. But when we have 
 said that, it remains true that the conditions of 
 knowledge are more rigid than those of practice, 
 and the goal of inquiry requires more strict defini- 
 tion. Hence we find that what passes for a cause in 
 practical life may seem, from the scientific point of 
 
456 A TEXT-BOOK OF LOGIC 
 
 view, altogether inadequate, if not false, and, con- 
 sequently, that a more thorough analysis of the 
 antecedent and concurrent circumstances has to be 
 undertaken if the end of scientific truth is to be 
 reached. Now, whether or not, for the purpose of 
 science, all or only part of the circumstances and 
 conditions of an event are included in its cause will 
 depend on the particular and immediate purpose it 
 is intended to satisfy. No doubt, the ultimate goal 
 of science is to discover laws of connection which 
 are capable of extension to other than the observed 
 phenomena, but, at the same time, we should observe 
 that it can reach this end only by the determination 
 of the particular connections of one empirical event 
 with another in human experience. But even in 
 this more restricted field of scientific effort, a cer- 
 tain rigid demand is usually made and observed, 
 namely, that all and only those factors which can 
 be regarded as essential conditions of a fact or 
 event should be enumerated as its cause. It is only 
 when there is a lapse from strict scientific precision 
 that any thing less is possible ; and even when such 
 lapse takes place, the scientist feels himself obliged 
 to fill out, on demand, the scantier statement by 
 restoring all the enumerated elements that are of 
 material importance to our understanding of the 
 case. 
 
 The Necessity of Causal Events. The two fac- 
 tors of Mill's view of Causation that we have con- 
 sidered are, first, that causes are invariable ante- 
 cedents of the facts or events we call effects, ani 
 
CAUSATION 457 
 
 second, that causes are always complex groups of 
 fact, the sum total of conditions, as Mill says, 
 requisite to bring the effect into existence. There 
 is still a third factor to which we may now give 
 attention, a factor, it would seem, that occupies, in 
 Mill's total view, a place which gives it a peculiarly 
 special prominence. For, according to Mill, you 
 may have a sequence displaying the features of com- 
 plexity and invariability and not have one that is 
 definitely causal. That is to say, B may have fol- 
 lowed A invariably in our experience, and yet the 
 ground or cause of the sequence A-B may really 
 not be in A at all. The illustration, borrowed from 
 Reid, that Mill uses is the sequence of night and 
 day, in neither of which can the cause of the other 
 be found, although there is no doubt that the em- 
 pirical connection extends throughout human expe- 
 rience. Some other factor, therefore, is required 
 to complete the idea of cause, for, as Mill says, "it 
 is necessary to our using the word cause that we 
 should believe not only that the antecedent always 
 has been followed by the consequent, but that as 
 long as the present constitution of things endures 
 it always will be so." Unless the sequence can also 
 be regarded as 'unconditional,' we are not war- 
 ranted, by Mill's view, in considering it to be caus- 
 ally determined. "This is what writers mean when 
 they say that the notion of cause involves the idea 
 of necessity. . . . That which is necessary, that 
 which must be, means that which will be, whatever 
 supposition we may make in regard to all other 
 
458 A TEXT-BOOK OF LOGIC 
 
 things. . . . That which will be followed by a 
 given consequence when, and only when, some third 
 circumstance also exists, is not the cause, even 
 though no case should ever have occurred in which 
 the phenomenon took place without it. Invariable 
 sequence, therefore, is not synonymous with caus- 
 ation, unless the sequence besides being invariable, 
 is unconditional." 
 
 It will be seen, at once, that in this statement, 
 and only here, do we come, in Mill's view, face to 
 face with the question, crucial for our comprehen- 
 sion of causal relations, of what we must mean 
 when we say that one event is necessarily connected 
 with another. Now it should be remarked that this 
 statement of Mill's raises questions which for their 
 adequate discussion would require us to go outside 
 the limits of inductive logic into the field of general 
 metaphysics ; and this is true, not only for a student 
 of the theory Mill proposes, but it is admitted as 
 necessarily so by Mill himself. For, as he says, it is 
 only so long as we can believe that the "present 
 constitution of things endures," only so long, that 
 is, as "the ultimate laws of nature (whatever they 
 may be) as distinguished from the derivative laws 
 and the collocations" remain unchanged, that what 
 happens in experience can become a clue to what 
 is true outside experience. In other words, it is 
 only so long as the nature of reality is and remains 
 what it is that we can argue from what has been 
 to what will be in human experience. But the 
 determination of the nature of reality, and of the 
 
CAUSATION 459 
 
 relation that we as thinking and active individuals 
 sustain toward it, is the definite problem of meta- 
 physics, and only indirectly does this problem come 
 into view in the discussion of logical questions. But 
 even incidentally it is worth while to remark that 
 the relation of logic to metaphysics that the position 
 of Mill raises is such that, unless we can presuppose 
 an ordered system of reality of some sort, our con- 
 fidence in human knowledge is ultimately shaken, 
 and the distinction between truth and error to a 
 large extent is obliterated. For, as we have seen 
 throughout, the nerve of human knowledge is to be 
 found in the confidence we have that in all science 
 and philosophy, and, we should say, in all art and 
 religion as well, we are interpreting, not the empty 
 shadows of a merely temporal experience, but the 
 real nature of the world which is not only the sub- 
 stance of all our knowing, but the very centre and 
 core of the being which we as individuals possess. 
 
 Turning, now, from these rather abstruce con- 
 siderations, we must try to interpret Mill's position 
 with respect to its logical implications. In order 
 that we may understand exactly what Mill had in 
 mind to say, it will be necessary to gain and secure 
 a correct notion of the term in which he translates 
 the necessity that belongs, as he and Hume before 
 him admit, to our notion of cause. According to Mill, 
 the necessity that we ascribe to a causal sequence 
 has its foundation in the unconditional character 
 of the causal sequence. What, then, does Mill mean 
 by unconditional? The meaning that Mill attaches, 
 
460 A TEXT-BOOK OF LOGIC 
 
 in a general way, to this word is perhaps not diffi- 
 cult to detect, although he does not state definitely 
 the sense in which it is understood. Most of his 
 statements about it are negative. He says, for in- 
 stance, that "that which will be followed by a given 
 consequent when, and only when, some third cir- 
 cumstance exists, is not the cause," the meaning 
 evidently being that it is a cause only when the 
 consequent follows without such mediation. And, 
 again, he says that "if we adopt the convenient 
 modification of the meaning of the word cause which 
 confines it to the assemblage of positive conditions 
 without the negative, then instead of "uncondition- 
 ally," we must say, "subject to no other than neg- 
 ative conditions," where, again, the absence of some 
 third circumstance is necessary for determining an 
 unconditional sequence. The point that Mill seems 
 to make is that a sequence is unconditional when the 
 consequent is seen to follow from the totality of 
 conditions which constitute its cause, without any 
 aid from any other circumstance which falls outside 
 its cause as thus determined. 
 
 Two remarks may help to make the meaning of 
 this statement clearer. In the first place, Mill's 
 view leaves out of account, as indeed it has a right 
 to, such metaphysical considerations as were re- 
 ferred to a little while ago. However impossible 
 such a procedure would be if Mill were discussing 
 the causal problem from the standpoint of the phil- 
 osophy of knowledge, it is quite possible and even 
 necessary when he is concerned merely with the 
 
CAUSATION 461 
 
 invariable connections that are built up in the course 
 of human experience. The denial, therefore, that 
 any "third circumstance" operates in an uncondi- 
 tional sequence cannot be meant, by Mill, to refer 
 to the "constitution of things" which, as we saw, 
 is in some sort the foundation on which all human 
 knowledge in the long run depends. In the second 
 place, we may remark that the "third circumstance," 
 on the absence of which from any sequence the 
 unconditionality of the cause is determined, must be 
 interpreted to mean some third phenomenal circum- 
 stance, some further fact or event of human expe- 
 rience the same in kind as those that enter into the 
 causal relation. What this statement amounts to 
 is the declaration that whenever any causal se- 
 quence has been determined, it will be found to 
 include all those positive factors on which the occur- 
 rence of the phenomenon depends, and that it is 
 only when all such factors are present that the 
 sequence is necessary, or, in Mill's term, uncondi- 
 tional. It may help to bring out the significance of 
 such a statement if we say that when the stated 
 conditions are satisfied in any given case, we can 
 argue not only from the occurrence of the cause to 
 the occurrence of the effect, but also from the occur- 
 rence of the effect to the occurrence of the cause. 
 The presence of either the cause or effect necssarily 
 implies the presence also of the effect or the cause. 
 The Plurality of Causes. In view of the fact that 
 the aim of science is to point out a connection be- 
 tween a particular event and the totality of condi- 
 
462 A TEXT-BOOK OF LOGIC 
 
 tions on the presence of which the event takes place, 
 and on the absence of which it does not take place, 
 we may ask how this conception of the aim of 
 science is affected by the fact that the same event 
 may occur for very different reasons. Now about 
 such a fact there is no qusetion. It was fully recog- 
 nised, for instance, by Mill who tersely remarks 
 that "it is not true that the same phenomenon is 
 always produced by the same cause." The fact, 
 then, is that an event M may be caused now by A, 
 and, again, by B or C or D. This fact is known, in 
 the terminology of Mill, as the plurality of causes. 
 What effect, we may ask, does the recognition of 
 such a plurality of causes have upon our view of 
 the nature of causation as expounded in the pre- 
 ceding paragraphs? 
 
 If we consider this question strictly from the 
 point of view of what we have seen the relations 
 between cause and effect in a causal sequence must 
 be, it is obvious that we can not regard those events 
 whose occurrence depends on a possible plurality of 
 antecedents as causally related events at all. It 
 was said just now that in a causal sequence we must 
 be able, not only to argue from the occurrence of 
 the antecedent to that of the consequent, but also 
 to argue from the occurrence of the consequent to 
 that of the antecedent. Now the significance of 
 such a connection between antecedent and conse- 
 quent in a causal sequence is that it goes far beyond 
 what, in an earlier chapter, we saw was formally 
 possible when we were considering merely hypo- 
 
CAUSATION 463 
 
 thetical statements of fact. The rule concerning 
 hypothetical statements, 'If A then B' for example, 
 made it clear that from the occurrence of B we 
 could say nothing with respect to the occurrence 
 of A, and the reason assigned was that B might 
 have occurred for some other reason than A. In 
 other words, we had to recognise the possibility of 
 what Mill calls the plurality of causes. Now the 
 necessity for such a rule for dealing with the facts 
 of our general experience is quite obvious when we 
 consider that, with the development of science, there 
 has come to be recognised a marked difference be- 
 tween empirically connected events and causally 
 related events, and, consequently that until the 
 causal character of a particular sequence has been 
 established, we cannot be certain that one rather 
 than another group of possible antecedent condi- 
 tions, as a matter of fact, has been the occasion of 
 any given consequent. 
 
 We may also point out that the recognition of a 
 plurality of causes, if we emphasise the word cause 
 in Mill's phrase, would necessarily throw our whole 
 conception of cause into confusion, and there would 
 remain for us no means of distinguishing between 
 those events which were really connected 'as cause 
 and effect, and those whose connections depended, 
 in MilPs words, on some "third circumstance," 
 events, that is to say, which are connected merely 
 after the manner of an empirical juxtaposition. 
 The distinction between causal sequences and em- 
 pirical ones is important, it marks one of the gains 
 
464 A TEXT-BOOK OF LOGIC 
 
 that have been acquired as the result of much 
 labour, and it serves the distinctive purpose of map- 
 ping out the fields with respect to which we may 
 claim to have different degrees of knowledge. It 
 is certainly true, for instance, that the inferences 
 drawn from our ordinary experience are enter- 
 tained much less confidently than are those that 
 rest on the foundation of a scientific induction. In 
 the latter case alone do we have certainty; in the 
 former, we reach only a higher or lower degree of 
 probability. And the difference between certainty 
 and probability rests, in part at least, on the fact 
 that in the case of certain knowledge all the factors 
 material to it are known, and in the case of prob- 
 ability we have no reason for believing that this 
 requirement has been satisfied. And this statement 
 enables us to see why it is that analysis plays so 
 large a part in the method not only of the sciences 
 but of philosophy as well, and why it is that, from 
 the times of the Greeks, the distinction, based on the 
 application of a method of analysis to the facts of 
 experience, between opinion and knowledge, be- 
 tween the popular beliefs of an age on the one hand, 
 and carefully established truths on the other, has 
 been regarded as a condition of intellectual culture 
 and progress. We cannot, therefore, entertain any 
 suggestion of treating the two classes of connection, 
 the causal and the empirical, as if no distinction had 
 been made between them, and we cannot do so be- 
 cause all scientific advancement depends on it, and 
 
CAUSATION 465 
 
 because it would leave us without any adequate 
 conception of what we should mean by a cause. 
 
 The result of our consideration of the conception 
 of a plurality of causes amounts to this, that when 
 we look at the conception from the standpoint of a 
 carefully stated view of what causation implies, it 
 seems to be a quite misleading, if not mischievous, 
 conception. But, it may be objected, this result can 
 be reached and maintained only if we allow a some- 
 what strict interpretation of the causal relation to 
 determine the view we take as to the possibility of a 
 plurality of causes. That is exactly true. But the 
 recognition of its truth does not require us to alter 
 our notion of the causal relation, but to indicate the 
 field within which the operation of more than a 
 single set of antecedents as a condition of the occur- 
 ,rence of a given fact or event may be said to occur. 
 What we have seen is that the field of causally estab- 
 lished relations is not such a field. For science in the 
 strict sense of that term there is only one group of 
 conditions that can be inferred from the occurrence 
 of any given event. But when we remark that, as 
 compared with the broad extent of our ordinary 
 experience, the causal field is only a very small 
 area, we see at once that, when we go outside this 
 field, there must be possible some other than a 
 causal interpretation of the sequences that occur. 
 It follows, therefore, that we must go outside the 
 field of the natural sciences if, looking at our expe- 
 riences from the standpoint of their temporal rela- 
 
466 A TEXT-BOOK OF LOGIC 
 
 tions, we wish to emphasise and illustrate the possi- 
 bility and nature of a plurality of causes. Nowhere, 
 except in the sciences, can we argue from conse- 
 quent to antecedent. The relations of antecedent 
 and consequent, therefore, that occur in our ordi- 
 nary experience, are not, in the strict sense, causal 
 relations at all. And because they are not, it seems 
 altogether misleading to speak of these relations as 
 involving a plurality of causes. What a discussion 
 of the possibility of a plurality of causes forces on 
 us is, then, the recognition of a type of experience 
 which implies no more than a plurality of ante- 
 cedent or concurrent conditions. To call these con- 
 ditions, in their relation to the event with which 
 they are connected in our experience, causal is to 
 go beyond what we know about them; for, as we 
 have said, the test of a causal relation is that we 
 can argue, not only from a given set of conditions 
 to the conditioned, but also from the conditioned 
 to a particular set of conditions. It is exactly the 
 impossibility of doing this latter that led Mill, in 
 the class of cases we are now considering, to speak 
 of a pluarlity of causes, and which leads us to speak 
 of a plurality of conditions. If, by our terminology, 
 we can keep clearly before ourselves the fact that 
 the relations which we are now considering are not 
 causal, in the strict sense of that word, but that they 
 are connected empirically merely in our experience, 
 it will be passible to set over against each other the 
 two types of experience, and to entertain the prob- 
 lem, which the non-causal relations certainly sug- 
 
CAUSATION 467 
 
 gest, whether these latter can all be reduced to a 
 single causal type. Although it takes us outside the 
 limits of our present inquiry, we may hazard the 
 remark that perhaps human life and experience are 
 too rich and complex to be capable of interpretation 
 throughout in terms of any single class of relations. 
 
 REFERENCES 
 
 H. A. Aikins, The Problem of Logic, Chs. XXVI., XXVII., 
 XXVIII., XXIX. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
 XVI., XVII. 
 
 J. G. Hibben, Logic, Deductive and Inductive, Chs. IV., V., 
 VI., VII., VIII., IX., X. 
 
 W. S. Jevons, Elementary Lessons in Logic, Lessons XXVIII., 
 XXIX. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. IX. 
 
 W. Minto, Logic, Inductive and Deductive, Chs. III., IV., V., 
 VI., VII. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Chs. 
 XIV., XVI. 
 
 W. J. Taylor, Elementary Logic, Ch. XVII. 
 
 ADVANCED 
 
 B. Bosanquet, Logic, Vol. I., Book I., Ch. VII. 
 
 F. H. Bradley, The Principles of Logic, Book. II., Part II., 
 
 Ch. III., Book III., Part II., Ch. II. 
 W. R. B. Gibson, The Problem of Logic, Chs. XLII., XLIV., 
 
 XLV., XLVI. 
 H. W. B. Joseph, An Introduction of Logic, Chs. XIX., XX., 
 
 XXII. 
 J. S. Mill, A System of Logic, Book III., Chs. V., VI., VIII., 
 
 IX., X., V. 
 
468 A TEXT-BOOK OF LOGIC 
 
 F. C. S. Schiller, Formal Logic, Chs. XX., XXI. 
 J. Venn, Empirical Logic, Ch. XVII. 
 
 J. Welton, A Manual of Logic, Vol. II., Book V., Chs. I., 
 143, 144, V., 155. 
 
 QUESTIONS 
 
 1. In what general fact of observation does the problem of 
 causation originate? 
 
 2. How, in view of this fact, may the causal problem be 
 stated? 
 
 3. Explain what is meant by saying that the causal prob- 
 lem is practical before it is theoretical. Illustrate. 
 
 4. In what way does the practical aspect of the problem of 
 causation tend to develop human intelligence? 
 
 5. Describe as accurately as you can the precise nature of 
 the regularities in experience which we are led to ob- 
 serve from the practical point of view. 
 
 6. In what two respects does the theoretical differ from the 
 practical view of causation, and what advantages are 
 thereby secured? 
 
 7. State and illustrate Mill's criticism of the practical and 
 theoretical conceptions of cause. 
 
 8. Show, by means of illustrations, that the practical and 
 theoretical conceptions of cause are genetically related. 
 
 9. In what way has the theoretical notion of cause reacted 
 upon the practical to give it a more definite and extended 
 meaning? 
 
 10. What is meant by saying that the causal problem arises 
 from the importance of order in human experience? 
 
 11. 'The causal problem is concerned with the question of 
 how things happen as they do.' Explain. 
 
 12. What, according to Mill, is the first characteristic of a 
 causal relation? 
 
 13. What is meant by the time relations of causal events? 
 
 14. How far do you agree with Mill that the cause of an 
 event is its invariable antecedent? 
 
CAUSATION 469 
 
 15. What can you say with respect to the view that there 
 is no essential difference between a cause and an effect. 
 
 16. Explain what is meant by the temporal continuity of 
 causal events. 
 
 17. What, according to Mill, is the second characteristic of 
 causal relations, and to what two facts of importance 
 does it direct attention? 
 
 18. What does Jevons mean by the occasion of an event as 
 contrasted with its cause? What other term is some- 
 times used for Jevons' 'occasion'? 
 
 19. Give three reasons for emphasising the complex charac- 
 ter of causes. 
 
 20. What can be said for and against selecting one of the 
 conditions of an event and calling that the cause? 
 
 21. In what way would your answer to the previous ques- 
 tion be affected by the consideration that one's interest 
 in the causal relation is practical and not theoretical? 
 
 22. What, according to Mill, is the third characteristic of 
 causal relations? 
 
 23. Does Mill recognise the 'necessity' of causal relations, 
 and, if so, what does he mean by necessity? 
 
 24. Does Mill's view of causation imply an appeal to meta- 
 physics, and, if so, in what respect? 
 
 25. Explain what Mill means by unconditional. 
 
 26. Is it possible, on Mill's view of causation, to argue from 
 the occurrence of an effect to that of the cause? 
 
 27. What is meant by the plurality of causes? 
 
 28. If in any particular instance we admit a possible plu- 
 rality of causes, how does that admission affect our con- 
 ception of its strictly causal character? 
 
 29. What is the difference between causally and hypothet- 
 ically connected series of events? 
 
 80. Why would it be preferable to speak of a plurality of 
 eonditions instead of a plurality of causes? 
 
470 A TEXT-BOOK OF LOGIC 
 
 EXERCISES 
 
 1. Enumerate six instances of regularity in the order of 
 particular events which are of importance for the prac- 
 tical life. 
 
 2. Develop, from the theoretical point of view, the in- 
 stances mentioned in your answer to the previous ques- 
 tion in order to show to what question of scientific in- 
 terest each may lead. 
 
 3. Examine six instances of scientific causation for the 
 purpose of showing how each satisfies the three condi- 
 tions of a cause mentioned in the text. 
 
 4. Examine the following and show in what respects they 
 are, and in what respects they are not, statements of 
 strictly causal relations. 
 
 (1) In myexperience A has been invariably preceded 
 by B, and we may therefore conclude that B is 
 the cause of A. 
 
 (2) Scarlet poppies, scarlet verbenas, the scarlet haw- 
 thorne and honeysuckle are all odourless, there- 
 fore we may conclude that all scarlet flowers are 
 destitute of odour. 
 
 6. Mention six instances which illustrate, what Mill calls, 
 a plurality of causes. State for each instance the pos- 
 sible causes. 
 
CHAPTER XVII 
 
 MILL'S EXPERIMENTAL METHODS 
 
 Their Historical Position. The publication of 
 Mill's System of Logic in 1843 gave, no doubt, a 
 great impetus to the study of what is commonly 
 known as inductive logic, and especially to the con- 
 sideration of the principles that underlie the meth- 
 ods by which, in the several sciences, causal relations 
 are determined. Prior to Mill, however, interest in 
 the inductive inquiry had had a somewhat long his- 
 tory, and the reader will find in Minto's Logic (pp. 
 243-272) an account of the course that this interest 
 took from the time of the Franciscan monk, Roger 
 Bacon (1214-1292), to the modern era which was 
 ushered in, and whose development was determined 
 by the progress of experimental science. That the 
 advancement of learning, of which Francis Bacon 
 (1561-1626) may be taken as the modern herald, 
 should have maintained itself successfully for over 
 two centuries, and that during that period natural 
 science should have extended its scope as well as 
 secured its position, could not be without its in- 
 fluence upon the conception that was held of the 
 nature and value of logical inquiries. In the pres- 
 ence of such a solid body of achievement as came 
 rapidly to the credit of the natural sciences, it was 
 inevitable that interest should be aroused in the 
 methods by which such results were gained. Con- 
 
 (471) 
 
472 A TEXT-BOOK OF LOGIC 
 
 sequently, we find that men of learning in this 
 period gave considerable attention to the study of 
 scientific methods, and in the first half of the nine- 
 teenth century HerscheFs discourse On the Study 
 of Natural Philosophy, (1831), and Whewell's two 
 large volumes on the History of the Inductive Sci- 
 ences, (1837), and his Philosophy of the Inductive 
 Sciences, (1840), stand out prominently as contri- 
 butions of capital importance to our understanding 
 of the inductive procedure. Based as they are upon 
 the facts of experimental science, and containing a 
 description and analysis of the methods by which 
 conclusions had been reached in the sciences, they 
 constitute a repository of great value for any one 
 who would study the theory of inductive science. 
 With these books before him, Mill set out in his 
 Logic, as he says, to "generalise the modes of inves- 
 tigating truth and estimating evidence, by which so 
 many important and recondite laws of nature have, 
 in the various sciences, been aggregated to the 
 stock of human knowledge." In the chapter on The 
 Four Methods of Experimental Inquiry/ Mill gives 
 an account of the various ways in which causal 
 relations are or may be determined. In what fol- 
 lows, we propose to describe these methods briefly, 
 and shall limit ourselves chiefly to the task of stating 
 and illustrating them. To determine the view that 
 Mill took of them as a whole, or to estimate their 
 value in detail, falls outside the scope of an elemen- 
 tary study of logical problems. 
 
MILL'S EXPERIMENTAL METHODS 473 
 
 The Nature of the Problem to which these Methods 
 Apply. In the foregoing chapter, we have seen that 
 the causal relation, strictly interpreted, is reciprocal, 
 that is, it is a relation between phenomena of such 
 a kind that from the presence or absence of either 
 term of the relation we can argue to the presence 
 or absence of the other. The rise and fall of the 
 mercury in a thermometer, for example, are recip- 
 rocally related to the varying degrees of tempera- 
 ture. To the establishment of such relations the 
 sciences doubtless aspire in their investigation of 
 the processes of nature. And that a considerable 
 degree of success in this particular has been achieved 
 in those sciences, such as physics and astronomy, 
 which rest upon a mathematical foundation is suffi- 
 cient to suggest, to those who are interested in the 
 logic of the sciences, an inquiry to which the meth- 
 ods of Mill are the direct answer. Mill's methods, in 
 other words, are a statement of the processes which 
 have been found useful in the establishment of those 
 causal relations in which the antecedent and conse- 
 quent reciprocally imply each other. But since recip- 
 rocal relations have not been established between 
 the antecedent and the consequent of all known 
 phenomena, we should be putting an unnecessary 
 strain upon these methods if we did not regard them 
 as applying, in the strict sense, only to those special 
 cases in which a relation of the kind in question 
 had been determined. We may also remark that 
 these methods are not offered by Mill as a substitute 
 for the specialised modes of investigation which are 
 
474 A TEXT-BOOK OF LOGIC 
 
 developed by each special science according to its 
 needs. Indeed, the methods are quite general in 
 nature, and could not have been formulated had not 
 relations of the kind they imply been already suc- 
 cessfully established. They must be understood, 
 therefore, as revealing the logic of causal inquiries, 
 when these inquiries have led to the determination 
 of reciprocal relations between causes and effects. 
 
 Elimination as a Method of Causal Inquiry. We 
 have just seen that Mill's methods aim to state the 
 general modes of procedure in those instances in 
 which reciprocal causal relations have been estab- 
 lished. In the light of this statement, it might seem 
 superfluous to ask whether the causal inquiry rests 
 upon the process of eliminating from the cause, or 
 effect, those data whose presence or absence from a 
 phenomenon makes no difference either to its occur- 
 rence or non-occurrence. This is, indeed, the posi- 
 tion that we should be inclined to adopt were it not 
 for the fact that a difference of opinion exists as to 
 whether, and in what sense, the methods, as Mill 
 expounds them, depend upon such process of 
 elimination. 
 
 Joseph, for example, takes the view that "the 
 causal circumstances are indicated by a process of 
 exhaustive elimination." His position, more fully 
 stated, is that, in view of the nature of causal rela- 
 tions, certain particular requirements must be satis- 
 fied by any instance which claims to involve a causal 
 relation, and that the failure to satisfy any one of 
 these requirements disproves that relation between 
 two given phenomena. These requirements he enu- 
 
MILL'S EXPERIMENTAL METHODS 475 
 
 merates as grounds of elimination, and are as fol- 
 lows: 
 
 1. Nothing is the cause of a phenomenon in the 
 absence of which it nevertheless occurs. 
 
 2. Nothing is the cause of a phenomenon in the 
 presence of which it nevertheless fails to occur. 
 
 3. Nothing is the cause of a phenomenon which 
 varies when it is constant, or is constant when it 
 varies, or varies in no proportionate manner with it. 
 
 4. Nothing is the cause of a phenomenon which 
 is known to be the cause of a different phenomenon. 
 
 These grounds of elimination are said by Joseph 
 to be the foundations of Mill's inductive methods. 
 The first is the foundation of the Method of Agree- 
 ment ; the second, of the Method of Difference ; the 
 first and second combined, of the Joint Method of 
 Agreement and difference; the third, of the Method 
 of Concomitant Variations; and the fourth, of the 
 Method of Residues. It thus comes about, according 
 to Joseph, that "Mill has not formulated four (or 
 five) but one "Method of Experimental Inquiry" 
 ... of which the essence is that you establish 
 a particular hypothesis about the cause of a phe- 
 nomenon by showing that, consitently with the 
 nature of the relation of cause and effect, the facts 
 do not permit you to regard it as the effect of any- 
 thing else (and mutatis mutandis if you are inquir- 
 ing into the effect of anything) ." Thus if I know 
 that S must be caused by L or M or P or Q, because 
 these are the instances in which the phenomenon 
 occurs, then by testing each instance by the canons 
 
476 A TEXT-BOOK OF LOGIC 
 
 of elimination I am able to discover the one rela- 
 tion in which S stands that is reciprocally causal. 
 
 Against this position Gibson argues that there 
 is in Joseph's account a confusion between physical 
 and logical elimination, and that when Mill speaks 
 of the Methods of Agreement and Difference as 
 methods of elimination he must be understood to 
 mean the former and not the latter kind of elimina- 
 tion. The meaning of this contention is quite clear 
 if by physical elimination is understood the method 
 of excluding from a phenomenon certain elements 
 which are found not to have an effect upon the occur- 
 rence or non-occurrence of the phenomenon. By 
 logical elimination, on the other hand, is meant the 
 rejection of certain hypotheses as, for example, 
 some of the alternatives in a disjunctive proposi- 
 tion with respect to the causal connection. In 
 this case, we are rejecting the non-causes as a 
 means of discovering the true causes. There is a 
 certain presumption in favour of Gibson's conten- 
 tion, for Mill himself says that elimination is a term 
 "well suited to express the operation . . . which 
 has been understood since the time of Bacon to be 
 the foundation of experimental inquiry namely, 
 the successive exclusion of the various circumstances 
 which are found to accompany a phenomenon in a 
 given instance, in order to ascertain what are those 
 among them which can be absent consistently with 
 the existence of the phenomenon." But whether 
 any or all of Mill's Methods are based upon a single 
 type of elimination can be decided only by exam- 
 
MILL'S EXPERIMENTAL METHODS 477 
 
 ining the methods themselves. For the present, it is 
 enough to have stated the nature of the difference 
 between the views that are held of the relation of 
 elimination to the Methods that we are about to 
 study. 
 
 The Method of Agreement. Mill states the prin- 
 ciple upon which this Method rests as follows: 
 If two or more instances of the phenomenon under 
 investigation have only one circumstance in common, 
 the circumstance in which alone all the instances agree 
 is the cause (or effect) of the given phenomenon. 
 The requirement that the instances in question 
 shall have only one circumstance in common can not 
 be satisfied unless all the other circumstances that 
 are relevant to the phenomenon are different. Not 
 any enumeration of instances, therefore, would sat- 
 isfy the conditions of this Method, but only one in 
 which all the instances, however much they may 
 differ from one another, are alike in only a single 
 particular. When, then, two or more instances of a 
 phenomenon are shown to have only one circum- 
 stance in common, that circumstance, according to 
 Mill, is the cause or the effect of the phenomenon. For 
 this reason, the Method has been called the Method 
 of Single Agreement, and is formulated by Jevons 
 as follows : The sole invariable antecedent of a phe- 
 nomenon is probably its cause. An illustration bor- 
 rowed from Bain, may be given. "The North-East 
 wind," Bain writes, "is generally detested in this 
 country ; as long as it blows, few people are at their 
 best. Occasional well known causes of a wind being 
 
478 A TEXT-BOOK OF LOGIC 
 
 injurious are violence, excessive heat or cold, ex- 
 cessive dryness or moisture, electrical condition, the 
 being laden with dust or exhalations. Let the hypo- 
 thesis be that the last is the cause of the North- 
 East wind's unwholesome quality; since we know 
 it is a ground current setting from the pole toward 
 the equator and bent westward by the rotation of 
 the earth; so that, reaching us over thousands of 
 miles of land, it may well be fraught with dust, 
 effluvia, and microbes. Now, examining many 
 cases of North-East wind, we find that this is the 
 only circumstance in which all the instances agree; 
 for it is sometimes cold, sometimes hot; generally 
 dry ; but sometimes wet ; sometimes light, sometimes 
 violent; and of all electrical conditions. Each of 
 the other circumstances, then, can be omitted with- 
 out the North-East wind ceasing to be noxious ; but 
 one circumstance is never absent namely, that it 
 is a ground current. That circumstance, therefore, 
 is probably the cause of its injuriousness." 
 
 It will be observed from this illustration that the 
 Method is essentially a method of elimination; its 
 use depends upon the possibility of analysing the 
 phenomenon into its constituent parts, and of select- 
 ing from among them the one that is causal. It is 
 evident, therefore, that the method cannot begin to 
 be put into operation until we have before us at 
 least two instances of the phenomenon, and that 
 the reliability of the Method is much increased with 
 an increase in the number and variety of the in- 
 staces that are examined. In view of such facts 
 
MILL'S EXPERIMENTAL METHODS 479 
 
 as these, Mellone has formulated the method as 
 follows: When observation shows that two events 
 accompany one another (either simultaneously or in 
 succession), it is probable that they are causally con- 
 nected; and the probability increases with the number 
 and variety of the instances. 
 
 When this Method speaks of causes as single 
 antecedents, it is evident that it presupposes that 
 the phenomenon under investigation has been sub- 
 jected to analysis, and that in this way its elements 
 have been distinguished. Now, with respect to the 
 supposition that causes are to be discovered among 
 the elements into which the phenomenon is anal- 
 ysed, there are two question to be asked. The first 
 is, are we certain, in view of the inter-connection 
 of all parts of the known universe, that single events 
 ever do act in isolation from all the rest? But not 
 to press the point in that form, are we certain that 
 within particular universes, that is, with reference 
 to particular groups of events, we can analyse a 
 point for point concomitance between causes and 
 effects? For instance, is the "ground current" of 
 the illustration used above, on any supposition, a 
 single antecedent? Is it not merely another name 
 for "dust, effluvia, and microbes"? If, however, it 
 be replied that the object of science is to establish 
 causal connections between single antecedents and 
 consequents, we may ask, in the second place, 
 whether there exists any means of assuring our- 
 selves that the analysis of a particular phenomenon, 
 however complete it may seem, has succeeded in 
 
480 A TEXT-BOOK OF LOGIC 
 
 detecting all of the factors present in the event that 
 we call its cause? For a long time, for example, 
 air was regarded as an element; and even since its 
 analysis into oxygen, nitrogen, hydrogen, carbon 
 dioxide, etc., modern chemistry has discovered still 
 other elements in certain quantities. It may very 
 well happen, therefore, that any supposed single 
 antecedent is really complex. In most cases, it is 
 only a relative simplicity that can be attained, a 
 simplicity that is met with at the point where our 
 methods of analysis are unable to carry us any 
 further. We conclude, therefore, that the Method 
 states an ideal that, in practice, is difficult to attain, 
 and, when attained, to definitely certify. 
 
 What degree of confidence, we may ask, may be 
 reposed in the results that are attained by the use 
 of this Method ? In other words, what are the limits 
 of its usefulness? To be more specific still, is it 
 distinctively a method by which we are able to ex- 
 plain the occurrence of phenomena? This question 
 we must answer in the negative. The Method of 
 Agreement is, as one has said, "a mode of recon- 
 noitering," a method for delimiting the area. within 
 which causal relations may, with some degree of 
 confidence, be expected to exist. But for the estab- 
 lishment of such relations we should have to pass 
 beyond the method itself. Let us suppose, for 
 example, that three instances of a phenomenon may 
 be analysed in the following schematic way: 
 
MILL'S EXPERIMENTAL METHODS 481 
 
 [ABC x / z] 
 
 Antecedents 1 A E' C x/wj- Consequents 
 
 Are we certain, in such a case, that A, the circum- 
 stance in which all the antecedents agree, is the 
 cause of the phenomenon ? Starting with the obser- 
 vation of x, does it follow, because our analysis of 
 all the instances of x shows A to be the one element 
 that is common to these instances, that A is, there- 
 fore, the cause of x ? Mill has pointed out in answer 
 to such questions that their affirmative answer 
 would take us beyond the limits of this Method, 
 when and so long as we are obliged to consider, in 
 our interpretation of the instances, the possibility 
 of a plurality of causes, the possibility, that is, that 
 x may be produced by more than one cause. If the 
 instances of the phenomenon were known to be 
 reciprocal, or if we were certain that we had all 
 the instances before us, the situation would be 
 different; but so long as neither condition is guar- 
 anteed, it only remains probable, as Jevons' and 
 Mellone's formulations of the Method indicate, that 
 the "one circumstance in common" is the cause of 
 the phenomenon in question. It thus appears, to 
 quote Mill, that the Method of Agreement "leads 
 only ... to unifomities, which either are not laws 
 of causation, or in which the question of causation 
 must for the present remain undecided. The Method 
 of Agreement is chiefly to be resorted to as a means 
 of suggesting applications of the Method of Differ- 
 
 31 
 
482 A TEXT-BOOK OF LOGIC 
 
 ence, ... or as an inferior resource in case the 
 Method of Difference is impracticable; which . . . 
 generally arises from the impossibility of artificially 
 producing the phenomena/' that is, when experi- 
 mentation is not possible. 
 
 The Method of Difference. The Method of Agree- 
 ment, as we saw, is a method of systematic obser- 
 vation, and its object, negatively stated, is to elim- 
 inate from the occurrences of a particular phenom- 
 enon those elements which, because they are not 
 constant in all the instances, cannot be regarded as 
 being the cause, or part of the cause of the phenom- 
 enon, and thus, affirmatively stated, to map out the 
 area within which the cause may probably be found. 
 Turning now to the Method of Difference, we find 
 that it is a method of scientific experiment, and 
 the formulation given it by Mill is as follows: If 
 an instance in which the phenomenon under inves- 
 tigation occurs, and an instance in which it does not 
 occur, have every circumstance in common save one, 
 that one occurring only in the former, the circum- 
 stance in which alone the two instances differ is the 
 effect, or the cause, or an indispensable part of the 
 cause, of the phenomenon. Let us suppose, for ex- 
 ample, that two instances of a phenomenon can be 
 analysed schematically as follows : 
 
 f A B C x y zl 
 
 Antecedents } I Consequents 
 
 B C y z 
 
MILL'S EXPERIMENTAL METHODS 483 
 
 then we may say, according to this Method, that A 
 is the cause of x. Thus, let us suppose that in two 
 glasses equal quantities of lemon juice and water 
 are mixed, and that in one of them a given quantity 
 of sugar is dissolved. The taste of the liquid which 
 contains the sugar, we shall say, is pleasant, and 
 the taste of the liquid which does not contain sugar 
 is unpleasant. What is the cause of the pleasant 
 taste? The circumstance, says Mill, in which alone 
 the two instances differ, namely, the sugar. 
 
 In calling the Method of Difference a method of 
 scientific experiment, we may observe that scientific 
 experimentation, as this was defined above, involves 
 a definite control of the conditions under which a 
 phenomenon occurs, and a definite inquiry to which 
 the experiment is expected to give an affirmative or 
 negative answer. Scientific experiment is like a 
 shafted arrow, it is aimed at a mark, and its course 
 toward that mark is controlled, as is the arrow 
 which is sped from the bow. To illustrate, let us 
 suppose that we wished to know why a feather, 
 dropped simultaneously from the same height as a 
 coin, reaches the ground after the coin. Our ques- 
 tion will be, Is the greater resistance offered by the 
 air to the feather the cause of the observed phe- 
 nomenon? To answer this question, we must insti- 
 tute an experiment, and to do this, as we said, it is 
 necessary to bring the phenomenon under controlled 
 conditions. Thus, we first drop the two objects 
 from the same level and at the same time in, let us 
 say, the receiver of an air-pump. The feather is 
 
484 A TEXT-BOOK OP LOGIC 
 
 observed to flutter to the base of the pump after 
 the coin. We perform the same experiment again, 
 with the exception that we take care to remove all 
 the air from the receiver. Under these conditions, 
 the coin and the feather reach the base of the re- 
 ceiver at the same time. The conclusion is that the 
 only circumstance in which the two instances differ, 
 namely, the presence of air in the former, is the 
 cause of the phenomenon. Because, as in this ex- 
 ample, the Method proceeds systematically by 
 changing one condition at a time, it is known as 
 the Method of Single Difference, and the following 
 formulation has been given by Mellone: When 
 the addition of an agent is followed by the ap- 
 pearance, or its subtraction by the disappearance, of 
 a certain event, other circumstances remaining the 
 same, that agent is causally connected with the event. 
 Or, to state the principle on which any formulation 
 of the Method relies, we may say that the circum- 
 stance in the absence of which a phenomenon fails to 
 occur is the cause, or part of the cause, of the phe- 
 nomenon. 
 
 It will add to the clearness of our apprehension 
 of the meaning of this Method, if we distinguish 
 the instances of the phenomenon that are success- 
 ively observed. For this purpose, let us call the 
 instance in which the suspected cause occurs the 
 positive instance, and the one in which it does not 
 occur the negative instance. By this terminology 
 is meant that, in what is called the positive in- 
 stance, we have the occurrence of the observed phe- 
 
MILL'S EXPERIMENTAL METHODS 485 
 
 nomenon along with the occurrence of its supposed 
 cause, and, in the negative instance, the absence of 
 the phenomenon together with the absence of the 
 supposed cause. 
 
 In view of this distinction, it will be seen that 
 the Method depends, for its validity, on the negative 
 instances through which a suspected cause is either 
 proved or disproved. And, for this reason, it rightly 
 insists on the importance of varying only one condi- 
 tion of the phenomenon at a time. For if we were to 
 vary simultaneously two of a phenomenon's condi- 
 tions, and found that some change resulted, we 
 should be unable to tell whether this change was due 
 to one of the altered conditions, or to the other, or 
 to the joint action of both. And if no change en- 
 sued, we could not safely conclude that neither con- 
 dition was affective, for the action of the one may 
 have been neutralised by that of the other. And 
 even when only a single condition is varied at any 
 one time, it is important, as Mill pointed out, that 
 the experiment should be conducted with dispatch, 
 and its entire process brought as rapidly as possible 
 to an end. The reason for this caution is that if the 
 experiment is to serve the purpose for which it was 
 instituted, the effect must be the effect solely of the 
 one altered condition. If, on the contrary, during 
 the course of an unusually prolonged experiment, 
 the original conditions of the experiment were mod- 
 ified by the development of changes which deter- 
 mined in part the character of the observed effect we 
 should have, what Mill called, an inter-mixture of 
 
486 A TEXT-BOOK OF LOGIC 
 
 effects ; and this would be as destructive of the value 
 of the Method as any unsystematic variation in the 
 conditions themselves. 
 
 It is a well known fact that not all problems are 
 capable of experimental handling, and that those 
 that are, are liable to have their results affected by 
 the operation of conditions which we can in no 
 wise eliminate. In the former case, the Method of 
 Difference cannot be used. In the latter, the condi- 
 tions referred to are those that belong to the struc- 
 ture of the universe to which the particular phenom- 
 enon belongs. Such conditions Mill called perma- 
 nent causes. "The pendulum, for example, has its 
 oscillations disturbed by the vicinity of a mountain." 
 What, in such a case, can be done to make the 
 Method applicable? It is evident that we cannot 
 remove the mountain, but, as Mill points out, we 
 can take the pendulum to a locality where the 
 mountain's intereference is reduced to a minimum. 
 In this way, it ceases to be an "influencing agent," 
 and becomes merely a "co-existing fact." When an 
 experiment cannot be removed outside the sphere of 
 the operation of such permanent causes, recourse 
 may be had to the Method of Concomitant Variations 
 which is discussed below. 
 
 The Joint Method of Agreement and Difference. 
 There is, no doubt, something ideal in the require- 
 ments that are laid down as conditions of the use of 
 the Methods of Agreement and of Difference. It is 
 rarely that in the course of common life or scientific 
 investigation a number of instances are given which 
 
MILL'S EXPERIMENTAL METHODS 487 
 
 agree or differ in only a single instance. There 
 seems to be, therefore, a breach between experience, 
 on the one hand, and these modes of establishing 
 causal relations, on the other. Either, then, we 
 shall have to say that the Methods of Agreement 
 and of Difference are of only limited application, 
 and that causal connections cannot be established 
 in a great deal of our experience, or that, with re- 
 spect to that part of experience which does not come 
 directly within the scope of these Methods, some 
 other means of determining causal connections must 
 be used. It is to meet the latter of these alternatives 
 that the Joint Method of Agreement and Difference 
 is particularly useful. The formulation of this 
 Method by Mill was made necessary in view of the 
 fact, as he says, that there are "many cases in which, 
 though our power of producing the phenomenon is 
 complete, the Method of Difference either cannot be 
 made available at all, or not without a previous em- 
 ployment of the Method of Agreement. This occurs," 
 says Mill, "when the agency by which we can pro- 
 duce the phenomenon is not that of one single ante- 
 cedent, but a combination of antecedents, which we 
 have no power of separating from each other and ex- 
 hibiting apart." Besides those cases in the natural 
 sciences which Mill had in mind, the Joint Method 
 will be found applicable, as Creighton has pointed 
 out, when we try "to reach generalizations regard- 
 ing the behaviour of human individuals or human 
 societies in looking for moral, or social or eco- 
 nomic laws." 
 
488 
 
 A TEXT-BOOK OF LOGIC 
 
 The Joint Method is formulated by Mill as fol- 
 lows: If two or more instances in which the phe- 
 nomenon occurs have only one circumstance in com- 
 mon, while two or more instances in which it does 
 not occur have nothing in common save the absence 
 of that circumstance, the circumstance in which alone 
 the two sets of instances differ is the effect, or the 
 cause, or an indispensable part of the cause, of the 
 phenomenon. Thus, we are concerned, in this 
 Method, with two sets of instances, one set of posi- 
 tive instances, in which thei phenomenon with its 
 suspected cause is present, and one of negative 
 instances, in which the phenomenon with its sus- 
 pected cause is absent. When these conditions are 
 satisfied, the Method affirms that the circumstances 
 in which the two sets of instances differ is causally 
 connected with the phenomenon. Let us suppose, 
 for example, that two sets of instances, positive and 
 negative, can be, schematically, analysed as follows : 
 
 Antecedents 
 
 POSITIVE INSTANCES 
 
 ABCD xyzw 
 
 x y v u 
 
 A B E F 
 A C F G 
 
 X Z U t 
 
 Consequents 
 
 Antecedents 
 
 NEGATIVE INSTANCES 
 
 B C D E y z 
 
 C F G H z 
 
 E H J K v 
 
 z w vl 
 u t s L 
 s r qj 
 
 Consequents 
 
 A comparison of these instances shows that when 
 x is present A is present,' and that when x is absent 
 
MILL'S EXPERIMENTAL METHODS 489 
 
 A is absent, and this suggests that A and x are 
 causally connected. But we cannot prove this by 
 the Method of Agreement, because there are no two 
 instances which agree in having only a single cir- 
 cumstance is common; and we cannot prove it by 
 the Method of Difference, because there are no two 
 instances which differ in no respect except in the 
 presence of A and x in the positive instances, and 
 their absence in the negative ones. Moreover, it 
 will be observed that the instances supposed do not 
 conform strictly to the requirements of Mill's state- 
 ment, and that it is exactly this divergence that sets 
 the problem which this Method is intended to solve. 
 In other words, the agreements and differences are 
 greater in the instances we have supposed than they 
 have any right to be on a strict interpretation of 
 Mill's statement. The reason for this divergence is 
 that Mill's statement of the Method, as Mellone 
 remarks, "is vague, and it is incorrect in more than 
 one point; two positive instances would never be 
 enough, still less could two negative instances ; and it 
 is not necessary that the negative instances should 
 have 'nothing in common'," and, as our illustration 
 shows, it is not necessary that the positive instances 
 should agree in only a single circumstance. With 
 these amendments in view, we may quote Mellone's 
 proposed formulation of the Method : Whatever is 
 present in numerous observed instances of the pres- 
 ence of the phenomenon, and absent in observed 
 instances of its absence, is probably connected caus- 
 ally with the phenomenon. 
 
490 A TEXT-BOOK OF LOGIC 
 
 How, now, can we proceed to apply the Method? 
 If we examine the positive instances, employing for 
 that purpose the general principle of the Method 
 of Agreement, we shall see that in the first two 
 cases A or B or AB is the cause of the phenomenon 
 x, since A and B are the only conditions present in 
 both. For a similar reason, we see that A or C or 
 AC is the probable cause of the phenomenon in the 
 first and third cases; and that the cause in the 
 second and third cases is probably A. Now if the 
 probable cause in all these instances is the same, that 
 cause must be A, since that is the only particular in 
 which they all agree. If, now, we examine the neg- 
 ative instances, employing for that purpose the gen- 
 eral principle of the Method of Difference, we note 
 that they all agree in the absence of A and x, and 
 that this is the only relevant circumstance in which 
 they do agree. The absence in the negative instances 
 of the supposed cause of x along with the absence of 
 x, when taken in connection with the relative 
 unimportance of the other circumstances, greatly 
 strengthens the supposition that was reached as the 
 result of examining the positive instance, namely, 
 that A is the cause of x. Such a Method as the one 
 here outlined has been called by various names. Mill 
 spoke of it sometimes as "a double employment of the 
 Method of Agreement," whence it is often called the 
 Method of Double Agreement. Mill also spoke of it 
 as the Indirect Method of Difference. But the name 
 by which it is commonly known is the Joint Method 
 
MILL'S EXPERIMENTAL METHODS 491 
 
 of Agreement and Difference, a name which Mill 
 also used in referring to the method. 
 
 The following application of the Joint Method 
 to a social problem illustrates so well, not only its 
 usefulness in this class of problem, but the nature 
 of the Method itself, that we shall quote it entire. 
 "We may suppose," Creighton writes, "that in a 
 certain part of the country it was noticed that a 
 considerable difference existed in the number of 
 criminal offenses committed, in proportion to the 
 number of inhabitants, in the various towns. In 
 several towns the percentage was high, while in 
 others it was relatively small. This being so, a 
 question naturally arose as to the cause of the high 
 percentage. Now there were among the people 
 various opinions concerning the matter. . . . Not 
 being able to agree about the matter, it was decided 
 to appoint a committee to investigate the circum- 
 stances existing in various towns where the same 
 general conditions prevailed, and upon the basis of 
 this comparison to decide. The towns with a high 
 criminal percentage were examined first. The re- 
 port of conditions there was as follows : 
 
 Town A: Small police force efficient schools severe pen- 
 alties inactive churches licensed saloon. 
 
 Town B: Small police force efficient schools light penal- 
 ties active churches licensed saloons. 
 
 Town C : Large police force inefficient schools severe pen- 
 alties active churches licensed saloons. 
 
 Town D: Large police force inefficient schools light pen- 
 alties inactive churches licensed saloons. 
 
492 A TEXT-BOOK OF LOGIC 
 
 "This report revealed the fact that in each of 
 these towns having a high criminal percentage there 
 was one circumstance, and only one, invariably 
 present, the licensed saloon. This rendered it 
 probable that the saloon was the cause of the high 
 percentage of crime. Still, before finally deciding, 
 it was thought well to investigate negative instances 
 as well ; that is, towns in which the high percentage 
 of crime did not occur. The report of conditions 
 there was as follows: 
 
 / 
 
 Town E: Large police force efficient schools light penal- 
 ties active churches no licensed saloons. 
 
 Town F: Large police force inefficient schools light pen- 
 alties active churches no licensed saloons. 
 
 Town G: Small police force efficient schools light penal- 
 ties inactive churches no licensed saloons. 
 
 Town H : Small police force inefficient schools severe pen- 
 alties active churches no licensed saloons. 
 
 "This table showed that in the absence of the 
 phenomenon (high criminal percentage) one and 
 only one of the conditions concerned was invariably 
 absent ; namely, the licensed saloon. This confirmed 
 the previous report and established to the satisfac- 
 tion of all that the saloon was, at least, the main 
 cause of the high criminal percentage in the cities 
 concerned." 
 
 The Method of Concomitant Variations. Mill 
 states this Method as follows : Whatever phenom- 
 enon varies in any manner whenever another phe- 
 nomenon varies in some particular manner, is either 
 
MILL'S EXPERIMENTAL METHODS 493 
 
 a cause or an effect of that phenomenon, or is con- 
 nected with it through some fact of causation. The 
 Method presupposes two classes of cases. Whenever, 
 for example, any variation in one phenomenon ac- 
 companies a variation in another, these phenomena 
 may either be related directly as cause and effect, 
 or they may be "two different effects of a common 
 cause." The Method itself, however, does not enable 
 us to decide, in any particular instance, which of 
 these alternative possibilities is realised. In order 
 to decide that point, as Mill says, we should have to 
 determine whether one set of the variations in ques- 
 tion were capable of being produced by means of the 
 other. In that case, the relation is one of cause and 
 effect. If, on the other hand, the variations in ques- 
 tion were not capable of being produced in the man- 
 ner indicated, we should have to regard them as 
 effects of a cause that is common to both. In both 
 cases the principle on which the Method rests is 
 that "anything on whose modifications, modifica- 
 tions of an effect are invariably consequent, must 
 be the cause (or connected with the cause) of that 
 effect," As an example, "let us suppose," to quote 
 Gibson, "that an electric bell is placed ringing under 
 the receiver of an air-pump. The air is now grad- 
 ually exhausted, and it is noticed that, parri passu 
 with the exhaustion of the air, the sound of the 
 bell grows fainter and fainter, until a point is 
 reached at which it is no longer heard at all. The 
 air is now allowed to pass back gradually into the 
 receiver, and, as it does so, the sound of the bell is 
 heard, at first faintly, then more and more loudly, 
 
494 A TEXT-BOOK OF LOGIC 
 
 until the clearness of the original note is repro- 
 duced." 
 
 The Method of Concomitant Variations, as Mill 
 himself indicated, is applicable particularly to those 
 cases in which the Method of Difference, on account 
 of the impossibility of removing the phenomenon 
 under observation from the influence of permanent 
 causes, entirely fails. Let us suppose, to take one 
 of Mill's illustrations, that we wished to know what 
 influence the moon exerts on the surface of the 
 earth. "We cannot try an experiment in the absence 
 of the moon, so as to observe what terrestrial phe- 
 nomena her annihilation would put an end to; but 
 when we find that all the variations in the position 
 of the moon are followed by corresponding varia- 
 tions in the time and place of high water, the place 
 being always either the part of the earth which is 
 nearest to, or that which is most remote from, the 
 moon, we have ample evidence that the moon is, 
 wholly or partially, the cause which determines the 
 tides." 
 
 Sometimes it is not the mere concomitance 
 of varying phenomena, but the varying quantities 
 of the associated phenomena, that leads to the deter- 
 mination of a causal relation between these phenom- 
 ena. If, for example, a connection between heat and 
 expansion is suspected, we can increase or diminish 
 the amount of heat, and observe whether, under 
 the varying conditions, any corresponding varia- 
 tions occur in the expansions of a heated body. That 
 increase of heat is followed by increased expansion, 
 and decreased heat is followed by decreased expan- 
 
MILL'S EXPERIMENTAL METHODS 495 
 
 sion, is all the evidence we need that there is a 
 causal connection between the two occurrences. It 
 is by the use of a method such as this in cases like 
 the last that precise quantitative variations between 
 phenomena may often be made out. We may, that 
 is to say, measure the increases and decreases in 
 amounts of accompanying phenomena, and deter- 
 mine the exact correlation between them. Some- 
 times only one of the quantities can be measured, 
 as, for instance, the correlation between the inten- 
 sity of a stimulus and the resulting sensation which 
 is formulated in what is known as Weber's law. 
 Whenever we experiment with variations of quantity 
 in accompanying phenomena, it should be observed, 
 in general, that the greater the number and variety 
 of the instances in which the correlation is known 
 to hold, the greater the certainty that attaches to a 
 given conclusion. The desirability of extending our 
 observation of accompanying variable phenomena 
 over a considerable range of instances is further 
 emphasised by the fact that only in this way can 
 we determine the limits within which their correla- 
 tion holds good. In this way, for example, the upper 
 and lower limits of the correlation between intensity 
 of stimulus and sensation in each of the sense fields 
 has been ascertained. Beyond these limits, the cor- 
 relation no longer holds good either because the phe- 
 nomenon changes its character or ceases altogether. 
 Notwithstanding the necessity for exercising care 
 in the use of this Method, it is particularly service- 
 able in those cases in which the amounts of varia- 
 
496 A TEXT-BOOK OF LOGIC 
 
 tion can be measured. "Although," as Mill re- 
 marks, "the most striking applications of the 
 Method of Concomitant Variations takes place in 
 the cases in which the Method of Difference, strictly 
 so called, is impossible, its use is not confined to 
 those cases; it may often usefully follow after the 
 Method of Difference, to give additional precision 
 to a solution which that has found. When by the 
 Method of Difference it has first been ascertained 
 that a certain object produces a certain effect, the 
 Method of Concomitant Variations may be usefully 
 called in to determine according to what law the 
 quantity or the different relations of the effect fol- 
 low those of the cause." 
 
 The Method of Residues. Most of the phenomena 
 with which the sciences have to deal are complex. 
 The experimental methods, as they have been for- 
 mulated by Mill, are, as we have seen, statements 
 of ways that have been devised for the purpose of 
 analysing various kinds and degrees of complexity 
 in the material facts that constitute the subject- 
 matter of the particular sciences. We have seen 
 that when particular phenomena do not conform to 
 the requirements of either of the fundamental 
 Methods of Agreement or of Difference, the joint use 
 of these Methods is then often necessary if we are 
 to determine whether and, if so, in what respects, 
 phenomena are causally connected. Sometimes our 
 analysis of phenomena by this Method enables us 
 merely to show that complexes are probably con- 
 
MILL'S EXPERIMENTAL METHODS 497 
 
 nected together in a causal way. We may find, for 
 example, in the series of instances: 
 
 POSITIVE INSTANCES 
 
 fA B C D x y z wl 
 
 Antecedents J i Consequents 
 
 [A B E F x y v uj 
 
 NEGATIVE INSTANCES 
 
 {BCDE yzwu] 
 
 ) Consequents 
 CFGH zutsj 
 
 that the negative instances confirm what the positive 
 instances suggest, namely, that AB and xy are, in all 
 probability, causally related. But the Method itself 
 does not, in this case, enable us to analyse the phe- 
 nomenon further to determine whether A is causally 
 connected with x or not. If, however, we supple- 
 ment the Joint Method by the Method of Concom- 
 itant Variations, we may be able, by varying A 
 or x, to ascertain whether the two phenomena 
 are related as cause and effect. It is obvious, 
 further, that we may employ the same Method 
 for the purpose of ascertaining whether, in the 
 above instances, B is causally connected with y, 
 and C with z. Now, if experiment should show 
 that A and x, B and y, C and z are causally connected 
 then, the Method of Residues, which we have to 
 discuss, assures us that the remaining phenomena, 
 namely D and w, are also causally connected. Thus, 
 
 32 
 
498 A TEXT-BOOK OF LOGIC 
 
 the Method virtually says that any remainder which 
 is left over after other portions of a complex phe- 
 nomenon have been explained, are themselves 
 causally connected. Mill's statement is as follows: 
 Subduct from any phenomenon such part as is known 
 by previous inductions to be the effect of certain ante- 
 cedents, and the residue of the phenomenon is the 
 effect if the remaining antecedents. 
 
 The Method of Residues, as it has just been 
 stated, is constantly employed in the sciences. To 
 take one illustration only, as this is given by Jevons. 
 "In chemical analysis," he writes, "this method is 
 constantly employed to determine the proportional 
 weight of substances which combine together. Thus 
 the composition of water is ascertained by taking 
 a known weight of oxide of copper, passing hydro- 
 gen over it in a heated tube, and condensing the 
 water produced in a tube containing sulphuric acid. 
 If we subtract the original weight of the condensing 
 tube from its final weight, we learn how much water 
 is produced; the quantity of oxygen in it is found 
 by subtracting the final weight of the oxide of 
 copper from its original weight. If we then sub- 
 tract the weight of the oxygen from that of the 
 water, we learn the weight of the hydrogen which 
 we have combined with the oxygen. When the 
 experiment is carefully performed ... we find that 
 88.9 parts by weight of oxygen unite with 11.11 
 parts of hydrogen to form 100 parts of water." 
 
 Mill calls our attention to the fact that the 
 Method of Residues is specially serviceable in those 
 
MILL'S EXPERIMENTAL METHODS 499 
 
 cases where several causes acting together produce 
 an effect which is the joint result of all the causes 
 taken together. In such cases, we have, what Mill 
 calls, an "intermixture of effects." What is meant 
 by an intermixture of effect has been explained by 
 Jevons as follows: "If in one experiment friction, 
 combustion, compression, and electric action are all 
 going on at once, each of these causes will produce 
 quantities of heat which will be added together, and 
 it will be difficult or impossible to say how much 
 is due to each cause separately. We may call this 
 a case of the homogeneous intermixture of effects, 
 the name indicating that the joint effect is of the 
 same kind as the separate effects. There are several 
 causes, each producing a part of the effect, and we 
 want to know how much is due each." What is here 
 called by Jevons a homogeneous intermixture of 
 effects, Mill also called a Composition of Causes. He 
 writes : "I shall give the name of the Composition 
 of Causes to the principle which is exemplified in 
 all cases in which the joint effect of several causes 
 is identical with the sum of their separate effects." 
 In contradistinction to the case just mentioned, the 
 intermixture of effects may also be heterogeneous 
 when, as Mill says, "the agencies which are brought 
 together cease entirely, and a different set of phe- 
 nomena arise: as in the experiment of two liquids 
 which, when mixed in certain proportions, instantly 
 become, not a larger amount of liquid, but a solid 
 
500 A TEXT-BOOK OF LOGIC 
 
 We may remark, further, that the Method of 
 Residues is significant because it operates in the 
 interests of thoroughness in scientific observation. 
 It sets a barrier against carrying over into science 
 the popular attitude towards what is small and 
 insignficant, and its use has taught the scientist 
 that what appears small and insignficant if often 
 the hinge upon which scientific discoveries of the 
 first important turn. "Almost all the greatest dis- 
 coveries in astronomy," says Herschel, "have re- 
 sulted from the consideration of residual phenomena 
 of a quantitative or numerical kind. . . It was thus 
 that the grand discovery of the Procession of the 
 Equinoxes resulted as a residual phenomenon, from 
 the imperfect explanation of the return of the sea- 
 sons by the return of the sun to the same apparent 
 place among the fixed stars." The discovery of the 
 planet Uranus, to which we have referred in an- 
 other connection, and the invention of the steam 
 engine, are other instances of the importance of 
 paying attention to residual phenomena. What one 
 calls 'luck' in ordinary life, what one calls 'genius' 
 in scientific life, and what one calls 'success* in 
 commercial life are all of them very often merely 
 the result of giving heed to details that the average 
 person passes lightly by. In this regard, the fol- 
 lowing quotation from Darwin's 'Life and Letters' 
 has its value. "A point apparently slight and un- 
 connected with his present work is passed over by 
 many a man almost unconsciously, with some half- 
 considered explanation, which is really no explana- 
 
MILL'S EXPERIMENTAL METHODS 501 
 
 tion. It was just these things that he (Darwin) 
 seized upon to make a start." 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Chs. XXVI., XXVII., 
 XXIX. 
 
 J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
 XVI., XVII. 
 
 S. H. Mellone, An Introductory Text-Book of Logic, 3d Edi- 
 tion, Ch. IX., 3-9. 
 
 W. Minto, Logic, Inductive and Deductive, Book II., Chs. IV., 
 V., VI. 
 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 
 
 XVI. 
 
 ADVANCED 
 
 W. R. B. Gibson, The Problem of Logic, Ch. XLV. 
 L. T. Hobhouse, The Theory of Knowledge, Chs. XIII., XIV., 
 XV. 
 
 D. Hume, Treatise of Human Nature, Book I., Part III., XV. 
 H. W. B. Joseph, An Introduction to Logic, Ch. XX. 
 
 H. Lotze, Logic, Book II., Ch. VII. 
 
 J. S. Mill, A System of Logic, Book III., Chs. VIII., IX. 
 
 C. Sigwart, Logic, Vol. II., Part III., Ch. V., 
 
 QUESTIONS 
 
 1. State briefly the relation of Mill's 'Logic' to the history 
 of inductive logic in the modern era. 
 
 2. With what problem does Mill's chapter on 'The Four 
 Methods of Experimental Inquiry' deal? 
 
 3. What is meant by calling causal relations reciprocal? 
 
 4. Are all causal relations reciprocal? Explain. 
 
 5. What relation have Mill's Methods to the special modes 
 of inquiry developed by each science to meet its own 
 problems? 
 
502 A TEXT-BOOK OF LOGIC 
 
 6. Explain as well as you can exactly what Mill's Methods 
 undertake to do. 
 
 7. In what sense can it be said that Mill's Methods rest 
 upon a process of elimination? 
 
 8. What is Joseph's view of elimination as applied to 
 causal problems? 
 
 9. What view, according to Gibson, does Mill take of the 
 nature of elimination? 
 
 10. What is the characteristic feature of the Method of 
 Agreement? 
 
 11. What is Jevons' formulation of Mill's Method of Agree- 
 ment? 
 
 12. What criticisms may be passed on this Method for de- 
 manding a point of single agreement among the phe- 
 nomena which it examines? 
 
 13. Is the Method of Agreement one of observation or 
 explanation? Give reasons for your answer. 
 
 14. What degree of certinty attaches to the conclusions 
 reached by the Method of Agreement? 
 
 15. What are the chief features of the Method of Differ- 
 ence as formulated by Mill? 
 
 16. What is meant by calling the Method of Difference a 
 method of scientific experiment? 
 
 17. How does Mellone formulate the Method of Difference? 
 
 18. What two kinds of instances are presupposed by the 
 Method of Difference, and by what names are they 
 called? 
 
 19. Why is it necessary to vary only one condition at a time 
 in a series of scieintific experiments? 
 
 20. What does Mill mean by a permanent cause? 
 
 21. How does the operation of permanent causes affect the 
 applicability of the Method of Difference? 
 
 22. Under what conditions does the Joint Method of Agree- 
 ment and Difference become effective? 
 
 23. To what two classes of problems is the Joint Method 
 applicable? 
 
MILL'S EXPERIMENTAL METHODS 503 
 
 24. What are the chief features of the Joint Method as 
 formulated by Mills? 
 
 25. Show, by the enumeration of supposed instances to 
 which the Methods of Agreement and of Difference do 
 not apply, the conditions which call for the use of the 
 Joint Method. 
 
 26. What criticism can be made of the way in which Mill 
 formulates the Joint Method? 
 
 27. What statement has been given by Mellone of this 
 Method so as to avoid such criticism? 
 
 28. Explain carefully and in detail how you would apply the 
 Joint Method. 
 
 29. Verify each step of your answer to the previous ques- 
 tion by using the analysis of the social example given 
 in the text. 
 
 30. What is the Method of Concomitant Variations? 
 
 31. What two classes of cases are presupposed by Mill's 
 statement of the Method of Concomitant Variations? 
 
 32. How can you determine which of these two cases is 
 present in any particular instance? 
 
 33. On what general principle does the Method of Concom- 
 itant Variations rest? 
 
 34. What is the relation of this Method to that of Differ- 
 ence? How is it affected by the operation of permanent 
 causes? 
 
 35. In what way does the Method of Concomitant Variations 
 enable us to determine causal relations between quan- 
 titative phenomena? 
 
 37. Illustrate how the measurements of quantitative phe- 
 nomena enable us to determine causal relations, first, 
 in instances where both antecedent and consequent can 
 be measured, and, second, where only antecedent can be. 
 
 38. What, according to Mill, are the chief uses of the 
 Method of Concomitant Variations? 
 
504 A TEXT-BOOK OF LOGIC 
 
 39. State briefly the relations of the Methods of Agreement 
 and Differences, the Joint Method, and the Method of 
 Concomitant Variations to one another with a view to 
 shrow what Mill means by the Method of Residues. 
 
 40. Illustrate the Method of Residues. 
 
 41. What does Mill mean by the intermixture of effects? 
 
 42. Why should the Method of Residues be specially applic- 
 able to cases which involve an intermixture of effects? 
 
 43. In what way does the Method of Residues operate in 
 the interests of thoroughness in scientific observation? 
 
 EXERCISES 
 
 1. Examine each of the examples of inductive reasoning 
 given below, and state by what method or combination 
 of methods the conclusion in each case is reached. 
 
 (1) It is found that sun-lit air has been the means of 
 eliminating some diseases, and of diminishing the 
 severity of a number of others; whence it seems 
 to follow that for maintaining a high degree of 
 health sun-light air is essential. 
 
 (2) Other conditions remaining the same, children who 
 are taught in classes which average from twenty 
 to twenty-five in number attain in the same amount 
 of time a higher degree of proficiency than those 
 taught in classes which average from forty to fifty, 
 or attain the same degree of proficiency in a 
 shorter amount of time. 
 
 (3) Sachs maintained, in 1862, that starch is formed 
 by the decomposition in chlorophyl of carbon- 
 dioxide gas under the influence of light. He found 
 that when all other conditions were constant, and 
 light was excluded from a plant, no starch was 
 formed; the single circumstance of readmitting 
 light was accompanied by renewed formation of 
 starch. Further, he found that if certain portions 
 
MILL'S EXPERIMENTAL METHODS 505 
 
 of the leaves of an illuminated plant were covered 
 with black paper, no starch was found in these 
 portions. 
 
 (4) Tyndall found that of twenty-seven sterilised flasks 
 containing infusion of organic matter, and opened 
 in pure Alpine air, not one showed putrefaction; 
 while of twenty-three similar flasks, opened in a 
 hay loft, only two remained free from putrefaction 
 in three days. He concluded that putrefaction is 
 due to floating particles in the air. 
 
 (5) In 1675 Leeuwenhoek discovered infusoria, or ani- 
 malculae under the microscope, and it was thought 
 that such minute organisms as these might be 
 spontaneously generated, even if the larger were 
 not. About 1745 Needham performed a number 
 of experiment to test this conclusion. He extracted 
 the juices of meat by boiling, enclosed them in 
 bottles, which were carefully corked and sealed 
 with mastic, then subjected the closed bottles to 
 heat and set them away to cool. In due course of 
 time, the fluids thus treated became infected with 
 microscopic life, and inasmuch as he believed that 
 he had killed all living germs by repeated heating, 
 he concluded that the living forms had been pro- 
 duced by spontaneous generation. 
 
 (6) Spellanzi, however, thought that Needham 's ex- 
 periments had not been conducted with sufficient 
 care. He, therefore, made a great number of sim- 
 ilar experiments, using different kinds of infusions. 
 But he placed them in thin flasks with slender 
 necks, which were then hermetically sealed in 
 flame, after which he immersed the flasks in boil- 
 ing water for three-quarters of an hour, in order 
 to destroy all germs that might be contained in 
 them. Under these conditions no infusoria ap- 
 
506 A TEXT-BOOK OF LOGIC 
 
 peared in them. Needham was not satisfied with 
 these results, however, and objected that such pro- 
 longed boiling would destroy not only germs, but 
 the generative force of the infusion itself. Spell- 
 anzi easily disposed of this objection by showing 
 that when the infusions were again exposed to the 
 air, no matter how severe or prolonged the boiling 
 to which they had been subjected, the infusoria re- 
 appeared. 
 
 (7) Goldschn eider proved that muscular sensations 
 play no considerable part in our consciousness of 
 the movement of our limbs, by having his arm sus- 
 pended in a frame and moved by an attendant. 
 Under these circumstances, where no work de- 
 volved on his muscles, he found that he could dis- 
 tinguish as small an angular movement of the arm 
 as when he moved and supported it himself. 
 
 (8) The case has been supposed of a man who, having 
 a taste for cucumber, attributes his chronic indi- 
 gestion now to the salmon, now to the cheese, now 
 to the pastry no one of which is an invariable 
 feature of his evening meal but never to the 
 cucumber, which he takes every evening. However, 
 after having dined without cucumber on several 
 consecutive evenings, whilst taking salmon one 
 evening, pastry the next, and so on through the 
 whole list of suspicious dishes, he cannot but notice 
 that on no one of these evenings did any indiges- 
 tion occur, and is thus brought to confess that the 
 cucumber, after all, must have been the offending 
 cause. 
 
 (9) Frri, in his Criminal Sociology, writes: I have 
 shown that in France there is a manifest corre- 
 spondence of increase and decrease between the 
 number of homicides, assaults and malicious 
 
MILL'S EXPERIMENTAL METHODS 507 
 
 wounding, and the more or less aboundant vintage, 
 especially in the years of extraordinary variations, 
 whether of failure of vintage (1853-5, 1859, 1867, 
 1873, 1878-80), attended by a remarkable diminu- 
 tion of crime (assault and woundings), or of abun- 
 dant vintages (1850, 1856-8, 1862-3, 1865, 1874-5), 
 attended by an increase of crime. 
 
CHAPTER XVIII 
 
 FALLACIES 
 
 Fallacy Defined. The earliest systematic account 
 of fallicies was given by Aristotle in his treatise 
 
 Was On sophistical arguments (-n-epl O-O^HO-TIKWJ/ eAeyx^)- 
 
 The aim of this treatise was to name and examine 
 the various tricks that were relied on by many of 
 the sophists to win the applause of their audience. 
 We may say, therefore, that it contains an exami- 
 nation of the various forms of 'sophistry' current 
 among the Greeks of the fourth century B. C. To 
 this practical employment of the term corresponds, 
 in a general way, the meaning that must be assigned 
 to it when, at the present day, it is used in a popular 
 sense. From this point of view, a fallacy may be 
 said to be any error of statement or belief. If, for 
 example, any one should believe that the sun revolves 
 around the earth, such a belief would be called fal- 
 lacious, and the statement of that belief would 
 be called a fallacy. This meaning of the word, 
 however, is too indefinite for the purposes of logic, 
 and it covers too miscellaneous a group of cases to 
 be of much service in directing its inquiries. It 
 is customary, therefore, to narrow the interpreta- 
 tion of the term by confining its application to any 
 breach of the principles and rules of logical pro- 
 cedure. In the foregoing pages, we have become 
 acquainted with a number of the principles and 
 
 (508) 
 
FALLACIES 509 
 
 rules to which we must submit our thought and our 
 speech if what we assert and what we express are 
 to carry logical conviction. And, doubtless, our 
 study of these principles and rules, and our effort 
 to put them into practice, have convinced us both 
 of the necessity and of the difficulty of conforming 
 our thought and speech to their requirements. Now 
 whenever our thinking fails to conform to such 
 principles and rules, we are said, in the strict sense 
 in which the term is used in logic, to be guilty of a 
 fallacy. A fallacy, therefore, may be defined as any 
 breach of a logical principle or rule. 
 
 This statement of what we understand in logic 
 by a fallacy needs to be safeguarded in one par- 
 ticular. As it stands, and especially if one does 
 not regard strictly the context in which it occurs, 
 it will seem capable of including, not only those 
 breaches of logical procedure to which the definition 
 is intended to confine it, but also those errors which 
 arise from other than logical sources, and to which 
 the term fallacy can be applied only in a popular 
 and conventional sense. There are, no doubt, nat- 
 ural limitations of mind which prevent all of us 
 at some time from attaining, in the character of our 
 intellectual life, anything that can be called with 
 propriety logical exactness. Indeed, the ordinary 
 course of life, as we have so often said, does not 
 depend for the attainment of its objects on the 
 strictness with which logical requirements are met 
 in the field of the interests by which that life is 
 controlled. And, doubtless, mistakes occur here 
 
510 A TEXT-BOOK OP LOGIC 
 
 which have their roots in the mental process by 
 means of which that life is carried on. We have 
 pointed out, for instance, that perception does not 
 provide a secure foundation of knowledge, and if 
 we were to add that the organisation of our ordi- 
 nary experience proceeds very largely upon prin- 
 ciples of association, it would be evident, in the 
 light of our previous studies, that association cannot 
 guarantee against logical error the conclusions to 
 which it is the means of conducting us. In so far, 
 then, as we have regard to the mistakes that arise 
 in this field, it would be quite misleading to apply 
 the term fallacy to these mistakes, and they must 
 be considered as falling outside the scope of our 
 definition. We may point out also that lapses into 
 this more usual method of procedure are likely to 
 occur in the course of our efforts to reach more 
 strictly scientific results. The exclusion of these 
 cases from the field of the fallacies is made on the 
 principle that such cases do not involve ignorance 
 of the methods of logical procedure, but carelessness 
 in their application; just as, for example, ignorance 
 of a mathematical rule would not be attributed to 
 one whose mistake was obviously due to haste or 
 inattention in its application to a given case. We 
 must regard as logical fallacies, therefore, only 
 those instances of erroneous conclusions which rest 
 upon grounds which are demonstrably false. It is 
 in this sense, then, that a fallacy was defined above 
 as any breach of a logical principle or rule. 
 
FALLACIES 511 
 
 Classification of Fallacies. Although Aristotle 
 was limited in his treatment of fallacies by the 
 practical purpose to which reference has been made, 
 and although he had before him chiefly those errors 
 to which the Sophists were exposed by their desire 
 for popular favour, his classification of fallacies 
 has remained the basis of what may be regarded in 
 logic as the traditional position on this subject. In 
 the work referred to, Aristotle divided fallacies into 
 two main classes, a division which corresponds, in a 
 general way, to the distinction on which we have in- 
 sisted in our discussions of logical doctrine, the dis- 
 tinction, namely, between truth in the form of judg- 
 ments, and truth expressed in the form of proposi- 
 tions. According to this distinction, fallacies may 
 arise from the way in which we express or interpret 
 propositions, or, as Aristotle said, they may be due 
 directly to language (napa T^V Ae'&v; in dictione) ; or 
 they may exist in the thoughts or judgments that 
 we assert, or, as Aristotle expressed it negatively, 
 they may not be due to the language we employ 
 (ew IT/? Ae'^ews; extra dictionem). Under the first 
 class Aristotle enumerates six kinds of fallacy, some 
 of which are trifling and dependent wholly on the 
 syntax of the Greek language ; and under the second 
 class, he enumerates seven. Beyond the distinction 
 of these two main classes we are not directly inter- 
 ested in Aristotle's classification. 
 
 There is, perhaps, no entirely satisfactory class- 
 ification of fallacies, and the most that can be 
 attempted here is to bring under some practical and 
 
512 A TEXT-BOOK OF LOGIC 
 
 intelligible scheme the various errors to which log- 
 ical thinking is exposed. It will help us to do this 
 if we recall, in the first place, that the proposition 
 was said to be an expression in words of the truth 
 asserted in a judgment. We saw that, for the per- 
 son speaking, the problem was to find words which 
 express adequately the thought that he desires to 
 convey, and, for the person spoken to, it was to 
 interpret the words in which a judgment is ex- 
 pressed in the sense that they had for the person 
 who first used them as the embodiment of an idea. 
 In either case, the logical value of a proposition 
 depends to a large extent on language, on the fitness 
 of the verbal forms which are chosen as the medium 
 of ideas. If one realises the great difficulty, which 
 the masters of literature alone have at all adequately 
 overcome, of choosing words that reveal the mean- 
 ing their employment is intended to convey, he will 
 understand why logicians, since Aristotle, have con- 
 tinued to regard language as one main source of 
 logical fallacy. The study of the fallacies which 
 beset our interpretation of propositions through 
 the ambiguous use of language will form for us the 
 first group of fallacies. 
 
 Our second main group of fallacies will comprise 
 those mistakes which threaten our comprehension 
 of the full meaning of propositions. It will be 
 remembered that we pointed out that our relation 
 to propositions is two fold. In the first place, prop- 
 ositions need interpreting, and, as we have just now 
 intimated, the difficulties in the way of interpreting 
 
FALLACIES 513 
 
 propositions constitutes the first main class of fal- 
 lacies. But, in the second place, it was pointed out 
 that propositions contain implications which limit 
 in certain determinate directions what we can think 
 about the subject-matter of their assertion. For 
 instance, we said that if we admit the truth or 
 falsity of a given proposition we are thereby com- 
 mitted to the truth or falsity of a number of other 
 propositions. An examination of the possible 
 sources of error in this region, the region of logical 
 implication, will enable us to avoid one of the most 
 frequent pitfalls in the way of that accuracy and 
 precision that is the desideratum of the intellectual 
 life. 
 
 The fallacies that are included under the two 
 heads just mentioned refer to the meaning of prop- 
 ositions taken singly, they are the fallacies which 
 arise in the field of simple, unmediated assertion. 
 When, however, we go beyond this region, and our 
 assertions take the more complex forms that we 
 have studied in the syllogism and induction, a 
 special group of fallacies has to be recognised, be- 
 cause here thought is guided in its efforts to reach 
 logically sound conclusions by special principles and 
 rules. The mistakes that occur in connection with 
 the control of thought by these principles and rules 
 will constitute a third main group of fallacies. 
 
 A fourth group of fallacies may be recognised 
 if we recall that no logical assertion, whether simple 
 or complex, is ever a wholly detached unit, and 
 
 33 
 
514 A TEXT-BOOK OF LOGIC 
 
 that, if such assertions are to be interpreted cor- 
 rectly, they must be brought into relation to the 
 contexts out of which their original meaning was 
 forged. Every assertion, we have said, implies a 
 certain universe of discourse. Now we often find 
 that the plausibility of statements and arguments 
 depends on suggestions derived from their contexts 
 which are not directly related to the truth char- 
 acter of the statements and arguments themselves, 
 and for these extrinsic reasons are frequently, 
 though fallaciously, accepted as true. They are 
 cases of this kind that we shall classify under the 
 present head. 
 
 For the sake of convenience, we shall refer to 
 the four main classes of fallacy that have just been 
 distinguished, in the order in which we have con- 
 sidered them, as fallacies of interpretation, of im- 
 plication, of inference, and of the context. A cer- 
 tain latitude must be allowed in the use o*f this 
 classification, as indeed it must of any classification, 
 of fallacies. The only justification that any scheme 
 can receive is that it brings together, in a way that 
 connects with the development of logical doctrine, 
 the errors to which we are exposed in our efforts 
 to think accurately and convincingly. If, in addi- 
 tion, it groups the fallacies in a way that is easily 
 remembered, it has a still further advantage. 
 
 Fallacies of Interpretation. These are due, as we 
 have said, to the deceptiveness of the language in 
 which propositions are expressed. They all, there- 
 fore, fall under the defect of ambiguity. But since 
 
FALLACIES 515 
 
 ambiguity may attach either to the words or to the 
 structure of our statements, we may distinguish 
 two classes of error to which our interpretation of 
 propositions is exposed. Among the fallacies due to 
 verbal ambiguity we may include equivocation, 
 accent, composition, division, accident, and converse 
 fallacy of accident; and among those due to struc- 
 tural ambiguity, amphibole and false parenthesis. 
 
 Verbal Ambiguity. In discussing the fallacies 
 that are due to verbal ambiguity, we may remind 
 ourselves that ambiguity is not identical with mere 
 indefiniteness in the meaning of words, and that, 
 in view of a certain unavoidable indefiniteness in 
 the meanings of the words we employ, propositions 
 can attain only a non-ambiguous signification. The 
 principle of non-ambiguity, we said, controlled all 
 our efforts after logical exactness both with respect 
 to terms and propositions. We cannot, therefore, 
 convict of any of the verbal fallacies a proposition 
 whose terms are indefinite, if this indefiniteness 
 does not spread to the meaning of the proposition 
 taken as a whole. When, however, the indefiniteness 
 of the parts affects the meaning of the whole prop- 
 osition, we have a case that falls under the class 
 of fallacies that we are now considering. With this 
 reminder, we take up seriatim the several fallacies 
 that originate in verbal ambiguity. 
 
 Equivocation, or indefiniteness in the denotation 
 or connotation of a term, gives rise to a fallacy 
 when either term of a proposition is interpreted in 
 a different sense by the speaker and by the person 
 
516 A TEXT-BOOK OF LOGIC 
 
 spoken to, and this affects the meaning of the prop- 
 osition as a whole ; or when, for the same individual, 
 any term which appears in a continuous discourse 
 fails to retain the same meaning in the various 
 propositions in which it occurs, and this affects 
 the conclusion to which one is led. The latter is, 
 perhaps, the more usual, as it is, certainly, the more 
 insidious, form of the fallacy of equivocation. Any 
 form of continuous address, and especially of public 
 address, exposes one to the danger of equivocation, 
 and the most careful writers sometimes fall into it. 
 A familiar example is the following taken from 
 Mill's argument in support of the position that hap- 
 piness is the chief aim or good of life. He says, 
 "The only proof capable of being given that an 
 object is visible is that people actually see it. The 
 only proof that a sound is audible is that people 
 hear it. And so of the other sources of our expe- 
 rience. In like manner, I apprehend, the sole evi- 
 dence it is possible to produce that anything is 
 desirable is that people do actually desire it." For 
 the purpose of his argument, the word desirable 
 must have the meaning 'worthy to be desired/ but 
 this is a meaning that is not analogous to visible 
 and audible in the context. Visible and audible 
 mean able to be seen or heard, and/ therefore, all 
 that Mill has a right to argue is that desirable 
 means 'able to be desired/ But from this meaning 
 he could not argue that happiness is the summum 
 bonum or chief good of life, for the fact that a 
 person desires an object is no proof that it is, in the 
 
FALLACIES 517 
 
 sense Mill uses the word, the most desirable. 
 Against committing or being imposed on by the 
 fallacy of equivocation we may submit the meanings 
 of our terms to the methods of translation and defi- 
 nition, as these terms have been explained above. 
 
 Accent. The fallacy of accent is any misconcep- 
 tion due to the emhasis placed on a word or group 
 of words in a sentence. It was for Aristotle the 
 mistaken accentuation of a word in writing Greek. 
 "A ludicrous instance of this fallacy," to quote 
 Jevons, "is likely to occur in reading Chapter XIII 
 of the First Book of Kings, verse 27, where it is 
 said of the prophet, 'And he spake to his sons, say- 
 ing, Saddle me the ass. And they saddled him.' 
 The italics indicate that the word him was supplied 
 by the translators of the authorised version, but it 
 may suggest another meaning. The commandment, 
 Thou shalt not bear false witness against thy 
 neighbour/ may be made by a slight emphasis of the 
 voice on the last word to imply that we are at liberty 
 to bear false witness against other persons." We 
 may, however, give certain words or groups of words 
 a prominence that does not really belong to them in 
 another way. For example, in quoting an author 
 we may separate a word from its context, italicise 
 a word which was not italicised in the original, or, 
 by leaving out qualifying words and phrases, we 
 may give certain ideas a prominence which they did 
 not have for the author himself. Connected with 
 this latter interpretation, the fallacy, as Creighton 
 
518 A TEXT-BOOK OF LOGIC 
 
 observes, "appears in connected arguments of any 
 kind in which, while the facts are not actually mis- 
 stated, certain aspects of them are so disproportion- 
 ately dwelt upon and emphasised, at the expense of 
 the rest, that a false idea of the subject in its en- 
 tirety is the result. In this wider form, this fallacy 
 is one that may be described as the particular vice 
 of special pleading; and the caution that may be 
 suggested against it is, in the language of the 
 astronomer, to make allowances for the 'personal 
 equation' both in one's own thinking and in that of 
 others." 
 
 Composition. The fallacy of composition, like 
 its converse, the fallacy of division, turns on the 
 distinction between the distributive and collective 
 use of terms. This distinction, it will be remem- 
 bered, is based on the fact that we may predicate 
 qualities and relations of a class without at the 
 same time predicating those qualities or relations 
 of the individuals that constitute the class; and, 
 conversely, we may predicate qualities and relations 
 of the individuals that constitute a class without at 
 the same time predicating those qualities or rela- 
 tions of the class. Now, we are guilty of the fal- 
 lacy of composition when, having predicated some- 
 thing of a' term used distributively, that is, of each 
 of the individuals that fall under the term, we sup- 
 pose that the predicate belongs to the term in its 
 collective sense, that is, of the individuals taken as 
 a group. "We must not argue," to use Jevons' illus- 
 
FALLACIES 519 
 
 trations, "that because every member of a jury is 
 very likely to judge erroneously, the jury as a whole 
 is also very likely to judge erroneously; nor that be- 
 cause each of the witnesses in a law case is liable to 
 give false or mistaken evidence, no confidence can 
 be reposed in the concurrent testimony of a number 
 of witnesses. It is by a fallacy of Composition that 
 protective duties are still sometimes upheld. Be- 
 cause any one or any few trades which enjoy pro- 
 tective duties are benefited thereby, it is supposed 
 that all trades at once might be benefited similarly; 
 but this is impossible, because the protection of one 
 trade by raising prices injures others." 
 
 Division. The fallacy of division is, as was said, 
 the converse of the fallacy of composition. It was 
 so considered by Aristotle. It occurs when we sup- 
 pose that a statement that is true of a group is true 
 of the individuals of the group. If, for example, 
 it is true that a particular class of college students 
 are bright, it does not follow that this is true of 
 each or any particular one of the members of the 
 class, any more than it follows that because a jury 
 can be relied on to reach a just verdict that a sim- 
 ilar confidence can be placed in any one of the jury- 
 men. Gibson has called attention to an interesting 
 illustration of this fallacy to be found in Thomas a 
 Kempis' Imitatio Christi. In the paragraph refer- 
 red to, the writer is exhorting the 'good monk' not 
 to seek any earthly delight, but to remain alone in 
 his cell. The argument by which this advice is sup- 
 ported reads: "What canst thou see elsewhere 
 
520 A TEXT-BOOK OF LOGIC 
 
 which here thou seest not? Behold the sky and the 
 earth, and all the elements, for of these are all 
 things made." Expressing this argument syllogis- 
 tically, Gibson detects the fallacy of division in the 
 middle term. Thus: 
 
 The elementary substances (in organised combination) 
 
 are the whole material world. 
 The objects included in the prospect from your cell are 
 
 the elementary substances (not so combined). 
 Therefore, the objects included in the prospect from your 
 
 cell are the whole material world. 
 
 As this ilustration suggests, the fallacy of division, 
 in common with many others, is most liable to occur 
 in continuous discourse, and the value of putting 
 the subject-matter of such discourse into the logical 
 forms suitable to them is that we may the more 
 easily detect any fallacy lurking in our thought, or 
 in the forms in which that thought is expressed. 
 
 Accident. The fallacy of accident occurs when 
 we suppose that what is true of a term used in a 
 relatively indeterminate or unconditioned sense, is 
 true of the term when used in a relatively deter- 
 minate or conditioned sense. The Latin name of 
 the fallacy is, Argumentum a dicto simpliciter ad 
 dictum secundum quid. It is, that is to say, a tran- 
 sition from what is true of an indeterminate state- 
 ment to what is true of the same statement 'with a 
 modification/ In other words, it consists in secur- 
 ing assent to a statement in a general form, and 
 then proceeding as if it held under some special 
 
FALLACIES 521 
 
 circumstance. If we supposed, for example, that 
 because it is right for a man to inculcate his own 
 opinions, it is, therefore, right for a magistrate to 
 use his position to enforce his own political views, 
 we should be guilty of this fallacy. For, as Mellone, 
 from whom this illustration is taken, remarks, "we 
 cannot infer of his special powers as a magistrate 
 what is only true of his general rights as a man." 
 We may often detect the fallacy in our thoughts 
 about moral questions. Thus, in discussing such 
 questions, "one may insist that all men by nature 
 seeks after the good, meaning that each man acts 
 sub specie boni, and is therefore seeking after some 
 kind of good, even when he is pursuing his own 
 pleasure. But, in continuing the argument, he may 
 use the term 'good' in a differentiated sense e. g., 
 in the sense of the common good, or the good of 
 humanity and come thereby, through a fallacy of 
 accident, to the conclusion that all men by nature 
 seek the general good." 
 
 The Converse Fallacy of Accident occurs when 
 we suppose that what is true of a term used in a 
 determinate or conditioned sense is true of the term 
 when used in an indeterminate or unconditioned 
 sense. The Latin name of the fallacy is, Argumen- 
 tum a dicto secundum quid ad dictum simpliciter. 
 The following illustrations will be sufficient to make 
 the nature of this fallacy obvious. For example, 
 let us suppose that it can be shown that the syllo- 
 gism is of no use in the discovery of new truth, are 
 we warranted in supposing, as the early modern 
 
522 A TEXT-BOOK OF LOGIC 
 
 critics of the syllogism seem to have done, that it 
 is, therefore, of no use whatever ? Or, if philosophy 
 'bakes no bread/ is it, therefore, useless? The 
 affirmative answer to both these questions involves 
 the converse fallacy of accident. 
 
 Structural Ambiguity. In the chapter on the 
 proposition, it was pointed out that particular 
 statements are often ambiguous, not because the 
 terms in which they are expressed are ambiguous, 
 but because the structure of the sentences in which 
 ideas are expressed are so. It is to the grammatical 
 structure of sentences, for example, that we must 
 attribute, in part, the difficulty sometimes expe- 
 rienced in determining the subject and predicate 
 terms of given propositions. Whenever syntactical 
 relations obscure the meaning of sentences or para- 
 graphs, there is presented a hindrance to the correct 
 interpretation of propositions. Difficulties of the 
 kind in question are more possible in the classical 
 languages where the word order in sentences is 
 more variable, and where oblique constructions are 
 more common, than in English; but something of 
 the same sort is seen in English poetry in which a 
 departure from the relative simplicity of the ordi- 
 nary prose sentence is often made necessary by the 
 demands of metrical composition. 
 
 Amphibole. Now, whenever the structure of the 
 sentences in which ideas are expressed, in prose 
 or in poetry, leads to opposed interpretations of 
 such sentences, we have the typical fallacy of amphi- 
 bole. Sometimes sentences whose structure renders 
 
FALLACIES 523 
 
 their interpretation difficult, although not neces- 
 sarily ambiguous, are spoken of as amphibolic. 
 This is a view similar to that sometimes taken of 
 words, when any degree of indefiniteness is thought 
 sufficient to render them equivocal. This seems to 
 us too loose an interpretation of these fallacies. As 
 we have pointed out in regard to words, there is 
 also a certain freedom in the use of syntactical 
 relations that is allowable and necessary if partic- 
 ular shades of meaning are to get expressed in the 
 sentences we employ. The object that the transla- 
 tion of sentences into propositions keeps in view 
 is, not to give all statements an equal clearness, but 
 to bring out the exact degree of clearness that be- 
 longs to each of our statements. A certain indefi- 
 niteness of meaning may be characteristic of propo- 
 sitions, therefore, without involving them in the 
 fallacy of amphibole. Before we can convict any 
 statement of being amphibolic, we must have ex- 
 hausted all the means at our disposal to interpret 
 the statement, and to give it an expression which 
 truly represents its meaning. If it then remains 
 ambiguous, if, that is, our attempt to give the state- 
 ment a prepositional form is defeated on account of 
 its equivocal syntax, we may properly regard it as 
 an example of the fallacy of amphibole. An illus- 
 tration of this statement may be found in the often 
 quoted lines of Shakespeare, The Duke yet lives 
 that Henry shall depose.' We are baffled in any 
 attempt to put this sentence into the form of a 
 proposition, because its structure does not enable 
 
524 A TEXT-BOOK OF LOGIC 
 
 us to determine whether it means, The Duke yet 
 lives who shall depose Henry/ or, The Duke yet 
 lives who shall be deposed by Henry/ Such a 
 statement, therefore, is essentially amphibolic. The 
 student will recall, in further illustration, many of 
 the utterances of the oracles, for instance, 'If 
 Croesus should wage war against the Persians, he 
 would destroy a mighty empire/ As further ex- 
 amples we may cite, 'It is possible for thee the 
 enemy to overcome/ The lion David slew/ 
 
 False Parenthesis. Closely connected with the 
 foregoing, is the fallacy of false parenthesis. It 
 consists essentially in an uncertainty with regard 
 to the relations of the main and subordinate clauses 
 of a sentence. For example, 'I ruined the cause 
 and injured my own prospects which I deeply re- 
 gret/ a statement that may mean either, 'I ruined 
 the cause, and injured my own prospects which I 
 deeply regret/ or, 'I ruined the cause and injured 
 my own prospects, which I deeply regret/ A sim- 
 ilar fallacious statement is 'I will begin and finish 
 the task tomorrow/ The advertising columns of 
 our newspapers are sometimes said to provide us 
 with humorous illustrations of the fallacy of paren- 
 thesis. For instance: 
 
 LOST A valuable silk umbrella belonging to a gentle- 
 man with a curiously carved head. 
 
 WANTED A groom to look after two horses of a pious 
 frame of mind. 
 
 FOR SALE A Newfoundland dog ; will eat anything, 
 particularly fond of children. 
 
FALLACIES 525 
 
 We introduce these instances, not in order to 
 subscribe to the view that they are amphibolic in 
 character, but to point out that if these are to be 
 admitted as examples of amphiboly, then any badly 
 constructed sentence would have to be included 
 whether or not their meaning was involved in am- 
 biguity. This is a view to which, as we said above, 
 we cannot subscribe. 
 
 Fallacies of Implication. The second main class 
 of fallacies which we have now to consider com- 
 prises those that occur when for any reasons we 
 mistake the implications of prepositional state- 
 ments. The difficulties that confront our efforts to 
 give to any statement a prepositional form have 
 been considered already, and in contrast to these, 
 the ones with which we are now concerned presup- 
 pose that those difficulties have been overcome, and 
 that we know unequivocally the significance that 
 particular statements have. Until we are sure what 
 the asserted meaning of a proposition is, tre cannot 
 raise the question whether, and if so what, further 
 or implied meaning it can have. 
 
 It will be remembered that by implication is 
 meant the unexpressed signification of a logical 
 proposition, and that implications may assume one 
 or the other of two forms. In the first form, the 
 unexpressed or implied propositions may be related 
 to the given proposition in the way of opposition, 
 in the second form, they may be related to the 
 given proposition in the way of eduction. These 
 
526 A TEXT-BOOK OF LOGIC 
 
 distinctions will provide us a natural and easy 
 method of classifying the fallacies of implication. 
 
 Fallacies of Opposition occur when, from state- 
 ments accepted as true or false, other statements 
 dealing with the same subject-matter are derived, 
 the truth or falsity of which is, mistakenly, sup- 
 posed to rest upon the principles that determine the 
 relations of opposed propositions. It has been 
 shown above that there are four kinds of relation 
 between propositions in opposition, contrariety, 
 subcontrariety, subalternation, and contradiction. 
 These relations have been studied, and the propo- 
 sitions between which each obtains have been indi- 
 cated. ' In view, therefore, of what we have learned 
 with respect to this class of implication, it is readily 
 seen that, in respect to this class, our thought be- 
 comes fallacious when we suppose that the prin- 
 ciples of opposition justify a statement which, as 
 a matter of logic, they are incapable of support- 
 ing. Or, to put it another way, any statement 
 which avowedly rests upon the principles of opposi- 
 tion is fallacious if it can be shown that those prin- 
 ciples fail to give it the necessary support. 
 
 In general, it is quite obvious that there are as 
 many fallacies of opposition as there are pairs of 
 propositions between which relations of opposition 
 may hold. Some of these relations are in themselves 
 so obvious, the relation of contradiction, for in- 
 stance; and others lose so readily whatever obscur- 
 ity they may have when they occur between certain 
 pairs of propositions, that it is not necessary to 
 
FALLACIES 527 
 
 consider all the possible fallacies of opposition. All, 
 therefore, that we shall attempt is to point out 
 some of the difficulties that may be experienced in 
 the effort to conform our thinking to the principles 
 of opposition. 
 
 And, in the first place, we may consider the 
 fallacy of contrariety which occurs when we sup- 
 pose that the falsity of one universal proposition, 
 A or E, involves the truth or falsity of the other, 
 E or A. It may be false, for example, that 'None 
 of the members of the team are bona fide students/ 
 but it does not , therefore, follow that 'All the 
 members of the team are bona fide students,* 
 and it does not follow because, it might still be 
 true that 'Some of the members of the team are not 
 bona fide students.' It is certainly very easy for 
 the untrained mind to proceed from the falsity of a 
 universal to the truth of its logical contrary, and 
 one is particularly exposed to this error when the 
 latter statement is separated in our discourse from 
 the former by an appreciable lapse of time. But, 
 as we saw above, the statement of what is false in 
 a universal form does not enable us to say anything 
 with respect either to the truth or falsity of its 
 contrary. In such cases the contrary is always in- 
 volved in doubt. 
 
 In the second place, we are exposed to a 
 fallacy of sub contrariety when we attempt to argue 
 from the truth of a particular proposition, I or 
 O, to the falsity of another particular proposition, 
 or I. We run into this error when we forget 
 
528 A TEXT-BOOK OF LOGIC 
 
 that two particular propositions dealing with the 
 same subject-matter, one of which is affirmative 
 and the other negative, may both be true. From the 
 statement, for example, that 'Some of those who 
 have given their word are keeping it faithfully/ it 
 does not follow that 'Some of those who have given 
 their word are not keeping it faithfully' is false, 
 since this latter statement might be true of any of 
 those not included in the original statement. 
 
 In the third place, fallacies of sub alternation may 
 arise when we argue either from the falsity of a 
 universal propostion, or from the truth of a par- 
 ticular proposition. The falsity of a universal propo- 
 sition, 'All that I have done for you has gone for 
 nought/ might very well seem to involve the falsity 
 of the particular subaltern, 'Some of the things I 
 have done for you have gone for nought;' but this 
 would not necessarily be the case, because the truth 
 or falsity of the subaltern proposition depends in 
 this case upon the degree of falsity of the original 
 proposition, and it is exactly this that we cannot de- 
 termine from that proposition itself. Unless it were 
 so common, one would hardly think it necessary to 
 call 1 attention to the other fallacy of subalternation, 
 the fallacy, namely, that is involved in proceeding 
 from the truth of a particular statement to the truth 
 of its corresponding universal. It may, for example, 
 be quite clear that from the statement that 'Some 
 books are dull/ we cannot proceed to the statement 
 that 'All books are dull/ but we dare say, it is not 
 equally obvious that we cannot proceed from the 
 
FALLACIES 529 
 
 statement, 'Some planets move in their own orbits', 
 to, 'All planets move in their own orbits.' The rea- 
 son why we cannot argue from the truth of a part- 
 ticular statement to either the truth or falsity of 
 the universal of the same quality seems to be that 
 we have no means of determining, by an examina- 
 tion of the original statement, the precise' amount 
 of truth that is claimed by it, that is, whether it 
 states the whole truth about its subject, or only 
 part of it. 
 
 Fallacies of Eduction. Eductions were defined 
 above as those relations which propositions dealing 
 with the same subject-matter have to one another 
 when they express what is true about this subject- 
 matter from different points of view. There are, 
 as we said, two fundamental methods for deter- 
 mining these relations, obversion and conversion, 
 and it is with respect to these methods, therefore, 
 that fallacies are likely to occur. An eductive fal- 
 lacy may, consequently, be defined as an error of 
 implication due to a misunderstanding of obversion, 
 of conversion, or of both. 
 
 The fallacy of obversion is most likely to occur 
 when for the contradictory of the predicate of an 
 original proposition we substitute its contrary in 
 the obverse proposition. Now by contrary terms 
 we mean those which, although opposed to one an- 
 other, do not exhaust between them the particular 
 universe of discourse to which they both belong. 
 Black and white are, in this sense, contrary, but 
 they are not contradictory, terms. By a contra- 
 
 34 
 
530 A TEXT-BOOK OF LOGIC 
 
 dictory term we mean one that, together with the 
 original term, does exhaust the universe of discourse 
 to which both terms belong. Thus, black and not- 
 black are contradictory, but they are not contrary, 
 terms. It is, then, a confusion of contrary with 
 contradictory terms, in the sense in which these 
 have been defined, that gives rise to the fallacy of 
 obversion. Thus, it would be quite fallacious, for 
 the reason already assigned, if we supposed that 
 we were warranted in saying of a particular indi- 
 vidual that he was bad, if all we knew was that he 
 is not good; good and bad are contrary, they are 
 not contradictory, terms. Again, if we supposed 
 that the obverse of the proposition 'He is not happy, 
 was 'He is unhappy/ there would be as complete 
 misunderstanding of what was implied in the first 
 statement as if we supposed that because a certain 
 object was not red that it was, therefore, green. 
 
 Fallacies of Conversion are most likely to occur 
 in the case of the universal affirmative, and the 
 particular negative propositions. In the latter case, 
 the fallacy occurs when we suppose that from a 
 particular negative proposition anything can be 
 asserted merely by converting it. It is quite true, 
 for example, that 'Some elements are not liquid/ 
 and also that 'Some liquids are not elements/ but 
 the one statement does not follow from the other 
 by simple conversion. Again, a fallacy of conver- 
 sion occurs when we suppose that the universal 
 affirmative proposition can be simply converted, a 
 supposition that is based on the false assumption 
 
FALLACIES 531 
 
 that both terms of the proposition are distributed. 
 In universal affirmative propositions, as we have 
 seen, the predicate terms are undistributed; and, 
 consequently, when, through conversion, these terms 
 become the subjects of new propositions, these prop- 
 ositions must be particular in quantity. The neg- 
 lect of this consideration leads directly to a fallacy 
 of conversion. 
 
 Fallacies of Inference. The class of fallacies to 
 which we now direct attention includes the errors 
 to which our thinking is exposed when it is con- 
 fronted by the difficulties that are involved in the 
 more complex logical processes known as argu- 
 ments. The two classes of fallacy already con- 
 sidered, the fallacies of interpretation and implica- 
 tion, are concerned with the errors to which thought 
 is liable when it deals with single statements; but 
 it is not until these simpler errors have been avoided, 
 not until single statements have been given a strictly 
 logical form and content, that there comes into view 
 the class of fallacy that is connected with our at- 
 tempt to put into their logical relations such logically 
 determined propositions. For, in an argument, not 
 only must the constituent propositions be free from 
 ambiguity, but the relations between these proposi- 
 tions must be precisely determined. It is perfectly 
 obvious, therefore, that the avoidance of the fal- 
 lacies of interpretation and implication is essential, 
 if we are to meet and overcome the difficulties that 
 are occasioned by the more complex character of 
 our thinking in the process of argument. We may, 
 
532 A TEXT-BOOK OF LOGIC 
 
 therefore, say that just as the avoidance of the fal- 
 lacies of interpretation are presupposed by any 
 attempt to avoid the fallacies of implication, so the 
 avoidance of both these classes of fallacy is presup- 
 posed by any attempt to overcome the fallacies of 
 inference. 
 
 Arguments, from the time of Aristotle, have 
 been recognised to be of two kinds: those, namely, 
 that start with the recognition of some general 
 principle, and those that start with the collection 
 of a number of particular facts. In the former, the 
 aim is to bring, through the mediation of a middle 
 term, some particular fact under the principle which 
 constitutes what is called the major premise of the 
 argument; in the latter, it is, through an analysis 
 of particular facts, to state a principle that shall 
 exhibit what is common to all the facts examined, 
 and, if possible, to extend that principle to other 
 facts which either have not been examined, or which 
 are not known to exist. It is usual to call the 
 former kind of argument deductive, and the latter, 
 inductive; and, although there is a danger of sup- 
 posing, falsely, that they constitute quite separate 
 logical processes, we may use these names, deductive 
 and inductive, for the purpose of classifying the 
 fallacies of inference. The deductive fallacies will 
 include those errors that arise in connection with 
 the syllogism, and the inductive fallacies will include 
 those that arise in connection with the various steps 
 through which it is necessary to pass in our efforts 
 to establish causal connections. 
 
FALLACIES 533 
 
 / 
 
 The Deductive Fallacies. Whenever an argument 
 starts from the conscious acceptance of a general 
 truth about its subject-matter, and proceeds to show 
 that some particular fact is a special instance of that 
 truth, it is said to be a deductive argument. Now, 
 since we accept such general truths as are the 
 starting points of deductive arguments in either 
 one or the other of three forms, in the forms, 
 namely, of categorical, hypothetical, or disjunctive 
 propositions, these arguments, as we have seen, 
 assume a form and character which corresponds to 
 the difference in the method and principle by which 
 thought, in each case, proceeds to its conclusion. 
 In consequence of this fact, we found it necessary 
 to consider categorical arguments, hypothetical 
 arguments, and disjunctive arguments separately, 
 and to give special attention to the rules by which 
 thought, in each type of argument, is controlled. 
 It follows, from this statement with respect to the 
 various forms of deductive arguments, that the 
 deductive fallacies can be classified most conve- 
 niently by following the line of cleavage between 
 the arguments in connection with which they are 
 likely to occur. In the following sections, therefore, 
 we shall pass in review what we may call the cate- 
 gorical, hypothetical, and disjunctive fallacies, the 
 fallacies which occur, or are liable to occur, in those 
 types of argument to which similar descriptive 
 names have been given. 
 
 Categorical Fallacies may be defined as those mis- 
 takes in reasoning which render the conclusions of 
 
534 A TEXT-BOOK OF LOGIC 
 
 categorical arguments erroneous. These fallacies 
 fall conveniently into two groups, according as the 
 error lies in the terms, or in the character of the 
 proposition of the syllogism. To the former group 
 we may assign the fallacies of four terms, and to 
 the latter, the fallacies of insufficient premises. 
 
 Fallacies of Four Terms occur as a breach of 
 the rule which states that a syllogism must contain 
 three, and only three, terms. Their occurrence is 
 due to a failure to rid the terms of a syllogism of 
 ambiguity. Now, since ambiguity may occur either 
 in the connotation or in the denotation of a term, 
 and may attach to any one of the terms of a syllo- 
 gism, it is evident that the fallacies of four terms 
 are of two kinds ; those, namely, which occur when 
 the meaning of any of the terms of a syllogism is 
 ambiguous, and those which are due to a mistaken 
 distribution of any of the terms of a syllogism. 
 Among the former, it is usual to call special atten- 
 tion to the case of the middle term, but it should 
 be remembered that the ambiguity of the major or 
 of the minor term may also invalidate an argu- 
 ment by giving rise to the fallacy of four terms. 
 When the fallacy of four terms invalidates a syllo- 
 gism on account of the connotative ambiguity of the 
 middle term, it takes the special name of ambiguous 
 middle; when an argument is invalid on account of 
 a similar ambiguity of the major term, the fallacy is 
 called ambiguous major; and when ambiguity in the 
 meaning of the minor term destroys the validity of 
 an argument, the fallacy is called ambiguous minor. 
 
FALLACIES 535 
 
 It is not necessary to give illustrations of all these 
 fallacies. The following will serve to show the form 
 in which they are likely to occur. If, as Jevons 
 remarks, we argue "that 'all metals are elements and 
 brass is a metal, therefore it is an element/ we 
 should be using the middle term 'metal' in two dif- 
 ferent senses, in one of which it means the pure sim- 
 ple substances known to chemists as metals, and in 
 the other a mixture of metals commonly called metal 
 in the arts, but known to chemists by the name 
 alloy." Or, if we argued "that 'what is right should 
 be enforced by law, and that charity is right and 
 should be enforced by law' . . . it is evident that 
 'right' is applied in one case to what the conscience 
 approves, and in another use to what public opinion 
 holds to be necessary for the good of society." 
 
 The other type of fallacy which results in break- 
 ing an argument under the weight of four terms, 
 is due to a disregard of the denotation or distribu- 
 tion of the terms of a syllogism. In these cases, the 
 erroneous conclusion results from a neglect of the 
 extent of a term's meaning, rather than to a dis- 
 regard of the meaning itself. In other words, it is 
 a fallacy of the division, not a fallacy of the defi- 
 nition, of a term. Now, as we have seen, the dis- 
 tribution of the terms of a syllogism is subject 
 to special rules. In respect of the middle term, the 
 rule states that this term must be distributed in one, 
 at least, of the premises ; and in respect of the major 
 and minor terms, the rule states that if either of 
 these terms is distributed in the conclusion, it must 
 
536 A TEXT-BOOK OF LOGIC 
 
 have been distributed in the corresponding premise. 
 When the rule relating to the middle term is dis- 
 regarded, the resulting fallacy is known as undis- 
 tributed middle; and when the rule relating to the 
 terms of the conclusion is disregarded, the resulting 
 fallacy, in the case of the major term, is known as 
 illicit process of the major, and, in the case of the 
 minor, as illicit process of the minor. The fol- 
 lowing illustrations will throw light on these state- 
 ments. If we should argue, for example, that be- 
 cause "all rash men are confident, and all brave men 
 are confident," therefore, "all rash men are brave," 
 we should be guilty of the fallacy of undistributed 
 middle. Again, if we argued "that 'because many 
 nations are capable of self-gvoernment, and and 
 that nations capable of self-government should not 
 receive laws from a despotic government, therefore 
 no nation should receive laws from a despotic gov- 
 ernment/ we should be clearly exceeding the con- 
 tents of our premises. The minor term, many 
 nations, was undistributed in the minor premise," 
 and must not, consequently, be used in a distributed 
 sense in the conclusion. While it is comparatively 
 easy to detect an illicit process of the minor, it is 
 much more difficult as a rule to detect an illicit 
 process of the major. The following from Creighton 
 is an example of the latter fallacy. "All rational 
 beings are responsible for their actions ; brutes are 
 not rational beings; therefore, brutes are not re- 
 sponsible for their actions." 
 
FALLACIES 537 
 
 Fallacies of Insufficient Premises. These consti- 
 tute the second class of categorical fallacies, and 
 they may be described as breaches of those rules of 
 the syllogism that were considered and illustrated 
 above as rules of quality and rules of quantity. The 
 rules of quality refer to the grounds on which affir- 
 mative and negative conclusions can be based, and 
 the rules of quantity to the grounds on which uni- 
 versal and particular conclusions can be based. In 
 the main, we apprehend that these rules have caused 
 the student no great difficulty, and that he will have 
 become familiar with their application. But because 
 limiting instances are liable to cause more or less 
 confusion, because, that is, we find it difficult to keep 
 strictly within the boundaries within which any set 
 of rules applies, we direct attention again to the fact 
 that there are conditions which preclude certain 
 prepositional statements from rendering valid con- 
 clusions. It is a general fact that conclusions do 
 not follow from any combination of propositions. 
 If we wish to support a conclusion by premises or 
 grounds, those premises must have a character from 
 which the conclusion can be shown to follow, and 
 that means that a certain other character is strictly 
 forbidden. Now, if this is true of particular con- 
 clusions, we may go further and ask whether there 
 are any combinations of propositions which support 
 no conclusion whatever, that is, whether there are 
 any limits of strictly categorical argumentation. 
 Now such limits to all categorical inference we find 
 in the two cases that are included here for con- 
 
538 A TEXT-BOOK OF LOGIC 
 
 \ 
 
 sideration, the cases, namely, of negative and par- 
 ticular premises. We have shown above that any 
 attempted reasoning on the grounds of particular or 
 negative premises involves us in one or other of the 
 fallacies of distribution; but what is more impor- 
 tant to remark now is that the study of these two 
 cases enables us to insist upon certain character- 
 istics of syllogistic reasoning which are fundamental 
 to our understanding and employment of this type 
 of argument. The syllogism, it should be observed, 
 rests upon the possibility of making with respect 
 to the subject-matter of the argument an affirmative 
 and universal statement. The universal statement 
 need not be affirmative, and the affirmative state- 
 ment need not be universal ; but unless the premises 
 contain the statement of universal affirmative rela- 
 tions, no conclusion whatever can be drawn. Con- 
 versely, if we wish to ground a belief on premises 
 from which it can be shown to follow, these prem- 
 ises, considered as a combination of propositions, 
 must be universal and affirmative. Indeed, this is 
 only to say that any categorical argument must con- 
 form to the character of syllogistic reasoning. For, 
 to speak of syllogistic reasoning at all, is to imply 
 that conclusions are inferred from, or rest upon, 
 statements about a given subject-matter which are 
 affirmative and universal in the sense in which those 
 terms have been explained. Now, if this is the true 
 character of the syllogism, it follows that particular 
 premises, whether they be both negative, or both 
 affirmative, or one negative and the other affirm- 
 
FALLACIES 539 
 
 ative, cannot express the structure of a syllogistic 
 argument, because they do not contain the note of 
 universality; and that negative premises also fail 
 to do so, whether both premises are universal or 
 only one is, since they fail to express the note of 
 affirmation. To ground a conclusion upon premises 
 which fulfil only one of the conditions of a cate- 
 gorical -argument, that is, upon propositions which 
 are affirmative without being universal, or upon 
 propositions which, although universal, are not 
 affirmative, is to fall into one or the other of the 
 fallacies of insufficient premises. In the former 
 case, we have the fallacy of particular premises, 
 and in the latter, the fallacy of negative premises. 
 
 Hypothetical Fallacies may be defined as those 
 mistakes in reasoning which render the conclusions 
 of hypothetical arguments erroneous. Hypothetical 
 arguments, as we have seen, derive their character 
 from the relation of antecedence and consequence 
 which is expressed in their major premise. Two 
 observations only need to be made to remind our- 
 selves of the nature and limits of hypothetical 
 arguments. The first is that the major premises of 
 such arguments are always hypothetical proposi- 
 tions, that is, propositions which state a relation 
 between two possibilities. From the fact that a 
 relation of antecedence and consequence is always 
 affirmed between these two possibilities in hypothet- 
 ical propositions, it follows that the acceptance of a 
 hypothetical statement commits us to the belief that 
 the possibility which is expressed as the consequent 
 
540 A TEXT-BOOK OF LOGIC 
 
 can be regarded as an actual fact, only when the 
 possibility expressed as the antecedent states a con- 
 dition which is known to be fulfilled. We cannot 
 argue in the reverse order, that is, from the known 
 existence of the consequent to the existence of the 
 antecedent. The second remark is that the major 
 premise affords no guarantee that the condition it 
 states is anywhere fulfilled, and, consequently, no 
 guarantee that the fact stated in the consequent is 
 any where to be met with. Whether the antecedent 
 or consequent is a fact that the minor premise can 
 affirm or deny, depends upon whether either has 
 been observed. Thus, the possibility of a hypothet- 
 ical argument rests upon our ability to affirm or 
 deny, for some other reason than the major premise 
 itself affords, one or other of the possibilities be- 
 tween which the major premise postulates a rela- 
 tion; but within these limits the validity of such 
 arguments depends upon a proper interpretation of 
 the relation between antecedent and consequent as- 
 serted by the major premise. It is, consequently, to 
 a misunderstanding of this relation that we must 
 look for the source of the fallacies which render the 
 conclusions of hypothetical arguments erroneous. 
 
 The hypothetical fallacies are due, as we said 
 just now, to a wrong interpretation of the relation 
 between antecedent and consequent asserted in a 
 hypothetical proposition. Now, since there are two 
 terms in a hypothetical proposition each of which 
 we may affirm or deny, the relation between ante- 
 cedent and consequent may be interpreted, theo- 
 
FALLACIES 541 
 
 retically, in any one of four possible ways. It might 
 be interpreted to mean that (1) if the antecedent 
 is affirmed, the consequent may also be affirmed; 
 (2) if the antecedent is denied, the consequent may 
 also be denied; (3) if the consequent is affirmed, 
 the antecedent may also be affirmed; (4) if the con- 
 sequent is denied, the antecedent may also be denied 
 Now, as we pointed out before, it is only when the 
 minor premise either affirms the antecedent or 
 denies the consequent that the relation asserted in 
 the major premise is interpreted correctly; only 
 two, therefore, of the alternatives enumerated above 
 represent truly the relations involved in a hypo- 
 thetical proposition. When either of the other rela- 
 tions is asserted in the minor premise of an argu- 
 ment, that is, when the minor either affirms the con- 
 sequent or denies the antecedent, ; the argument 
 must be rejected as fallacious. The fallacy of deny- 
 ing the antecedent leads to an eroneous denial of 
 the consequent, and the fallacy of affirming the con- 
 sequent leads to an erroneous affirmation of the 
 antecedent. Both fallacies, as we shall see, arise 
 from the neglect of an underlying material fact of 
 considerable importance for a correct understanding 
 of the hypothetical syllogism. 
 
 In general, it may be remarked that the hypo- 
 thetical fallacies are due, on the material side, to a 
 failure to recognize the complexity and interconnec- 
 tion of natural events. It is true that the object 
 of our study of nature is to determine, in the strict 
 sense, causal connections, that is, relations between 
 
542 A TEXT-BOOK OF LOGIC 
 
 phenomena of such a nature that, not only does the 
 consequent follow from the antecedent, but the 
 stated antecedent is implied in the occurrence of 
 the consequent. Our knowledge of natural events, 
 however, frequently falls below this standard, and 
 we have to be satisfied with the affirmation of a one- 
 sided relation, that is, with the statement of a rela- 
 tion between antecedent and consequent of such a 
 nature that while the former is always followed by 
 the latter, it does not always and necessarily pre- 
 cede the latter. There are large areas of knowl- 
 edge, in other words, in which the relations involved 
 fail to display the characteristics of causal con- 
 nections, and in reference to them we are bound 
 to recognise what Mill called a plurality of causes. 
 Now it seems to be the neglect of this consideration 
 that is really at the foundation of the fallacies 
 which befall hypothetical arguments. For, as Mel- 
 lone states, "if we deny the antecedent, we cannot, 
 therefore, deny the consequent, for the latter may 
 be true for other reasons, and if we affirm the con- 
 sequent, we cannot affirm the antecedent, for the 
 consequent may result from other reasons." In 
 either case, that is to say, we must recognise the 
 possible existence of more connections between 
 antecedent and consequent than the one which is 
 made the subject of statement by the major 
 premise, and this possibility places limitations 
 upon the interpretation which we can give to 
 hypothetical statements. It is true that, if the major 
 premise states a causal connection between the 
 
FALLACIES 543 
 
 antecedent and consequent, we may argue from 
 the affirmation or denial of the former to the affir- 
 mation or denial of the latter, and vice versa. In 
 any other case, the possible operation of a plurality 
 of causes must be allowed to determine the limits 
 which we place upon hypothetical arguments. From 
 this point of view, it seems quite clear that when 
 we argue, "If a man's character is avaracious, he 
 will refuse to give money for useful purposes; this 
 man refuses to give money for useful purposes, 
 therefore, this man's character is avaracious," the 
 conclusion is erroneous, not merely because the 
 minor premise affirms the consequent, but because, 
 as we all know, there are other reasons, not at all 
 connected with a man's character, which may make 
 a refusal of the kind in question the necessary and 
 right course for him to pursue, And it seems 
 equally obvious that when we argue, 'If some agree- 
 ment is not speedily arrived at between employers 
 and workmen, the trade of the country will be 
 ruined, an agreement will not be arrived at and 
 therefore the trade of the country will be ruined/ 
 the conclusion is erroneous, not merely because the 
 antecedent is denied, but because the prosperity of 
 a country depends upon other conditions than the 
 one specified in the antecedent of the major premise. 
 In both these instances we see that the breach of the 
 formal rule of hypothetical arguments is tanta- 
 mount, on the material side, to the neglect of the 
 plurality of causes, that is, to the failure to recog- 
 
544 A TEXT-BOOK OF LOGIC 
 
 nise the complexity and interconnection of natural 
 events. 
 
 Disjunctive Fallacies may be defined as those mis- 
 takes in reasoning which render the conclusions of 
 disjunctive arguments erroneous. Disjunctive argu- 
 ments, as we have seen, derive their character from 
 the fact that the major premises of such arguments 
 state a series of alternative predicates any one or 
 more of which, as a matter of fact, may be found 
 to qualify their subjects. Any conclusion which is 
 reached on the basis of a disjunctive major premise 
 is valid or erroneous according as the enumerated 
 alternatives do or do not conform to the conditions 
 of disjunctive statements, and as the inference is 
 or is not warranted by the premises on which it is 
 made to rest. With respect to the nature of dis- 
 junctive statements, it is sufficient to recall that 
 these must satisfy three conditions. First, the 
 alternatives must all fall within a single universe; 
 not any set of terms that we can state in the form 
 of 'either or' are, in the logical sense, disjunctive. 
 Second, the terms of the disjunction must be ex- 
 haustive; all the species that fall within the uni- 
 verse must be enumerated disjunctively. Third, we 
 saw that the alternatives do not necessarily, although 
 they sometimes do, exclude each other; it does not 
 follow, therefore, that only one of the predicates 
 can belong to the subject under the conditions that 
 determine a particular argument. Whenever we 
 fail to observe either one of these requirements of 
 disjunctive statements in the process of argument, 
 
FALLACIES 545 
 
 we are guilty of one or another of the disjunctive 
 fallacies. 
 
 The fallacy of false disjunction occurs when we 
 proceed to a conclusion on the ground of a major 
 premise in which the presented alternatives do not 
 all belong to a single genus. The neglect of the first 
 positive condition of disjunctive statements leads 
 necessarily to fallacious arguments, because, where 
 it is not satisfied, there is no common field within 
 which the systematic connections of things, as set 
 forth in disjunctive statements, may be said to fall. 
 A failure to keep clearly before oneself the fact 
 that disjunctive alternatives are definitely alter- 
 natives within a single field of knowledge, reveals 
 an .entire misapprehension of the nature of disjunc- 
 tive statements, and leads unavoidably, therefore, 
 to erroneous conclusions. When, for example, we 
 are prepared to find in a stranger to whom we have 
 been introduced all sorts of social virtues merely on 
 the ground that he has come from our home town, 
 or when race prejudices make us blind to the vir- 
 tues that individuals of a particular race display, 
 we are, in all probability, guilty of the fallacy of 
 false disjunction. The logical process underlying 
 social attitudes of the kind in question may be illus- 
 trated as follows : 'Either from my home town or 
 devoid of all or certain current social virtues ; from 
 my home town, therefore not devoid, etc/ 
 
 The fallacy of incomplete disjunction occurs when 
 we proceed to a conclusion on the ground of a major 
 
 35 
 
546 A TEXT-BOOK OF LOGIC 
 
 premise in which the presented alternatives are 
 not exhaustively enumerated. It is true, of course, 
 that the observation of single facts may lead to a 
 disjunctive statement which does not meet the con- 
 dition of complete enumeration. We may say, for 
 example, This tree is an oak or an ash/ But prop- 
 ositions of the kind just illustrated, while they may 
 serve as minor premises of disjunctive arguments, 
 cannot serve as major premises, for the reason that, 
 although the universe within which the alternatives 
 fall has been accurately determined, the alternatives 
 within that universe have not been completely enu- 
 merated. The necessity of a complete enumeration 
 of the alternatives is due to the fact that the dis- 
 junctive syllogism is intended to show, not only 
 what a thing is, but also to determine, within the 
 genus to which it belongs, what it is not. Let us 
 suppose that a particular tree is either an oak or an 
 ash. Then, if we argue, This tree is an oak or an 
 ash, it is an oak, and therefore it is not an ash/ the 
 argument would be formally valid, and the conclu- 
 sion would be true ; but if we supposed that the con- 
 clusion stated the whole truth about the subject, we 
 should fall into error due to the incomplete disjunc- 
 tion of the major premise. Or, to take another illus- 
 tration, let us suppose that a particular ore is not 
 either gold or copper. If, then, we were to argue, 
 This specimen of ore is either gold or silver or 
 copper or antimony ; it is not either gold or copper, 
 and therefore it is either silver or antimony/ we 
 have fallen clearly into a conclusion which is not at 
 
FALLACIES 547 
 
 all necessarily true, for the specimen in question 
 might be none of those enumerated in the major 
 premise. Such a conclusion is erroneous because all 
 the species of the genus to which the particular 
 specimen belongs were not enumerated. But, some 
 one may say, we cannot always meet this require- 
 ment of complete enumeration, and are we, there- 
 fore, precluded from arguing validly to a disjunctive 
 conclusion ? The answer is that we must express the 
 indeterminate state of our knowledge about objects 
 in a complete enumeration if we are to reach valid 
 conclusions, and we may do this without necessarily 
 possessing an exhaustive knowledge of the subject 
 to which the argument refers. Thus, to state the 
 above argument in a form from which a valid con- 
 clusion may be drawn we may say, This specimen 
 of ore is either gold or silver or copper or antimony 
 or some other species/ a statement which does not 
 claim complete knowledge of the subject-matter of 
 the argument, but does rest upon a complete deter- 
 mination of the knowledge that is possessed about it. 
 The fallacy of ambiguous disjunction occurs when 
 we proceed to a conclusion on the ground of a major 
 premise in which the presented alternatives are not 
 precisely determined with respect to their exclusion. 
 We have seen that any proposition of the form *S is 
 either A or B' strictly interpreted means *S is either 
 A or else B,' but we also saw that the alternatives 
 do not necessarily preclude the possibility that *S 
 may be both A and B.' Unless, therefore, we take 
 special pains to make clear, in particular instances, 
 
548 A TEXT-BOOK OF LOGIC 
 
 in which of these two ways the disjunctive major 
 is to be interpreted, we are likely to be led to a con- 
 clusion which leaves us in doubt as to the meaning 
 of that conclusion. If we argue, for instance, that 
 'Because all male students of the university either 
 drill, or play football, or baseball or tennis, and be- 
 cause X drills, therefore, he does not play football 
 or baseball or tennis/ we are stating a conclusion 
 of the individual which may be true, but it is not 
 true for the reason assigned; for there is nothing 
 in the universe of physical education as conducted 
 by the university that makes an exclusive -interpre- 
 tation of the enumerated alternatives necessary. If, 
 then, we give an exclusive interpretation to a non- 
 exclusive series of alternatives, or a non-exclusive 
 interpretation to an exclusive series, we are guilty 
 of the fallacy of ambiguous disjunction. 
 
 REFERENCES 
 
 SEE THE END OF THE NEXT CHAPTER 
 
 QUESTIONS 
 
 1. What is the name and character of Aristotle's treatise 
 on fallacies? 
 
 2. In what senses is the term fallacy used at the present 
 time? 
 
 3. In what two main groups did Aristotle classify the fal- 
 lacies? 
 
 4. To what distinctions drawn in the text do Aristotle's 
 main groups correspond? 
 
 5. Describe the chief features of each of the four main 
 classes into which the text divides fallacies, and by what 
 names are they distinguished? 
 
FALLACIES 549 
 
 6. Into what subdivisions, and according to what prin- 
 ciple, may the fallacies of interpretation be divided? 
 
 7. What do understand by verbal ambiguity, and how does 
 it differ from mere indetterminateness in the meaning 
 of words? 
 
 8. Describe and illustrate the fallacy of equivocation. 
 
 9. What is the fallacy of accent, and in what respect does 
 the corresponding Greek fallacy differ from it? 
 
 10. In what several ways may one fall into a fallacy of 
 accent? Illustrate. 
 
 11. Describe and illustrate the fallacies of composition and 
 division. 
 
 12. What is the Latin name for the fallacy of accident? 
 Illustrate the fallacy. 
 
 13. Give an illustration of the converse fallacy of accident, 
 and by what Latin name is it known? 
 
 14. Describe the character of structural ambiguity. 
 
 15. What is the fallacy of amphibole, and from what other 
 kinds of ambiguity must it be distinguished? 
 
 16. State and illustrate the fallacy of false parenthesis. 
 
 17. What do you understand by fallacies of implication, 
 and into what two classes may they be divided? 
 
 18. What is a fallacy of opposition? 
 
 19. To what fallacies are the following logical relations 
 particularly liable: contrariety, subcontrariety, subal- 
 ter nations? 
 
 20. What is a fallacy of education? 
 
 21. State what is meant by a fallacy of obversion. 
 
 22. What is a fallacy of conversion, and in respect of what 
 propositions, and why, is it likely to occur? 
 
 23. What are fallacies of inference, and into what two 
 classes may they be divided? 
 
 24. What is a deductive fallacy, and how are such fallacies 
 classified? 
 
 25. What is a categorical fallacy? 
 
 26. What is meant by a fallacy of four terms, and state in 
 what two ways such fallacies arise 
 
550 A TEXT-BOOK OF LOGIC 
 
 27. Classify and describe each of the fallacies of four terms. 
 
 28. What are fallacies of insufficient premises, and what 
 rules of the syllogism do they break? 
 
 29. Show, in relation to the nature of syllogistic reasoning, 
 how the fallacies of particular and of negative premises 
 occur. 
 
 30. Describe as fully as you can the character of an hypo- 
 thetical fallacy. 
 
 31. State and illustrate the two hypothetical fallacies. 
 
 32. How does the fact that natural events are complex 
 affect our interpretation of hypothetical statements? 
 
 33. What do you understand by a disjunctive fallacy? 
 
 34. Into what classes, and according to what principle, may 
 disjunctive fallacies be divided? 
 
 35. State and illustrate the fallacy of false disjunction. 
 
 36. Describe the fallacy of incomplete disjunction. Illus- 
 trate. 
 
 37. What is the fallacy of ambiguous disjunction? Illus- 
 trate. 
 
 EXERCISES 
 
 Examine the following arguments and state in what respect, 
 if any, they are fallacious, the technical name of the 
 fallacy of which each is guilty, and the class to which 
 the fallacy belongs: 
 
 (1) It is sometimes argued that the communication of 
 an infectious disease to another person should be 
 punished by law, since the law exists for the pur- 
 pose of protecting people from harm. 
 
 (2) I have made thee free a slave. 
 
 (3) How can you argue that it is wrong for me to 
 assist my friend to obtain the office by offering 
 business or financial considerations to the voters 
 of my acquaintance if you agree that it is right 
 for a man to do what he can for his friend's good? 
 
 (4) A commercial traveller wrote to his chief: Dear 
 Sir, On Wednesday next I want you to allow me 
 
FALLACIES 551 
 
 the day off. My wife having lost her mother is 
 being buried on that date and I should like to at- 
 tend the funeral. 
 
 (5) A, B, C, are all the known instances of the class 
 X, and since they are all found to possess the 
 characteristic p we may conclude that All X is p. 
 
 (6) Large numbers, though not all, of the instances 
 of the class X have invariably been found to ex- 
 hibit the character p, therefore, All X is p. 
 
 (7) If it is false that no men are immortal, it must 
 certainly be true that all men are mortal, since 
 there is no middle position between mortal and im- 
 mortal. 
 
 (8) If you perform an unfriendly act, I may certainly 
 conclude that your attitude is hostile. 
 
 (9) He who is content with what he has is truly rich, 
 but the covetous man is not content with what he 
 has, no covetous man, therefore, is truly rich. 
 
 (10) All Parisians are Frenchmen indeed, when the only 
 reason you have to advance for that statement is 
 that all Parisians and all Frenchmen are Euro- 
 peans ! 
 
 (11) What is not compound is an element, gold is not 
 compound, and is, therefore, not an element. 
 
 (12) If a substance is a metal, it is a good conductor 
 of heat and electricity, but this substance does not 
 conduct either well, and so it cannot be a metal. 
 
 (13) If man were not capable of progress, he would 
 not differ from the brutes, but since he does differ 
 he must be regarded as capable of progress. 
 
 (14) What you speak of must be either blue or green 
 or yellow, but since you say that it is neither of 
 these it must be devoid of colour. 
 
 (15) That happened on Monday or Thursday or in April, 
 but it was not in April for I remember that it was 
 Harvest; it must, therefore, have happened on 
 Monday or Thursday. 
 
CHAPTER XIX 
 
 FALLACIES (CONTINUED) 
 
 Inductive Fallacies. By fallacies of induction, 
 as was stated above, we understand those errors to 
 which thought is exposed in its endeavour to deter- 
 mine the principle of connection between a number 
 of particular facts. Now, since induction requires, 
 as a condition of the explanation of the particulars 
 of experience, that the facts of experience be care- 
 fully observed, it is obvious that we are exposed 
 mainly to two classes of inductive error, to those, 
 namely, which arise in connection with our obser- 
 vation of facts, and to those which arise in connec- 
 tion with our explanation of facts. But since lan- 
 guage is an indispensible instrument both for record- 
 ing what we observe, and for stating the methods 
 and results of the explanations that we have to offer 
 of what is observed, we may include in the present 
 discussion a brief statement of the nature and 
 sources of the fallacies into which a careless use of 
 language may be the means of leading us. The fal- 
 lacies of induction will, then, be studied under three 
 heads ; first, those which originate in our use of lan- 
 guage; second, those which involve errors of obser- 
 vation; and third, those which occur in connection 
 with the so-called inductive inference, the errors, 
 that is to say, which invalidate explanation. 
 
 (552) 
 
FALLACIES 553 
 
 Fallacies of Language. Readers of Plato cannot 
 fail to have remarked that the difficulties that he 
 sometimes experienced in making clear to himself 
 and to others the character of some of the more 
 elementary logical distinctions was due, in great 
 measure, to the fact that the nature of even simple 
 grammatical distinctions was not clearly under- 
 stood by him and his contemporaries. The fact 
 that Aristotle attributed, as we have seen, a large 
 number of the fallacies to the influence of language, 
 also points to the close connection that there is 
 between thought and human speech. In more mod- 
 ern times, Bacon, Hobbes, Locke, and others, have 
 remarked upon the dangers to which we are liable 
 through the words that we employ to express our 
 ideas, and Mill wrote two chapters in which he 
 discusses the requirements and principles of what 
 he calls a "philosophical language." These refer- 
 ences, which might be indefinitely extended, are 
 enough to show that while our acquired speech 
 may be sufficient for the ordinary purposes of life, 
 it must be carefully employed if, in regard to the 
 subjects of scientific investigation, it is not to become 
 a source of embarrassment and error. 
 
 Bacon gave the name of Idols of the Market- 
 place (Idola fori) to the fallacies which were due 
 to language, and he puts the sum of the matter as 
 follows: "Men imagine that their reason governs 
 words whilst, in fact, words react upon the under- 
 standing; and this has rendered philosophy and the 
 sciences sophistical and inactive." The same truth 
 
554 A TEXT-BOOK OF LOGIC 
 
 is dwelt upon at length by Locke, and the general 
 nature of the influence that language is capable of 
 exerting prejudicially upon thought, the only point 
 with which we are here concerned, is evident from 
 the following quotation: "Men," he says, "having 
 been accustomed from their cradles to learn words 
 which are easily got and retained, before they knew 
 or had framed the complex ideas to which they were 
 annexed, or which were to be found in the things 
 they were thought to stand for, they usually con- 
 tinue to do so all their lives; and, without taking 
 the pains necessary to settle in their minds deter- 
 mined ideas, they use their words for such unsteady 
 and confused notions as they have, contenting them- 
 selves with the same words other people use, as if 
 their very sound necessarily carried with it con- 
 stantly the same meaning. . . . This inconsistency 
 in men's words when they come to reason concerning 
 either their tenets or interest, manifestly fills their 
 discourse with abundance of empty, unintelligible 
 noise and jargon, especially in moral matters, where 
 words, for the most part, standing for arbitrary 
 and numerous collections of ideas not regularly and 
 permanently united in nature, their bare sounds are 
 often only thought on, or at least very obscure and 
 uncertain notions annexed to them. Men take the 
 words they find in use amongst their neighbours; 
 and, that they may not seem ignorant what they 
 stand for, use them confidently, without much 
 troubling their heads about a certain fixed meaning ; 
 whereby, besides the ease of it, they obtain this 
 
FALLACIES 555 
 
 advantage: That, as in such discourses they seldom 
 are in the right, so they are as seldom to be con- 
 vinced that they are in the wrong; it being all one 
 to go about to draw those men out in their mistakes 
 who have no settled notions, as to dispossess a 
 vagrant of his habitation who has no settled abode." 
 Fallacies of Observation. Observation may be 
 defective chiefly in two respects. It may be insuffi- 
 cient in amount, or incomplete or imperfect in 
 detail. If we consider these two cases separately, it 
 must not be forgotten that, frequently and perhaps 
 usually, the fallacies which depend upon observation 
 occur as the result of both kinds of defect. Induc- 
 tion, as we have seen, depends upon the collection 
 of data sufficient in amount to suggest a law of con- 
 nection; but, more important than the number of 
 the facts observed, is the degree of thoroughness 
 with which we are able to analyse them. Mere col- 
 lections of fact, if such a thing were possible, have, 
 as we have seen, no special value for science, and 
 alone can lead to the formulation of no general 
 principles of connection. The particular data which 
 are the material of science are brought under obser- 
 vation by the exercise of discrimination, comparison, 
 synthesis, in a word, judgment; and this differs 
 in no essential respects from the process by which 
 we detect, within collected groups of fact, the fea- 
 tures that are common, and the connections that 
 are causal. But while this should be kept clearly in 
 mind, it is nevertheless true that we may be led into 
 an inductive fallacy, either because the amount of 
 
556 A TEXT-BOOK OF LOGIC 
 
 data available does not warrant an inference, or 
 because, although sufficient in amount, our analysis 
 of the data has not been carried out with sufficient 
 care and thoroughness. 
 
 Observation, then, is defective, in the first place, 
 when the number of the observed data is not suffi- 
 cient in amount to guarantee the conclusion that is 
 based upon it. In view of the situations which this 
 statement has in view, we are particularly inter- 
 ested, in logic, to ascertain what are the conditions 
 that lead to insufficient observation. One important 
 condition is the general tendency to neglect the 
 observation and collection of what are called nega- 
 tive instances. By a negative instance is meant an 
 instance in which a given phenomenon is observed 
 not to occur. If we take, for example, the popular 
 superstitions, such, for instance, that it is un- 
 lucky to begin any new task or undertake any new 
 enterprise on Friday, for people to be associated 
 together in groups of thirteen, or to walk under a 
 ladder that is inclined against a wall, we are 
 seriously expected, by those who entertain them, to 
 share these superstitions in view of the instances 
 that these persons are able to enumerate in which 
 some untoward result has occurred. An enumer- 
 ation of the instances in which no such consequence 
 has followed, it would seem, is sufficient to show that 
 the superstitituous conclusion is defective if not 
 fallacious by reason of the failure to observe these 
 negative instances. 
 
FALLACIES 557 
 
 To have called our attention to this tendency to 
 neglect the evidence afforded by negative instances 
 is one of the merits of Bacon. The following quo- 
 tation from the Novum Organum, not only states 
 the nature of the fallacy, but indicates also its scope. 
 Bacon writes: "The human understanding, when 
 any proposition has been once laid down (either 
 from general admission and belief or from the 
 pleasure it affords), forces everything else to add 
 fresh support and confirmation; and although most 
 cogent and abundant instances may exist to the con- 
 trary, yet either does not observe or despises them, 
 or gets rid of and rejects them by some distinction, 
 with violent and injurious prejudice, rather than 
 sacrifice the authority of its first conclusions. It 
 was well answered by him who was shown in a 
 temple the votive tablets suspended by such as had 
 escaped the peril of shipwreck, and was pressed as 
 to whether he would then recognise the power of 
 the gods : But where are the portraits of those who 
 have perished in spite of their vows? All super- 
 stition is much the same, whether it be that of 
 astrology, dreams, omens, retributive judgment, or 
 the like, in all of which the deluded observers 
 observe events which are fulfilled, but neglect and 
 pass over their failure, though it be much more 
 common. But this evil insinuates itself still more 
 craftily in philosophy and the sciences, in which a 
 settled maxim vitiates and governs every other cir- 
 cumstance, though the latter be much more worthy 
 pf confidence. Besides, even in the absence of that 
 
558 A TEXT-BOOK OF LOGIC 
 
 eagerness and want of thought (which we have 
 mentioned), it is the peculiar and perpetual error 
 of the human understanding to be more moved and 
 excited by affirmatives than by negatives, whereas 
 it ought duly and regularly to be impartial ; nay, in 
 establishing any true axiom the negative instance 
 is the more powerful." 
 
 The testimony of Darwin is to the same effect. 
 He says : "The success of the 'Origin' may, I think, 
 be attributed in large part to my having long before 
 written two condensed sketches, and to my having 
 abstracted a much larger manuscript, which was 
 itself an abstract. By this means I was enabled to 
 select the more striking facts and conclusions. I 
 had also, during many years, followed a golden rule 
 namely, whenever a published fact, a new obser- 
 vation or thought, came across me, which was op- 
 posed to my general results, to make a memorandum 
 of it without fail and at once; for I had found by 
 experience that such facts and thoughts were far 
 more apt to escape from memory than favourable 
 ones. Owing to this habit, very few objections were 
 raised against my views which I had not at least 
 noticed and attempted to answer." 
 
 Another condition of insufficient observation 
 that may be mentioned is education. Whatever our 
 conception of the aim of education may be, there is 
 no doubt that a large part of the educative process, 
 as we actually experience it, is taken up with an 
 effort to gain familiarity with a body of knowledge 
 that is regarded as traditionally important and fun- 
 
FALLACIES 559 
 
 mental. This statement is true for all grades of 
 education from the grammar school to the univer- 
 sity. Now it is not only inconceivable, but contrary 
 to experience, that the acquisition of any con- 
 erable body of knowledge should be without its 
 effect upon our mental habits; for acquaintance 
 with any class of facts means, in terms of men- 
 tal habit, a trained ability to perceive with in- 
 creasing facility other facts that are the same in 
 kind as these, and a corresponding inability to per- 
 ceive facts that differ considerably from them in 
 kind. A particular illustration of this general truth 
 is found in the case of those individuals whose edu- 
 cation assumes a special character, as it does, for 
 instance, in law, medicine, theology, engineering, 
 etc. And even if we consider the case of those 
 whose common school education is not followed by 
 a university training, but by apprenticeship in some 
 business, it is quite apparent, even then, that the 
 knowledge of the business, of its material, methods, 
 and aims, acts exactly in the same way to sharpen 
 the perception to observe a specialised group of 
 facts, and to limit the facility with which facts 
 dissimilar to these are perceived. The truth is 
 that all of us perceive what we are educated to 
 perceive, and that we are limited in respect to the 
 kinds of things that we perceive by the education 
 that we have received. 
 
 Bacon referred to the errors into which we are 
 led as the result of the limitations that education 
 and inherited beliefs may have upon the range of 
 
560 A TEXT-BOOK OF LOGIC 
 
 our perceptions as Idols of the Theatre (Idola The- 
 atri) . Doubtless, as is shown by his illustrations, 
 he had in mind the cramping effect of the traditions 
 of the Schoolmen upon the new learning in his day. 
 Bacon lived at the dawn of the modern scientific 
 era, and he was acquainted with some of the ob- 
 stacles that it had to encounter on account of theo- 
 logical prejudice (odium theologicum) of the times. 
 But if we have passed beyond the stage where the 
 prejudices which come from a one-sided theological 
 position and training are allowed to interfere with 
 the freedom of thought and investigation, it is still 
 possible that prejudices the same in kind, though 
 different in form, may hamper the human mind in 
 its search for truth. The fact that these hindrances 
 are not officially administered, but are grounded in 
 that specialisation, upon which our modern educa- 
 tion lays so much importance, would make the ten- 
 dency to which we are referring the more insidious, 
 and hence more difficult to detect and avoid or over- 
 come. "The success of modern scientific methods," 
 as Creighton remarks, "has sometimes led investi- 
 gators to despise and belittle the work of those who 
 do not carry on their investigations in laboratories, 
 or do not weigh and measure everything." Thus 
 the mechanical conceptions which were worked out 
 successfully in the realm of physics and astronomy, 
 have been extended to psychology, ethics, and polit- 
 ical science, without any consideration being given 
 to the differences in the material which is the sub- 
 ject-matter of this latter group of sciences. In our 
 
FALLACIES 561 
 
 own day, the evolutionary hypothesis has provided 
 us with a point of view for looking at all the details 
 of human experience; but it is not impossible that 
 the limitations of this point of view and the errors of 
 observation to which it has led, may, at some future 
 time, be as clear as today are the insufficiencies of 
 the notion of mechanism as employed by the thinkers 
 of the eighteenth century. 
 
 In the second place, observation may be defective 
 either because it is incomplete or imperfect in detail. 
 The instances of fallacious inference which belong 
 in this group are those which arise from the fact 
 that the collected data, upon which the inferences 
 rest, have not been examined with sufficient thor- 
 oughness. Defects of the kind here in question may 
 be due either to the fact that only part of the mate- 
 rial has been studied, or to the fact that, while all 
 the material may have been studied, this has not 
 been done for all or parts of the material with suffi- 
 cient minuteness. In either case, the inference will 
 be erroneous on account of a failure to carry our 
 analysis of the phenomenon under observation into 
 sufficient detail. 
 
 A number of conditions may operate to arrest 
 our analysis of observed data at a point which falls 
 short of that at which it is possible to determine 
 with some degree of accuracy the law of their 
 connection, but two are, from the logical point 
 of view, of sufficient interest to require brief men- 
 tion. There is no doubt, in the first place, that great 
 
562 A TEXT-BOOK OF LOGIC 
 
 differences exist in the ability of different investi- 
 gators to perform the task of analysing a group of 
 collected facts. Some individuals, it is found, are 
 splendid collectors, and are exceedingly fertile in 
 devising ways and means of bringing under obser- 
 vation specimens that entirely escape the notice of 
 others not gifted as themselves. But it sometimes 
 happens that among these born collectors there are 
 many who can go but a little way toward that com- 
 plete analysis of their collected material upon which 
 alone any general conclusion can safely be based. 
 The recognition of this fact has led, in practice, to 
 the introduction of a large amount of cooperation 
 between workers in the same line of research, and 
 has tended to make the laboratory a workship in 
 which there is found employment for a great variety 
 of talent. It is only the exceptional man who, like 
 Darwin, combines the collector's skill with a keen 
 analytic mind that brings to light the common fea- 
 tures that lie hidden under a mass of differences in 
 any group of facts. Natural limitations, then, of 
 the sort we are discussing operate frequently to 
 render the observation of details incomplete, and to 
 throw doubt upon any conclusion which rests upon 
 such imperfectly analysed data. 
 
 Another condition which tends to make analysis 
 defective is an imperfectly developed technique or 
 method. We have spoken above of the importance 
 of the construction and use of apparatus if the work 
 of scientific observation is to be successfully carried 
 on. Indeed, we may say that the progress of modern 
 
FALLACIES 563 
 
 science has been dependent, in large measure, on 
 the success that has attended the development of 
 special methods for bringing the structure of col- 
 lected data under detailed observation. In the bio- 
 logical sciences, for example, the methods of hard- 
 ening, embedding, and staining the various tissues 
 have gone a long way toward placing these sciences 
 on the same experimental plane as physics and 
 chemistry. The further progress of these, as of the 
 other, sciences depends upon the adaptation of the 
 methods already in vogue to new material, and the 
 development of new methods to meet new conditions 
 and situations as they arise. But whenever we 
 speak of improvement, and recognise the possibility 
 of new discoveries, we at the same time imply that 
 our present knowledge is defective in just those 
 respects in which advancement may be expected. 
 This, however, is only to say that so long as the 
 technique of any science is capable of improvement, 
 the conclusions of that science must be entertained 
 with caution and subject to certain reservations. 
 
 Fallacies of Explanation. There are two sources 
 of error in inductive processes of reasoning to which 
 we shall direct attention: hasty generalisation and 
 false analogy. It is exceedingly difficult to give a 
 concise statement of what is meant by hasty general- 
 isations, since any explanation may be rendered 
 erroneous by undue haste at any of the stages of the 
 inductive process. For instance, an inductive con- 
 clusion may be fallacious on account of haste at 
 either the stage of what was called above empirical 
 
564 A TEXT-BOOK OF LOGIC 
 
 generalisation, or at the stage of hypothesis, or at 
 the stage of verification. Whenever, therefore, any 
 part of the task of explanation is not thoroughly 
 performed, our conclusion, resting as it does upon 
 an incomplete or imperfect acquaintance with the 
 details of the phenomenon, may be called a hasty 
 or premature generalisation. The essential nature 
 of the fallacy consists, then, in the absence of an 
 analytic thoroughness requisite for a true explana- 
 tion, without respect to the part of the explanatory 
 process in which the failure to be sufficiently thor- 
 ougs occurs. 
 
 We may remark, however, that we are not guilty 
 of this fallacy when we consciously arrest our anal- 
 ysis of a phenomenon to be explained at a point 
 which falls short of completeness, or when imper- 
 fectly observed or analysed data are generalised, 
 but are not offered as an explanation. The fallacy 
 occurs only when an incomplete analysis is presumed 
 to be complete, or when a preliminary generalisation 
 is mistaken for a final one. As has been said, the 
 value of logic consists in calling attention to the fact 
 that, not only must conclusions be true, but the 
 reasons for the truth of conclusions must be defi- 
 nitely ascertained, if science is to exist. Science, as 
 we have seen, is a consciously controlled process, a 
 process of arriving at a certain conclusion, by means 
 of a method; which is definitely regulated at all the 
 stages through which it passes from the earliest 
 observation to the finally accepted explanation. 
 When the control of the method by which conclu- 
 
FALLACIES 565 
 
 sions are reached gets out of hand, when we become 
 careless in the use of the methods we adopt for the 
 examination of phenomena, our explanation of such 
 phenomena is erroneous, because it involves, in the 
 sense in which the term has been explained, a hasty 
 generalisation. Such conclusions are fallacious be- 
 cause they do not rest upon a sufficiently detailed 
 basis of fact. 
 
 Analogy may give rise to erroneous conclusions 
 when it is supposed that the phenomenon under 
 observation has all the characteristics of the instance 
 which provides us with the analogical resemblance. 
 We have seen that analogy is a useful method, or 
 step in the method, of scientific explanation, but 
 unless it is strictly guarded it is likely to arouse all 
 sorts of distracting associations which lead to mis- 
 understanding and error. When considered as a 
 possible source of error, analogy has certain affin- 
 ities with figurative language, on the one hand, and 
 with the disregard of negative instances, on the 
 other. With respect to its relation to figurative 
 language, analogy leads us astray when the illustra- 
 tion which provides us with the analogical resem- 
 blance engages the whole attention, and we are 
 thereby led to predicate of the phenomenon under 
 investigation qualities that have been actually ob- 
 served only in the illustration. It was with the dan- 
 gers of analogical reasoning in mind that a professor 
 was wont to say to his students that they should 
 not try to make the parables of the New Testament 
 "go on all fours," that is, they must not try to find 
 
566 A TEXT-BOOK OF LOGIC 
 
 a point for point resemblance between the truth of 
 the parable and the story which provided the basis 
 of the analogy. It is neglect of such counsel that 
 leads in the sciences to the fallacy of false analogy. 
 With respect to its relation to negative instances, 
 analogy is likely to lead us into error if the points 
 of difference between a phenomenon and its illus- 
 tration are lost sight of, and only the resemblances 
 are retained. "For instance," to borrow an illus- 
 tration from Sidgwick, "during the recent Boer 
 War various analogies were appealed to by various 
 people as helping to throw light on the situation. 
 It was compared to the operations of America in 
 the Philippines, to the Armenian massacres, to the 
 American Civil War, and even to the high-handed 
 action of Spain in the Netherlands in the time of 
 Elizabeth. Our action in South Africa was sup- 
 posed (by different people) to be analogous to those 
 and other historical precedents, and the analogies 
 were used to support the various judgments passed 
 by these various people on the rights of the war and 
 its probable outcome. It is easy to see that in all 
 these comparisons there is some likeness and also 
 some difference, and that the justice of the analogy 
 depends upon the relevance of the likeness and the 
 difference." But if the difference is a relatively 
 important one, and we proceed nevertheless to build 
 up an explanation on the ground of the likeness 
 alone, we are guilty of the fallacy of false analogy. 
 The fallacy assumes the converse form if we are led 
 to underestimate the value of a resemblance because 
 
FALLACIES 567 
 
 it is accompanied by striking differences. In any 
 case, the fallacy arises when we forget that analog- 
 ical reasoning depends upon what Sidgwick calls 
 "the relevance of the likeness and difference." 
 
 Fallacies of the Context. The fallacies that we 
 have considered in the foregoing pages arise out of 
 a failure to determine precisely the nature and rela- 
 tions of the subject-matter which constitutes the 
 contents of particular arguments. The group of 
 fallacies to which we have now to direct attention 
 arises from the fact that the meaning of particular 
 arguments, as we have shown, is determined in part 
 by their relation to a context which they imply with 
 varying degrees of clearness. Now when we say 
 that the context supplies part of the meaning that 
 an argument may rightly be said to have, it is im- 
 portant to bear in mind that the context may be 
 said to refer, not only to the undetermined aspects 
 of the subject-matter under discussion, but also to 
 the interests or purposes which sustain, as we have 
 seen, our inquiries into truth and our search for 
 knowledge. Any discussion of what knowledge or 
 truth is cannot fail to be inadequate, as we have 
 shown, if attention is not given to the part played 
 by the complex character of the material about 
 which knowledge is desired, and also to the character 
 of the interest which knowledge is intended to sat- 
 isfy. Because, therefore, of its relation to a context, 
 every argument is liable to errors which do not arise 
 directly out of the facts and relations which are 
 expressed by its constituent propositions. There 
 
568 A TEXT-BOOK OF LOGIC 
 
 may be imported, that is to say, into the meaning 
 of arguments elements from their contexts which 
 lead to conclusions which are at variance with what 
 the premises, logically interpreted, really support. 
 Whenever this happens, whenever, that is, we accept 
 arguments on the ground of suggestions, derived 
 from their contexts, which are not related to the 
 truth character of the arguments themselves, there 
 ensues a fallacy of the context. A fallacy of the 
 context may be defined, therefore, as an error in 
 reasoning which is due to the influence that some 
 feature or features of a context, not related to the 
 truth character of the argument, has upon our inter- 
 pretation of the subject-matter of the argument, 
 such influence inducing us to accept a statement 
 about the subject-matter of the argument as true for 
 reasons which, apart from the influence referred to, 
 would fail wholly or in part, to justify its accept- 
 ance. 
 
 The nature of these fallacies may be made still 
 clearer, if we observe that in arguments of the kind 
 under consideration the context may contribute 
 irrelevant elements derived from either of the fac- 
 tors by which, as was pointed out, human knowledge 
 is determined, from the world of relatively inde- 
 pendent objects on the one hand, and from the world 
 of our interests, on the other. An imperfect deter- 
 mination of the universe within which an argument 
 is intended to be considered leads to a group of fal- 
 lacies of which Petitio Principii, Ignoratio Elenchi, 
 Non Sequitur, and Complex Question are the chief; 
 
FALLACIES 569 
 
 and a failure to confine the interests by which we 
 are guided in our search for truth to those which 
 have a direct relation to that end leads to another 
 group of which Post Hoc, Argumenta ad Hominen, 
 ad Populum, ad Verecundiam, ad Misericordiam, 
 may be taken as the most important. In the former 
 group, we are considering how the relations which 
 a given object has to other objects may become a 
 source of error in our knowledge of the world of 
 relatively objective things, and to these we may give 
 the name, fallacies of assumption. In the latter, we 
 are studying the ways in which knowledge may be 
 deflected by reason of the operation of certain nat- 
 ural and acquired characteristics of the mental life ; 
 and to these we may give the name, fallacies of 
 interest. In both cases the fallacy is due to the 
 admission into our reasoning of elements which have 
 no direct bearing upon the truth character of the 
 judgments in which our knowledge is asserted. 
 
 Fallacies of Assumption are those errors in rea- 
 soning which occur when the assumptions on which 
 an argument rests are not clearly distinguished from 
 the judgments of which the argument consists. ^ An. 
 
 ^assumption, in this connection, is anything we take 
 for granjejL-but do not assert, about the subject- 
 matter of anjirgument. It is the equivalent of what 
 we have had occasion hitherto to speak of as the 
 universe of discourse. Interpreted from this point 
 of vtew f it is readily seen that an assumption is not 
 
 <^afl-assertion. and forms no part of the asserted con- 
 tents of an argument, although, as we have seen, it 
 
570 A TEXT-BOOK OF LOGIC 
 
 has a relation to the argument, a relation which is 
 indicated with sufficient clearness by saying that it 
 points out the sphere of reference in which what is 
 asserted may or not be accepted. Now it is a misin- 
 terpretation of the relation betweeji what an argu- 
 ment assumes and what it asserts that lies at the 
 foundation of the fallacies that we have here to con- 
 sider. Thus, when what is taken for granted or as- 
 sumed is allowed to function in any part of an argu- 
 ment as an assertion or judgment, or when the as- 
 sumption on which an argument proceeds is ambig- 
 uous, the resulting fallacy is one of assumption. 
 
 Petitio Princpii is the name of an argument which 
 assumes the conclusion that is to be proved. It is, 
 as Sidgwick says, "the surreptitious assumption of 
 a truth you are pretending to prove." Since, then, 
 the fallacy is one of assumption, it is evident that 
 its source must be found, not in what is definitely 
 asserted, but in the world of reality or existence in 
 which what is asserted has a definite meaning or 
 fulfillment, that is to say, in the universe of dis- 
 course from the standpoint of which the argument 
 is interpreted. The nature of the fallacy is seen in 
 the confusion that exists, for the person guilty of 
 it, between the asserted grounds of a conclusion, 
 and the assumptions that thought postulates with 
 respect to the subject - matter of an argument, 
 Whenever it exists, the fallacy directs attention to 
 the fact that the truth of what an argument asserts 
 depends in part upon what assumptions the argu- 
 ment makes ; and, in view of the nature of an argu- 
 
FALLACIES 571 
 
 ment, it follows that when assumptions are put 
 forward as reasons we necessarily fail to establish 
 a conclusion, and fall into the merest dogmatism 
 unless we are willing to have these assumptions 
 called into question. "When," for instance, "Galileo 
 maintained that the earth goes round the sun, he 
 fully believed it and yet was willing to treat it as a 
 disputable question ; but when Pope Urban VIII and 
 his cardinals maintained that the earth stood still, 
 they shut their eyes to the arguments, and said their 
 view was only disputable by any one who chose to 
 be burnt alive." Now, with respect to the right to 
 call into question any of the grounds on which con- 
 clusions are supposed to rest, we can only say that 
 this right must be conceded, or that the fallacy we 
 are now considering can have no logical standing. 
 But further, if we cannot go behind the premises, 
 nor consider ^e rights of assertions to stand as 
 premises, but must accept any set of assertions at 
 their face value as grounds of argument, then the 
 whole of logic has been reduced to a mere formal 
 science, and its processes are valuable only as they 
 enable us to secure consistency of statement. Either 
 this, or we must admit that there is a real difference 
 between assertions and assumptions, between judg- 
 ments and postulates, that the human mind is likely 
 at times to fail to keep the distinction clearly before 
 it, and, consequently, that the one may sometimes 
 slip, in the course of argument, into the place of the 
 other. Now, when this happens, when in the course 
 of argument assumptions take the place of reasoned 
 
572 A TEXT-BOOK OP LOGIC 
 
 judgments, the argument is fallacious because, for 
 the reason assigned, it involves a petitio principii. 
 
 The English language, as Whately pointed out, 
 is peculiarly "suitable for the fallacy of Petitio 
 Principii, from its being formed from two distinct 
 languages, and thus abounding in synonymous ex- 
 pressions which have no resemblance in sound, and 
 no connection in etymology, so that a Sophist may 
 bring forth a proposition expressed in words of 
 Saxon origin, and give as a reason for it the very 
 same proposition stated in words of Norman origin ; 
 e. g. To allow every man an unbounded freedom of 
 speech must always be, on the whole, advantageous 
 to the State ; for it is highly conducive to the inter- 
 ests of the community, that each individual should 
 enjoy a liberty perfectly unlimited of expressing 
 his sentiments/ * 
 
 When the fallacy of petitio principii is com- 
 mitted in a single step it is called vvrepov irporepw 
 (hysteron proteron) ; and when it involves more 
 than a single step it is called circulus in probando or 
 reasoning in a circle. 
 
 Closely connected with the foregoing is the fal- 
 lacy of the Complex Question. By a complex ques- 
 tion, in the broadest meaning of that term, is meant 
 one that suggests its own answer. Any question, 
 for instance, that forces us to select, and assert in 
 our answer to it, one of the elements of the question 
 itself, while some other possibility is really open, is 
 complex in the sense in which that term is here em- 
 ployed. If, for example, one were to ask whether 
 
FALLACIES 573 
 
 you were going to New York or London, or if your 
 favourite colour were red or blue, or if you had 
 given up a particular bad habit, he would be guilty 
 of the fallacy of the complex question, if, in each 
 case, the alternatives, as a matter of fact, were more 
 numerous than, or were in any way different from, 
 those stated in the question. Any leading question 
 which complicates an issue by over simplification is 
 fallacious for the same reason. Now, in the light 
 of what we have said with respect to the petitio 
 principii, it is not difficult to see that the fallacy of 
 the complex question is occasioned by the character 
 of the assumption on which the question rests. In 
 the petitio principii an assumption with respect to 
 the subject-matter of an argument functions as a 
 premise, in the complex question it is a similar as- 
 sumption that shuts out some of the material possi- 
 bilities of a situation and confines an issue within 
 too narrow limits. As in the former case, so here, 
 the only way of meeting the difficulty is to raise the 
 previous question, that is, to call the assumption 
 which lies back of the fallacy into question. 
 
 Ignoratio Elenchi, according to Aristotle, is a 
 fallacy which arises from "ignorance of the nature 
 of refutation." In order to refute an assertion, 
 Aristotle says we must prove its contradictory; the 
 proof, consequently, of a proposition which stood in 
 any other relation than that to the original, would 
 be an ignoratio elenchi. 
 
 Since Aristotle, the scope of the fallacy has been 
 extended to include all cases of proving the wrong 
 
574 A TEXT-BOOK OF LOGIC 
 
 point. Thus, when H. Spencer, in arguing against 
 the advocates of a classical education, says that 
 "Throughout his after career, a boy, in nine cases 
 out of ten, applies his Latin and Greek to no prac- 
 tical purposes," he is guilty of an ignoratio elenchi, 
 for the argument, as Welton points out, "ignores 
 the fact that the advocates of a classical education 
 do not claim that Latin and Greek are of direct use 
 in practical life. What they do urge is that the 
 study of the classics furnishes an unrivalled mental 
 training; and it is this proposition which a true 
 cAcyxo? (elenchus) must disprove." With this inter- 
 pretation of the fallacy Whately is in agreement. 
 He writes : "I am required to prove a certain con- 
 clusion ; I prove, not that, but one which is likely to 
 be mistaken for it; in that lies the fallacy. . . For 
 instance, instead of proving that 'this person has 
 committed an atrocious fraud/ you prove that 'this 
 fraud he is accused of is atrocious / instead of prov- 
 ing, as in the well-known tale of Cyrus and the two 
 coats, that 'the taller boy had a right to force the 
 other boy to exchange coats with him/ you prove 
 that 'the exchange would have been advantag- 
 eous to both/ instead of proving that 'a man 
 has not a right to educate his children or dis- 
 pose of his property in the way he thinks best/ you 
 prove that 'the way in which he educates his chil- 
 dren or disposes of his property is not really the 
 best;' instead of proving that 'the poor ought to be 
 relieved in this way/ you prove that 'they ought to 
 be relieved.' " The fallacy usually occurs, as Jevons 
 
FALLACIES 575 
 
 remarks, "in the course of long harangues, when 
 the multitude of words and figures leaves room for 
 confusion and forgetfulness." Hence, an ignoratio 
 elenchi has been called by Aikins the fallacy of the 
 forgotten issue. Thus it is frequently necessary, 
 for example in debate, to call the discussion back to 
 the point at issue. For example, in a speech in the 
 House of Commons, Canning is reported to have 
 said, in reply to Mr. Percival, that "The question is 
 not, as assumed by my opponent, whether we shall 
 continue the war in the Peninsula, but whether it is 
 essential to our success in the war that our present 
 system of currency remain unchanged." 
 
 The nature of the fallacy, then, consists in sub- 
 stituting for a certain issue another which is more 
 or less closely related to it, and arguing the substi- 
 tuted issue. The fallacy does not take into account 
 whether the arguments do or do not really support 
 the substituted issue, it only calls attention to the 
 fact that they do not constitute a proof of the orig- 
 inal one. Sudents are quite often guilty of an 
 ignoratio elenchi when in reply to questions they 
 substitute some other though related question and 
 allow their answers to be guided by it. It is a par- 
 ticularly prevalent and subtle fallacy and it assumes 
 a great variety of forms. But whenever it occurs 
 and whatever form it takes, it is brought about by 
 an assumption that leads the person guilty of it to 
 substitute for a definite subject of inquiry another 
 which is in close relation with it. In the petitio 
 principii the fallacy may be described as an assump- 
 
576 A TEXT-BOOK OF LOGIC 
 
 tion of the premises ; in the complex question, as an 
 assumption of the answer; and in the ignoratio 
 elenchi, as an assumption of the question at issue. 
 
 Whenever, for any reason, a conclusion does not 
 follow from the assigned premises, we have, in the 
 literal sense of the term, a Non Sequitur. When 
 used in this sense to include all the errors in reason- 
 ing which leads to erroneous conclusions, the term 
 is generic, and must be understood as synonymous 
 with 'fallacy.' Any kind of loose or inconsequential 
 argument, from this point of view, would be a non 
 sequitur. 
 
 More particularly considered, the fallacy of non 
 sequitur, as was indicated by Aristotle, is the name 
 we apply to the erroneous conclusion of a hypo- 
 thetical syllogism. Aristotle regarded it as an 
 "argument from the affirmation of the consequent," 
 and for this reason it is sometimes called the fallacy 
 of the consequent. If, for example, we argue that 
 a particular individual who has no visible means of 
 support must be a prefessional thief, because "if 
 a man is a professional thief, he will have no visible 
 means of support," the argument will be fallacious 
 because, as we have seen, no conclusion can be 
 reached by affirming the consequent of hypothetical 
 propositions. The term non sequitur may also be 
 applied to the other hypothetical fallacy of denying 
 the antecedent. In both the cases to which the term 
 has been said to apply, the assumption is made that 
 the relation between antecedent and consequent of 
 the major premise is causal, an assumption which 
 
FALLACIES 577 
 
 we have no right to make in view of the complex 
 interconnection of the facts with which our human 
 knowledge has always to deal. But if it is made, 
 the only way we can avoid a possible fallacy is to 
 call into question the assumption, and thereby to 
 raise definitely the question whether antecedent and 
 consequent are causally connected or not. 
 
 The attempt has sometimes been made to apply 
 the name non sequitur to the fallacies which occur 
 in connection with categorical arguments. This 
 cannot be considered a useful employment of the 
 term. For if the term applies to any and all of 
 these errors, it must be regarded, as we have said 
 above, as a generic term, and loses all particular 
 significance, and if it is used of a particular kind 
 of categorical fallacy, it immediately takes its place 
 as a synonym of the name of that fallacy. Some 
 logicians, however, do not take this view of the case, 
 and they assign the term to a group of cate- 
 gorical arguments of which the following may 
 be said to be fairly representative : 'Episcopacy is 
 of scriptural origin, the Church of England is the 
 only established church in England, therefore the 
 church established in England is the only church 
 that should be supported.' Again, 'Pennsylvania 
 contains rich coal and iron mines, Pennsylvania has 
 no sea coast, therefore the battle of Gettysburg was 
 fought in that state/ These examples are so flimsy, 
 as examples of argument, that the only sensible 
 course to take with regard to the class of reasoning 
 
 37 
 
578 A TEXT-BOOK OF LOGIC 
 
 for which they stand is to deny that it can have any 
 logical recognition at all. Logic presupposes at the 
 least some development of common sense on the 
 part of those to whom it addresses itself, and one 
 can hardly be expected to take so low an estimate of 
 logic as to think that it can be of any possible service 
 to the individual upon whom such so-called argu- 
 ments would have the least chance to impose. The 
 logician has absolutely nothing to do with such an 
 individual who, in the interests of society, had much 
 better be placed in the care of an alienist. 
 
 We conclude, therefore, that non sequitur is a 
 name that can be applied only to fallacies of the kind 
 that occur in the course of hypothetical arguments. 
 The fallacy consists in misinterpreting the implica- 
 tions of the relation of antecedent and consequent 
 stated in the major premise of hypothetical syllo- 
 gisms. 
 
 Fallacies of Interest. Knowledge, as we have 
 shown, depends for one of its conditions upon what 
 we call interest. But knowledge is not secured and 
 advanced by any or any kind of interest. It is only 
 when, as we have seen, the interest is directed 
 toward, and is accompanied by a desire to ascertain, 
 the nature and relations of the objects by which it 
 is stimulated that it can be considered to be of 
 service in the establishment of knowledge in the 
 strict sense of that term. The interest that must be 
 recognised as an indispensable condition of all 
 knowledge whatever is specifically an interest that 
 points toward and terminates in the establishment 
 
FALLACIES 579 
 
 of the knowledge relation. Whenever any other 
 interest than this is allowed, consciously or uncon- 
 sciously, to influence the steps we take toward 
 knowledge, or the conclusions we accept, the process 
 and the conclusion are for that reason fallacious. 
 Instances of the kind of argument just indicated 
 will be considered in the following paragraphs, and 
 they are grouped together because they all imply 
 that some other interest has been substituted for 
 the one which alone, as we have said, can be of 
 service in the attainment of truth. 
 
 Perhaps the most reputable of the fallacies of 
 the kind in question is that which is known as post 
 hoc, ergo propter hoc. In discussing the problems 
 connected with the establishment of causal relations, 
 we have seen that a succession of events is to be 
 interpreted always as containing the suggestion of 
 a possible causal connection between the events in 
 question, or with other with which they are con- 
 stantly associated ; but we saw also that the succes- 
 sion itself is never to be taken as evidence of such 
 connection. If, therefore, neglecting this latter con- 
 sideration, we should argue from an observed suc- 
 cession of events to the causal connection of the 
 events, the conclusion would be fallacious because 
 the only reason that could be assigned for the infer- 
 ence, namely, that, since the one event had followed 
 the other, it was, therefore, caused by that other, 
 is never sufficient to establish a causal relation. The 
 fallacy arises, then, from neglect of the negative 
 criterion of causal relations to which we have just 
 
580 A TEXT-BOOK OF LOGIC 
 
 referred, namely, that mere succession is never a 
 sufficient reason for a causal inference. 
 
 The relative prevalence of this fallacy, and the 
 charitable attitude most of us take toward those who 
 are guilty of it, suggest that the error which it 
 implies lies somewhat deeper in the mental life than 
 some others that have come before us. If this is 
 true, the explanation and full exposition of the 
 nature of the fallacy belong to psychology rather 
 than to logic. In a general way, however, we can 
 see that whenever the scientific interest, which seeks 
 to safeguard conclusions from possible sources of 
 error, is not strictly emphasised, or when it is for 
 some reason temporarily weakened, it is easy for the 
 human mind to slip into one of the more usual or 
 conventional attitudes toward the objects of its ex- 
 perience, and thus to arrive at conclusions which, 
 to the extent that this has taken place, are fallacious. 
 In these fallacies, we observe a tendency to confuse 
 associative combinations with causal connections, a 
 tendency which is emphasised whenever the prac- 
 tical takes the place of the theoretical interest in 
 determining our relations to the objects of our ex- 
 perience. An example of this fallacy, frequently 
 met with in educational circles, is the contention 
 that because students who are handicapped by the 
 necessity of earning their livelihood usually manage 
 to pass their examinations, while others who are 
 not so handicapped sometimes fail, the handicap is 
 part of the cause of their success. In similar 
 fashion, we have heard it argued that because Spur- 
 
FALLACIES 581 
 
 geon, who never went to college, was a great 
 preacher, that this was due to the fact that he never 
 attended college. There is more common sense and 
 logic in Spurgeon's remark, referring to the above 
 contention, that the result was accomplished in 
 spite of his lacking a collegiate training. 
 
 There are a number of fallacies which are due 
 still more obviously to the way in which arguments 
 connect themselves with interests which are distinct 
 from the one with which our search for truth is 
 more particularly associated, and in which the con- 
 clusion assumes a character in conformity with 
 these interests. When, for instance, an argument 
 makes an appeal to the character, principles, pro- 
 fession, or interests of an individual, and it is ac- 
 cepted or rejected for that reason, there results a 
 fallacy which is called an argumentum ad hominem. 
 If, for example, the evidence for the movement of 
 the earth round the sun is rejected because it is 
 inconsistent with one's religious convictions, the 
 rejection is fallacious because the argument reaches 
 its conclusion by the substitution of the religious 
 for the scientific interest. If, again, the fact that 
 one owns stock in a brewery is allowed to influence 
 his judgment as to what conclusion, with respect to 
 the sale of alcoholic beverages, is warranted by the 
 scientific evidence that is available on the physio- 
 logical effects of alcohol on the human system, he is 
 guilty of the fallacy under consideration. When, 
 once more, the demands of religion upon the indi- 
 vidual are rejected because preachers or church 
 
582 A TEXT-BOOK OF LOGIC 
 
 members are not free from obvious faults, or when 
 they are accepted because thereby business will be 
 helped, the position in each case involves an ad 
 hominem fallacy. 
 
 The admission, by courts of law, of testimony 
 bearing upon the character of witnesses, requires 
 a word of explanation, because it seems to be in 
 contravention of the recognised fallacious nature 
 of the arguments we are now considering. The 
 difficulty created by this instance is removed when 
 we observe that courts of law do not admit testi- 
 mony as to the character of witnesses for the pur- 
 pose of deciding whether the verdict shall be for 
 or against the plaintiff, but for the purpose of 
 eliminating, from the evidence that comes before it, 
 testimony that is irrelevant to the issue, that is, 
 testimony which, because it is prejudicially affected 
 by the character of the individual who gives it, 
 involves an argumentum ad hominem. Prejudiced 
 or perjured evidence is fallacious in exactly the 
 sense in which any ad hominem argument is falla- 
 cious. 
 
 When an argument is accepted because it enlists 
 on one side or other of the question at issue, our 
 feelings, passions or prejudices, it is called an argu- 
 mentum ad populum. This is essentially the fallacy 
 of public address. Any cause, as we all know, that 
 can bring impressive oratory and brilliant metaphor 
 to its aid is very likely to secure the support of many 
 upon whom the cause itself and the arguments which 
 really support it, would have little or no influence. 
 
FALLACIES 583 
 
 Conspicuous examples of fallacious reasoning of 
 this kind may be found on almost every page of the 
 voluminous writings of the late Robert Ingersoll. 
 A somewhat similar fallacy is that which is known 
 as argumentum ad misericordiam. In this case, our 
 judgment is determined by the appeal that is made 
 to our pity or sympathy. Whenever, for example, 
 we recommend a cause by emphasising the plight of 
 those whom it is intended to benefit, or give our sup- 
 port because of our interest in the individuals who 
 advocate it, or give alms to a beggar because he is 
 in rags, we are guilty of letting our sympathy inter- 
 fere with our judgment, and this is exactly what 
 occurs in any argumentum ad misericordiam. 
 
 The influence of a great name or of long estab- 
 lished customs is pretty generally recognised as serv- 
 ing a useful purpose in the development of the indi- 
 vidual and the race. When, however, our reverence 
 for individuals or institutions leads us to accept, 
 without consideration of the arguments which may 
 be advanced for and against them, positions which 
 receive the support of or are in conformity with 
 any established authority, we are said to be guilty 
 of the fallacy, argumentum ad verecundiam. This 
 is a fallacy to which the conservatives among us 
 are particularly prone. Our interest in order, in 
 things as they are, unless balanced by a due regard 
 for change, may lead us to accept a position merely 
 because it is in agreement with some established 
 custom, or to reject another merely because it re- 
 quires the rejection of some accepted authority. A 
 
584 A TEXT-BOOK OF LOGIC 
 
 peculiarly aggravated form of the fallacy comes to 
 light in those instances where an individual's right 
 to speak with authority in one field of knowledge is 
 taken as the ground of our acceptance of that indi- 
 vidual's opinion in another field with respect to 
 which he has no special acquaintance. "The pres- 
 tige of a great name," as Creighton remarks, "is 
 thus irrelevantly invoked when no significance prop- 
 erly belongs to it. Thus, for example, a successful 
 general is sometimes supposed to speak with author- 
 ity upon problems of statescraft, and the opinions 
 of prominent clergymen are quoted regarding the 
 latest scientific or political theories." 
 
 REFERENCES 
 
 H. A. Aikins, The Principles of Logic, Chs. XVIII., XIX., XX. 
 J. E. Creighton, An Introductory Logic, 3d Edition, Chs. 
 
 XII., XX. 
 J. G. Hibben, Logic, Deductive and Inductive, Part I., Ch. 
 
 XIX., Part II., Ch. XVI. 
 W. S. Jevons, Elementary Lessons in Logic, Lessons XX., 
 
 XXI. 
 S. ' H. Mellone, An Introductory Text-Book of Logic, 3d 
 
 Edition, Ch. X. 
 C. Read, Logic, Deductive and Inductive, 3d Edition, Ch. 
 
 XXIV. 
 W. J. Taylor, Elementary Logic, Ch. XVIII. 
 
 ADVANCED 
 
 W. R. B. Gibson, The Problem of Logic, Ch. XXVIII. 
 H. W. B. Joseph, An Introduction to Logic, Ch. XXVII. 
 J. S. Mill, A System of Logic. Book V. 
 F. C. S. Schiller, Formal Logic, Ch. XXIII. 
 
FALLACIES 585 
 
 A. Sidgwick, Fallacies. 
 
 J. Welton, A Manual of Logic, Vol. II., Book VII. 
 
 QUESTIONS 
 
 1. What is an inductive fallacy, and into what classes 
 may such fallacies be divided. 
 
 2. What testimony can you quote showing the importance 
 of a careful and accurate use of language for logical 
 thinking? 
 
 3. What did Bacon mean by Idols of the Market Place? 
 
 4. How does Locke explain the fact that language often 
 renders thought fallacious? 
 
 5. In what two ways may the observation of facts be 
 fallacious? 
 
 6. State and illustrate the fallacy of insufficient observa- 
 tion. 
 
 7. What do you understand by a negative instance? 
 
 8. What is the testimony of Bacon and Darwin as to the 
 importance of negative instances? 
 
 9. In what respect does education predispose one to the 
 neglect of negative instances? 
 
 10. What does Bacon mean by Idols of the Theatre? 
 
 11. In what form is the fallacy described by Bacon in 
 these terms likely to appear at the present day? 
 
 12. What is the fallacy of incomplete or imperfect obser- 
 vation? 
 
 13. Explain how the personal factor may lead to incomplete 
 or imperfect observation. 
 
 14. In what way does technique affect the thoroughness of 
 observation? 
 
 15. What are the two fallacies of explanation considered 
 in the text? 
 
 16. Explain what is meant by a hasty generalisation. 
 
 17. To what consideration of scientific importance does the 
 possibility of hasty generalisations point? 
 
 18. What is the fallacy of false analogy? 
 
586 A TEXT-BOOK OF LOGIC 
 
 19. In what respect is the fallacy of false analogy similar 
 to the fallacy of figurative language? 
 
 20. In what respect does false analogy resemble the fallacy 
 of negative instances? 
 
 21. What is the general character of the fallacies of the 
 context? 
 
 22. Into what two classes may fallacies of the context be 
 divided? Describe each class, naming the particular 
 fallacies that belong therein. 
 
 23. What do we mean by a fallacy of assumption? 
 
 24. Describe the essential character of a petitio principii. 
 
 25. How may we proceed to break down a petitio principii? 
 
 26. How may a verepov irporepov be distinguished from a 
 circulus in probando, and how are they related to a 
 petitio principii? 
 
 27. What is the fallacy of the complex question? 
 
 28. What, according to Aristotle, is an ignoratio elenchi? 
 
 29. What is an ignoratio elenchi according to modern logic? 
 
 30. What is Aikin's term for an ignoratio elenchi, and dis- 
 cuss its appropriateness. 
 
 31. From the standpoint of the assumptions involved, how 
 do the petitio principii, the complex question, and the 
 ignoratio elenchi differ from one another? 
 
 32. What is the genereic meaning of the non sequitur? 
 
 33. What, according to Aristotle, is a non sequitur, and 
 what, accordingly, is another name for the fallacy? 
 
 34. With what meaning is the term non sequitur now used 
 in modern logic? 
 
 35. Discuss the relation of the non sequitur to categorical 
 arguments. 
 
 S6. What are the fallacies of interest? 
 
 37. Describe the post hoc, ergo propter hoc fallacy. 
 
 38. What is understood by an argumentum ad hominem? 
 
 39. Does the admission of evidence as to the character of 
 accused persons, or of those giving evidence, by courts 
 of law involve the verdict in the ad hominem fallacy? 
 Explain. 
 
FALLACIES 587 
 
 40. What is the argumentum ad populum? Illustrate. 
 
 41. State and illustrate the argumentum ad misericordiam. 
 
 42. Show by means of illustrations the nature of the argu- 
 mentum ad verecundiam. 
 
 EXERCISES 
 
 Examine the following arguments, and state in what re- 
 spects, if any, they are fallacious, the technical name of 
 the fallacy of which each is guilty, and the class to 
 which the fallacy belongc: 
 
 (1) In the act of landing on the African coast, Caesar 
 accidentally stumbled, and, as he did so, he ex- 
 claimed, 'Africa! I embrace thee.' Against what 
 fallacy on the part of his followers was this ex- 
 clamation intended to guard? 
 
 (2) It is a dictum of the Cartesian philosophy that 
 whatever can be clearly conceived exists. Is this 
 fallacious, and if so, why? 
 
 (3) The opponents of the Copernican system argued 
 that if the earth moved, a stone let fall from the 
 top of a tower would not reach the ground at the 
 foot of the tower, but at a point some distance 
 from it, in a direction opposite to the earth's 
 movement. Such, however, is not the fact. 
 
 (4) It is reported by travelers that the negroes among 
 whom coral is worn as an amulet affirm that it is 
 always affected by the state of health of the 
 wearer, becoming pale in disease. This is not 
 true. 
 
 (5) Women, as a class, are supposed not to have 
 hitherto been equal in intellect to men, therefore 
 they are necessarily inferior. 
 
 (6) The twenty-five years of Republican tariff legis- 
 lation have been a nera of unparallelled prosperity. 
 Why kill the goose that lays the golden egg? 
 
588 A TEXT-BOOK OF LOGIC 
 
 (7) The metropolis of a country may be compared to 
 the heart of a living body, hence we may infer that 
 any considerable increase in size of the metropolis 
 is evidence of a diseased condition of the body 
 politic. 
 
 (8) The early Teutonic societies were held together 
 by ties of kinship, because all societies were so 
 held together originally. 
 
 (9) It is sometimes contended that because punishment 
 can only intimidate it is brutalising, and therefore, 
 it should not be employed, but that only shows that 
 there are persons who are so brutalised that they 
 can be influenced only through fear. 
 
 (10) The apologists of Charles I., McCaulay complains, 
 defend the king by urging that he was a good 
 judge of pictures and indulgent to his wife. 
 
 (11) This is a party measure and therefore we must 
 vote for it. 
 
 (12) A religion which elevates the soul above the body 
 can survive persecution, and since the Christian 
 religion has survived persecution, it enables its 
 devotees to prefer the interests of the soul to 
 those of the body. 
 
 (13) It is frequently assumed, because the animals and 
 men native to countries of inclement climates, 
 where the conditions of life are severe, are usually 
 robust, that the hardships they are forced to 
 undergo in youth are the cause of their hardiness. 
 
 (14) I do not know that you will approve it, but I gave 
 him a pair of shoes, an old coat, and something 
 to eat. I felt so sorry for him. 
 
INDEX 
 
 Abelard, on universals, 93 
 Accent, fallacy of, 5l7f 
 Accident, as predicable, 186 
 
 converse fallacy of, 521 
 fallacy of, 620f 
 
 Acquipollence, education by, 279f 
 Affirming the consequent, fallacy of, 
 
 540f 
 Agreement, Method of, 477f 
 
 a method of observation, 
 
 480, 482 
 
 elimination and, 478 
 Jevon's formulation of, 477 
 Kmits of, 480f 
 Mellone's formulation of, 
 
 479 
 
 method of single. 477 
 method of double, 490 
 Mill's formulation of, 477 
 states an ideal, 479f 
 Agreement and Difference, Method of, 
 
 486f 
 
 application of, 490f 
 conditions of its use, 486f, 
 
 496 
 
 field of application, 487 
 Melone's formulation of, 
 
 489 
 
 Mill's formulation of, 488 
 Aikins, on the forgotten issue, 575 
 Ambiguity, as fundamental logical 
 
 problem, 164 
 criticism of traditional 
 
 view of, 163f 
 fallacy and, 614 
 judgment and, 54 
 structural, 522f 
 
 traditional view of, 162f 
 translation and, 165f 
 verbal, 515f 
 
 of terms, fallacies of, 534f 
 Ambiguous disjunction, fallacy of, 
 
 547f 
 
 Amphibole, fallacy of, 522f 
 Analogy, conditions of, 413f, 41"f 
 false, fallacy of, 565f 
 function of, in induction, 
 
 416f 
 
 limits of, 412f, 418 
 logical character of, 411f, 
 
 419f 
 
 meaning of, 409f 
 translation and, 165f 
 Anselm, on universals, 93 
 Aquinas, on universals, 93 
 Arguments, basis of categorical, 297f 
 categorical, 297f, SOlf, 326f 
 circular, 572 
 constructive hypothetical, 
 
 361f 
 
 deductive, 532 
 destructive hypothetical, 
 
 353f 
 
 dilemmatic, 354f 
 disjunctive, 343f, 644f 
 hypothetical, 348f, 539f 
 inductive, 532 
 logical problem of cate- 
 gorical, 298 
 
 mixed disjunctive, 343f 
 simple disjunctive, 343f 
 validity of disjunctive, 
 
 345f 
 
 Argumentum, a dicto secundum quid, 
 521 
 
 589 
 
590 
 
 INDEX 
 
 a dicto simpliciter, 520 
 ad hominem, 581 
 ad misericordiam, 583 
 ad populum, 582f 
 ad verecundiam, 583f 
 Aristotle, list of Predicables, 181 
 on analogy, 409 
 on fallacies, 508 
 on ignoratio Elenchi, 573 
 on logic, 12, 18 
 on non seguitur, 576 
 on the categories, 369 
 on the classification of fal- 
 
 lacies, 511 
 on the fallacy of division, 
 
 519 
 
 on what can be defined, 182 
 Assertion, conditions of relevant, 36f 
 grounded, 302 
 grounds of, 302 
 judgment as, 28f 
 relevant, 36f 
 truth and, 58 
 Assumption, fallacies of, 669f 
 
 B 
 
 / 
 
 Bacon, on Idols of the Market Place, 
 
 653f 
 
 on Idols of the Theatre, 559f 
 on imperfect induction, 375 
 on negative instances, 375, 567f 
 on perfect induction, 374 
 on the interrogation of nature, 
 
 442 
 the herald of modern learning, 
 
 471 
 
 Bosanquet, on negative terms, 152 
 Bradley, on disjunction, 342 
 
 on the real subject of judg- 
 
 ment, 55 
 on the 'that' and the 'what* 
 
 of judgment, 49 
 Brodie, on scientific imagination, 424 
 
 Categories, defined, 369 
 
 predication and, 369 
 Causation, analysis and, 455f 
 
 complex characts, of facts 
 
 of, 449f 
 elimination as a method of, 
 
 474f 
 hypothetical statements and, 
 
 462f 
 
 metaphysics of, 458f 
 Mill's Methods and, 473f 
 necessity and, 457f 
 practical aspect of, 436f 
 problem of, 435f, 442f, 451 { 
 purpose and, 4.55 
 reciprocal, 461, 473f 
 relation of practical and 
 theoretical aspects of, 
 440f 
 
 relation of purpose to, 449 
 temporal sequence and, 445f 
 theoretical aspect of, 438f 
 Cause, analysis, 4i55f 
 
 certainty and, 455 
 
 complex character of, 449f, 
 
 453f 
 
 conditions and, 451 
 effect and, 447f, 453f 
 indeterminateness of, 452 
 necessity of, 456f 
 occasion and, 461 
 probability and, 464f 
 purpose and, 449, 455 
 reciprocity of effect and, 461f 
 temporal antecedence and, 445f 
 Causes, composition of, 499 
 
 criticism of plurality of, 466f 
 permanent, 486 
 plurality of, 461f, 542f 
 Classification, artificial, 215 
 
 comparison and, 212f, 
 
 377 
 
 conditions of, 214f 
 defined, ffllf 
 definition and, 212f 
 
INDEX 
 
 591 
 
 division and, 213f 
 induction and, 216 
 kinds of, 2l5f 
 Mill's doctrine of, criti- 
 cised, 216 
 natural, 215 
 practical, 2l7f 
 purpose and, 214, 216f 
 scientific and popular, 
 
 377f 
 statistical methods and, 
 
 ml 
 
 theoretical, 217 
 Colligation, nature of, 378f 
 
 value of, 380 
 
 Comparison, classification and, 214 
 definition and, 169, 190 
 relation of judgment and 
 
 reasoning to, 303 
 
 Complex Question, fallacy of, 572f 
 Composition, converse fallacy of, 519 
 
 fallacy of, 518f 
 
 Concept, conceptualist view of, 93 
 logical view of, 98f 
 nominalist view of, 93 
 psychological view of, 93 
 realist view of, 92f 
 Conclusion, as grounded assertion, 302 
 
 denned, 304 
 Concomitant Variations, Method of, 
 
 486, 492f 
 conditions of its use, 
 
 493, 494f, 497 
 field of its application, 
 
 496 
 Mill's formulation of, 
 
 492 
 quantitative phenomena 
 
 and, 494f 
 
 the principle of, 493 
 Conditions, cause and, 461 
 
 essential, 456 
 
 Context, relation of judgment and 
 proposition to, 54, 82, 87 
 
 Contradiction, basis of, 211 
 fallacy of, 627 
 meaning of, 272f 
 Contradictories, meaning of, 210 
 Contraposition, education by, 288f 
 
 table of, 289 
 
 Contrariety, meaning of, 266f 
 Connotation, meaning of, 109f, 158 
 of collective term, 128 
 of general term, 125 
 of individual term, 122f 
 of positive term, 144f 
 problems of, 117, 158 
 relation to denotation, 
 
 llOf 
 
 Conversion, contrapositive, 288f 
 fallacies of, 530f 
 meaning of, 283f 
 method of, 284f 
 per accidens, 286 
 rule of, 285 
 simple, 285f 
 table of, 288 
 Copula, as "sign of predication", 94, 
 
 234 
 
 existential views of, 95f 
 function of, 91f, 234 
 how expressed, 91 
 relational view of, 92f 
 Creighton, on argumentum ad vere- 
 
 cundiam, 684 
 on fallacy of accent, 618 
 on the Joint Method, 487f, 
 
 491f 
 
 on the connotation of 
 proper names, 122 
 
 Darwin, on theorising, 399 
 
 on negative instances, 658 
 Definition, classification and, 212f 
 
 comparison and, 109, 190, 
 
 212f 
 
 conditions of, I67f 
 convertible with definien- 
 dum, 179 
 
592 
 
 INDEX 
 
 dichotomy and, 207f 
 elementariness of, I79f 
 genetic, 176 
 homogeneity of terms in, 
 
 179 
 
 indeterminateness of, 196f 
 negative, 180f 
 per genus tt differentiam, 
 
 171f 
 
 positive, 180 
 problem of, 159, I80f 
 real, 173f 
 relation of division to, 190, 
 
 198f 
 relation of purpose to, 
 
 I76f 
 
 structural, 175 
 synonyms and, 180 
 tests of, 176f 
 too broad, I77f 
 too narrow, 178 
 verbal, I73f 
 when employed, 167f, 170, 
 
 190 
 
 Denotation, meaning of, 108f, 114f 
 of collective term, 128f 
 of general term, 125 
 of individual term, 122f 
 of positive term, 144f 
 problems of, 117, 168 
 relation to connotation, 
 
 HOf 
 Denying the antecedent, fallacy of, 
 
 MM 
 
 Designation, as concrete term, 121 
 meaning of, 122f, 124 
 Dichotomy, definition and, 207f 
 division by, 205f 
 nature of, 206f, 210 
 value of, 208f 
 Difference, Method of, 482f 
 
 a method of experiment, 
 
 482 
 
 grounds of validity, 485f 
 indirect method of, 490 
 intermixture of effects and, 
 486 
 
 Hellene's formulation of, 
 
 484 
 
 Mill's formulation of, 482 
 single method of, 484 
 Differentia, as predicable, 185f 
 
 meaning of, 172f 
 Dilemma, classes of, 357f 
 
 constructive, 357f 
 denned, 355 
 destructive, 8&8f 
 nature of, 354f 
 structure of, 356f 
 validity of, 359f 
 Distributed, meaning of, 114f 
 
 terms in categorical prop- 
 osition, 259f 
 
 Disjunction, basis of, 340f 
 exclusive, 341f 
 exhaustive, 342f 
 Division, by dichotomy, 205f 
 
 classification and, 213f 
 conditions of, 213f 
 cross, 201 
 fallacy of, 519f 
 logical, exhaustive, 205 
 meaning of logical, 191f, 198, 
 
 196 
 
 metaphysical, 194 
 physical, 195 
 principle of, 195, 196f 
 rules of logical, 192, f, 200f 
 terminology of logical, 199f 
 verbal, 195 
 
 Eductions, by aequipollence, 279f 
 by contraposition, 288f 
 by conversion, 288 
 by inversion, 290f 
 by negation, 288f 
 by obversion, 279f 
 by permutation, 279f 
 classes of, 279f 
 fallacies of, 529f 
 meaning of, 278f 
 
INDEX 
 
 593 
 
 schema of, 292 
 summary of, 291 
 table of, 292 
 Effect, cause and, 447f 
 
 conditions and, 461 
 
 intermixture of, 485f, 499 
 
 nature of, 452 
 
 occasion and, 461 
 
 reciprocal character of cause 
 
 and, 461f 
 
 temporal sequence and, 445f 
 Enthymeme, denned, 328 
 
 elliptical nature of, 329 
 Figure of, 329 
 Mood of, 329 
 Orders of, 328 
 syllogistic character of, 
 
 328 
 
 Enumeration, generalisation and sim- 
 ple, 386 
 simple, 376f 
 
 Episyllogism, polysyllogism and, 330 
 Epicheirema, nature and classes of, 
 
 335f 
 
 Equivocation, fallacy of, 515f 
 Error, characteristic of assertion, 58 
 compatibility of asserted con- 
 tent in, 68f 
 conditions of, 82, 97 
 not irrelevance, 66f 
 purpose and, 66 
 Exclamations, logic of, 31f 
 Experiment, controlled conditions, 403 
 limitations of, 401 
 nature of scientific, 400, 
 
 402f, 483f 
 
 observation and, 400 
 relation of purpose to, 
 
 402f 
 scientific 402f, 483 
 
 Fact, a coexistent, 486 
 
 colligation and, 378f 
 meanings of, 367f 
 
 38 
 
 relation to judgment, 368 
 
 relations of, 370f 
 
 world of, 37lf 
 Fallacies, categorical, 533 
 
 classification of, 511f 
 
 deductive, 633f 
 
 defined, 508f 
 
 disjunctive, 544f 
 
 hypothetical, 539f 
 
 inductive, 552f 
 
 a dicto secundum quid, 521 
 
 a dicto simpliciter, 520 
 
 ad hominem, 581 
 
 ad misericordiam, 583 
 
 ad populum, 582f 
 
 ad verecundiam, 583f 
 
 categorical, 533 
 
 classification of, 511f 
 
 deductive, 633f 
 
 defined, 508f 
 
 disjunctive, 644f 
 
 hypothetical, 539f 
 
 ignoratio elenchi, 573 
 
 inductive, 652f 
 
 non sequitur, 576f 
 
 of accent, 517f 
 
 of accident, 520f 
 
 of accident, converse, 521f 
 
 of ambiguous disjunction, 
 
 547f 
 
 of amphibole, 522f 
 of assumption, 669f 
 of complex question, 672f 
 of composition, 518f 
 of contrariety, 627f 
 of conversion, 530f 
 of division, 619f 
 of eduction, 529f 
 of education, 529f 
 of equivocation, 615f 
 of explanation, 563f 
 of false analogy, 565f 
 of false disjunction, 646 
 of false parenthesis, 524 
 of four terms, 534f 
 of hasty generalisation, 663f 
 
594 
 
 INDEX 
 
 of incomplete disjunction, 
 MM 
 
 of implication, 625f 
 
 of inference, 631f 
 
 of insufficient premises, 637f 
 
 of interest, 578f 
 
 of interpretation, 614f 
 
 of language, 663f 
 
 of observation, 655f 
 
 of obversion, 529f 
 
 of opposition, 526f 
 
 of subalternation, 628f 
 
 of subcontraiety, 627f 
 
 of the consequent, 676 
 
 of the context, 667f 
 
 petitio principii, 670f 
 
 post hoc, 679f 
 
 structural ambiguity and, 
 
 522 
 verbal ambiguity and, 615 
 
 Generalisation, causal sequence and 
 
 empirical, 463f 
 classification and, 377f 
 empirical, 376f, 385f 
 hasty, fallacy of, 663f 
 Mill on, 376 
 presuppositions of, 377 
 simple enumeration 
 
 and, 386 
 statistical methods 
 
 and, 391f 
 value of empirical, 
 
 378, 385 
 
 Genus, meaning of, I72f 
 as predicable, 185f 
 
 Gibson, on elimination in causal in- 
 quiries, 476f 
 
 on experimentation, 403 
 on statistical method, 391 
 Green, on colligation, 379 
 Grote, on knowledge of acquaintance 
 and knowledge about, 83 
 
 H 
 
 Hegel, on the syllogism of analogy, 412 
 Herschel, his contributions to induc- 
 tive logic, 472 
 
 on residual phenomena, 600 
 Huxley, on intellectual observation, 
 
 400 
 Hobbes, on language, 553 
 
 on the scientific imagination, 
 
 425 
 Hypothesis, analysis and, 421 
 
 imagination and, 426f 
 limits of, 420f 
 living, 427 
 nature of, 420 
 objections to, 422f 
 theory and, 429f 
 truth and, 427 
 verification of, 427f 
 
 Imagination, science and,424f 
 Imperatives, logic of, Slf 
 Implication, classes of, 264f 
 fallacies of, 526f 
 meaning of, 263f, 278, 626f 
 Induction, analogy and, 416f 
 
 explanatory methods of, 
 
 406f 
 
 ground of truth of, 387f 
 hypothetical statements and, 
 
 389 
 
 imperfect, 373 
 number of instances and, 
 
 386, 386f, 665 
 perfect, 372, 376f 
 problem of, 366f, 372 
 simple enumeration and, 
 
 372f 
 
 two factors of, 386f 
 Inference, by private conception, 279f 
 fallacies of, 531f 
 immediate, 263f. 
 
 Instances, negative, 875, 484f, 556f 
 positive, 484f 
 
INDEX 
 
 595 
 
 Intelligence, nature and development 
 of, 395f 
 
 Interest, assertion and, 36f 
 
 cansation and, 449, 455 
 classification and, 214, 216f 
 designation and, I23f 
 error and, 66 
 experiment and, 402f 
 general term and, 125f 
 judgment and, 44f, 67, 117 
 knowledge and, 44f, 578f 
 meaning and, 117 
 and opinion, 464 
 observation and, 397, 402f. 
 
 Interrogatives, logic of, 31f 
 
 Inversion, method and nature of, 290 
 obversion and, 291 
 tables of, 291 
 
 Irrelevance, nature and forms of, 65f 
 
 James, definition of conception, 26 
 
 on knowledge of acquaintance 
 
 and knowledge about, 83. 
 on the meaning of term 
 thought, 25 
 Jevons, on analogy, 419 
 
 on ignoratio etenchi, 674f 
 on imperfect induction, 374f 
 on the antecedent of causal 
 
 events, 450f 
 on the dilemma, 359 
 on the fallacy of accent, 517 
 on the intermixture of effects, 
 
 499 
 on the Method of Single 
 
 Agreement, 477 
 on the occasion of an event, 
 
 in 
 
 Joseph, on elimination in causal in- 
 quiries, 474f 
 
 Judgment, actual subject of, 52, 55 
 ambiguity of, 54f 
 as assertion, 28f, 29f, 36f 
 as grounded assertion, 302 
 belief and, 97 
 
 comparison and, 303 
 conditions of, 36f 
 content of, 29, 82 
 defined, 29, 50, 55 
 difference and, 240 
 empirical, general, 385f 
 enumerative, 374 
 error and, 65f 
 fact and, 368 
 fragmentariness of, 83, 87 
 groundless statements and, 
 
 33f 
 
 identity and, 239 
 incompleteness of, 54 
 interest and, 44f, 67, 117 
 limits of, 67 
 logical subject of, 52. 
 mental attitudes akin to, 
 
 31f 
 nature of, 28f, 35f, 51, 55, 
 
 303 
 
 object of, 47f, 50, 368 
 objective of, 50 
 origin of, 77f 
 practical aspect of, 357 
 presupposition of, 52, 97 
 probable, 62f 
 proposition and, 76f, 84, 94, 
 
 303 
 scientific, and probability, 
 
 62f 
 
 social, and probability, 62f 
 subject-matter of, 29, 47f 
 theoretical aspect of, 35f, 
 
 41f 
 
 thought and, 28f 
 truth of, 58f 
 
 K 
 
 Knowledge, about, 83 
 
 error and, 65f 
 interest and, 44f, 578f 
 meaning of, 5f 
 method of, logic as, 20 
 of acquaintance, 83. 
 opinion and, 464 
 
596 
 
 INDEX 
 
 relation of syllogism to, 
 
 298f 
 
 systematic, 6f, 391f 
 truth and, 58f , 60f, 366 
 .Knowledges, logic and the, 9f, 18 
 meaning of, 9 
 thought and the, lOf 
 
 Language, Hobbes on, 553 
 
 judgment and, 76, 84f, 96, 
 
 98f 
 
 Locke on, 554f 
 the sciences and, 160 
 
 Locke, on language, 664f 
 
 Logic, as an art, 17f, 20f. 
 
 as method of thinking, 19 
 as science, 21f 
 as science of meaning, 20 
 as scientia scientiarum, llf 
 as scientific method, 19 
 Herschel's contributions, 472 
 humanistic influence in, 12f 
 Mill's historical position of, 472 
 psychology and, 14f, 20 
 subject-matter of, If, lOf 
 the knowledges and, 9f 
 the sciences and, lOf 
 thought and, lOf 
 
 Lotze, on observation, 400 
 
 M 
 
 Major, ambiguous, fallacy of, 534 
 
 illicit process of, 536 
 Marketplace, idols of, 553f 
 Mathematical proportion, analogy and 
 
 400f 
 
 syllogism and, 300f 
 Meaning, absolute and relative, dis 
 
 tinction between, 140f 
 abstract, 130f 
 
 abstract, development of 
 134f 
 
 abstract, partial views of, 
 
 131f 
 
 collective, 126f 
 concrete, 118, ISOf 
 concrete and abstract, basis 
 of distinction between, 
 139 
 
 contrary, 155 
 disparate, 155 
 general, 124f, 126 
 incompatible, 238 
 individual, 124f 
 individual concrete, kinds 
 
 of, 121f 
 
 interest and, 117 
 negative, 143f, 236f 
 negative, conditions of, 
 
 145f 
 negative interpretation of, 
 
 149f, 154 
 
 positive, 143, 2S5f 
 privative, 143f, 236f 
 Meinong, on object and objective of 
 
 judgment, 49f 
 Mellone, on analogy, 416 
 
 on denying the antecedent, 
 
 542 
 
 on induction, 416 
 on the Joint Method, 489 
 on the Method of Agree- 
 ment, 479 
 on the Method of Differ 
 
 ence, 484 
 Methods, experimental, their historical 
 
 position, 47lf 
 problem to which they apply, 
 
 473f, 496 
 
 statement of, 477f 
 Middle, ambiguous, fallacy of, 534 
 
 undistributed, 536 
 Mill, his meaning of unconditional, 
 
 459f 
 historical position of his Logic, 
 
 47lf 
 
 on analogy, 419 
 on a philosophical language, 553 
 
INDEX 
 
 597 
 
 on causation, 444f 
 
 on colligation, 378f 
 
 on empirical generalisation, 376 
 
 on hypothesis, 427 
 
 on imperfect induction, 375 
 
 on invariable sequence, 445f 
 
 on parity of reasoning, 381 
 
 on perfect induction, 374 
 
 on permanent causes, 486 
 
 on purpose and cause, 449 
 
 on the complex character of 
 
 causal events, 449f, 457 
 on the composition of causes, 
 
 499 
 on the connotation of proper 
 
 names, 12f 
 on the copula, 95f 
 on the intermixture of effects, 
 
 48Sf 
 
 on the Joint Method, 486f 
 on the necessity of causal 
 
 events, 456f 
 
 on the plurality of causes, 461f 
 on the relation of metaphysics 
 
 to causal problems, 458f 
 on the Method of Agreement 
 
 477f 
 on the Method of Concomitant 
 
 Variations, 492f 
 on the Method of Difference,. 
 
 482f 
 
 on the Method of Residues, 496f 
 on the Methods of Experimen- 
 tal inquiry, 47lf 
 
 Minto, on Aristotelian logic, 13, 21 
 on the history of logic ,471 
 
 N 
 
 Names, connotation of proper, 112, 
 121f 
 
 denotation of proper, 121 
 
 meaning of, 88f 
 
 terms and, 88 
 Necessity, causal, 457f 
 
 Negation, bare, 152 
 
 conditions of, 145f 
 double, 279 
 eduction by, 288f 
 function of, 238 
 meaning of, 149f, 153f, 238 
 Non-ambiguity, division and, 190f 
 fallacy and, 515 
 language and, 160 
 limits of, 161f 
 
 Nonsense, logical status of, 238 
 Non sequitur, fallacy of, 576f 
 
 Object, affected by mode of apprehen- 
 sion, 24f 
 implication of, in conscious 
 
 process, 24f 
 meaning of, 24 
 Observation, analytic character of, 
 
 398f 
 
 development of, 395f 
 experimental, 400f, 453 
 experimental, limits of, 
 
 401 
 
 imagination and, 426 
 limits of, 556, 556f 
 perceptual, 396f 
 qualitative methods of, 
 
 of, 399f 
 scientific, 397f 
 scientific and Method 
 
 of Residues, 500 
 selective character of, 
 
 399f 
 
 theoretical, 401f, 453 
 Obversion, fallacy of, 529f 
 meaning of, 279f 
 method of, 281f 
 rules of, 290 
 table of, 282 
 
 Occasion, meaning of, 451 
 Opposites, contradictory, 210 
 Opposition, contradictory, 272f 
 contrary, 266f 
 fallacies of, 526f 
 
598 
 
 INDEX 
 
 kinds of, 266 
 meaning of, 265 
 subaltern, 269f 
 subcontrary, 273f 
 square of, 276f 
 table of, 279 
 Optatives, logic of, 31f 
 
 Pearson, on the objectivity of science, 
 
 423 
 
 Permutation, education by, 279f 
 Petitio principii, fallacy of, 570f, 573 
 
 575f 
 Polysyllogism, defined, 330 
 
 progressive, 331 
 prosyllogism and, 330 
 regressive, 331 
 types of, 33lf 
 Post hoc, fallacy, 679f 
 Porphyry, list of Predicables, 181 
 
 on the subject of predica 
 
 tion, 182 
 Tree of, 210f 
 
 Predicables, Aristotle on, 181f 
 commensurate, 183 
 lists of, 181 
 meaning of, 181 
 non-commensurate, 183 
 
 185f 
 
 Porphyry on, 181f 
 problem of, 160, 181f 
 Predication, basis of, 239 
 
 categories and, 369 
 
 degrees of, 222 
 
 kinds of thing and, 160 
 
 181f 
 
 meaning of, 85f, 222 
 Premises, as grounds of assertion, 302 
 function of, 305 
 major and minor, 305 
 negative, fallacy of, 537f 
 particular, fallacy of, 537f 
 propositions as, 304f 
 
 Probability, causation and, 464f 
 
 characteristic of assertion, 
 
 58 
 
 conditions of, 62f 
 scientific judgments and, 
 
 62, 64f 
 Propositions, affirmative, 235f, 238f 
 
 affirmative and negative, 
 
 relation of, 238f 
 ^analysis of, 84f 
 apodeictic, 250f 
 as premises, 304 
 assertoric, 247f 
 categorical, 99, 102f 
 categorical, classification 
 
 of, 222f 
 categorical, implications 
 
 of, 255f 
 
 causation and hypothet- 
 ical, 462f 
 compound, 244f 
 compound hypothetical, 
 
 355f 
 
 context and, 82 
 contraposition of, 288f 
 degrees of certainty of, 
 
 247 
 
 distribution and the cate- 
 gorical, 259f 
 disjunctive, 99, lOOf 
 eductive, 278f 
 eductive, fallacies of, 
 
 529f 
 
 eductive, schema of, 292 
 eductive, table of, 292 
 exclusive, 241, 243f 
 exceptive, 241 f 
 exponible, 244 
 hypothetical, 347f 
 hypothetical, and causa- 
 tion, 462f 
 ideas and, 77 
 import of, 79f 
 indesignate, 232f 
 induction and hypotheti- 
 cal, 389 
 
INDEX 
 
 599 
 
 x interpretation of, 263f 
 inversion of, 290f 
 judgment and, 76f, 84, 
 
 308 
 
 kinds of, 98f 
 ^meaning of, 76, 85, 96, 
 
 98f 
 
 modality of, 225, 246f 
 negative, 236f 
 opposed, 265f 
 opposed, fallacies of, 526f 
 opposed, table of, 279 
 opposition of, 265f 
 origin of, 78f 
 particular, 230f 
 problematic, 248f 
 quality of, 224f, 234f, 259f 
 quality and quantity, re- 
 lation of, 255f 
 quantity of, 224, 225f, 259 
 relations of, 222f, 225 
 simple hypothetical, 99, 
 
 lOlf 
 
 singular, 228f 
 statement import of, 79f, 
 
 84 
 structural formulae of, 
 
 256f 
 
 terms and, 84f, 107 
 the sentence and, 85 
 truth import of, 79, 84 
 types of, 222f 
 universal, 229f 
 universal, kinds of, 230 
 Proprium, meaning of, 184f 
 Prosyllogism, polysyllogism and, 330 
 Psychology, definition of, 26 
 logic and, 14f, 20 
 of thought, 25f, 35f 
 Purpose, see Interest 
 Pythagoras, on the mathematical in- 
 terpretation of nature, 393 
 
 "C 
 
 Quantity, of propositions, 224, 225f, 
 
 269 
 Quality, of propositions, 224f, 234f, 259f 
 
 Reality, belief in, 97 
 
 judgment and, 52, 55 
 meaning of, 370f 
 spheres of, 97f 
 Reasoning, parity of, 380f 
 Residues, Method of, 496f 
 
 intermixture of effects and, 
 
 498f 
 
 Mill's formulation of, 498 
 scientific observation and, 
 
 600 
 
 Roman Church, realism of, 93 
 Roscellinus, on universals, 93 
 
 Schoolmen, on universals, 92 
 Sciences, aims of the, 406f, 423 
 
 co-operation in the, 562f 
 imagination and the, 424f 
 language and the, 160 
 method of, logic as, 19 
 nature of the, 21 
 objectivity of the, 423 
 starting point of the, 443f 
 subject-matter of, If 
 thought and the, 2f 
 Series, causal, 448f 
 
 continuous, 203 
 
 Sidgwick, an analogical reasoning, 566 
 on petit io principii, 570 
 on subject and predicate 
 
 terms, 87 
 
 Sorites, Aristotelian, 332 
 defined, 332 
 Goclenian, 332f 
 rules of, 335f 
 
 Statistical Methods, as methods of 
 observation, 393 
 
600 
 
 INDEX 
 
 empirical generalisation 
 
 and, 391f 
 
 induction and, 391f 
 logical character of, 389f 
 quantitative, 392f 
 Subalternation, fallacies of, 528f 
 meaning of, 269f 
 Subcontrariety, fallacies of, 526f 
 meaning of, 273f 
 Syllogism, as method, 209, 305 
 categorical, 297f, 326f 
 categorical, Figures of, 310f 
 categorical, Moods of, 315f 
 disjunctive, 343f 
 disjunctive, Moods of, 344f 
 disjunctive, validity of, 345f 
 hypothetical, 348f, 539f 
 hypothetical, Moods of, 350f 
 judgment and, 298f 
 major term and, 304 
 mathematical proportion 
 
 and, 300f 
 
 minor term and, 304 
 mixed disjunctive, 343f 
 nature of, 301f, 326, 538f 
 problem of, 298f 
 propositions and, 304 
 place of conclusion in, 301f 
 quality of propositions in, 
 
 307f 
 quantity of propositions in, 
 
 308f 
 
 relation of Moods to Fig- 
 ure in, 318f 
 
 relation of premises to, 302 
 rule of disjunctive, 344 
 rules of categorical, 305f 
 rules of Figures in cate- 
 gorical, 312f 
 simple disjunctive, 343f 
 structural view of cate- 
 gorical, 303f 
 
 two ways of regarding, 326f 
 valid Moods of categori- 
 cal, 816f, 34 
 
 Tautology, logical status of, 238, 240 
 Terms, absolute, 141 
 
 abstract, 130f 
 
 classification of, 169 
 
 collective, 128f 
 
 common, 125f 
 
 complementary, 211 
 
 concrete, 118, 119f 
 
 connotative use of, 109f 
 
 contradictory, 529f 
 
 contradictory opposite, 210 
 
 contrary, 155, 529 
 
 correlative, 143 
 
 definition of, 159 
 
 denotative use of, 108f, 114f 
 
 designations as, 122f 
 
 disparate, 155 
 
 distribution of, 114f, 116 
 
 extent of, 115 
 
 fallacies of, 534f 
 
 general, 125f, 213 
 
 indefinite, 151 
 
 indesignate, 151 
 
 indeterminate, 211 
 
 individual, 120f, 126, 141 
 
 individual collective, 129 
 
 infinite, 151 
 
 many worded, 91 
 
 names and, 88f 
 
 negative, I51f, 154, 237f 
 
 positive, 144 
 
 predicate, 85, 86f, 237 
 
 privative, 153f 
 
 problems of the connotative 
 and denotative use of, 117, 
 158 
 
 proper names as, 121f 
 
 propositions and, 85, 107, 234 
 
 relation of connotative and 
 denotative use of, HOf 
 
 relation of individual to gen- 
 eral collective, 130 
 
 relative, 141f 
 
 sign of distributed, 115 
 
 sign of undistributed, 116 
 
INDEX 
 
 601 
 
 single-worded, 91 
 singular, I20f, 126 
 subject, 85, 86f 
 syllogism and, 304 
 thing and concrete, 118f 
 width of, 115 
 Theatre, idols of, 569f 
 Theory, hypothesis and, 429f 
 Thing, concrete term and, 118f 
 meaning of, 119 
 predication and kinds of, 160, 
 
 181f 
 Thorndike, on statistics of individuals, 
 
 390f 
 Thought, as assertion, 28 
 
 comparison and, 303 
 conditions of systematic, 7f 
 content and, 29 
 immediate, 303 
 judgment and, 28f 
 knowledge and, 2f 
 logical meaning of, 26f, 28 
 logic and, lOf 
 mediate, 303 
 method of, logic as, 29 
 nature of, 2f, 28 
 practical aspect of, 35f 
 syllogistic, 304 
 theoretical aspect of, 35f 
 uses of the term, 26f 
 Translation, ambiguity and, 165f 
 
 when employed, 166f 
 Truth, assertion and, 58 
 fact and, 366f 
 
 grounds of, in induction, 387f 
 hypothesis and, 427 
 nature of, 58f 
 systematic, 367 
 syllogism and, 327 
 
 tests of, 59, 60f 
 the proposition and, 76f 
 Tyndall, on the proof of an induc- 
 tion, 427 
 
 on the scientific imagination, 
 422, 424, 426 
 
 u 
 
 Unconditional, meaning of, 459f 
 
 necessity and, 456f 
 Undistributed, meaning of, 115 
 Universals, problem of, 92 
 Universe of Discourse, indeterminate- 
 ness of, 53f 
 nature of, 52f 
 plurality of, 57f 
 relation of judgment and 
 proposition to, 54, 82, 87 
 vvrepov Trporepov, fallacy of, 572 
 
 Verification, of hypothesis, 427f 
 
 the test of truth, 59, 60f 
 
 w 
 
 Welton, on ignoratio elenchi, 574 
 
 on experimentation, 403 
 Whateley, on ignoratio elenchi, 574 
 on petitio principii, 572 
 Whewell, his contribution to inductive 
 
 logic, 472 
 
 on colligation, 378f 
 on practical inferences, 397 
 Words, categorematic, 90 
 
 indefiniteness in meaning of, 
 
 161f 
 
 logical classification of, 90 
 significant, as terms, 89, 160 
 syncategorematic, 90 
 
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