A text-book of logic

Front matter

pROFsaaoK OF Philosophy in The Ohio State University

COPYRIGHT, 1915

BY

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 requirements in various parts of the world. Both in Europe and in America instruction in this subject has to a large extent been controlled by what may be called the classical tradition of which Api«totle 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 academic waters on this subject will result at some time in a larger freedom in the choice of the material and methods of logical instruction, and to that extent will reduce the possibility of attributing to the subject the imperfections of temper and understanding of those who teach it.

I hold no brief for traditionalism in logic, and while I sympathise with and, according to my

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ability, appreciate the value of much that the advocates 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 dispossess 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 same^. A similar interest may stimulate one to observe, in all the ways that modern logic is making familiar to us, the wonderful changefulness and practical resourcefulness of the mind's approach to truth ; but if one were to identify logic with the observation and description of these shifting 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 neglect 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 thousand 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 doctrine 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

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practical way of teaching it where its main difficulties are found, and who has not had an opportunity afforded him of devising methods of overcoming 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, therefore, 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 g^oblem^-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 mistaken, current controversy in philosophy would sometimes have been simplified, if indeed the occasion 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 diflicult chapters of the book. I do not believe that the judgment chapter is insuperably dijfficult; it is not more difficult, for example, than is the neurological 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 problem. 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.

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With respect to other features of the book, I may, perhaps, be expected to say something in justification 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 superfluous 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 fallacies 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 positive 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 discussed 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,

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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 xo 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 discussion; 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-

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gising to myself for failing to expound to my elementary students so recondfte a subject. I really have never found that any attempt to interest beginners 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 opportunity.

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 disappointed if the way had not been prepared for an intelligent study of the larger treatises on the subject, 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 philosophy itself. About the former point, it is only necessary to say that the lists of advanced references at the end of the chapters, limited as they necessarily had to be, are intended to invite individual 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

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to which reference is also made in the first lists of books. An experiment on the possibility of profitably 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 introductory 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 ot understanding what the problems are, much less of contributing to their solution, if one has not acquired a mastery of the instruments of logical thinking. But not only is this true in respect of philosophy 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 literature 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

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with the statement that I have learned from the masters of many schools, and have retained a grateful 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 canstantly 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 colleagues 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 xvii

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.

CONTENTS CHAPTER I.

PAGE

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

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

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XX CONTENTS

PAGE

Truth, Probability and Error 58

Chapter III. The Proposition

Judgment and the Proposition 76

The Import of Propositions 79

Formal Analysis of Propositions 84

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

Chapter IV. Terms

Proposition and Terms 107

Connotative and Denotative Use of Terms. 107

Relation of the Connotative and Denotative Use of

Distribution of Terms 114

Some Other Characteristics of Terms 117

Concrete Meaning 118

Individual Meaning: Proper Names and Designations 120

General Meaning 124

Collective Meaning: Individual and General 126

CONTENTS XXI

PAGE

Abstract Meaning 130

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

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

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PAGE

The Non-Commensurable Predicables 185

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

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 XXlll

PAGE

Quality of Propositions 234

The Affirmative Proposition 235

The Negative Proposition 236

The Relation of Affirmative and Negative Propositions 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

Chapter IX. Implications Op Categorical Propositions

Relation of Quantity and Quality in Categorical Propositions 255

Structural Formulae Indicating the Quantity and Quality of Propositions 256

Distribution of the Terms of the Four Categorical Propositions ' 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

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PAGE

Summary of Eductions 291

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

Chapter XI. Other Forms Of Categorical Argument

Their Relation to the Syllogism 326

Enthymeme 328

Polysyllogism 329

Types of Polysyllogism 331

Sorites 332

Epicheirema 335

CONTENTS XXV

Chapter XII. Disjunctive And Hypothetical Propositions And

ARGUMENTS. ^^^^

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

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

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

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PAGE

The Nature of Scientific Observation 395

Experimental Observation 400

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

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

CONTENTS XXVll

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

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

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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

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

Chapter I

The Starting, Point. It is customary to begin the exposition of a branch of knowledge with a statement and explanation of its definition. This is a useful mode of procedure when it can be presumed that those for whom one writes have previouslyacquired an elementary knowledge of the subject to which the definition relates. But since no such presumption 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 contain 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 presupposes 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 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 describes.

The Thought Element in Knowledge. If we consider further how the several sciences are constituted, it soon becomes evident that the material selected for study is only one condition of the existence of a science. The scientist must also think about his material before his knowledge concerning 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 differentiating 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. Thinking, in other words, is a specialised sort of mental activity, an activity that taxes to the utmost, and 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 uselessness 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 knowledge, 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 something, 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 brief, unless we think about the material that observation 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 emphasise the importance of thought for all forms of human knowledge. We all know what a picture puzzle is, — a collection of odd-shaped and variously coloured pieces of cardboard which, when put together in their proper relations, form a complete and consistent whole. All of us, moreover, have experienced difficulty in putting the pieces of cardboard 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 bringing out the pattern was not due to the lack of anything in our material, — all the pieces, we shall suppose, 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 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 favorable 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 prominence, 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 necessary to knowledge. Objects that no one thinks about are only the materials of knowledge, and thoughts that are not thoughts - about something in particular 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+thought. In later sections, we shall have more to say about these two factors of knowledge.