An introduction to modern logic

Preface

This book is intended to be precisely what the title implies — an introduction to modern logic. By ''modern" logic is understood that body of logical theories and methods which is usually associated with the names of Lotze, Sigwart, Bradley, Bosanquet, Wundt, Erdmann, and Dewey. The writer has endeavored to place himself in the center of this movement taken as a whole, and to set forth the characteristic doctrines of the modern school, so far as this has seemed possible in a book which is professedly introductory. The traditional or Aristotelian logic, which has played so great a part in the past history of thought, is entirely omitted from consideration, as are also symbolic logic and the various attempts at inventing a logical calculus. For all such omissions, as well as for what is included, the sole justification is the nature of an introductory treatise. It has seemed best to avoid polemics on the one hand, and an unmanageable multiplicity of hypotheses on the other, in favor of a certain singleness of purposi and organic unity of thought.

The exercises and suggestions for further reading at the end of the different chapters should be regarded as an integral portion of the book. To attempt to study logic without working one's way through appropriate exercises is like trying to study mathematics without solving problems, and leads inevitably to a certain superficiality of mental grasp which it is the avowed aim of logical treatises to fight and destroy. So also to confine one's reading to a single text-book is to shut one's mind to the interest and infinite variety, as well as to the concreteness and usefulness, of an important branch of modern science.

The writer's obligations are too numerous to mention. The influence of Plato and Kant, on the one hand, and of Locke, Hume, and Mill, on the other, is sufficiently obvious. But in the case of more recent writers and teachers it would be invidious to single out any one group. The chapter headings of Part III are in large part taken from Wundt's AUgemeine Methodenlehre, but for the contents of the chapters in question Wundt is in no special sense responsible. University of Minnesota.

September, 1918.

SYNOPSIS

Chapter Part I

JUDGMENT

The elements and chief stages of judgment I

The sensory element in judgment II

Sensory validity in judgment Ill

The intellectual element — identity, difference,

and organisation IV-VIII

Intellectual validity in judgment IX

General validity — theory of judgment X

Part II INFERENCE General characteristics of inference XI

(a) dependent or hypothetical XII

(b) analytical and expansive XIII

(c) novelty-seeking XIV

(d) constructive and systematic XV

Sensory and intellectual elements in inference. . XVI

Validity — theory of inference XVII

Part III SCIENTIFIC METHOD

Methods of investigation, and forms of exposition

(a) Analysis and synthesis XIX-XXI

(b) Abstraction and determination XXII-XXIII

(c) Induction and deduction XXIV-XXVI

(d) Definition XXVII

(e) Classification XXVIII

(f) Proof XXIX

(g) Fallacy XXX

(h) System of the sciences XXXI

Theory of scientific method XXXII

vii

Chapter XII

Dependent or hypothetical nature of inference — Kinds of dependence — From cause — From absence of cause — From effect — From absence of effect — Conclusion — Further consideration — Conclusion concerning empirical cases — Hypothetical versus categorical — Concluding summary 127

CONTENTS xi

Chapter XXI

Analysis and synthesis — Is analysis synthetical? — Mind-made entities, and natural phenomena — Is synthesis analytical? — Mind-made entities, and natural phenomena — Summary — Differences between analysis and synthesis — Apparent starting-point, conclusion, and method — Is synthesis a more advanced method? — Summary 230

Chapter XXII

Nature of abstraction — Aim of abstration — How far realisable? — With mind-made entities, and with natural phenomena — Types of abstraction — Validity of these methods — Summary 243

Chapter XXIII

Nature of determination — Aim of determination — How far realisable? — With mind-made entities, and with natural phenomena — Validity of determination — Summary — Abstraction and determination — Does abstraction involve determination? — Does determination involve abstraction? — Comparison with analysis and synthesis 252

CONTENTS xiii

Chapteb XXIV Page

Nature of induction — Aim of induction — How far realisable? — With mind-made entities, and with natural phenomena — Types of inductive method — Validity of induction — Summary 263

Chapter XXXII

Description of scientific method — Sensory elements in scientific method — Intellectual elements in scientific method — Summary — Validity of scientific method — In dealing with mind-made entities, and with natural phenomena — Conclusion 346

Index I 355

Index II . - .357

Introduction

The Logical Attitude of Mind. — The natural behavior of men, as of other animals, is not logical, but instinctive, We tend to react to most of the concrete situations of life in a way determined by inherited neural dispositions rather than by "reasoning things out." The life of most men appears to be spent in acquiring food and shelter, a family, and money to expend in purchasing houses, automobiles, education and luxuries for the rising generation, and insurance against disaster. That is to say, the main outlines of life — power, love, and protection of the family — are fixed in the main by inherited racial tendencies, and it is around these that almost all our activities are grouped. And it is not only the outlines which are instinctive. Nearly all our more detailed everyday experiences are of the same kind. Taking meals, sleeping, feeling aggressive or timid in our work and play, day-dreaming as we plan for the morrow, feeling elated or depressed at the progress we are making — all these experiences are fundamentally instinctive, and we should be seriously puzzled, if we were called upon to account for them in purely rational terms. To the average man, indeed, it never even occurs to make any such enquiry. "He eats because the food tastes good and makes him want more. If you ask him ichy he should want to eat more of what tastes like that, he will probably laugh at you. The connection between the savory sensation and the act it awakens is for him absolute and selostvei stdndlich, an a priori synthesis of the most perfect sort, needing no proof but its own evidence. To the metaphysician alone can such questions occur as: Why do we smile, when pleased, and not scowl? Why are we unable to talk to a crowd as we talk to a single friend? Why does a particular maiden turn our wits so upside down? The common man can only say, '0/ course we smile, of course our heart palpitates at the sight of a crowd, of course we love the maiden, that beautiful soul clad in that perfect form, so palpably and flagrantly made from all eternity to be loved!' "i i William James, Principles of Psychology, chapter xxiv, pp. 386- 387.

2 INTRODUCTION

Thus we see that not only the mainsprings of behavior, but also the moulds which shape and direct our multifarious particular activities are, in the end, animal, racial, instinctive. The mind is no receptive waxen tablet on which any and every element of the physical world can equally impress its sensory image. We see and hear only what attracts our attention; we notice only what awakens our interest and stimulates, directly or indirectly, those dispositions developed in the long course of evolution, which we call instincts. In fact, so large a part do instinct and habit play in our lives, that it is seriously maintained by a great psychologist^ that man seldom reasons and that other animals never reason.

But while the behavior of men is naturally instinctive, it is sometimes forced by circumstances to be something more. The insects, it is true, live a life almost purely instinctive; but then, the problems which they have to face are almost unvarying, so that one hard and fast chain of instincts can advantageously direct the honey-comb construction of the Mason bee, or the egg-laying activities of the solitary wasp or Yucca moth. Our human problems, however, are far too unstable and novel. No inherited disposition could keep pace with the enormous changes which have come over civilized life within the last two generations; and even within the brief span of one generation, our habits need to be readjusted and remodeled, again and again. There is thus in our lives something more than instinct or habit, something continuously readjusting, re-shaping our ways, forever solving problems forever new, inventive, creative — in a word, what we call intelligence, thought, or reason.

How is this done? How does intelligence re-shape our lives? How does thought add moral or economic cubits to our stature? How does reason enable us to lead lives more nearly approaching the ideal? Let us consider briefly some of the ways by which we rise above instinct and habit. One of these is definition, fixing the meaning of an idea in such a way that, amid all the changes and chances of our fluctuating experience, we hold fast to that one meaning, that one direction of our thought. Another is analysis, the splitting up some complex whole into parts so simple that we can readily apprehend their nature, and readily grasp the plan of the whole

2Wilhelm Wundt.

LOGICAL ATTITUDE 3

constructed out of such parts. Yet another is inference or reasoning, with all its various forms, by which from a given situation we construct mentally the probable consequences or antecedents, and generally enlarge our mental horizon and Vlear up our ideas. All of these are forms of scientific method, the indispensable handmaid of efficiency and success in commerce, in education, and in all the organized institutional activities of the present day.

The logical attitude of mind, then, is concerned with the solution of problems, the bridging of gaps,, the removal of inconsistencies and inefficiencies, in cases where instinct and habit alone would be insufficient. There is none of the "ofcourse-ness" of instinct about this mental attitude. It is reasoned, deliberate, thought-out activity. It has also none of the warmth and immediacy, and none of the vagueness and confusion, of feeling. It is calculating, cool, calm, clear-cut, precise; deals little in promises and much in proofs: little in speed and much in sureness; hesitates in drawing conclusions, but succeeds broadly and inevitably in the end; and is not without its own vision, its uplifting trust in the final rationality of the universe.

The Study of Logic. — The value of cultivating such a mental attitude is beyond question. Without it much of our art and all of our science would disappear; the religion of Apollo would give way to the worship of Pan; and the reign of Chaos Find Old Night would come again. But how to cultivate this attitude — by studying logic? This has been, and still is, called in question. Plato reasoned sublimely before Aristotle wrote the Analytics; and many of our foremost scientists have never opened the pages of our logical manuals. And we must consider a second point: if we study the logic of mathematics, does this make us mathematicians — or logicians? If we study the logic of the emotions, does this teach us to feel — or to reason ourselves out of feeling? If we study the logical principles of any subject, does this give us practical mastery of the subject — or theoretical mastery of the principles? Common sense and a wide experience of men come to the same conclusion. It is well known that theoretical masters in the field of Pedagogy — men like Kant and Pestalozzi — sometimes make poor teachers; and authorities in the field of Aesthetics are seldom themselves creative artists. To put it briefly: if the attitude comes without studying the theory, and if mastery

4 INTRODUCTION

of the theory is consistent with almost total absence of the practical attitude, what, if any, is the value of studying logic?

To this question there are two answers. The first answer is given by Hegel, Bosanquet, and many other writers in the field of logic. With great modesty they disclaim any practical value for their study, and assign to it only that theoretical value to which any pure science can lay claim. If we desire to know what are the laws of thought, the principles on which the validity or correctness of our thinking depend, we have as much right to raise such questions as we have to study pure physics or pure mathematics. All such studies, like metaphysics, have their sufficient justification in that reaching out after knowledge as such, which is fundamental in our human nature, even apart from practical values. There is a satisfaction in knowing, quite apart from the question of using our knowledge; and many logicians are content to leave on one side the question of use, in their certain enjoyment of that satisfaction which comes from finding, discovering, knowing.

It is possible, however, to answer the question differently. While it is true that, in its higher branches, logical study is somewhat remote from every-day concerns, still, even at its deepest, it intensifies and quickens our vision of Truth, and justifies, by the insight which it brings, that confidence in the intelligibility of things, which is fundamental in the logical attitude of mind; and as to its more elementary branches — it is merely self-deception if we suppose that there was ever a great scientist who was not also a good logician. Every scientific text-book and every laboratory course lays especial weight on questions of method, methods of observation, methods of evaluating results, methods of establishing conclusions. But these methods are not peculiar to physics or biology as such. They belong to the general theory of method, which is a branch of logic. Again, the researches of advanced scientists, on which so much of the progress of knowledge depends, are almost always investigations to test the validity of inferences, the theoretical value to be assigned to conclusions, perhaps even to the theoretical assumptions underlying scientific reasoning. All these, however, fall within the province of logic. The simple truth of the matter is this: a little experience, a little common sense, enables each one of us, as we say, to reason correctly, whether we have studied technical logic or no; and so long as we move only within the more elementary

STUDY OF LOGIC 5

reaches of experience, our common sense standards of truth are, perhaps, sufficient. But if we wish to raise ourselves beyond this elementary and limited sphere; if we wish to think clearly and consecutively in order to reach conclusions above the level of mere common sense; if we wish to acquire business efficiency, or to succeed beyond the average in life or in science, we need to withdraw, for a season, from the more active concerns of mere living, and reflect carefully and systematically on the principles and methods of right thinking. Then, having acquired some grasp of the theory beyond what the average man knows or suspects, we can apply our deeper insight in order to attain a higher level of efficiency and success than is possible without such reflection; and in order to cultivate the best fruits of the logical attitude of mind, it is necessary to make ourselves thoroughly familiar with the principles and methods of right thinking — in a word, to study logical theory.

Preliminary Definition of Logic. — Logic, then, is the study of thought — systematic reflection on the principles and methods of right thinking. This statement is correct, but is not sufficiently precise to serve as a scientific definition of logic. Psychology, for instance, includes a study of the thought-processes, and to some extent deals with the methods of right thinking. Is logic, then, a branch of psychology? If, as its name implies, psychology were studied as the general science of mind, or the general science of behavior, it would include the study of logical behavior or right thinking, and logic would certainly be a department of psychological investigation. But in present day practice, psychologists tend to regard their science, not as the general science of mind or behavior, but as one special mental science; and while they do study logical behavior, they do so in a very restricted way, and from a view-point entirely different from that taken by logic.

Let us consider an instance. Suppose Mr. A to have recently become a member of the Republican party, or of the Congregational Church. Psychological explanation of this change of heart would lay especial emphasis upon the various elements in Mr. A's personal history and environment which had led him to take the step in question: the influence of old and new associations, the weight of social pressure, the greater appeal of the new opinions — what he would himself, perhaps,

6 INTRODUCTION

call their greater reasonableness. In other words, the viewpoint of psychological explanation is genetic, and traces the steps in his personal evolution which gradually led up to the change in question. This genetic, historical kind of analysis is, however, sharply to be distinguished from logical analysis. The logical analysis of this conversion, for instance, would consist of a clear setting forth of the arguments pro and con. in such a way that we could see the greater comprehensiveness, consistency, and truth of the new opinions. It would be concerned, not at all with the historical side of the thought-processes as such, but wholly with their meaning, with the hanging together of the thoughts in a consistent system, in accordance with the standards of truth. Whether reasoning is consistent or inconsistent, whether conclusions are true or false, no psychology can tell us. Truth and consistency are not mere matters of history or personal evolution, but have their own standards and laws, and the scientific study of these laws is logic. Psychology deals with the process-side, logic with the validity-side of thought.

If, then, we wish to mark out the field of investigation with a preliminary definition, we can say: logic is the scientific study of the laws or principles on which tne validity of right thinking depends: or, more briefly, logic is the study of validity.

A. E. Avery, Tlie Present Day Conception of Logic : Philosophical Review, Vol. XXVII, pp. 405-412. B. Bosanquet, Essentials of Logic, pp. 1-34. J. Dewey, Essays in Experimental Logic, pp. 1-74. B. Erdmann, Logik, (2nd Edit.), pp. 1-33. E. Husserl, Logische Untersuchungen, pp. 3-8. H. Lotze, Logic, pp. 1-9. Chr. Sigwart, Logic, pp. 1-2. W. Wundt, Logik, (3rd Edit.), Vol. I, pp. 1-9.

PART I JUDGMENT i

1 The word judgment is used in modern logic, in order to emphasise sharply the difference between logic — which studies what we think or actually judge, i. e., the actual living thought — and grammar, which studies the verbal expression of thought. Historically, the two have frequently been confused, so that in place of an analysis of the living thought, the logician has given a grammatical analysis of the dry bones of verbal expression, i. e., of "propositions" or statements, in place of judgments or thoughts.

Chapter I Typical Stages Of Judgment

The Simple&t Judgments. — In every scientific study, we start with the simple and proceed gradually to the complex. Logical study also starts with the simple. ■ What, then, is the simplest kind of valid thinking, the unit, as it were, of thought? Let us consider an example. "If the sun is shining, we will go to the woods; but if it is wet, we will stay in and read." We have here a single thought. But though single, it is obviously not what we should call simple, but is evidently complex. Let us analyse it, or split up the complex thought into simpler parts. "The sun is shining"; "We will go to the woods"; "It is wet"; "We will stay in"; "We will read." If we compare each one of these brief statements with the original example, we see at once that they are much less complex. Let us further compare them with one another. "The sun is shining" and "It is wet" appear to belong together, to represent two forms of the same kind of judgment. Let us regard them as one group, group A. Similarly "We will go to the woods," "We will stay in," "We will read," seem to express one and the same kind of thought, and thus to belong to a "we will" group, which represents a kind of thought different from that expressed in group A. Let us call the "we will" group, group B. The thoughts in group B are judgments of purpose, and seem more complex than judgments of sense-perception such as "The sun is shining." We shall therefore regard group A, i. e.. judgments of sense-perception, as the simplest kind of judgment revealed by a consideration of our example.

Are such perceptual judgments, however, to be considered as ultimate? Are they, in fact, the simplest judgments we can make? Perhaps we should draw a further distinction. "It is wet," for instance, might be thought less complex than "The sun is shining." Perhaps the distinction will become plainer if we compare "It is fine" with "The sun is shining," and "It is wet" with "The rain is heavy." Many logicians

10 TYPICAL STAGFS OF JUDGMENT

have, in fact, regarded such impersonal judgments at the simplest thoughts we can have.2 It seems better, however, to speak of more primitive or less developed forms of the same type of judgment, rather than of greater simplicity or less complexity. "It is fine" and "The sun is shining" have, after all, substantially the same meaning. The only logical difference is, that the meaning is more clearly expressed in the more developed form. We shall accordingly take as the simplest and most elementary acts of thought which we can discover, judgments such as "This is red," "It is warm," "There is a noise," "This is heavy," "That tastes bitter," "There is an odor," etc. — i. e., simple judgments of sense-perception.

The Elements of Judgment. — In the above instances we have judgments so simple, that here, if anywhere, we should be able to pick out some of the elements upon which the validity of judgments depends. In cases which were more complex we might be unable to see our way. But in these simple cases, if anywhere, we should be able to discover at least the more obvious elements. Let us therefore consider these judgments of perception closely. Can we discover any simple factors, any constituent elements of such judgments?

Two elements, upon which perhaps the validity of judgment depends, we can discover almost at once. These elements are (a) sensory, and (b) intellectual, (a) All judgments of perception are thoughts about something present, something given to us in perception, given to us through the senses, sensory. "This-red," "Warm-feeling," "Noise-here," "That-bitter-taste," etc. It may be that all judgments whatever, and not merely perceptual judgments, are similarly thoughts about something which is, in the end, given to us in sensation. In this case, all thought would have this sensory element, and the function of sensation would be, to furnish us with a channel by means of which we could come to know objects, or thingswhich-we-can-experience. (b) On the other hand, so far as judgments of perception are thoughts about something present, they undoubtedly contain an element which we should call intellectual. This is in such cases, not so easily noticed as is the sensory element. In order, then, to bring out more

2 For a recent study of the whole subject of the impersonal judgment, see S. F. MacLennan, The Impersonal Judgment, 1897.

ELEMENTS OF JUDGMENT 11

clearly the presence of the intellectual element, we shall proceed to take a number of slightly more developed cases of perceptual judgment. "This paper is red," "It is warm near the stove," "There is a noise at the door," "This oook is heavy." These instances are all perceptual, but we can at once observe that certain intellectual elements are now more prominent. Instead of reference to the undifferentiated "this" as the sensory given, we refer to the paper, stove, door, book, etc., i. e., to determinate objects, the recognition of which involves distinction, comparison, classification, etc., which are processes predominantly intellectual. Let us. further consider yet more developed perceptions. "This paper is a brighter red than that," "It is warmer near the stove than near the door," "This book is heavier than that." We have here much the same general sensory elements as before. But we now have in a very clear and explicit form the intellectual act of comparison. "This paper" and "That paper" are held together in one intellectual act, and are compared in respect of their brightness-value. So too "Near the stove" and "Near the door" in respect of their warmth. In fact, the more highly developed such judgments become, the more plainly can we observe the presence of intellectual elements. But in the very elementary and primitive cases too we can now see the presence of abstraction and recognition at least. The "This" is differentiated into red, warm, heavy, etc., and these are not only clearly apprehended, but are apprehended in distinction from one another. In other words, in these simplest of all judgments there is present, not only a sensory, but also an intellectual element.

Typical Stages of Judgment. — With the sensory element in judgment, logic is not, as a rule, much concerned. It is in epistemology or the theory of knowledge, that the function of sensation as a factor in knowledge is especially studied, and it is still a question whether the theory of knowledge should or should not be regarded as constituting an integral part of modern logical investigation. 3 We shall therefore postpone, for the moment, further discussion of the sensory factor in

3 Schuppe (ErkenntwtetheoretisLche Logil'J, Wundt. and YTindelband (Encyclopadie der philosophischen Wissenschaften. Vol. I) regard the theory of knowledge as falling within the field of' logic, or vice versa. Erdmann incorporates "corollaries" from the theory, of knowledge in his logical Element arlehre. Bradley and Bosanquet are also to be reckoned among the epistemological logicians.

judgment, and shall consider more closely the intellectual factor.

In order, however, to deal with the intellectual element in judgment in any adequate way, we can certainly not confine ourselves to elementary perceptual judgments. It is no longer a question of picking out the least complex type of judgment in order to avoid obscurity, and in order to enable our unaccustomed eyes to see their way in a simple case. We have now to face the more general problem of validity in judging as such, and this involves consideration, not only of the elementary cases, but also of the more highly developed forms or stages of judgment, in order that nothing vital may be overlooked. In order, then, to clear the way for our whole subsequent investigation into the sensory and intellectual factors, we must be able to cover, in some clear and brief way, the whole field of judgment. This we shall do by arranging different kinds or stages of judgment in a table, starting with the more elementary and proceeding to the more advanced — i. e., proceeding from judgments in which the intellectual element is less prominent to cases in which it is more prominent.

TABLE OF JUDGMENTS

L Judgments of Perception. — E. g., "This room is warm," "This oak has less foliage than that beech."

2. Judgments of Experience, — E. g., "The freight-trains passing over the bridge grow more troublesome every year," "Noise is usually a compound of tones."

3. Symbolic Judgments. — E. g., "Rome was occupied by Caesar," "Strathcona lies on the North Saskatchewan," (where the evidence is not direct experience, but a textbook account of a place we have never seen). So too "The theory of the synapse is fundamental for the explanation of conscious behavior" (where we have had no direct experience of synapses).

4. Transcendent Judgments. — E. g., "God is a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality," "Things-in-themselves are absolutely unknowable," "True evolution is the progressive self-organization of a system of timeless selves."

Let us explain briefly the above distinctions. A judgment of experience differs from a perceptual judgment, in that it depends more on memory of previous perceptions than on direct present perception. It is more developed, and sums up many previous experiences, as a composite photograph gives us the result of many direct likenesses of actual persons. For instance, "Most writing-paper is white" sums up many experiences of writing-paper, and while on the one hand less direct and immediate than "This writing-paper before me is white," on the other is more advanced, more representative, more intellectual, than the simple perceptual judgment. Still, even in the perceptual judgment there is some appeal to previous experiences. For we know the object before us to be "writing-paper" and "white." The distinction between judgment of perception and judgment of experience is thus not absolute, but is a question of more or less, a matter of degree. Where the sensory element predominates, we have the stage of judgment which we call judgment of perception. Where the intellectual element plays the greater part, we have the judgment of experience.

A symbolic judgment differs from a judgment of experience, in that we are here dealing with a sort of extension of our experience, based indeed on previous experiences, but constructing, on the analogy of these past experiences, new objects of similar type, objects which we might possibly have experienced, or might possibly experience in the future, but which in actual fact we have never experienced. Thus, if we had lived in Rome at the time of its occupation by Caesar, our thought would be a judgment of experience, if not, indeed, a perceptual judgment. But where we have had direct experience of cities differing from Rome, and can only construct for ourselves imperfectly, in the light of very inadequate past experience, what it meant for a city to be occupied in wartime by the forces of Caesar, our judgment is only symbolical. The less directly the case happens to be related to our personal experience, the harder do we find it to spread out our experience so as to make vivid to ourselves scenes so remote from what we have seen and felt, and the further do we tend to fall short of full realisation of the meaning of our judgment. We have the bare skeleton of experience. The flesh and blood, the living elements, are almost totally missing. In such judgments, while the sensory element may be weak, the intellectual element of construction is far more prominent than in judgments which remain contentedly within the circle of our own experience. And yet, in judgments of experience also there is some construction, some putting together of past experiences in order to produce something new, the composite result which — as a composite unity, at any rate — was never actually experienced. We see then that here also the difference is a question of more and less, a matter of degree only. Where the sensory element is relatively greater and the intellectual construction relatively less, we have a judgment of experience. Where the constructive, intellectual element decidedly predominates, we have the symbolic judgment.