The essentials of logic

Contents

I. Introductory

A Definition of Logic — The Value of Logic — The Kinds of Logic — Introductory Logic — Relation of Logic to Other Sciences — The Material of Logic — References.

II. The Nature and Setting of Thought .

Chapter I

A Definition of Logic. Logic may be defined as the science of the principles and conditions of connect thinking. To the beginner, a definition serves mainly as a guide-post to direct his attention to the general character of the subject which he is about to study. The above definition should therefore be taken merely as an indication of the field. The terms of which it is composed will gather content and meaning as the various topics are covered. Toward the end of the course, it is to be hoped that the student will be able to come back to the definition with a fuller grasp of its significance.

Logic is a science in the sense that it is organized knowledge involving principles. The various sciences have different fields for investigation, but all of them agree in their purpose, which is the establishment of satisfactory information bound together and illuminated by laws. Thus, physics studies the most general characteristics of the physical world and seeks to reduce to order and interpret the facts it discovers ; botany examines the structures, functions, and histories of plants ; and psychology gives its attention to the behavior of creatures possessing consciousness. All these sciences seek to replace the loose and hazy notions of popular thought by exact and systematic knowledge. Now logic has the same purpose, but its field is peculiar. It cannot be classed among the physical sciences which depend upon perception and measurement, nor among the biological sciences, nor, finally, among the social sciences. In a very real sense modern logic presupposes all these sciences and is somehow a science at second remove from things. It is a science about the mental aspect of the sciences. The mediaeval logicians pointed out that the mind first ' intends,' or directs itself upon, the external world, and that only afterwards does it direct itself upon the mental processes and methods it has used. We may say, then, that logic involves a thinking about thinking.

Because man is naturally outward-looking and desirous of practical results he is seldom clearly conscious of his methods and of the mental processes involved in thinking. It requires an effort for him to take this new attitude and to think about thinking, about those mental operations which make knowledge possible. But when he does so, he finds that the mind does work in an orderly fashion. It is the nature of this orderliness that logic seeks to bring into clear consciousness.

The Value of Logic. So far as logic is a pure science, its value is essentially of the same kind as that of any other pure science. It satisfies an intellectual curiosity, a desire to know. Before a teacher can appeal strongly to such a value, the student must have experienced it; at some past time he must have forgotten himself as an individual with private ambitions in the enjoyment of seeing problems solved, of watching meaning replace confusion ; he must have felt pleasure in knowledge for its own sake. The logician who is loyal to his subject because he has faith in it asserts that logic has a value as a pure science, that man likes to know the working of his own mind just as he likes to know the laws of celestial mechanics. Why not, indeed? Is not the mind the supreme instrument which all must employ?

But a pure science need not lack practical value. Logic is not only a pure science, but also an art or an applied science. An applied science is one which is able to work out suggestions and rules based on a broad study of the field involved. Looked at from this angle, logic may be considered " a free study of some of the chief risks of error in reasoning." 1 What logic can do for an individual is to render him conscious of the best methods and the main difficulties in the various stages of actual thinking so that he will be more exacting in his mental operations. It should put him on his guard against dangers. It calls his attention incessantly to the value of clear and unambiguous ideas and to the proper level of scrutiny to be maintained before a fact is accepted, an inference drawn, or a proposition admitted as a premise in reasoning. The mind is an instrument, and it should be polished instead of being left in a state of nature. It is true that the exigencies of life force us to be critical, but such criticism is too rough-and-ready to be entirely satisfactory. Is there good reason to doubt that care of the mind will pay at least as much as care of the body? There are good mental habits just as there are good physical habits; and neither comes without effort and reflection. "Its [logic's] practical value in general education is firstly this : that it demands very

1 Sidgwick, Elementary Logic, p. 8, Introduction.

careful and exact thinking about its own subject-matter, and thus tends to produce a habit of similar carefulness in the study of any other subject. In this it only does for the mind what a thorough training in any other science might do. Secondly, it makes us realize better what the general forms of speech that we habitually use really mean, and familiarizes us with the task of examining our reasonings and looking to see whether they are conclusive. In this it has an effect which the study of some special science like botany is not equally calculated to produce. Thirdly, it brings into clearer consciousness, as aforesaid, our ideal of what knowing is, and so furnishes us with a sort of negative standard ; it makes us more alive to shortcomings in our ordinary opinions. But its chief value lies in its bearing upon those ultimate problems, concerning the nature of reality, and man's place and destiny in the world, from which at first sight it might seem far remote." l

If logic can do even a part of this, it justifies itself as a practical study. While logic does not create new capacities in the mind of an individual, it helps to train and sharpen the capacities already there.

The Kinds of Logic. Logic is one of the oldest of the sciences and has had a varied history. The result has been the growth of different branches emphasizing different aspects of thinking and somewhat different interpretations of the aim of logic. At times, these ' kinds of logic' have seemed opposed to one another, but, of late, they are seen to supplement one another and to make logic a broader investigation than it would have been without this branching. One kind of logic (exact

1 Joseph, An Introduction to Logic, p. 10.

or symbolic) seeks to assimilate itself to mathematics in its methods ; another (concrete) stresses its relation to general philosophy, especially to theory of knowledge ; another (empirical or inductive) lays its emphasis upon the methods of the experimental and observational sciences. Back of these historically and linking itself with them in various ways — sometimes welcomed, sometimes an outcast — is what is called 'Formal Logic/ We shall have a better idea of the limitations of Formal Logic as we cover various topics such as the 6 syllogism,' 4 immediate inference,' and the 'logical form' of statements. Certain doctrines and technicalities must be discussed and given as true and adequate a setting as possible. They have their value, though this value must not be overestimated.

Introductory Logic. The Introductory Logic of to-day in America seeks to organize together the essentials of the various kinds of logic. It retains as much of Formal Logic as seems valuable and combines it with a concreter study of actual thinking with a view to determine the principles and conditions of correct thinking. In this effort, it has been aided immensely by the growth of psychology and philosophy, and the increasing reflection, by scientists themselves, upon their methods. Logic has acquired a new lease of life and is genuinely growing. More is known about thinking than ever before, and this added knowledge has stimulated logic to break away from formalities. Yet logic has a rich inheritance from the past which must not be belittled. What is needed is a new perspective and a more vital setting. We want to know the structure of our actual thinking so as to guard against the risks of error.

Relation of Logic to Other Sciences. The sciences most closely related to logic are rhetoric and psychology. The connection with psychology is obvious and we must examine it in some detail. But first let us examine its relation to grammar and rhetoric.

Thinking is intimately bound up with language; language is, in fact, a necessary instrument to any sustained thinking which involves general ideas. For grammar, language is itself the subject-matter; for logic, it is the instrument of thought. The function of words is the fixation of meanings in our own mind and their suggestion to others. In another chapter we shall discuss the relation between thought and language. At present we only wish to point out that the law of language under its logical aspect is that of non-ambiguity . Statements must, so far as possible, be clear as regards their significance. Accuracy and appropriateness in the use of words go hand in hand with the discrimination of ideas.

Rhetoric is more nearly akin to logic than is grammar. While grammar treats of words largely apart from their meanings, rhetoric concerns itself with the expression of thought. Such expression is studied in relation to the purpose in hand, which may be exposition, description, argumentation or persuasion. It is impossible to draw any hard-and-fast line between these disciplines, for each is influenced by the results of the other ; we may say, however, that to-day both rhetoric and logic presuppose grammar as a preliminary and differ from each other in that which they stress. Logic is more interested in the meaning which is expressed, its implications, foundation, and validity, than in the mode or style in which it is expressed. Rhetoric, on the other hand, culminates in the artistic use of language. The fact that language is a necessary instrument of thought brings these disciplines together ; but logic has wider relations because thought is greater than its instrument. Language is, after all, a tool.

The logician reflects upon the mental processes by means of which knowledge is achieved and naturally finds much assistance in psychology. So far as he investigates how the individual thinks and the conditions of this thinking, he works hand in hand with the psychologist. Both examine perception, conception, judgment and reasoning and reach harmonious conclusions. The main difference between them is that psychology concerns itself more with the mental content, while logic stresses the value of the product. Just because the mind is a unity, it is impossible to find other than a working distinction between them due to a division of labor. They overlap, then, in the higher mental processes, and logic passes on to a study of the structure of knowledge and its validity, while psychology concerns itself with the structure of consciousness, its relation to conduct, and its physiological conditions and concomitants. The logician has the right to make use of the knowledge psychology has achieved which bears upon his own task. Their relation should be one of mutual helpfulness.

The Material of Logic. All sciences are objective ; that is, they consist of recognized facts and of principles which organize and interpret these facts. Now, logic is, as we have already pointed out, a science about the sciences. It is interested in the nature of proof and the laws of evidence ; it desires to see hoio knowledge is built up and how the parts of knowledge depend upon one another. This interest cannot be satisfied byintrospection alone, but requires a close study of the various sciences. In these it finds knowledge, and in their history the record of the steps by which it was obtained. We may say, then, that the material of logic is to be found in generally accepted knowledge and that this is approached with the purpose of discovering the processes involved. Knowledge is the material of logic much as the organism is the material of the biologist and the inorganic world the material of the physicist.

Inductive logic has always paid close attention to the sciences which have so splendidly developed since the Renaissance. It is an attempt to formulate the methods which grew up unconsciously, or largely unconsciously, in this new and wonderful extension of human knowledge. The assumption controlling the series of investigations which have given us the inductive branch of logic has been very well expressed by Whewell : " We may best hope to understand the nature and conditions of real knowledge by studying the nature and conditions of the most certain knowledge which we possess ; and we are most likely to learn the best methods of discovering truth by examining how truths, now universally recognized, have really been discovered." 1

BuF logic must concern itself with all sorts of thinking, with the conversations of daily life, with the arguments to be found in the social sciences, in political speeches, in essays, in editorials ; otherwise, it is apt to

1 Whewell, History of Scientific Ideas (3d ed.),vol. I, p. 4.

become too formal and pedantic and to lose touch with the flexibility and variety of actual thought. There is another reason why the logician puts this emphasis on less specialized thinking and refuses to let it be elbowed away by the more technical levels of thought. We can know what thinking is only by thinking ourselves and then retracing our steps in memory to see exactly what we have been doing. The material of logic can be found ultimately only in consciousness. And, if the subject-matter is to be realized and really reflected upon, it must be reproduced and revivified in our own thought. But it is not always easy to do this with past thinking when this is technical and has an atmosphere of its own. And, when all is said, familiar thinking illustrates the essentials of the thinking process. Any one who studies logic seriously must be willing to think for himself and to think about his thinking.

Creighton, An Introductory Logic, chap. I. Sigwart, Logic, vol. I, General Introduction. Joseph, An Introduction to Logic, chap. I. Sidgwick, Elementary Logic, Introduction. Schiller, Formal Logic, chap. I.

Chapter II

What is Thought ? Thinking is the central operation for logic. It is the operation which underlies knowledge and opinion and makes them possible. It behooves us, therefore, to gain as clear an idea of its nature and conditions as we can. If it is affected by mental habits, we want to know what are the best habits ; if it is controlled by feeling and emotion, we want to know how to lessen such control. In short, we wish to study the ways in which the human mind assimilates and develops knowledge — especially that knowledge which is called true.

It is not easy to define that mental process designated thinking. " No words are of tener on our lips than thinking and thought. So profuse and varied, indeed, is our use of these words that it is not easy to define just what we mean by them. Assistance may be had by considering some typical ways in which the terms are employed. In the first place, thought is used broadly, not to say loosely. Everything that comes to mind, that 'goes through our heads,' is called a thought. To think of a thing is just to be conscious of it in any way whatsoever. Second, the term is restricted by excluding whatever is directly presented ; we think (or think of) only such things as we do not directly see, hear, smell, or taste. Then, third, the meaning is further limited to beliefs that rest upon some kind of evidence or testimony. Of this third type, two kinds — or, rather, two degrees — must be discriminated. In some cases, a belief is accepted with slight or almost no attempt to state the grounds that support it. In other cases, the ground or basis for a belief is deliberately sought and its adequacy to support the belief examined. This process is called reflective thought." 1 Now, logic is chiefly interested in this higher level of thinking where ideas are under control and organized in relation to one another. In fact, many logicians define logic as the science of proof or evidence.

Certain terms are used by logicians as practically synonymous. Thus we shall have occasion to speak of reflective thought, reasoning, and inference at various times. These processes are much the same, though the context will show slight differences of emphasis. Taking them as essentially the same, our present task is to find out what is the nature of the mental operation involved. What do we do when we reason or infer? What we want now is a suggestion of the general character of the operation, leaving it to later chapters to study the various steps in methodical reasoning.

Discovery and Proof. There are two parts to any complete act of reasoning, discovery, and proof. We reason when we are confronted by problems, by unforeseen situations to which our habits and usual ideas are not immediately applicable. We are, as we say, at a loss ; we don't know what to think or to do. But this perplexity lasts for a time only. We make shift to size up the situation, to compare it with what in the past seems most like it, to analyze the various features, and

1 Dewey, How We Think, pp. 1-2.

so on, until some idea suggests itself as a possible solution. Such is the stage of tentative discovery. But another stage immediately sets in. The suggested solution must be tested or proved. In practical affairs, this proving consists, in the main, of overt action. The new idea is tried out to see whether it will work. The proud possessor of a new auto finds himself compelled to reason in this rough-and-ready way only too often. This practical level of reasoning is sometimes called 4 trial-and-error.' The process is familiar to all.

In more theoretical reasoning, both the stage of discovery and the stage of proof are reflective. The scientist who makes a discovery has, as a rule, long brooded over the problem. The idea of universal gravitation did not come to Newton as a mere chance thought ; his mind was ripe for it. Archimedes had long been pondering over his particular problem before he took his famous bath and discovered the principle of specific gravity. But after the brilliant idea has suggested itself, it must be proved in the light of the facts. It must be shown to follow from certain premises or data; it must be guaranteed by its reasons or grounds. And this second task is often the more perplexing of the two. By proof we mean the process of establishing an idea on a firm intellectual foundation. Newton had to work out the method of fluxions and make delicate calculations on the basis of known measurements before he could consider his hypothesis reasonably proved, while Darwin had to make numerous experiments and collect data of the most varied kinds before he was willing to publish his theory. Proof must be considered a very important part of reasoning. Scrupulousness in regard to its standards is the sign of a trained mind. It is not too much to say that logic is primarily the science of proof. The question before the logician's mind is, 'Is such and such a given conclusion warranted ? ' Logic is retrospective and probative.

The Psychologist's View of Reasoning. In the preceding chapter, we came to the conclusion that logic and psychology overlap, that no hard-and-fast line can be drawn between them. It may be of interest, therefore, to examine the psychologist's view of reasoning. "To define reasoning fully it must be distinguished from imagination and memory when observed from the inside, and from instinct and habit when expressed in action. Reasoning may be distinguished from memory and imagination, not so much by the character of the mental states or by the way that they are obtained, as by the attitude that is taken toward them when they arise. The idea that is attained by reasoning may be exactly like an idea that on other occasions or by another man is merely remembered. The laws that govern the appearance of rational ideas are the laws of association, controlled in the same way as in memory and imagination. The important differences are : that the results of reasoning are new and are accepted as true ; the results of memory are true, but not new ; and the results of imagination are new, but not true" 1 It is well to bear these contrasts in mind. Reasoning is a mental process taking some time to occur and controlled by the purpose of reaching accepted results. The logician makes the further demand that these results be established by relation to their ground.

1 Pillsbury, Essentials of Psychology, p. 217.

Examples of Reasoning. Let us take a case of reasoning in regard to heavenly phenomena which was made quite early in the history of civilization. Man soon discovered that a shadow was caused by the intervention of an opaque body between a source of light and a distant surface. He did not know exactly what took place, but he knew that the light was cut off from the region back of the opaque body. Thus he arrived at the universal proposition, * All shadows are caused by the intervention of an opaque body.' But an eclipse was soon recognized to be a case of shadow. Hence an opaque body must have intervened between the earth and the source of light. Here is a case of reasoning in which the conclusion is reached by resemblance or analogy. An eclipse is a case of the intervention of an opaque body because it is a case of shadow. This reasoning contains the ground. Let us now examine a case of bad reasoning. " According to some accounts, the wise men of Spain argued with Columbus that he could not reach India by sailing west, because if the earth were round, as he asserted, he would at some time reach a point where the ship would be going downhill and ultimately fall off, just as a minature vessel would fall, if it should attempt to travel around an artificial globe. If A is true (earth round), B must be true (circumnavigation impossible). If there is a resemblance between earth and artificial globe in contour of surface, there must be a further resemblance, so it was held, in the relation of each to the objects upon its surface. ... In making their comparison, the wise men overlooked an important point of difference, viz., that for an object on the artificial globe the point towards which it gravitates is outside the globe, while for objects on the earth this point is within the earth itself." 1

Thinking may be more or less conscious and more or less methodical. Logic seeks to induce individuals to take thinking seriously, to make their thinking methodical and reflective. Especially does it stress evidence. Reflective thought is careful, and evidence-loving. It notes all the facts which can be thought to have bearing upon the problem and tests any conclusion by its consequences.

The Conditions and Occasions of Thought. Reflective thought or reasoning rests upon and grows out of experience. It has its causes and conditions. Thought does not arise just for no reason at all, but has its definite conditions. These reasons for thinking can be classified as social and personal.

The stimuli which lead individuals to think usually come from the social environment. The pity is that this environment is so moderately stimulating. The more there is the spirit of intellectual and social adventure, the more alive will men be. When the environment favors tradition and mere repetition and imitation, comparatively little vital and creative thinking is done. Life takes on the aspect of routine and habit, and classification of a formal kind overshadows discovery. Actions are repeated in the customary grooves, and no attempt is made to better them. There are periods, as during certain parts of the Middle Ages, when this social attitude is largely dominant. At such times, beliefs are handed down by tradition and are not criti- 1 Bode, An Outline of Logic, pp. 2-3.

cally examined. Such an atmosphere is not favorable to thinking. The individual is not taught to analyze and observe, to doubt and to form hypotheses. Thus, there is a sociology of logic, or, rather, logic has its social aspects which must not be lost sight of. Let me, by means of an example, contrast the lethargy of thought during the later Middle Ages with the eager spirit of science at its best.

It is said that Francesco Sizzi, a Florentine astronomer, argued against Galileo's discovery of a new planet in the following way : —

" There are seven windows in the head : two nostrils, two eyes, two ears, and a mouth ; so in the heavens there are two favorable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many other similar phenomena of nature, such as the seven metals, etc., which it were tedious to enumerate, we gather that the number of planets is necessarily seven.

" Moreover, the satellites are invisible to the naked eye, and therefore can have no influence on the earth, and therefore would be useless, and therefore do not exist.

" Besides, the Jews and other ancient nations as well as modern Europeans have adopted the division of the week into seven days and have named them from the seven planets ; now, if w r e increase the number of the planets this whole system falls to the ground." 1

The present is, on the whole, a period of skepticism and inquiry. The individual is taught to think for himself, along certain lines at least, and not to accept ideas

1 Lodge, Pioneers of Science, p. 106.

unless he has pretty assured evidence for them. This social atmosphere, encouraging to thought, is a veryimportant condition of thinking. Logic has a perfect right to champion such conditions. It is not called upon to be a passive judge of consistency alone.

The personal conditions of thought are also important. The prime condition is the recognition of a problem. Back of this recognition lies the attitude which faces problems and even goes to meet them halfway. This attitude is partly temperamental, partly the consequence of training. On the practical side of life, so long as our habitual ways of acting are sufficient to meet the conditions which confront us, there is little reflective thought because there is little need for it. There is mental activity, of course, because we must constantly recognize and classify things and situations ; but this classificatory interpretation is usually so immediate that the individual does not need to pause, or, if he does pause, it is only for a moment. Difficulties arise, however, frequently enough, and the course of action is stayed. New adjustments must be worked out, and these adjustments depend upon the proper location of the difficulty and the discovery of its nature and remedy. Thinking intervenes at such a time. It is the sign and consequence of uncertainty, doubt, inability to interpret. How successfully the individual meets the problem depends upon his training, capacity, and character.

The Setting of Thought. Thinking arises and takes its course in the mind of an individual endowed with a fund of past experiences. The problem which occasions thinking involves a conflict within experience and calls into play all that is in any way relevant. Familiar ideas, prejudices, habits, memories, all enter into the council-chamber and demand audience. Thinking is the individual's experience in process of internal adjustment.

We may say, then, that thinking is purposive and selective. It is an expression of the growth of the mind. But the mind is distorted by old beliefs and prejudices and is very frequently deflected from the truth. It is like a river whose banks throw the current from side to side and produce in it all sorts of treacherous eddies. The logician must do the work of an engineer. He must point out the dangers which confront the mind which desires to think truly.

Why we think. Our study of the conditions and setting of thought enables us to answer the question, * Why do we think ? ' There is both a practical and a theoretical urgency behind thought. Life demands that problems be solved in order that we may act wisely. When our habits push us in , different directions, we must work out some suggestion which satisfies our mind or we are distraught. Besides, we know from past experience how dangerous it is to trust to a chance idea. We want to have a fair degree of assurance of the consequences before we act. To think is to rehearse the course of events beforehand and to meet every emergency with its appropriate interpretation.

But psychologists inform us that it is the very nature of the mind to work out harmonious ideas. The things we see are the products of adjustments. However far down we go in our. mental life, we find the endeavor to harmonize various elements with one another. " The sensations that are received are added to or changed to make them correspond more exactly to what from our different earlier experiences we know they must be. One always corrects the shape of the table-top as it appears in perspective. The angles are right angles as we see them, although the image must have acute and obtuse angles. One always makes an allowance for distance in the size of an object that is seen. The same object is always given the same size no matter how far away it may be, while the image on the retina diminishes constantly as the distance increases." 1 Thus, processes of adjustment are characteristic of the mental life at its different levels. This same tendency expresses itself in thinking. Thinking arises naturally and inevitably when the adjustment cannot be made almost automatically.