Popular Science Monthly/Volume 67/June 1905/The Teaching of Logic

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THE TEACHING OF LOGIC.
By Professor ARTHUR H. DANIELS,

UNIVERSITY OF ILLINOIS.

IT is a well-known fact that logic is not so generally studied to-day as formerly, and that, on the whole, the attitude towards its educational value is one of indifference. If, however, we try to account for its present status in our colleges by granting that logic is an inherently difficult and uninteresting subject, our explanation is both inadequate and unfair to the subject itself. True, logic does require a distinctively analytic and reflective quality of mind. It does not afford the possibility that some subjects do, of getting through it by leaning upon memory, or by appropriating the thoughts of another; but, on the other hand, it constantly demands a conscious effort to think, in the absence of those substitutes for thinking things out for themselves which the weak and lazy-minded resort to. True, logic can make no exclusive claim to being an intellectual discipline. Other academic studies furnish just as severe tests of mental power. The real truth of the matter is that the formal conception and abstract presentation of logic are responsible for a large share of its unattractiveness and needless difficulties.

What I have to write has reference only to elementary or introductory logic. As to the metaphysics or the higher problems of logic I have nothing to say, in this connection, save to express my firm belief that the less an elementary course in logic has to do with metaphysical questions the better. In fact, the discredit into which logic has fallen is in part due to the teaching of the subject from the philosophic standpoint. To hold the place that it deserves in the college curriculum, logic must be shown to have some practical value. I know that this word is in disfavor. We are told of the mathematician who thanked heaven that he had at last discovered a truth which no one would ever be able to make any use of. Perhaps this seeker after truth was but voicing the common antipathy for the word practical. If it is a hopelessly obnoxious term, why not adopt a word used by President Eliot and then always aim to make truth serviceable? It is my purpose in this article to point out some changes in the mode of presenting logic, whereby it may be modernized and made an attractive and useful undergraduate study.

In the first place, the definition of logic should convey to the beginner's mind a comprehension of its scope and purpose as concrete as possible. I can think of no better way of accomplishing this than by stating at the outset that the business of logic is to formulate and systematically present the methods of our thinking for the purpose of acquiring knowledge of the correct methods and skill in their use. This would make logic a science, treating its subject matter descriptively rather than philosophically.

Then proceeding to what is properly the first division of logic, namely, the study of words or terms, it should be made clear that logic treats language from the standpoint of meaning. In reality, logic, so far as its discussion of terms and propositions extends, is one of the trinity of subjects which have to do with the use of language. Its relation to grammar and rhetoric may be best made clear by regarding as the primary interest of logic the function of words as expressing the thought of the speaker or writer. Of course, logical analysis is inseparable from the correct teaching of grammar and rhetoric. But the actual practise is frequently such as to warrant the criticism that sense is sacrificed to grammatical and rhetorical niceties. One is also reminded of that portion of Mr. Huxley's criticism of the teaching of English literature at Oxford, where he writes: "I venture to doubt the wisdom of attempting to mold one's style by any other process than that of striving after clear and forcible expression of definite conceptions; in which process the Glassian precept, 'first catch your conceptions,' is probably the most difficult to obey."[1]

If students take up logic with the idea, carried over from their study of grammar and their use of dictionaries, that words get their character as nouns, or verbs, or what not, from their origin or form, they should be made to understand early that it is quite an erroneous idea. "The logical character of a name is not something fixed and stable, but quite the reverse. It is function, not structure, that determines logical character, and the function of words in asserting is variable. The different actual uses of names are what logic needs to distinguish, not different sorts of names apart from their actual use, words in their context, not words as grammar conceives them or as they lie side by side in a dictionary. . . . Since words are adaptable instruments of assertion, and not restricted to a single function, we might as well ask whether a penny stamp in the pocket is a receipt stamp or a postage stamp, as ask whether a word apart from its particular use has this or that logical character."[2] The logical treatment of terms is essentially the question of how they are used in this or that connection.

The same point of view should be maintained when we come to the next division of logic— the study of propositions. Here, likewise, the meaning side of language, and not the form, is of primary interest. Many students have difficulty in realizing that the meaning of a proposition does not depend upon its form; that affirmative, or negative, or categorical forms are not necessarily expressions of affirmative, or negative, or categorical thoughts. For example, the last clause of the verse, 'Because strait is the gate, and narrow is the way, which leadeth unto life; and few there be that find it' is very frequently interpreted as meaning 'some do find it'

In this connection there is another not uncommon error, namely, that of regarding two propositions, worded differently, as different assertions, when, in fact, they assert the same thing.

But traditional logic is of little help in the whole matter of logical analysis. For instance, its treatment of conversion makes dry reading and a perfunctory task for the student. It is even worse; it savors of the artificial and useless. That a subject of such importance as conversion should be presented in a way so unnatural and forbidding as that of the traditional logic is much to be regretted. Logic should teach in this matter, not traditional rules, nor discussions of formal subtleties, but the simple truth that the Tightness or wrongness of every converse rests on precisely the same basis as that of the original proposition, namely, known facts and laws. The proposition that ignorant people are superstitious is true because it agrees with the facts. But if we change it into superstitious people are ignorant we do not get a good converse, because this proposition does not agree with the facts. In the next place, the syllogism needs more radical change in treatment than either of the two previously mentioned divisions of so-called deductive logic. The traditional treatment has overloaded the subject with dry discussions, rules and symbolical schemes, so that there is hardly left the slightest appearance of any connection with actual thinking. Better omit all mention of figure, mood, reduction, and the question whether there are three or four figures, than miss the important lesson of the syllogism. "There is little," says Mr. Sidgwick,[3] "that need be taught about the syllogism, since the process itself — which is merely that of bringing a particular case under a general rule—is used instinctively by every one from childhood onwards."

Examples like these, (Five francs are a dollar, four shillings are a dollar; therefore five francs are four shillings'; or, 'Some men are not fools, yet all men are fallible' are not suited to bring out the real 'process' much less to train the mind in accurately applying a general truth to a particular case. In fact, too many of the arguments selected by authors of text-books for illustration and training in syllogistic reasoning serve little more than to show the machinery of the syllogism. Others are either too hackneyed, transmitted as they have been from one generation of writers to another, or are lifeless fragments and consequently mean scarcely more than so many words. Then, again, cases of faulty argument constitute too large a proportion of text-book exercises. If selected with discretion, defective reasoning may be used to bring out in the most emphatic manner certain mistakes commonly made in thinking. If, however, examples of bad reasoning are too patently wrong, or if they appeal simply to the instinct of curiosity and afford an excess of amusement, they are likely to fail in elucidating principles and establishing correct habits of thought. On the whole, fresh arguments taken from living thought, which are also models of accurate thinking, should be more extensively used.

At this point in the teaching of logic comes the real test of the instructor's skill. Instead of relying upon the text-book, he must depend for illustration upon his own resources. And, as far as possible, the illustrations should be presented in their full form, as actual arguments, and not in the condensed and lifeless way that text-books from lack of space are forced to do. Moreover, what is of even more consequence, he must be able to stimulate students to find material for themselves. There is no more direct and practical way than this for the student to cultivate the critical habit of mind in reading newspapers and periodical literature, as well as the literature of the various subjects of his college course. Such material would constitute what John Morley has somewhere called 'reasoning in real matter.' "It would make such a manual as no other matter could, for opening plain men's eyes to the logical pitfalls among which they go stumbling and crashing when they think they are disputing like Socrates or reasoning like Newton. They would see how a proposition or an expression that looks straightforward and unmistakable is yet, on examination, found to be capable of having several distinct interpretations and meaning several distinct things."

Of course there is danger of using exercises that for one reason or another are beyond the grasp of the sophomore or even the average senior. And yet, I am inclined to think that whatever pedagogical mistakes have been made in this connection have for the most part been in the direction of making the illustrations and problems so commonplace and simple as to seem silly. Indeed there is much to justify the student in real life in making the criticism of the student in the story, who says: "When they spring those tricks on you about the flying arrow not moving, and all the rest, and prove it by pure logic, you learn what pure logic amounts to when it cuts loose from common sense."

It is more evident in the ordinary treatment of inductive logic than in the case of deductive, that the subject is descriptive in character, with its data taken from the work of scientific investigators and discoverers, and its purpose to set forth the approved ways of thinking. Nevertheless, more might be done to anticipate a first impression, not at all uncommon with students, that the subject matter of inductive logic is abstract and quite removed from daily human interests. There is no danger of over-emphasizing the relation of what is taught in the class room to the realities of life, by way of showing that the content of logic is not the invention of text-book writers, and is not esoteric in its nature and use; that the methods described and analyzed in treatises on logic may be said to have their primitive forms in the uncultivated state of the human mind whether in savage or in civilized society. What is scientifically known as the uniformity of nature and the method of difference are but the tendencies of the human mind to expect similar coexistences and sequences under similar conditions, and to regard the new antecedent as the cause of the new phenomenon, tendencies as strong in the savage as in the civilized mind. In brief, we should show the student that the difference between the principles and methods of common life, and those studied in logic, is the difference between spontaneous and attentive observation; between rash and rationally guided theorizing; between verification that is heedless and insufficient, and that which is exact and exhaustive.

Induction should be understood in its proper connotation. To conceive it as simply the reverse process of deduction, to regard it as identical with case-counting, or mere generalization based upon facts, is to remain ignorant of the complex and varied nature of scientific method, in which generalization plays but one part. A logical analysis of inductive method should be so complete as to make it unmistakably evident that to be a scientific investigator is to be more than a collector of facts and a propounder of theories. Darwin once remarked that any fool could generalize and speculate. The verification of theories by appeal to facts and known laws is the step in inductive procedure quite frequently overlooked or hastily taken. And yet the importance of it is emphasized by what has been said of eminent scientific investigators, namely, that the process of deduction has played a more important part in their work than induction; that their days were spent in verifying their theories and establishing the further consequences of them.

The failure to understand the complex nature of inductive method appears now and then in another form. It finds expression in the opinions of those who profess to speak authoritatively upon the study of science from the pedagogical point of view. According to this view, the distinction between the observational and the experimental sciences is of insignificant value, and the arrangement of science courses might well enough be determined by local and economic conditions.

This misconception should be classed with that of mistaking general for singular terms, as is often done in the case of moral law and natural law. For it regards science as all one and the same, having one invariable procedure in all branches of scientific research, regardless of the peculiar nature of any particular group of phenomena. Consequently a study of any one of the sciences ought to satisfy the modern demand for science study and should qualify the more brilliant students as competent and reliable investigators in any branch of science whatsoever. If this were true, then, so far as pertains to method, the chemist might at once turn psychologist and pursue his work as successfully as though he had received his training in psychology instead of chemistry. The ideal man of science would be the last person to make any such claim. For he well knows that, besides the common features of the scientific method which appear everywhere in their broad outlines, there are numerous variations due to individual characteristics possessed by the data of the various sciences or different groups of sciences, and that to be a good scientist requires a preparation in the field in which one is to work. A better understanding of these facts might do much towards dispelling illusions as to a model science and the superiority of one science over another. Unfortunately scientists often assume an unscientific attitude towards one another. The physicist, for example, declares that for one to undertake the scientific study of psychical phenomena is to sound his death knell as a scientist. There is much need, among investigators in the various fields of human interest, of increased respect for one another's methods and results; of an intelligent conception of the peculiar conditions and difficulties of problems other than one's own; and instead of ridicule and depreciation, a just and cordial recognition of contributions honestly made, even though they lack the precision and finality which characterize results obtained elsewhere.

In addition to an orderly presentation of scientific methods and analysis of important and interesting conceptions such as the uniformity of nature, cause, hypotheses, theory, law, inductive logic should make it very evident that the data of our thinking are varied, and that the character of many conclusions is problematical. The facts of human experience, the problems of the world at large, do not lend themselves to any 'secure method' or yield conclusions that are certain. At one time we must act decisively on inferences which are far from approximating to certainty; and then again when it is not a question of choosing or starving, we need that suspended judgment which has been called the greatest triumph of intellectual discipline. In brief, a course in minor logic constructed along the following lines will, to my mind, render the best educational service: Definition and classification, with special emphasis upon use as determining the meaning of terms. The interpretation of propositions and the relation between form and meaning, with much stress laid upon the complexity of actual thinking rather than upon categories, predicables and symbols. The study of the syllogism as a form to which arguments may be reduced for the purpose of critical analysis. Training in ability to examine the validity of premises and their application to particular cases. And finally, the study of inductive methods with the view of familiarizing students with the actual ways by which knowledge is discovered.

All this means that logic is essentially a psychological rather than a philosophical study; that its content is mental phenomena, because the study of methods is but the study of the human mind engaged in the search of truth; that induction and deduction are in reality two constantly interplaying processes and are never found to be what the time-honored division of text-books suggests. Discussions of controversial topics, in which logicians delight, and from which no text-book, so far as I know, is wholly free, should be excluded. They have little interest for most students and besides obscuring the real content of minor logic, are likely to produce the impression that logic lacks definiteness and substantial basis. It is much better to hand over speculative questions to philosophy proper. Enough will be left for the course in logic in the time usually allotted it. What Professor Hyslop has said is eminently true: "Logic has been made too formal for usefulness and postponed too late in the course. It ought to follow mathematics immediately, to correct the confidence in reasoning that that science inculcates consciously or unconsciously."[4]

A word, in closing, upon a possible criticism of that part of logic which treats of inductive method. Why study logic in order to become familiar with the methods of science? Why not go directly to the several sciences themselves?

"We sometimes can not see the wood for the trees; and lose the broad outlines in the multiplicity of details." Just as we need to get out from among the trees to look at the wood; to stand some distance from the building to get a full view of it, so the scientist must needs view the structure of scientific knowledge from outside his own special field.

It is a frequent experience that students become so engaged in the multiplicity of fascinating phenomena of one science, or charmed by mechanical manipulations, that they are oblivious to underlying truths shared in common with their own and other subjects, or perhaps fail to appreciate the individual characteristics of a particular subject or group of allied subjects.

It can not be gainsaid that "a scientific habit of mind can be acquired only by the methodical study of some part at least of what the human race has come scientifically to know." But logic may supplement this indispensable kind of training. In it the methods themselves are made the direct objects of study. Brought together from near and far they may be compared, analyzed and classified with the attention focused upon them in their broad outlines. So presented, with a good body of illustrations, they may be above criticism as too formal or abstract, and furnish both layman and specialist with means of cultivating the sense of discrimination and widening their interests and sympathies.

  1. 'Life and Letters,' vol. 2, p. 302.
  2. Sidgwick, 'Use of Words in Reasoning,' p. 243.
  3. Sidgwick, 'Use of Words in Reasoning,' p. 354.
  4. The Psychological Review, 1903, p. 180. Sidgwick's 'Use of Words in Reasoning,' and Aikins' 'The Principles of Logic,' show an encouraging tendency away from the traditional treatment of logic.