How to Study Part 2

"A friend of mine visiting a school, was asked to examine a young cla.s.s in geography. Glancing at the book, she said: 'Suppose you should dig a hole in the ground, hundreds of feet deep, how should you find it at the bottom--warmer or colder than on top?' None of the cla.s.s replying, the teacher said: 'I'm sure they know, but I think you don't ask the question quite rightly. Let me try.' So, taking the book, she asked: 'In what condition is the interior of the globe?' and received the immediate answer from half the cla.s.s at once; 'The interior of the globe is in a condition of igneous fusion!'"

Perhaps it may be thought that an incident like the foregoing would only occur in an elementary school. As a matter of fact, college students and graduates, and indeed most of us, {24} do this very thing more often than we realize, even in subjects like mathematics or mechanics; and terms like "energy," "momentum," "rate of change,"

"period of vibration," "value," "social justice," etc., are often used without a clear understanding, and sometimes without any understanding at all, of what they mean.

(_a_) THE STUDENT SHOULD ACQUIRE AND INSIST UPON EXERCISING THE HABIT OF FORMING DEFINITE IDEAS.--This is one of the most important injunctions to be observed as an essential principle of intelligent study.[1] It is self-evident that facts or things cannot be reasoned about intelligently unless a definite idea is formed of the facts or things themselves. Vagueness of idea not alone precludes a proper conception of the thing itself, but may vitiate all reasoning regarding it. The student must resolutely make up his mind that he must not rest satisfied with hazy, uncertain, half-formed ideas. A half knowledge of a thing may not be useless, but it is generally found that it is the other half that is needed. If the student could learn this one precept and continually apply it, he would have little difficulty in studying properly.

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It is not easy to state just how the habit of forming definite ideas may be acquired. To a certain extent it is intuitive. Some students have it, while others do not; some can cultivate it, while others apparently cannot. It is probably safe to say, however, that a student who cannot cultivate it should not study books, or enter into a profession, but should go to work with his hands instead of taking a college course. Such a man will be always likely to be misled, his conclusions can never be depended upon, and what we term education may do him harm rather than good.

A definite idea is one that leaves no room for ambiguity--which means just one thing. The habit of forming such ideas habitually may be cultivated in several ways, as for instance:

1. STUDY THE DICTIONARY.--By study of the dictionary, the student may train himself to distinguish slight differences in meaning between words, and habitually to use precisely the word with the proper meaning to express his idea. A knowledge of the derivation of words will often a.s.sist, and such books as Archbishop Trench's on "The Study of Words,"

or a course in English composition under a good teacher, accompanied by exercises in expression, will all contribute to {26} the formation of the habit.[2] Sometimes, however, the dictionary may give little a.s.sistance, for it may be found that one term is defined by means of another and on looking up that other, it will be found to be defined by means of the first. Sometimes also a definition of a word will be given in terms even more difficult to understand than the one which is defined. There are differences in dictionaries. The study of language, and particularly of the cla.s.sics, if properly pursued, may be of great benefit, because it involves translating {27} from one language into another, and should include much practice in discovering the precise word or phrase to express an idea. The reason why a study of the cla.s.sics may be better than that of modern foreign languages, is that in studying the latter the object is more often considered--by the student at least--to become able to read professional books in a modern language, or to get a smattering which will be of use in travel or in business; while in the study of the cla.s.sics these objects are entirely absent, and the attention is more apt to be concentrated on studying delicate shades of meaning. However, everything depends upon the teacher and the way the subject is taught.[3]

2. The habit of forming definite ideas may also be cultivated by each day attempting to define a certain number of common words, and after making as good a definition as possible comparing the result with that in the dictionary. If the student will practise this, he will at first receive many surprises, for any word may be defined in various ways, all correct as far as they go, but only one of which is a true definition. For instance, a cow may be defined as a {28} four-legged animal, but this, while correct, obviously does not define a cow, for the same definition would apply to many other animals that are not cows. What const.i.tutes a definition?

This subject is clearly allied with the discussion of the question as to what const.i.tutes perfect knowledge; what elements, for instance, go to make up what may be called a perfect conception of a thing.

According to Liebnitz, perfect knowledge is clear, distinct, adequate, and intuitive. The student will do well to look up the discussion of this subject in Jevon's "Elementary Lessons in Logic" (Lesson VII).

The importance of forming definite ideas, as an essential of proper study, and of understanding what is read, cannot be exaggerated.

Without it one cannot acquire more than a partial knowledge, and one is always liable to those errors of reasoning which arise from the use of equivocal language, which may lead us unconsciously from one meaning of a word to another--a logical error which is perhaps the most fruitful cause of fallacious reasoning.

3. STUDY LOGIC.--Logic is the science of correct reasoning. It teaches us how to discover truth, how to recognize it when discovered, how to arrive at general laws from facts collected by {29} observation or experiment, and how to deduce new facts from those already found to be true. It is thus the science of sciences, and finds its application in every branch of knowledge. The training of his power of logical thought is, therefore, one of the things that should be constantly aimed at by the student.

Now all thinking is concerned, first of all, with _terms_ or names for things or qualities or conceptions of some sort. Then, it is concerned with comparisons of things, and the discovery of their ident.i.ty or dissimilarity, as when I say "Iron is a metal" or "all metals are elements," each of which statements is a _proposition_, the truth or falsity of which I must be able to discover. Finally, it is concerned in deducing new propositions from old ones, and so arriving at new truths, as when I discover from the two propositions stated above, the new truth that "Iron is an element."

But there are many chances for error in this process; for instance, I might say:

"To call you an animal would be to state the truth"--to which you would agree; and, "To call you an a.s.s would be to call you an animal"--to which you would also agree; from which I might conclude that, "To call you an a.s.s would {30} be to state the truth"--which you might have a vague idea was not true. If you wish to be sure that this conclusion is incorrect, you must be able to show just why it is incorrect. The study of logic would enable you to see just where the error lies. You must not be governed by vague ideas, or you will be intellectually at anybody's mercy.

In the logical study of _terms_, they are cla.s.sified and distinguished, and the importance made manifest of having in mind a clear definition of the meaning of a term before reasoning about it. Many terms are ambiguous, as already explained, and may mean many different things, as for instance the terms "bill," "church," "evil," "value," "social justice." Here, then, the importance of definite ideas will be manifest.

Pascal laid down the essentials of logical method in the statement "Define everything and prove everything." In other words, do not attempt to think about a term until you have defined the term and have a clear idea what it means; and insist upon proving every statement at which you arrive, before accepting it finally and definitely; although for want of time, you may be obliged sometimes to accept or form a conclusion tentatively or provisionally. You may be able to draw correct conclusions from stated {31} premises even though you do not understand the terms of the premises. For instance, if I say, "Selenium is a dyad element" and "A dyad element is one capable of replacing two equivalents of hydrogen," I can correctly draw the conclusion that, "Selenium is capable of replacing two equivalents of hydrogen," but I cannot know that the conclusion is correct unless I understand the meaning of the terms in the premises and so can be sure of the correctness of those premises.

Every student should, therefore, in the writer's opinion, take a systematic course in logic, or carefully study by himself such books as Jevons' "Elementary Lessons in Logic" or John Stuart Mill's "Logic."[4]

(_b_) LEARN TO STATE A THING IN DIFFERENT WAYS OR FROM DIFFERENT POINTS OF VIEW.--Almost anything may be looked at from different points of view, or a truth stated in different ways, {32} and it may appear very different from different viewpoints. A student should practise doing this, first stating a principle perhaps from the mathematical point of view, and then in simple untechnical language that can be understood by one who is not a mathematician. The habit of stating even technical matters in simple untechnical language should be practised continually.

As Bishop Berkeley urged, we should "think with the learned and speak with the vulgar." If you clearly understand a proposition, you can state it in clear and unambiguous language, though perhaps not in Addisonian English. Students frequently say "I understand that, but I cannot explain it." Such a student deceives himself: he does not understand it. If he understands it thoroughly, he can explain it clearly and without ambiguity, and so that others will understand him.

For this reason an acute observer can get the mental measure of a man after a few minutes' conversation. Inaccurate or slipshod thinking will surely show itself in speech.

(_c_) STATE A THING NOT ONLY POSITIVELY BUT NEGATIVELY.--That is to say, state not only what it is, but what it is not, even if incompletely. Perceive not only what it includes, but what it excludes. When a result or a {33} principle is arrived at, it is essential not only to see that it is true, but how far the _reverse_ is _untrue_. The student does not really understand a thing unless he recognizes it from any point of view, can describe it from any point of view, can state it in language to suit the particular emergency, and can see why the other thing is untrue. As Aristotle says:

"We must not only state the truth, but the cause of the untrue statement; this is an element in our belief; for when it is made apparent why a statement not true appears to be true, our belief in the truth is confirmed."

In other words, we must a.n.a.lyze every statement which is the result of reasoning, or a statement of opinion, and see what objections, if any, can be brought against it, and then convince ourselves where the truth lies and why. The lawyer has excellent practice in doing this, for in making his own argument he is obliged to scrutinize it closely to discover what objections he would make to it, if he were the counsel on the opposite side. The lawyer, however, does not always limit himself to the discovery of the truth, but often seeks to discover and bring to bear unsound but plausible arguments to refute the other side; and by his skill in dialectics he may often deliberately "make the worse appear {34} the better reason." The student of mathematics, on the other hand, does not gain in that study much practice in weighing evidence or seeking objections to an argument, for he deals with principles which are rigid and not open to question. Professor Palmer, in his interesting book, "The Problem of Freedom," says: "Until we understand the objection to any line of thought, we do not understand that thought; nor can we feel the full force of such objections until we have them urged upon us by one who believes them." This is precisely what the advocate endeavors to do beforehand, and in the court room he is very sure to have the objections to his line of thought urged upon him and the jury by one who at all events _appears_ to believe them.

(_d_) IN STUDYING A STATEMENT, OBSERVE WHICH ARE THE NECESSARY WORDS AND WHETHER THERE ARE ANY UNNECESSARY ONES WHICH MIGHT BE OMITTED.--For instance, in the following sentence, "When a force acts upon a body, and the point of application of the force moves in the direction of the line of action of the force, the force is said to do work on the body,"

what is the necessity and significance of the qualifying phrase "in the direction of the line of action of {35} the force?" Are these words necessary, or could they be omitted?

Note whether another word could be subst.i.tuted for one used, without rendering a statement incorrect, or whether such change would improve it and make it more accurate. For instance, in the definition "Matter is that which can occupy s.p.a.ce" would it be proper to subst.i.tute "does"

for "can" or "occupies" for "can occupy"?

Note what word or words should be emphasized in order to convey the intended meaning. In the sentence "Thou shalt not bear false witness against thy neighbor," several widely different meanings may be conveyed according to the word which is emphasized.

Students frequently seem to lack all sense of proportion and fail to acquire definite ideas because they do not see the meaning or necessity of qualifying words or phrases, or because they do not perceive where the emphasis should be placed.

(_e_) REFLECT UPON WHAT IS READ: ILl.u.s.tRATE AND APPLY A RESULT AFTER REACHING IT, BEFORE Pa.s.sING ON TO SOMETHING ELSE.[5]--Apply it to cases entirely different from those {36} shown in the book, and try to observe how generally it is applicable. Do not leave it in the abstract. An infallible test of whether you _understand_ what you have read is your ability to _apply_ it, particularly to cases entirely different from those used in the book. An abstract idea or result not ill.u.s.trated or applied concretely is like food undigested; it is not a.s.similated, and it soon pa.s.ses from the system. In ill.u.s.trating, so far as time permits, the student should use pencil and paper, if the case demands, draw sketches where applicable, write out the statement arrived at in language different from that used by the author, study each word and the best method of expression, and practise to be concise and to omit everything unnecessary to the exact meaning. Herndon in his "Life of Lincoln" says of that great man, "He studied to see the subject matter clearly and to express it truly and strongly; I have known him to study for hours the best way of three to express an idea."

This kind of practice inevitably leads to a thorough grasp of a subject.

Some of these principles may be ill.u.s.trated by considering the study of the algebraical conditions under which a certain number of unknown quant.i.ties may be found from a number of {37} equations. The student will perhaps find the necessary condition expressed by the statement that "the number of independent equations must equal the number of unknown quant.i.ties." Now this statement makes little or no concrete impression upon the minds of most students. They do not understand exactly what it means, and they can easily be trapped into misapplying it. To study it, the student should ask himself what each word of the statement means, and whether all are necessary. Can the word "independent" be omitted? If not, why not? What does this word really mean in this connection? Must each equation contain all the unknown quant.i.ties? May some of these equations contain none of the unknown quant.i.ties? What would be the condition of things if there were fewer equations than unknown quant.i.ties? What if there were more equations than unknown quant.i.ties?

This problem too, affords a good ill.u.s.tration of the advantage of translation into other terms? What, for instance, is an equation anyway? Is it merely a combination of letters with signs between? The student should translate, and perceive that an equation is really an intelligible sentence, expressing some statement of fact, {38} in which the terms are merely represented by letters. An equation tells us something. Let the student state what it tells in ordinary non-mathematical language. Then again, a certain combination of equations, taken together, may express some single fact or conclusion which may be stated entirely independent of the terms of the equations.

Thus, in mechanics the three equations _[sigma]H_=0; _[sigma]V_=0; _[sigma]M_=0; taken together, merely say, in English, that a certain set of forces is in equilibrium; they are the mathematical statement of that simple fact. If the equations are fulfilled, the forces are in equilibrium; if not fulfilled, the forces are not in equilibrium.

Following this farther, the student should perceive, in non-mathematical language, that an equation is independent of other equations if the fact that it expresses is not expressed by any of the others, and cannot be deduced from the facts expressed in the others.

The benefit of translation into common, everyday language, may be shown by another mathematical ill.u.s.tration. Every student of Algebra learns the binomial theorem, or expression for the square of the sum of two quant.i.ties; but he does not reflect upon it, ill.u.s.trate it, or perceive {39} its every-day applications, and if asked to give the square of 21, will fail to see that he should be able to give the answer instantly without pencil or paper, by mental arithmetic alone. Any student who _fully grasps_ the binomial theorem can give (without hesitation) the square of 21, or of 21.5, or any similar quant.i.ty. With practice and reflection, results which seem astonis.h.i.+ng may be attained.

(_f_) KEEP THE MIND ACTIVE AND ALERT.--Do not simply sit and gaze upon a book, expecting to have ideas come to you, but exert the mind. Study is active and intelligent, not dreamy. By this is not meant that haste is to be practised. On the contrary, what might perhaps be called a sort of dreamy thinking often gives time and opportunity for ideas to clarify and take shape and proportion in the mind. We often learn most in hours of comparative idleness, meditating without strenuous mental activity upon what we have read. Such meditation is of the greatest value, but it is very different from the mental indolence of which the poet speaks when he says:

"'Tis thus the imagination takes repose In indolent vacuity of thought, And rests and is refreshed."

{40} This is beneficial to the proper extent; but it is rest, not study.

(_g_) WHEN YOU MEET WITH DIFFERENCES OF OPINION UPON A SUBJECT, REFLECT UPON THE REASONS WHICH MAY CAUSE INTELLIGENT MEN TO ARRIVE AT DIFFERENT CONCLUSIONS.--These reasons are:

1. One or both may fail to grasp all the pertinent facts, or even the problem itself, or may a.s.sume, as true, facts or principles which are really erroneous. This should easily be ascertainable.

2. One or both may reason incorrectly even from accurate premises.

This also should be discoverable.

3. One or both may see facts out of proportion--may lack a true mental balance or perspective.

4. One or both may ill.u.s.trate the inherent stubbornness or imperviousness of the human mind.

Whether the student can discover the last two sources of error will depend upon his own mental characteristics. He must not forget, however, that on many matters no definite demonstrable conclusion is possible, and that the result must remain more or less a matter of opinion.