(_h_) REMEMBER THAT A STATEMENT IS NOT A PROOF. MANY STUDENTS THINK THEY PROVE A STATEMENT BY MERELY REPEATING IT IN DIFFERENT WORDS. YOU DO NOT UNDERSTAND A CONCLUSION UNLESS YOU CAN SEE THE STEPS IN ITS LOGICAL DEMONSTRATION.
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It is quite surprising how many students commit this error. For instance, if I am asked why can I see through gla.s.s and I reply, because it is transparent, I am giving no reason at all, for transparent means what can be seen through, so I am simply saying that I can see through gla.s.s because I can see through gla.s.s. The same error often occurs in arguments or syllogisms. For instance, suppose I make the following statements:
No unsportsmanlike act should be done; Smith"s act was unsportsmanlike; Therefore, Smith"s act should not have been done.
Now, this of itself is not correct reasoning, for the reason that the word "unsportsmanlike" simply means something which no sportsman should do. The conclusion, therefore, is simply a repet.i.tion of the second statement. The real thing to be proved in this case is whether Smith"s act was or was not unsportsmanlike.
[1] "General ideas and great conceit are always in a fair way to bring about terrible misfortune."--_Goethe_.
[2] "I tell you earnestly and authoritatively (I know I am right in this) you must get into the habit of looking intensely at words, and a.s.suring yourself of their meaning, syllable by syllable--nay, letter by letter."--_Ruskin: Sesame and Lilies_.
"Neither is a dictionary a bad book to read--it is full of suggestions."--_Emerson_.
Benjamin Franklin, writing to a lady who asked him to give her advice about reading said:
"I would advise you to read with a pen in your hand, and enter in a little book short hints of what you find that is curious or that may be useful ... and as many of the terms of science are such as you cannot have met with in your common reading, and may therefore be unacquainted with, I think it would be well for you to have a good dictionary at hand to consult immediately when you meet a word you do not know the precise meaning of. This may at first seem troublesome and interrupting, but it is a trouble that will daily diminish, and you will daily find less and less occasion for your dictionary, as you will become more acquainted with the terms; and in the mean time you will read with more satisfaction because with more understanding."
[3] "A man who has no acquaintance with foreign languages, knows nothing of his own."
[4] "The Principles of Argumentation" by Baker and Huntington, is another excellent book, not treating of formal logic, but discussing the general principles which should govern the preparation of a paper or argument, the principles of evidence, and the logical fallacies in reasoning. It is recommended to readers. This book is, or has been, used in the course in English at Harvard University, and similar books are used in other colleges. A thorough training in English under a good teacher is a good training in logic, for clear and logical writing requires clear and logical thinking. Nevertheless, the writer strongly advocates the study of formal logic also.
[5] "It is not enough to know, we must also apply; it is not enough to will, we must also do."--_Goethe_.
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III
THE THIRD ESSENTIAL FOR A PROPER METHOD OF STUDY IS SYSTEM
(_a_) DISCOVER THE FUNDAMENTAL IDEA OF THE SUBJECT.--Strip off the detail and get down to the root of the thing. See the really important point. Then, after this has been clearly perceived and mastered, arrange the details in their proper relations to the fundamentals. The subject will thus have a skeleton, and upon this the details will be placed. A subject of study thus viewed may be compared to the human body, with its bony skeleton or framework, and all the various organs and parts supported by it; or to a tree, with its trunk, branches and leaves. Thus to consider the relative importance of facts, to sift out the essential ones, will train the power of mental discrimination and cultivate the judgment.
When this is done, subsequent facts relating to the subject can be correlated with what is already known, and will in this way be easily retained by the memory. Remember and observe Jacotot"s maxim, "Learn something accurately, and refer {43} the rest to that." Unessential facts, or those of secondary importance, may be pa.s.sed over in the first reading, and left for a second or later reading, for a proper method of study _always involves re-reading_, perhaps many times.
You cannot possibly know everything even of a single subject, hence the importance of knowing the fundamental things about it and knowing them thoroughly. Even if you gain but an elementary knowledge of a subject, that knowledge may be thorough and should include fundamentals.
Thorough elementary knowledge must not be confused with _a smattering_.
The latter is worse than useless, and is marked by vagueness, uncertainty, and failure to grasp fundamentals. But elementary knowledge, if clear and definite as far as it goes, is valuable, and the first step toward more complete knowledge. Many students deceive themselves and others into thinking that they know something of a subject, because they have looked into it, while their knowledge may be entirely superficial and valueless.
When the fundamental principle or fact is perceived, study this carefully until it is thoroughly mastered. One who knows how to study properly will thus pick out the sentence or the paragraph which contains the key to the {44} subject--the fundamental fact or principle--and will read and re-read this many times until its full meaning is clearly grasped. When this is done it is sometimes remarkable how quickly the rest of the chapter or subject may be mastered, for it will often be found to consist of discussions or ill.u.s.trations, which will be obvious once the fundamentals are clearly in the mind. The ordinary student, however, does not do this. He does not see the fundamental principle, and each ill.u.s.tration is like a separate problem, different from the others, which has to be studied by itself, and is never fully mastered, because the underlying fundamental principle is not grasped.
(_b_) BEFORE YOU BEGIN TO STUDY A SUBJECT, THINK IT OVER CAREFULLY AND FIND OUT WHAT YOU ALREADY KNOW OF IT OR WHAT YOU CAN ARRIVE AT BY YOUR UNAIDED EFFORTS.--Try also to perceive what you expect to get out of the study of the subject, and how it is related with what you have already studied, and how it is to find application.[1] The historian, Edward Gibbon, states in his autobiography that before reading any book, he made it a rule to reflect {45} upon the subject, arranging and cla.s.sifying what he already knew of it.
This method may be followed to different degrees, depending on the subject. A student beginning the study of a new science which he has never studied before, can do comparatively little; but at least he can insist upon getting a clear idea of what the subject or problem is, its extent, what its objects and methods are, how it is related to other subjects, what its uses are, and how other studies will find their application in it.
(_c_) CLa.s.sIFY AND ARRANGE WHAT YOU HAVE LEARNED.--When you have finished part of a subject, stop and think over the ground that has been covered, and arrange the various points made. Draw up a topical index and compare it with the table of contents. Note the correlation or interdependence of facts and link them together. By the principle of a.s.sociation the retention of facts and principles in the memory will be much facilitated. Note down concisely the steps of an argument in your own words, and see if the conclusion is justified. Close the book from time to time and go over in your mind what you have learned.
The importance of systematic cla.s.sification is very great. The minds of many students are {46} like a library without arrangement or catalogue; the books may be there, but cannot be found when wanted, and so are valueless for use.[2]
[1] "We must keep carefully that rule of Aristotle which teaches that the best way to learn anything well which has to be done after it is learned, is always to be a-doing while we are a-learning."--_Richard Mulcaster_.
[2] "There"s a vast difference between having a carload of miscellaneous facts sloshing around loose in your head and getting all mixed up in transit, and carrying the same a.s.sortment properly boxed and crated for convenient handling and immediate delivery."--_Lorimer: Letters from a Self-made Merchant to his Son at College_.
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IV
MENTAL INITIATIVE
It will become evident from the foregoing that a fourth essential for proper study is mental initiative. The student must have a definite purpose, and must do what is the proper thing without it being suggested to him. He must not simply do as he is told. If he have not initiative and cannot develop it, he will probably never study intelligently, nor gain a thorough understanding of what he reads, but will merely memorize.
Memory is a most important faculty; it is not, however, a _subst.i.tute_ for thought, but should be based upon it. Thinking is essential in order to decide what to memorize. Memory, however, is often made the sole factor in study. Fundamental principles should frequently be memorized, so that by numberless repet.i.tions they may be permanently impressed upon the consciousness, and can be repeated verbatim as a guide in any concrete case where they are to be applied.
Some suggestions may be useful as to the use and cultivation of mental initiative.
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(_a_) CULTIVATE AN INTEREST IN WHAT YOU ARE STUDYING, AND SOME IDEA OF WHAT IT LEADS TO.--Without interest your study will be perfunctory and of little use to you. Make yourself believe that for you, at that time, it is the most important thing in the world. It is of course true that in most schools students are required to study definite subjects according to a curriculum arranged by the faculty. In some of these subjects a student may take little interest; indeed they may be so foreign to his natural tastes that he is not able to cultivate any interest in them. In such a case his study of them will be of little value to him. If, relying upon the judgment of those who prescribe the curriculum as necessary or desirable for the object which he has in view, he cannot persuade himself that they have value for him or make himself take an interest in them, it would probably be better for him to drop them even though he may thereby become a special student in the school or lose his degree. A degree which simply means slipshod, unintelligent and uninterested study of a considerable number of subjects embraced in the curriculum, is verily a "sc.r.a.p of paper" not worth having. If you wish to concentrate your entire attention upon certain subjects in which {49} you take an active interest you may become proficient in those, but you may become very narrow minded and altogether lacking in that all-around breadth of view which comes from the cultivation of other subjects which well informed men consider necessary.
(_b_) INSIST UPON FIRST CLEARLY FORMULATING THE PROBLEM, IF ONE IS BEFORE YOU.--Many students literally do not know what they are doing, because they neglect this injunction, which is a necessary corollary of the necessity of forming definite ideas. Do not proceed to endeavor to solve the problem until it is clearly formulated, no matter how long it may take. See what the data of the problem are, whether definite or not, and what is required. See also how variations of the data, if indefinite, would affect the result.
(_c_) WORK INDEPENDENTLY OF OTHERS.--Solve your own difficulties and welcome them. Do not expect things to be easy. You will never gain strength by being shown, but only by the exercise of your own unaided powers. Therefore, do everything for yourself, so far as possible.
Seek only _suggestions_ from your teacher, when you need help, except in regard to mere matters of fact, which you could not be expected to {50} reason out. Let the suggestions be as slight as possible.
If you have problems a.s.signed, solve them entirely by yourself, even if you make mistakes. Then, when those mistakes are pointed out, consider them with great care and discover the causes for them, and _remedy them_, so that you will not again make the same mistake or one a.n.a.logous to it. You should delight in discovering difficulties which give you an opportunity to test and increase your strength and so avoid future errors. In the same way, examinations should be welcomed, not dreaded. The teacher does not mark you--you mark yourself; the teacher merely records the mark. Even if you fail in the examination, that should indicate to you what you lack, and so be a benefit. Indeed, it is better to fail than to sc.r.a.pe through.[1] There must be a line somewhere. The man just above the line pa.s.ses, and the man just below the line fails. The former may not be as capable as the latter, but, having pa.s.sed, he does not remedy his faults; while the man who has failed is required to remedy his. Huxley said that the next best thing to being right is to be completely and wholesomely wrong.
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(_d_) DRAW YOUR OWN CONCLUSIONS, WHENEVER POSSIBLE, BEFORE YOU KNOW THOSE OF THE WRITER You ARE STUDYING.--When you read, "From the above it is evident," stop, close the book, and see if you can state what is evident. When you have written this down, compare with the result reached by the writer. Practise such exercises in whatever form they present themselves. If your conclusions are different from those of the writer, in kind or in character, see which is right, or whether both are right. If you are right, why did the writer not reach your conclusion? Was it because it was not pertinent to his problem? Is it simply a difference of expression?
The process of investigating any subject is a process of question and answer. The student must first propound to himself a question, and it must be the proper question. He must be able to perceive what the proper question is, under the circ.u.mstances. Then he must give to himself the proper answer out of all the possible answers that are verbally correct, namely, the answer that affords a new vantage ground from which another question may be asked; and so the problem may be gradually unravelled.