In the logical study of terms, they are classified 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 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, 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 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 analyze 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 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 the force?" Are these words necessary, or could they be omitted?
Note whether another word could be substituted 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 space" would it be proper to substitute "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.