Induction, then, is reasoning from the particular to the general; the establishment of an hypothesis by showing that the facts agree with it. It is preëminently the scientific method. By observing natural phenomena, the scientist conceives what the law which governs them must be. This idea of the general principle is then the hypothesis which he attempts to prove; and his method is to examine the facts under all conditions possible, establishing his proposition by showing that the facts are in accord with it.
Deduction is the converse of this, and consists in drawing out particular truths from general ones. A universal proposition may be regarded as a bundle in which are bound together many individual ones. It is the work of deduction to take these out,—to separate any one of them from the rest. The general truth, “All metals are elements,” includes in it the especial truths, “Iron is an element,” “Gold is an element,” and so on for each metal which could be named. Deduction is the process of separating one of these from the whole. Speaking broadly, scientific reasoning is more likely to be inductive, while other reasoning is more likely to be deductive.
As a matter of practical composition, Argument is the statement of a proposition, and the arrangement of the proofs which the writer believes will establish its truth. The essential matter is to begin with some truth or fact generally acknowledged, and to lead the mind of the reader on by deductions which cannot be disputed, until the proposition to be proved is reached as an unassailable conclusion.
This process may be very simple, or extremely complex; the steps may be slight, or they may be, like the platforms of the pyramids, barely scalable. In discussing methods, it is necessary to use some technical expressions which it is well to define:—
A Term is a word or combination of words used to name some thing or idea in reasoning.
A Proposition is a statement of the relation between two terms.
If we say, “The man is a patriot,” we have a sentence in which is a statement of the relation between the thing “man” and the thing “patriot.” This is therefore a proposition. Here the terms are “man” and “patriot,” because these are the names of the things of which we speak in reasoning.
We might now make another proposition, this time general, and say, “A patriot is a valuable citizen.” Here the terms are “patriot” and “valuable citizen,” and the proposition asserts a relation between them.
If these two propositions are examined, they are found to have in common the term “patriot,” and it is seen to be possible to draw from them another proposition. If the man of whom mention is made is a patriot, and a patriot is a valuable citizen, it is evident enough that the man must be a valuable citizen. It is merely an application of the principle that things which are equal to the same thing are equal to each other. And this brings us to a third definition:—
A Syllogism is a group of three propositions, of which, if the first two are true, the third must follow as a deduction from them.