Induction, then, is a real process of Reasoning or Inference. Whether, and in what sense, as much can be said of the Syllogism, remains to be determined by the examination into which we are about to enter.
§ 1. The analysis of the Syllogism has been so accurately and fully performed in the common manuals of Logic, that in the present work, which is not designed as a manual, it is sufficient to recapitulate, _memoriæ causâ_, the leading results of that analysis, as a foundation for the remarks to be afterwards made on the functions of the syllogism, and the place which it holds in science.
To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or proposition to be proved, and two other propositions which together prove it, and which are called the premises. It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclusion, and another called the middleterm, which must be found in both premises, since it is by means of it that the other two terms are to be connected together. The predicate of the conclusion is called the major term of the syllogism; the subject of the conclusion is called the minor term. As there can be but three terms, the major and minor terms must each be found in one, and only one, of the premises, together with the middleterm which is in them both. The premise which contains the middleterm and the major term is called the major premise; that which contains the middleterm and the minor term is called the minor premise.
Syllogisms are divided by some logicians into three _figures_, by others into four, according to the position of the middleterm, which may either be the subject in both premises, the predicate in both, or the subject in one and the predicate in the other. The most common case is that in which the middleterm is the subject of the major premise and the predicate of the minor. This is reckoned as the first figure. When the middleterm is the predicate in both premises, the syllogism belongs to the second figure; when it is the subject in both, to the third. In the fourth figure the middleterm is the subject of the minor premise and the predicate of the major. Those writers who reckon no more than three figures, include this case in the first.