Syllogism

In Aristotelian logic a syllogism is an argument consisting of three propositions. The last is called the conclusion, which is a necessary consequence of the two preceding, which are called premisses. The conclusion has two terms, a subject and a predicate. The predicate is called the major term, its subject the minor term. To entail the conclusion, each of its terms must be compared in the premises with a third term, the middle term. Thus one premise has the major term and the middle term, and is called the major premise. The other has the minor term and the middle term, and is called the minor premise.

Structure of the syllogism

Thus the syllogism consists of three propositions: the major, the minor, and the conclusion. and though each has two terms, a subject and a predicate, there are only three different terms in all. The major term is always the predicate of the conclusion, and so is either the subject or predicate of the major premiss. The minor term is always the subject of the conclusion, and is either the subject or predicate of the minor premise. The middle term is never in the conclusion, but is in both premises, either as subject or predicate.

The figure of the syllogism depends on the the positions which the Middle Term may have in the premises. There are on four possible positions. It may be the subject of the major premise, and the predicate of the minor, and then the syllogism is of the first figure; or it may be the predicate of both premises, and then the syllogism is of the second figure; or it may be the subject of both, which makes a syllogism of the third figure; or it may be the predicate of the major premise, and the subject of the minor, which makes the fourth figure.

Another division of syllogisms is by mode. The mode is determined by the Quality and Quantity of the propositions. Any propositions must be either a universal affirmative, or a universal negative, or a particular affirmative, or a particular negative. These four kinds of propositions, were named by the four vowels A, E, I, O. Thus, AAA is the mode in which the major, minor and conclusion, are all universal affirmatives. EAE is the mode in which the major and conclusion are universal negatives and the minor is an universal affirmative. And so on.