But we have no guarantee that the same relation between the terms of a syllogism will hold, when one of the premisses is negative or particular. Thus, the syllogism—No M is P, All S is M, therefore, No S is P—yields as one case
where the major term may be the smallest in extent, and the middle the largest. Again, the syllogism—No M is P, Some S is M, therefore, Some S is not P—yields as one case
where the major term may be the smallest in extent and the minor the largest.
Whilst, however, the middle term is not always a middle term in extent, it is always a middle term in the sense that by its means the two other terms are connected, and their mutual relation determined.
287 198. The Propositions of the Syllogism.—Every categorical syllogism consists of three propositions. Of these one is the conclusion. The premisses are called the major premiss and the minor premiss according as they contain the major term or the minor term respectively.
| Thus, | All M is P | (major premiss), |
| All S is M | (minor premiss), | |
| therefore, | All S is P | (conclusion). |
It is usual (as in the above syllogism) to state the major premiss first and the conclusion last. This is, however, nothing more than a convention. The order of the premisses in no way affects the validity of a syllogism, and has indeed no logical significance, though in certain cases it may be of some rhetorical importance. Jevons (Principles of Science, 6, § 14) argues that the cogency of a syllogism is more clearly recognisable when the minor premiss is stated first. But it is doubtful whether any general rule of this kind can be laid down. In favour of the traditional order, it is to be said that in what is usually regarded as the typical syllogism (All M is P, All S is M, therefore, All S is P) there is a philosophical ground for stating the major premiss first, since that premiss gives the general rule, of which the minor premiss enables us to make a particular application.
199. The Rules of the Syllogism.—The rules of the categorical syllogism as usually stated are as follows:—
(1) Every syllogism contains three and only three terms.
(2) Every syllogism consists of three and only three propositions.