The actual validity of these moods may be established by shewing that the axiom of the syllogism, the dictum de omni et nullo, applies to them; or by taking them severally and shewing that in each case the cogency of the reasoning is self-evident.
The special rules and the legitimate moods of Figure 2.
The position of the terms in figure 2 is shewn thus,—
P – M
S – M
⎯⎯
S – P ;
312 and its special rules (which the reader is recommended to deduce from the general rules of the syllogism for himself) are,—
(1) One premiss must be negative ;
(2) The major premiss must be universal.
The application of these rules again leaves six moods, namely, AEE, AEO, AOO, EAE, EAO, EIO.
Recourse cannot now he had directly to the dictum de omni et nullo in order to shew positively that these moods are legitimate. It may, however, be shewn in each case that the cogency of the reasoning is self-evident. The older logicians did not adopt this course; their method was to shew that, by the aid of immediate inferences, each mood could be reduced to such a form that the dictum did apply directly to it. The doctrine of reduction resulting from the adoption of this method will be discussed in the following [chapter].
The special rules and the legitimate moods of Figure 3.