Fig. 1. Fig. 2. Fig. 3. Fig. 4.
M – PP – MM – PP – M
S – MS – MM – SM – S
⎯⎯⎯⎯⎯⎯⎯⎯
S – PS – PS – PS – P

By the mood of a syllogism is meant the quantity and quality of the premisses and conclusion. For example, AAA is a mood in which both the premisses and also the conclusion are universal affirmatives; EIO is a mood in which the major is a universal negative, the minor a particular affirmative, and the conclusion a particular negative. It is clear that if figure and mood are both given, the syllogism is given.

244. The Special Rules of the Figures; and the Determination of the Legitimate Moods in each Figure.[329]—It may first of all be shewn that certain combinations of premisses are incapable of yielding a valid conclusion in any figure. A priori, there are possible the following sixteen different combinations of premisses, the major premiss being always stated first:—AA, AI, AE, AO, IA, II, IE, IO, EA, EI, EE, EO, OA, OI, OE, OO. Referring back, however, to the syllogistic rules and corollaries (as given in sections [199], [200]), we find that EE, 310 EO, OE, OO (being combinations of negative premisses) yield no conclusion by rule 5; that II, IO, OI (being combinations of particular premisses) are excluded by corollary i.; and that IE is excluded by corollary iii., which tells us that nothing follows from a particular major and a negative minor.

[329] The method of determination here adopted is only one amongst several possible methods. Another is suggested, for example, in sections [212], [233].

We are left then with the following eight possible combinations:—AA, AI, AE, AO, IA, EA, EI, OA ; and we may go on to enquire in which figures these will yield conclusions. In pursuing this enquiry, special rules of the various figures may be determined, which, taken together with the three corollaries established in section [200], replace the general rules of distribution. These special rules, supplemented by the general rules of quality and the corollaries,[330] will enable the validity of the different moods to be tested by a mere inspection of the form of the propositions of which they consist.

[330] The general rules of quality and the corollaries can be directly applied without reference to the position of the terms in the premisses of a syllogism. This is not the case with the general rules of distribution. The object of the special rules is, in the case of each particular figure, to substitute for the general rules of distribution special rules of quantity and quality.

The special rules[331] and the legitimate moods of Figure 1.

[331] As indicated in section [209], the special rules of figure 1 follow immediately from the dictum de omni et nullo.

The position of the terms in figure 1 is shewn thus,—

M – P
S – M