The conclusion in each case is assumed to be S-P. The names of the terms and of the premises are based on this assumption. Now, these variations in the positions of the terms of a syllogism are called differences of figure. It will be seen that the above four arrangements of terms are the only possible ones, and they are known respectively as the first, second, third and fourth figure. The first arrangement is the most natural and most common. In it the term which becomes the subject of the conclusion is the subject of its premise, and the term which becomes the predicate of the conclusion is the predicate of its premise. In the fourth figure the arrangement of terms is just the reverse of what it is in the first. In the second figure the middle term is the predicate in both premises. In the third figure it is the subject in both prem ises. Each figure is obviously a kind of scheme or schema which might remain the same while the premises vary in quality and quantity. In considering the figures of syllogisms, we abstracted from, or ignored, differences in the quality and quantity of the component propositions and only attended to the positions of the terms. But the propositions have, of course, quality and quantity.
And the differences in the quality and quantity of the propositions in a syllogism constitute what are known as the different moods of syllogisms. Prima facie each figure may have various moods. The first figure, e.g., contains the moods MaP, SaM, therefore SaP, also MeP, SaM, therefore SeP, and so on. It is consequently desirable to determine how many valid moods there are in each figure. This may be done as follows : From the point of view of their quality and quantity, there are four types of proposition, namely, A, E, I, 0. Any one of these might conceivably be the major premise or the minor premise of a syllogism. There are, therefore, 16 conceivable combinations of premises, namely, AA, Al, AE, AO, IA, II, 1E, 10, EA, El, EE, E0, OA, 01, OE, 00—in these combinations the first letter rep resents the major, the second the minor, premise. By applying to these the general rules of the syllogism it will be seen that eight of the i6 combinations of premises cannot justify a conclusion in any figure. These eight are EE, E0, OE, 00 (rules) II, 10, 01, IE (rule 3 or 4). Only the following eight are, therefore, likely to warrant a conclusion in some figure or other, namely, AA, AI,