[413] We should have a corresponding case if we were to infer No S is P from the premisses given in the preceding example.
All danger of fallacy is avoided by breaking up the U proposition into two A propositions. In the case before us we 381 have,—All P is M, All M is S ; All P is M, All S is M. From the first of these pairs of premisses we get the conclusion All P is S ; in the second pair the middle term is undistributed, and therefore no conclusion is yielded at all.
(6) YAI in figure 3 is valid:—
| Some M is all P, | |
| All M is some S, | |
| therefore, | Some S is some P. |
The conclusion is however weakened, since from the given premisses we might infer Some S is all P.[414] It will be observed that when we quantify the predicate, the conclusion of a syllogism may be weakened in respect of its predicate as well as in respect of its subject. In the ordinary doctrine of the syllogism this is for obvious reasons not possible.
[414] Or, retaining the original conclusion, we might replace the major premiss by Some M is some P ; hence, from another point of view, the syllogism may be regarded as strengthened.
Without quantification of the predicate the above reasoning may be expressed in Bramantip, thus,
| All P is M, | |
| All M is S, | |
| therefore, | Some S is P. |
We could get the full conclusion, All P is S, in Barbara.
329. Table of valid moods resulting from the recognition of Y and η in addition to A, E, I, O.—If we adopt the sixfold schedule of propositions obtained by adding Only S is P (Y) and Not only S is P (η) to the ordinary fourfold schedule, as in section [150], every proposition is simply convertible, and, therefore, a valid mood in any figure is reducible to any other figure by the simple conversion of one or both of the premisses. Hence if the valid moods of any one figure are determined, those of the remaining figures may be immediately deduced therefrom.