FIGURES AND MOODS OF THE SYLLOGISM 321 



lar major with a negative minor. Rejecting, then, those eight com 

 binations [enclosed in brackets above, (160)], which, being invalid 

 in all four figures, give us at once thirty-two as invalid out of the 

 sixty-four possible forms, we are left with the following eight 

 combinations : A A, A I, A E, A O, I A, E A, E I, O A. These 

 we shall now examine in each of the figures. 



I. Special Rules and Lawful Moods of the First Figure. 

 The scheme of the first figure is 



MP 

 SM 



.-. SP. 



(a) Its special rules one of quality and one of quantity 

 are 



(1) The minor premiss must be affirmative ; 



(2) The major premiss must be universal ; 

 or, as expressed in Scholastic logic : 



Minor sit affirmans ; major generalis. 



(1) Were the minor negative the major would have to be 

 affirmative (Rule 5) and the conclusion negative (Rule 6). The 

 major extreme would therefore be undistributed in its premiss 

 (being predicate of an affirmative) and distributed in the conclusion 

 (being predicate of a negative). And this illicit process violates 

 Rule 4. 



(2) Were the major premiss a particular proposition the 

 middle term, being its subject, would be undistributed ; and it is 

 also undistributed in the minor premiss where it is predicate of an 

 affirmative. Hence we should have a violation of Rule 3. 



Those two rules follow directly from the Dictum de omni et nullo, which 

 applies directly to this figure. 



() Of the eight combinations of premisses given above, the 

 first special rule of this figure excludes A E and A O. The second 

 excludes I A and O A. This leavesy^r combinations of premisses, 

 viz., A A, A I, E A, E I. What conclusions can these yield? 

 Bearing in mind the general rules and corollaries, that the con 

 clusion follows the weaker premiss, and that a negative conclusion 

 requires a negative premiss, we find that A A will yield A or I ; 

 E A will yield E or O ; A I will yield I only ; E I will yield O 

 only. Thus we have in the first figure six valid moods : 



A A A, (A A I), E A E, (E A O), A I I, E I O. 



VOL. I. 21 



