FIGURES AND MOODS OF THE SYLLOGISM 323 



ject, 5, which is undistributed in its premiss, being there the 

 predicate of an affirmative proposition : thus we should have 

 illicit minor (Rule 4). 



(fr) Subjecting the eight combinations of premisses to these 

 rules, we find that the first of them eliminates A E and A O, thus 

 leaving six combinations, from each of which, according to the 

 second rule, only a particular conclusion can follow, viz. I if 

 both premisses be affirmative, O if one premiss be negative. 

 These six valid moods of the third figure are : 



A A I, I A I, A I I, E A O, O A O, E I O. 



IV. Special Rules and Lawful Moods of the Fourth Figure. 

 The scheme of the fourth figure 1 is 



PM 

 MS 



c p 



* * O JL 



(a) Its special rules are somewhat complex. In each of the 

 three preceding figures we were able to commence by laying down 

 some definite, categorical rule about the quality of the premisses. 

 This, then, helped to determine the other categorical rule for 

 quantity? Here, however, we can lay down no special categori 

 cal rule about the quality of the premisses (beyond the general 

 rule that both carmot be negative). Both may be affirmative, or 

 either negative and the other affirmative. These hypotheses give 

 the following hypothetical rules of quantity. 



1 . If the major premiss be affirmative, the minor must be uni 

 versal ; 



2. If the minor premiss be affirmative, the conclusion must be 

 particular ; 



1 The scheme for the indirect moods of the first figure would be 



MP 



SM 



.-. PS 



which really differs from the scheme of the fourth figure only in the order in which 

 the premisses are written. Since the conclusion is not expressed in its natural order, 

 Aristotle would still regard the premiss containing P as the major, and that con- 

 taining S as the minor, i.e. he would describe the syllogism as belonging to the first 

 figure with the conclusion drawn indirectly about the major in terms of the minor. 

 Cf. infra, 171. 



2 Whereas quality affects only the propositions, and is independent of quantity, 

 this latter affects the terms of the propositions, and is, itself, so far as regards the 

 predicate, dependent on, and determined by, the quality of the proposition. Hence 

 the special rules of quality come first, helping to determine those of quantity. 



2T * 



