322 THE SCIENCE OF LOGIC 



II. Special Rules and Lawful Moods of the Second Figure. 

 The scheme of the second figure is 



P M 

 SM 



. . SP 



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



(1) One of the premisses must be negative ; 



(2) The major premiss must be universal ; 

 or, as expressed in Scholastic logic : 



Una negans esto ; et major generalis. 



(1) One of the premisses must be negative in order to dis 

 tribute M which is twice predicate and thus avoid the fallacy 

 of undistributed middle (Rule 3). 



(2) Were the major particular, its subject, P, would be undis 

 tributed, while as predicate of the negative conclusion it would 

 be distributed, thus involving illicit major (Rule 4). 



(b) Of the eight combinations of premisses to be submitted 

 to these two rules, A A, A I, I A are eliminated by the first rule ; 

 I A (again) and O A by the second : thus leaving A E, A O, E A, 

 E I. Tested by the general rules and corollaries, these forms yield 

 the following conclusions respectively : A E yields E and O ; A O 

 yields O alone ; E A yields E and O ; E I yields O alone. Thus 

 we have in the second figure six valid moods : 



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

 III. Special Rules and Lawful Moods of the Third Figure, 

 The scheme of the third figure is 



M P 

 MS 

 . .SP 

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



(1) The minor premiss must be affirmative ; 



(2) The conclusion must be particular ; 

 or, as expressed in Scholastic logic : 



Minor sit affirmans ; conclusio particulars. 



(1) Were the major negative, the conclusion would have to 

 be negative (Rule 6), thus distributing its predicate, the major ex 

 treme, P ; and the major would have to be affirmative (Rule 5), 

 thus leaving its predicate, the major extreme, P, undistributed : 

 thus we should have illicit major (Rule 4). 



(2) Were the conclusion universal it would distribute its sub- 



