328 THE SCIENCE OF LOGIC 



results somewhat more scientifically by inquiring directly, through 

 the general rules of syllogism, or through the fundamental 

 laws of thought (12, 14), in how many ways the A, E, I, and O 

 propositions, respectively, may be proved. Professor Welton gives 

 both methods. 1 They are so instructive that we take the liberty 

 of reproducing here his Determination of the Valid Moods by Re 

 ference to the General Rules of Syllogism. 



(1) To prove A. Both premisses must be affirmative (Rule 6), 

 and will therefore distribute their subjects only. 5, being distri 

 buted in the conclusion, must be distributed in its premiss, i.e. it 

 must be subject of the minor premiss, leaving M undistributed as 

 predicate. M must, therefore, be distributed in the major premiss, 

 i.e. must be subject of the latter. Thus we get the one single 

 form of syllogism 



M aP 

 S a M 



.-. S aP 



That is to say, //fo? h. proposition can be proved only in ONE way 

 in one mood of one figure viz. Barbara of the first figure. 



A cannot be proved in the second figure, for the second figure proves only 

 negatives ; or in the third figure, for this proves only particulars ; or in the 

 fourth figure, because it would involve Illicit Minor (or what, in the corre 

 sponding indirect mood of the first figure, would be called Illicit Major\ 



(2) To prove E. One premiss must be negative (Rule 6) and 

 one affirmative (Rule 5). 5 and P, being both distributed in the 

 conclusion, must also be distributed in the minor and major pre 

 misses (Rule 4). J/must also be distributed in one of the premisses 

 (Rule 3). But in order to distribute three terms between them the 

 premisses must both be universal and one of them negative one A, 

 the other E. Hence we may either have the major A and the 

 minor E, or vice versa ; and in either alternative the E premiss may 

 be written in two ways, being simply convertible. This gives us 



four possible forms : 



:.S e P . . S eP . , S e P S e P 



That is to say, the E proposition can be proved in FOUR ways, viz. by 

 E A E (Celarent) in the first figure ; 



l of&amp;gt;.cit. t pp. 315-22. 



