FIGURES AND MOODS OF THE SYLLOGISM 3*9 



E A E and A E E (Cesare and Camestres) in the second ; 



A E E (Camenes) in the fourth figure 



E cannot be proved in the third figure, which proves only particulars. 



(3) To prove I. Both premisses must be affirmative (Rule 6). 

 As neither 5 nor P are distributed in the conclusion, it does not 

 matter whether they are distributed in the premisses or not. But 

 since we are searching for premisses which will prove S i P only 

 (and not for premisses which would warrant , a P), we shall have 

 to confine ourselves to those in which 5 is undistributed. Nor does 

 it matter whether M is distributed twice. The distribution of M 

 in one premiss, and the non-distribution of 5, are all that need to 

 be secured. Every combination of affirmative premisses in which 

 M is, and 5 is not, the subject of an A proposition, will fulfil 

 these conditions. 5 may, therefore, be either (i) subject, or (2) 

 predicate of an I minor, with M a P as major ; or it may be the 

 predicate of an A minor (M a S), distributing M, and thus leaving 

 four alternatives for M in the major, i.e. (3) subject of I, (4) sub 

 ject of A, (5) predicate of I, (6) predicate of A. Thus we have 

 six forms : 



(0 (2) (3) (4) (5) (6) 



MaP MaP MiP MaP PiM PaM 



Si M Mi S M a S M a S M a S M a S 



.-. S i P .-. S i P . . SiP . . 5 i P . : S i P . . 5 i P 



That is to say, the I proposition can be proved in SIX ways 

 (besides the subaltern mood of Barbara) viz. by 

 A I I (Darii) in the first figure ; 



AI I, I A I, AA I (Datisi, Disamis, Darapti] in the third figure ; 

 I A I, A A I, (Dimaris, Bramantip) in the fourth. 



I cannot be proved in the second figure, which proves only negatives. 



(4) To prove O. One premiss must be negative (Rule 6). 

 P, being distributed in the conclusion, must be distributed in the 

 major premiss, and M must also be once distributed. Further 

 more, as we are seeking premisses which prove O only, and not E, 

 vS will be undistributed in the minor. 



(a) If the major premiss is E, both P and M are distributed 

 in it whether it be M eP orPeM, and no term need be distributed 

 in the minor premiss, though M may be. This allows an I minor 

 written either 5 i M or M i S, or an A minor written M a S. 

 Hence we have the six forms : 



