FIGURES AND MOODS OF THE SYLLOGISM 325 



In Figure i, A A A, E A E, A I I, E I O, (A A 1), (E A O), 



In Figure 2, E A E, A E E, E I O, A O O, (E A O), (A E O), 



In Figure 3, A A I, 1 A I, A I I, E A O, O A O, E I O, 



In Figure 4, A A I, A E E, I A I, E A O, E I O, (A E O). 



Of these twenty-four, however, the five we have bracketed 



and brought to the ends of the lines are superfluous^ inasmuch as 



a particular conclusion is derived in them from premisses which 



warrant a corresponding universal conclusion from which latter 



the particular could be got by subalternation. Hence, these five 



moods are called subaltern moods. 



A SUBALTERN MOOD is one in which we derive a particular 

 conclusion from premisses which warrant the corresponding universal 

 conclusion about the same subject?- We may distinguish these 

 five, as &quot;superfluous&quot; from the other nineteen, as &quot;useful&quot; moods. 

 And, since these nineteen have got each a special name, and are 

 hence called the &quot;named&quot; moods, the five subaltern moods are 

 sometimes called the &quot;unnamed&quot; moods although, indeed, 

 modern logicians have coined names for them too. The con 

 clusion of a subaltern mood is also sometimes called a &quot; weakened &quot; 

 conclusion. 



There must, obviously, be a subaltern mood corresponding to 

 each mood (of the twenty-four) which has a universal conclusion. 

 There are five such : two in the first figure, two in the second, 

 and one in the fourth. The third figure can have no subaltern 

 mood because one of its special rules forbids a universal con 

 clusion. 



The subaltern moods are of no practical importance, because 

 we do not usually draw a particular conclusion from premisses 

 which warrant the corresponding universal conclusion ; and if 

 we want the particular, we can get it by subalternation from the 

 latter. The inclusion of the subaltern moods gives, of course, a 

 certain symmetry to the treatment of the syllogism. 



Of the nineteen &quot; named &quot; moods, four belong to the first 

 figure, four to the second, six to the third, and five to the fourth. 

 Their &quot;names&quot; are given in the italicized words of the following 

 traditional mnemonic lines each &quot;name&quot; having three of the 

 four vowels (#, , z, 6} to indicate the quality and quantity of the 



1 i.e. about S in terms of P. From A A in the fourth figure we may draw the 

 conclusion P a S instead of S * P. But the latter is not the subaltern of the former ; 

 it is not about the same subject as the former (P). Hence A A I in the fourth figure 

 is not a subaltern mood, though A A I in the first figure is such. 



