THE DOCTRINE OF REDUCTION 35 1 



as the minor, and the second (M S) as the major, in Camenes 

 and Dimaris, our conclusions, P e S and P i S, will be the con 

 verses of the conclusions of Celarent and Darii ; and that, on the 

 same hypothesis, the conclusion we get from the premisses of 

 Bramantip, viz. P a S, contains in it the converse of the conclu 

 sion of Barbara. But it is not true that from the premisses of 

 Fesapo or Fresison we can get, by the first figure, a conclusion 

 which will be the converse of that of Ferio : we can, in fact, get 

 no conclusion at all in the first figure about P in terms of S from 

 the premisses of those two moods of the fourth figure ; though 

 the conclusion which we can get about 5 in terms of P was 

 recognized by Aristotle in his treatment of the first figure. 



Aristotle had a truer conception of the relation of what Galen 

 afterwards called the fourth figure, to the first. Although he 

 did not recognize the former in name, he recognized it implicitly 

 in fact ; and his immediate successor, Theophrastus, gave its five 

 moods as supplementary, or Indirect, Moods of the First Figured 

 We can best describe what an &quot; indirect mood &quot; of the first 

 figure is by recalling the fact already referred to (148, 159), that 

 it is the conclusion of the syllogism that determines which of 

 the premisses is major and which is minor. If, therefore, we 

 abstract from the conclusion and consider the premisses alone, 

 we shall have three figures of syllogism instead oifour, viz. (i) one 

 in which M is subject in one premiss and predicate in the other, 

 (2) one in which M is twice predicate, and (3) one in which M is 

 twice subject. But in the first of these figures the extremes will 

 either retain the same position in the conclusion as they had in 

 the premisses, or the reverse. In the former case, the moods will 

 be called the Direct Moods of the First Figure ; in the latter, they 

 will be called Indirect Moods, and the conclusions Indirect Con 

 clusions, of the First Figure. We may, therefore, define an indirect 

 mood of the first figure as a mood in which the position of both 

 extremes in the conclusion is the reverse of their position in the 

 premisses. We know that the direct moods of the first figure 

 are four : that there are four ways of drawing a conclusion about 

 the extreme which is subject in the premisses (S\ in terms of the 

 extreme which is predicate there (P). How many ways are 

 there of drawing a conclusion about the extreme which is predic 

 ate in the premisses (P\ in terms of that which is subject in the 

 premisses (5) ? We can do so in the case of A A (I), E A (E), and 

 1 JOSEPH, op. cit., pp. 258-60. 



