342 THE SCIENCE OF LOGIC 



rule given by the c in Baroco holds good for all the moods of the 

 second figure : it is the premiss preceding c (i.e. the minor) we 

 are to omit. And, similarly, Bocardo gives the rule for all the 

 moods of the third figure: i.e. it is the original major we are to 

 omit. These rules are embodied in the mnemonic lines given in 

 some Scholastic treatises : 



Majorem servat, variatque SECUNDA Minorem. 

 TERTIA Majorem variat, servatque Minor em.^ 

 By recognizing the processes of obversion and contraposition, 

 we may extend the doctrine of reduction in various directions, 

 beyond that of reducing the moods of the other figures to some 

 mood of the first. We may, for instance, by obversion, reduce 

 any given mood to another mood of different quality in the same 

 figure. For example, Darapti may be thus reduced to Felapton. 



MaP- MeP 



MaS- &amp;gt;MaS 



Si P S o P 



\ 

 SiP&amp;lt; SiP 



Again, we may show that every mood of the &quot; imperfect &quot; 

 figures may be reduced not merely to some one or other of the 

 moods of the first figure, but to any mood we may choose of this 

 figure. This will be shown to be possible if we can show that 

 the moods of the first figure are mutually reducible to one 

 another. But Barbara may be thus reduced to Celarent : 



MaP- &amp;gt; M eP 

 S a M ~ &amp;gt; S a M 



S aP S eP 



I 

 S aP &amp;lt; - S aP 



Similarly Celarent may be reduced to Barbara. So, also, Darii 

 may be reduced to Ferio ; and, vice versa, Ferio to Darii. Hence, we 

 have only to show that Celarent is reducible to Ferio and vice 

 versa, or that Barbara is reducible to Darii and vice versa. 

 Some, indeed, maintain that it is not really necessary to reduce 

 Darii to Barbara, or Ferio to Celarent ; that Darii is really the 

 same as Barbara, and Celarent the same as Ferio, since we know 

 that the l&amp;lt; Some S s &quot; referred to in the conclusions of Darii and 



1 ZlGLIARA, op. Clt., (35), X. 



