324 THE SCIENCE OF LOGIC 



3. If either premiss is negative the major must be universal ; 

 or, as expressed in Scholastic logic : 



1 . Si major affirmat, sit minor generalis ; 



2. Si minor affirmat, sit condusio particulars ; 



3. Si una pramissarum neget, sit major generalis. 



(1) If the major be affirmative, M, which is its predicate, is 

 undistributed. It must therefore be distributed in the minor 

 premiss (Rule 3). It is subject in the latter : therefore this must 

 be universal. 



(2) This rule has the same reason as the second special rule 

 of the third figure. 



(3) This rule has the same reason as the second special rule 

 of the second figure. 



It follows as a corollary from the first and third of these rules 

 that neither of the premisses of a syllogism in the fourth figure can 

 be a particular negative (O) proposition. 



(b) Applying these three rules to the eight combinations of 

 premisses, we eliminate A I and A O by the first, and O A by the 

 third, thus leaving five combinations. Of these five A E is the 

 only combination which can here yield two conclusions, viz. E 

 and O. For, the second of the rules given above forbids an A 

 conclusion from A A, and an E conclusion from E A ; while E I 

 and A I yield only particular conclusions (Cor. 2, 156). 



Thus we have in the fourth figure six valid syllogisms, 1 

 namely : A A I, A E E, (A E O), I A I, E A O, E I O. 



l62. THE &quot;ORIGINAL&quot; OR &quot;NAMED&quot; MOODS AND THE 



&quot; SUBALTERN &quot; MOODS. The result of our investigation, there 

 fore, is this, that out of the sixty -four possible moods, twenty-four 

 only are valid, viz. six in each of the four figures. These are re 

 spectively : 



1 Mediate axioms, applicable to the second and third figures respectively, will 

 be given below (169, 170). Various unsuccessful attempts have been made to frame 

 an axiom expressive of the line of inference in the fourth figure unsuccessful be 

 cause the lines of inference embodied in its moods are not distinct from those of the 

 other three figures (171). The following purely extensive or class-inclusion axiom, 

 suggested by Mr. Johnson (apud KEYNES, op. cit., p. 338), is not without interest : 

 &quot; Three classes cannot be so related, that the first is wholly included in the second, 

 the second wholly excluded from the third, and the third partly or wholly included 

 in the first &quot;. This is sufficiently evident, but how it applies to the fourth figure is 

 not at first sight apparent. It &quot; affirms the validity of two antilogisms ; in other 

 words it declares the mutual incompatibility of each of the following trios of pro 

 positions : X a F, Y e Z, Z i X; X a 7, Y e Z, Z a X ; and it will be found that these 

 incompatibles yield the six valid moods [including Camenop] of the fourth figure &quot; 

 (ibid.). 



