ABRIDGED AND CONJOINED SYLLOGISMS 381 



If A then X 



If X then V 



If Y then Z 



If Z then C 

 [. .I/A then C] 



But A [or, But not C] 

 .-. C[or, not A\ 



The following may be taken as an example of the mixed 

 hypothetical Goclenian sorites : &quot; If the human soul can form 

 abstract, universal concepts, it has an activity beyond the power 

 of all material agencies ; if it has such an activity, its being must 

 be superior to that of matter ; if its mode of being is above matter, 

 it is spiritual; if it is spiritual, its existence is independent of its 

 union with the body ; if this be so, it will continue to exist after 

 the dissolution of the body ; if it continues so to exist, then it 

 must be immortal ; but the soul can form abstract, universal con 

 cepts ; therefore the soul is immortal &quot;. 



1 89. FIGURES, MOODS, AND SPECIAL RULES OF THE SORITES. 

 The forms of sorites we have been dealing with so far, yield 

 constituent syllogisms in the first figure. The special rules for 

 their validity will, therefore, be mere applications of the special 

 rules of the first figure, and will be grounded on the same general 

 rules of syllogism as these were (161). 



Taking the Aristotelean sorites, we see that the first premiss is 

 a minor, that the others are majors, that the suppressed con 

 clusions are minors. Now the minors, whether expressed or 

 understood, must be all affirmative ; for if any of them were nega 

 tive the major would have to be affirmative, leaving its predicate 

 undistributed, and the immediate conclusion would have to be 

 negative, distributing that same predicate : hence illicit major. 

 Furthermore, only the last [major] premiss can be negative ; for 

 were any preceding [major] premiss negative it would yield a 

 negative conclusion to be combined as minor premiss with the 

 succeeding major ; and thus some constituent syllogism would 

 have two negative premisses. Hence the rule of quality : 

 ( I ) Only one premiss, and that the last, can be negative. 

 Since, then, all the premisses except the last must be affirma 

 tive, it follows that all of them, except the first, must be universal ; 

 for, were any, except the first, particular, the succeeding syllogism 

 (in the first figure) would have a particular major, thus involving 

 undistributed middle. Hence the rule of quantity : 



