380 THE SCIENCE OF LOGIC 



in the Aristotelean, form. In the Goclenian sorites, the j^/ pre 

 miss is a majot and the remaining premisses minors ; in the 

 Aristotelean the first is a minor and the remaining ones majors. 

 This is the best practical test for discerning the form to which 

 any given example belongs. Other features of each form have 

 suggested other definitions for the sorites, and other means of dis 

 tinguishing between the two forms. Omitting the bracketed pro 

 positions from the examples given above, we have (i ) the Goclenian 

 and (2) the Aristotelean forms expressed thus : 



(0 (2) 



Every Z is P Every S is X 



Every Y is Z Every X is Y 



Every X is Y Every Y is Z 



Every S is X Every Z is P 



. . Every S is P. .: Every S is P. 



In both cases the premisses are the same, but the order is re 

 versed. Although the order of the premisses in the Goclenian ap 

 proaches nearer to the usual order of premisses in the simple 

 syllogism, still the Aristotelean form, in which each new term 

 appears first as predicate and then as subject, is the more com 

 monly recognized form. 



In either form all the constituent propositions may be hypo- 

 theticals ; and such pure hypothetical chains of reasoning are not 

 uncommon. 



We may also derive a categorical conclusion from such 

 hypothetical sorites by having the concluding syllogism a mixed 

 hypothetical. 



In the Goclenian form the last premiss and the conclusion may 

 be categorical ; for example (where X, Y, Z, etc., stand for pro 

 positions) : 



If Z then C 

 If Y then Z 

 IfX then Y 

 If A then X 

 But A [or, But not C] 

 . . C [or, not A]. 



In the Aristotelean form a categorical minor must be added 

 to the final hypothetical [major] premiss, and be taken in conjunc 

 tion with the suppressed conclusion from this latter, in order to 

 yield a categorical conclusion. Thus : 



