CHAPTER V. 

 HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS. 



174. THE PURE HYPOTHETICAL SYLLOGISM. In classifying 

 syllogisms in a previous chapter (149), we remarked that the rules 

 of the pure categorical syllogism will be found to apply to the 

 forms of reasoning called &quot; pure hypothetical &quot; and &quot; pure dis 

 junctive &quot; syllogisms. The pure hypothetical (or pure conditional) 

 syllogism is one in which a hypothetical (or conditional) conclusion 

 is inferred from two hypothetical (or conditional) premisses. Here, 

 instead of terms subject and predicate we have simple proposi 

 tions antecedent and consequent. These constituent factors must 

 be three in number : the antecedent and consequent of the conclu 

 sion, and the factor which serves as &quot; middle term &quot;. The typical 

 form of such a syllogism, answering to Barbara in the first figure, 

 is the following : 



If B then C ; 



If A then B ; 

 .-. If A then C ; 



where A, B, and C stand for simple propositions, and where the 

 &quot; middle term,&quot; viz. the proposition B, gives the reason why the 

 &quot; minor term,&quot; viz. the proposition A, is asserted in the conclusion 

 as the ground for asserting the &quot; major term,&quot; viz. the proposition 

 C. The reason why A is the ground of C is found in the com 

 parison of both with B. 



The general rules and corollaries which regulate the categori 

 cal syllogism are applicable here. This is most clearly seen when 

 the premisses and conclusion are expressed in the quantified or 

 denotative, rather than in the abstract or modal, form. The words 

 &quot;always,&quot; &quot;never,&quot; &quot;sometimes,&quot; &quot;sometimes not,&quot; determine 

 the quantity of the antecedent of the &quot; If&quot; proposition just as the 

 words &quot;all,&quot; &quot;none,&quot; &quot;some,&quot; &quot;some not,&quot; determine the quan 

 tity of the subject of the categorical proposition. The quantity 

 of the consequent in each &quot;If&quot; proposition depends upon the 



356 



