362 THE SCIENCE OF LOGIC 



shown by the context to be equivalent to &quot;Since&quot; (134), then 

 the hypothetical proposition If (Since) A is B y C is D is really 

 the condensed expression of a mixed hypothetical syllogism, 

 omitting the major premiss and combining in one single state 

 ment the minor premiss and the conclusion. 



179. THE PURE DISJUNCTIVE (ALTERNATIVE) SYLLOGISM. 

 The form of syllogism in which both premisses are disjunctives as 

 distinct from the mixed disjunctive syllogism (180) is so rare, if, 

 indeed, it occurs at all, as scarcely to call for mention. It would 

 appear to be at all events theoretically possible : since pure hypo 

 thetical syllogisms are possible, and their constituent propositions 

 may be expressed as disjunctives. We know that the proposition, 

 If S is not P it is Q (with its contra positive, If S is not Q it is P) 

 is the hypothetical expression of the disjunctive : 5 is either P or 

 Q (146). Similarly, the hypothetical If S is P it is Q (with its 

 contrapositive, If S is not Q it is not P\ expresses the disjunctive, 

 S is either P or Q. 



But, by confining ourselves to alternative premisses we 

 confine ourselves to affirmative premisses : for all alternatives are 

 affirmatives. Hence, the syllogistic rules of quality have no appli 

 cation here. Professor Welton further states 1 that &quot; we only 

 secure a middle term when one of the alternatives in the minor 

 premise negatives one of those in the major premise. From 

 5 is either P or Q 

 S is either P or R 



no conclusion can be drawn, except that 5 is either P or Q or R 

 which simply sums up the premises. But from 

 5 is either P or Q, 

 S is either P or R, 



we can draw the conclusion 5 is either Q or R. This will 

 perhaps be more clearly seen if each premise is expressed as a 

 hypothetical proposition. We can write the premises in the form 



If Sis Pitt s Q, 

 If S is~R itis~P y 



whence it follows that If S is R it is Q, which expresses the dis 

 junctive 5 is either Q or R.&quot; 



Indeed it may be doubted whether we ever draw a conclusion 

 from two such disjunctive premisses without thus mentally 

 changing them into hypotheticals. 



l op.cit.&amp;gt; p. 350. 



