HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 373 



is just) ; the love of the gods and the hatred of men, from the 

 other. Granting the truth of the two majors, the two dilemmas are 

 valid : which shows that if we attempt to &quot; rebut &quot; a conclusive di 

 lemma, the &quot; rebutting&quot; dilemma will be either inconclusive itself, 

 or it will reach a conclusion not really incompatible with the original 

 conclusion. But a rebutting dilemma is really successful only 

 when it conclusively establishes a proposition incompatible with 

 the original conclusion. 



The rebutting of a complex constructive dilemma by transposition and 

 negation of consequents may be represented thus : 



IfP then R, and if Q then S; 



But either P or Q; 



Therefore, either R or S ; 

 which is rebutted by 



If P then not S, and if Q then not R; 



But either P or Q; 



Therefore, either not S or not R, 



There is no theoretical reason why the complex destructive dilemma could 

 not be similarly rebutted. Thus the dilemma : 



If P then R, and if Q then S ; 



But either not R or not S ; 



Therefore, either not P or not Q; 

 may be rebutted by 



If not P then S, and if not Q then R, 



But either not S or not R ; 



Therefore, either P or Q. 



But, practically, it is impossible to form new hypotheticals with any 

 plausible show of truth in them by combining the negative of each original 

 antecedent with the other original consequent. The complex destructive 

 must, therefore, be reduced to the complex constructive before being rebutted. 

 Simple dilemmas cannot be thus rebutted, because a transposition of antece 

 dents and consequents cannot be effected. 



(3) The dilemma has often a practical aspect : being used to 

 show that something ought, or ought not, to be, or to have been, 

 done, i.e. to inculcate a line of conduct An apocryphal story 

 represents the Caliph Omar as thus justifying the destruction of 

 the famous Alexandrian library : 



If the books are in conformity with the Koran they are super 

 fluous ; if not they are pernicious. 



Either they are or they are not in such conformity. 



Therefore, being either superfluous or pernicious, they ought to be 

 destroyed. 



This dilemma, though formally valid, is not demonstrative, 



