370 THE SCIENCE OF LOGIC 



patriotic : but either he did or he did not ; therefore, he is either 

 inconsistent or unpatriotic &quot; (Demosthenes, On the Crown]. 



(3) The simple destructive : &quot; If I am to carry out my plan, I 

 must keep my pupils and write my book ; but either I must drop 

 my pupils or I must drop my book ; therefore I cannot carry out 

 my plan &quot;. 



(4) The complex destructive : &quot; If you are rich, you are able 

 to give me five pounds, and if you are kind you are willing to do 

 so ; but you are either unable or unwilling ; therefore, you are 

 either not rich, or not kind &quot;. 



184. REDUCTION AND VALIDITY OF THE VARIOUS FORMS 

 OF DILEMMA. As in the mixed hypothetical syllogism, so in 

 the dilemma, the constructive and destructive forms are reducible 

 to one another by taking the obverted or full contrapositives of 

 the majors. Thus, the simple constructive^ given in symbols in the 

 preceding section, may be reduced to the following : 



&quot; If E is not F, A is not B ; and if E is not F, C is not D ; 

 But Either A is B or C is D ; 

 Therefore E is F :&quot; 



which is the simple destructive form. As a concrete example, 

 the simple destructive dilemma &quot; If I am to regain health I 

 must give up work and take a sea trip ; but I cannot do both ; 

 therefore I cannot regain my health &quot; may be put in the simple 

 constructive form &quot; If I either continue to work, or abandon the 

 sea trip, I cannot regain my health ; but I must do either ; there 

 fore I cannot regain my health V 



A dilemma ^formally valid i.e. its conclusion follows neces 

 sarily from its premisses, and is necessarily true if they are true 

 provided its conclusion is drawn in the way explained, viz. by 

 alternatively positing antecedents, or sublating consequents, of 

 a compound hypothetical major. The principle on which the 

 reasoning is based is that involved in all inferences from hypo- 

 theticals : that the antecedent is a &quot; sufficient reason &quot; for the 

 consequent. 



A conclusive or demonstrative dilemma must, however, not 

 only be formally valid : it must, in addition, be materially valid, 

 i.e. its premisses must be true. Defect of truth in the premisses 

 is a material fault ; but the conditions required for truth, in the 

 peculiar premisses of the dilemma, are such that defect of truth 



l apud WELTON, Logic, i., p. 881. 



