THE SCIENCE OF LOGIC 



consequents ; and these may follow either from the same ante 

 cedent (which may be either a simple categorical, a copulative, or 

 an alternative proposition), or from different antecedents. If they 

 follow from the same antecedent we have a simple destructive 

 dilemma ; if they follow from different antecedents we have a 

 complex destructive dilemma. 



We have thus four main forms, which will be better understood 

 from the following symbolic illustrations. They are : 



(1) The s,imple constructive 



If A is B, E is F ; and if C is D, E is F ; 

 but, either A is B&amp;gt; or C is D ; 

 therefore, E is F. 1 



(2) The complex constructive 



If A is B, E is F; and if C is D, G is H ; 

 but, either A is B, or C is D ; - 

 therefore, Either E is F or G is H. 



(3) The simple destructive 



If A is B, C is D ; and if A is B, E is F ; 

 but, either C is not D, or E is not F ; 

 [or, not both C is D, and E is F~\ ; 

 therefore A is not B. 2 



1 The &quot; simple constructive&quot; may yield an alternative conclusion, if the single 

 consequent of the major be an alternative, e.g. : 



If A is B, either E is F or G is H ; and if C is D, either E is F or G is H; 



but, either A is B t or C is D ; 



therefore, either E is F, or G is H. 



Compare the analogous syllogism given above (180) : &quot; M is either P or Q ; S is M ; 

 therefore, S is either P or Q &quot; : which is categorical even though it has a disjunctive 

 conclusion. 



So, too, by prefixing a condition &quot; // X is y,&quot; for example, to the alternative 

 premise &quot; either A is B or C is D, 1 we should get for conclusion &quot; ifX is Y, then either 

 E is F or G is H &quot;. This condition makes the whole dilemma hypothetical, but does 

 not change in any way the character of the reasoning : it is a mere accidental varia 

 tion. 



z The same conclusion may be reached by substituting for the denial contained 

 in the alternative or disjunctive minor, the more complete denial contained in the 

 remotive minor &quot; neither C is D or E is F &quot;. This would give us the two distinct 

 mixed hypothetical syllogisms: 



(a) If A is B,Cis D ; (b) If A is B, E is F; 



but C is not D ; but E is not F ; 



therefore, A is not B. therefore, A is not B. 



But, though these reach the same conclusion as the dilemma, the reasoning in 

 them must not be confounded with the peculiar alternative character of dilemmatic 

 reasoning. 



The following are simple, not complex, destructive dilemmas (cf. preceding 

 note) : 



