HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 369 



(4) The complex destructive 



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



but, either E is not F, or G is not //[or, not both E is F 



and G is H} ; 

 therefore, either A is not B&amp;gt; or C is not D [or, not both A is 



B and C is D\ 



It will be noticed that in the simple destructive dilemma both consequents 

 must follow (conjointly) from the antecedent of the major : it would not suffice 

 that either follow (alternatively) : from the major &quot;If A is B, either C is D 

 or E is /%&quot; we can derive nothing by means of the alternative minor &quot; Either 

 C is not D or E is not F&quot; ; for the latter does not deny or sublate the con 

 sequent of the hypothetical, &quot; Either C is D or E is F &quot; : the two propositions 

 are compatible. To get a conclusion from the given major, we should need as 

 minor the remotive proposition &quot; Neither C is D nor E is F : which would 

 give us not a dilemma, but a mixed hypothetical syllogism in the Modus 

 To I lens. 1 



Similarly in regard to the complex destructive dilemma, we could not have 

 as major the proposition &quot; If W then Y or Z ; and if X then Y or Z &quot; instead 

 of &quot; If W then Y; and if X then Z &quot; for, in order to get a conclusion from 

 the former major by the destructive way of sublating consequents we should 

 need as minor &quot; Neither Y nor Z &quot; / which would give us not a dilemma but 

 a compound or double mixed hypothetical syllogism in the Modus Tollens 

 with conclusion &quot; Neither W nor X &quot;. 



The following simple examples will help to familiarize the 

 learner with those forms of argument : 



(1) The simple constructive : &quot; If I tell the truth or if I tell a 

 lie, I shall get into trouble ; I must either tell the truth or tell 

 a lie ; therefore, I must get into trouble &quot;. 



(2) The complex constructive : &quot;If Aeschines joined in the 

 public rejoicings, he is inconsistent ; if he did not, he is un- 



(// both A is B and C is D, then E is F ; and in the same hypothesis G is H ; 

 but, either C is not D or G is not H [or, not both C is D and G is H] ; 

 therefore, Either A is not B or C is not D [or, not both A is B and C is D]. 

 (If eitlier A is B or C is D, then E is F ; and in the same hypothesis G is H ; 

 (b) 1 but either C is not D or G is not H [or, not both C is D and G is H] ; 

 [therefore, Neither A is B nor C is D. 



1 Mr. Joseph recognizes this form of argument as a simple destructive dilemma, 

 citing as an example one of Zeno s arguments against the reality of motion (op. cit., 

 P- 332) : 



&quot; If a body moves it must either move in the place where it is, or in the place 

 where it is not ; 



&quot; But it can neither move in the place where it is nor in the place where it is 

 not ; 



&quot; Therefore, it cannot move.&quot; 



Probably most people would be inclined to regard such an argument as a dilemma, 

 because it has a hypothetical premiss and offers alternatives ; but it offers them only 

 to sublate them totally ; hence it does not fall within the definition we have adopted 

 (cf. 185). 



VOL. I. 24 



