HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 375 



it is proportionately dangerous ; and it may be retorted with very 

 disconcerting results if not skilfully used. 



UEBERWEG 1 emphasizes &quot; choice of alternatives, all leading to the same 

 conclusion &quot; as the essential character of the dilemma. This would exclude 

 the complex forms altogether, while it would include some forms of argument 

 which are really mixed hypothetical or mixed disjunctive syllogisms. 



HAMILTON 2 and LOTZE 3 give as the dilemma a form of argument which 

 is really the Modus Tollens of the mixed hypothetical syllogism. It may be 

 expressed as follows : 



If X then either Y or Z ; 

 But neither Y nor Z ; 

 Therefore not X. 



This, evidently, gives no choice of alternatives ; but the dilemma is sup 

 posed to give such a choice : and it cannot do so unless there be a disjunctive 

 premiss. 



THOMSON S definition 4 of a dilemma as &quot; a syllogism with a conditional 

 premiss, in which either the antecedent or the consequent is disjunctive &quot; is 

 altogether too wide. It does not demand an alternative minor, and so it in 

 cludes many forms of mixed hypothetical syllogism, such as that given above. 



Mr. JOSEPH defines the dilemma as &quot; a hypothetical argument offering 

 alternatives and proving something against an opponent in either case &quot;. 

 This makes room for the form illustrated by the example of Zeno s argument, 

 as a simple destructive dilemma. 



MANSEL, WHATELY, JEVONS, and CLARKE reject the simple destruc 

 tive form of the dilemma, apparently because the same conclusion may be 

 reached by totally denying the consequents of the major, as by alternatively 

 denying them, i.e. by the Modus Tollens of the mixed hypothetical syllogism. 

 This is true, but it is no reason why we should not recognize both ways of 

 reaching the conclusion as distinct. Moreover, the same is true of the simple 

 constructive form : we can get the same conclusion by conjunctively (copula- 

 tively) affirming the antecedents of the major, as by alternatively affirming 

 them, i.e. by the Modus Ponens of the mixed hypothetical syllogism. Hence, 

 to be consistent, those logicians should reject the simple constructive, as well 

 as the simple destructive, dilemma. Besides, these are mutually reducible ; 

 hence, they must stand or fall together. 



The view of the dilemma set forth above (183) is that propounded by 

 WELTON, KEYNES, FOWLER, and STOCK, among others. It attaches the 

 name dilemma to a form of argument sufficiently distinct from those previously 

 set forth in the present chapter. It seems, therefore, preferable, and more 

 conducive to clearness than any of the other views just mentioned. 



WELTON, op. cit., bk. iv., chap. v. KEYNES, Formal Logic, pp. 354 sqq. 

 JOSEPH, Logic, p. 166 sqq., 312 sqq. 



1 Logic (Eng/tr.), p. 455. * Lectures on Logic, i., p. 350. 



3 Logic (Eng, tr.), i., p. 127. 4 Laws of Thottght, p. 203. 



