HYPOTHETICAL AND DISJUNCTIVE SYLLOGISMS 367 



183. THE DILEMMA: ITS VARIOUS FORMS. Logicians have 

 designated by this title types of arguments more or less closely 

 resembling one another, but not quite identical. This has led to 

 a great variety of definitions. We shall select for special treat 

 ment the form of argument which seems the most important and 

 most deserving ol the title ; referring afterwards to some other 

 lines of treatment 



By the Dilemma (149) we mean a syllogism in which one of 

 the premisses is a conjunctive combination of two or more hypothetical 

 propositions, whose antecedents are alternatively affirmed, or conse 

 quents alternatively denied, in the other premiss, which is a dis 

 junctive or alternative proposition. 



The hypothetical premiss is conjunctive or copulative, i.e. it 

 must contain at least two antecedents, or at least two consequents, 

 so as to yield two distinct hypothetical propositions united con 

 junctively together. This premiss is usually referred to as the 

 major. The disjunctive or alternative premiss which is usually 

 called the minor, though it is usually stated in the first place 

 either alternatively affirms the antecedents, or alternatively denies 

 the consequents, of the major : thus giving us a right to affirm the 

 consequent (categorically) or consequents (alternatively), or to deny 

 the antecedent (categorically) or antecedents (alternatively) of the 

 major, in the conclusion. 



Strictly speaking, where there are three distinct hypothetical and alter 

 nants, the argument should be called a trilemma; when there are/0z/ror more, 

 a tetralemma QI poly lemma; but the name dilemma is used generically for 

 all. 



The dilemma differs from the mixed hypothetical syllogism 

 only in having a combination of hypothetical propositions instead 

 of a single one, for major premiss, and an alternative instead of 

 a categorical minor. In other respects it resembles the mixed 

 hypothetical syllogism. Like the latter it has two moods : it is 

 constructive or destructive according as the minor posits the ante 

 cedents, or sublates the consequents, of the major. 



In the constructive form the major must have (at least) two 

 separate antecedents ; and these may have the same consequent 

 (which may be either categorical or disjunctive), or they may have 

 different consequents. If they have the same consequent they 

 form a simple constructive dilemma ; if they have different con 

 sequents they form a complex constructive dilemma. Similarly, 

 in the destructive form the major must have (at least) two separate 



