A REPLY TO SOME CHARGES AGAINST LOGIC 407 



three terms, and of three and only three propositions. But 

 it is a commonplace among present-day logicians that the 

 excessive claims made on behalf of the Aristotelian syllogism 

 by, e.g., Whately, 1 and no less by J. S. Mill, 2 must be rejected. 3 

 The adduction of arguments which do not conform to syllogistic 

 rules is not, therefore, either so startling or so novel as Dr. 

 Mercier seems to suppose. Nevertheless, many of the arguments 

 which he does adduce are really syllogisms in disguise — that is to 

 say, they are arguments only if there be assumed premisses the 

 production of which suffices to turn the argument into a correct 

 syllogism. 



Let us examine some of these examples. 



(1) Argument with only two propositions : 



If The bed contains nothing but geraniums and violas, 

 then It contains no asters. 



This argument is valid because, and only because, neither 

 geraniums nor violas are also asters. It could be thrown into 

 the form of a syllogism, e.g. : 



All the flowers in the bed are geraniums and violas, 

 No geranium or viola is an aster ; 

 Therefore No flower in the bed is an aster. 



(2) Argument without a middle term : 



If His hands were tied behind him, 

 then He could not wipe his nose. 



This argument is clearly elliptical and only appears to be 

 immediately self-evident because of its triviality and great 

 familiarity. The unexpressed middle term which is the neces- 

 sary link of connection between the premisses is the necessity 

 of having a free use of his hands. A similar explanation must 

 be applied to the other arguments on p. 215, designed to 

 illustrate the achievement of this impossibility. 



(3) Argument with an undistributed middle term : 



If Hannibal crossed the Alps, 

 and The part of the Alps that he crossed is impassable for elephants ; 

 then He took no elephants across with him. 



Here Dr. Mercier argues that " the Alps " is not distributed 

 because it is the predicate of an affirmative premiss, and con- 

 sequently " although we do in fact refer to the whole class of 



1 Logic, p. 12. * Logic, ii. 2, I. 3 See Keynes, Formal Logic, p. 387. 



