292 REASONING. 



done, for the purpose of showing the falsity of the assumption ; 

 which is called a reductio ad absurdum. In such cases, the 

 reasoning is as follows : a is a mark of b, and b of c ; now if c 

 were also a mark of d, a would be a mark of d ; but d is known 

 to be a mark of the absence of a ; consequently a would be a 

 mark of its own absence, which is a contradiction ; therefore c 

 is not a mark of d. 



5. It has even been held by some writers, that all 

 ratiocination rests in the last resort on a reductio ad absur 

 dum ; since the way to enforce assent to it, in case of ob 

 scurity, would be to show that if the conclusion be denied 

 we must deny some one at least of the premises, which, as 

 they are all supposed true, would be a contradiction. And 

 in accordance with this, many have thought that the peculiar 

 nature of the evidence of ratiocination consisted in the impos 

 sibility of admitting the premises and rejecting the conclusion 

 without a contradiction in terms. This theory, however, is 

 inadmissible as an explanation of the grounds on which ratio 

 cination itself rests. If any one denies the conclusion not 

 withstanding his admission of the premises, he is not involved 

 in any direct and express contradiction until he is compelled 

 to deny some premise ; and he can only be forced to do this 

 by a reductio ad absurdum, that is, by another ratiocination : 

 now, if he denies the validity of the reasoning process itself, 

 he can no more be forced to assent to the second syllogism 

 than to the first. In truth, therefore, no one is ever forced 

 to a contradiction in terms : he can only be forced to a con 

 tradiction (or rather an infringement) of the fundamental 

 maxim of ratiocination, namely, that whatever has a mark, has 

 what it is a mark of; or, (in the case of universal propositions,) 

 that whatever is a mark of anything, is a mark of whatever 

 else that thing is a mark of. For in the case of every correct 

 argument, as soon as thrown into the syllogistic form, it is 

 evident without the aid of any other syllogism, that he who, 

 admitting the premises, fails to draw the conclusion, does not 

 conform to the above axiom. 



