DEMONSTRATION, AND NECESSARY TRUTHS. 341 



own absence, which is a contradiction ; therefore c is 

 not a mark of d. 



5. It has even been held by some philosophers, 

 that all ratiocination rests in the last resort upon a 

 reductio ad absurdum ; since the way to enforce assent 

 to it, in case of obscurity, would be to show that if 

 the conclusion be denied we must deny some one at 

 least of the premisses, 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 premisses and rejecting the 

 conclusion without a contradiction in terms. This 

 theory, however, is quite inadmissible as an explana- 

 tion of the grounds on which ratiocination itself rests. 

 If any one denies the conclusion notwithstanding his 

 admission of the premisses, he is not involved in any 

 direct and express contradiction until he is compelled 

 to deny some premiss ; 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 contradic- 

 tion in terms : he can only be forced to a contradic- 

 tion (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 

 a thing, 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 premisses, fails to draw 



