170 REASONING. 



§ 5. It has even been held by some philosophers, that all ratiocina- 

 tion rests in the last resort upon a reductio ad abstirdum ; 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 contradic- 

 tion. And, in accordance with this, many have thought that the pecu- 

 liar nature of the e\adence of ratiocination consisted in the impossibility 

 of admitting the premisses and rejecting the conclusion without a con- 

 tradiction in tei-ms. This theory, however, is quite inadmissible as an 

 explanation of the gi-ounds on which ratiocination itself rests. If any 

 one denies the conclusion notwithstanding his admission of the prem- 

 isses, 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 rcditctm ad ahsurdum, 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 contradiction (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 con-ect argument, as soon 

 as thrown into the syllogistic foiTn, it is evident without the aid of any 

 other syllogism, that he who, admitting the premisses, fails to draw 

 the conclusion, does not conform to the above axiom. 



Without attaching exaggerated importance to the distinction now 

 drawTi, I think it enables us to characterize in a more accurate manner 

 than is usually done, the nature of demonstrative evidence and of logi- 

 cal necessity. That is necessary, fi-om which to withhold our assent 

 would be to \'iolate the above axiom. And since the axiom can only 

 be violated by assenting to premisses and rejecting a legitimate con- 

 clusion from them, nothing is necessary except the connexion between 

 a conclusion and premisses ; of which doctrine, the whole of this and 

 the preceding chapter are submitted as the proof. 



We have now proceeded as far in the theory of Deduction as we 

 can advance in the present stage of our inquiry. Any further insight 

 into the subject requires that the foundation shall have been laid of 

 the philosophic theory of Induction itself; in which theory that of 

 deduction, as a mode of induction, which we have now shown it to be, 

 ■will assume spontaneously the place which belongs to it, and will re- 

 ceive its share of whatever light may be thrown upon the great intel- 

 lectual operation of which it forms so important a part. 



We here, therefore, close the Second Book. The theory of Induc- 

 tion, in the most comprehensive sense of the term, will form the sub- 

 ject of the Third. 



