THEORIES CONCERNING AXIOMS. 19b 



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

 in the last resort on a reductio ad absurdum; since the way to enfoi'ce as- 

 sent 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 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 ratiocina- 

 tion consisted in the impossibility 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 ratiocination itself 

 rests. If any one denies the conclusion notwithstanding his admission of 

 the promises, he is not involved in any direct and express contradiction un- 

 til he is compelled to deny some premise; and he can only be forced to do 

 this by a reductio ad ahsurdiim, 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, there- 

 fore, 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 any 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 syllogis- 

 tic 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. 



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

 vance 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 spontaneous- 

 ly the place which belongs to it, and will receive its share of whatever light 

 may be thrown upon the great intellectual operation of which it forms so 

 important a part. 



CHAPTER VII. 



EXAMINATION OF SOME OPINIONS OPPOSED TO THE PRECEDING DOCTRINES. 



§ 1. Polemical discussion is foreign to the plan of this work. But an 

 opinion which stands in need of much illustration, can often receive it most 

 effectually, and least tediously, in the form of a defense against objections. 

 And on subjects concerning which speculative minds are still divided, a 

 writer does but half his duty by stating his own doctrine, if he does not 

 also examine, and to the best of his ability judge, those of other thinkers. 



In the dissertation which Mr. Herbert Spencer has prefixed to his, in 

 many respects, highly philosophical treatise on the Mind,* he criticises some 

 of the doctrines of the two preceding chapters, and propounds a theory of 

 his own on the subject of first principles. Mr. Spencer agrees with me in 

 3onsidering axioms to be " simply our earliest inductions from experience." 

 But he differs from me " widely as to the worth of the test of inconceiva- 



* Principles of Psychology. 

 13 



