THEORIES CONCERNING AXIOMS. 301 



present ;* let us suppose it (with Mr. Spencer) to be the in- 

 oonceivableness of its reverse. 



Let us now add a second step to the argument : we require, 

 what ? Another assumption ? No : the same assumption a 

 second time ; and so on to a third, and a fourth. I confess I 

 do not see how, on Mr. Spencer s own principles, the repeti 

 tion of the assumption at all weakens the force of the argu 

 ment. If it were necessary the second time to assume some 

 other axiom, the argument would no doubt be weakened, 

 since it would be necessary to its validity that both axioms 

 should be true, and it might happen that one was true and 

 not the other : making two chances of error instead of one. 

 But since it is the same axiom, if it is true once it is true 

 every time; and if the argument, being of a hundred links, 

 assumed the axiom a hundred times, these hundred assump 

 tions would make but one chance of error among them all. 

 It is satisfactory that we are not obliged to suppose the 

 deductions of pure mathematics to be among the most uncer 

 tain of argumentative processes, which on Mr. Spencer s 

 theory they could hardly fail to be, since they are the longest. 

 But the number of steps in an argument does not subtract 

 from its reliableness, if no new premises, of an uncertain cha 

 racter, are taken up by the way. 



To speak next of the premises. Our assurance of their 

 truth, whether they be generalities or individual facts, is 

 grounded, in Mr. Spencer s opinion, on the inconceivableness 

 of their being false. It is necessary to advert to a double 

 meaning of the word inconceivable, which Mr. Spencer is 

 aware of, and would sincerely disclaim founding an argument 

 upon, but from which his case derives no little advantage 

 notwithstanding. By inconceivableness is sometimes meant, 

 inability to form or get rid of an idea ; sometimes, inability to 

 form or get rid of a belief. The former meaning is the most 

 conformable to the analogy of language ; for a conception 



* Mr. Spencer is mistaken in supposing me to claim any peculiar &quot;neces 

 sity&quot; for this axiom as compared with others. I have corrected the expression* 

 which led him into that misapprehension of my meaning. 



