306 REASONING. 



attempting to construct the philosophy of the mathe- 

 matical and physical sciences on the basis of the 

 doctrine against which I now contend. Whoever is 

 anxious that a discussion should go to the bottom of 

 the subject, must rejoice to see the opposite side of the 

 question worthily represented. If what is said by 

 such a man as Mr. Whew ell, in support of an opinion 

 which he has made the foundation of a systematic 

 work, can be shown not to be conclusive, enough 

 will have been done without going further to seek 

 stronger arguments and a more powerful adversary. 



It is not necessary to show that the truths which 

 we call axioms are originally suggested by observa- 

 tion, and that we should never have known that two 

 straight lines cannot inclose a space if we had never 

 seen a straight line : thus much being admitted by 

 Mr. Whewell, and by all, in recent times, who have 

 adopted his view of the subject. But they contend, 

 that it is not experience which proves the axiom ; but 

 that its truth is perceived a priori, by the constitution 

 of the mind itself, from the first moment when the 

 meaning of the proposition is apprehended; and without 

 any necessity for verifying it by repeated trials, as is 

 requisite in the case of truths really ascertained by 

 observation. 



They cannot, however, but allow that the truth of 

 the axiom, Two straight lines cannot inclose a space, 

 even if evident independently of experience, is also 

 evident from experience. Whether the axiom needs 

 confirmation or not, it receives confirmation in almost 

 every instant of our lives; since we cannot look at any 

 two straight lines which intersect one another, without 

 seeing that from that point they continue to diverge 

 more and more. Experimental proof crowds in upon 

 us in such endless profusion, and without one instance 



