DEMONSTRATION, AND NECESSARY TRUTHS. 153 



mathematical ami physical sciences on the basis of the doctrine against 

 which I now coiUcnil. Wlioever is anxious that a discussion should go 

 to the bottom ot'the subject, must rejoice to see the opposite side of 

 the question worthily represented. If what is said by such a man as 

 Mr. Whewell, in support of an opinion which he has made the founda- 

 tion 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 observation, 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 miaid itself, 

 from the first moment when the meaning of the proposition is appre- 

 hended ; and without any necessity for verifying it by repeated trials, 

 as is requisite in the case of ti-uths really ascertained by observa- 

 tion. 



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. Wliether 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 inter- 

 sect one another, without seeing that fi-om that point they continue to 

 diverge more and more. Experimental proof crowds in upon us in 

 such endless profusion, and without one instance in which there can be 

 even a suspicion of an exception to the rule, that we should soon have 

 a stronger ground for believing the axiom, even as an experimental 

 truth, than we have for almost any of the general truths which we con- 

 fessedly learn from the evidence of our senses. Independently of a 

 priori evidence, we should certainly believe it with an intensity of con- 

 viction far greater than we accord to any ordinary physical truth ; and 

 this too at a time of life much earlier than that from which we date al- 

 most any part of our acquired knowledge, and much too early to admit 

 of our retaining any recollection of the history of our intellectual ope- 

 rations at that period. Where then is the necessity for assuming that 

 our recognition of these truths has a different origin from the rest of our 

 knowledge, when its existence is perfectly accounted for by supposing 

 its origin to be the same ? when the causes which produce belief in all 

 other instances, exist in this instance, and in a degree of strength as 

 much superior to what exists in other cases, as the intensity of the be- 

 lief itself is superior 1 The burden of proof lies upon the advocates of 

 the contrary opinion : it is for them to point out some fact, inconsistent 

 with the supposition that this part of our knowledge of nature is derived 

 from the same sources as every other part. 



This, for instance, they would be able to do, if they could prove 

 chronologically that we have the conviction (at least practically) so 

 early in infancy as to be anterior to those impressions on the senses, 

 upon which, on the other theory, the conviction is founded. This, 

 however, cannot be proved ; the point being too far back to be wnthin 

 the reach of memory, and too obscure for external observation. The 

 advocates of the a priori theory are obliged to have recourse to other 



