152 



HIJASONING. 



straight lines cannot enclose a space 

 — or, in other words, two straight 

 lines which have once met do not 

 meet again, but continue to diverge 

 — is an induction from the evidence 

 of our senses. 



This opinion runs counter to a 

 scientific prejudice of long standing 

 and great strength, and there is pro- 

 bably no proposition enunciated in 

 this work for which a more unfavour- 

 able reception is to be expected. It 

 is, however, no new opinion ; and 

 even if it were so, would be entitled 

 to be judged, not by its novelty, but 

 by the strength of the arguments by 

 which it can be supported. I con- 

 sider it very fortunate that so emi- 

 nent a champion of the contrary 

 opinion as Dr. Whewell has found 

 occasion for a most elaborate treat- 

 ment of the whole theory of axioms, 

 in attempting to construct the philo- 

 sophy of the mathematical and physi- 

 cal sciences on the basis of the doc- 

 trine 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 Dr. Whewell, in 

 support of an opinion which he has 

 made the foundation of a systematic 

 work, can be shown not to be con- 

 clusive, enough will have been done, 

 without going elsewhere in quest of 

 stronger arguments and a more power- 

 ful 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 enclose 

 a space if we had never seen a straight 

 line : thus much being admitted by 

 Dr. Whewell and by all, in recent 

 times, who have taken his view of the 

 subject. But they contend that it 

 is not experience which proves the 

 axiom ; but that its truth is per- 

 ceived d priori, by the constitution 

 of the mind itself, from the first 

 moment when the meaning of the 

 proposition is apprehended, and with- 



out any necessity for verifpng 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 enclose a space, 

 even if evident independently of ex- 

 perience, is also evident from expe- 

 rience. Whether the axiom needs 

 confirmation or not, it receives con- 

 firmation 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 

 in which there can be even a suspicion 

 of an exception to the rule, that we 

 should soon have stronger ground for 

 believing the axiom, even as an ex- 

 perimental truth, than we have for 

 almost any of the general truths which 

 we confessedly learn from the evi- 

 dence of our senses. Independently 

 of d priori evidence we should cer- 

 tainly believe it with an intensity of 

 conviction 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 almost 

 any part of our acquired knowledge, 

 and much too early to admit of our 

 retaining any recollection of the his- 

 tory of our inteUectuaal operations at 

 that period. Where then is the neces- 

 sity 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 pro- 

 duce 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 belief itself is superior? The 

 burden of proof lies on the advo- 

 cates of the contrary opinion : it is 

 for them to point out some fact in- 

 consistent with the supposition that 

 this part of our knowledge of nature 



