260 REASONING. 



conviction far greater than \ve 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 know 

 ledge, and much too early to admit of our retaining any 

 recollection of the history of our intellectual operations 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 belief itself 

 is superior? The burden of proof lies on the advocates of 

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

 inconsistent with the supposition that this part of our know 

 ledge 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 had the conviction (at least 

 practically) so early in infancy as to be anterior to those im 

 pressions 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 within the reach of memory, and 

 too obscure for external observation. The advocates of the 

 d priori theory are obliged to have recourse to other arguments. 



* Some persons find themselves prevented from believing that the axiom, 

 tWo straight lines cannot inclose a space, could ever become known to us 

 through experience, by a difficulty which may be stated as follows. If the 

 straight lines spoken of are those contemplated in the definition lines abso 

 lutely without breadth and absolutely straight ; that such are incapable of 

 inclosing a space is not proved by experience, for lines such as these do not pre 

 sent themselves in our experience. If, on the other hand, the lines meant are 

 such straight lines as we do meet with in experience, lines straight enough for 

 practical purposes, but in reality slightly zigzag, and with some, however 

 trifling, breadth ; as applied to these lines the axiom is not true, for two of 

 them may, and sometimes do, inclose a small portion of space. In neither case, 

 therefore, does experience prove the axiom. 



Those who employ this argument to show that geometrical axioms cannot be 

 proved by induction, show themselves unfamiliar with a common and perfectly 



