VI CONCERNING NECESSARY TRUTHS 141 



between the event remembered and the present 

 time. It is wholly inconceivable to me that the 

 event did not happen, so that my assurance respect- 

 ing it is as strong as that which I have respecting 

 any other necessary truth. In fact, the man is either 

 very wise, or very virtuous, or very lucky, perhaps 

 all three, who has gone through life without 

 accumulating a store of such necessary beliefs 

 which he would give a good deal to be able to dis- 

 believe. 



It would be beside the mark to discuss the 

 matter further on the present occasion. It is 

 sufficient to point out that, whatever may be 

 the differences between mathematical and other 

 truths, they do not justify Hume's statement. 

 And it is, at any rate, impossible to prove that the 

 cogency of mathematical first principles is due 

 to anything more than these circumstances ; that 

 the experiences with which they are concerned are 

 among the first which arise in the mind ; that 

 they are so incessantly repeated as to justify us, 

 according to the ordinary laws of ideation, in 

 expecting that the associations which they form 

 will be of extreme tenacity ; while the fact, that 

 the expectations based upon them are always 

 verified, finishes the process of welding them 

 together. 



Thus, if the axioms of mathematics are innate, 

 nature would seem to have taken unnecessary 

 trouble ; since the ordinary process of association 



