138 HUME vi 



between these numbers. Propositions of this kind are discover- 

 able by the mere operation of thought without dependence on 

 whatever is anywhere existent in the universe. Though there 

 never were a circle or a triangle in nature, the truths demon- 

 strated by Euclid would for ever retain their certainty and 

 evidence. 



"Matters of fact, which are the second objects of human 

 reason, are not ascertained in the same manner, nor is an 

 evidence of their truth, however great, of a like nature with 

 the foregoing. The contrary of every matter of fact is still 

 possible, because it can never imply a contradiction, and is con- 

 ceived by the mind with the same facility and distinctness, as 

 if ever so conformable to reality. That the sun will not rise 

 to-morrow, is no less intelligible a proposition, and implies no 

 more contradiction, than the affirmation, that it will rise. We 

 should in vain, therefore, attempt to demonstrate its falsehood. 

 Were it demonstratively false, it would imply a contradiction, 

 and could never be distinctly conceived by the mind." (IV. 

 pp. 32, 33.) 



The distinction here drawn between the truths 

 of geometry and other kinds of truth is far less 

 sharply indicated in the " Treatise," but as Hume 

 expressly disowns any opinions on these matters 

 but such as are expressed in the " Inquiry," we may 

 confine ourselves to the latter ; and it is needful 

 to look narrowly into the propositions here laid 

 down, as much stress has been laid upon Hume's 

 admission that the truths of mathematics are 

 intuitively and demonstratively certain ; in other 

 words, that they are necessary and, in that respect, 

 differ from all other kinds of belief. 



What is meant by the assertion that " pro- 

 positions of this kind are discoverable by the 



