vi CONCERNING NECESSARY TRUTHS 139 



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 

 demonstrated by Euclid would for ever retain their cer- 

 tainty 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 

 conceived by the mind with the same facility and distinct- 

 ness, 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 demon- 

 strate its falsehood. Were it demonstratively false, it would 

 imply a contradiction, and could never be distinctly con- 

 ceived 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 need- 

 ful 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 in- 

 tuitively and demonstratively certain; in other 

 words, that they are necessary and, in that re- 

 spect, differ from all other kinds of belief. 



What is meant by the assertion that " pro- 

 positions of this kind are discoverable by the 



