DEMONSTRATION, AND NECESSARY TRUTHS. 313 



is asserted. That there are such truths cannot be 

 doubted. We may take, for example, all relations of 

 number. Three and Two, added together, make Five. 

 We cannot conceive it to be otherwise. We cannot, 

 by any freak of thought, imagine Three and Two to 

 make Seven*." 



Although Mr. Whewell has naturally and properly 

 employed a variety of phrases to bring his meaning 

 more forcibly home, he will, I presume, allow that 

 they are all equivalent ; and that what he means by 

 a necessary truth, would be sufficiently defined, a 

 proposition the negation of which is not only false 

 but inconceivable. I am unable to find in any of 

 Mr. WhewelPs expressions, turn them what way you 

 will, a meaning beyond this, and T do not believe he 

 would contend that they mean anything more. 



This, therefore, is the principle asserted: that pro- 

 positions, the negation of which is inconceivable, or 

 in other words, which we cannot figure to ourselves 

 as being false, must rest upon evidence of a higher 

 and more cogent description than any which experi- 

 ence can afford. And we have next to consider 

 whether there is any ground for this assertion. 



Now I cannot but wonder that so much stress 

 should be laid upon the circumstance of inconceiv- 

 ableness, when there is such ample experience to 

 show, that our capacity or incapacity of conceiving a 

 thing has very little to do with the possibility of the 

 thing in itself ; but is in truth very much an affair 

 of accident, and depends upon the past history and 

 habits of our own minds. There is no more generally 

 acknowledged fact in human nature, than the extreme 

 difficulty at first felt in conceiving anything as pos- 



Philosophy of the Inductive Sciences, i., 54, 55. 



