DEMONSTRATION, AND NECESSARY TRUTHS. 311 



posing, therefore, such to be the case, we can trans- 

 port ourselves thither in imagination, and can frame a 

 mental image of the appearance which one or both of 

 the lines must present at that point, which we may 

 rely upon as being precisely similar to the reality. 

 Now, whether we fix our contemplation upon this 

 imaginary picture, or call to mind the generalizations 

 we have had occasion to make from former ocular 

 observation, we shall either way be equally satisfied, 

 that a line which, after diverging from another straight 

 line, begins to approach to it, produces the impression 

 on our senses which we describe by the expression, 

 "a bent line/' not Jby the expression, "a straight 

 line." 



6. The first of the two great arguments in support 

 of the theory that axioms are a priori truths, having, 

 I think, been sufficiently answered; I proceed to the 

 second, on which most stress is usually laid, and which 

 is chiefly insisted upon by Mr. Whewell. Axioms 

 (it is asserted) are conceived by us not only as true, 

 but as universally and necessarily true. Now, experi- 

 ence cannot possibly give to any proposition this 

 character. I may have seen snow a hundred times, 

 and may have seen that it was white, but this cannot 

 give me entire assurance even that all snow is white ; 

 much less that snow must be white. "However many 

 instances we may have observed of the truth of a 

 proposition, there is nothing to assure us that the 

 next case shall not be an exception to the rule. If it 

 be strictly true that every ruminant animal yet known 

 has cloven hoofs, we still cannot be sure that some 

 creature will not hereafter be discovered which has the 

 first of these attributes, without having the other. . . . 

 Experience must always consist of a limited number 



