DEMONSTRATION, AND NECESSARY TRUTHS. 265 



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 ob- 

 served 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 of observations ; and, how- 

 ever numerous these may be, they can show nothing with re- 

 gard to the infinite number of cases in which the experiment 

 has not been made." Besides, Axioms are not only universal, 

 they are also necessary. Now " experience cannot offer the 

 smallest ground for the necessity of a proposition. She can 

 observe and record what has happened ; but she cannot find, 

 in any case, or in any accumulation of cases, any reason for 

 what must happen. She may see objects side by side ; but she 

 cannot see a reason why they must ever be side by side. She 

 finds certain events to occur in succession ; but the succession 

 supplies, in its occurrence, no reason for its recurrence. She 

 contemplates external objects ; but she cannot detect any in- 

 ternal bond, which indissolubly connects the future with the 

 past, the possible with the real. To learn a proposition by ex- 

 perience, and to see it to be necessarily true, are two altogether 

 different processes of thought."* And Dr. Whewell adds, " If 

 any one does not clearly comprehend this distinction of neces- 

 sary and contingent truths, he will not be able to go along 

 with us in our researches into the foundations of human know- 

 ledge ; nor, indeed, to pursue with success any speculation on 

 the subject."t 



In the following passage, we are told what the distinction 

 is, the non-recognition of which incurs this denunciation. 

 " Necessary truths are those in which we not only learn that 

 the proposition is true, but see that it must be true ; in which 



* History of Scientific Ideas, i. 65-67. t Ibid. 60. 



