156 REASONING. 



understood, suffices to verify it." The 

 more this observation is considered 

 the more (I am convinced) it will be 

 felt to go to the very root of the con- 

 troversy. 



§ 6. The first of the two arguments 

 in support of the theory that axioms 

 are d priori truths, having, I think, 

 been sufficiently answered, I proceed 

 to the second, which is usually the 

 most relied on. Axioms ( it is asserted) 

 are conceived by us not only as true, 

 but as universally and necessarily true. 

 Now, experience 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 assur- 

 ance even that all snow is white ; much 

 less that snow must be white. " How- 

 ever 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 of observa- 

 tions ; and, however numerous these 

 may be, they can show nothing with 

 regard 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 re- 

 cord what has happened ; but she can- 

 not find, in any case, or in any accu- 

 mulation 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 sup- 

 plies, in its occurrence, no reason for 

 its recurrence. She contemplates ex- 

 ternal objects ; but she cannot detect 

 any internal bond, which indissolubly 



connects the future with the past, the 

 possible with the real. To learn a 

 proposition by experience, and to see 

 it to be necessarily true, are two alto- 

 gether dififerent processesof thought."* 

 And Pr. Whewell adds, " If any one 

 does not clearly comprehend this dis- 

 tinction of necessary and contingent 

 truths, he will not be able to go along 

 with us in our researches into the 

 foundations of human knowledge ; nor, 

 indeed, to pursue with success any 

 speculation on the subject." f 



In the following passage we are told 

 what the distinction is, the non-recog- 

 nition of which incurs this denuncia- 

 tion. " Necessary truths are those in 

 which we not only learn that the pro- 

 position is true, but see that it must 

 be true ; in which the negation of the 

 truth is not only false, but impossible ; 

 in which we cannot, even by an effort 

 of imagination, or in a supposition, 

 conceive the reverse of that which is 

 asserted. That there are such truths 

 cannot be doubted. We may take, 

 for example, all relations of number. 

 Three and Two added together made 

 Five. We cannot conceive it to be 

 otherwise. We cannot, by any freak 

 of thought, imagine Three and Two 

 to make Seven." + 



Although Dr. Whewell has natu- 

 rally and properly employed a variety 

 of phrases to bring his meaning more 

 forcibly home, he would, 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 his expres- 

 sions, turn them what way you will, 

 a meaning beyond this, and I do not 

 believe he would contend that they 

 mean anything more. 



This, therefore, is the principle 

 asserted : that propositions, the nega- 

 tion of which is inconceivable, or in 

 other words, which we cannot figure to 

 ourselves as being false, must rest on 

 evidence of a higher and more cogent 



* History of Scientijie Ideas, i. 65-67. 

 t Ibid. 60. } Ibid. 58, 59. 



