DEMONSTRATION, AND NECESSARY TRUTHS. 1V7 



are conceived by us not only as true, but as universally and necessarily 

 true. Now, experience can not possibly give to any proposition this char- 

 acter. I may have seen snow a hundred times, and may have seen that it 

 was white, but this can not give me jentire 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 can not be sure that some creature will not hereafter be discov- 

 ered which has the first of these attributes, without having the other 



Experience must always consist of a limited number of observations ; and, 

 however numerous these may be, they can show nothing with I'egard 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 " ex- 

 perience can not offer the smallest ground for the necessity of a proposi- 

 tion. She can observe and record what has happened; but she can not 

 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 can not see a reason 

 why they must ever be side by side. She finds certain events to occur in 

 euccession ; but the succession supplies, in its occurrence, no reason for its 

 recurrence. She contemplates external objects ; but she can not detect any 

 internal bond, which indissolubly connects the future with the past, the pos- 

 sible with the real. To learn a proposition by experience, 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 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- 

 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 m^ust he true; in which the negation of the truth is not only false, but 

 impossible ; in which we can not, even by an effoi-t of imagination, or in 

 a supposition, conceive the reverse of that which is asserted. That there 

 are such truths can not be doubted. We may take, for example, all rela- 

 tions of number. Three and Two added together make Five. We can 

 not conceive it to be otherwise. We can not, by any freak of thought, 

 imagine Three and Two to make Seven."J 



Although Dr. Whewell has naturally 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 any thing moi'e. 



This, therefore, is the principle asserted : that propositions, the negation 

 of which is inconceivable, or in other words, which we can not figure to 

 ourselves as being false, must rest on evidence of a higher and more cogent 

 description than any which experience can afford. 



Now I can not but wonder that so much stress should be laid on the cir- 

 cumstance of inconceivableness, when there is such ample experience to 



* History of Scientific Ideas, i. , 65-67. t Ibid, , i. , 60. % Ibid. , 58, 59. 



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