DEMONSTRATION AND NECESSARY TRUTHS. 



i6i 



The other instance which I shall 

 quote is a truly astonishing one, and 

 may be called the reductio ad absur- 

 dum of the theory of inconceivableness. 

 Speaking of the laws of chemical com- 

 position, Dr. Whewell says : * ** That 

 they could never have been clearly 

 understood, and therefore never firmly 

 established, without laborious and ex- 

 act experiments, is cei-tain ; but yet 

 we may venture to say, that being 

 once known, they possess an evidence 

 beyond that of mere experiment. For 

 how in fact can we conceive combina- 

 tions otherwise than as definite in kind 

 and quality ? If we were to suppose 

 each element ready to combine with 

 any other indifferently, and indiffer- 

 ently in any quantity, we should have 

 a world in which all would be con- 

 fusion and indefiniteness. There 

 would be no fixed kinds of bodies. 

 Salts, and stones, and ores would 

 approach to and graduate into each 

 other by insensible degrees. Instead 

 of this, we know that the world con- 

 sists of bodies distinguishable from 

 each other by definite differences, cap- 

 able of being classified and named, 

 and of having general propositions 

 asserted concerning them. And as 

 we cannot conceive a world in which 

 this shduld not be the case, it would 

 appear that we cannot conceive a 

 state of things in which the laws of 

 the combination of elements should 

 not be of that definite and measured 

 kind which we have above asserted." 



That a philosopher of Dr. Whewell's 

 eminence should gravely assert that 

 we cannot conceive a world in which 

 the simple elements should combine 

 in other than definite proportions ; 

 that by dint of meditating on a 

 scientific truth, the original discoverer 

 of which was still living, he should 

 have rendered the association in his 

 own mind between the idea of com- 

 bination and that of constant propor- 

 tions so familiar and intimate as to 

 be unable to conceive the one fact 

 without the other, is so signal an 



* History of Scientific Idea*, ii. 25, 26, 



instance of the mental law for which 

 I am contending, that one word mor« 

 in illustration must be superfluous. 



In the latest and most complete 

 elaboration of his metaphysical system, 

 (the Philosophy of Discovery, ) as well 

 as in the earlier discourse on the 

 Fundamental Antithesis of Philosophy, 

 reprinted as an appendix to that 

 work. Dr. Whewell, while very can- 

 didly admitting that his language was 

 open to misconception, disclaims hav- 

 ing intended to say that mankind in 

 general can now perceive the law of 

 definite proportions in chemical com- 

 bination to be a necessary truth. All 

 he meant was that philosophical 

 chemists in a future generation may 

 possibly see this. " Some truths may 

 be seen by intuition, but yet the 

 intuition of them may be a rare and 

 a difficult attainment."* And he 

 explains that the inconceivableness 

 which, according to his theory, is 

 the test of axioms, " depends entirely 

 upon the clearness of the ideas which 

 the axioms involve. So long as those 

 ideas are vague and indistinct, the 

 contrary of an axiom may be assented 

 to, though it cannot be distinctly con- 

 ceived. It may be assented to, not 

 because it is possible, but because we 

 do not see clearly what is possible. 

 To a person who is only beginning to 

 think geometrically, there may appear 

 nothing absurd in the assertion that 

 two straight lines may enclose a space. 

 And in the same manner, to a person 

 who is only beginning to think of 

 mechanical truths, it may not appear 

 to be absurd, that in mechanical pro- 

 cesses, Reaction should be greater or 

 less than Action ; and so, again, to 

 a person who has not thought steadily 

 about Substance, it may not appear 

 inconceivable, that by chemical opera- 

 tions, we should generate new matter, 

 or destroy matter which already 

 exists." t Necessary truths, there- 

 fore, are not those of which we can- 

 not conceive, but " those of which we 

 cannot distinctly conceive the con- 



rhil. of J)itc,. p. 339. 



t Ibid. p. 338. 



