DEMONSTRATION AND NECESSARY TRUTHS. 



159 



simple inspection, we cannot so much 

 as call up in our imagination two 

 straight lines, in order to attempt to 

 conceive them enclosing a space, with- 

 out by that very act repeating the 

 scientific experiment which establishes 

 the contrary. Will it really be con- 

 tended that the inconceivableness of 

 the thing, in such circumstances, 

 proves anything against the experi- 

 mental origin of the conviction ? Is 

 it not clear that in whichever mode 

 our belief in the proposition may have 

 originated, the impossibility of our 

 conceiving the negative of it must, 

 on either hypothesis, be the same? 

 As, then, Dr. Whewell exhorts those 

 who have any difficulty in recognising 

 the distinction held by him between 

 necessary and contingent truths to 

 study geometry, — a condition which 

 I can assure him I have conscien- 

 tiously fulfilled, — I, in return, with 

 equal confidence, exhort those who 

 agree with him, to study the general 

 laws of association ; being convinced 

 that nothing more is requisite than a 

 moderate familiarity with those laws 

 to dispel the illusion which ascribes 

 a peculiar necessity to our earliest 

 inductions from experience, and 

 measures the possibility of things in 

 themselves by the human capacity of 

 conceiving them. 



I hope to be pardoned for adding, 

 that Dr. Whewell himself has both 

 confirmed by his testimony the effect 

 of habitual association in giving to an 

 experimental truth the appearance of 

 a necessary one, and afforded a striking 

 instance of that remarkable law in his 

 own person. In his Philosophy of the 

 Inductive Sciences he continually as- 

 serts, that propositions which not only 

 are not self-evident, but which we 

 know to have been discovered gradu 

 ally and by great efforts of genius and 

 patience, have, when once established, 

 appeared so self-evident that, but for 

 historical proof, it would have been 

 impossible to conceive that they had 

 not been recognised from the first 

 by all persons in a sound state of 

 their faculties, " We now despise 



those who, in the Copemican contro- 

 versy, could not conceive the apparent 

 motion of the sun on the heliocentric 

 hypothesis ; or those who, in opposi- 

 tion to Galileo, thought that a uni- 

 form force might be that which 

 generated a velocity proportional to 

 the space ; or those who held there 

 was something absurd in Newton's 

 doctrine of the different refrangibility 

 of different coloured rays ; or those 

 who imagined that when elements 

 combine, their sensible qualities must 

 be manifest in the compound ; or 

 those who were reluctant to give up 

 the distinction of vegetables into 

 herbs, shrubs, and trees. We cannot 

 help thinking that men must have 

 been singularly dull of comprehension 

 to find a difficulty in admitting what 

 is to us so plain and simple. We 

 have a latent persuasion that we in 

 their place should have been wiser 

 and more clear - sighted ; that we 

 should have taken the right side, and 

 given our assent at once to the truth. 

 Yet in reality such a persuasion is a 

 mere delusion. The persons who, in 

 such instances as the above, were on 

 the losing side, were very far, in most 

 cases, from being persons more preju- 

 diced, or stupid, or narrow-minded, 

 than the greater part of mankind now 

 are ; and the cause for which they 

 fought was far from being a mani- 

 festly bad one, till it had been so 

 decided by the result of the war. . . , 

 So complete has been the victory of 

 truth in most of these instances, that 

 at present we can hardly imagine the 

 struggle to have been necessary. The 

 very essence of these triumphs is, that 

 they lead us to regard the views we 

 reject as not only false but inconceiv- 

 able."* 



This last proposition is precisely 

 what I contend for ; and I ask no 

 more, in order to overthrow the whole 

 theory of its author on the nature of 

 the evidence of axioms. For what 

 is that theory? That the truth of 

 axioms cannot have been learnt from 



* Ifovum Organum Renovatum, pp. 32, 33. 



