DEMONSTRATION, AND NECESSARY TRUTHS. 275 



which, according to his theory, is the test of axioms, " de- 

 pends entirely upon the clearness of the Ideas which the 

 axioms involve. So long as those Ideas are vague and indis- 

 tinct, the contrary of an Axiom may be assented to, though 

 it cannot be distinctly conceived. 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 asser- 

 tion, that two straight lines may inclose 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 processes, 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 operations, we should generate new matter, 

 or destroy matter which already exists."* Necessary truths, 

 therefore, are not those of which we cannot conceive, but 

 " those of which we cannot distinctly conceive, the contrary."t 

 So long as our ideas are indistinct altogether, we do not know 

 what is or is not capable of being distinctly conceived ; but, 

 by the ever increasing distinctness with which scientific men 

 apprehend the general conceptions of science, they in time 

 come to perceive that there are certain laws of nature, which, 

 though historically and as a matter of fact they were learnt 

 from experience, we cannot, now that we know them, distinctly 

 conceive to be other than they are. 



The account which I should give of this progress of the 

 scientific mind is somewhat different. After a general law of 

 nature has been ascertained, men's minds do not at first acquire 

 a complete facility of familiarly representing to themselves the 

 phenomena of nature in the character which that law assigns 

 to them. The habit which constitutes the scientific cast of 

 mind, that of conceiving facts of all descriptions conformably 

 to the laws which regulate them phenomena of all descrip- 

 tions according to the relations which have been ascertained 

 really to exist between them ; this habit, in the case of newly 



* Phil, of Disc., p. 338. f It>. P- 463. 



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