10 



doubt whether these Axioms are evident at all ; should 

 think that it is an error to assert that there exist, in such 

 sciences as Mechanics or Chemistry, Fundamental Ideas, fit 

 to be classed with Space, as being, like it, the origin of 

 Axioms. 



In speaking of all the Fundamental Ideas as being alike 

 the source of Axioms when clearly possessed, without dwelling 

 sufficiently upon the amount of mental discipline which is re- 

 quisite to give the mind this clear possession of most of them ; 

 and in not keeping before the reader the different degrees of 

 evidence which, in most minds, the Axioms of different sciences 

 naturally have, I have, as I have said, given occasion to my 

 readers to misunderstand me. I will point out one or two 

 passages which show that this misunderstanding has occurred, 

 and will try to remove it. 



The character of axiomatic truths seen by intuition is, 

 that they are not only seen to be true, but to be necessary ; 

 that the contrary of them is not only false, but inconceivable. 

 But this inconceivableness depends entirely upon the clear- 

 ness 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 

 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 assertion, 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 Sub- 

 stance, it may not appear inconceivable, that by chemical 

 operations, we should generate new matter, or destroy matter 

 which already exists. 



