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 requisite 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. 8. 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 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 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 Substance, it may not appear inconceivable, that by chemical operations, we should generate new matter, or destroy matter which already exists. Here then we have a difficulty:--the test of Axioms is that the contrary of them is inconceivable; and yet persons, till they have in some measure studied the subject, do not see this inconceivableness. Hence our Axioms must be evident only to a small number of thinkers; and seem not to deserve the name of self-evident or necessary truths. This difficulty has been strongly urged by Mr. Mill, as supporting his view, that all knowledge of truth is derived from experience. And in order that the opposite doctrine, which I have advocated, may not labour under any disadvantages which really do not belong to it, I must explain, that I do not by any means assert that those truths which I regard as necessary, are all equally evident to common thinkers, or evident to persons in all stages of intellectual development. I may even say, that some of those truths which I regard as necessary, and the necessity of which I believe the human mind to be capable of seeing, by due preparation and thought, are still such, that this amount of preparation and thought is rare and peculiar; and I will willingly grant, that to attain to and preserve such a clearness and subtlety of mind as this intuition requires, is a task of no ordinary difficulty and labour.