2. There is another mode in which the distinction of the two elements of knowledge appears, as I have already said (c. i. sect. 2): namely in the distinction of _necessary_, and _contingent_ or _experiential_, truths. For of these two classes of truths, the difference arises from this;--that the one class derives its nature from the one, and the other from the other, of the two elements of knowledge. I have already stated briefly the difference of these two kinds of truths:--namely, that the former are truths which, we see, must be true:--the latter are true, but so far as we can see, might be otherwise. The former are true necessarily and universally: the latter are learnt from experience and limited by experience. Now with regard to the former kind of truths, I wish to show that the universality and necessity which distinguish them can by no means be derived from experience; that these characters do in reality flow from the ideas which these truths involve; and that when the necessity of the truth is exhibited in the way of logical demonstration, it is found to depend upon certain fundamental principles, (Definitions and Axioms,) which may thus be considered as expressing, in some measure, the essential characters of our ideas. These fundamental principles I shall afterwards proceed to discuss and to exhibit in each of the principal departments of science. I shall begin by considering Necessary Truths more fully than I have yet done. As I have already said, necessary truths are those in which we not only learn, that the proposition _is_ true, but see that it _must be_ true; in which the negation of the truth is not only false, but impossible; in which we cannot, even by an effort of imagination, or in a supposition, conceive the reverse of that which is asserted. 3. That there are such truths cannot be doubted. We may take, for example, all relations of number. Three and Two added together make Five. We cannot {59} conceive it to be otherwise. We cannot, by any freak of thought, imagine Three and Two to make Seven. It may be said that this assertion merely expresses what we mean by our words; that it is a matter of definition; that the proposition is an identical one.