was taken for granted? The geometrician never attempts, and is not called upon, to prove that he has in his mind those conceptions which he calls lines, circles, and triangles. This is always conceded to him. He merely proves what the nature and properties and relations of these ideal figures are. So in regard to knowing and being; I hold these conceded, and merely prove what they are in their nature and relations.
Before leaving this head, I have just a remark or two to make on the law of contradiction, and the distinction of necessary and contingent truths. I never set up the law of contradiction as the test of truth; but only as the test of one class of truths, the necessary class. I shall take this opportunity of explaining the point by means of a very simple illustration. Suppose that we wish to test as necessary the truth of the proposition, "two straight lines cannot enclose a space," the way in which we set about it is this: we lay down the counter-statement, "two straight lines can enclose a space," we then perceive that this contradicts the conception which we must form of two straight lines, if we are to form any conception of them at all; in other words, we see that it is equivalent to the proposition, "two straight lines are not two straight lines;" but this again is equivalent to the assertion that "a thing is not what it is," but this contradicts the testing law, the law to which all necessary truth
