seem to us to be true, it must not only explain the facts; it must harmonize with the rest of the contents of our minds, must fill up, so to speak, an empty place therein and be in keeping with the rest of its furniture. In order, then, that we may carry on the reasonings of ordinary life as well as those of science, we must assume the trustworthiness of memory within certain limits, the uniformity of nature, and that an hypothesis that explains a particular group of facts, and at the same time harmonizes with the rest of our beliefs, is true.
Of the axioms of mathematics and the laws of logic, it appears to me that we have self-evident knowledge,—self-evident in the only proper sense of that much abused term, in the sense that doubt of them is impossible. And when I say that doubt of them is impossible, I do not mean that we are unable to rid ourselves of the feeling that they are true; for, as we have seen, that feeling has no evidential or intellectual value whatever. In spite of the fact that it constitutes the foundation of the Theory of Knowledge of the Scottish School, since the feeling that a thing is true when we cannot ascertain its causes is identical with Hamilton's testimony of consciousness, we have seen that it attaches itself to ideas and images which we know do not correspond with reality, and that it cannot, therefore, be a criterion of truth. But when I say that doubt of the axioms of mathematics and the laws of logic is impossible, I mean that the mind cannot even entertain the idea of their being false. We may say that two straight lines can inclose a space, but we cannot think it. The judgment of which the proposition purports to be the expression, not only does not exist, but cannot even be con- ceived. Such propositions, then, as the axioms of mathematics and the laws of logic, we may call necessary truths,—necessary in the sense that the mind must think them; in the sense that their contradictories are 'absurd, inconceivable, impossible.'
Examining these cases, we can formulate a test of truth: any proposition whose contradictory is inconceivable and impossible is true. But a superficial examination of it enables
