“How far we can advance independently of all experience, in à priori knowledge, is shown by the brilliant example of mathematics.”17 Mathematical knowledge is necessary and certain; we cannot conceive of future experience violating it. We may believe that the sun will “rise” in the west to—morrow, or that some day, in some conceivable asbestos world, fire will not burn stick; but we cannot for the life of us believe that two times two will ever make anything else than four. Such truths are true before experience; they do not depend on experience past, present, or to come. Therefore they are
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