The Story of Philosophy

by Will Durant

“How far we can advance independently of all experience, in à priori knowledge, is shown by the brilliant example of mathematics.” 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 tomorrow, or that someday, 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 absolute and necessary truths; it is inconceivable that they should ever become untrue. But whence do we get this character of absoluteness and necessity? Not from experience; for experience gives us nothing but separate sensations and events, which may alter their sequence in the future.201 These truths derive their necessary character from the inherent structure of our minds, from the natural and inevitable manner in which our minds must operate.