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.
A slight of hand here, moving from observed phenomenon to definitional
