 The problem here becomes even more obvious in non-mathematical cases. For example, philosophers have wanted to claim not merely that our concepts of red and green exclude the possibility of our thinking that something is both colors all over, but that this possibility is ruled out for the actual colors, red and green, themselves (if such there be). It is therefore no accident that Bonjour’s (1998, pp. 184–5) defense of a priori knowledge turns on resuscitating views of Aristotle and Aquinas, according to which the very properties of red and green themselves are constituents of the propositions we grasp. But it is just such a wonderful coincidence between merely our concepts and actual worldly properties that a linguistic semantics alone obviously cannot ensure.