That Mill holds that even mathematics is founded upon inductive reasoning is perhaps most interesting because it demonstrates the radical and thoroughgoing nature of his empiricism. Indeed, Mill saw this aspect of his work in just this way—combatting the a priori and intuitionist school by “driv[ing] it from its stronghold” (Autobiography, I: 233). Mill’s denial of the a priori status of mathematical propositions, of course, challenges the commonplace idea that, when true, such propositions are