 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 true necessarily. Indeed, the rejection of the possibility of a priori knowledge as such challenges the notion that there are any necessary truths. Mill does not shy away from this implication. Truths can be better or worse established—central or peripheral to our understanding of the world—and we can therefore be more or less willing to abandon them. But Mill shows little interest in principled or absolute modal distinctions between necessary and contingent truths. Rather, Mill argues, some propositions seem to us necessary because of processes of psychological association make them so ingrained that their denial seems to us inconceivable.