Deductive Pluralism

This paper proposes an approach to the philosophy of mathematics, deductive pluralism, that satisfies the criterion of inclusiveness of mathematical practice. The basic argument is as follows: there are existing varieties of mathematics with incompatible foundations; given these varieties, a philosophy of mathematics should be inclusive; the criterion of inclusiveness and the fact of incompatible varieties implies a pluralistic philosophy; this in turn requires a deductivist approach within each variety; thus deductive pluralism. The advantages of deductive pluralism include the elimination of ontological problems, epistemological clarity, and objectivity