Abstract

This paper proposes an approach to the philosophy of mathematics, deductive pluralism, that is designed to satisfy the criteria of inclusiveness of and consistency with mathematical practice. Deductive pluralism views mathematical statements as assertions that a result follows from logical and mathematical foundations and that there are a variety of incompatible foundations such as standard foundations, constructive foundations, or univalent foundations. The advantages of this philosophy include the elimination of ontological problems, epistemological clarity, and objectivity. Possible objections and relations with some other philosophies of mathematics are also considered.