Mathematical Metaphysics

The fundamental question of metaphysics is what exists, not in any particular structure, but in general. To answer this question requires determination of the nature of existence, or more concretely, what it means for something to exist. Thus a worthwhile metaphysics should provide an explicit criterion for existence. A wide variety of such criteria have been proposed, and these can be divided into broad categories based on how they handle abstracta, in particular mathematical objects. Platonistic metaphysical accounts incorporate physical objects and mathematical objects as disjoint categories, but require an account of how these two categories of objects interact, which is a vexing philosophical question [6]. One way to handle this issue is to eliminate one of these two categories, and this is precisely what is done in nominalistic accounts, which admit the existence of physical objects but not of mathematical objects.