  The position subdivides. On a reductionist view, mathematics is taken at logico-grammatical face value but its objects (numbers, functions, sets, etc.) are taken to be spatiotemporal. This view is advocated for sets in Armstrong (1991) and more generally in Bigelow (1988). Non-reductionist views are manifold. They include taking mathematics as meaningless symbol-manipulation (formalism), or as the exploration of what is true in all structures obeying the axioms (structuralism), or as the exploration of what is true in all possible structures obeying the axioms (modal-structuralism). Bueno (forthcoming) discusses various nominalisms, i.e., views which countenance only spatiotemporal entities. Since many of these nominalisms are compatible with non-naturalist as well as ontologically naturalist motivations, we do not discuss them here. We concentrate on a handful of issues relating mainly to reductionist versions of ontological realism.