Metaphysical dependence : the role of mathematical structure in physical modality

I develop a novel metaphysical theory of the modal structure of the physical world, which has important consequences for debates regarding laws of nature, scientific explanation, the nature of physical properties, and the applicability of mathematics to science. The theory holds that modal properties of the physical world metaphysically depend on properties of mathematical structures. I show that the relation of metaphysical dependence is naturalistically acceptable by offering examples of non-causal scientific explanation that tacitly make use of such a notion. My view offers a non-Humean understanding of nomological necessity, a unification of the epistemology of modality with the epistemology of mathematics, and an explanation of the success of mathematics in predicting and explaining empirical phenomena.