This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal structure of (...) the physical world. The no-miracles argument is the primary motivation for scientific realism. It is a presupposition of this argument that unobservable entities are explanatory only when they determine the empirical phenomena they explain. I argue that mathematical entities should also be seen as explanatory only when they determine the empirical facts they explain, namely, the modal structure of the physical world. Thus, scientific realism commits us to a metaphysical determination relation between mathematics and physical modality that has not been previously recognized. The requirement to account for the metaphysical dependence of modal physical structure on mathematics limits the class of acceptable solutions to the applicability problem that are available to the scientific realist. (shrink)

_Metaphysics: The Fundamentals_ presents readers with a systematic, comprehensive introductory overview of modern analytic metaphysics. Presents an accessible, up-to-date and broad-ranging survey of one of the most dynamic and often daunting sub-fields in contemporary philosophy Introduces readers to the seminal works of contemporary and historic philosophers, including Descartes, Leibniz, Russell, David Lewis, Alvin Plantinga, Kit Fine, Peter van Inwagen, John Hawthorne and many others Explores key questions while identifying important assumptions, axioms, and methodological principles Addresses topics in ontology, modality, causality, (...) and universals; as well as issues surrounding material composition, persistence, space, and time. (shrink)