We advance a framework for an inferential conception of physical laws, addressing the problem of the application of mathematical structures to the relevant structure of physical domains. Physical laws, we argue, express generalizations that work as rules for deriving physically informative inferences about their target systems, hence guiding us in our interaction with various domains. Our analysis of the application of mathematics to the articulation of physical laws follows a threefold scheme. First, we examine the immersion of the relevant structure of physical domains into mathematical structures. Second, we assess the inferential power of laws resulting from the mathematical formalism employed in the immersion step. And third, we provide a suitable physical interpretation for the extant mathematical structures obtained from the inferential step. We demonstrate that a deflationary, empiricist framework for an inferential conception of physical laws delivers both an understanding of the mathematical character of physical laws, and a way of responding to some of the standard philosophical riddles associated with laws.
I examine the current state of the debate on the metaphysics of science (MS for short). In 1, I identify some of the main questions belonging to the MS, looking into the relationship between science and metaphysics. In 2, I expound the rise of the old wave in the MS, which endorses the belief that metaphysics is a guide to, or a heuristic for, science and outlines the stronger idea that metaphysics makes science possible. In 3, I examine the maximalist MS. This is a contemporary revival of the old wave, reformulating the claim that metaphysics makes science possible. In 4, I look into the new wave in the MS, which argues that science is a guide to metaphysics and, more radically, that metaphysics is to be motivated by, and restricted to, science. In 5, I briefly introduce my own minimalist MS, which contends that science sets the epistemic, methodological and ontological criteria which should work as desiderata of the MS. I close this chapter in 6 with some concluding remarks.
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