A Critique of the Philosophy of Laws of Nature – Or: Abductive Scientific Realism Meets Mathematical Realism

Mr Cristian Soto (University of Melbourne)

Abstract
This paper presents a general critique of the philosophy of laws of nature and outlines a new mathemtico-realist approach based on a metaphysics of science which I call abductive scientific realism. First, I will briefly describe the current state of the metaphysics of science debate, indicating in particular the metaphysical framework I assume in examining the problem of laws of nature. Second, I will present a general critique of the philosophy of laws of nature, considering the anti-realist theories of Lewis, van Fraassen, and Giere; the realist proposals of Armstrong, Ellis, and Bird; and, finally, the somewhat intermediate positions of Cartwright, Mumford, and Psillos. Third, I will critically analyse the problem of the desiderata for a theory of laws, examining the criteria independently developed by Ellis and Mumford, and presenting my own desiderata for the ontology, epistemology, and semantics of laws of nature. Finally, I will outline a mathematico-realist theory of laws, evaluating the standard indispensability argument for mathematical entities, the principle of causal isolation, the make-no-difference argument, the viability of an ontology of mixed physico-mathematical facts, the role of inference to the best explanation, and the mathematical explanations of physical facts in science. I will conclude that there are good reasons for elaborating a systematic mathematico-realist theory of laws of nature if we want to account for one of the core elements of a metaphysics that takes science seriously.