Samantha Wakil, Department of Philosophy, University of Las Vegas, Nevada
— The debate surrounding mathematical platonism has effectively come to a standstill. With indispensability arguments as the stopping point, the literature now focuses almost exclusively on vetting purported examples of distinctively mathematical explanations of empirical phenomena. But there is a plausible alternative position that denies the supposed explanatory role of mathematics in science. According to the indexing account, mathematics can only map or ‘index’ physical systems in the sciences. The merits of this view, and the corresponding pitfalls of the received view, have not been recognized or are underappreciated. This state of affairs is likely due to the fact no one has responded to the platonist’s set of criticisms: (1) It’s not clear mathematics can index in complex scientific cases; (2) Indexing proponents have not undermined the paradigm cases of seemingly genuine mathematical explanations of scientific phenomena; (3) The exact details of the indexing proposal are underdeveloped and is therefore philosophically impoverished. I defend the indexing account against these objections and argue that this debate should stop focusing on indispensability arguments and start analyzing other inferential roles mathematics may have in scientific reasoning.