Circularity, indispensability, and mathematical explanation in science. (August 2021) - Baker, Alan
Abstract: In this paper I consider the objection that the Enhanced Indispensability Argument (EIA) is circular and hence fails to support mathematical platonism. The objection is that the explanandum in any mathematical explanation of a physical phenomenon is itself identified using mathematical concepts. Hence the explanandum is only genuine if the truth of some mathematical theory is already presupposed. I argue that this objection deserves to be taken seriously, that it does sometimes undermine support for EIA, but that there is no reason to think that circularity is an unavoidable feature of mathematical explanation in science. Highlights: The Enhanced Indispensability Argument for platonism depends on there being mathematical explanations of physical phenomena. The circularity objection claims that the explananda in mathematical explanations can only be identified using mathematics. Two types of circularity are distinguished, concerning the truth of the explanandum and concerning its explanatory urgency. In each case I argue that circularity is not inevitable, hence there is room for EIA to escape the circularity objection.