The Metarepresentational Role of Mathematics in Scientific Explanations
Abstract Several philosophers have argued that to capture the generality of certain scientific explanations, we must count mathematical facts among their explanantia. I argue that we can better understand these explanations by adopting a more nuanced stance toward mathematical representations, recognizing the role of mathematical representation schemata in representing highly abstract features of physical systems. It is by picking out these abstract but non-mathematical features that explanations appealing to mathematics achieve a high degree of generality. The result is a rich conception of the role of mathematics in scientific explanations that does not require us to treat mathematical facts as explanantia.