Explanation and Prediction: Strategies for Extending Scientific Realism to Mathematics

Abstract

One central question in the philosophy of mathematics concerns the ontological status of mathematical entities. Platonists argue that abstract, mathematical entities exist, while nominalists argue that they do not. Scientific realism is the position that science is (roughly) true and the objects it describes exist. There are two major competing arguments for platonism on the basis of scientific realism: Indispensability and Explanation. In this paper I consider which argument the platonist ought to prefer by comparing their motivations and results. I conclude that, given the current role of mathematics in our best scientific theories, Explanation does not support platonism. Thus, Indispensability is preferable.