This chapter involves an extended examination of Mark Steiner’s 1998 book The Applicability of Mathematics as Philosophical Problem. Steiner distinguishes several applicability problems which are considered in this chapter and related to the proposals of part one. Steiner argues that the most pressing issue concerns the role of mathematics in scientific discovery and the resulting evidence against naturalism. Pincock argues that Steiner’s objections to naturalism are not successful. The problems arise partly from Steiner’s conception of pure mathematics and partly from the philosophical premises which he advances. The discussion of varying interpretations from chapter 4 is used to argue that scientists can prefer to deploy the mathematics they already understand without giving up naturalism.
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