The application of mathematics to science and the enormous success that derives from it is, perhaps, the strongest evidence in favour of mathematical realism. Quine and Putnam have taken the indispensability of mathematics in doing science as the main premise in an argument for both the truth of mathematics and the existence of mathematical objects. This argument has been criticized, among other things, for presupposing a realist position with regard to science. In this chapter, I propose a new argument, the pragmatic indispensability argument that avoids the problem by failing to presuppose that our best scientific theories are true. I argue that the justification for doing science also justifies our accepting as true, the mathematics that science uses.
Keywords: application of mathematics, indispensability, justification, mathematical realism, pragmatic, Putnam, Quine, success