An indispensability argument uses the central role of mathematics in science to argue for a particular interpretation of pure mathematics. This chapter considers three different indispensability arguments offered by Quine, Putnam and Colyvan. Pincock argues that each author deploys a different definition of what the indispensability of mathematics requires. A related point is that different conclusions seem to be supported by the premises of each argument. While Quine’s argument supports platonism, his premises are difficult to defend. By contrast, Putnam’s and Colyvan’s arguments support a realism about the truth-value of mathematical statements. While somewhat sympathetic to Colyvan’s argument, Pincock argues that mathematics requires prior support so that it can make its contributions to the success of science.
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