The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four avenues for replying to Melia. We will argue that the three replies pursued in the literature so far are unpromising. We will then propose one new reply that is much more powerful, and—in the light of this—advise participants in the debate where to focus their energies.
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We would like to thank Chris Daly, Joe Morrison, Leo Tarasov, and two anonymous referees for their comments on earlier drafts. Rob Knowles gratefully acknowledges the award of a Jacobsen Studentship by the Royal Institute of Philosophy, which supported the work presented here.
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Knowles, R., Liggins, D. Good weasel hunting. Synthese 192, 3397–3412 (2015). https://doi.org/10.1007/s11229-015-0711-7
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