Good weasel hunting

Synthese 192 (10):3397-3412 (2015)
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Abstract

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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Author Profiles

Robert Knowles
Swansea University
David Liggins
University of Manchester

References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
Theory and Evidence.Clark N. Glymour - 1980 - Princeton University Press.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Grounding: Toward a Theory of the I n-Virtue-Of Relation.Paul Audi - 2012 - Journal of Philosophy 109 (12):685-711.

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