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A Revealing Flaw in Colyvan's Indispensability Argument

Published online by Cambridge University Press:  01 January 2022

Christopher Pincock†
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Abstract

Mark Colyvan uses applications of mathematics to argue that mathematical entities exist. I claim that his argument is invalid based on the assumption that a certain way of thinking about applications, called ‘the mapping account,’ is correct. My main contention is that successful applications depend only on there being appropriate structural relations between physical situations and the mathematical domain. As a variety of non-realist interpretations of mathematics deliver these structural relations, indispensability arguments are invalid.

Type
Research Article
Information
Philosophy of Science , Volume 71 , Issue 1 , January 2004 , pp. 61 - 79
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

This paper is a longer version of my “The Structure of Indispensability Arguments,” presented at the 2002 Annual Meeting of the Association for Symbolic Logic, Las Vegas, June 2002. I would like to thank William Tait for organizing the session on the philosophy of mathematics and the members of the audience, especially Penelope Maddy and Mark Balaguer, for their questions. Paolo Mancosu, Martin Curd, and two anonymous referees also gave helpful suggestions.

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