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On What Exists Mathematically: Indispensability without Platonism

Newstead, Anne and Franklin, James (2009) On What Exists Mathematically: Indispensability without Platonism. In: [2009] Metaphysics of Science (Melbourne, July 2-5, 2009).

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    Abstract

    According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage.


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    Item Type: Conference or Workshop Item (UNSPECIFIED)
    Keywords: indispensability; ontological commitment; Quine; Armstrong; Aristotelian realism; truthmaker
    Subjects: General Issues > Realism/Anti-realism
    Conferences and Volumes: [2009] Metaphysics of Science (Melbourne, July 2-5, 2009)
    Depositing User: Anne Newstead
    Date Deposited: 14 Jul 2009
    Last Modified: 07 Oct 2010 11:18
    Item ID: 4757
    URI: http://philsci-archive.pitt.edu/id/eprint/4757

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