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from Part III - Metaphysics
Published online by Cambridge University Press: 18 April 2020
This chapter demonstrates how thinking about truthmakers can bring some clarity to the ongoing debate concerning the ontological status of mathematical entities, and advances one position on the topic. It begins with what is nowadays the most familiar argument in the ontology of mathematics: the indispensability argument. Close inspection of it reveals that the notion of truthmaking is indeed playing a role, and that by thinking about indispensability and truthmaking in tandem, both ideas emerge with greater clarity. Focusing on indispensability will shed light on what the ontological stakes are in the overall debate, so the second section presents what is seen to be the most tenable ontological positions. It then offers a personal (rather deflationary) contribution to the truthmaking question about mathematics, and concludes by comparing and contrasting that view with a recent brand of mathematical trivialism.
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