Existence, Mathematical Nominalism, and Meta-Ontology: An Objection to Azzouni on Criteria for Existence

Philosophia Mathematica 26 (2):251-265 (2018)
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Abstract

Jody Azzouni argues that whilst it is indeterminate what the criteria for existence are, there is a criterion that has been collectively adopted to use ‘exist’ that we can employ to argue for positions in ontology. I raise and defend a novel objection to Azzouni: his view has the counterintuitive consequence that the facts regarding what exists can and will change when users of the word ‘exist’ change what criteria they associate with its usage. Considering three responses, I argue Azzouni has best reason to take one that ultimately renders unsuccessful his arguments against mathematical abstracta.

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Farbod Akhlaghi
Cambridge University

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Supervenience and mind: selected philosophical essays.Jaegwon Kim - 1993 - New York, NY, USA: Cambridge University Press.
Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Second philosophy: a naturalistic method.Penelope Maddy - 2007 - New York: Oxford University Press.

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