Philosophia Mathematica 27 (1):88-104 (2019)

Authors
David Mark Kovacs
Tel Aviv University
Abstract
In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism.
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DOI 10.1093/philmat/nky019
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References found in this work BETA

Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical Grounding. Cambridge University Press. pp. 37--80.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
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What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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Citations of this work BETA

Debunking Arguments.Daniel Z. Korman - 2019 - Philosophy Compass 14 (12).

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