Structure and Categoricity: Determinacy of Reference and Truth Value in the Philosophy of Mathematics

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Philosophia Mathematica 24 (3):283-307 (2016)
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Abstract

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

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10.1093/philmat/nkw007

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Tim Button
University College London

Citations of this work

Arithmetic is Determinate.Zachary Goodsell - 2021 - Journal of Philosophical Logic 51 (1):127-150.
Tracing Internal Categoricity.Jouko Väänänen - 2020 - Theoria 87 (4):986-1000.
Abstractionism and Mathematical Singular Reference.Bahram Assadian - 2019 - Philosophia Mathematica 27 (2):177-198.
The semantic plights of the ante-rem structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):1-20.
Physical Possibility and Determinate Number Theory.Sharon Berry - 2021 - Philosophia Mathematica 29 (3):299-317.

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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.
Realism and reason.Hilary Putnam (ed.) - 1983 - New York: Cambridge University Press.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.

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