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

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

Authors
Tim Button
University College London
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.
Keywords structuralism  categoricity  philosophy of mathematics  realism  model theory
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DOI 10.1093/philmat/nkw007
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References found in this work BETA

Putnam’s Paradox.David K. Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Mathematical Thought and its Objects.Charles Parsons - 2007 - Cambridge University Press.

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Citations of this work BETA

The Semantic Plights of the Ante-Rem Structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):1-20.
Abstractionism and Mathematical Singular Reference.Bahram Assadian - 2019 - Philosophia Mathematica 27 (2):177-198.

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