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

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

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.

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,879

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2016-02-25

Downloads
206 (#58,058)

6 months
10 (#73,804)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Realism and Reason.Hilary Putnam - 1983 - Cambridge University Press.
Introduction to Mathematical Logic.Alonzo Church - 1944 - Princeton: Princeton University Press.
Introduction to Mathematical Logic.Alonzo Church - 1944 - London: Oxford University PRess.

View all 106 references / Add more references

Citations of this work

Arithmetic is Determinate.Zachary Goodsell - 2022 - Journal of Philosophical Logic 51 (1):127-150.
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 - forthcoming - Philosophia Mathematica:nkab013.
Abstractionism and Mathematical Singular Reference.Bahram Assadian - 2019 - Philosophia Mathematica 27 (2):177-198.
Tracing Internal Categoricity.Jouko Väänänen - 2021 - Theoria 87 (4):986-1000.

View all 7 citations / Add more citations

Similar books and articles

Relative Categoricity and Abstraction Principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
On an Application of Categoricity.Alexander Paseau - 2005 - Proceedings of the Aristotelian Society 105 (3):411–415.
Categoricity and Indefinite Extensibility.James Walmsley - 2002 - Proceedings of the Aristotelian Society 102 (3):217–235.
Categoricity Spectra for Rigid Structures.Ekaterina Fokina, Andrey Frolov & Iskander Kalimullin - 2016 - Notre Dame Journal of Formal Logic 57 (1):45-57.
On the Complexity of Categoricity in Computable Structures.Walker M. White - 2003 - Mathematical Logic Quarterly 49 (6):603.
Second Order Logic or Set Theory?Jouko Väänänen - 2012 - Bulletin of Symbolic Logic 18 (1):91-121.
Categoricity.John Corcoran - 1980 - History and Philosophy of Logic 1 (1):187-207.
Internal Categoricity in Arithmetic and Set Theory.Jouko Väänänen & Tong Wang - 2015 - Notre Dame Journal of Formal Logic 56 (1):121-134.
Categoricity in Homogeneous Complete Metric Spaces.Åsa Hirvonen & Tapani Hyttinen - 2009 - Archive for Mathematical Logic 48 (3-4):269-322.
Categoricity and Ranks.Jürgen Saffe - 1984 - Journal of Symbolic Logic 49 (4):1379-1392.