Kearney, Peter (2020) Mathematical determinacy and internal categoricity. [Preprint]

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Abstract

The issue of arithmetical determinacy may be stated as follows: does our concept of natural number define a unique mathematical structure (the natural numbers) and, if so, how? The issue of set-theoretic determinacy may likewise be stated as: does our concept of set define a unique mathematical structure (the universe of sets) and, if so, how?

In recent work, Tim Button and Sean Walsh have argued that arithmetical and set-theoretic determinacy follow from certain internal categoricity results proved in second-order logic. In this paper I critically evaluate this claim and argue that such internal categoricity results fail to entail determinacy as claimed. In order to concentrate on the key issues in some depth, I focus on arithmetical determinacy.

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Item Type:	Preprint
Creators:	Creators Email ORCID Kearney, Peter p.kearney@uqconnect.edu.au
Keywords:	arithmetical determinacy; set-theoretic determinacy; categoricity; internal categoricity
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics
Depositing User:	Dr Peter Kearney
Date Deposited:	26 Sep 2023 14:26
Last Modified:	26 Sep 2023 14:26
Item ID:	22576
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics
Date:	8 June 2020
URI:	https://philsci-archive.pitt.edu/id/eprint/22576

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