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Mathematical determinacy and internal categoricity

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:
CreatorsEmailORCID
Kearney, Peterp.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-dev.library.pitt.edu/id/eprint/22576

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