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Cantor, Choice, and Paradox

DiBella, Nicholas (2024) Cantor, Choice, and Paradox. [Preprint]

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Abstract

I propose a revision of Cantor's account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor's if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor's account, blocks paradoxes--most notably, that a set can be partitioned into a set that is bigger than it--that can arise from Cantor's account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor's account, and sheds philosophical light on one of the oldest unsolved problems in set theory.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
DiBella, Nicholasdibella@cmu.edu0000-0002-3572-5672
Additional Information: Forthcoming in The Philosophical Review
Keywords: Set Theory, Axiom of Choice, Infinity, Cantor, Set Size
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics
Depositing User: Nicholas DiBella
Date Deposited: 12 Mar 2024 16:24
Last Modified: 12 Mar 2024 16:24
Item ID: 23191
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics
Date: 11 March 2024
URI: https://philsci-archive.pitt.edu/id/eprint/23191

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