Barrett, Thomas William and Manchak, JB and Weatherall, James Owen (2022) On Automorphism Criteria for Comparing Amounts of Mathematical Structure. [Preprint]

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Abstract

Wilhelm (2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM * , another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM *. We then formulate a new criterion that improves on both SYM * and Subgroup, answering Wilhelm's criticisms of SYM * along the way. We conclude by arguing that no criterion that looks only to the automorphisms of mathematical objects to compare their structure can be fully satisfactory.

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Item Type:	Preprint
Creators:	Creators Email ORCID Barrett, Thomas William thomaswb@princeton.edu Manchak, JB jmanchak@uci.edu Weatherall, James Owen weatherj@uci.edu
Keywords:	Structure, automorphism group, giraffe
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics
Depositing User:	James Owen Weatherall
Date Deposited:	26 Apr 2022 15:15
Last Modified:	26 Apr 2022 15:15
Item ID:	20515
Subjects:	Specific Sciences > Mathematics Specific Sciences > Physics
Date:	2022
URI:	https://philsci-archive.pitt.edu/id/eprint/20515

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