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On Automorphism Criteria for Comparing Amounts of Mathematical Structure

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:
CreatorsEmailORCID
Barrett, Thomas Williamthomaswb@princeton.edu
Manchak, JBjmanchak@uci.edu
Weatherall, James Owenweatherj@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-dev.library.pitt.edu/id/eprint/20515

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