PhilSci Archive

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]

[img]
Preview
Text
main.pdf - Submitted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (330kB) | Preview

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

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.pitt.edu/id/eprint/20515

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item