Wilhelm, Isaac (2021) Comparing the Structures of Mathematical Objects. Synthese.
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Abstract
A popular method for comparing the structures of mathematical objects, which I call the `subset approach', says that X has more structure than Y just in case X's automorphisms form a proper subset of Y's automorphisms. This approach is attractive, in part, because it seems to yield the right results in some comparisons of spacetime structure. But as I show, it yields the wrong results in a number of other cases. The problem is that the subset approach compares structure using automorphism sets. So a different approach is needed: structure should be compared using automorphism groups.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | structure, metaphysics, philosophy of science, philosophy of physics, group theory | ||||||
| Subjects: | Specific Sciences > Mathematics Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory |
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| Depositing User: | Isaac Wilhelm | ||||||
| Date Deposited: | 16 Dec 2025 20:02 | ||||||
| Last Modified: | 16 Dec 2025 20:02 | ||||||
| Item ID: | 27486 | ||||||
| Journal or Publication Title: | Synthese | ||||||
| Subjects: | Specific Sciences > Mathematics Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory |
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| Date: | 2021 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/27486 |
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