On automorphism criteria for comparing amounts of mathematical structure.
Wilhelm (Forthcom Synth 199:6357–6369, 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 SY...
| Publicado en: | Synthese Vol. 201; no. 6; pp. 1 - 15 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Jun2023
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| Acceso en línea: | Ver este registro en EBSCOhost |
| Sumario: | Wilhelm (Forthcom Synth 199:6357–6369, 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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