March, Eleanor (2025) Points, curves, and hypersurfaces: Reassessing the historical geometric object concept. [Preprint]
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Abstract
In contemporary philosophy of physics, there has recently been a renewed interest in the theory of geometric objects - a programme developed originally by geometers such as Schouten, Veblen, and others in the 1920s and 30s. However, as yet, there has been little-to-no systematic investigation into the history of the geometric object concept. I discuss the early development of the geometric object concept, and show that geometers working on the programme in the 1920s and early 1930s had a more expansive conception of geometric objects than that which is found in later presentations - which, unlike the modern conception of geometric objects, included embedded submanifolds such as points, curves, and hypersurfaces. I reconstruct and critically evaluate their arguments for this more expansive geometric object concept, and also locate and assess the transition to the more restrictive modern geometric object concept.
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| Item Type: | Preprint | ||||||
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| Keywords: | Geometric objects, geometry, general covariance | ||||||
| Subjects: | General Issues > History of Philosophy of Science Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Depositing User: | Eleanor March | ||||||
| Date Deposited: | 12 Jan 2025 13:47 | ||||||
| Last Modified: | 12 Jan 2025 13:47 | ||||||
| Item ID: | 24517 | ||||||
| Subjects: | General Issues > History of Philosophy of Science Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances |
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| Date: | 10 January 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/24517 |
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