Assadian, B. (2024) Mathematical structuralism and bundle theory. Ratio: an international journal of analytic philosophy. ISSN 0034-0006
Abstract
According to the realist rendering of mathematical structuralism, mathematical structures are ontologically prior to individual mathematical objects such as numbers and sets. Mathematical objects are merely positions in structures: their nature entirely consists in having the properties arising from the structure to which they belong. In this paper, I offer a bundle-theoretic account of this structuralist conception of mathematical objects: what we normally describe as an individual mathematical object is the mereological bundle of its structural properties. An emerging picture is a version of mereological essentialism: the structural properties of a mathematical object, as a bundle, are the mereological parts of the bundle, which are possessed by it essentially.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. Ratio published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | bundle theory; individuation; mathematical structuralism; mereological essentialism; ontological dependence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Philosophy, Religion and History of Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Apr 2024 10:41 |
Last Modified: | 16 May 2024 14:18 |
Published Version: | http://dx.doi.org/10.1111/rati.12397 |
Status: | Published online |
Publisher: | Wiley-Blackwell |
Identification Number: | 10.1111/rati.12397 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:210594 |
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