Document Type
Article
Publication Date
2-28-2024
Abstract
Structuralism in philosophy of mathematics has largely focused on arithmetic, algebra, and basic analysis. Some have doubted whether distinctively structural working methods have any impact in other fields such as differential equations. We show narrowly construed structuralism as offered by Benacerraf has no practical role in differential equations. But Dedekind’s approach to the continuum already did not fit that narrow sense, and little of mathematics today does. We draw on one calculus textbook, one celebrated analysis textbook, and a monograph on the Navier–Stokes equation to show structural methods like Dedekind’s have long been central to differential equations, and have philosophically respectable ontology and epistemology.
Keywords
benacerraf, dedekind, differential equations, mathematics, structuralism
Language
English
Publication Title
Synthese
Rights
© 2024, The Author(s). This is an Open Access work distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
McLarty, C. Structuralism in differential equations. Synthese 203, 83 (2024). https://doi.org/10.1007/s11229-024-04522-1
Manuscript Version
Final Publisher Version