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Structuralism in differential equations

McLarty, Colin (2024) Structuralism in differential equations. [Preprint]


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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.

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Item Type: Preprint
McLarty, Colincolin.mclarty@case.edu0000-0002-3181-7537
Keywords: structuralism; mathematics; Dedekind; Benacerraf; differential equations
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Depositing User: Dr Colin McLarty
Date Deposited: 10 Feb 2024 20:25
Last Modified: 01 Mar 2024 04:03
Item ID: 23065
DOI or Unique Handle:
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics
Date: 8 February 2024

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