McCullough-Benner, C (2022) Applying Unrigorous Mathematics: Heaviside's Operational Calculus. Studies in History and Philosophy of Science, 91. pp. 113-124. ISSN 0039-3681
Abstract
Applications of unrigorous mathematics are relatively common in the history and current practice of physics but underexplored in existing philosophical work on applications of mathematics. I argue that perspicuously representing some of the most philosophically interesting aspects of these cases requires us to go beyond the most prominent accounts of the role of mathematics in scientific representations, namely versions of the mapping account. I defend an alternative, the robustly inferential conception (RIC) of mathematical scientific representations, which allows us to represent the relevant practices more naturally. I illustrate the advantages of RIC by considering one such case, Heaviside's use of his unrigorous operational calculus to produce and apply an early generalization of Ohm's law in terms of “resistance operators.”
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier Ltd. This is an author produced version of an article published in Studies in History and Philosophy of Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Mathematical representation; Mathematical rigor; Oliver Heaviside; Operational calculus; Inferentialism; Mapping account |
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) > School of Philosophy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Nov 2021 14:14 |
Last Modified: | 13 Jun 2023 00:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.shpsa.2021.11.013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180654 |