Himelright, Jack (2022) Applied Mathematics without Numbers. [Preprint]
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Applied Mathematics without Numbers, 10 Apr 2023.pdf Download (438kB) |
Abstract
In this paper, I develop a "safety result" for applied mathematics. I show that whenever a theory in natural science entails some non-mathematical conclusion via an application of mathematics, there is a counterpart theory that carries no commitment to mathematical objects, entails the same conclusion, and the claims of which are true if the claims of the original theory are "correct": roughly, true given the assumption that mathematical objects exist. The framework used for proving the safety result has some advantages over existing nominalistic accounts of applied mathematics. It also provides a nominalistic account of pure mathematics.
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Item Type: | Preprint | ||||||
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Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Proof |
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Depositing User: | Dr Jack Himelright | ||||||
Date Deposited: | 08 Jul 2025 21:43 | ||||||
Last Modified: | 08 Jul 2025 21:43 | ||||||
Item ID: | 25884 | ||||||
DOI or Unique Handle: | 10.1093/philmat/nkac032 | ||||||
Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics > Proof |
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Date: | 16 December 2022 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/25884 |
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