Danne, Nicholas (2022) Is Fourier Analysis Conservative over Physical Theory? [Preprint]
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Abstract
Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization of conservativeness by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and non-nominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness.
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| Item Type: | Preprint | ||||||
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| Keywords: | mathematical realism, fourier analysis, reflectance physicalism | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Ontology General Issues > Scientific Metaphysics General Issues > Realism/Anti-realism |
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| Depositing User: | Dr. Nicholas Danne | ||||||
| Date Deposited: | 18 Dec 2022 23:03 | ||||||
| Last Modified: | 18 Dec 2022 23:03 | ||||||
| Item ID: | 21567 | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Ontology General Issues > Scientific Metaphysics General Issues > Realism/Anti-realism |
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| Date: | 2022 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21567 |
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