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Is Fourier Analysis Conservative over Physical Theory?

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
Creators:
CreatorsEmailORCID
Danne, Nicholasdann0027@umn.edu0000-0002-5893-9358
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
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
Date: 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21567

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