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Document Details : Title: Is Fourrier Analysis Conservative over Physical Theory? Author(s): DANNE, Nicholas Journal: Logique et Analyse Volume: 258 Date: 2022 Pages: 135-149 DOI: 10.2143/LEA.258.0.3291673 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 nonnominalizable 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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