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An Extra-Mathematical Program Explanation of Color Experience

Danne, Nicholas (2021) An Extra-Mathematical Program Explanation of Color Experience. [Preprint]

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Abstract

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia and physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Danne, Nicholasdann0027@umn.edu0000-0002-5893-9358
Keywords: extra-mathematical explanation; Enhanced Indispensability Argument; Program Explanation; mathematical nominalism; mathematical realism; color objectivism; reflectance physicalism; Fourier analysis
Subjects: Specific Sciences > Mathematics > Applicability
General Issues > Scientific Metaphysics
General Issues > Explanation
General Issues > Models and Idealization
General Issues > Realism/Anti-realism
Depositing User: Dr. Nicholas Danne
Date Deposited: 22 Feb 2023 14:21
Last Modified: 22 Feb 2023 14:21
Item ID: 21786
Official URL: https://doi.org/10.1080/02698595.2021.1951637
Subjects: Specific Sciences > Mathematics > Applicability
General Issues > Scientific Metaphysics
General Issues > Explanation
General Issues > Models and Idealization
General Issues > Realism/Anti-realism
Date: 2021
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/21786

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