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 | ||||||
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| 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 |
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| 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 |
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| Date: | 2021 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21786 |
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