Danne, Nicholas (2021) A Counterexample to Deflationary Nominalism. Erkenntnis, 88. pp. 1721-1740. ISSN 0165-0106
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Abstract
According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in Azzouni’s account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question.
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| Item Type: | Published Article or Volume | ||||||
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| Keywords: | mathematical nominalism | ||||||
| Subjects: | Specific Sciences > Mathematics > Ontology General Issues > Scientific Metaphysics General Issues > Realism/Anti-realism |
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| Depositing User: | Dr. Nicholas Danne | ||||||
| Date Deposited: | 21 May 2025 12:30 | ||||||
| Last Modified: | 21 May 2025 12:30 | ||||||
| Item ID: | 25371 | ||||||
| Journal or Publication Title: | Erkenntnis | ||||||
| Publisher: | Springer (Springer Science+Business Media B.V.) | ||||||
| Official URL: | https://doi.org/10.1007/s10670-021-00425-6 | ||||||
| Subjects: | Specific Sciences > Mathematics > Ontology General Issues > Scientific Metaphysics General Issues > Realism/Anti-realism |
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| Date: | 3 June 2021 | ||||||
| Page Range: | pp. 1721-1740 | ||||||
| Volume: | 88 | ||||||
| ISSN: | 0165-0106 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/25371 |
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