Explanation, Extrapolation, and Existence
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Yablo_Explanation.pdf
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238.49 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Yablo, Stephen
Date Issued
October 2012
Journal
Mind
Publisher
Oxford University Press
Citation
Yablo, S. “Explanation, Extrapolation, and Existence.” Mind 121, no. 484 (October 1, 2012): 1007–1029.
Version
Author's final manuscript
Abstract
Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains.
MIT Department
Massachusetts Institute of Technology. Department of Linguistics and Philosophy
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/mind/fzs120
