Explanation, Extrapolation, and Existence
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 Ring...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press
2014
|
| Online Access: | http://hdl.handle.net/1721.1/85648 https://orcid.org/0000-0002-9486-8323 |
| _version_ | 1826196259839410176 |
|---|---|
| author | Yablo, Stephen |
| author2 | Massachusetts Institute of Technology. Department of Linguistics and Philosophy |
| author_facet | Massachusetts Institute of Technology. Department of Linguistics and Philosophy Yablo, Stephen |
| author_sort | Yablo, Stephen |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:24:06Z |
| format | Article |
| id | mit-1721.1/85648 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:24:06Z |
| publishDate | 2014 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | mit-1721.1/856482022-09-30T20:50:25Z Explanation, Extrapolation, and Existence Yablo, Stephen Massachusetts Institute of Technology. Department of Linguistics and Philosophy Yablo, Stephen 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. 2014-03-14T18:40:44Z 2014-03-14T18:40:44Z 2012-10 Article http://purl.org/eprint/type/JournalArticle 0026-4423 1460-2113 http://hdl.handle.net/1721.1/85648 Yablo, S. “Explanation, Extrapolation, and Existence.” Mind 121, no. 484 (October 1, 2012): 1007–1029. https://orcid.org/0000-0002-9486-8323 en_US http://dx.doi.org/10.1093/mind/fzs120 Mind Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press MIT web domain |
| spellingShingle | Yablo, Stephen Explanation, Extrapolation, and Existence |
| title | Explanation, Extrapolation, and Existence |
| title_full | Explanation, Extrapolation, and Existence |
| title_fullStr | Explanation, Extrapolation, and Existence |
| title_full_unstemmed | Explanation, Extrapolation, and Existence |
| title_short | Explanation, Extrapolation, and Existence |
| title_sort | explanation extrapolation and existence |
| url | http://hdl.handle.net/1721.1/85648 https://orcid.org/0000-0002-9486-8323 |
| work_keys_str_mv | AT yablostephen explanationextrapolationandexistence |