Multiple Reductions Revisited
Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). Ther...
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| Veröffentlicht in: | Philosophia mathematica 2008-06, Vol.16 (2), p.244-255 |
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| container_title | Philosophia mathematica |
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| creator | Clarke-Doane, Justin |
| description | Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this paper I develop a difficulty for Benacerraf's argument against reductionism that is of comparable severity to the now widely recognized difficulty with his general argument against realism. |
| doi_str_mv | 10.1093/philmat/nkm034 |
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| ispartof | Philosophia mathematica, 2008-06, Vol.16 (2), p.244-255 |
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| source | Oxford University Press Journals All Titles (1996-Current) |
| title | Multiple Reductions Revisited |
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