Benacerraf, Field, and the agreement of mathematicians

Synthese 197 (5):2095-2110 (2020)
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Abstract

Hartry Field’s epistemological challenge to the mathematical platonist is often cast as an improvement on Paul Benacerraf’s original epistemological challenge. I disagree. While Field’s challenge is more difficult for the platonist to address than Benacerraf’s, I argue that this is because Field’s version is a special case of what I call the ‘sociological challenge’. The sociological challenge applies equally to platonists and fictionalists, and addressing it requires a serious examination of mathematical practice. I argue that the non-sociological part of Field’s challenge amounts to a minor reformulation of Benacerraf’s original challenge. So, I contend, Field’s challenge is not an improvement on Benacerraf’s. What is new to Field’s challenge is as much a problem for the fictionalist as it is for the platonist.

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Eileen S. Nutting
University of Kansas

References found in this work

On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
True Enough.Catherine Z. Elgin - 2017 - Cambridge: MIT Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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