What is the Benacerraf Problem?

In Fabrice Pataut Jody Azzouni, Paul Benacerraf Justin Clarke-Doane, Jacques Dubucs Sébastien Gandon, Brice Halimi Jon Perez Laraudogoitia, Mary Leng Ana Leon-Mejia, Antonio Leon-Sanchez Marco Panza, Fabrice Pataut Philippe de Rouilhan & Andrea Sereni Stuart Shapiro (eds.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity (Fabrice Pataut, Editor). Springer (2017)
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Abstract

In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem that satisfies all of the constraints which have been placed on the Benacerraf Problem. The point generalizes to all arguments with the structure of the Benacerraf Problem aimed at realism about a domain meeting certain conditions. Such arguments include so-called "Evolutionary Debunking Arguments" aimed at moral realism. I conclude with some suggestions about the relationship between the Benacerraf Problem and the Gettier Problem.

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original Clarke-Doane, Justin (2016) "What Is the Benacerraf Problem?". In Pataut, Fabrice, Truth, Objects, Infinity: New Perspectives on the Philosophy of Paul Benacerraf, pp. : Springer Verlag (2016)

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Justin Clarke-Doane
Columbia University

Citations of this work

Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
Modal Security.Justin Clarke-Doane & Dan Baras - 2019 - Philosophy and Phenomenological Research 102 (1):162-183.

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References found in this work

Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
Philosophical explanations.Robert Nozick - 1981 - Cambridge: Harvard University Press.
Knowledge and lotteries.John Hawthorne - 2004 - New York: Oxford University Press.

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