Paul Joseph Salomon Benacerraf (born 1931)^{[1]} is an American philosopher working in the field of the philosophy of mathematics who has been teaching at Princeton University since he joined the faculty in 1960. He was appointed Stuart Professor of Philosophy in 1974, and retired in 2007 as the James S. McDonnell Distinguished University Professor of Philosophy.^{[2]}
He was born in Paris to parents who were Sephardic Jews from Morocco and Algeria.^{[3]} His brother was the Venezuelan Nobel Prizewinning immunologist Baruj Benacerraf.
Benacerraf is perhaps best known for his two papers "What Numbers Could Not Be" (1965) and "Mathematical Truth" (1973), and for his anthology on the philosophy of mathematics, coedited with Hilary Putnam. He was elected a Fellow of the American Academy of Arts and Sciences in 1998.^{[1]}
Work
In "What Numbers Could Not Be", he argues against a Platonist view of mathematics, and for structuralism, on the ground that what is important about numbers is the abstract structures they represent rather than the objects that number words ostensibly refer to. In particular, this argument is based on the point that Zermelo and von Neumann give distinct, and completely adequate, identifications of natural numbers with sets.
In "Mathematical Truth", he argues that no interpretation of mathematics offers a satisfactory package of epistemology and semantics; it is possible to explain mathematical truth in a way that is consistent with our syntacticosemantical treatment of truth in nonmathematical language, and it is possible to explain our knowledge of mathematics in terms consistent with a causal account of epistemology, but it is in general not possible to accomplish both of these objectives simultaneously. He argues for this on the grounds that an adequate account of truth in mathematics implies the existence of abstract mathematical objects, but that such objects are epistemologically inaccessible because they are causally inert and beyond the reach of sense perception. On the other hand, an adequate epistemology of mathematics, say one that ties truthconditions to proof in some way, precludes understanding how and why the truthconditions have any bearing on truth.
Publications
Works
 Benacerraf, Paul (1960) Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
 Benacerraf, Paul (1965) What Numbers Could Not Be, The Philosophical Review, 74:4773.
 Benacerraf, Paul (1967) God, the Devil, and Gödel, The Monist, 5l: 933.
 Benacerraf, Paul (1973) Mathematical Truth, The Journal of Philosophy, 70: 661679.
 Benacerraf, Paul (1981) Frege: The Last Logicist, The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: l735.
 Benacerraf, Paul (1985) Skolem and the Skeptic, Proceedings of the Aristotelian Society, Supplementary Volume 56: 85ll5.
 Benacerraf, Paul and Putnam, Hilary (eds.) (1983) Philosophy of Mathematics : Selected Readings 2nd edition, Cambridge University Press: New York.
 Benacerraf, Paul (1996) Recantation or Any old ωsequence would do after all, Philosophia Mathematica, 4: 184189.
 Benacerraf, Paul (1996) What Mathematical Truth Could Not Be  I, in Benacerraf and His Critics, A. Morton and S. P. Stich, eds., Blackwell's, Oxford and Cambridge, pp 9–59.
 Benacerraf, Paul (1999) What Mathematical Truth Could Not Be  II, in Sets and Proofs, S. B. Cooper and J. K. Truss, eds., Cambridge University Press, pp. 27–51.
Books about Benacerraf
 Zimmermann, Manfred (1995) Wahrheit und Wissen in der Mathematik. Das Benacerrafsche Dilemma, 1. Auflage, Transparent Verlag, Berlin.
 Gupta, Anoop K. (2002) Benacerraf's Dilemma and Natural Realism for Mathematics. Ph.D. Dissertation, Ottawa University.
Papers about Benacerraf
 Hilton, P. What 'What Numbers Could Not Be', by Paul Benacerraf', is.
 Ebert, Philip A. (2007) What Mathematical Knowledge Could Not Be, in St Andrews Undergraduate Philosophy Society Journal, 1 (1) pp. 46–70.
 Hale, Bob and Wright, Crispin (2002) Benacerraf's Dilemma Revisited European Journal of Philosophy, Issue 10:1.
 Lucas, J. R. (1968) Satan stultified: a rejoinder to Paul Benacerraf, The Monist, vol.52, No.1, pp. 145–158.
Writings on Benacerraf
 Benacerraf Interview by The Dualist and the Stanford Philosophy Department
 "Whatever I am now, it happened here" by Caroline Moseley
References
 ^ ^{a} ^{b} "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved June 2, 2011.
 ^ http://philosophy.princeton.edu/content/paulbenacerrafsymposium
 ^ Moseley, Caroline (November 23, 1998). "'Whatever I am now, it happened here'". Princeton Weekly Bulletin (Princeton University). Retrieved October 13, 2011.
External links
 Paul Benacerraf's homepage at Princeton
 Paul Benacerraf's lecture series at UNMSM (Lima, Peru)^{[dead link]}
