Paul Benacerraf

Paul Benacerraf
Born	1931 Paris, France
Alma mater	Princeton University
Era	Contemporary philosophy
Region	Western philosophy
School	Analytic philosophy
Main interests	Philosophy of mathematics
Notable ideas	Mathematical structuralism

Paul Joseph Salomon Paul Benacerraf (born 1931) is a French-born 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.

Life

Benacerraf was born in Paris to parents who were Sephardic Jews from Morocco and Algeria. In 1939 the family moved to Caracas and then to New York City.

When the family returned to Caracas, Benacerraf remained in the United States boarding at the Peddie School in Hightstown, NJ. He attended Princeton University for both his undergraduate and graduate studies.

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, co-edited with Hilary Putnam. He was elected a Fellow of the American Academy of Arts and Sciences in 1998.

His brother was the Venezuelan Nobel Prize-winning immunologist Baruj Benacerraf.

Work

In "What Numbers Could Not Be", Benacerraf 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 Ernst Zermelo and John 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 syntactico-semantical treatment of truth in non-mathematical 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 truth-conditions to proof in some way, precludes understanding how and why the truth-conditions have any bearing on truth.

Sexual harassment allegation

Elizabeth Lloyd has alleged that while she was a PhD student at Princeton, Benacerraf "petted and touched" her every day. She said, “It was just an extra price I had to pay, that the men did not have to pay, in order to get my Ph.D.” Benacerraf has responded by denying the allegations, stating, “I am not the sort of person that she describes in her interview. Yet I do not doubt her sincerity or the depth of the feelings that she reports.”

Publications

• Benacerraf, Paul (1960) Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
• Benacerraf, Paul (1965) "What Numbers Could Not Be", The Philosophical Review, 74:47-73.
• Benacerraf, Paul (1967) "God, the Devil, and Gödel", The Monist, 5l: 9-33.
• Benacerraf, Paul (1973) "Mathematical Truth", The Journal of Philosophy, 70: 661-679.
• Benacerraf, Paul (1981) "Frege: The Last Logicist", The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: l7-35.
• Benacerraf, Paul (1985) "Skolem and the Skeptic", Proceedings of the Aristotelian Society, Supplementary Volume 56: 85-ll5.
• 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 ω-sequence would do after all", Philosophia Mathematica, 4: 184-189.
• 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.

See also

• Benacerraf's identification problem
• American philosophy
• List of American philosophers

Further reading

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.

Articles on Benacerraf

• "Benacerraf Interview" by The Dualist and the Stanford Philosophy Department
• "Whatever I am now, it happened here" by Caroline Moseley

External links

• Paul Benacerraf's homepage at Princeton
• Paul Benacerraf's lecture series at UNMSM (Lima, Peru)