Paul Benacerraf  

Born  1931 Paris, France 
Education  Princeton University (PhD, 1960) 
Era  Contemporary philosophy 
Region  Western philosophy 
School  Analytic philosophy 
Thesis  Logicism, Some Considerations (1960) 
Doctoral advisor  Hilary Putnam 
Doctoral students  John Earman Alvin Goldman Richard Grandy 
Main interests  Philosophy of mathematics 
Notable ideas  Mathematical structuralism (eliminative variety)^{[1]} Benacerraf's identification problem for settheoretic realism Benacerraf's epistemological problem for mathematical realism 
Influences
 
Influenced

Paul Joseph Salomon Benacerraf (/bɪˈnæsərəf/; born 26 March 1931)^{[2]}^{[3]} is a Frenchborn 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.^{[4]}
Life and career
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.^{[5]}
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.^{[5]}
He was elected a Fellow of the American Academy of Arts and Sciences in 1998.^{[3]}
His brother was the Venezuelan Nobel Prizewinning immunologist Baruj Benacerraf.
Philosophical work
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.
In "What Numbers Could Not Be" (1965), 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 (see Zermelo ordinals and von Neumann ordinals). This argument is called Benacerraf's identification problem.
In "Mathematical Truth" (1973), 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 (this argument is called Benacerraf's epistemological problem). 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.
Sexual harassment allegation
Elisabeth 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."^{[6]} Benacerraf has denied the allegations, stating in an email to The Chronicle, Mr. Benacerraf said he was “genuinely puzzled” by the accusations and does not know what prompted them. “I am not the sort of person that she describes in her interview,” he said. “Yet I do not doubt her sincerity or the depth of the feelings that she reports,” he added.^{[6]}
Publications
 Benacerraf, Paul (1960) Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
 Benacerraf, Paul (1965) "What Numbers Could Not Be", The Philosophical Review, 74:4773.
 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.
See also
References
 ^ Stewart Shapiro, "Mathematical Structuralism", Philosophia Mathematica, 4(2), May 1996, pp. 81–2.
 ^ "Paul Joseph Salomon Benacerraf  Oxford Reference". www.oxfordreference.com. doi:10.1093/oi/authority.20110803095458163 (inactive 20200401). Retrieved 20181229.
 ^ ^{a} ^{b} "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved June 2, 2011.
 ^ "Paul Benacerraf Symposium  Department of Philosophy". philosophy.princeton.edu. Retrieved 20171130.
 ^ ^{a} ^{b} Moseley, Caroline (November 23, 1998). "Whatever I am now, it happened here". Princeton Weekly Bulletin. Princeton University. Retrieved October 13, 2011.
 ^ ^{a} ^{b} "Tracking Higher Ed's #MeToo Moment: Updates on Sexual Assault and Harassment". Chronicle of Higher Education. 1 Dec 2017. Archived from the original on 20171211. Retrieved 1 Dec 2017.
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"^{[permanent dead link]}, in St Andrews Undergraduate Philosophy Society Journal, 1(1) pp. 46–70.
 Hale, Bob and Wright, Crispin (2002) "Benacerraf's Dilemma Revisited"^{[permanent dead link]} 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