|Education||Princeton University (PhD, 1960)|
|Thesis||Logicism, Some Considerations (1960)|
|Doctoral advisor||Hilary Putnam|
|Doctoral students||John Earman|
Ronald de Sousa
|Philosophy of mathematics|
|Mathematical structuralism (eliminative variety)|
Benacerraf's identification problem for set-theoretic realism
Benacerraf's epistemological problem for mathematical realism
Paul Joseph Salomon Benacerraf (//; born 26 March 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 and career
When the family returned to Caracas, Benacerraf remained in the United States, boarding at the Peddie School in Hightstown, New Jersey. 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.
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 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 (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 truth-conditions to proof in some way, precludes understanding how and why the truth-conditions 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." 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.
- Benacerraf, Paul (1960) Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
- ———— (1965) "What Numbers Could Not Be", The Philosophical Review, 74:47–73.
- ———— (1967) "God, the Devil, and Gödel", The Monist, 51: 9–33.
- ———— (1973) "Mathematical Truth", The Journal of Philosophy, 70: 661–679.
- ———— (1981) "Frege: The Last Logicist", The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: 17–35.
- ———— (1985) "Skolem and the Skeptic", Proceedings of the Aristotelian Society, Supplementary Volume 56: 85–115.
- ———— and Putnam, Hilary (eds.) (1983) Philosophy of Mathematics : Selected Readings 2nd edition, Cambridge University Press: New York.
- ———— (1996) "Recantation or Any old ω-sequence would do after all", Philosophia Mathematica, 4: 184–189.
- ———— (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.
- ———— (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.
- Stewart Shapiro, "Mathematical Structuralism", Philosophia Mathematica, 4(2), May 1996, pp. 81–2.
- "Paul Joseph Salomon Benacerraf - Oxford Reference". www.oxfordreference.com. Retrieved 2018-12-29.
- "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 2017-11-30.
- Moseley, Caroline (November 23, 1998). "Whatever I am now, it happened here". Princeton Weekly Bulletin. Princeton University. Retrieved October 13, 2011.
- "Tracking Higher Ed's #MeToo Moment: Updates on Sexual Assault and Harassment". Chronicle of Higher Education. 1 Dec 2017. Archived from the original on 2017-12-11. Retrieved 1 Dec 2017.
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