Paul Joseph Salomon Benacerraf (; 26 March 1930 – 13 January 2025) was a French-born American philosopher working in the field of the

philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...

who taught at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

his entire career, from 1960 until his retirement in 2007. Benacerraf was appointed Stuart Professor of Philosophy in 1974, and retired as the James S. McDonnell Distinguished University Professor of Philosophy.

Life and career

Benacerraf was born in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

on 26 March 1930, to a Moroccan-Venezuelan

Sephardic Jewish Sephardic Jews, also known as Sephardi Jews or Sephardim, and rarely as Iberian Peninsular Jews, are a Jewish diaspora population associated with the historic Jewish communities of the Iberian Peninsula (Spain and Portugal) and their descendant ...

father, Abraham Benacerraf, and Algerian Jewish mother, Henrietta Lasry. In 1939 the family moved to

Caracas Caracas ( , ), officially Santiago de León de Caracas (CCS), is the capital and largest city of Venezuela, and the center of the Metropolitan Region of Caracas (or Greater Caracas). Caracas is located along the Guaire River in the northern p ...

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, New Jersey. He attended

for both his undergraduate and graduate studies. He was elected a fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1998. Benacerraf died on 13 January 2025, at the age of 94. His older brother was the Venezuelan

Nobel Prize The Nobel Prizes ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...

-winning immunologist Baruj Benacerraf.

Philosophical work

Benacerraf was 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 Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of ...

. In "What Numbers Could Not Be" (1965), Benacerraf argues against a

Platonist Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundam ...

view of mathematics, and for

structuralism Structuralism is an intellectual current and methodological approach, primarily in the social sciences, that interprets elements of human culture by way of their relationship to a broader system. It works to uncover the structural patterns t ...

, 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 Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel set theory, Z ...

and

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

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'' that 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.

Publications

*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.

References

External links

* *
The Benacerraf epistemological problem
''

Internet Encyclopedia of Philosophy The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia with around 900 articles about philosophy, philosophers, and related topics. The IEP publishes only peer review, peer-reviewed and blind-refereed original p ...

'' {{DEFAULTSORT:Benacerraf, Paul 1930 births 2025 deaths American Mizrahi Jews 20th-century American Sephardic Jews 21st-century French Sephardi Jews 20th-century American philosophers 21st-century American philosophers American people of Moroccan-Jewish descent American people of Algerian-Jewish descent American logicians Analytic philosophers Fellows of the American Academy of Arts and Sciences Jewish philosophers Mathematical logicians American metaphysicians French expatriates in Venezuela Peddie School alumni American philosophers of mathematics Princeton University faculty Structuralism (philosophy of mathematics) Writers from Paris American metaphysics writers French emigrants to the United States 20th-century French Sephardi Jews 21st-century American Sephardic Jews

Life and career

Philosophical work

Sexual harassment allegation

Publications

See also

References

Further reading

Books about Benacerraf

Papers about Benacerraf

Articles on Benacerraf

External links