Paul Joseph Salomon Benacerraf (; born 26 March 1931) is a French-born American philosopher working in the field of the

philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in peop ...

who taught at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

his entire career, from 1960 until his retirement in 2007. He 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 and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

Moroccan Jewish Moroccan Jews ( ar, اليهود المغاربة, al-Yahūd al-Maghāriba he, יהודים מרוקאים, Yehudim Maroka'im) are Jews who live in or are from Morocco. Moroccan Jews constitute an ancient community dating to Roman times. Jews b ...

parents. In 1939 the family moved to

Caracas Caracas (, ), officially Santiago de León de Caracas, abbreviated as 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 ...

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 Hightstown is a borough in Mercer County, New Jersey, United States. As of the 2010 United States Census, the borough's population was 5,494,Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

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 (abbreviation: AAA&S) 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, a ...

in 1998. His brother was the Venezuelan

Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

-winning 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, co-edited with Hilary Putnam. 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 of the doctrines of Plato. Platonism had a profound effect on Western thought. Platonism at l ...

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 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 axiomatic se ...

and

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

give distinct, and completely adequate, identifications of natural numbers with sets (see Zermelo ordinals and

von Neumann ordinals In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least n ...

). This argument is called

Benacerraf's identification problem In the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument developed by Paul Benacerraf against set-theoretic Platonism and published in 1965 in an article entitled "What Numbers Could Not Be".Paul Benacerraf ...

. 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 Elisabeth Anne Lloyd (born September 3, 1956) is an American philosopher of science specialising in the philosophy of biology. She is currently Distinguished Professor of History and Philosophy of Science and Medicine - as well as Adjunct Professo ...

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

Paul Benacerraf's homepage at Princeton

The Benacerraf epistemological problem
''

Internet Encyclopedia of Philosophy The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original pape ...

'' {{DEFAULTSORT:Benacerraf, Paul 1931 births American Mizrahi Jews 20th-century Sephardi Jews 21st-century Sephardi Jews 20th-century American philosophers 21st-century American philosophers American people of Moroccan-Jewish descent American logicians Analytic philosophers Fellows of the American Academy of Arts and Sciences Jewish philosophers Living people Mathematical logicians Metaphysicians French expatriates in Venezuela Peddie School alumni Philosophers of mathematics Princeton University faculty Structuralism (philosophy of mathematics) Writers from Paris American metaphysics writers French male writers French emigrants to the United States

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