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Paul Benacerraf

March 13, 2024

Paul Joseph Salomon Benacerraf (/bɪˈnæsərəf/; born March 26, 1931)[2][3] is a French-born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University 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.[4]

Life and career edit

Benacerraf was born in Paris to a Moroccan-Venezuelan father and an Algerian mother. 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, New Jersey. 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 Prize-winning immunologist Baruj Benacerraf.

Philosophical work edit

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 edit

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 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.[6]

Publications edit

  • 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"[dead link], 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.

See also edit

References edit

  1. ^ Stewart Shapiro, "Mathematical Structuralism", Philosophia Mathematica, 4(2), May 1996, pp. 81–2.
  2. ^ "Paul Joseph Salomon Benacerraf - Oxford Reference". www.oxfordreference.com. Retrieved 2018-12-29.
  3. ^ a b "Book of Members, 1780–2010: Chapter B" (PDF). American Academy of Arts and Sciences. Retrieved June 2, 2011.
  4. ^ "Paul Benacerraf Symposium | Department of Philosophy". philosophy.princeton.edu. Retrieved 2017-11-30.
  5. ^ a b Moseley, Caroline (November 23, 1998). "Whatever I am now, it happened here". Princeton Weekly Bulletin. Princeton University. Retrieved October 13, 2011.
  6. ^ a b . Chronicle of Higher Education. 1 Dec 2017. Archived from the original on 2017-12-11. Retrieved 1 Dec 2017.

Further reading edit

Books about Benacerraf edit

  • 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 edit

  • Hilton, P.
  • Ebert, Philip A. (2020-06-15). "What mathematical knowledge could not be". Aporia St Andrews Journal of the Philosophy Society. 1: 46–70. Retrieved 2022-03-18.
  • Hale, Bob; Wright, Crispin (2002-12-16). (PDF). European Journal of Philosophy. 10 (1): 101–129. doi:10.1111/1468-0378.00151. Archived from the original (PDF) on 2016-01-10.
  • Lucas, J. R. (1968) "Satan stultified: a rejoinder to Paul Benacerraf", The Monist, vol.52, No.1, pp. 145–158.

Articles on Benacerraf edit

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

External links edit

March 13, 2024
paul, benacerraf, paul, joseph, salomon, benacerraf, born, march, 1931, french, born, american, philosopher, working, field, philosophy, mathematics, taught, princeton, university, entire, career, from, 1960, until, retirement, 2007, appointed, stuart, profess. Paul Joseph Salomon Benacerraf b ɪ ˈ n ae s er e f born March 26 1931 2 3 is a French born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University 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 4 Paul BenacerrafBorn 1931 03 26 March 26 1931 age 92 Paris FranceEducationPrinceton University PhD 1960 EraContemporary philosophyRegionWestern philosophySchoolAnalytic philosophyThesisLogicism Some Considerations 1960 Doctoral advisorHilary PutnamDoctoral studentsJohn EarmanAlvin GoldmanRichard GrandyGideon RosenRonald de SousaMain interestsPhilosophy of mathematicsNotable ideasMathematical structuralism eliminative variety 1 Benacerraf s identification problem for set theoretic realismBenacerraf s epistemological problem for mathematical realism Contents 1 Life and career 2 Philosophical work 3 Sexual harassment allegation 4 Publications 5 See also 6 References 7 Further reading 7 1 Books about Benacerraf 7 2 Papers about Benacerraf 7 3 Articles on Benacerraf 8 External linksLife and career editBenacerraf was born in Paris to a Moroccan Venezuelan father and an Algerian mother 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 New Jersey 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 Prize winning immunologist Baruj Benacerraf Philosophical work editBenacerraf 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 editElisabeth 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 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 6 Publications editBenacerraf 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 Godel dead link 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 w 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 See also editAmerican philosophy List of American philosophersReferences edit 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 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 2017 11 30 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 2017 12 11 Retrieved 1 Dec 2017 Further reading editBooks about Benacerraf edit 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 edit Hilton P What What Numbers Could Not Be by Paul Benacerraf is Ebert Philip A 2020 06 15 What mathematical knowledge could not be Aporia St Andrews Journal of the Philosophy Society 1 46 70 Retrieved 2022 03 18 Hale Bob Wright Crispin 2002 12 16 Benacerraf s Dilemma Revisited PDF European Journal of Philosophy 10 1 101 129 doi 10 1111 1468 0378 00151 Archived from the original PDF on 2016 01 10 Lucas J R 1968 Satan stultified a rejoinder to Paul Benacerraf The Monist vol 52 No 1 pp 145 158 Articles on Benacerraf edit Benacerraf Interview by The Dualist and the Stanford Philosophy Department Whatever I am now it happened here by Caroline MoseleyExternal links editPaul Benacerraf s homepage at Princeton The Benacerraf epistemological problem Internet Encyclopedia of Philosophy Retrieved from https en wikipedia org w index php title Paul Benacerraf amp oldid 1188833557, wikipedia, wiki, book, books, library,

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