Paul Benacerraf
Encyclopedia
Paul Joseph Salomon Benacerraf (born 1931) is an American philosopher working in the field of the philosophy of mathematics
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
who has been teaching at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
since he joined the faculty in 1960. He was appointed Stuart Professor of Philosophy in 1974, and recently retired as the James S. McDonnell Distinguished University Professor of Philosophy. Born in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, his parents were Sephardic Jews from Morocco
Morocco
Morocco , officially the Kingdom of Morocco , is a country located in North Africa. It has a population of more than 32 million and an area of 710,850 km², and also primarily administers the disputed region of the Western Sahara...
(father) and Algeria
Algeria
Algeria , officially the People's Democratic Republic of Algeria , also formally referred to as the Democratic and Popular Republic of Algeria, is a country in the Maghreb region of Northwest Africa with Algiers as its capital.In terms of land area, it is the largest country in Africa and the Arab...
(mother). His brother is the Venezuelan
Venezuelan people
Venezuelan people are from a multiethnic nation in South America called Venezuela. Venezuelans are predominantly Roman Catholic and speak Spanish, and a majority of them are the result of a mixture of Europeans, Africans, and Amerindians.-Demography:...
Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...
-winning immunologist Baruj Benacerraf
Baruj Benacerraf
Baruj Benacerraf was a Venezuelan-born American immunologist, who shared the 1980 Nobel Prize in Physiology or Medicine for the "discovery of the major histocompatibility complex genes which encode cell surface protein molecules important for the immune system's distinction between self and...
.
Benacerraf is perhaps best known for his two papers What Numbers Could Not Be (1965) and Mathematical Truth (1973), and for his highly successful anthology on the philosophy of mathematics, co-edited with Hilary Putnam
Hilary Putnam
Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...
. He was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1998.
In What Numbers Could Not Be, he 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 Zermelo and von Neumann give distinct, and completely adequate, identifications of natural numbers with sets.
In Mathematical Truth, 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. 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.
Works
- Benacerraf, Paul (1960) Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
- Benacerraf, Paul (1965) What Numbers Could Not Be, The Philosophical Review, 74:47-73.
- Benacerraf, Paul (1967) God, the Devil, and Gödel, The Monist, 5l: 9-33.
- Benacerraf, Paul (1973) Mathematical Truth, The Journal of Philosophy, 70: 661-679.
- Benacerraf, Paul (1981) Frege: The Last Logicist, The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: l7-35.
- Benacerraf, Paul (1985) Skolem and the Skeptic, Proceedings of the Aristotelian Society, Supplementary Volume 56: 85-ll5.
- 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 ω-sequence would do after all, Philosophia Mathematica, 4: 184-189.
- 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.
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 Benacerra', is.
- Ebert, Philip A. (2007) What Mathematical Knowledge Could Not Be, in St Andrews Undergraduate Philosophy Society Journal, 1 (1) pp. 46–70.
- Hale, Bob and Wright, CrispinCrispin WrightCrispin Wright is a British philosopher, who has written on neo-Fregean philosophy of mathematics, Wittgenstein's later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge, and objectivity....
(2002) Benacerraf's Dilemma Revisited 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.
Writings on Benacerraf
- Benacerraf Interview by The Dualist and the Stanford Philosophy Department
- "Whatever I am now, it happened here" by Caroline Moseley