Paul Benacerraf | |
|---|---|
 | |
| Born | (1930-03-26)26 March 1930 |
| Died | 13 January 2025(2025-01-13) (aged 94) |
| Education | |
| Education | Princeton University (PhD, 1960) |
| Thesis | Logicism, Some Considerations (1960) |
| Doctoral advisor | Hilary Putnam |
| Philosophical work | |
| Era | Contemporary philosophy |
| Region | Western philosophy |
| School | Analytic philosophy |
| Doctoral students | Paul Boghossian John Earman Alvin Goldman Richard Grandy Gideon Rosen Ronald de Sousa |
| Main interests | Philosophy of mathematics |
| Notable ideas | Mathematical structuralism (eliminative variety)[1] Benacerraf's identification problem forset-theoretic realism Benacerraf's epistemological problem formathematical realism |
Paul Joseph Salomon Benacerraf (/bɪˈnæsərəf/; 26 March 1930 – 13 January 2025) was a French-born American philosopher working in the field of thephilosophy of mathematics who taught atPrinceton University 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.[2]
Benacerraf was born inParis on 26 March 1930,[3][4] to a Moroccan-VenezuelanSephardic Jewish father, Abraham Benacerraf, and Algerian Jewish mother, Henrietta Lasry. In 1939 the family moved toCaracas and then to New York City.[5]
When the family returned to Caracas, Benacerraf remained in the United States, boarding at thePeddie School inHightstown, New Jersey. He attendedPrinceton University for both his undergraduate and graduate studies.[5]
He was elected a fellow of theAmerican Academy of Arts and Sciences in 1998.[4]
Benacerraf died on 13 January 2025, at the age of 94.[6][7][8] His older brother was the VenezuelanNobel Prize-winning immunologistBaruj Benacerraf.
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 withHilary Putnam.
In "What Numbers Could Not Be" (1965), Benacerraf argues against aPlatonist view of mathematics, and forstructuralism, 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 thatErnst Zermelo andJohn von Neumann give distinct, and completely adequate, identifications of natural numbers with sets (seeZermelo ordinals andvon Neumann ordinals). This argument is calledBenacerraf'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 calledBenacerraf'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.
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."[9] Benacerraf has denied the allegations, stating in an email toThe 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.[9]
