Paul Benacerraf
| Paul Benacerraf | |
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| Born | 1931 Paris, France |
| Era | 20th-century philosophy |
| Region | Western philosophy |
| School | Analytic philosophy |
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Main interests
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Philosophy of mathematics |
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Notable ideas
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Mathematical structuralism |
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Influences
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Influenced
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Paul Joseph Salomon Benacerraf (born 1931) is a French-born American philosopher working in the field of the philosophy of mathematics who has been teaching at Princeton University since he joined the faculty in 1960. He was appointed Stuart Professor of Philosophy in 1974, and retired in 2007 as the James S. McDonnell Distinguished University Professor of Philosophy.
Benacerraf was born in Paris to parents who were Sephardic Jews from Morocco and Algeria. His brother was the Venezuelan Nobel Prize-winning immunologist Baruj Benacerraf.
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. He was elected a Fellow of the American Academy of Arts and Sciences in 1998.
In "What Numbers Could Not Be", 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.
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.
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