Paul Benacerraf
American philosopher (1930–2025)
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Through Paris and Natural number
Life and career
Benacerraf was born in Paris on 26 March 1930, to a Moroccan-Venezuelan Sephardic Jewish father, Abraham Benacerraf, and Algerian Jewish mother, Henrietta Lasry. In 1939 the family moved to Caracas 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, New Jersey. He attended Princeton University for both his undergraduate and graduate studies.
He was elected a fellow of the American Academy of Arts and Sciences in 1998.
Benacerraf died on 13 January 2025, at the age of 94. His older brother was the Venezuelan Nobel Prize-winning immunologist Baruj Benacerraf.
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Philosophical work
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 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.