Benacerraf is perhaps best known for his two papers "What Numbers Could Not Be" and "Mathematical Truth", and for his anthology on the philosophy of mathematics, co-edited with Hilary Putnam. 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. This argument is called Benacerraf's identification problem. 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.
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." Benacerraf has denied the allegations, stating in an email to The Chronicle, Mr. Benacerraf said 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.
Publications
Benacerraf, Paul Logicism, Some Considerations, Princeton, Ph.D. Dissertation, University Microfilms.
Benacerraf, Paul "What Numbers Could Not Be", The Philosophical Review, 74:47–73.
Benacerraf, Paul "Frege: The Last Logicist", The Foundations of Analytic Philosophy, Midwest Studies in Philosophy, 6: l7–35.
Benacerraf, Paul "Skolem and the Skeptic", Proceedings of the Aristotelian Society, Supplementary Volume 56: 85–ll5.
Benacerraf, Paul and Putnam, Hilary Philosophy of Mathematics : Selected Readings 2nd edition, Cambridge University Press: New York.
Benacerraf, Paul "Recantation or Any old ω-sequence would do after all", Philosophia Mathematica, 4: 184–189.
Benacerraf, Paul 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 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.
