Paul Benacerraf: The identity of numbers and structuralism

Kazemi, Ramin

doi:10.30465/ps.2026.54903.1839

Paul Benacerraf: The identity of numbers and structuralism

Document Type : .

Author

Ramin Kazemi

Professor of Statistics, Imam Khomeini International University

10.30465/ps.2026.54903.1839

Abstract

Paul Joseph Salomon Benacerraf, a professor of the philosophy of mathematics at Princeton University, passed away in 2025 at the age of 93. By raising a number of fundamental questions, he transformed the philosophy of mathematics from a primarily logical enterprise into a profound epistemological and metaphysical inquiry. His papers are widely regarded as among the most influential works in twentieth-century philosophy of mathematics and played a pivotal role in the emergence and development of mathematical structuralism. This paper examines the two articles that brought him international recognition and briefly reviews the reactions they elicited from other philosophers. Benacerraf argued that numbers lack an intrinsic identity independent of the mathematical structures in which they occur; what matters is the “role” they occupy within a numerical structure. He also formulated a challenge that later became known as the “Benacerraf Problem”: how is it possible for human beings to have knowledge of abstract mathematical object

Keywords

Numbers

the Benacerraf problem

mathematical epistemology

structuralism

Subjects