 The discussion of structuralism, as a major position in English-speaking philosophy of mathematics, is usually taken to have started in the 1960s. A central article in this connection was Paul Benacerraf’s “What Numbers Could Not Be” (1965; cf. also Benacerraf 1996, a later follow-up). The background and foil for this article was the position, dominant at the time, that axiomatic set theory provides the foundation for modern mathematics, including allowing us to identify all mathematical objects with sets. For example, the natural numbers 0, 1, 2, … can be identified with the finite von Neumann ordinals (starting with \(\emptyset\) for 0 and using the successor function \(f: x \rightarrow x\cup \{x\})\); similarly, the real numbers can be identified with Dedekind cuts constructed set-theoretically. Arithmetic truths are then  truths about these set-theoretic objects; and this generalizes  to other mathematical theories, all of whose objects are taken to be sets as well.