 According to Benacerraf, such a set-theoretic foundationalist position misrepresents the structuralist character of arithmetic in particular and of mathematics more generally. To begin with, instead of working with the finite von Neumann ordinals, we can equally well work with the finite Zermelo ordinals (starting again with \(\emptyset\) for 0 but using the alternative successor function \(f: x \rightarrow \{x\})\); and there are infinitely many other choices that are equivalent. Similarly, instead of working with a set-theoretic construction of the real numbers in terms of Dedekind cuts, we can work with a construction based on equivalence classes of Cauchy sequences on the rational numbers as suggested by Cantor and others. This basic observation is hard to deny, and even set-theorist foundationalists can agree with it (more on that below). But Benacerraf draws some further, more controversial conclusions from this basic observation. 