 In current approaches it is sometimes added that any other set-theoretically constructed system that is isomorphic to the system of Dedekind cuts or to the system of finite von Neumann ordinals, respectively, would do as well, i.e. be usable mathematically as “the real numbers” or “the natural numbers” for most practical purposes. This means that contemporary set theory is, often implicitly and without further elaboration, supplemented by a “set-theoretic structuralist”  view about the nature of mathematical objects (Reck &amp; Price 2000). The resulting philosophical position is different from Dedekind’s. (But see again Sieg &amp; Morris 2018; in it Dedekind is interpreted as  changing his position over time, i.e., as having adopted a position close to set-theoretic structuralism by 1888.) Nor does Dedekind’s position coincide with several other forms of structuralism prominent in contemporary philosophy of mathematics, e.g., those defended by Geoffrey Hellman, Michael Resnik, and Stewart Shapiro.