Cross-structural identity statements

According to realist or ‘non-eliminative’ versions of mathematical structuralism, mathematical objects are merely positions in structures, ontologically dependent on them. This raises questions about identity statements linking positions across distinct structures, such as ‘the natural number 2 is identical to the real number 2’. I develop a novel Aristotelian account on which structures ontologically depend on their corresponding systems. On this in re version of structuralism, cross-structural identities are false, while the expressions flanking the identity sign are referentially indeterminate, even if isomorphism suffices for the numerical identity of structures.