 If Hilbert’s worry is wellfounded in the sense that there are no concrete physical systems that make the postulates of mathematical analysis true, then the above nominalist structuralist rendering of the content of a sentence \(\phi\) of the language of analysis gets the truth conditions of such sentences wrong. For then for every universally quantified sentence \(\phi\), its paraphrase will come out vacuously true. So an existential assumption to the effect that there exist concrete physical systems that can serve as a model for RA is needed to back up the above analysis of the content of mathematical statements. Perhaps something like Field’s construction fits the bill.