 The upshot is that mathematics in general becomes metamathematics, a contentful theory—Curry’s sentences express propositions with truth values—setting out the truths about what is provable from what in underlying formal systems whose interpretation, or rather interpretations, are not taken to be mathematically important. This standpoint, however, threatens to collapse into structuralism, into viewing mathematical utterances as schemata implicitly generalising over a range of (in general) abstract structures which satisfy the schemata. As to the problem of the metatheory, Curry does not seek to answer this; there is no real attempt to avoid commitment to a rich ontology of objects, except that, by considering only standard formal systems, one could make do with a countable ontology which can play the role of linguistic expressions. Only, however, at the cost of grossly distorting mathematical practice. Set theorists, topologists, analysts et al. entertain conjectures, and try to prove things ‘about’ sets, topological spaces, functions on the complex numbers and so on. In their philosophical moments they may wonder just what the concepts they are wrestling with are ‘about’, but they do not in general entertain conjectures or try to prove things ‘about’ expression strings, except where it is of instrumental value to them in proving things about sets, spaces, the complex plane and so on (cf. Resnik pp. 70–71).