 Wittgenstein’s unorthodox position here is a type of structuralism that partially results from his rejection of mathematical semantics. We erroneously think, e.g., that GC has a fully determinate sense because, given “the misleading way in which the mode of expression of word-language represents the sense of mathematical propositions” (PG 375), we call to mind false pictures and mistaken, referential conceptions of mathematical propositions whereby GC is about a mathematical reality and so has just a determinate sense as “There exist intelligent beings elsewhere in the universe” (i.e., a proposition that is determinately true or false, whether or not we ever know its truth-value). Wittgenstein breaks with this tradition, in all of its forms, stressing that, in mathematics, unlike the realm of contingent (or empirical) propositions, “if I am to know what a proposition like Fermat’s last theorem says”, I must know its criterion of truth. Unlike the criterion of truth for an empirical proposition, which can be known before the proposition is decided, we cannot know the criterion of truth for an undecided mathematical proposition, though we are “acquainted with criteria for the truth of similar propositions” (RFM VI, §13).