 Frege’s lack of clarity about his reasons for rejecting Hilbert’s procedure leaves an interpretive gap, with respect to which there is room for controversy. We should recall, to begin with, that Hilbert is clearly right that his own reinterpretation strategy suffices for the relative consistency and independence results he claims. If consistency and independence are understood, as above, in terms of non-provability, and if proof is, as Hilbert assumes, independent of the meanings of geometric terms, then \(\textit{AX}_{R}\), \(\textit{AX}_{G}\), and even AX itself are all consistent if one of them is. Frege’s rejection of Hilbert’s technique must involve, then, either some confusion about what Hilbert has established, or a different understanding of what is at issue in claims of consistency and independence. 