 From Hilbert’s point of view, of course, there is no need for such a justification. The differences that Frege insists on over and over again between the sets of sentences (AX) and the different sets of thoughts (\(\textit{AX}_{G}\), \(\textit{AX}_{R}\) etc.) are entirely inconsequential from Hilbert’s standpoint. Because consistency as Hilbert understands it applies to the “scaffolding” of concepts and relations defined by AX when its geometric terms are taken as place-holders, the consistency he has in mind holds (to put it in terms of thoughts) of \(\textit{AX}_{G}\) iff it holds of \(\textit{AX}_{R}\), since both sets of thoughts are instantiations of the same “scaffolding”. The same point can be put in terms of sentences: Frege insists that the consistency-question that arises for the sentences under their geometric interpretation is a different issue from the one that arises for those sentences under their real-number interpretation; for Hilbert on the other hand, there is just one question, and it is answered in the affirmative if there is any interpretation under which the sentences express truths. Hence while Frege takes it that Hilbert owes an explanation of the inference from the consistency of \(\textit{AX}_{R}\) to that of \(\textit{AX}_{G}\), for Hilbert there is simply no inference.