 Together with his collaborators Ackermann and Bernays, Hilbert developed metamathematics considerably during the 1910–1920s.  This served as the basis of  Hilbert’s (1922) lecture wherein he replied to Poincaré by making a systematic distinction between “formal“ occurrences of mathematical induction in the object language and the metatheoretic use of induction as a “contentual“ [inhaltliche] principle used in order to reason about proofs as finite combinatorial objects.  It was also in this context in which Hilbert connected the latter form of induction to the “construction and deconstruction of number signs” (1922, 1123).  