According to Solomon Feferman, in his [slide presentation](https://math.stanford.edu/~feferman/papers/BernaysLecture1.pdf) "Three Problems for Mathematics", Hilbert wrote (in regards to Gödel's second incompleteness theorem):



> 
> ...the end goal [is] to establish as consistent all our usual methods
>  of mathematics. With respect to this goal, I would like to emphasize
>  the following: the view which temporarily arose and which maintained
>  that certain results of Gödel showed that my proof theory can't be
>  carried out, has been shown to be erroneous.
> 
> 
> In fact that result shows only that one must utilize the finitary standpoint in a sharper way for the further reaching consistency proofs..." 
> 
> 
> 


(Hilbert, Einführung to [Hilbert and Bernays 1934]).


What did Hilbert mean by that statement?


Is there a more complete account from Hilbert regarding that statement and what is it? 



What was Hilbert's view of Gödel's Incompleteness Theorems?
Some related information :


1) Volume 2 of Hilbert & Bernays, [Grundlagen der Mathematik](https://en.wikipedia.org/wiki/Grundlagen_der_Mathematik) (1939) include full proofs of Gödel's 1st and 2nd Theorems (for the 2nd one, it was the first published complete proof), as well as Gentzen's concistency proof, with detailed discussion of their "impact" on the finitist standpoint. 


See Wilfried Sieg & Mark Ravaglia, [David Hilbert and Paul Bernays Grundlagen der Mathematik I and II : A Landmark](http://repository.cmu.edu/cgi/viewcontent.cgi?article=1130&context=philosophy).


2) See in : David Hilbert, [Lectures on the Foundations of Arithmetic and Logic 1917-1933](https://books.google.it/books?id=v7YfBAAAQBAJ&pg=PA788) (Wilfried Sieg ed - 2013), the Introduction to the *Appendices*, page 788-on, regarding Hilbert's lectures of the '30s (and thus, "affected" by Gödel's Theorems). 


3) Assuming that the the work on *Grundlagen* was at least "supervised" or "agreed on" by Hilbert, we can see Paul Bernays' [paper](http://www.phil.cmu.edu/projects/bernays/Pdf/bernaysHilbert_2003-05-17.pdf) of 1967 : it seems that Hilbert carried on with his foundational project post-1930, in order to take into account Godel's works : 



> 
> "One step in this direction [ enlarging of the methods of proof theory, from the original *finite Standpunkt* ], made by Hilbert himself, was to replace the schema of complete induction by the stronger rule later called infinite induction (“[Die Grundlegung der elementaren Zahlenlehre](https://books.google.it/books?id=v7YfBAAAQBAJ&pg=PA967)” (1931a) and “[Beweis des Tertium non datur](https://books.google.it/books?id=v7YfBAAAQBAJ&pg=PA983)” (1931b))." [see page 24].
> 
> 
> 


About *Beweis des Tertium non datur*, here is Wilfried Sieg's [comment](https://books.google.it/books?id=v7YfBAAAQBAJ&pg=PA788) :



> 
> Hilbert 1931a brings in a new technique to address syntactic completeness questions for arithmetic, whereas Hilbert 1931b formulates quite novel, but also somewhat obscure, directions for further proof-theoretic work. It is clear that they react to what Hilbert and others in his School knew at the time of Gödel’s Incompleteness Theorems, and are important at the very least on that account. The last paper is also significant since it influenced Gentzen’s early attempt, starting in late 1931, to establish the consistency of full elementary number theory.
> 
> 
> 




---


Sieg's introductions are expanded into :


* Wilfried Sieg, [Hilbert's Programs and Beyond](https://books.google.it/books?id=4lDrwqo-8TkC&pg=PA129) (2013) : **II Analyses : Historical**, page 129-on.


