Finitism and primitive recursive arithmetic

[martdowd at aol.com]

FOM:
Joe Shipman wrote:   Did Hilbert or his collaborators ever explicitly either accept or reject the claim that Ackerman’s function was finitistic?
This has been a longstanding debate in the history of the subject.
  Lieber Herr Bernays!, Lieber Herr Gödel!
  Gödel on finitism, constructivity and Hilbert's program  https://math.stanford.edu/~feferman/papers/bernays.pdfby Solomon Feferman is a good reference.  He includes the following quote from Godel in 1969:
In order to eliminate the quantifiers ...one would use a nested recursion... But nested recursions are not finitary in Hilbert’s sense (i.e. not intuitive) ... Or don’t you believe that? (CW IV, p. 271)
Martin Dowd
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