> On another matter: some members of this list have wondered about
> Landau's remark in the Preface that one cannot prove the consistency
> of the Peano axioms. How could he claim this in 1929, before the
> publication of G\"odel's second incompleteness theorem? Indeed, an
> abstract announcing the incompleteness theorems was first made public
> in October 1930, almost a year after the date of Landau's Preface. But
> surely some people, mainly in Vienna, must have known about these
> results before they were made public. Could Landau have heard about
> them through the grapevine before writing his Preface?
>
Very unlikely given the record.
Relevant are:
John Dawson's fine biography of Go"del: LOGICAL DILEMMAS (AK Peters 1997)
John Dawson, "Discussion on the Foundation of Mathematics" History &
Philosophy of Logic, 5(1984) 11-129.
Paolo Mancosu, "Between Vienna and Berlin: the Immediate Reception of
Go"del's Incompleteness Theorems" preprint.
The first public announcement by Go"del was at a conference in Ko"nigsberg on
September 7, 1930. Von Neumann who was a participant learned about the first
incompleteness theorem at that conference. He and Go"del independently saw
that the underivabilty of consistency followed in the following weeks. Not
long before the conference Go"del had told Carnap about the first
incompleteness theorem in a Vienna coffee shop.
Martin Davis