[FOM] Goedel Volumes 4 and 5

[Alasdair Urquhart]

I've just finished reading Goedel's
Collected Works Volumes 4 and 5 cover
to cover, so I thought I'd post
a few of my reactions, partly as a means
of calling FOM readers' attention to these
wonderful volumes.  ASL members should note
that they can get them at a 35% discount --
see the ASL web site.

The volumes are beautifully edited and produced,
and a delight to read.  They are devoted entirely
to Goedel's correspondence -- the original plan to
edit some of the unpublished notebooks apparently
fell through.  I'd read extracts from quite 
a few of the letters before, but nevertheless, 
the correspondence with Bernays, Cohen, Church, 
Post, Robinson, Tarski, Zermelo and many others 
is quite wonderful to read.  

I was interested to see that the young Goedel 
expressed himself much more incautiously and
sharply than the older Goedel.  For example,
in writing Carnap in 1932, he refers to 
"Zermelo's nonsensical criticism of my paper"
(the Zermelo correspondence printed here confirms
this rather brutal judgment).

Among logicians with whom Goedel corresponded, 
there was one and only one whom he addressed
as "Du" in German, and by his first name in English.
The identity of this logician and the warmth of
their friendship surprised me.

Logical surprises -- the biggest was the following 
passage from a letter from von Neumann of 
January 1931:

	Incidentally, the other day I developed a 
	method that always allows a finite decision
	for the effective provability question concerning
	propositions that are built up solely by means
	of the concepts "not", "or" (thus also "and",
	"follows", etc.), "provable" (starting from the
	identical truth -- consistency is for example
	such a proposition.

This appears to say that in 1931 von Neumann had already
solved the 35th of Harvey Friedman's 102 problems (first
published solution by Boolos 1976).

Only major disappointment -- the independence proof
for the Axiom of Choice in simple type theory that 
Goedel allegedly discovered in 1942 remains a mystery,
even though it is discussed at length in correspondence
with Church and Rautenberg.  Goedel claimed to have
some notes on the subject.  Is there really nothing
in his papers other than the correspondence on the
subject?  It seems unlike Goedel to refer to notes
that did not in fact exist.  Can any FOM subscriber
shed light on this mystery?