[FOM] Godel Centenary Meeting 3

Harvey Friedman friedman at math.ohio-state.edu
Sat May 27 15:50:40 EDT 2006

You can find these manuscripts of mine in connection with the Godel
Centenary Meeting, Horizons of Truth, Logics, Foundations of Mathematics,
and the Quest for Understanding the Nature of Knowledge, An International
Symposium Celebrating the 100th Birthday of Kurt Godel, April 27 to 29,

PDF files under Lecture Notes:

29. 'Forty years on his shoulders', Godel Centenary, April 25, 2006, 9

30. 'Remarks on Godel Phenomena and the field of reals', Godel Centenary,
April 27, 2006, 6 pages.

31. 'Remarks on the unknowable', Godel Centenary, April 28, 2006, 6 pages.

#29 was my main talk delivered on April 29.

#30 was a talk that I was asked to prepare in case Georg Kreisel was too ill
to deliver his talk on April 27. Fortunately, Kreisel recovered and was able
to give his talk.

#31 was my brief talk at the panel 'On Unknowability', on April 28.

For #30, before the meeting, I was specifically asked on behalf of the
organizers to react to Angus Macintyre's first talk of the meeting, with his
"How much has Mathematics been Affected by Godel's Work?" Macintyre's
general views were already known from his abstract, which was available well
before the meeting.

Here is an executive summary. Macintyre's answer is "Very very little". My
answer is "For general mathematical culture, a great deal. For the focused
working mathematician, little, but little YET".

In #31, I propose an example of the "unknowable", and mention that Chaitin
has been publishing on related matters for some time. I outline a research
program there, and make excuses for not having done certain things. Any
comments on the relationship between this work and that of Chaitin's would
be particularly welcomed.

As an aside, Angus Macintyre stated in his talk that

it is relatively straightforward to show that FLT can be proved in PA.

This matter has been discussed on the FOM recently, and in particular
"relatively straightfoward" has been disputed on the FOM by Robert Solovay.
I hope that a Macintyre/Solovay dialog will take place on this matter
(probably not on the FOM).

Harvey Friedman  



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