[FOM] Godel Centenary Meeting 1

[Harvey Friedman]

I just came back from the 100-th birthday celebration of Kurt Godel, held in
Vienna. There were a lot of interesting talks at the meeting. I want to
discuss some of this, concentrating mainly on my participation - after all,
that is what I know best.

I prepared three talks. One, the talk I gave, "Forty years on his
shoulders". A second, a 5 minute talk at the first of two panel discussions.
A third talk, prepared in case Georg Kreisel was too sick to deliver his
talk. Kreisel did deliver this talk.

In this first installment, I will just discuss the opening remarks I made in
my regular talk. (All regular talks were 45 minutes in length, but I managed
to bully my moderator into a bit more than 5 more minutes).

I opened with thank yous and pleasantries, and this:

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Godel's legacy is still very much in evidence. It must be noted that a
careful analysis reveals that this great insights raise more issues than
they resolve. The Godel legacy practically begs for renewal and expansion at
a fundamental level.

When I entered the field some forty years ago, I seized on one glaring
opportunity for renewal and expansion. The independence results from ZFC and
significant fragments lied in a very narrow range, and had systemic features
that are glaringly unrepresentative of mathematics and mathematical subjects
generally. 

This state of affairs suggests obvious informal conjectures to the effect
that there are severe systemic limitations to the incompleteness phenomena,
culminating in informal conjectures to the effect that, in principle, there
is no relevance of set theoretic methods to "genuine" mathematical activity.

Now, there is no question that this central aspect of Godel's legacy,
incompleteness, will diminish over time if such informal conjectures are not
addressed in a substantial way. I have devoted the major part of my efforts
over forty years to this effort.

I view this effort as part of a perhaps slow but steady evolutionary
process. I have every confidence that this process will steadily continue in
a striking manner as long as mathematics remains a vibrant activity.

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Harvey Friedman