FOM: Feferfest impressions
Stephen G Simpson
simpson at math.psu.edu
Tue Dec 22 17:52:09 EST 1998
Stephen G Simpson writes:
> In addition, I want to initiate a discussion of the Feferfest, a
> recent symposium in honor of Solomon Feferman's 70th birthday,
> which I attended. This was a very interesting conference. I had a
> lot of fun. Many leading contemporary figures in f.o.m. were
> present. Many of the talks were directly relevant to issues that
> we have been discussing here on FOM. My talk dealt directly with
> an issue that Feferman has returned to many times: predicativity.
> Charles Parsons gave an interesting talk on the reasons advanced by
> Hilbert and Bernays and others for rejecting the predicativist
> program.
I will get into these scientific issues in later FOM postings. Right
now I want to simply record some impressions of the Feferfest itself.
The banquet on Saturday night (December 12, Stanford Faculty Club) was
huge, more than 150 people and a lot of after-dinner speeches and
testimonials honoring Feferman, who was aglow with all the attention
being paid to him. Rick Sommer was the master of ceremonies. Pat
Suppes and Anita Feferman gave major speeches. As for the scientific
sessions (December 11-13), the level was uneven, but there were a fair
number of exciting talks. Between talks, there was not always enough
time for questions and discussion, but the session chairmen made a
point of inviting Feferman himself to comment on each talk, which he
did. The range of Feferman's contributions in f.o.m. is enormous. He
has played a huge role in this field.
My own talk, entitled `Predicativity: The Outer Limits', went well. I
made the point that there is a big difference between Feferman's
system IR, explicating predicative provability, and the system ATR0,
which explicates predicative reducibility and is of key importance in
reverse mathematics. This is despite the fact that IR and ATR0 are
proof-theoretically equivalent. Feferman had several comments: (0) He
agreed with the distinction I made. (1) He seemed to feel I had not
done justice to IR because I didn't go into the motivation in terms of
autonomous progressions. (2) He made a point, which I didn't really
understand, to the effect that, although each individual theorem of IR
is predicative, the whole system is not. (3) He said there is need for
systems with a rich type structure explicating predicative provability
in that context. I heartily agree with (0) and (3). I plan to write
this up in the Feferfest proceedings.
Some notable absences from the Feferfest: Gerhard J"ager (absent due
to illness), Wilfried Buchholz (last minute change in plans), Harvey
Friedman, Georg Kreisel, Paul Cohen, Craig Smorynski.
At the Feferfest, Feferman's new book `In the Light of Logic', a
collection of essays on f.o.m.), was much in evidence. It can be
ordered for 44 dollars from a current Oxford University Press sale
catalog, as I did, or by phoning 1-800-451-7556 and mentioning
promotion code J375. The sale ends February 28.
Speaking of books, I was glad I had a copy of my own new book
`Subsystems of Second Order Arithmetic' in hand to show everybody at
the Feferfest. Feferman himself had a lot to do with this book,
notably as an editor of the Perspectives in Mathematical Logic series.
Many Feferfest participants congratulated me on finally publishing
this book and/or said that they plan order it. Information about it
is available at
http://www.math.psu.edu/simpson/sosoa/
I am making some Feferfest information and web links available at
http://www.math.psu.edu/simpson/feferfest/
Many Feferfest participants are here on FOM. I urge everyone to join
in the discussion.
Best wishes to all!
-- Steve
Name: Stephen G. Simpson
Position: Professor of Mathematics
Institution: Penn State University
Research interest: foundations of mathematics
More information: www.math.psu.edu/simpson/
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