FOM: Kreisel's "unwinding" program
pratt at cs.Stanford.EDU
Tue Mar 3 06:00:06 EST 1998
From: Solomon Feferman <sf at Csli.Stanford.EDU>
>There is no need to formulate this in terms of general intellectual
>interest vs. mathematical interest, but what has apparently resulted
>in such essays as MacIntyre's (if Simpson's report is accurate)
>is an unfortunate snobbism or dismissal of foundational work, and
>that only applications of logic to "real", "hard" mathematics is to
My one meeting with MacIntyre was in Hanover in 1979. We were staying at
the same hotel, and had breakfast together one morning. We found we had
something in common: we were both speakers at the International Congress
on Logic, Philosophy and Methodology of Science (both invited I think).
But that turned out to be about all we had in common. For some reason
the conversation soon turned to the importance of hard mathematics.
I took the position that the results themselves and their uses were what
mattered and that simplicity of proof was a virtue. MacIntyre viewed
mathematics as a challenge and the more difficult the better.
While I certainly sympathized with the idea of mathematics as a strenuous
recreation, like climbing Mt. Everest, for me mathematics was more
importantly a tool, and it seemed obvious to me that the harder a tool is
to use the less useful it is: easier to make mistakes with, and harder
to pass along to the next generation. MacIntyre stuck to his guns:
mathematics was no good unless it was hard, and the harder the better.
I bring this up now because I was struck by how unreasonably extreme his
position seemed to me. I've met plenty of pure mathematicians in my life,
but none have advocated difficulty over utility as single-mindedly as
he did then.
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