FOM: Kreisel's "unwinding" program

Vaughan Pratt 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
>be valued.

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.

Vaughan Pratt

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