FOM: attitudes of core mathematicians and applied model theorists toward f.o.m.
Stephen G Simpson
simpson at math.psu.edu
Wed Jan 26 13:00:20 EST 2000
Here is some follow-up to my FOM posting of 24 January 2000, the one
where I mentioned that Connes also found it necessary to discuss
G"odel's theorem.
This was originally private correspondence, but Mark Steiner gave me
permission to post it here on FOM. I have edited my comments
slightly.
-- Steve
----------
From: Mark Steiner <marksa at vms.huji.ac.il>
To: simpson at math.psu.edu
Subject: Re: FOM: Millenium Conference
Date: Mon, 24 Jan 2000 23:05:53 +0200
Steve--
I prefer to answer this privately, because Harvey asked me the same
questions--and I answered in the course of my previous postings (take a
look):
> It is very interesting that, when top core mathematicians talk to a
> general scientific audience, they often feel a need to discuss
> G"odel's theorem. Why? Could it be because G"odel's theorem has
> g.i.i. (general intellectual interest)?
Of course. And not only g.i.i., but it is of fundamental importance to
core mathemathematicians, because (as Kazhdan put it) it threatens
mathematics. Kazhdan was not able to pick a theorem proved in the
twentieth century which he could discuss in this lecture, so the lecture
was basically about the philosophy and history of mathematics, not
mathematics. To this, of course Goedel's theorem is particularly
relevant.
>
> Note that the applied model theorists such as van den Dries and
> Cherlin strenuously reject the idea that G"odel's theorem and
> f.o.m. generally have g.i.i. (See for instance the ``g.i.i. brawl''
> between Harvey and Lou in the early months of FOM.) Why? Are the
> applied model theorists trying to reflect what they think is the
> attitude of the core mathematicians toward f.o.m.? If so, then the
> reflection seems to be far from perfect.
>
I hope what you say is not true. I myself think that model theory has
great intellectual interest. Actually, as a philosopher, I find that if
we think that a scientific field has no intellectual interest, it pays
to look harder at that field. My views about model theory as a route
to giving explanations in mathematics I posted earlier.
> Steiner:
>
> > I therefore have to agree with some of the remarks that
> > have been made on this list, though I didn't expect to.
>
> Which remarks? The claim by me and Harvey that f.o.m. has g.i.i.?
Of course not. I meant the claim that core mathematicians are biased
against f.o.m.
>
> -- Steve
----------
From: Stephen G Simpson <simpson at math.psu.edu>
To: Mark Steiner <marksa at vms.huji.ac.il>
Subject: Re: FOM: Millenium Conference
Date: Mon, 24 Jan 2000 16:39:37 -0500 (EST)
OK Mark, thanks. I did look at your other postings, and they partly
answered my questions, but I wanted further clarification, which you
have now provided.
> I myself think that model theory has great intellectual interest.
Me too. I myself am quite interested in both pure and applied model
theory.
What I was referring to is the hostility that the current generation
of applied model theorists routinely exhibit toward f.o.m. But I
understand how this hostility comes about. For reasons of their own,
they are trying very hard to reorient mathematical logic away from
its roots in f.o.m. (Frege, Russell, Hilbert, G"odel, et al) and
toward direct applications to core math, especially algebra and
number theory. The result is that they tend to take an aggressively
anti-f.o.m. attitude, saying that f.o.m. is of little interest
compared with core math. For instance, van den Dries said on FOM
that there are dozens of 20th century core mathematicians whose work
is of greater interest than G"odel's. And he is unfazed when you
point out to him that the general scientific public does not agree
with this evaluation. And he even goes so far as to deny the
meaningfulness of the concept g.i.i. and the statement that G"odel's
theorem has g.i.i.
> > Which remarks? The claim by me and Harvey that f.o.m. has g.i.i.?
>
> Of course not. I meant the claim that core mathematicians are biased
> against f.o.m.
The long abstract by Kazhdan that Harvey just posted on FOM shows me
that Kazhdan is much *less* biased against f.o.m. than most of the
core mathematicians that I have encountered. The typical attitude of
core mathematicians is that G"odel's theorem is simply irrelevant to
what they do and they don't care about it, period. Kazhdan is
obviously not as bad as that.
-- Steve
----------
From: Mark Steiner <marksa at vms.huji.ac.il>
To: simpson at math.psu.edu
Subject: Re: FOM: Philosophy and platonism
Date: Wed, 26 Jan 2000 16:29:09 +0200
Stephen G Simpson wrote:
>
> Mark,
>
> Would it be OK with you if I put our most recent off-line
> correspondence (about the millenium conference, the applied model
> theorists, etc) on FOM?
>
> If not, don't worry, I will find some other way to make my points on
> FOM.
>
> -- Steve Simpson
Steve,
Go ahead, on condition you answer the question that I asked and Harvey
passed to you: namely, I asked for the difference, as you understand it,
between f.o.m. and what used to be called "proof theory."
Mark
P. S. [omitted, not part of this discussion]
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