FOM: attitudes of core mathematicians and applied model theorists toward f.o.m.

[Stephen G Simpson]

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]