FOM: dimly lit pubs; some questions for the applied model theorists

[Stephen G Simpson]

Lou van den Dries 9 Mar 1998 21:42:51 writes:
 > about Macintyre. Not a bad description, these "darkly lit pubs" (or
 > words to that effect). ...  But the part about students and junior
 > colleagues listening in silence to a "pontificating" Macintyre is
 > the total opposite of my experience.  The picture conjured up by
 > Steve in this regard is just silly.

If the "dimly lit pubs" picture is silly, then why has Macintyre
declined to promulgate and defend his noxious views here in the light
of day provided by the FOM list?  Lou, can you answer this?

 > From a general intellectual point of view, isn't it odd to be more
 > or less permanently preoccupied with the foundations of a subject
 > to the point of loosing interest in the subject itself?

I don't find it odd.  G"odel is an f.o.m. hero, and he wasn't
interested in chatting about algebraic topology with his mathematical
colleagues at IAS.  Also, it depends on what you mean by "loosing
interest" (I assume you intended "losing interest").  For example,
standard key mathematical theorems are part of the stock in trade of
my own work in Reverse Mathematics.  (This aspect of Reverse
Mathematics seems to be extremely irritating to Kreisel and Macintyre.
Why?  Lou, can you explain this?)  Also, Harvey has gone to great
lengths to bring the G"odel incompleteness phenomenon closer to core
mathematics.  Doesn't this interest you?

 > I guess division of labour is a possible answer,

Yes.  What you and Macintyre fail to realize is that f.o.m is a
subject in its own right, distinct from pure mathematics, with its own
aims, goals, methods, issues, and programs, quite different from the
aims and methods of pure mathematics.  You and Macintyre also fail to
realize that f.o.m. is inherently of greater general intellectual
interest than pure mathematics.

 > this clearly presents difficulties if serious intellectual
 > communication with the practitioners of the subject itself is
 > endangered.)

Not necessarily.  The practitioners in question may be mere
second-rate "working mathematicians", caught up in narrow technical
issues and therefore temporarily or permanently unable to appreciate
the big picture.  However, as an f.o.m. researcher, I can and do
communicate successfully with first-rate mathematicians about
f.o.m. issues and programs.  For instance, Barry Mazur once ran a
seminar on Reverse Mathematics at Harvard.  Recently H. Furstenberg
visited Penn State; he attended my seminar talk on f.o.m. and later we
had a nice chat about intuitionism.

Lou, since you seem to be willing to discuss pictures of Macintyre, I
have another picture for you to confirm or deny.  The "dimly lit pubs"
picture was based on some first-hand accounts, but this other picture
is solely a product of my imagination.  The picture is of Atiyah
rushing from a seminar on K-theory to another seminar on quantum
groups, with Angus Macintyre trotting along behind trying
unsuccessfully to interest Atiyah in the latest results in applied
model theory.  Is this picture accurate, in spirit at least?

To put this question in a more serious and scholarly way: I know that
Lou van den Dries, Angus Macintyre, Anand Pillay, and other applied
model theorists seek to overcome "communication difficulties" by
attempting to apply model-theoretic tools to technical questions in
core mathematics.  My question is, how successful has this strategy
been?  Are the core mathematicians duly appreciative?

-- Steve