FOM: What is the role of philosophy in math. logic research?

[Stephen G Simpson]

Andrew Arana Wed, 14 Jun 2000 13:01:52 -0500 (EST) writes:

 > [...] the panelists failed to mention the importance of interplay
 > between philosophy and math. logic, or whether they think that such
 > interplay is even relevant for math. logic. [...]

Yes.  And that failure is representative of how logic has evolved in
recent decades.  

Many of the leading contemporary logicians exhibit what I consider a
strong and regrettable tendency to dismiss any and all
foundational/philosophical concerns.  One of the ASL 2000 after-dinner
speakers (Shoenfield) explicitly mentioned the ASL's trend away from
philosophy.  In the NSF's Foundations Program, f.o.m. research has
been largely displaced by purely technical research, motivated not by
foundational/philosophical considerations but by the hope/longing to
interact with or imitate, however superficially, core math and/or
computer science.

Harvey and I started the FOM list partly in order to combat the
anti-foundational trend and restore f.o.m. to its rightful place as
the motor of mathematical logic.  This has been a consistent theme of
Harvey's and my FOM postings over the years.  See for example Harvey's
series on "Central Issues in Foundations", FOM, September 1999,
http://www.math.psu.edu/simpson/fom/postings/9909/.  See also Harvey's
planned future series of postings, "Mathematical Logic: What Went
Wrong".

-- Steve

PS.  Andrew, I inadvertently omitted you from my long list of "FOM
faces at ASL 2000" in my posting of Tue, 13 Jun 2000 20:47:00 -0400
(EDT).  My apologies.  It happened because of the way I compiled the
list.  I went through the list of preregistered participants and
checked off the FOM names, but apparently you did not preregister.