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

Stephen G Simpson simpson at
Thu Jun 15 14:34:24 EDT 2000

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,  See also Harvey's
planned future series of postings, "Mathematical Logic: What Went

-- 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.

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