FOM: accentuating the positive; an administrative note

[Stephen G Simpson]

Dear FOM subscribers:

1. The tone of some recent messages by me and Lou was rather negative,
so let me now try to strike a positive note.

a. There is a marvelous subject knows as "foundations of mathematics".
In a nutshell, my definition of f.o.m. is as follows: F.o.m is the
study of the most basic concepts and logical structure of mathematics,
with an eye toward the unity of human knowledge.  This is elaborated
in my little essay at

   www.math.psu.edu/simpson/Hierarchy.html

Obviously this definition of f.o.m. is open to criticism, elaboration,
revision, etc.  So far as I know, I am the only person on the FOM
mailing list who has publicly attempted to define the nature and scope
of f.o.m., but obviously I and everyone here would be glad to hear of
alternative definitions.

b. Many of the great mathematicians of the past, such as Dedekind,
Poincare, Hilbert, Brouwer, and von Neumann, took a lively interest in
f.o.m. and wrote fruitfully and extensively on it.  Indeed, f.o.m. was
part of their central concern as mathematicians.  Unfortunately,
today's leading mathematicians are far less interested.  Nevertheless,
f.o.m is a very active research field with much to contribute to the
global intellectual enterprise.  F.o.m. has a wealth of ideas,
techniques, issues, and programs.  For examples I would point to the
Friedman volume, "Harvey Friedman's Research in Foundations of
Mathematics," North-Holland, 1985.

c. Let's try to focus on the positive aspects of f.o.m.: what can
f.o.m.  contribute to mathematics, philosophy, science, and the unity
of human knowledge?  What does f.o.m. mean to you?

2. An administrative remark.  Over the coming weekend, I may not be
able to access my e-mail.  Therefore, your remarks sent to
fom at math.psu.edu may not appear immediately.  Be patient!

Sincerely,
-- Steve