FOM: RE: What is f.o.m., briefly?

[Ayan Mahalanobis]

It appeared to me (after first reading) that you are putting too much
emphasis on axiomatics. As it stands today, we understand a certain type of
mathematics from the set of axioms that defines them, yet in the core there
is something that appeals to us, some pretty geometric figure or may be a
cute looking equation like Fermat's last theorem. I think that study of
foundation of mathematics has to go deeper than set of axioms. Say for
example,  What is continuum? May be one can escape this by saying,
"I have real numbers which I got somehow and I want to study them!", then
probably you are right, it is axiomatics. But if I want to argue as what
should be the definition of continuum then that is foundation of mathematics
and probably not axiomatics.

--Ayan

-----Original Message-----
From: owner-fom at math.psu.edu [mailto:owner-fom at math.psu.edu]On Behalf Of
Matthew Frank
Sent: Friday, October 05, 2001 3:31 PM
To: fom at math.psu.edu
Subject: FOM: What is f.o.m., briefly?


A belated response to Peter Schuster's question a week ago:

I use the term "foundations of math" to mean:  Axiomatics with related
conceptual and methodological investigation of mathematics.

That's pretty brief, but you can see my fom post of Jan 19 for more
clarification.  --Matt