FOM: definition of f.o.m.; brief reply to Simpson

[Martin Davis]

At 01:29 PM 1/13/98 -0500, simpson at math.psu.edu wrote:

>Sol cites postings by Martin Davis and himself offering other "ideas
>of what f.o.m. is up to", though not definitions of f.o.m.  I
>acknowledge the interest of those postings, but I don't think they say
>enough to distinguish f.o.m. from other subjects.  Sol quotes Martin as
>saying:
>
> > "It is the problematic character of mathematical truth at a
> > (shifting) boundary of what is understood that provides the
> > problems for workers in FOM".
>
>I agree with this, but I don't see how it sets f.o.m. apart from a
>zillion other mathematical research topics, which are also working at
>the boundary of what is understood. 

What I claimed to be crucial for fom is THE PROBLEMATIC CHARACTER OF
MATHEMATICAL TRUTH AT A (SHIFTING) BOUNDARY ...

In ordinary mathematical research, one is working at the boundary of what is
known, but in a context where the legal methods and acceptable techniques
are understood and agreed upon. Foundational problems arise when this
understanding breaks down because of new developments.

>From my point of view, this historical understanding is more to the point
than attempting an ad hoc delimitation of fom.

Martin