FOM: hostility toward f.o.m.
Doug McKay
mckay003 at maroon.tc.umn.edu
Wed Jul 22 20:05:50 EDT 1998
On Wed, 22 Jul 1998, Stephen G Simpson wrote:
> Thomas Forster writes:
> > Nobody enjoys watching their activity being explained to the world
> > by someone who doesn't do it (or, they think) understand it.
> > ...and that is the position that some mathematicians think they are
> > in vis-a-vis logicians.
>
/snip/
>
> I think it has something to do with compartmentalization. I have
> observed that many pure mathematicians automatically resent any
> subject that is of broad interest. That is why computer science and
> statistics split off from math a long time ago; they couldn't stand
> the resentment that they were experiencing in math departments.
> Perhaps f.o.m. will eventually follow in those footsteps.
>
My theory on this is that FOM is by it's nature a philosophical pursuit,
as well as mathematical. It's a hybrid. It's not pure mathematics and not
exactly applied math either. How many mathematicians can "do philosophy"?
And for that matter, how many philosophers can do high level mathematics?
A philosopher without mathematical aptitude may not shy away from talk of
FOM, but a mathematician without philosophical concerns simply doesn't
"get the point" of FOM.
Question: Since mathematics is always growing, is it constrained in its
growth by a particular theory of its foundation? Or must a theory of FOM
evolve with the inevitable growth of mathematics? In other words, "who's
the boss"?
Also, in what sense does a theory of FOM "explain" or "clarify"
mathematics. Is FOM a pursuit of what could be called the "quantum
level" of mathematics, whereas the Category Theory/Topos Theory
viewpoint could be called more "macro" oriented?
Are these questions even coherent?
Doug McKay
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