FOM: hostility toward f.o.m.

Doug McKay mckay003 at
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.
> 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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