FOM: hostility toward f.o.m.

[Stephen G Simpson]

Dan Halpern writes:

 > ...  Steve started the problem by his rather disingenuous
 > interpretation of your interesting point - namely, that many
 > mathematicians believe "that logicians think that they (the
 > logicians) understand the meaning and purpose of mathematics better
 > than other mathematicians."  Neil propagated the problem by failing
 > to notice Steve's disingenuousness.

Me, disingenuous?? :-)

I think we should really blame the problem on Heidegger and Derrida
and the other deconstructionists, for writing so obscurely that they
confuse everybody.  After all, philosophy is supposed to be a guide to
life, so philosophers more than anyone else ought to write
intelligibly ....

Oh well, let's not bicker about irrelevant issues.  Let's get back to
discussing Thomas Forster's point about hostility to f.o.m., which I
agree is very interesting.

Thomas's point was that mathematicians sometimes resent the logicians'
tone of superiority, because logicians claim to be analyzing the
logical structure of mathematics.  Thomas also said that this was
aggravated by the mathematicians' belief that the logicians don't
really know what they are talking about half the time.

 > Let's face it - some of us logicians might be contributing to the
 > hostility of mathematicians on this score.  What do you think,
 > Steve?

There may be something to this.  I have observed that some logicians
sometimes make exaggerated claims, e.g. the claim that projective sets
of reals are part and parcel of core mathematics, or the claim that
the axiom of choice is needed to prove various theorems.  In these
cases, perhaps some of the hostility is justified.

However, I also think there are deeper reasons for the hostility,
involving general trends within academia.  Among these trends are
compartmentalization and anti-foundationalism.  Let's try to get some
more opinions on this.

Doug McKay 22 Jul 1998 19:05:50 writes:

 > My theory on this is that FOM is by it's nature a philosophical
 > pursuit, as well as mathematical. It's a hybrid. ....

Yes, but does this dual nature of f.o.m. justify the mathematicians'
hostility?  I don't think so.  Mathematicians ought to be concerned
and respectful about the various interfaces between mathematics and
the rest of human knowledge.  The fact that they often aren't is a
shame and is in the long run harmful to mathematics.

 > 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"?

A very interesting question.  I would say this much: Mathematicians
ought to pay more attention to foundational issues.  If they see that
mathematics is growing in a direction that isn't consistent with the
rest of human knowledge, then they ought to occasionally pause, take
stock, and regroup.  I believe that this kind of activity would make
mathematics better and more vital.  For instance, we wouldn't have the
phenomenon of math PhD's who can't compute anything.

-- Steve