FOM: Hostility toward F.O.M.

[JoeShipman@aol.com]

Let me clear up what I think are some misunderstandings before this thread
degenerates further.  The following valid points have been made:

1) Some mathematicians suspect logicians and f.o.m. researchers of claiming to
understand the meaning and purpose of mathematics better than other
mathematicians.  (My comment: this suspicion is generally unjustified; I think
that when mathematics is done badly (i.e. with insufficient rigor) criticism
by logicians is quite appropriate, but can result in an impression of
logicians as pests and a distaste for the higher level of formalization the
critic demands.)

2) Most academic disciplines, and latterly mathematics, have been attacked by
post-modernist critics on methodological grounds, occasionally with some
cogency.  This mode of attack, which is typically practiced by people with no
detailed knowledge of the subject and tends to question the motives of the
scholars attacked, is a popular and cheap way of scoring academic points, and
is to be regarded with great suspicion and loudly scorned except in the (very
occasional) situations where the critic has found a genuine problem.

3) 'Deconstructionism' is a technical term referring to a mode of criticism in
which texts are analyzed for subtexts and hidden agendas, but is often
conflated with the more general criticism referred to in the previous
paragraph. (Comment:  The post-modern critics of mathematics are rarely able
to genuinely deconstruct a mathematical text, but logicians and f.o.m.
researchers frequently do exactly this, though with the innocent purpose of
identifying unarticulated mathematical or logical assumptions rather than the
ulterior one of imputing politically incorrect motives, beliefs, etc., to the
writer.)

The Tymoczko "New Directions" anthology is avowedly "anti-foundationalist" and
also contains many criticisms of mathematical practice that have a post-
modernist slant.  The f.o.m. analysis of mathematical practice is a special
target of the post-modernist critics because it represents an alternative and
rigorous form of deconstructionism which does not allow critics cheap
political satisfactions.  The hostility to f.o.m. by mathematicians (rather
than post-modernist critics) is an overreaction to the pestiness of the
logicians (see paragraph 1 above) due to hypersensitivity to methodological
criticism occasioned by the unfair attacks referred to in paragraph 2 above.

Disingenuosness has its pitfalls, and one should clarify what the author of an
FOM posting meant exactly before getting touchy!  

-- Joe Shipman
(no longer at Bloomberg Financial Markets; current e-mail is
JoeShipman at aol.com
while I try to choose between academia and industry).