FOM: The Banality of Hostility to fom

[Robert Tragesser]

        Steve's suggestion that hostility to
fom might be located (in part) in academic
compartmentalization does point up what I
have been thinking,--the banality of much of
the hostility to fom and mathematical logic
more generally.

[1]  There is no underrating academic apartheid
as a powerful,  limiting force.  At every
level drawing lines on the ground followed by
a bout of male chimp display behavior
is part of the daily routine of academic life.
An amazing case is what was the almost ubiquitous
denial by geophysicsts,  atmospheric chemists,
etc. that life has any substantive influence,
e.g.,  that our atmosphere is significantly
regulated by living organisms;  this was
reenforced by life scientists,.  both groups clearly
very interested in maintaining a separation
of geophysics(etc) and life science.  I've
seen the most comical male chimp display behavior
aimed at refusing to acknowledge the
_significance_ of the fact of
(while not denying the fact of)
that our atmosphere is nowhere near
chemical equillibrium, e.g., were life
erased,  the free oxygen would "quickly"
vanish.

[2] Repressive tolerance.  When approached on
the matter of mathematical logic and fom,  
I've long encountered this ploy from 
academic mathematicians -- that mathematical
logic is a branch of mathematics.  This
is to grudgingly concede the mathematical
significance of mathematical logic while
stripping from it any special privileges or
protection (e.g., that ought to
accrue to a discipline with a capacity for
foundational achievements in mathematics),
putting it at the mercy of the forces of
natural selection (e.g.,  mathematical
fashion) like any other branch of mathematics.

[3]  I've long observed in mathematicians
a hostility to the very word 'logic' and
to symbolic logic.  This was especially
brought home to me when I was on a 
committee for the selection of a
linear algebra textbook in the 70's
when it was being conceded that "linear
algebra" was best presented in something
like a Definition/Axiom/Satz-Beweis form.
The book settled on had a meager two page
chatty introduction to logic and set.  The
word 'logic" appeared nowhere,  not by accident.
The chapter was called "the English language".
The classical meaning of the propositional
connectives and quantifiers and simple logical
principles were explained.  Think about it. 
Mathematicians with a powerful sense of the
abstract and the general were so hostile
to the very word logic that they cheerfully
embraced a chapter on logic and set very
misleadingly and incoherently called "The
English Language". (The author did manage
to blush when he was asked just how one
would translate the book,.esp. the first
chapter,  into German or Japanese --
the title implies that the first chapter
would have to be dropped).

[4] [ How mathematicians learn a new subject.]
Mathematical logic is after all a formidible
discipline.  After a certain age,  mathematicians
learn or get into other mathematical subjects either
when they are forced to teach them or,  much
more significantly,  when their own research
work leads them into the other subject,
giving them an angle from which to take it in,
and also quite taking the drudgery out of learning.
Mathematical logic does not really impinge;
and since foundational and philosophical
concerns are pretty much dead in (the sciences and)
mathematics,  mostly because of the philosophical
puerility of most mathematicians,  few
mathematicians feel any thing to tickle their interest
in mathematical logic.  That is,
their hostility springs from what would be
for them the drudgery of learning mathematical
logic.  

[5] Perhaps a deeper motive for resisting
fom (and of which present "quasi-empiricism"
is a bastardization) is being of a mathematical
frame of mind like that of Felix Klein,
the valuing of non-axiomatic thinking over axiomatic
thinking in mathematics.  A clarifying and
fascinating account is given in Herman
Weyl's lost lecture "Axiomatic vs.
constructive procedures in mathematics",
MathIntellingencer 1985,  Vol.7, no.4,  pp
10-38.  Here Weyl grudgingly compels himself
to defend the axiomatic approach!  N.B.,
"constructive" in Weyl's title means
NONAXIOMATIC (rather than constructive in
our more limited, e.g., Bishop's,  sense).

robrt tragesser