FOM: g.i.i.

[Colin McLarty]

Stephen G. Simpson writes

>General intellectual interest:
>
>  Colin McLarty writes:
>   > Those on fom who insist "fom is of more general interest than other
>   > math" have still not even distinguished the many things this could
>   > mean, let alone picked one it does mean. Does it mean:
>   > 
>   > 1) More people actually want to hear about fom than other math.
>   > 
>   > 2) More people would want to hear about fom than other math, if
>   >         they knew more about it.
>   > 
>   > 3) People would benefit more from learning fom than other parts of math
>  
>  All of statements (1)-(3) are true.  

        Statement 1 asserts a fact which can be checked empirically. Every
empirical measure I can think of shows it to be false with one possible
exception. It is false according to: popular book sales, technical books
sales, newspaper coverage, TV coverage, elective course enrollments, and
major course enrollments. The only possible exception that anyone has raised
is Harvey's popularity as a lecturer at math departments. I was pleased, and
not at all surprised, to hear of that popularity, but I wonder how "general"
those audiences were. I suspect they contained more of the reviled
"mainstream mathematicians" than barbers. Certainly the invitations to
speak, at very nice schools, came from mathematicians and not barbers. I
think mainstream mathematicians are much less the enemy than Harvey has said.

        Statements 2 and 3 are not factual, but declare ideals. I think them
worthy ideals--but I think promoting other math is also worthy.

>And it is also true that
>  
>    (4) F.o.m. (foundations of mathematics) is of much greater general
>    intellectual interest than pure mathematics.
>  
>  But (1)-(3) are not the essence of (4).  They are only consequences of
>  (4).  And to understand (4), we need to first understand very clearly
>  what f.o.m. is.

        Precisely. This is a special sense of "general intellectual
interest" which can only be understood by understanding f.o.m. Its "essence"
is nothing more nor less than the fact that f.o.m. has much more of it than
mainstream math. It has nothing to do with other, un-fom-informed meanings
of "interest" or "intellectual". 

        Once we understand this special meaning, further argument is
useless. It would be like the argument Harvey quoted in his post of Mon, 12
Jan 1998 08:33:45 +0100, as to whether Wittgenstein is a greater philosopher
than Frege. Just a chain of "is so" and "is not" lightened by a little name
calling. Indeed the arguments on it so far on fom have been pretty much like
that.

        A while ago Harvey announced some new results that will convince all
the world. I look forward to these. And if they create wide excitement I'll
be thrilled--at the general effect as no doubt by the results themselves.
That's great. But insisting that your work is "interesting" is like sitting
in a closed room and insisting that it's not snowing outside: You may be
right, may be wrong, but arguing it is worthless. Let's go see.


Colin McLarty
Assoc. Prof. Philosophy and Mathematics
Case Western Reserve Univ. Cleveland 


P.S. Whether I am a professional on foundations is actually a debated point
on this list. I work in category theory and am currently writing an
historical/philosophical study of homology theories from topology to number
theory. Each reader will decide for themselves. I'll mention that my book on
elementary topos theory is in the Oxford Logic Guides.