FOM: hostility toward f.o.m.

[Stephen G Simpson]

Thomas Forster writes:
 >                    SET THEORY SEMINAR
 >        Prof. F. Utterbunk: Subsets of $\emptyset$

This strikes me as a childish prank, nothing more.  I can't see any
real hostility here.  I thought you were speaking of serious hostility
to f.o.m., such as telling students that f.o.m. is a dead subject, or
requiring students to pass specialized exams in other subjects before
allowing them to take courses on f.o.m.

 > As for the roots of this hostility, the best i can do is point to
 > the theories of my Doktorvater, Adrian Mathias (who is probably
 > reading this) who traces it back to Bourbaki, and he has an article
 > in which he makes a very detailed case.

I like Adrian's article "The Ignorance of Bourbaki", which has been
discussed here on FOM.  In particular, my posting of 17 Nov 1997
16:20:11 contains a review from Mathematical Reviews.  But I don't
think Bourbaki is the only source of hostility to f.o.m.  The full
explanation of the hostility is unclear, but my best analysis is that
it's part of a general trend toward anti-foundationalism and
compartmentalization in academia.

By the way Thomas, I agree with you that infinitary combinatorics is
fun.  I got into it for serious foundational reasons (looking for
places in mathematics where strong axioms are needed), but it's also
fun in a recreational sense.

 > I think the idea that set theory provides a foundation for
 > mathematics only gets us into trouble.  So we can interpret all
 > mathematical theories into theories in a language with equality and
 > one binary relation. Who cares?

There's a lot more to set-theoretic foundations than this caricature,
which overlooks all of the important issues about proper choice of
axioms, the origin of the set concept, independence results, etc. etc.
Perhaps there is need for a restatement of the classical issues and
programs in set-theoretic foundations.

Thomas, I don't think you really subscribe to the caricature above.
If I may try to psychoanalyze you, I think your remarks about the
paradoxes and predication reveal that you are in fact foundationally
oriented.

I'll post more later about the 04 vs 03E issue.

-- Steve