FOM: MSC abolishes Set Theory !!!
Thomas Forster
T.Forster at dpmms.cam.ac.uk
Thu Jul 9 04:36:28 EDT 1998
Steve asks for a `tale from the front'. The most lapidary
is this one. The Pure maths dept at Cambridge has (had) a
large whiteboard with the days of the week printed on it so
that the secretaries could write each week thereon in felt-tip
the times and titles of seminars for each day. One day i found
written in one slot the announcement
SET THEORY SEMINAR
Prof. F. Utterbunk: Subsets of $\emptyset$
(forgive use-mention confusion!). I'm not quite sure what
the `F' stood for: any ideas? (Perhaps the joke is on them
because after all there are non-trivial theorems in set theory
about permutations of atoms - which are subsets of $\emptyset$
- but that is by-the-by). 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.
Steve asks what set theorist think we are doing. I'm not mad
keen on transfinite combinatorics (as he seems not to be), tho'
it's quite fun, the punters like it, i teach it, and it buys me
good relations with the local combinatorists. (My Erd\"os number
is as high as 4, so you can see i'm not really into it.)
However, i part company with Steve with his next paragraph. 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? Most mathematicians don't. (See intro to ch 1 on Conway -
ONAG). My reason for doing set theory is the slightly different - and
more general - one that it is the area of mathematics where the (i
suppose) philosophical questions raised by the paradoxes can be most
clearly seen for what they are. The fact that $\in$ arose from an
attempt to formalise predication reveals Set Theory's roots in
philosophical logic / metaphysics - and my first degree was in
philosophy and music, not mathematics. That's probably why i do
NF rather than ZF !
Thomas Forster
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