[FOM] Re: counting arguments?

[Timothy Y. Chow]

On Fri, 24 Oct 2003 Stephen G Simpson <simpson at math.psu.edu> wrote:
> This seems wrong, or at least imprecise.  Probabilistic arguments in
> finite combinatorics always come down to counting.  Isn't that so?

Actually, this seems to me to be an extremely interesting question from
the point of view of reverse mathematics.

Certainly, I have heard more than one practitioner of probabilistic
combinatorics claim something to the effect that some of the more advanced
probabilistic proofs "do not reduce to counting."  What I think they mean
is that they appeal to theorems that are typically stated and proved in
the context of general measure theory.  A natural question from the f.o.m.
point of view is whether these appeals to infinitary mathematics are a
posteriori eliminable.  It seems to me that this question has not been
systematically addressed but could be quite a fruitful topic for further
investigation.

Tim