[FOM] Re: counting arguments?
Timothy Y. Chow
tchow at alum.mit.edu
Sun Oct 26 17:13:46 EST 2003
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
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