FOM: unimpressed by reverse mathematics?
Stephen G Simpson
simpson at math.psu.edu
Wed Feb 28 14:46:01 EST 2001
Charles Silver Tue, 27 Feb 2001 17:54:25:
> I personally think reverse mathematics seems foundational, but
> several mathematicians I've spoken to seem not to hold it in high
> regard. I don't know what exactly this implies, but I'm
> speculating that they don't consider it either to be "interesting"
> math logic or they think it has no foundational interest.
In order to confirm this speculation, you would have to know more
about the intellectual/academic perspective of the mathematicians in
question. For instance, maybe the mathematicians you talked to have
no interest whatsoever in mathematical logic. A large number of
mathematicians, probably the majority, are in this camp. Or, it could
be that the mathematicians you talked to have little or no interest in
foundational issues. A large number of logicians, maybe the majority,
are in this category.
On the other hand, I have found that certain other mathematicians,
especially top-ranked ones like Barry Mazur, find reverse mathematics
appealing. In particular, they like the idea of reverse mathematics
as a classification program -- classifying a large number of
mathematical theorems into a small number of equivalence classes,
according to the axioms needed to prove them.
Also, for whatever reason, reverse mathematics seems to be getting
quite a bit of play lately in the mathematical logic community. For
instance, I am organizing a special session and participating in a
panel discussion, both on reverse mathematics and both by invitation,
at meetings of the Association for Symbolic Logic this spring. Also,
I am being invited to a number of other meetings to talk about reverse
mathematics, e.g., an upcoming meeting in Pisa on the Hilbert
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