[FOM] Alain Connes' approach to Analysis
Timothy Y. Chow
tchow at math.princeton.edu
Tue Sep 18 10:53:31 EDT 2018
Joe Shipman wrote:
> I don't understand why suspicion of nonmeasurable sets and ultrafilters
> should make a number theorist distrust proofs which use them, it is well
> known that they can be constructively eliminated from the proof of any
> Arithmetical statement.
I can't speak for Connes or for any particular number theorist, but in
general, there is a difference of philosophy between f.o.m. and f.o.X.
that one should keep in mind. In f.o.X., one may reject a concept or an
approach as being "wrong" in the sense that it fails to track the true
essence of the X under study, or presents some psychological impediment to
understanding X more deeply, even if it does not lead to false theorems.
Actually, this sense of "wrong" is important in f.o.m. too. It's just
that in f.o.X., it's by far the most important sense of "wrong." Except
in the relatively rare cases where some important argument is being
criticized for lack of *rigor*, it's almost always what people in f.o.X.
are concerned about.
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