[FOM] Alain Connes' approach to Analysis

José Manuel Rodriguez Caballero josephcmac at gmail.com
Tue Sep 18 08:09:42 EDT 2018

> JS 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.

Connes' rejection of nonmeasurable sets is not motivated by suspicions, but
rather by a sort of Platonism (maybe what Connes calls primordial
mathematical reality). Indeed,

Connes said in an interview:
> I had been working on non-standard analysis, but after a while I had found
> a catch in the theory.... The point is that as soon as you have a
> non-standard number, you get a non-measurable set. And in Choquet's circle,
> having well studied the Polish school, we knew that every set you can name
> is measurable; so it seemed utterly doomed to failure to try to use
> non-standard analysis to do physics.

Link to the interview: http://www.alainconnes.org/docs/Inteng.pdf

Kind Regards,
Jose M.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20180918/16798c5a/attachment.html>

More information about the FOM mailing list