[FOM] Alain Connes' approach to Analysis

[José Manuel Rodriguez Caballero]

>
> 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.
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