[FOM] Apartness topology and (constructive) nonstandard analysis

[katzmik at macs.biu.ac.il]

Hi Frank,

Thanks for your post.  Note that one should neither conflate the
notions of "structure" and "construction" nor assume that there are
any ultrafilter products to be found in the outside world.  If there
is any message that should have come through clearly in Sam Sanders'
posting is that Nelson's system represents a syntactic approach.  Here
infinitesimals are found within the ordinary real number system
itself.  The system does not suffer from nonconstructive aspects
any more than the traditional real numbers.  If this seems to be a
philosophical challenge to the customary platonist intuitions about
the real numbers, then so be it.

MK

On Sat, September 5, 2015 22:10, Frank Waaldijk wrote:
> Let me
> finish by saying that -even though my interest lies largely in constructive
> mathematics- my conviction is that all mathematics is in some way about
> `structures' (often beautiful structures...like ultrafilter products). If
> we manage to match any such structure to phenomena in the outside world,
> then this is special (in my eyes, regardless of whether the structure was
> defined constructively or not).
> Frank
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>