FOM: rigor and intuition

Vladimir Sazonov V.Sazonov at
Tue Feb 12 14:22:03 EST 2002

Peter Schuster wrote:

> >Some conflict is inevitable, as it is shown by the example of quite
> >intuitive Axiom of Choice leading to non measurable sets and other
> >"paradoxes".
> How can you call a principle "quite intuitive" among whose consequences
> there are some which are commonly considered to be contra-intuitive?

Who knows in advance which consequences some "quite intuitive" 
axiom can have. Getting these consequences we could start think 
more about this axiom. But, e.g. AC seems to me (and seemingly 
to most of  mathematicians), nevertheless, sufficiently intuitive. 

> ----
> Name: Peter M. Schuster
> Instituition: University of Munich, Mathematics Department
> Research interest: constructive mathematics

Vladimir Sazonov                        V.Sazonov at 
Department of Computer Science          tel: (+44) 0151 794-6792
University of Liverpool                 fax: (+44) 0151 794 3715
Liverpool L69 7ZF, U.K.

More information about the FOM mailing list