FOM: rigor and intuition

[Gordon Fisher]

Vladimir Sazonov wrote:

> 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.
>

Intuitive with respect to countable infinities, not so intuitive with
respect to uncountable infinities?

Gordon Fisher     gfisher at shentel.net