In article <email@example.com>, "Gene Ward Smith" <firstname.lastname@example.org> wrote:
> The difference is that we've given up on the idea that there is a > single correct geometry, but still feel (and that's nothing but > intuition speaking) that there is a single true set theory, just as we > think there is a single true number theory.
The other difference is that we never said that all mathematics is based on geometry, can be expressed in terms of geometry, can be justified on the basis of geometry. We do hear that all of mathematics can be expressed in ZFC (or at any rate all the mathematics that isn't specifically designed to be done outside ZFC), and this makes the independence results of set theory a bit more worrisome than those of geometry.
-- Gerry Myerson (email@example.com) (i -> u for email)