On Wed, 19 Jun 2013 13:12:36 +0100, Peter Percival <firstname.lastname@example.org> wrote:
>email@example.com wrote: > >> >> Look: Zermelo has "proved" that the real numbers can be well-ordered. But it has been proved that the real numbers in fact cannot be well-ordered. That is as certain as that you cannot get a 13 with two dice. > >I think you're confusing two different results. There are models of ZFC >in which a well-ordering is a not definable. That does not mean that R >cannot be well ordered, it just means that if phi(x,y) is the ordering >relation, phi is not a formula of ZFC.
You haven't been paying attention. The sort of subtlety you attribute to WM here is beyond him. When he says it's been proved that the reals cannot be well-ordered he means that it's been "proved" by _him_. By a vague argument that takes various fuzzinesses as premises - premises which he justifies by nothing but bald assertion.