Re: "basis for mathematics"

From: Tim Mellor (timm_at_amsta.leeds.ac.uk)
Date: 10/29/04 

Date: 29 Oct 2004 02:58:58 -0700

"Shmuel (Seymour J.) Metz" <spamtrap@library.lspace.org.invalid> wrote in message news:<4181a46a$2$fuzhry+tra$mr2ice@news.patriot.net>...
> In <992b156f.0410281246.14dcc83@posting.google.com>, on 10/28/2004
> at 01:46 PM, greeneg@cs.unc.edu (George Greene) said:
>
> >Why the ? ? It would be hard to see how it could be otherwise. WHere
> >are you getting "The real number system" FROM? IF you are getting it
> >from axioms over a first-order language then 0 *IS* distingusihed;
> >you cannot state the axioms without a name for 0.
>
> Sure you can; they're just more complicated than necessary.

Yes, but only because 0 is \emptyset-definable as the additive
identity, and thus clearls a "distinguished element".