Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/09/04 

Date: 9 Nov 2004 11:41:26 -0800

"Shmuel (Seymour J.) Metz" <spamtrap@library.lspace.org.invalid> wrote in message news:<4181a33d$1$fuzhry+tra$mr2ice@news.patriot.net>...
> In <320e992a.0410271136.4479a210@posting.google.com>, on 10/27/2004
> at 12:36 PM, examachine@gmail.com (Eray Ozkural exa) said:
>
> >However, if he can settle the following metamathematical theorem:
>
> That's not a Metamathematical theorem absent definitions of
> "infinitary reasoning" and "abstraction of actual infinity". Without
> the definitions it's just Philosophy.

The first is a piece of cake as it means that there is no halting
program which can output a 0 or 1 for falsehood or truth of the
proposition under consideration. (I cannot see why Brown thought it
was hard) The second seems harder, but it would involve the usage of
the magnitude of an infinite object, as a symbol, in any logical
language. (But as you can see it's hard to define it in the only
defensible language of metamathematics, e.g. discrete computation)

You may have given a better answer by defining these in a suitable
metamathematical framework yourself. What do you think?

Regards, 

--
Eray