Date: Feb 11, 2013 1:07 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
On 11 Feb., 16:40, William Hughes <wpihug...@gmail.com> wrote:

> On Feb 11, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > On 11 Feb., 11:55, William Hughes <wpihug...@gmail.com> wrote:

>

> > > On Feb 11, 8:50 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > > There exists a natural number m such that d is line number m is false.

>

> > Yes so, alas not quite correct if d is assumed to "exist".

>

> > If d is assumed to exist, we have

>

> > 1) We cannot *find* a natural number m such that d is the m-th line of

> > the list.

>

> According to you

>

> if L is a potentially infinite list, and d is

> the potentially infinite diagonal

>

> if for every natural number n, d is not the nth

> line of L then

>

> *There does not exist* a natural number m such that

> d is the mth line of L

>

> Do you wish to withdraw this claim?

No. This claim is obviously correct.

Only *if the complete existence of the not completely existing

diagonal d is assumed*, it would be necessary to have it in the list

and (since every line of the list contains everything that is

contained by its predecessors) to have it in a line of the list. But

obviously a potentially infinite diagonal does not exist completely

(as the potentially infinite list does not exist completely).

So why should anything be withdrawn?

Regards, WM