Date: Feb 11, 2013 1:07 PM
Subject: Re: Matheology § 222 Back to the roots

On 11 Feb., 16:40, William Hughes <> wrote:
> On Feb 11, 4:03 pm, WM <> wrote:

> > On 11 Feb., 11:55, William Hughes <> wrote:
> > > On Feb 11, 8:50 am, WM <> 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So why should anything be withdrawn?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