Date: Feb 11, 2013 1:07 PM
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So why should anything be withdrawn?