Date: Feb 21, 2013 5:02 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 21 Feb., 20:23, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 21, 6:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 21 Feb., 14:18, William Hughes <wpihug...@gmail.com> wrote:
>
> > > According to WM
>
> > > i.;
>
> > >     A) For every natural number n, P(n) is true.
> > >       implies

>
> > that this claim A holds for every natural number from 1 to n, but not
> > necessarily for infinitely many following.

>
> > >     B) There does not exist a natural number n such that P(n) is
> > > false.


In fact we cannot find such a number. Nevertheless we cannot exclude
its existence. Please consider what I wrote about the sets A and B.
We cannot find a last finite number that has left A. Nevertheless it
must exist.
>
> > In potential infinity you have to distinguish between existence and
> > the possibility to identify.
> > Every potentially infinite set of natural numbers has a last element.
> > But you cannot identify it.

>
> I do not understand.  You made the claim that A implies B.


For every number from 1 to n.

> Now you seem to be arguing against this.  Note that the statement
> in B is that the natural number n does not exist, not that
> the natural number n cannot be identified.  I remind you again
> that the words are yours.-


The statement is that the natural number does not exist between 1 and
n inclusively.

Find a FIS of d that is not in a line of the list or agree that you
cannot prove that there is no natural number such that line(n) = d.

Regards, WM