Date: Feb 21, 2013 7:14 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<13ce0f7f-5580-456f-8db1-bd1afe7e227e@n2g2000yqg.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.


Outside of Wolkenmuekenheim it not only need not exist, it cannot exist.

> > > Every potentially infinite set of natural numbers has a last element.
> > > But you cannot identify it.


Then no such set can exist, since in every sane set theory what WM here
claims is false.
> >
> > I do not understand.  You made the claim that A implies B.

>
> For every number from 1 to n.


But not for n+1?
>
> > 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.


I do not recall that that provision *between 1 and n) was included in
the original.
>
> 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.


For each nth line l of lenght n,
there is a FIS_(n+1) of d having lenght n + 1.
Thus line(n) =/= d.

So unless WM has a list of lines longer than every natural, he loses!!!
--