Date: Mar 24, 2013 1:09 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 24 Mrz., 16:59, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 24, 4:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> > > > > Have you shown that "one can or cannot".
>
> > > > > Yes or no please.
>
> > > Please answer the question.
>
> > I did so. Given ZFC: one can
>
> So WM has made two claims
>
> Given ZFC: I cannot show if one can or cannot


Wrong. Do you really find it necessary to lie in order to maintain
your position? And what is the reason to defend a position that is
based upon blatant lies? Given ZFC, everybody can easily see what I
have shown. Alas, nobody has looked for it hitherto.
>
> Given ZFC: I can show that one can
>
> Seems that in Wolkenmuekenheim everything can
> change including what WM is able to show.
>

> > Please answer this question (the best way for our readers to
> > understand the difference between pot. and act. infinity):
> > What is the difference between the Binary Tree that constains only all
> > finite paths and the Binary Tree that contains in addition all
> > actually infinite paths?

>
> In both cases you have the same nodes so they look identical.


So it is not meaningful to talk about two cases at all.

> The only difference is that in the second case you consider
> some subsets of the nodes to be paths, that are not considered
> to be paths in the first case.


Well, that is a correct description. It implies that these additional
subsets cannot be distinguished by nodes from the finite subsets and
from each other. Why do you believe that the situation in Cantor's
list is different? There the principle of proof is based upon the
possibility to distinguish different infinite "paths" from each other
by "nodes".

Regards, WM