Virgil
Posts:
4,655
Registered:
1/6/11
|
|
Re: Matheology � 191
Posted:
Jan 12, 2013 4:58 PM
|
|
In article
<f62302b5-c3c6-4b54-8437-6f9d7bc00006@4g2000yqv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> Matheology § 191
>
>
> The complete infinite Binary Tree can be constructed by first
> constructing all aleph_0 finite paths and then appending to each path
> all aleph_0 finiteley definable tails from 000... to 111...
>
> 0
> 1, 2
> 3, 4, 5, 6
> 7, ...
>
> This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.
Aleph_0 * aleph_0 = aleph_0 but 2 ^ aleph_0 > aleph_0, and that is the
number of paths.
>
> If there were further discernible paths, someone should be able to
> discern one of them. But since all possible combinations of nodes
> (including all possible diagonals and anti-diagonals of possible
> Cantor-lists) that can occur in the mathematical discourse already are
> present, a human being cannot discern anything additional.
But there are still more of them there, just inaccessible.
>
> Matheologians may claim that God can discern more. But God is not
> present in mathematics. Mathematicians have no pipeline to God, as
> Brouwer put it. At least God does never reveal mathematical secrets.
> Or has any reader ever heard God tell a mathematical secret?
>
> Regards, WM
If a god can discern more, then more exists, even if it is beyond our
view.
--
|
|
