In article <email@example.com>, WM <firstname.lastname@example.org> 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. --