On 12 Jan., 22:58, Virgil <vir...@ligriv.com> wrote: > In article > <f62302b5-c3c6-4b54-8437-6f9d7bc00...@4g2000yqv.googlegroups.com>, > > WM <mueck...@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.
Can you name, define, or at least "discern" one of the paths missing in my Binary Tree? Note: I do not hide my receipe of construction any longer. I use every tail that can be described and communicated in any language. > > > > 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.
If this is claimed in mathematics, then it is usual that the claimer is able to give at least one example. (In matheology this is not so.)
Nevertheless, many matheologians claim that undefinable paths are discernible. So every matheologian is invited to discern a further path. > > > > 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? > > If a god can discern more, then more exists, even if it is beyond our > view.
I agree to your conclusion but not to your premise.