In article <email@example.com>, firstname.lastname@example.org wrote:
> On Friday, 2 May 2014 20:35:19 UTC+2, Dan Christensen wrote: > > > > > But we know that every expression that can appear in eternity in the > > > whole, possibly infinite, universe belongs to a countable set. Therefore > > > also every expression that can appear in the mathematical discourse > > > belongs to a countable set. > > > > > > How do "we" know this? Is it too much to ask for a formal proof? > > Yes
Things that cannot be proved from prior assumptions must be themselves assumed, so until WM can give us a complete list of all the things he assumes without proof, he is in no position to claim, or prove, any of his alleged consequences of those assumptions. > > > > > > Nothing that can appear in this discourse, which *is* mathematics, can be > > > uncountable. > > > Makes no sense. > > What? That only things that can appear in discourse can belong to > mathematics?
There are lots of subjects of discourse outside of mathematics whose "things" need not be at all mathematical. Including WM's wild weird world of WMytheology.
> Otherwise you would have to believe in things that cannot be > mentioned.
One can mention that there are real numbers that are defined as members of large sets but which do not have individual definitions.
> We need not count numbers only. We can count everything that can be > mentioned. Numbers are a subset of this set of all things that can be > mentioned.
WM has just claimed that everything that can be mentioned can be counted, so let him present a counting of the set of all subsets of the set of integers, 2^|N, which certainly can bem and has been mentioned, but is provably not countable.
WM again makes a claim that he cannot justify because there is a simple proof that his claim is wrong.
> > You need some kind of workable formalism. > > Only disabled need crutches.
Then it is shame that WM, in his condition, is not wise enough to use any of the many offered to him. --