> > > > And shows that if countably many of them can exist then uncountably > > > > many > > > > of them must also exist.
> > > Yes, he shows that uncountably many real numbers then must exist.
> > > We (including you) know that this is not the case. Conclusion?
> > Does WM now claim the skill of mind-reading at great distance
> I read what you wrote: There are only countably many definable numbers.
What I actually said was that there may be only countably many INDIVIDUALLY definable real numbers, but that does not mean that there cannot be uncountably many COLLECTIVELY defined real numbers not all of which have individual definitions. And that latter situation is the reality everywhere outside of WM's wild weird world of WMytheology.
Another example of a set not all of whose members can be individually defined is the set of all subsets of any at least countably infinite set, like the set of all naturals, which has a provably uncountable power set. --