In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 19 Jun., 16:18, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > > Well, I see, you think mathematical logic is nonsense. > > To great parts, yes. > > > > No. I mean exactly that: The set of finite words over a finite > > > alphabet is countable. > > > > Right. > > > > > The set of meanings of these words, i.e., the > > > set of languages, is countable. > > > > Is it? I would state that the set of meanings of each of those words can > > indeed be countable (I do not know), nothing more. > > Every meaning of every word is defined by a language.
In mathematics, not every word need have a meaning. For example, in set theory, "is a member of" need not have meaning, though it will have a grammar.
WM is hung up on his ow particular model of set theory, but his is not the only possible model, and, in general, one can, and possibly should, do set theory without any particular model in mind at all.