In article <email@example.com>, firstname.lastname@example.org wrote:
> On Sunday, 4 May 2014 19:36:16 UTC+2, Zeit Geist wrote: > > On Sunday, May 4, 2014 2:52:48 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > > > On Sunday, 4 May 2014 00:25:49 UTC+2, Zeit Geist wrote: > > > > > > > > > > > Take Set of Aleph_0 Symbols, call it S. > > > > > > > > > > This set would not allow uncountably many finite expressions. > > > > > > > > Are you talking about being able to be written on paper, of course not! > > > > But, that does not mean that it doesn't contain uncountably many > > expressions. > > Expressions that cannot be expressed are not expressions. In order to express > one of the sets in mathematical discourse you need a finite expression. There > are only countably many.
But a single finite expression can define a set of more than countably many individuals, more that there are individual definitions to apply to them.
> > > How many are there? > > > > > > > > Lots. > > Countably many.
One definition, at least outside of WM's wild weird world of WMytheology, can define a set of more than countably many members. > > > > > > > > Just give me, in English, a Finite Definition that list All of the > > Definable Reals. > > I give you a finite definition that lists all finite expressions. Expressions > defining reals are a subset, hence countable.
It is not just a count of the expressions themselves but what they can express which prove WM wrong.
But finite expressions are STILL able to define sets whose members are not all individually definable and which are collectively uncountable. --