On Sunday, May 4, 2014 2:04:30 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Sunday, 4 May 2014 00:25:49 UTC+2, Zeit Geist wrote: > > > > A language need be spoken or written, that means it must be learned. For that sake you need a dictionary, at least one. But the number of dictionaries in the infinite and eternal universe is at most countable. > > > You continuously confuse things that Do Exist ( the Physical Universe ) with things that Can Exist ( the Logical/Mathematical Universe ). > > Languages belong to practical life.
Again the confusion.
> > As you said above, nothing Infinite Exists in "Reality". > > Hence, we are obviously not talking about what "Really" Exists. > > But in order to talk, we need real languages.
We do need Natural Languages to discuss the Abstract Mathematical Language.
> > > Languages belong to real life. real life is never infinite. Only fools can believe and swindlers can assert that uncountably many languages are possible. > > > Take Set of Aleph_0 Symbols, call it S. > > You cannot. Every symbol you can choose belongs to a finite set. It is your big mistake to confuse potential infinity and completed infinity.
By your first sentence, I can Not take a Pair, because each belongs to a singleton.
No confusion on my part. I take a Countable Infinite Set, something like the Natural Numbers.
> > If its Well Constructed that all you need. > > It has to be applied. But in order to shorten your phantasies, let us fix the constraints.
You may "fix" what you please. Howere, those of us who engage in Mathematics already know the System we work within. From you discussion with Dan, it seems you have no clue what that is.
> Everything that can be mentioned in the mathematical discourse in English (or any other language that is derived from English or can be translated into English) belongs to a countable set.
Just because All the Finite Beings in the Physical Universe can't produce, say, or write down Every Individual Mathematical Entity does Not mean they do Not Exist.
> Therefore all elements of mathematics that can appear in this discourse belong to a countable set. Further all known set theory can be expressed in English or a formal language derived from English. This set theory "proves" that *in this discourse* there are uncountably many elements existing.
> This is a contradiction.
This is incorrect.
> > This discussion of Language has nothing to do with you Inability to produce a Definable Listing of All the Definble Reals. > > No. It is another way of proof. If we could go only always the same way, we would never obtain contradictions. But hear we have a contradiction - at least in the mathematical discourse that can be run in English.
Your "Proofs" in plain Language run into Naive pitfalls.