On Dec 8, 1:49 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 8 Dez., 10:41, Zuhair <zaljo...@gmail.com> wrote: > > I will give two answers, the first one depends on the finity of the > universe, the second one does not. > > > Mathematics is "discourse > > and discourse needs the tools available to us. They all are finite. > > > > > How those forms are known to us? the answer is through their > > exemplification as part of the discourse of consistent theories about > > form. > > Consistent means that discourse about all elements is possible. > We know that all finite words belong to a countable set. We know that > no infinite word can be mentioned without having a finite name. > > Therefore this silly argument is really silly: > "I can decide for a real number x whether a real number y deviates in > its decimal (or any other) expansion from that of x." > The complete infinite expansion of x is never known, not even in an > infinite universe, but only the finite formula allowing expansion to > any required level. > > So the argument is silly that there are uncountably many x because x > has an infinite expansion. No x is known without a finite formula, > name, word, ... > > Regards, WM
I don't agree with what you say. There is no known inconsistency with uncountability of the reals, and accordingly uncountability of the reals is a possibility, and since we can interpret reals as forms in the set hierarchy, then we are having a discourse about possible form, and thus uncountability of the reals is mathematical. Mathematics only needs to speak about possible forms. Now whether it is TRUE that we have uncountably many reals in the real world, this is another matter that belong to applied mathematics and not to pure mathematics.
All the rest of your speech is restrictive without a clear justification other than personal favoritism for the finite and concrete descriptions. Mathematics need not yield to such wimps.