On 5 Feb., 16:18, fom <fomJ...@nyms.net> wrote: > On 2/5/2013 3:51 AM, WM wrote: > > <snip> > > > More means more than all rational points of the universe. > > Gödel and Cohen doubted the continuum hypothesis. They estimate the > > cardinality of the continuum as being much larger. > > So, points exist?
I must confess that I cannot understand their point of view. If one stands on ZFC, then it is impossible to prove CH or its contradiction. Therefore their belief it is completely meaningless. How should it be realized?
> Goedel's doubts arose from mistaken logic.
The acutally infinite, aleph_0 and 2^aleph_0, arose from mistaken logic. > > Cohen's opinions arose from the failure to > recognize the relation of names to model > theory. > > Although Russell wrote about the possibility > of points existing, his stated opinions about > geometry in the sense of sensible externality > was that the geometric primitives are the > lines and planes--that is, the parts different > from points.
Compare Cavalieri: Indivisisbles of lines are lines, of surfaces are surfaces, ob bodies are bodies. > > The extensionality of mathematics, in general, > is an artifact of Scholasticism. As another > author who did not conform to this view, one > has Leibniz--at least with regard to his logical > investigations. > > So, points exist?
Atoms exist. By means of atoms we can measuere lengths and define points or small intervals.
Anyhow: All rational space-time quadruples of the universe belong to a countable set. It is impossible to construct anything A, not even a thought, that would not cover at least one of these quadruples Q_n such that Q_n could be uniquely attached to A. Therefore, everything that ever can exist anywhere in the universe belongs to a countable set. The Q_n surject the set of all A including all possible mathematical ideas in all possible heads and other thinking devices, even all the thoughts and dreams of matheologians about objects of matheology.
the notion of uncountability is the stupendest stupidity ever heard of.