> Lester Zick wrote: > > On 23 Jul 2006 12:14:22 -0700, "Jiri Lebl" <email@example.com> wrote: > > > >> Aatu Koskensilta wrote: > >>> Zick is no doubt mistaken about many things, but your > >>> rebuttal of his ideas is itself rather confused. The continuum > >>> hypothesis does not provide an example of an A such that "A, not A" do > >>> not exhaust all possibilities. > >> So it is true? or it is false? > > > > True? What does it mean to be true? > > The continuum hypothesis is true iff every set of reals is either > countable or has the cardinality of the continuum.
We know that every set of reals is in some sense countable according to Skolem`s paradox, I mean that there is a bijection between the real and naturals if naturals are outside of model of set theory. Still Cantor`s theorem in set theory, which is of course valid, says that the reals are uncountable. To me it seems that there is a theorem in set theory that can`t be true in sense I understand you see it. You have said before that the axioms of set theory are true. How can you explain this - or am I missing something?
> Aatu Koskensilta (firstname.lastname@example.org) > > "Wovon man nicht sprechen kann, daruber muss man schweigen" > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus