On Monday, June 17, 2013 11:10:27 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Monday, June 17, 2013 5:23:11 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > On Monday, 17 June 2013 07:43:58 UTC+2, Zeit Geist wrote: > > > > > > > > In some systems consisting of ZFC + Some "Large Cardinal Axiom" CH, even GHC, can be proved or disproved. Perhaps Godel foresaw the coming power of Inner Model Theory and Descriptive Set Theory. > > > > > > > > > > > >> In some axiom systems it is possible to prove that the reals can be well-ordered, in other axiom-systems it is possible to prove that the reals cannot be well-ordered. This shows that these "proofs" are nonsense, only pursued by matheologians. No science would rely on modern logic. > > > > > > Why are you talking about the well-ordering of the reals? > > > > Because it is the most famous example. It can be "proved" in ZFC, it can be disproved in Mathematics. And it cannot be done in reality. >
Yes, but if we examine various aspects of "reality" and attempt to model them, as Science does, we find some of these models exist in ZF + "The reals are well-ordered." and some are modeled in ZF + "The reals are NOT well-ordered.".
> > > I thought this was about the Continuum Hypothesis? > > > > The same mess. But less known. >
However, CH is a different story. ZFC + CH, and especially ZFC + GCH, does not yield many scientifically fruitful models. It is too simplistic. The "real" real continuum is most likely more complex.
BTW, you brought up the Continuum Hypothesis. Why do evade the subject.