[FOM] Re: WHY DO SET THEORISTS DISLIKE CHRIS FREILING'S EVIDENCE AGAINST THE CONTINUUM HYPOTHESIS?
Timothy Y. Chow
tchow at alum.mit.edu
Thu Sep 2 13:35:54 EDT 2004
On Thu, 2 Sep 2004, Robert M. Solovay wrote:
> On Thu, 2 Sep 2004, Timothy Y. Chow wrote:
> > A less formal but maybe more striking way to put it is that since the
> > axiom of choice implies something as weird as the Banach-Tarski paradox,
> > what's to stop it from implying something as weird as the continuum
> > hypothesis?
> >
> Cohen proved in the early 60's that the Axiom of Choice does not
> imply the Continuum Hypothesis. Godel had shown in the 30's that the axiom
> of choice does not imply the negation of CH.
Yes, of course I understand that. I guess it is always dangerous to be
even slightly informal with this audience!
Let me try a less offensive phrasing. In a world where AC is true, we
expect to observe phenomena that violate our intuition about measure.
Freiling's argument shows that if CH is true, then we observe a phenomenon
that violates our intuition about probability. So what?
Tim
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