[FOM] Re: WHY DO SET THEORISTS DISLIKE CHRIS FREILING'S EVIDENCE AGAINST THE CONTINUUM HYPOTHESIS?

[Timothy Y. Chow]

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