[FOM] Re: WHY DO SET THEORISTS DISLIKE CHRIS FREILING'S EVIDENCE
Timothy Y. Chow
tchow at alum.mit.edu
Sat Sep 4 14:35:20 EDT 2004
LEMG wrote:
>On Thu, 2 Sep 2004, Timothy Y. Chow wrote:
> > 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.
>The axiom cannot be proved or disproved, it's an axiom. In which sense
>is it true? Also, there are weird results in mathematics that do not
>depend on AC. Constructive decompositions for which the AC is not
>necessary. See, for instance, the result by Foreman and Dougherty*
Foreman and Dougherty's result is very nice, although I don't find its
weirdness to be on a level with Banach-Tarski (for example, we already
know that a measure zero set like the rationals can have a closure with
arbitrarily large measure, so we're already conditioned to expect that
taking the closure of something can "expand" it enormously). Supposing it
is, though, then I take it you agree with me, and are saying that I can
strengthen my argument to, "In mathematics, 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
More information about the FOM
mailing list