[FOM] Repairing a bridge (reply to Tim Chow)
l.rempe at liverpool.ac.uk
Fri Jul 24 18:50:23 EDT 2009
>> My point of view is that in the presence of AC, we can't trust our
>> probabilistic intuitions. (Witness the Banach-Tarski paradox.)
>> Freiling's argument is just another demonstration of this fact and does not
>> really have much to do with CH per se.
> But Freiling's argument against the CH does seem quite plausible. What some
> have done -- merely identifyfing precisely how an attempt to *formalize*
> Freiling's argument in ZFC will (of course, neccessarily) fail -- must leave
> many non-f.o.m. practitioners shrugging their shoulders and writing it all
> off as just another "weird, but irrelevant-to-my-work" set theory result.
If I may venture my opinion as a "mainstream mathematician" (if such a
thing exists), more precisely as a complex analyst, I personally do not
find the argument outlined against CH very convincing, and I would be
rather surprised if many of my colleagues thought otherwise. Indeed, the
phenomenon outlined in the presence of CH does not seem any more
counterintuitive than the existence of non-measurable sets. We already
know that any well-ordering of the reals must be very strange indeed;
why should it behave in any way nicely with respect to Lebesgue measure?
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