[FOM] Repairing a bridge (reply to Tim Chow)
tom.dunion at gmail.com
Wed Jul 22 13:28:02 EDT 2009
On 7/17/09 Tim Chow wrote:
>Do you believe that all mainstreamers accept Freiling's
>argument but that all or some f.o.m.ers don't? This is certainly not the
>case. There is disagreement about Freiling's argument, but it does not
>split neatly along an f.o.m./mainstream boundary.
I did not intend to suggest a neat split along that boundary. My posting
claimed that there is a viewpoint "prevalent within the f.o.m. community"
which, it seems to me, overlooks a need to deal with a compelling intuition
against the CH.
>Is [your argument] supposed to bolster Freiling's argument, or undermine it?
To bolster it.
>or show that some apparent contradiction (what apparent contradiction do you
>have in mind?) does not exist?
That too -- my primary point was to show that an apparent contradiction need
not remain if we opt for not-CH. The "contradiction" is that, under CH, we
seem obligated to view two mutually exclusive and exhaustive events as each
having probability 0, when from the perspective of ordinary probabilistic
reasoning, they must each have probability 1/2.
>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.
That's the "bridge out" concern of mine.
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