LudovicoVan
Posts:
3,010
From:
London
Registered:
2/8/08
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Re: Matheology § 062
Posted:
Jul 8, 2012 9:32 AM
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"Virgil" <virgil@ligriv.com> wrote in message
news:virgil-B033DE.00281808072012@bignews.usenetmonster.com...
> In article
> <81559447-62a8-41de-a032-4f3d8e636903@h10g2000yqn.googlegroups.com>,
> William Hughes <wpihughes@gmail.com> wrote:
>> On Jul 7, 12:15 pm, "LudovicoVan" <ju...@diegidio.name> wrote:
>> > "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>> > news:6ed4b3b7-14a1-42ba-beb6-c0fe3a1cfd1c@5g2000vbf.googlegroups.com...
>> > <snip>
>> >
>> > > After 1 hour the urn is empty, because for every number the time of
>> > > removal can be determined. So for the set X of numbers residing in
>> > > the
>> > > urn we obtain
>> > > Lim |X| =/= |Lim X|
>> > > This prevents any application of set theory to reality although it
>> > > was
>> > > Cantor's outspoken aim to apply set theory to reality (cp., e.g., his
>> > > letter to Mittag-Leffler of Sept., 22, 1884).
>> >
>> > That argument is simply *wrong*, it does not show a problem in set
>> > theory
>> > (not in itself at least). From "every (finitely-labeled!) ball has
>> > been
>> > removed at step w" one cannot conclude "the vase is empty at step w",
>> > period.
>>
>> One can certainly conclude that the vase does not
>> contain any finitely-labeled balls. If we define
>> |X| to be the number of finitely-labeled balls
>> then WM's conclusion follows.
>
> The conclusion that the urn is empty (at least of those numbered balls)
> is one that WM has opposed in other posts, and he only presents it here
> to claim it makes standard set theory unreal.
> Whereas it is really WMatheology which partakes deeply of unreality.
Well, I am glad we all agree that the vase (provably!) does *not* in fact
end up empty (*). I am still unsure we all then concede that the
Ross-Littlewood paradox is just about the inability of some mathematicians
to count correctly when supertasks are involved.
(*) And that the conclusion does *not* depend on the conditions, nor the
problem is underspecified or ill-formed:
<http://en.wikipedia.org/wiki/Ross%E2%80%93Littlewood_paradox>
-LV
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