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Topic: Is continuum completely filled up?
Replies: 610   Last Post: Jun 9, 2012 10:57 AM

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 David Marcus Posts: 1,858 Registered: 12/13/04
Re: Is continuum completely filled up?
Posted: Jan 16, 2007 2:42 PM

toshiaki wrote:
> "David Marcus" <DavidMarcus@alumdotmit.edu> wrote in message
> news:MPG.2014416c9797797c989b24@news.rcn.com...

> > toshiaki wrote:
> > > My question is that why selfreferential statement is permited as theorem of
> > > mathematics.

> >
> > Why shouldn't it be?

> I cannot judge about it now.
> When we use the liar's statement in ordinary conversation, it only leads to

Luckily, math isn't the same as ordinary conversation. The best
explanation I've seen of the Liar's Paradox was in the journal
Mathematical Intelligencer. Basically, the author showed that the Liar's
Paradox is analogous to assuming that an equation without a solution has
a solution.

> Though ZF excluded Russel's paradox and other paradoxes from its system, why
> doesn't it inhibit
> to use this statement to prove the incompleteness theorem?

The proof of the incompleteness theorem has some similarity to the
Liar's Paradox, but it isn't the same. Instead of saying "I am not
true", you only say, "I am not provable". If provable statements must be
true, you can conclude that you are true.

> I'm afraid that this is nonsensical question?

More sensible than some of the other things you've said.

--
David Marcus

Date Subject Author
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12/28/06 tinyurl.com/uh3t
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2/13/07 Fede Ferreres
12/27/06 kunzmilan@atlas.cz
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12/27/06 mathedman@hotmail.com.CUT
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12/29/06 ooo
12/30/06 DontBother@nowhere.net
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1/30/07 magidin@math.berkeley.edu
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2/13/07 Fede Ferreres
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