Re: Liar's Paradox in Godel's Theorem (newbie question)

On 2 May 2006 21:02:44 -0700, "Charlie-Boo" <shymathguy@xxxxxxxxx>
wrote:

David C. Ullrich wrote:
On 30 Apr 2006 16:47:01 -0700, "Charlie-Boo" <shymathguy@xxxxxxxxx>
wrote:

Aatu Koskensilta, Charlie-Boo wrote:

You don't believe in correcting the record, now that you see the close
relationship between Liar and Godel?

There's nothing to correct. It's not particularly illuminating to know
that "this sentence is not true" is not equivalent to "this sentence is
not provable in PA".

It proves Godel's Theorem.

Right. Exactly how does this proof go?

As I said above, "Do you see how to derive Godel's Theorem based on
soundness given that truth and provability do not coincide?"

Uh, that doesn't answer the question. Given that truth and
provability do not coincide, now how do we prove Godel's theorem?

(Hint regarding why this is nonsense: There are some quantifiers
in the statement of the theorem: For _any_ theory T satisfying
certain conditions, ...)


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David C. Ullrich


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David C. Ullrich
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