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

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?

Where have you seen a simpler proof? Do
you believe in Occam's Razor (or its extension, C-B's Razor)?

That implication of the first incompleteness
theorem doesn't tell us anything substantial about the liar paradox.

How is that an implication of the first incompleteness theorem? Truth
can be different from provability, but that doesn't show that "This is
not true." (one use of truth) is different from "This is not provable."
(You're confusing an implication with its converse.)

C-B

There is a connection between the liar paradox and Gödel's proof; Gödel
arrived at his proof of the first incompleteness theorem after realizing
that arithmetical truth can't arithmetical as that would lead to the
liar being expressible. This does not mean that the incompleteness
theorems tell us anything about the paradox.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus


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David C. Ullrich
.

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