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

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

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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Relevant Pages

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