I've been thinking about Godel's thoerem and the liar's paradox. The liar's paradox, when flipped around, stops being a paradox and becomes valid logically whether the statement is true or not. "This statement is true" works if true or false. I was wondering how the Godel argument would work if it was also flipped. Perhaps it would read like "this statement is provable." I don't understand the logic language he used in his proof, so I have to think about these things in normal language, but I was hoping somebody could highlight what that might look like and what the interpretation would be.
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You can certainly write such a statement using Gödel, but it might be decidable, so it depends on what you mean by “works.” – Thomas Andrews May 03 '22 at 02:04
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2@ThomasAndrews In fact it will always be decidable - this is Lob's theorem. (See the linked duplicate question for further details about exactly what's needed to be confident about this.) – Noah Schweber May 03 '22 at 02:10
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To the OP, this is a great question but it is a duplicate. – Noah Schweber May 03 '22 at 02:11