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0 pointstensor_rank_08y ago0 comments

thanks for the breakdown. the example of a Godel statement is usually given in terms of set theory. ("S is the set of all sets that do not contain themselves. Does S contain itself?") or binary logic. ("this statement is false"). Do you know of an example in arithmetic?

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cgmg8y ago

The examples you mentioned are not Gödel sentences, but rather Russell’s paradox and the liar paradox, respectively. A Gödel sentence for a theory T says “This sentence is not provable by T.” Truth is very different from provability and, unlike provability, cannot be represented as an arithmetic formula.

See the section titled “Relationship with the liar paradox” in the Wikipedia article on the incompleteness theorems.

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cgmg8y ago

See the section titled “Relationship with the liar paradox” in the Wikipedia article on the incompleteness theorems.

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