I think it’s Gödel’s sentence. It’s basically that you find a way to encode a sentence into a number, then you find some crazy mathematical sentence that basically claims a given number corresponds to an unprovable sentence. You make another sentence that results in the truth value of the given sentence being plugged into itself. By plugging the number for the first sentence into the second, you have a sentence that states that it’s false.
You can say that Gödel’s sentence is false, and the one that’s made with that, etc. are all false, but that axiom schema introduces a new sentence. You can do that again, but then there’s another level. You can do it for an infinite number of levels, but there’s another level after that. You can only do so much recursion.
I’d be curious to see what said sentence is, and what said proof is.
I think it’s Gödel’s sentence. It’s basically that you find a way to encode a sentence into a number, then you find some crazy mathematical sentence that basically claims a given number corresponds to an unprovable sentence. You make another sentence that results in the truth value of the given sentence being plugged into itself. By plugging the number for the first sentence into the second, you have a sentence that states that it’s false.
You can say that Gödel’s sentence is false, and the one that’s made with that, etc. are all false, but that axiom schema introduces a new sentence. You can do that again, but then there’s another level. You can do it for an infinite number of levels, but there’s another level after that. You can only do so much recursion.