This does not cast doubt on Gödel's proofs. The strengthened liar paradox discussed in the video is "This statement is not true", whereas Gödel constructed a m

This does not cast doubt on Gödel's proofs. The strengthened liar paradox discussed in the video is "This statement is not true", whereas Gödel constructed a mathematical statement that says something along the lines of "This statement is not provable". Proving something is a different process than stating something.