A sentence says 'This statement is false.' Is it true?
Consider the sentence: 'This statement is false.' If it's true, then what it says is accurate, meaning it's false. If it's false, then what it says is wrong, meaning it's actually true. The sentence can't be consistently true or consistently false. Ancient Greek philosophers already knew something was wrong here; what exactly is it?
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The sentence refers to its own truth value, and self-reference like this breaks the normal assumption that every well-formed statement is either true or false. Logicians trace the puzzle back to the ancient Greek philosopher Eubulides, and it later inspired Kurt Gödel's proof that some mathematical truths can never be proven within their own system.