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liar-paradox
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Tarski showed in 1933 that a sufficiently strong language cannot define its own truth predicate, which blocks the paradox by moving truth to a metalanguage. Kripke's 1975 theory of truth allows gaps instead. Gödel used a relative of the paradox to prove incompleteness. Formal fixes exist; whether any captures ordinary truth is debated.
Posed c. 4th century BCE, attributed to Eubulides.
Related problems
- The original curation links this problem to Hilbert's second problem: consistency of arithmetic; the argument for the link has not been written yet.