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The Liar
Eubulides of Miletus · c. 4th century BCE
The puzzle
“This sentence is false.”
Note
If the sentence is true, it is false; if false, it is true. The trouble isn’t grammar — every word is in order — but self-reference. Earlier formulations attributed the puzzle to Epimenides the Cretan (“all Cretans are liars”), but Eubulides is credited with the sharpened form. Tarski’s 1933 resolution was that no language can consistently contain its own truth predicate; truth has to be assigned from a meta-language one level up. Kripke (1975) preferred a partial assignment in which the liar simply has no truth value, neither true nor false. Either repair sacrifices something most people take to be a built-in feature of language: that any well-formed sentence either is or isn’t the case.