Definition
The liar paradox arises from a sentence that says of itself that it is false. Consider the sentence: this very sentence is false. Call it L. If L is true, then what it says is the case — so L is false. But if L is false, then what it says fails to be the case — so L is true. Either assumption produces its own contradiction.
The paradox is ancient, traced to the Cretan Epimenides and sharpened by the Megarian logician Eubulides. Its persistence over millennia signals that it touches something structural in the concepts of truth and falsity, not a mere verbal slip.
Why it matters
How it works
The liar is dangerous because it combines two innocent-looking ingredients: a sentence can talk about itself, and 'true' and 'false' apply to sentences. Each is harmless alone. Together they trap us.
Logicians have responded in several ways. Tarski argued that a language cannot consistently contain its own truth predicate, forcing a hierarchy of meta-languages. Others propose that the liar sentence simply has no truth value — it falls into a gap. A bolder line, defended by Priest, accepts that the liar is both true and false, and builds a paraconsistent logic in which such contradictions can be tolerated without everything collapsing into triviality.