Liar paradox
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The liar paradox is attributed to Epimenides of Crete, who said "All Cretans are liars". The truth value of the statement cannot be evaluated because the statement refers to the truth value of itself. Kurt Gödel managed to encode this paradox into number theory and conclude that no sufficiently complete axiomatic system can be consistent, and vice versa.
In Titus 1:12-13, St. Paul makes a passing reference to Epimenides' paradox, in furtherance of a serious argument that Cretans were "evil beasts."
An alternative formulation, popular in medieval Europe, is:
- Plato: What Socrates is about to say is false.
- Socrates: Plato has spoken correctly.
In this case, the paradox does not consist of a single proposition, but a referential cycle of two propositions.