Liar's paradox

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Liar's paradox is a logical paradox. Consider the following sentence:

This sentence is false.

Is this sentence true or false? Both answers instantly lead to a logical contradiction.

One possible resolution of the paradox is that a well-formed logical sentence cannot refer to its own truth value. This idea of self-contradictory sentence is used in mathematics in many proofs, including Russell's Paradox and Godel's Incompleteness Theorems. It is also related to diagonalization.

The Bible mentions liar's paradox, see humor in the Bible.