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Liar paradox

the gist

The liar paradox arises from the statement 'I am lying' or the simpler 'This sentence is false'. If the speaker is lying, the statement is true, but if it is true, the speaker is lying, so no consistent truth value can be assigned. The problem is about self-reference, and logicians have built variants such as the card paradox and the Pinocchio paradox to explore it. It has puzzled thinkers for more than two thousand years, and it helped motivate modern work on truth and formal logic.

so what

It shows the limits of simple true-or-false thinking and drove much of twentieth-century logic, including Gödel's work on incompleteness.

fun fact

The ancient Greek philosopher Eubulides of Miletus is credited with the liar paradox.

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