The liar paradox is the classical problem in logic and philosophy that arises from a statement in which a speaker asserts that they themselves are lying, as in the sentence "I am lying." If the statement is true, then the speaker is indeed lying, which would make the statement false, and if it is false, the speaker is not lying, which would make the statement true. The paradox is often strengthened to the self-referential form "this sentence is false," which sharpens the contradiction for more rigorous logical analysis: assuming the sentence true forces acceptance of its own content, which asserts falsity, and assuming it false leads back to the same contradiction by the same reasoning. Trying to assign the strengthened liar sentence a classical binary truth value therefore leads directly to contradiction.
Facts
Origin YearSourced to the subject's own accountApproximate; marks the 4th century BCE floruit of Eubulides of Miletus, to whom one version of the paradox is attributed. The classical self-referential form is ancient but of disputed precise date. Sources
1. Liar Paradox (Wikipedia)
WikipediaLiar paradox Wikipedia introduction
In philosophy and logic, the classical liar paradox or liars paradox or antinomy of the liar is the statement of a liar that they are lying, for instance, declaring that I am lying.
Liar paradox Wikipedia on Eubulides
One version of the liar paradox is attributed to the Greek philosopher Eubulides of Miletus, who lived in the 4th century BC.
View the Source Frequently Asked Questions
Why does the sentence "this sentence is false" cause a genuine logical problem rather than simply being meaningless?
Assigning the sentence either truth value forces its own opposite, so classical logic cannot give it a consistent binary value at all.
The strengthened liar sentence causes a genuine problem because trying to assign it either classical truth value leads directly to contradiction. If the sentence is assumed true, that forces acceptance of its own content, which asserts that the sentence is false, a direct contradiction. If the sentence is assumed false, the same reasoning leads back to the identical contradiction. Because assigning either of the only two classical truth values produces a contradiction, the sentence cannot be given a consistent binary true or false value at all, which is what makes the liar paradox a real challenge for classical logic rather than an idle piece of wordplay.
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