Liar Paradox

In philosophy and logic, the liar paradox or liar's paradox (pseudomenon in Ancient Greek) is the statement "this sentence is false." Trying to assign to this statement a classical binary truth value leads to a contradiction (see paradox).

If "this sentence is false" is true, then the sentence is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on ad infinitum.

Similarly, if "this sentence is false" is false, then the sentence is true, which would in turn mean that it is actually false, but this would mean that it is true, and so on ad infinitum.

Read more about Liar ParadoxHistory, Explanation of The Paradox and Variants, Logical Structure of The Liar Paradox, In Popular Culture

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... "Logic of Paradox" ... "A Note on the Sorites paradox" ... "The Truth Teller Paradox" ...
Liar Paradox - In Popular Culture
... The liar paradox is occasionally used in fiction to shut down artificial intelligences, who are presented as being unable to process the sentence ... In Star Trek The Original Series episode I, Mudd, the Liar paradox is used by the characters of Captain Kirk and Harry Mudd to confuse and ultimately disable an android, and in the 1973 Doctor Who serial ... frequently muses on the axiom "all Cretans are liars" in her inner monologue ...
List Of Paradoxes - Logic - Self-reference
... Barber paradox A barber (who is a man) shaves all and only those men who do not shave themselves ... Does he shave himself? (Russell's popularization of his set theoretic paradox.) Berry paradox The phrase "the first number not nameable in under ten words" appears to name it in nine words ... Paradox of the Court A law student agrees to pay his teacher after winning his first case ...
Insolubilia
... In the Middle Ages, variations on the liar paradox were studied under the name of insolubilia (insolubles) ... Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it appears to have been reinvented independently of ancient ... Other ancient sources which could suggest the liar paradox, including Saint Augustine, Cicero, and the quotation of Epimenides appearing in the Epistle to ...

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