History Main / LiarsParadox

A presumed liar gives a statement [[SelfProclaimedLiar declaring that they are currently lying:]] "I am lying", "this is a lie". However, in doing so they create a paradox, as under the assumption that they are lying, that means what they just said is a lie and therefore they are in fact telling the truth. While the assumption that they are truthful means they are once again lying... and the cycle keeps on going.

This is known as the Liar's Paradox. A variant can be done with two people, where Alice states Bob is a liar, while Bob states Alice is telling the truth. Be careful about phrasing this. A variant like "Everything I say is a lie" is not a paradox (instead, one can deduce that ''not everything'' I say is a lie, but ''this'' particular statement is, which is logically sound).

Its most famous early formulation is ascribed to the Greek philosopher Epimenides, who came from Crete and said "All Cretans are liars". This version has a logical out (if it is untrue, then the implication is not "All Cretans tell the truth" but "Not all Cretans are liars ''but this one is''"). The stronger version was formulated by the Greek philosopher Eubulides of Miletus, and indepently by the Indian philosopher Bhartrhari.

A presumed liar gives a statement [[SelfProclaimedLiar declaring that they are currently lying:]] "I am lying", "this is a lie". However in doing so they create a paradox, as under the assumption that they are lying, that means what they just said is a lie and therefore are in fact telling the truth. While the assumption that they are truthful means they are once again lying...and the cycle keeps on going.

This is known as the Liar's Paradox. A variant can be done with two people, where Alice states Bob is a liar, while Bob states Alice is telling the truth. Be careful about phrasing this. A variant like "Everything I say is a lie" is not a paradox (rather, it means that ''not everything'' I say is a lie, but ''this'' particular statement is, which is logically sound).

In early works it was often used as a MindScrew for readers and viewers. However as it became popularized in fiction, it became the standard-issue LogicBomb for heroes to use against [[AIIsACrapshoot computers and robots]] due to the endless paradox loop.

* "Opposites Day" by Lloyd Cole, the two-sentence variant ("The next line is the truth| The last line was a lie" and later "The next line is a lie|This one is the truth"), both being equivalent to the standard paradox.

* ''Anime/GhostInTheShellStandAloneComplex'': During season one, the Tachikomas (who are {=AIs=} themselves) use this paradox to shut down a humanoid drone in order to take a look at the thing it was watching over. They promptly boast about how their own superior programming means that they understand that there isn't a correct answer to the question and consequently are immune to getting caught by it.
-->'''Tachikoma''': Folks who can't handle a self-reference paradox are real suckers!

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->"This sentence is a lie."

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