History Main / LiarsParadox

* In ''WesternAnimation/TheSimpsons'' episode "[[Recap/TheSimpsonsS6E4ItchyAndScratchyLand Itchy & Scratchy Land]]", Lisa tries to use this on a group of murderous robots in Itchy and Scratchy Land. Turns out their AI isn't complex enough to recognize the paradox, but Homer shows all the signs of suffering from the LogicBomb.

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).

A presumed liar gives a statement [[SelfProclaimedLiar inferring 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.

* ''VideoGame/KnightsOfTheOldRepublicIITheSithLords'': On Korriban, you find a computer terminal that has a test for trainee Sith which has the question "Which of these is not a paradox?" One of the answer choices is "I always lie." [[spoiler: It's also [[SubvertedTrope the correct answer]] thanks to ExactWords. The negation of the statement isn't "I never lie" (which would cause the paradox), but "I don't always lie," which doesn't tell us anything about whether the subject is ''currently'' lying or not, and if the subject ever told the truth even once (which is likely), then the statement is just plain false, not a paradox.]]

* ''Plan 7 of 9 from Outer Space''. [[Film/TheAdventuresOfCaptainProton Captain Proton]] tries the old "the next thing I say is a lie" trick on a KillerRobot only to have it smack him in the chops.

* "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.

* In ''Discworld/SmallGods'': One of the Ephebian philosophers gets into trouble when he tries to discuss this paradox with his fellows. Discworld intellects being what they are, Xeno takes offense:

A presumed liar gives a statement inferring 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).

KnightsAndKnaves is a prominent application of this trope.

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 comes from the Greek philosopher Eubulides of Miletus, and was independently developed in India by Bhartrhari.

** Speaking of which, [[VideoGame/{{Borderlands}} Claptrap]] has a [[DiscussedTrope conversation about these]] with [=GlaDOS=] and [[Franchise/SamAndMax Sam]] in ''VideoGame/PokerNight2''. He even ends up falling into one of these after Sam gives an example.

* ''VideoGame/KnightsOfTheOldRepublicIITheSithLords'': On Korriban, you find a computer terminal that has a test for trainee Sith which has the question "Which of these is not a paradox?" One of the answer choices is "I am lying."

* In ''WesternAnimation/TheSimpsons'', Lisa tries to use this on a group of murderous robots in Itchy and Scratchy Land. Turns out their AI isn't complex enough to recognize the paradox, but Homer shows all the signs of suffering from the LogicBomb.

[[folder: Miscellaneous ]]

* An old joke involves an explorer captured by natives and told that if his next sentence is true, he'll be thrown to the snakes, if false, he'll be thrown to the lions. Naturally, he predicts his death by lions and is let go.

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* In the second ''Literature/DeltoraQuest'' book, "Lake of Tears", when Lief gets given a riddle by a [[GateGuardian Bridge Guardian]] and tricked into the wrong answer, the guardian gives him another riddle to decide his method of death. Lief will say a statement, if it was true then the guardian would strangle Lief, if it was false he would cut his head off with his sword. Lief responds with the statement "You will cut off my head." It's then revealed the guardian was cursed by a Thaegan the sorcerer to guard the bridge "until truth and lies become one", so Lief's liar's paradox sets him free and he reverts to the form of an eagle.

A presumed liar gives a statement inferring that they are currently lying: "I am lying", "everything I say is a lie", "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.

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 lie all the time"). The stronger version comes from the Greek philosopher Eubulides of Miletus, and was independently developed in India by Bhartrhari.

-->"This sentence is a lie."

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[[AC:Western Animation]]
* In ''WesternAnimation/TheSimpsons'', Lisa tries to use this on a group of murderous robots in Itchy and Scratchy Land. Turns out their AI isn't complex enough to recognize the paradox, but Homer shows all the signs of suffering from the LogicBomb.

** Speaking of which, [[VideoGame/{{Borderlands}} Claptrap]] has a conversation about these with [=GlaDOS=] and [[Franchise/SamAndMax Sam]] in ''VideoGame/PokerNight2''. He even ends up falling into one of these after Sam gives an example.

--> He bloody well accused me of slander!
--> I didn't!
--> You did! You did! Tell 'em what you said!
--> Look, I merely suggested, to indicate the nature of paradox, right, that if Xeno the Ephebian said "All Ephebians are liars-"
--> See? See? He did it again!
--> -no, no, listen, listen... then, since Xeno is himself an Ephebian, this would mean that he himself is a liar and therefore-
* Parodied and subverted in the ''Literature/EighthDoctorAdventures'' novel ''Frontier Worlds'', in which the Doctor tries the Liar's Paradox on a security robot, which simply snaps, "Get off with you. You'll be asking me to calculate pi next," and keeps attacking him.

[[AC:Western Animation]]
* In ''WesternAnimation/TheSimpsons'', Lisa tries to use this on a group of murderous robots in Itchy and Scratchy Land. Turns out their AI isn't complex enough to recognize the paradox, but Homer shows all the signs of suffering from the LogicBomb.

[[AC:Miscellaneous]]
* An old joke involves an explorer captured by natives and told that if his next sentence is true, he'll be thrown to the snakes, if false, he'll be thrown to the lions. Naturally, he predicts his death by lions and is let go.

* In ''VideoGame/Portal2'', [[AIIsACrapshoot GLaDOS]] is afraid of the terrible effects this paradox can have in artificial intelligence. In fact, she uses this against Wheatley in an attempt to drive him insane. Unfortunately for her, he's TooDumbToFool.

* In a ''VideoGame/{{Minecraft}}'' storymode episode, "Access Denied", Jesse and several others are captured by a [[AIIsACrapshoot supercomputer named PAMA]]. Jesse notices that PAMA stalls whenever processing so he uses a paradox to loop it. One of the options to choose from is a Liar's Paradox.

-->''The next thing I say to you will be true
The last thing I said was false

* Robots in ''WesternAnimation/{{Futurama}}'' are susceptible to this... except [[TheImmune SantaBot]], as he has logic proof crumple zones.