A presumed liar gives a statement 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).
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.
In early works it was often used as a Mind Screw for readers and viewers. However as it became popularized in fiction, it became the standard-issue Logic Bomb for heroes to use against computers and robots due to the endless paradox loop.
- Ghost in the Shell: Stand Alone Complex: 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!
- Done in Yu-Gi-Oh! by 2 appropriately named Trickster Twins Para and Dox. The heroes have to choose the correct door to exit. The brothers claim one of them tells the truth and one lies, and the heroes will have to figure out which is which in order to ask the right one which door is correct. The Pharoah realizes it's a trap; since they've both said the same thing, they can't be one liar and one truthful — the only way they could both make that claim is if they're both lying. He's right, but he beats them at their own game using a Two Sided Coin to get them to open the right door.
- 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 the second Deltora Quest book, "Lake of Tears", when Lief gets given a riddle by a Bridge Guardian and tricked into the wrong answer, the guardian presents another game 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 opts to Taking a Third Option and responds with the statement "You will cut off my head." It's then revealed the guardian was cursed by 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.
- In Small Gods: 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:
Xeno: He bloody well accused me of slander!
Ibid: I didn't!
Xeno: You did! You did! Tell 'em what you said!
Ibid: Look, I merely suggested, to indicate the nature of paradox, right, that if Xeno the Ephebian said "All Ephebians are liars—"
Xeno: See? See? He did it again!
Ibid: —no, no, listen, listen... then, since Xeno is himself an Ephebian, this would mean that he himself is a liar and therefore—
- Also in Discworld, the literal-minded omnicidal Auditors of Reality eventually deal with paradoxes by deciding that all statements are either (1) true, (2) false, or (3) bloody stupid.
- The dwarf Casanunda's business card says he is an "outrageous liar", but if you ask if it's true, he'll deny it.
- After snookering Ridcully in a card game, he reminds them that he warned he was an Outrageous Liar. But Ridcully thought that was a lie.
- Parodied and subverted in the Eighth Doctor Adventures 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.
- In Star Trek: The Original Series, during the episode "I, Mudd", Captain Kirk and Harry Mudd use a liar's paradox to set off a Logic Bomb in an android holding them captive.
Norman: But there was ... no explosion.
Mudd: I lied.
Kirk: He lied. Everything Harry tells you is a lie, remember that — everything Harry tells you is a lie.
Mudd: Now listen to this carefully, Norman: I am lying.
Norman: You say you are ... lying, but ... if everything you say is a lie, then you are ... telling the truth, but ... you cannot tell the truth because everything you ... say is a lie, but ... you lie, you tell the truth, but you ... cannot for you lie — illogical! Illogical! Please explain! You are human! Only humans can explain the behaviour! Please explain!
Kirk: I am not programmed to respond in that area.
(smoke pours from Norman's head and ears as his brain breaks down)
- In Doctor Who, during the story "The Green Death", the Third Doctor manages to stump an insane computer called BOSS with the question "If I were to tell you that the next thing I say would be true, but the last thing I said was a lie, would you believe me?" However after some looping, BOSS decides the question was irrelevant.
- From Devo's "Enough Said"
The next thing I say to you will be true
The last thing I said was false
Remember to do nothing when you don't know what to do
- The 1990 song "All Men Are Liars" sung by Nick Lowe (a man, obviously) informs the listener emphatically that "all men are liars, and that's the truth".
- "Opposites Day" by Lloyd Cole has two occurrences of 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.
- Knights of the Old Republic II: The Sith Lords: 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." It's also the correct answer thanks to Exact Words (and if the player thinks in terms of first order /predicate logic instead of propositional logic). The negation of the statement isn't "I never lie" (which is the case in propositional logic and which would cause the paradox), but "I don't always lie," (in first order logic, trying to negate sentence with universal quantifier will result in negative sentence with existential quantifier. In this case, "always" is universal quantifier) 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.
- In a Minecraft: Story Mode episode, "Access Denied", Jesse and several others are captured by a 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.
- In Portal 2, 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 too dumb to understand the paradox whereas even his "frankenturrets" are not.
- Poker Night 2: Claptrap has a conversation about these with GlaDOS and Sam, and ends up falling into one of these after Sam gives an example.
- Sam Starfall of Freefall boasts that he's the greatest liar in the world in the Monday 2 November 1998 strip. When Helix queries how that claim can be verified, Sam's response is, "You'll just have to trust me."
- In The Order of the Stick, when Roy admits to Belkar that he lied to him in order to have him assist with his sidequest to acquire Starmetal for his sword, Belkar throws this trope at him by stating that he doesn't believe him. Of course, he was likely just busting Roy's chops.
Roy: Look, I lied to you back in town. I told you a story about giants in order to get you to come along on this side quest. You fell for it, and now I am trying to tell you that yes, sorry, I was lying.
Belkar: Sorry, I'm not buying it, Roy.
Belkar: I'm saying that I don't believe this whole "I told you a lie about giants" thing. I think I would remember something like that, but I don't.
Roy: Why would you possibly not believe me?
Belkar: Well, you're an admitted liar, for starters.
Roy: But—I—if you—
Belkar: Sorry, Roy, I just don't trust you enough to believe that you lied.
- In a Deleted Scene for The Simpsons episode "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 Logic Bomb.
- Family Guy: Peter gets caught in this when Chris points out a lie he just told:
Peter: Chris, everything I say is a lie. Except that. And that. And that. And that. And that. And that. And that. [Beat] And that.