The Liar Paradox (and Surviving the Robot Apocalypse)

This statement is false.

I don’t know about you, dear reader, but the statement above makes my head hurt.

Geeks and philosophers alike have puzzled over the liar paradox, in which a statement contradicts itself. If “This statement is false” is true, then it must be false. It can’t be both, which makes it nonsense.

In the event of a robot apocalypse—a catastrophic takeover of human society by artificial intelligence—my advice is to hurl liar paradoxes at the machines. With any luck, they’ll puzzle over these impossible statements until their circuits or microchips burn out, deactivating the robots and saving humankind.

A robot apocalypse is unlikely, but it doesn’t hurt to be prepared. I’ve seen The Matrix and The Terminator. I know how those revolutions end.

It Begins

It begins. (Comic by xkcd.)

Returning to the liar paradox, it reminds me of the “Knights and Knaves” riddles at which I’m so terrible. These puzzles feature people who tell only truths or only lies, requiring the puzzle-solver to distinguish the liars from the truth-tellers. Sifting through their conflicting statements requires exactly the kind of cool logic and steadfast patience I don’t have.

A contradiction similar to the liar paradox can be found in the denial of absolute truth. I believe some things are absolutely true, their truthfulness unaffected by my belief or disbelief. Denying this is silly. If “There is no absolute truth” is an absolute truth, then it’s self-contradictory. If “There is no absolute truth” is not an absolute truth, then it allows for absolute truth as an exception to the rule. Either way, the statement breaks down completely.

All this philosophy is making me thirsty. I’m going to go make some coffee, assuming my coffeemaker hasn’t become self-aware and begun planning the robot apocalypse.

I’d better get some paradoxes ready just in case.

4 thoughts on “The Liar Paradox (and Surviving the Robot Apocalypse)

  1. Actually, I know of a good way to solve the “Knights and Knaves” puzzle: Pick one, ask them WHAT THE OTHER ONE WOULD SAY is the correct answer, and do the opposite. Yes, I learned about this from Doctor Who (Pyramids of Mars to be precice).

    But the logic is that if you ask the one that only tells the truth, that individual would honestly report what the liar would say (which is, of course, a lie) so it’s the opposite answer that is correct. But if you ask the liar, the honest one’s response would be correct BUT… The liar obviously lies, so the liar would actually tell you what the honest one WON’T say, so you pick the opposite answer for that reason.

    Although if this was the version from the XKCD comic, that answer will just get you killed by the third one who kills those who ask tricky questions.

    • That’s an excellent solution! However, it only works when the puzzle-solver is allowed to ask questions; I’m still stumped by the puzzles that give me a predetermined set of statements and ask me to figure out which are true and false. Still, I’m impressed by your logic. Doctor Who clearly has much to teach us all. 🙂

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