( . . . ): The Liar's Paradox

20.3.07

The Liar's Paradox

A man says that he always lies. Is what he says true or false?

Labels: logic, paradox, those crazy greeks

2 Comments:

suttonhoo said...: here's a story from the annals:

A long time ago I had dinner with my soon-to-be-ex- at a cheap sushi joint just as things were winding down -- we had filed the paperwork, all that remained was to appear before the judge.

he was making one last tearful appeal to me and I explained to him that I didn't believe him -- that he had lied for so long and so persistently that he had lost all credibility.

during a lull in the conversation when it was clear that nothing more could be said he opened his fortune cookie and it read: "A liar is never believed, even when he is telling the truth."

it was one of the last laughs that we shared together.

(admittedly, not one of those belly laugh kind of laughs...)

but I'm afraid I don't know the answer to your question.; March 20, 2007 12:01 pm
mrtn said...: Well, as you've probably guessed (and like your story) the answer is that there is no answer. It really is a paradox. If he's saying something true, he's not lying, and therefore not telling the truth. If what he's saying is false, he's not lying, and therefore telling the truth.

The moral of the story is that some problems are created entirely by the way we use language, and can be circumvented by action, and that you therefore shouldn't trust a logician to do anything. No person tells only lies, no person tells only truth. In fact, most of the time, calling something true is just a way of giving yourself power. Oh, another moral of the story is that you shouldn't trust fortune cookies to determine important decisions about your life.

Here's another one of the same kinds of puzzles:

The following sentence is true. The previous sentence is false.; March 20, 2007 11:53 pm