Posted by: Alexandre Borovik | March 22, 2012

Liar’s paradox

From a letter from a colleague:

I am reminded of a commentary on logic puzzles of a certain kind; it
was perhaps in a letter to Martin Gardner, reprinted in one of his
books. The puzzles are those about getting about on an island where
each native either always tells the truth or always lies. You reach a
fork in the road, for example, and a native is standing there, and you
want to learn from him, with one question, which way leads to the
village. The “correct” question is “If I asked you if the left way
led to the village, would you say yes?” But why should the native’s
concept of lying conform to our own logical ideas? If the native is a
liar, it means he wants to fool you, and your logical trickery will
not work. The best you can do is say something like “Did you hear
they are giving away free beer in the village today?” and see which
way the native runs. You follow him, even if he says something like
“Ugh, I hate beer!” since then he probably really is lying.



  1. could some one explain the “correct” question ?

  2. Assuming the way to the village was left, a truth teller would answer ‘Yes’ since he would answer the question in the question ‘Yes’. A liar would also say ‘Yes’, since the liar would answer the question in the question ‘No’. Since he will lie about how he will answer the question a ‘Yes’ means thats what way the village is.

    Reverse it for the village not being to the left.

  3. If the first trickery won’t work, what makes one think that the second one will? The same assumption is made in both case, which is that the natives aren’t as perceptive as they may actually be.
    Am I missing the point?

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