Comments on: Liar Liar http://www.explananda.com/2008/09/30/liar-liar/ Mon, 12 Dec 2011 17:53:49 +0000 hourly 1 http://wordpress.org/?v=3.0.4 By: Paul http://www.explananda.com/2008/09/30/liar-liar/comment-page-1/#comment-6322 Paul Wed, 01 Oct 2008 18:15:08 +0000 http://www.explananda.com/?p=2517#comment-6322 Yeah, the first two of three possible answers to the contest (<a href="http://www.cambridgeblog.org/2008/10/win-a-new-martin-gardner-book-5/" rel="nofollow">revealed here</a>) involve "what would he say" questions. And there is definitely something fishy about such an answer when one is told that all answers must be one word, "yes" or "no." Yeah, the first two of three possible answers to the contest (revealed here) involve “what would he say” questions. And there is definitely something fishy about such an answer when one is told that all answers must be one word, “yes” or “no.”

]]> By: ben wolfson http://www.explananda.com/2008/09/30/liar-liar/comment-page-1/#comment-6321 ben wolfson Wed, 01 Oct 2008 18:07:46 +0000 http://www.explananda.com/?p=2517#comment-6321 Actually, I think that's the sort of answer that Gardner himself gives in one of the books in which this puzzle appears—I couldn't remember the right formulation of it, though. Actually, I think that’s the sort of answer that Gardner himself gives in one of the books in which this puzzle appears—I couldn’t remember the right formulation of it, though.

]]> By: Paul http://www.explananda.com/2008/09/30/liar-liar/comment-page-1/#comment-6320 Paul Wed, 01 Oct 2008 17:54:45 +0000 http://www.explananda.com/?p=2517#comment-6320 Cool. That's much better than the question I had devised, and you're right that it doesn't involve use/mention. But mine did: "If I were to ask the a member of the *other* tribe if this is the right road, what would he say?" The answer in this case would be a mentioning of either "yes" or "no," not a use of it. But it would work. So it's only a bad answer if the condition is "it must be a yes/no" question. I didn't win the book. :( Cool. That’s much better than the question I had devised, and you’re right that it doesn’t involve use/mention. But mine did:

“If I were to ask the a member of the *other* tribe if this is the right road, what would he say?”

The answer in this case would be a mentioning of either “yes” or “no,” not a use of it. But it would work. So it’s only a bad answer if the condition is “it must be a yes/no” question.

I didn’t win the book. :(

]]> By: ben wolfson http://www.explananda.com/2008/09/30/liar-liar/comment-page-1/#comment-6319 ben wolfson Wed, 01 Oct 2008 17:45:47 +0000 http://www.explananda.com/?p=2517#comment-6319 It's not a use-mention thing, it's secretly iterating the question and exploiting the fact that the honest man's answers are stable (you can depend on him!) whereas the liar's answers are unstable under that sort of condition. It’s not a use-mention thing, it’s secretly iterating the question and exploiting the fact that the honest man’s answers are stable (you can depend on him!) whereas the liar’s answers are unstable under that sort of condition.

]]> By: ben wolfson http://www.explananda.com/2008/09/30/liar-liar/comment-page-1/#comment-6318 ben wolfson Wed, 01 Oct 2008 17:44:59 +0000 http://www.explananda.com/?p=2517#comment-6318 Assume WLOG that the left road goes to the village. Ask the guy, "if I asked you to tell me which road goes to the village, would you tell me to take the left road?". The guy is a truth-teller: he would, so he says "yes". The guy is a liar: he wouldn't, so he says "yes". Suppose you ask instead "if I asked you to tell me which road goes to the village, would you tell me to take the right road?". The guy is a truth-teller: he wouldn't, so he says "no". The guy is a liar: he would, so he says "no". Thus you can always ask "would you tell me to take road X, if I asked", and if you get the answer "yes", that's the right road, and if you get the answer "no", it's the wrong road. Assume WLOG that the left road goes to the village. Ask the guy, “if I asked you to tell me which road goes to the village, would you tell me to take the left road?”.

The guy is a truth-teller: he would, so he says “yes”.
The guy is a liar: he wouldn’t, so he says “yes”.

Suppose you ask instead “if I asked you to tell me which road goes to the village, would you tell me to take the right road?”.

The guy is a truth-teller: he wouldn’t, so he says “no”.
The guy is a liar: he would, so he says “no”.

Thus you can always ask “would you tell me to take road X, if I asked”, and if you get the answer “yes”, that’s the right road, and if you get the answer “no”, it’s the wrong road.

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