There is a classic puzzle about two tribes of natives. One tribe always tells the truth, the other always lies. A traveler comes to a fork in the road. One path leads to fortune, the other to death. The natives know which is which. The traveler gets to ask one question. What question will reveal the right path? Here's one version: http://mathforum.org/dr.math/faq/faq.liar.html The classic answer is to ask either native what the other native would say is the path to fortune and then take the other path. The logic is that you will get one truth and one lie. It seems to me that there is a simpler solution that only involves one native. Wouldn't it work to ask any native this question: "If I ask you which path leads to the treasure, what will you say?" It seems to me that I will get either two true statements or two false ones. Either way, I get the right answer. The truth teller will tell the truth about the path and they will tell the truth about what they would say. The liar would lie about both, resulting in the same answer. Is there a flaw in that logic?
That's how the puzzle was presented to me first - as one person, asked one question. But it was a variant on the puzzle of determining the honesty status of a respondent, not the correct path to a treasure. And I preferred Klaus's answer: "I would ask him whether he was a tree toad".
In order for either of the tribes to consistently lie or tell the truth implies a bit of omniscience that is dubious enough all by itself to cast doubt on whatever they might tell you. Omniscience is a paradox all by itself. You only get one question, so asking a question that only ascertains which tribe the respondent is from does not get you any further down the road, safely or otherwise. The setup to the question does not hint at whether the members of the "truth" tribe know all of the members of the "liar" tribe either, even if those terms had any real mathematical meaning, which they emphatically do not. Truth is only a value; not an absolute. On a daily basis, we must selectively ignore millions of truths that are not of any interest to find only a handful that have any bearing on our continued happy existence. This is true of all truths, including and especially mathematical ones. The question you should ask if you are gullible enough to believe the setup is: "If I were to ask that fellow there which path is safe, which one would he indicate?". If you have chosen to ask the liar, he will of course indicate the path to certain death. If you have chosen to ask the question of the truthy one, he will likewise indicate the path to certain death. Take the path they did not indicate if you wish to have a chance of survival. Pray that the liar was not clever enough to anticipate the information he was also giving you about the other tribe would be useful enough to confound. The liar is also more apt to be the one who understands the nature of truth, because it is easier for finite minds to falsify something than it is to prove its truth. The former process is finite; the latter is not.
Ask the tribe that lies to say whether or not the other tribes answer is correct. If the other tribe says go left and the lying tribe says they lied then you get the truth.
