The Island of Truth and Lies, Part I
I have nothing against the logic puzzles with truthtellers and liars that I wrote about here, just the comparison between them and real-life liars. So, I'm writing a story that's full of these logic puzzles. This is the first installment. I'll be posting the other parts once a day for the next few days.
Part I: Journey to the Isle
An intrepid anthropologist, who was also an amateur logician, set forth on a trip to the dangerous but fascinating Island of Truth and Lies. Many of his friends, fearing for his life, warned him not to go to this island where many of the natives were cannibals who would have no qualms about eating a traveling anthropologist. But the anthropologist was determined to make the trip in the name of science because the island's inhabitants were of a most peculiar sort, not found anywhere else on the face or within the crevices of this Earth.
Two tribes of natives lived on this island, remarkably similar in dress and appearance, but remarkably different in their customs. The members of one tribe were perfectly honest. They always told the truth, without fail. The members of the other tribe followed an even more irregular code of speech: they were perfectly dishonest. Unlike other liars, who sunk to telling the truth whenever the pragmatics of the situation seemed to reward it, they made a false statement with every utterance. As an amateur logician, our anthropologist was particularly intrigued by this unique population.
But there were risks, serious risks, for the difference in values between the two tribes was not limited to the truth-values of the propositions they uttered. The one tribe consisted of kind and considerate people who would make the anthropologist feel welcome in their village and treat him with respect. The other consisted of cannibals who would capture and eat him if he ever got near their village. The anthropologist planned to head to a native village, and he was certainly was afraid of this possibility. He had heard that death from consumption by these natives was not the most pleasant way to go, but he had faith in his reasoning skills and his ability to find the tribe that could be trusted.
He undertook this dangerous venture because he knew that the upside to a successful trip would be enormous, since what was known about these two distinctive tribes did not extend much beyond what has already been presented here. The first anthropologists to visit the island had tried to visit the villages, and, though they may have learned a great deal about the tribes, they were unable to publish any of their findings.
Later anthropological visitors took a more cautious tack, limiting their investigation to individual natives who were interviewed far away from the villages. Unfortunately, the natives proved to be most uncooperative informants. Though any native would happily answer the first question that he or she was asked, in the manner of their tribesmen, they would often go days before responding to another question. They would happily converse with other natives, but, outside of their villages, the natives of the two tribes tended to intermingle, appear, and disappear in such a way that it was difficult for an anthropologist to follow their conversations without unethically infringing on their liberties. Since the tribes did not mix in their villages, our anthropologist realized that the only way to come to understand these tribes was to find the safe village, take advantage of their hospitality, and observe the tribal life around him.
Our anthropologist did not even have a map when he arrived at the Island of Truth and Lies, and the great risk of his journey had resulted in him coming companionless. Beginning cautiously, he landed on the end of the isle away from the two villages. He soon found a path through the forest towards the villages and walked along it without seeing another soul. He neared the villages along the island's one central path, until he reached the point where the path branched in two, with one trail towards each tribe's village. Which way was which, the anthropologist had no way of knowing.
No way of knowing, that is, until a native came out of the trees. The anthropologist paused for a moment, hoping that other natives might appear or that this one might open his mouth and reveal his tribe, but his wishes went unfulfilled as the native eyed him quizzically. The amateur logician realized that he had to take the one chance that he had been given and ask this native one question in order to figure out which way he wanted to go. What one question did our intrepid traveler ask?
Continue to Part II: All the Right Questions
Continue to Part III: To the Village
Continue to Part IV: An Honest Chief
Continue to Part V: Out of the Boiling Pot, Out of the Fire
Continue to Part VI: Death and Lies