A linguist in the land of logic puzzles
I recently stumbled across the following story in an old file on my hard drive. Judging by the modification date on the file, I seem to have written it near the end of 2002; in any case, it’s old enough that I was still using Microsoft Word (shudder), and because it was before I started this blog, I don’t think I did anything with it at the time. Anyway, it’s in the tradition of Raymond Smullyan’s knights-and-knaves logic puzzles and their many other imitators, but with a linguistic angle. I decided I still like it well enough to post it now (although if I were editing it I would probably tell myself not to use “smiled ” twice in such a short space).
A linguist on the Island of Knights and Knaves
Puzzle lore is rich in stories of a strange island on which everyone is either a ‘knight’ (someone who speaks only true statements) or a ‘knave’ (someone who speaks only false ones). A linguist recently visited this island to study the peculiar conventions of expression employed by its inhabitants.
When she landed, she was greeted by two women. “I’m Cass,” said the first one, “and this is my sister Sandra.” The second smiled indulgently. “Actually,” she said, “I’m Cass and she’s Sandra.” The first woman then said something inaudible. “I’m afraid I didn’t hear that,” said the linguist. “She asked you what country you come from,” said the second woman. “No, I didn’t,” said the first, “although I would be interested to know.” Which woman was which?
Once she had figured out which was which, the linguist learned a great deal about life on the island from Cass and Sandra. Eventually they began to talk about the relationships among the inhabitants, and Sandra announced, “Everyone on the island loves someone on the island.” Hearing this, Cass smiled enigmatically and said, “Everyone on the island loves someone on the island.” Such a short time elapsed between these two utterances that the linguist was quite sure nobody could have arrived at or departed from the island, or had a change of heart, during the interim. What did the linguist learn from these two statements?