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14 Marts 2017 @ 01:59
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 <adverb>” 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?

steorra.dreamwidth.org: mindsteorra.dreamwidth.org on 15. Marts, 2017 20:29 (UTC)
Cass is the truth-teller and Sandra is the liar.
I'm not sure whether the first or the second woman is Cass, though. My guess would be that the first woman is Cass for reasons that do not amount to proof: If she were addressing the linguist to ask where she was from, it's unlikely that her question would be inaudible when her previous and following statements are perfectly well audible.

Cass and Sandra are using two different meanings of an ambiguous sentence. Sandra asserts falsely that there is one particular person on the island whom everyone loves. Cass asserts truly that everyone on the island has someone that they love - but not necessarily all the same person. Between the two, the linguist knows that it *isn't* all the same person.
Q. Pheevrq_pheevr on 16. Marts, 2017 12:58 (UTC)
You’re entirely right about the second part. But there is a more solid basis for determining who is who.
butsuributsuri on 20. Marts, 2017 15:43 (UTC)
If the first woman is Sandra, then she asked where the linguist was from despite not being interested in knowing the answer to that question. This seems unlikely, though I don't think it qualifies as proof. Actually... If they can only speak true or false statements, does that mean they can't ask questions at all? If so then the first woman must be Cass.

RIP Raymond Smullyan, 1919—2017.
Q. Pheevrq_pheevr on 21. Marts, 2017 14:04 (UTC)
If they can only speak true or false statements, does that mean they can't ask questions at all?

That’s the solution I had in mind. (It’s a strange society indeed if no one can ask questions, but then the whole knights-and-knaves premise is a pretty strange society to begin with. And, as Cass demonstrates, it’s entirely possible to solicit information using only declarative sentences, as in “I’d be interested to know X.”

Edited at 2017-03-21 14:05 (UTC)