A linguist in the land of logic puzzles

[q_pheevr]

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.

Comments

[ext_237340]

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_pheevr]

You’re entirely right about the second part. But there is a more solid basis for determining who is who.

[butsuri]

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_pheevr]

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.”