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An oddity here (that I think Smullyan is often careful about when introducing his knight and knave puzzles) is that the goblins in the story appeared to agree w
by schoen 2y ago
An oddity here (that I think Smullyan is often careful about when introducing his knight and knave puzzles) is that the goblins in the story appeared to agree with each other about the surrounding context (that there is one liar and one truthteller, that there is one door that should be taken, etc.). They didn't contradict each other about that!
Smullyan's liars normally lie about everything in every statement, so an official Smullyan liar would not agree that there is one liar and one truthteller, that there is one safe door and one unsafe door, and so on.
I just watched the original scene, and the two goblins seem to agree with each other about all of that stuff! How confusing.
- DeathArrow 2y agoA liar claiming he lies tells the truth?
- Terr_ 2y agoSimilarly, can the always-liar state that "I have a penny, it is in my left pocket", when the reality is that it's a penny in the right pocket, or a quarter in the left pocket? Who decides which clauses or aspects are separable? For that matter, if either of them are perfect at their jobs, they are oracles, and could retire by attempting to say something about out the first, second, third, etc. digit of tomorrow's winning lottery number. If they're imperfect at their jobs, then they aren't actually "always" anything.
- robertlagrant 2y agoThe always-truth one would surely just say they didn't know tomorrow's lottery number?
- SilasX 2y agoStupid question: what about defining "lying" as "saying something that, if accepted, moves the believer away from the liar's worldmodel"? (Which I think matches general intuition.) Then you do get information once you know someone always lies (and has a correct worldmodel) because you know to update the opposite direction. I don't know the impact on these puzzles.
- Terr_ 2y ago> what about defining "lying" as "saying something that, if accepted, moves the believer away from the liar's worldmodel"? Then the definition becomes kinda-contradictory: The entity would sometimes tell the truth, because that would be the best choice to divert and ruin your model. So "always lies in a simple way" would become more like "always unhelpful in a superintelligently evil way."
- schoen 2y agoIn some contexts in computer science and computer security, this is also called "answering adversarially".
- SilasX 2y agoThat wouldn’t make it contradictory, it would make “always lying” just as effective a strategy as in the original problem statements. It’s a general problem that “being known to always lie” makes (the goals of) deception harder, and my definition just preserves that problem.
- schoen 2y agoIn Smullyan's formulation, the overall statement uttered by a liar must be logically false, even though it might contain conjuncts that are true, or might convey large amounts of useful and accurate information. For example, Smullyan would allow a liar to say "the sky is blue and cats are cute and 1+1=3". I might have phrased that confusingly when I said that they lie about everything in every statement. I should probably have said that they are never allowed to make any statement that they believe is true.
- JohnMakin 2y ago> You can also assume that both goblins are telling the truth right up until the moment they stop explaining the rules. It says this in the very beginning.
- schoen 2y agoI remembered that Smullyan usually handles this by having an outsider introduce the rules, rather than by having an islander (etc.) who is subject to the rules try to explain them. In the movie the goblins themselves are explaining their own behavior, which is not very helpful if you take them fully literally.