I have a question about the first logic puzzle here. The condition “Both sane and insane people are always perfectly honest, sane people have 100% true beliefs while insane people have 100% false beliefs” seems to be subtly different from Liar/Truth-teller. The Liar/Truth-teller thing is only activated when someone asks them a direct yes or no question, while in these puzzles the people are volunteering statements on their own.
My question is this: if every belief that an insane person holds is false, then does that also apply to beliefs about their beliefs? For example, an insane person may believe the sky is not blue, because they only believe false things. But does that mean that they believe they believe that the sky is blue, when in fact they believe that it is not blue? So all their meta-beliefs are just the inverse of their object-level beliefs? If all their beliefs are false, then their beliefs about their beliefs must likewise be false, making their meta-beliefs true on the object level, right? And then their beliefs about their meta-beliefs are again false on the object level?
But if that’s true, it seems like the puzzle becomes too easy. Am I missing something or is the answer to that puzzle “Vs lbh jrer gb nfx zr jurgure V nz n fnar cngvrag, V jbhyq fnl lrf”?
Edit: Another thought occurred to me about sane vs. insane—it’s specified that the insane people have 100% false beliefs, but it doesn’t specify that these are exact negations of true beliefs. For example, rather than believing the sky is not-blue, an insane person might believe the sky doesn’t even exist and his experience is a dream. For example, what would happen if you asked an insane patient whether he was a doctor? He might say no, not because he knew he was a patient but because he believed himself to be an ear of corn rather than a doctor.
I have a question about the first logic puzzle here. The condition “Both sane and insane people are always perfectly honest, sane people have 100% true beliefs while insane people have 100% false beliefs” seems to be subtly different from Liar/Truth-teller. The Liar/Truth-teller thing is only activated when someone asks them a direct yes or no question, while in these puzzles the people are volunteering statements on their own.
My question is this: if every belief that an insane person holds is false, then does that also apply to beliefs about their beliefs? For example, an insane person may believe the sky is not blue, because they only believe false things. But does that mean that they believe they believe that the sky is blue, when in fact they believe that it is not blue? So all their meta-beliefs are just the inverse of their object-level beliefs? If all their beliefs are false, then their beliefs about their beliefs must likewise be false, making their meta-beliefs true on the object level, right? And then their beliefs about their meta-beliefs are again false on the object level?
But if that’s true, it seems like the puzzle becomes too easy. Am I missing something or is the answer to that puzzle “Vs lbh jrer gb nfx zr jurgure V nz n fnar cngvrag, V jbhyq fnl lrf”?
Edit: Another thought occurred to me about sane vs. insane—it’s specified that the insane people have 100% false beliefs, but it doesn’t specify that these are exact negations of true beliefs. For example, rather than believing the sky is not-blue, an insane person might believe the sky doesn’t even exist and his experience is a dream. For example, what would happen if you asked an insane patient whether he was a doctor? He might say no, not because he knew he was a patient but because he believed himself to be an ear of corn rather than a doctor.