Logic0914 - Doubling difficulties 1. 2. Mad or Sane Puzzles...

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Corrections Typo on the last line of p.34: a knave => mad Pronunciation of “knave” [neiv] Unlike knack [næk] “Trough” anyone?
Ch.4 puzzles If one believes p, then one honestly says “p”. If one is sane, p is true. If one is mad, p is false. Every inhabitant is either sane or mad (not both). If a native doesn’t believe p, then the native believes not p. E.g., “I don’t believe I am mad” = “I be-

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E.g., if a native believes “I am mad”, then the native says "I am mad". If the native is sane, "I am mad" is a true belief, and the native is indeed mad. Therefore, a sane native cannot believe and say “I am mad”. If the native is mad, "I am mad" is a false belief, and the native is indeed sane. Therefore, a mad native cannot believe and say “I am mad”. Therefore, sane or mad, a native can
4.1 Can a native say “I believe I am mad”? A clearly different case from the above example If the native is sane, “I believe I am mad” is true, and s/he indeed believes s/ he is mad . Thus, s/he is indeed mad, which is impossible. If the native is mad, “I believe I am mad” is false, and s/he indeed doesn’t believe s/he is mad. Yet s/he (falsely) believes s/

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