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Philosophical Beliefs

  1. Jul 4, 2004 #1
    You are given that:
    Pure philosophers always tell the truth concerning their beliefs.
    Applied philosophers always lie concerning their beliefs.
    Sane philosophers beliefs are always correct.
    Insane pilosophers beliefs are always incorrect.

    Four philosophers {A,B,C,D}) have the following conversation:
    A - I am insane
    B - I am pure
    C - I am applied
    D - I am sane
    A - C is pure
    B - D is insane
    C - B is applied
    D - C is sane

    Describe A,B,C, and D.
  2. jcsd
  3. Jul 4, 2004 #2


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    A says "I am insane." Now, no person can really think they're insane. A sane person will know they're sane, and an insane person will incorrectly believe themselves to be sane. Since no person can believe themselves to be insane, A must be lying, so A is applied. At this point, A could be sane or insane.

    B says "I am pure." If B is pure, then he really believes he's pure, so he's sane. If he's applied, he believes he lied and believes he's applied, so again, he must be sane. B is sane, and could be pure or applied.

    If C is pure, and really think's he's applied, he must be insane. Otherwise, if he's applied, and really thinks he's pure, he's wrong again and must be insane. C is insane.

    D is pure, because everyone truly thinks their sane, so he must be telling the truth. Also, it's the only thing left after the first "round" of clues.

    A - applied
    B - sane
    C - insane
    D - pure

    Now, working from the bottom, D truly thinks C is sane, which is wrong, so D is insane. B is sane, so he knows D is insane, and he says it, so he's pure. B is pure, and C is insane, so C thinks B is applied. Since C says B is applied, he's telling what he believes, so C is pure. A says C is pure, but since A is applied, he really thinks C is applied. But C is pure, so A is wrong, and thus insane. So:

    A - applied insane
    B - pure sane
    C - pure insane
    D - pure insane
  4. Jul 5, 2004 #3
    A = Applied, Sane
    B = Pure, Sane
    C = Pure, Sane
    D = Applied, Sane

    Likely not to be right but I did it quickly.

    The Bob (2004 ©)
  5. Jul 5, 2004 #4
    Captain, this is not logical. [It is a personal opinion.]

  6. Jul 5, 2004 #5


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    Huh? No, it's perfectly logical. If A is sane, then A correctly knows himself to be sane. If A is insane, A incorrectly "knows" himself to be sane. Therefore, A necessarily "knows" himself to be sane. Q.E.D.

    EDIT: I can see that my wording seemed rather colloquial, and may have thrown you off, but it was still a logically rigourous and sound argument. All philosophers believe themselves to be sane (based on the riddle's definitions of "philosopher" and "sane").
  7. Jul 5, 2004 #6
    Sorry, AKG. I forgot the wording of the puzzle. :redface:
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