## Philosophical Beliefs

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.
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 Recognitions: Homework Help Science Advisor 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
 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 ©)

## Philosophical Beliefs

 Quote by AKG 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,
Captain, this is not logical. [It is a personal opinion.]

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Recognitions:
Homework Help