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Math Help - Fuzzy Logic

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    Fuzzy Logic

    An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber?? How do I proof this using a logical statement??
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    Quote Originally Posted by EquinoX View Post
    An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber?? How do I proof this using a logical statement??
    So this barber shaves the women? I suppose that's Sicilian women for you.

    See here.

    RonL
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    what do you mean this barber shaves the woman?
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    Quote Originally Posted by EquinoX View Post
    An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber?? How do I proof this using a logical statement??
    Poor title for this thread, Fuzzy Logic is a field of study in its own right and
    this problem does not fall within its remit (as usually understood)

    RonL
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    Quote Originally Posted by EquinoX View Post
    what do you mean this barber shaves the woman?
    Do the women shave themselves? Are the women people?

    Did you follow the link I gave you? If no go back and do so.

    RonL
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    Yes I did, but I did not understand the link on wikipedia
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    can someone explain it to me more clearly?
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    I know the answer to this question is that it's possible if the barber is a woman right? But I still dont get the explanation, after I read all the stuff in the link then I noticed something about separating something from a set? Can someone explain this to me
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    Quote Originally Posted by EquinoX View Post
    An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber?? How do I proof this using a logical statement??
    If this is worded carefully no such barber can exist because his existance
    contains a contradiction. The reason is that this is a version of the set of
    all sets that do not contain themselves.

    If this set contains itself then it does not contain itself, if it does not contain
    itself then it does contain itself. hence we conclude any system of set
    theory which allows such a set is inconsistent (that is contains
    contradictions).

    A more carefull wording goes:

    In a certain village all the men a clean shaven and there lives a (male) barber
    who shaves all those men of the village who do not shave themselves. Who
    shaves the barber.

    RonL
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    Quote Originally Posted by EquinoX View Post
    I know the answer to this question is that it's possible if the barber is a woman right? But I still dont get the explanation, after I read all the stuff in the link then I noticed something about separating something from a set? Can someone explain this to me
    Or has a beard

    RonL
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    Do you mean that the answer to this question is possible if the barber shaves a woman because a woman does not shave themselves??

    I am actually still confused with this question, what does "those men" mean here, does it mean people who lives near the barber or people who travels through a dangerous mountain??

    One more thing is that, I am still not clear of the answer of this question. Is it possible? If yes then why?
    Last edited by EquinoX; June 13th 2007 at 05:49 PM.
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    Here's the rule:
    The Barber shaves ONLY and ALL those who don't shave themselves.
    This Barber can't exist if you think of how gets shaved.

    The Barber shaves ONLY and ALL those who don't shave themselves.
    If he shaves himself, then he isn't one of those people who don't shave themselves, in which case he can't shave himself...

    The Barber shaves ONLY and ALL those who don't shave themselves.
    If he doesn't shave himself, then he is one of those people who don't shave themselves, in which case he must shave himself...

    This barber can't exist.

    It's like the person who says: "I always lie"
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    Quote Originally Posted by Quick View Post
    It's like the person who says: "I always lie"
    Except such a person can exist, they don't always lie, they just happen to be
    lying this time.

    RonL
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    Quote Originally Posted by EquinoX View Post
    Do you mean that the answer to this question is possible if the barber shaves a woman because a woman does not shave themselves??

    I am actually still confused with this question, what does "those men" mean here, does it mean people who lives near the barber or people who travels through a dangerous mountain??

    One more thing is that, I am still not clear of the answer of this question. Is it possible? If yes then why?
    The mention of women and/or beards is just to point out that your wording
    of the paradox is not tight enough to make it a paradox. If worded carefully
    women and/or beards don't appear, and we have a paradox, so then we
    have to conclude that there can be no such barber.

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    Except such a person can exist, they don't always lie, they just happen to be
    lying this time.

    RonL
    Well...

    This sentence is a lie.
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