Resolved Question [PARADOX]
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Why is this a paradox? Can you solve it?
There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?
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Best Answer - Chosen by Asker
OK. take a deep breath and read this slowly, because it is very tricky. First two definitions:def 1) All and only those who shave themselves = Sdef 2) All people in the village, including the barber, are either members of S or members of not-S. there is no one in the village that is a member of both.If the barber shaved himself then he would be a member of S.If the barber does not shave himself then he would be a member of not-S.A barber who must shave all and only not-S can not shave any SThe barber can not shave himself, because he would be shaving a member of Sif the barber is not a self shaver then he is a member of not-SThe barber must shave himself because he must shave all members of not-SThus he must both shave and not shave himselfThis is the paradox.No one else in the village can shave the barber because only the barber can shave members of not-S.This is a variation of Russel's paradox, and there are several ways to solve, or attempts, to solve this depending on how it is interpreted. I'm not even going to attempt a solution here. Someone could, and probably has, written a doctoral thesis on the subject.
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Source(s):
Paradoxes chapters 9 & 10- N. Rescherhttp://en.wikipedia.org/wiki/Russell's_paradox
1 month ago
192 Rating: Good Answer
56 Rating: Bad Answer
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Asker's Rating: [*****]
Asker's Comment:
I think you did the best job of stating the problem. Even though you bowed out of offering a solution, I have to credit you with giving the best response.
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ASK [?] ANSWER [:)] DISCOVER [:S]
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====================================================================
Why is this a paradox? Can you solve it?
There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?
------------------------------------------------------------------------------------------------
Best Answer - Chosen by Asker
OK. take a deep breath and read this slowly, because it is very tricky. First two definitions:def 1) All and only those who shave themselves = Sdef 2) All people in the village, including the barber, are either members of S or members of not-S. there is no one in the village that is a member of both.If the barber shaved himself then he would be a member of S.If the barber does not shave himself then he would be a member of not-S.A barber who must shave all and only not-S can not shave any SThe barber can not shave himself, because he would be shaving a member of Sif the barber is not a self shaver then he is a member of not-SThe barber must shave himself because he must shave all members of not-SThus he must both shave and not shave himselfThis is the paradox.No one else in the village can shave the barber because only the barber can shave members of not-S.This is a variation of Russel's paradox, and there are several ways to solve, or attempts, to solve this depending on how it is interpreted. I'm not even going to attempt a solution here. Someone could, and probably has, written a doctoral thesis on the subject.
-----------------------------------------------------------------------------------------------
Source(s):
Paradoxes chapters 9 & 10- N. Rescherhttp://en.wikipedia.org/wiki/Russell's_paradox
1 month ago
192 Rating: Good Answer
56 Rating: Bad Answer
Report Abuse
Asker's Rating: [*****]
Asker's Comment:
I think you did the best job of stating the problem. Even though you bowed out of offering a solution, I have to credit you with giving the best response.
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ASK [?] ANSWER [:)] DISCOVER [:S]
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