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Barber Paradox (Russell's Paradox)


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142 replies to this topic

#31 Wicker Brainpan

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Posted 25 November 2007 - 07:23 PM

The Barber could wear a beard and trim it with scissors.
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#32 ptcollins

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Posted 01 December 2007 - 12:42 AM

"in the village" is where the shaving is taking place. Perhaps the barber lives outside of the village and would therefore be exempt from the condition of being one who does not shave himself "in the village" and could therefore shave himself without contridiction?
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#33 splintercat

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Posted 03 December 2007 - 06:52 AM

Hmm. Russell didn't initially write this as a barber problem, so the solutions that assume other villages or they can shave each other or the barber is a woman, etc, answer this wording but aren't true to the spirit of the question. It's a mathematical logic problem - a contradiction in naive set theory. His paradox was "Does the set-of-all-sets-that-do-not-contain-themselves contain itself?"

The paradox is pretty clear in that wording: if the set-of-all-sets-that-do-not-contain-themselves doesn't contain itself, it SHOULD contain itself and once it does contain itself, it can no longer contain itself.

So if the barber only shaves people who do not shave themselves, does he shave himself? No, but then he should, but if he does, he shouldn't, etc, around and around.
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#34 yogieileen

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Posted 14 December 2007 - 08:55 PM

he can, of course, shave himself since as already mentioned in the reply section, the statement does not disallow the barber from shaving also those who shave themselves.
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#35 problemchild

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Posted 15 December 2007 - 03:10 AM

Analogue paradox to the paradox of liar formulated English logician, philosopher and mathematician Bertrand Russell.
There was a barber in a village, who promised to shave everybody, who does not shave himself (or herself).
Can the barber shave himself and keep the mentioned promise?

Of course, he never said he wouldn't shave anyone who did shave himself.

PS
Don't change the wording! It totally destroys my theory!
Edited (better wording?):
In a village, the barber shaves everyone who does not shave himself/herself, but no one else.
Who shaves the barber?
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#36 Winterfind

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Posted 17 December 2007 - 08:24 PM

Yes he can shave himself. He has only promised to shave evryone who hasn't shaved themselves, not promised not to shave anyone who has shaved themselves.
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#37 Bitlesskibbles

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Posted 19 December 2007 - 01:04 AM

If the barber promises to shave everyone who doesn't shave themselves if he doesn't shave himself it would mean he would have to but if he did shave himself it could mean that he would have to stop because he only shave people who don't shave themselves.
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#38 Kallab

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Posted 23 December 2007 - 11:40 PM

It's actually a loosely phrased version of Godel's illustration of its uncertainty theorem: Does the catalogue of all books not listing themselves lists itself?

Per se, it is not a paradox, as it does not introduce a strict formal contradiction in the set of logical rules governing the reasoning, but is, as defined by Godel, 'unsolvable', i.e. it requires introducing a bending of existing rules or the introduction of a new one to be resolved (in the formal logic understanding of the term)

As such, such so-called 'paradoxes' are at the base of all modern mathematics and physics (from non-Euclidian gemoetries to the formulaes governing the mechanics of a television set)
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#39 kconley

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Posted 01 January 2008 - 03:00 PM

Of course, anyone can shave the barber, but the barber.
Additionally, someone who doesn't shave - a child - could shave the barber.
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#40 alienendo88

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Posted 30 January 2008 - 03:46 AM

THE BARBERS JOB MAKES HIM A PERSON WHO SHAVES, SO HE MUST GO TO A BARBER TO BE SHAVED, OR GROW A BEARD, SO AS TO KEEP HIS WORD!
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