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There is a barber in Rivervale
this barber only shaves people who do not shave themselves
therefore the barber does not shave himself
Ah but if he doesn't shave himself then he must be in the set of people whom he shaves which was shown earlier that he could not be a member of. ;)
Russell's Paradox
Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.
Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves S. If S is a member of itself, then by definition it must not be a member of itself. Similarly, if S is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics.
;)
THE BARBOR GETS SHAVED
'HE' IS NOT FEMALE
Add those to the condition
It is a paradox :)
The barber in a certain village is a man who shaves all and only those men in the village who do not shave themselves.
The barber in a certain village is a man who shaves all and only those men in the village who do not shave themselves. Is he a man who shaves himself? If he is then he isn't, and if he isn't then he is. It follows that he is a man who both does and does not shave himself. This contradiction shows that the apparently innocent italicized description can apply to no one. Formally, the paradox resembles Russell's paradox of the class of all classes which are not members of themselves. The latter though is not so easy to dispose of, since it is generated by an assumption - that every predicate determines a class - which cannot simply be abandoned.
;)
Damnit Vini you made my head hurt= \
You can always chose to miss-read a statement, but theQuote:
This statement alone doesn't imply that the barber shaves (he could wear a beard) nor does it imply that he MUST shave himself.
should really be enough so you know that the barber does indeed shave! Im sure you can miss-read just about anything, but if you read it the way its supposed to be read then its indeed a paradox! (gawd I make sense!)Quote:
Who shaves the barber?
I'm going to agree with vini because she is sm4rtz.
I'm just trying to find a way out of the paradox the way Serendib presented it :p
I still think there is a way out of this paradox without resorting to giving the barber a sex change. :p
Although it's not possible to do that when it is stated in a stronger form. In that situation the solution is more final. The Barber paradox considers a town with a male barber who daily shaves every man who does not shave himself, and no one else. You have to conclude that such a town cannot exist. Therefore the barber paradox is resolved by showing that the so-called barber cannot exist.
:D
who cares :/
people use electric shavers to be able to stay at comp while shaving nowadays you know
Perhaps he waxes ;)
If Vinilaa is in a town in which she argues with everyone who does not argue with themselves, why is she a devil's advocate :P
It's Vinilaa, she is the meanest shadow knight ever to exist... that is why my friend I LUB VINI =o
Not a devil's advocate, I just like to look at an issue from all sides before making a decision. ;)
My only question with regard to the barber's paradox as you wrote it, is as follows:
Does that statement actually preclude the barber from shaving people who do shave themselves? Or do you have to say "The barber in Rivervale ONLY shaves everyone in the town who does not shave himself?"Quote:
Originally posted by Serendib
The Barber in Rivervale shaves everyone in the town who does not shave himself.
I know it's only a semantic distinction, but I think it's relevant since the barber's paradox is a variation of Russell's paradox and is used to prove the same flaw in naive set theory. It seems that in order to do that, the barber's paradox would need to retain the same form. :cool:
Besides arguments about set theory and logic are much more interesting to me than polls about peanut butter :p
/hug Rhedd
No way Rhedd, I am far meaner then Vini! She is however more annoying =D
I think you have that wrong Vid= )
No one could be more annoying than you Vid. :p
He shaves exactly the people who do not shave themselves
Right. You have to make that distinction ;)
you can divide it into three groups:
A - people who do NOT shave themselves.
B - people who DO shave themselves.
C - people the barber shaves.
The question basically states "C contains all elements of A".
At no point does the question state "C contains ONLY A". So to fit in the barber, we say that C contains all elements of A AND one element of B (the barber).
Problem solved. The barber shaves all people who do not shave themselves, and STILL manages to get his shave.
Btw, he can't grow a beard either. You can easily infer that all people are shaved one way or the other. because anyone who doesnt shave himself, is shaved by the barber.
EDIT: of course, now that I actually noticed theres a second page to the thread, it'd be quite clear that the barber is an impossibility if you consider he can ONLY shave people who do not shave themselves. But as the problem was originally stated, my solution still stands, I think.