Barber Paradox (Russell's Paradox)

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Gender is irrelevant. Some women do have beards, and besides, the question doesn't specify facial hair. But that's beside the point, really: the barber promised to shave each person who does not shave him or her self... not just those who actually need a shave.

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A lot of people seem to have missed the point. Say there is a guy in the village named Ted. One of the following must be true:

Ted shaves Ted, and the barber does not shave Ted.

Ted does not shave Ted, and the barber shaves Ted.

If Ted is the barber, you can replace "the barber" with "Ted":

Ted shaves Ted, and Ted does not shave Ted.

Ted does not shave Ted, and the barber shaves Ted.

This is not a trick question. There is no validity to any statement like, "Ted does not have a beard, so Ted does not count."

The barber cannot keep his promise, from a logical standpoint. From an ethical standpoint, on the other hand, most people would realise he was not including himself in "everyone", so he certainly could keep his promise.

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The barber is a women. She doesn't shave

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What women are you dating that don't shave?

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In this particular paradox, there are many small factors that need to be addressed first:

-when will the Barber die

-how many people are there in the village

-what item will he shave with, and what happens if it breaks

-how much hair do people have

-just head hair or also facial hair, body hair, etc.

-will the cooperation of the people be a factor

????????????????????????????????????????????????????????????????????????????????????

In a real world, all of these little factors contribute to the overall outcome. All of these need to be addressed before a realistic answer can be given

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

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"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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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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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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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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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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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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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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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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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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Barber Paradox (Russell's Paradox) - Back to the Paradoxes

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?

Yes, if the barber shaves himself, then the barber has shaved himself, and the barber does not then need to shave him. Conversely, if the barber has not shaven, then the barber will take the liberty of shaving himself for himself. Then, the barber will have shaved himself, and the barber need not then to shave him.

Edited (better wording?):

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.

Who shaves the barber?

Nobody shaves the barber. This is why you should read carefully before you enter into contract. Lesson learned.

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Saying that anyone can shave the barber would break the barber's promise because the barber promises to shave everyone who doesn't shave themselves. If someone shaved the barber he would have to shave himself because the barber didn't shave themselves, if that makes sense. My solution is that the barber is a woman who doesn't grow facial hair so there needn't be any shaving.

If the barber was a woman, she probably wouldn't have facial hair, although she might. Then there would have to be at least 2 barbers.

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Barber Paradox (Russell's Paradox) - Back to the Paradoxes

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?

Edited (better wording?):

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.

Who shaves the barber?

Maybe the barber has his or her slave shave him/herself and the barber as well.

Edited by mudkip201
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In a village, the barber shaves everyone who does not shave himself/herself, but no one else.

Who shaves the barber?

In this, no gender is given for the barber.

Thus, the barber is female and has no facial hair. She does not shave herself, but shaves everyone else.

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Barber Paradox (Russell's Paradox) - Back to the Paradoxes

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?

Edited (better wording?):

In a village, the barber shaves everyone who does not shave himself/herself, but no one else.

Who shaves the barber?

Why the hell do people keep such stupid promises. I mean look at the mess... he kept the promise n we are figuring out the solution so that he dosen't have to break his promise.

The barber promised to shave everybody who does not shave themselve. This means that being a barber its his job to shave people ... specially those who dont shave themselves(he's not doing this for free). The barber has not specified any clauses that [ONLY] who do not shave himself will be shaved by me. People who have shaved themselves obviously wont go to the barber n waste their money. Therefore his customers are the unshaven people. So as a good barber he promised to shave everybody, who does not shave himself (or herself). Therefore the barber can shave himself as he hasn't been selective about his customers.

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I understand that this is supose to tease saying that if he shaves everyone that doesnt shave and he doesnt shave he must shave himself but then if he continues to shave himself he must stop because he now does not not shave himself. Yet nowhere in the riddle does it say he is incapable of shaving someone who already shaves =] just saying.... and it is worded rather oddly like sharknateher said, so I'm not sure if I have this down right.

i'm not much of the nerd or "educationally challenged" if i may (no offense to everybody) but if i'm correct when you said "because he does not not shave himself" in my opinion it either: 1. sounds like your trying to make yourself sound more intelligent because of that statement... or 2.that statement just goes with the whole deal.

1. but wat im trying to say is if you do want to make yourself sound smarter then wouldn't it be more logical to just say simply: because he shaves himself

2. or by you saying that do you think it just fits better with that first sentence.. like i said "it just goes with the whole deal"?

i was just reading through these because i happen to be interested in these logical puzzles.. i came across some great points, i saw yours, and i questioned it... i thought what the heck why not just say wat i'm thinking right?... wrong because right now i'm sure i'm being laughed at because here i am a 9th grader correcting someone who is obviously much older than i am... trying to make myself sound smart.. hmm

oh well...i tend to point out the obvious alot :D

but.. if you think the first "paragraph" i just wrote had a point to it.. then let me know i wanna know whether i can be smart or am smart either/or..

preciate it!

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maybe the barbers beard doesn't grow it is possible (I've met people who do not need to shave) he keeps his promise and everybody is happy it does not say that his beard grows

true but who says he only shaves beards and mabey he is really a she and shaves her legs therefor shaving herself and breking that promise... :)

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He can do it he did not say that he would only shave those who didn't shave themselves so he could.

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The answer is simple and uncomplex. Its yes. No more no less. This "paradox" seems to me, to be a middle school logic puzzle. It almost mindless, but to each his own I guess.

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All females have facal hair even if its undectable it still there

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