Barber Paradox (Russell's Paradox)

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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?

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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?

Well, this appears to be a simple English rules question. Because of the location of the commas in this sentence, we could re-word the sentence to read: "There was a barber in a village who does not shave himself (or herself), who promised to shave everybody." Therefore the answer is yes, of course, the barber, who does not shave himself can shave himself and keep the promise to shave everybody.

However, given the nature of the question, I believe the question being asked is " There was a barber in a village, who promised to shave everybody who does not shave himself or herself." In which case the paradox lies in the concept that he promises to shave those people who do not shave themselves. He can, of course, keep this promise. There is nothing in the barber's promise that says he can only shave those people who do not shave themselves. He can shave people who shave themselves too, even himself.

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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.

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Just because the barber promises to only shave those who don't shave themselves doesn't mean they shave everyone who doesn't do it themselves.

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The mainpoint is that he (the barber) is part of "everyone."

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This is the original paradox, one that can't be solved

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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Perhaps there is another barber in the village and many of the villagers get shaved by him. This being the case our barber could keep his promise to shave everyone who does not shave him/her self including himself, because he too gets shaved by the other barber.

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The barber sets forward an action that causes him to be shaved.

In other words an external event caused by him result to the desired outcome.

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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

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What you say is very true 'Lordhydra2003' but let me tell you this; if I were that barber, you wouldn't be coming into my shop, nomatter how many heads you've got that need shaving!

Of course it's possible that all the men have gone off to war and there are no males left who need a shave. Maybe the barber gets shaved by his mother. This leaves his promise to shave everyone who doesn't shave him/herself highly questionable.

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ok, it actually can be solved. i see the paradox that he cant/wont shave anyone who shaves themselves, so if he goes to shave himself... he would break his creed. but anyone else can shave him. you see, anybody can shave the barber regardless if they shave themselves or not.

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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.

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i agree wid "jkirby1988".

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It is possible...

If and only if the barber is a girl or the barber is a young boy below age of 13 so his beard does not grow jet.

This is not a paradox but an puzzle or ridle if u wish...

"Dont try to seek the answer unles you fully understand the question."

retskcah eht 8.8.2007

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Technically, if the barber was to shave someone including himself, they were unshaven and in need of a shave. So at the moment prior to shaving himself he had not shaved himself; therefore making him eligible to be shaved by himself. It is a matter of timing.

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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 metiond promise.

______

I am suprised this is written by a logician and a mathematician.

with this wording the answer to this question is he could never keep his promise. Based on the rules of logic and the fact that this cannot be considered a parodox if it is based on assumption.

1) he did not specify if by everybody he meant everyone in the village. (he could not possibly shave everybody).

2) if he did mean the everyone in the village then all he would have to do to keep his promise is shave out side of the village. It would need to be worded like this:---There was a barber in a village, who promised to shave everybody in his village that does not shave him or herself.---

3) the best wording for this scenario is:---There was a barber in a village, who promised to shave everybody that is a resident of his village and does not shave himself (or herself).

With this wording logically all he would have to do to keep his promise and be able to shave himself would be to move out of his village and come to the village to shave everyone.

The reason this has been so hard to figure out is that it was written ignorantly.

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I bring to the table (as mentioned in earlier posts) that this is a matter of grammar.

The paradox reads:

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?

With the placement of the commas after "a village" and also after "shave everybody", the sentence can be reordered to read:

There was a barber in a village who does not shave himself (or herself) who promised to shave everybody.

Can the barber shave himself and keep the mentioned promise?

The first red herring is the question of the barber's gender. It is ambiguous in the statement. However, it is clearly revealed in the proposed question that this barber is clearly a man.

The second red herring that everyone gets stuck on is that the order of the wording (with the strategically placed commas) makes you believe that there is a condition to the rule where the barber can only shave those who don't shave themselves. This is not the case. Simply put- the barber does not shave himself. He promised to shave everybody. If the barber shaves himself, then the barber is in compliance with the promise to shave everyone. Therefore, the answer is yes.

The fact that the promise to shave everybody has absolutely no bearing on the fact that the barber does not shave himself. But by shaving himself would close the loophole of including the barber within the terms of "everyone".

The statement that he does not shave himself only indicates that this was fact when he made the promise. The act of him shaving himself would occur after the promise was made, so that would verify that statement in terms of a time line.

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1. the promise only applies to people who live in the village, the barber doesn't live there

2. the promise doesn't specify whether the promise is aimed at man or animal. if the promise is meant for animals the barber can shave himself/herself and not break the promise

3. there is no time parameter set for the promise. the promise may only apply between certain times, eg during his/her normal working hours, after which the barber can shave himself/herself.

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in order to make sure the barber only shaves people who don't shave themselves the barber must base his/her decision of who to shave on whether or not the person looks like they need to shave.

for this solution the barber is female, in order to look like she doesn't need to shave she removes hair by using wax; in doing this she hasn't broken her promise.

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Well, he can.

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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?

The simple solution is lying in the fact that the barber never promised to shave ONLY people who do not shave themselves. He could shave anyone, including himself.

This way there would not be any paradox at all.

The edited version does not mean exactly the same as the original, after all, since the original didn't say he was excluding anyone who shaved themselves. In fact, the edited version IS a paradox.. or at least, so it seems to me.

BoilingOil

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No one shaves the Barber. He does not shave himself. Or rather, personaly the barber does not shave, But he will shave anyone who wants to be shaved granted they live in the village.

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The original version, "There was a barber in a village, who promised to shave everybody, who does not shave himself" translates in pure logic (if trigger, then result) to:

(1-A) If someone does not shave himself, then the barber will shave him.

The contrapositive is:

(1-B) If the barber does not shave someone, then that person must have shaved himself."

The triggers here are:

(1-A) someone does not shave himself

(1-B) the barber does not shave someone

When the barber shaves himself, neither of these triggers is activated, and thus neither of the results is required. This resolves the paradox. There is no contradiction; the barber CAN keep his promise.

Now, if you consider rooki1ja's edited wording up front, "but no one else," or Boiling Oil's comment on "ONLY," we get to the heart of the matter. Now there is a contradiction because "but no one else" creates a second conditional statement:

(2-A) If someone does shave himself, then the barber does not shave him.

and its contrapositive,

(2-B) If the barber does shave someone, then that person does not shave himself.

NOW when the barber shaves himself, he triggers both 2-A and 2-B which then requires the results of both 2-A and 2-B. Naturally, both results are violated and we have a contradiction. The barber CANNOT keep his promise. This is a paradox that does not resolve.

I'm saying the same thing as Boiling Oil, except in the first scenario he says "no paradox" using the word paradox to mean specifically a paradox with no resolution. Dictionary.com allows in separate definitions that a paradox may or may not have a resolution, so we can say scenario 1 is a paradox that resolves, and scenario 2 is a paradox that does not resolve.

Cheers!

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I think the original didn't add 'herself', leading to much embarassment at the gaffe, today understood to be sexism. I wonder how many paradoxes result from linguistic errors of sorts. All?

So here, if I shave all those who don't shave 'themselves', it first depends on what that means. How many shavers shave their brows? If not shaving one's brows means not shaving 'oneself,' but 'shaving' refers (as it did in Russell's paradox) to beards, the paradox is gone with a woman barber.

There's also the previous point about a PROMISE to shave. Are we to expect the barber to be a Sweeney Todd, shaving willy-nilly anyone who passes by?

Avoid such barbers, or risk a close shave.

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Firstly, I love Russell's work. However, his paradox (again, not really a paradox) has a rather simple solution.

===============================

Barber Paradox (Russell's Paradox)

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

===============================

We have ten givens to consider in this challenge:

1) There exists bodies.

2) There exists a village; A village is a set of nonzero bodies.

3) There exists a kind of body called a Barber.

4) There exists an operation called Shaving.

5) Barbers may Shave bodies.

6) All barbers must be bodies.

7) All bodies must live in the village.

Some bodies may be barbers.

9) Some bodies may Shave themselves.

10) Barbers may shave bodies other than his own. (We assume female Barbers are called Barberellas and outside the scope of this challenge.)

The barber promises to shave everyone in the village who does not shave themselves.

This may be easier to understand if we restate the givens, substituting the word "Like" for the operation "Shave", Shape for Body, and Triangle for Barber. For kicks, let's finish up with substituting Box for Village.

1) There exists Shapes.

2) There exists a Box; A Box is a set of nonzero Shapes.

3) There exists a kind of Shape called a Triangle.

4) There exists an operation called Liking.

5) Triangles may Like (and therefore not Like) Shapes.

6) All Triangles must be Shapes.

7) All Shapes must live in the Box

Some Shapes may be Triangles.

9) Some Shapes may Like themselves.

10) a Triangle may Like Shapes other than his own.

Given: The triangle promises to like every shape in the Box that does not like itself.

In the Question we are given another truth:

Question: Can the triangle ("the" implies there is only one triangle in the box) like itself and like every shape in the box that does not like itself?

11) There is only one Triangle in the box.

Weeding through the extraneous data, the key to the solution lies in given 10. If a shape is a Triangle, it may like shapes other than his own. What given 10 does not say is that a shape may like shapes other than his own if and only if it is a triangle.

This is not a paradox, but rather a simple first-level logic exercise in the difference between if-then and if-and-only-if. Simply put, the people in the village can shave each other if the Barber cannot shave them. That would formulate the scenario that there is nobody in the village that needs a shave if the Barber shaves himself, therefore keeping the promise - The barber shaved everybody in the village that needed a shave after he shaved himself, and the number of needed villagers was zero.

Eric Mumford

Waterford, NY

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