The Paradox

[BoltWolf]

Okay. So I get home today and my wife, the lovely Bueno, says she has a paradox for me. After we got past me asking why I would need a pair of those...badumbum...she showed me the following:

I welcome all answers.

Mods: If it should be elsewhere, please move it!

There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?

[BoltWolf]

Anyone? No one?

[FutbolAmericano]

Anyone? No one?

Not a clue...............

[red star]

Someone else? Just because they don't shave themselves doesn't mean they can't shave someone else. (in this case the barber)


PS

My ACTUAL last name is Bueno. Is your wife a Bueno by name or nickname? (just curious)

[BoltWolf]

Someone else? Just because they don't shave themselves doesn't mean they can't shave someone else. (in this case the barber)


PS

My ACTUAL last name is Bueno. Is your wife a Bueno by name or nickname? (just curious)

I will give you a perhaps!

BuenoExcelente is a nickname for this site. Its from a couple sources, but mainly an spanish adult film we watched. The main "actress" kept saying that all scene and it stuck with us a long time.

[red star]

lol thats hilarious. I can only imagine the exclamations "bueno...excelente!" haha

now, about that paradox. Sounds to me that just because the barber shaves "all those and only those that do not shave themselves" doesn't necessarily mean that everyone in the town needs to shave. therefore, someone else in the town (even one that cannot shave him/herself) can shave the barber.

;)

[BoltWolf]

Come on....guess at least!

[red star]

see my post above.

[LA-Z-BOY--BE]

he's right, just because the barber shaves people that don't shave themselves doesn't mean no-one can shave him. But there is an even better answer to this and it is:

the barber is a woman

[red star]

he's right, just because the barber shaves people that don't shave themselves doesn't mean no-one can shave him. But there is an even better answer to this and it is:

the barber is a woman

Y'know. I thought of that too, but I took the barber's job to be the shaving of all body parts... including legs, armpits, etc.

lol so HOPEFULLY, even if the barber were a woman, she'd be a "tidy" one.

[AngusMcfisticuf]

He doesn't shave. What's wrong with a bearded barber?

[BoltWolf]

Very good answers. Sorry I missed yours Red.

I have heard several answers to it since I first read it. You all have given some of them.

[red star]

I assume that because it's a paradox, that there is no correct answer, but it seems like you have one specifically in mind. Care to share? ;-)

[BoltWolf]

Actually I dont . Woman is the one I have come up with and seen most. Next is barber is a robot/not human.

Of course, a woman would have to shave....ewww....or is all European or hippie...like I said, ewww!

[ArgersChayFan]

Okay. So I get home today and my wife, the lovely Bueno, says she has a paradox for me. After we got past me asking why I would need a pair of those...badumbum...she showed me the following:

I welcome all answers.

Mods: If it should be elsewhere, please move it!

There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?

I'm guessing there is no CORRECT answer, so i'll give it a go:

The barber cannot shave him/herself because he/she only shaves those who who do not shave themselves. But, because he does not shave him/herself, then he/her does shave the barber.

Or, as a barber only shaves faces (at least barbers I have visited,) then I'll go with the barber is a woman choice.

[BolteRon]

Has to be one of the other villagers.One might think.

[freakshow]

A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition; or, it can be an apparent contradiction that actually expresses a non-dual truth

This article is about a paradox of self-reference. For an unrelated paradox in the theory of logical conditionals with a similar name, introduced by Lewis Carroll, see the Barbershop paradox.

The Barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him.[1] It shows that an apparently plausible scenario is logically impossible.

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

Asking this, however, we discover that the situation presented is in fact impossible:

* If the barber does not shave himself, he must abide by the rule and shave himself.
* If he does shave himself, according to the rule he will not shave himself.

This paradox is often attributed to Bertrand Russell (e.g., by Martin Gardner in Aha!). It was suggested to him as an alternate form of Russell's paradox,[1] which he had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions. Of the Barber paradox, Russell said the following:

That contradiction [Russell's paradox] is extremely interesting. You can modify its form; some forms of modification are valid and some are not. I once had a form suggested to me which was not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, and those only, who do not shave themselves." The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. But in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i.e. that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just noise without meaning.

– Bertrand Russell, The Philosophy of Logical Atomism

A modified version of the Barber paradox is frequently encountered in the form of a brainteaser puzzle or joke. The joke is phrased nearly identically to the standard paradox, but omitting a detail that allows an answer to escape the paradox entirely. For example, the puzzle can be stated as occurring in a small town whose barber claims: I shave all and only the men in our town who do not shave themselves. This version omits the gender of the barber, so a simple solution is that the barber is a woman. The barber's claim applies to only "men in our town," so there is no paradox if the barber is a woman (or a gorilla, or a child, or a man from some other town--or anything other than a "man in our town"). Such a variation is not considered to be a paradox at all: The true Barber paradox requires the contradiction arising from the situation where the barber's claim applies to himself.

Notice that the paradox still occurs if we claim that the barber is a man in our town with a beard. In this case, the barber does not shave himself (because he has a beard); but then according to his claim (that he shaves all men who do not shave themselves), he must shave himself.

In a similar way, the paradox still occurs if the barber is a man in our town who cannot grow a beard. (Perhaps he lost all facial hair follicles in a painful accident). Once again, he does not shave himself (because he has no hair on his face), but that implies that he does shave himself.

[ArgersChayFan]

A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition; or, it can be an apparent contradiction that actually expresses a non-dual truth

This article is about a paradox of self-reference. For an unrelated paradox in the theory of logical conditionals with a similar name, introduced by Lewis Carroll, see the Barbershop paradox.

The Barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him.[1] It shows that an apparently plausible scenario is logically impossible.

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

Asking this, however, we discover that the situation presented is in fact impossible:

* If the barber does not shave himself, he must abide by the rule and shave himself.
* If he does shave himself, according to the rule he will not shave himself.

This paradox is often attributed to Bertrand Russell (e.g., by Martin Gardner in Aha!). It was suggested to him as an alternate form of Russell's paradox,[1] which he had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions. Of the Barber paradox, Russell said the following:

That contradiction [Russell's paradox] is extremely interesting. You can modify its form; some forms of modification are valid and some are not. I once had a form suggested to me which was not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, and those only, who do not shave themselves." The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. But in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i.e. that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just noise without meaning.

– Bertrand Russell, The Philosophy of Logical Atomism

A modified version of the Barber paradox is frequently encountered in the form of a brainteaser puzzle or joke. The joke is phrased nearly identically to the standard paradox, but omitting a detail that allows an answer to escape the paradox entirely. For example, the puzzle can be stated as occurring in a small town whose barber claims: I shave all and only the men in our town who do not shave themselves. This version omits the gender of the barber, so a simple solution is that the barber is a woman. The barber's claim applies to only "men in our town," so there is no paradox if the barber is a woman (or a gorilla, or a child, or a man from some other town--or anything other than a "man in our town"). Such a variation is not considered to be a paradox at all: The true Barber paradox requires the contradiction arising from the situation where the barber's claim applies to himself.

Notice that the paradox still occurs if we claim that the barber is a man in our town with a beard. In this case, the barber does not shave himself (because he has a beard); but then according to his claim (that he shaves all men who do not shave themselves), he must shave himself.

In a similar way, the paradox still occurs if the barber is a man in our town who cannot grow a beard. (Perhaps he lost all facial hair follicles in a painful accident). Once again, he does not shave himself (because he has no hair on his face), but that implies that he does shave himself.

He uses Nair!

[COLORADO]

He uses Nair!


Is that anything like.... hair today..gone tomorrow.......:rolleyes:....or hairs to ya.........:eek:


"No band wagon Charger fan"
_____________________
CHARGER TILL DEATH '63

[jackfrost]

Sorry wolfie..........but Im NO Folliclologist..........go ask Shammy !!!

[FCBolt]

The barber's a woman?

What was Bueno hinting at?
You have any hair left, Wolf?

[KillerSproles]

Everyone shaves themselves, including the barber.

[Chargers_Saints]

Anyone can shave the barber except the barber, it never specifically rules out that other people can shave other people.

If you don't like that, maybe there are 2 barbers.

[LA-Z-BOY--BE]

Anyone can shave the barber except the barber, it never specifically rules out that other people can shave other people.

If you don't like that, maybe there are 2 barbers.
That's the whole point of the paradox: people can't shave other people, only the barber can shave them. That's why it's a paradox. Because the barber cannot be shaved.

[WarGod]

Oooo! Isn't Google an amazing device.
A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition; or, it can be an apparent contradiction that actually expresses a non-dual truth

This article is about a paradox of self-reference. For an unrelated paradox in the theory of logical conditionals with a similar name, introduced by Lewis Carroll, see the Barbershop paradox.

The Barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him.[1] It shows that an apparently plausible scenario is logically impossible.

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

Asking this, however, we discover that the situation presented is in fact impossible:

* If the barber does not shave himself, he must abide by the rule and shave himself.
* If he does shave himself, according to the rule he will not shave himself.

This paradox is often attributed to Bertrand Russell (e.g., by Martin Gardner in Aha!). It was suggested to him as an alternate form of Russell's paradox,[1] which he had devised to show that set theory as it was used by Georg Cantor and Gottlob Frege contained contradictions. Of the Barber paradox, Russell said the following:

That contradiction [Russell's paradox] is extremely interesting. You can modify its form; some forms of modification are valid and some are not. I once had a form suggested to me which was not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, and those only, who do not shave themselves." The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. But in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i.e. that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just noise without meaning.

– Bertrand Russell, The Philosophy of Logical Atomism

A modified version of the Barber paradox is frequently encountered in the form of a brainteaser puzzle or joke. The joke is phrased nearly identically to the standard paradox, but omitting a detail that allows an answer to escape the paradox entirely. For example, the puzzle can be stated as occurring in a small town whose barber claims: I shave all and only the men in our town who do not shave themselves. This version omits the gender of the barber, so a simple solution is that the barber is a woman. The barber's claim applies to only "men in our town," so there is no paradox if the barber is a woman (or a gorilla, or a child, or a man from some other town--or anything other than a "man in our town"). Such a variation is not considered to be a paradox at all: The true Barber paradox requires the contradiction arising from the situation where the barber's claim applies to himself.

Notice that the paradox still occurs if we claim that the barber is a man in our town with a beard. In this case, the barber does not shave himself (because he has a beard); but then according to his claim (that he shaves all men who do not shave themselves), he must shave himself.

In a similar way, the paradox still occurs if the barber is a man in our town who cannot grow a beard. (Perhaps he lost all facial hair follicles in a painful accident). Once again, he does not shave himself (because he has no hair on his face), but that implies that he does shave himself.

[Chargers_Saints]

That's the whole point of the paradox: people can't shave other people, only the barber can shave them. That's why it's a paradox. Because the barber cannot be shaved.


There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?


Where in the quote does it say no one can shave the barber?

Does it rule it out? No, therefore by the rules of logic I can assume someone else may shave him.

[BoltWolf]

Where in the quote does it say no one can shave the barber?

Does it rule it out? No, therefore by the rules of logic I can assume someone else may shave him.

Makes sense to me. Wait, what?

[Chargers_Saints]

Makes sense to me. Wait, what?


I was trying to point out that using the following style of logic one cannot rule out another person in the town's ability to shave the barber.

Like this:

All plants leaves
All trees are plants
Therefore all trees have leaves

Or on a more question specific level:

Community members are allowed in the pool
The Smiths are not community members
Now here many people would come to the conclusion that the Smiths cannot use the pool, however it is never specifically said that if you are not a member of the community you are not allowed in the pool, so correct answer is The Smiths may or may not be allowed in the pool.

By using the form of logic above, and with the original question you posted NOT SPECIFICALLY RULING OUT SOMEONE ELSE SHAVING THE BARBER, the correct answer one can logically is:

Anyone can shave the barber, except for himself.

[WarGod]

These things make my head hurt. But I applaud your ability to use logic.

[LA-Z-BOY--BE]

Anyone can shave the barber, except for himself.
yes, I know all of that logics stuff you just said and I acknowledged on page 1 or 2 or something that someone else can shave the barber or the barber would be women, but this is a well-known paradox and normally it's like this (and yes, I used wikipedia in stead of typing it all):

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.
Under this scenario, we can ask the following question: Does the barber shave himself?
Asking this, however, we discover that the situation presented is in fact impossible:

If the barber does not shave himself, he must abide by the rule and shave himself.
If he does shave himself, according to the rule he will not shave himself.
normally the paradox clearly states that: either you shave yourself, or the barber shaves you. The paradox is meant to make you think: 'can the barber shave himself?', not: 'who shaves the barber?'. You can say: well, why doesn't someone else just shave him but that's just a weak solution. The other solution might be that the barber is a woman, but even then, like said earlier in this thread, the shaving might not only be limited to facial hair and that's quite the lame solution as well. It's supposed to be an impossibility. Thinking that something as easy as: 'well someone else just shaves him' would be the solution is quite idiotic.

[Chargers_Saints]

yes, I know all of that logics stuff you just said and I acknowledged on page 1 or 2 or something that someone else can shave the barber or the barber would be women, but this is a well-known paradox and normally it's like this (and yes, I used wikipedia in stead of typing it all):

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.
Under this scenario, we can ask the following question: Does the barber shave himself?
Asking this, however, we discover that the situation presented is in fact impossible:

If the barber does not shave himself, he must abide by the rule and shave himself.
If he does shave himself, according to the rule he will not shave himself.

normally the paradox clearly states that: either you shave yourself, or the barber shaves you. The paradox is meant to make you think: 'can the barber shave himself?', not: 'who shaves the barber?'. You can say: well, why doesn't someone else just shave him but that's just a weak solution. The other solution might be that the barber is a woman, but even then, like said earlier in this thread, the shaving might not only be limited to facial hair and that's quite the lame solution as well. It's supposed to be an impossibility. Thinking that something as easy as: 'well someone else just shaves him' would be the solution is quite idiotic.

Well maybe it USUALLY states either you shave yourself or the barber shaves you, BUT IT DIDNT THIS TIME so don't call my logic idiotic, youjust seem pissed becuase "that's not how it supposed to work"

It's called outside the box thinking, I was asked to give an answer to the question who shaves the barber? not "can the barber shave himself?" If that had been the question I would not have been able to give the answer i gave, but it wasn't, so don't get pissy.

[WarGod]

Now now boys. I am guessing the original poster was just wanting this to be a fun thing to do until football season. Don't need to get nasty with each other in here.

[LA-Z-BOY--BE]

Well maybe it USUALLY states either you shave yourself or the barber shaves you, BUT IT DIDNT THIS TIME so don't call my logic idiotic, youjust seem pissed becuase "that's not how it supposed to work"

It's called outside the box thinking, I was asked to give an answer to the question who shaves the barber? not "can the barber shave himself?" If that had been the question I would not have been able to give the answer i gave, but it wasn't, so don't get pissy.

nah, your logic isn't idiotic. That answer was just too simple, otherwise boltwolf (OP) wouldn't have asked this question. And I simply had to whine about it.

[Chargers_Saints]

nah, your logic isn't idiotic. That answer was just too simple, otherwise boltwolf (OP) wouldn't have asked this question. And I simply had to whine about it.
Fair enough completely understandable

[diego869]

Where in the quote does it say no one can shave the barber?

Does it rule it out? No, therefore by the rules of logic I can assume someone else may shave him.

You must be looking at it wrong. It's all in the way it is worded. Think of it like this. There are two and only two groups. Those that shave themselves and those shaved by someone else. There can be no other group. The barber shaves ALL those, meaning every last one of those, that don't shave themselves. It also says those are the ONLY ones he shaves. So in the two groups, everyone shaves themselves in one, and the barber shaves EVERYONE in the other group. Now the barber has to be in the village to shave people so he has to be included in one of the groups of people in the village. The ones that shave themselves can't shave anyone else as everyone else is in the group being shaved by the barber.
Now the way the question was worded in the first post does leave open the possibility that no one ever shaves the barber either cause it's a woman or it is a guy that keeps a constantly growing beard. But there is no way that anyone else can shave the barber.