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Question

The Barber paradox considers a town with a barber who shaves everyone who does not shave himself, and no one else. When you start to think about whether he should shave himself or not you will get puzzled...

I'm also rather curious to know how this affects the bearded men in the town. Or is this like those physics problems? "Assuming a frictionless, spherical cow..." —The preceding unsigned comment was added by Brion VIBBER (talk • contribs) ., 1:19, March 27, 2002 (UTC)

There can't be any bearded men in town. As stated, the barber shaves everyone who does not shave himself. —The preceding unsigned comment was added by The Anome (talk • contribs) ., 1:31, March 27, 2002 (UTC)

Sure, but with what frequency? Who says they don't sport a beard for a while and then go back to the smooth look after a month or two? Which, I suppose, answers my question. Brion VIBBER, 1:50, March 27, 2002 (UTC)

Woman?

However the most likely solution to this problem is that the barber, despite being male, doesn't shave.

Nope. Then he doesn't shave himself and so he has to.... see above. THe possible solution is that the barber is a woman ;-) -- Tarquin 12:51 Apr 9, 2003 (UTC)

The oldest of logical paradoxes

Actually, the oldest of this paradoxes dates back to the sixth century B.C., when Epimenides, (a Greek from the island of Crete) is supposed to have made his famous remark:" All Cretans are liars." The meaning of this is, of course: If I am telling the truth then I am lying, and if I am lying then I am telling the truth!!

Paul P Papadakis ppapad@ermis400.gr —The preceding unsigned comment was added by 195.167.16.131 (talk • contribs) ., 10:45, August 4, 2003 (UTC)

that's not quite the same paradox -- Tarquin 12:18, 4 Aug 2003 (UTC)

It is true that it isn't quite the same paradox... but they both have the same problem. Both of these paradoxes are based on the assumption that the individual is infallible, and acts in a manner that does not conflict with his/her talk. The answer to Epimenides is that some, but not all, Cretans lie... and he is one of them. The barber can deal with his stubble any way he pleases. You can't just construct an arbitrary set of rules like this barber paradox and shout 'my god, isn't this a paradox!' - it is not a paradox... it is a situation that would likely result in hypocrisy, but it is not a logical mind-boggler. I do have a solution to the 'paradox' without hypocrisy though, if you will. Since people insist that there is a male pronoun, so it cannot be a 'woman' ...and that it would be disingenuous to suggest that the barber just lets a beard grow... I have a few other solutions. 1)The barber is a female-to-male transgender. 2)The barber is too young to need to shave. 3)The barber was in a horrible fire, and the bottom half of his face was damaged to the point where he could not grow hair there. LOL, this is fun, making up possibilities. Rose Mara 02:19, 31 October 2006 (UTC)[reply]

"It's only a paradox because …"

It's only a paradox because the author deliberately introduced a self-contradiction into the rules. Talk about a circular argument. --Sir Cumference of the Round Table —The preceding unsigned comment was added by Lee M (talk • contribs) ., 1:56, May 16, 2004 (UTC)

barber paradoxon

The statement is: The barber shaves everybody who does not shave himself.

Clearly we must distinguish FOUR selections of people (and not two !):

Selection 1: The people who ARE shaved by the barber.
Selection 2: The people who are NOT shaved by the barber.
Selection 3: The people who do NOT shave themselves.
Selection 4: The people who DO shave themselves.

Selections 3 and 4 are NOT redundant repetitions of selections 1 and 2.

The statement, in effect, stipulates that selection 1 and selection 3 are opposites (or complements or mutually exclusive), which is not necessarily true, because they can overlap (in the case of the barber himself), as a matter of fact, it is NEVER true.

The barber, when he DOES shave himself, belongs into selection 1, but NOT into selection 3. When he does NOT shave himself, he belongs into selecton 3, but NOT into selection 1. So trying to resolve the question on the basis of this stipulation only unearths the fault built into the stipulation.

Clearly the statement must be more complex to reflect the obviously intended stipulation: If the barber DOES shave himself, then the barber shaves everybody who does not shave himself, and ADDITIONALLY he DOES shave himself - on the other hand - if the barber does NOT shave himself, then he shaves everybody who does not shave himself, EXCEPT himself.

The people shaved by the barber and the people not shaving themselves are NEVER the same people, so the statement is clearly wrong by way of oversimplification, omitting qualifications and not distinguishing slightly different selections.

In effect, the statement says(albeit in disguised form): It is true, that the barber DOES shave himself, AND it is also true, that the barber does NOT shave himself, then the question is asked: Does the barber shave himself? The obvious answer is yes AND no.

Kutte —The preceding unsigned comment was added by 217.95.45.30 (talk • contribs) ., 15:54, February 11, 2005 (UTC)

"The obvious answer is yes AND no." Hence the paradox. 137.190.86.211 18:01, 4 December 2007 (UTC)Jingles —Preceding unsigned comment added by 137.190.86.211 (talk) 17:55, 4 December 2007 (UTC)[reply]

The Barber paradox is not such a paradox …

The Barber paradox is not such a paradox but a (twice) sophism, because is logically incorrect. Let us explain,

It has one premise (statement):

"The barber shaves every man who does not shave himself, and no one else"

and two alternate (shave/not shave) conclusions:

1."If the barber does not shave himself, he must abide by the rule and shave himself"

2."If he does shave himself, according to the rule he will not shave himself"

Both conclusions are FALSE because the barber always shaves himself, and the rule is to shave who does not shave himself.

1. The condition is false (the barber always shaves himself), and so its conclusion.

2. The conclusion is false (the rule cann´t be applied to the barber).

The barber is the exception that proves the rule, as would be the men in town who shave themselves, like myself. My sophist conclusion would be that if the barber was Mr B. Russell, he should be wrong and bearded. —The preceding unsigned comment was added by Ex-act (talk • contribs) ., 22:57, May 19, 2005 (UTC)

And my logic conclusion, after the Wikipedia withdraw of my addition to the article, is that human society is not ruled by logic but by myths. —The preceding unsigned comment was added by 193.147.2.2 (talk • contribs) ., 08:43, July 13, 2005 (UTC)

Needless to say, the above statement is... well. It's needless to say. —The preceding unsigned comment was added by 67.160.30.127 (talk • contribs) ., 23:09, January 13, 2006 (UTC)

Removed content which makes no sense to me

I've removed two passage which make no sense to me:

"And in fact the Barber paradox is indeed merely a contradiction. As shown in the "impossible situation" analysis above, if the given definition of this barber can be used in a logical analysis, then one is led to the contradiction that the barber both does shave himself and does not shave himself. Thus it must be the case that the given definition cannot be used in a logical analysis. The actual contradiction in the Barber paradox, following Prior's analysis, is in the implicit assertion that the flawed definition of the barber can be used in a logical analysis.

"Even more than merely a contradiction (two opposite statements cannot be both true simultaneously) the so called Barber paradox is a real sophism, because both conclusions are wrong as shown in the article´s discussion.

Paul August ☎ 14:25, Jun 16, 2005 (UTC)

actual quote?

at the moment, the article says: The paradox considers a town with a male barber who shaves daily every man who does not shave himself, and no one else.

I am assuming that "daily" is NOT in the original quote.

As it is now, there is no paradox. If the barber shaves himself (e.g. non-daily), then he doesn't need to shave himself daily. —The preceding unsigned comment was added by Brewthatistrue (talk • contribs) ., 23:01, August 2, 2005 (UTC)

The current version does indeed allow confusion. I assume what the original author meant was "...who shaves daily every man who does not shave himself, and does not shave anyone else", which keeps the paradox, but if you interpret the last part as "...and does not shave daily anyone else" then you are right, there is no paradox. I'm removing "daily" from the article — it doesn't contribute anything. — Asbestos | Talk 10:38, 3 August 2005 (UTC)[reply]

Human is not the same as Profession

One of the published solutions to this paradox is to distinguish between cases where the word Barber means that-human-that-works-as-a-barber and where it means the-barber-during-his-working-hours.

Then the paradox can be rewritten as:

A human, who is employed as a barber, is required, during his working hours, to shave those who don't shave themselves.

The same human is free to do whatever he wants, including shaving himself, during his free time, because during that time, he is not considered a barber.

Can someone recal who wrote this solution? --Whichone 23:36, 6 June 2006 (UTC)[reply]

It could be that the barber isn't a man yet but still a kid. Or maybe the barber is from an alien race or something. I think those are not valid solutions because they take advantage of the fact that the meaning of the words is open to interpretation. In that case the statement would not be impossible, it would be insufficient information to answer the question.83.118.38.37 10:51, 7 November 2006 (UTC)[reply]

Paradox resolves with attention to language.

Surely the source of this paradox is the ambiguity that arises from using the word “shave” in two senses.

TO-SHAVE-ONESELF requires a mirror, and is usually done standing. Typically only one person is involved. Invariably, at the end of the act, the person doing the shaving has a smooth face.

TO-SHAVE-SOMEONE-ELSE requires a chair, and involves two people- one standing, one sitting. A mirror is not necessary, and at the end of the process, the person doing the shaving will have as much stubble as they had at the beginning of the process.

Yes, the end result is similar, but that is only true at the level of stubble. At the level of talking about the actions and movements of humans, (which is the level of the paradox) the two processes are clearly not the same- it is a quirk of language only that they are covered by the same verb in English- to shave.

Furthermore, if one visited this town, one would not find anything paradoxical or unusual about it. Certainly, the barber shaves himself, with razor, mirror, and no help. The problem, then, is in the ambiguity of the language used to describe what happens in the town, and this must be resolved by revising the language used in that description.

OK, rename the process of shaving-someone-else barbing; the infinitive is “to barb”.

The paradox is now simply exposed when rewritten;

HE BARBS ALL AND ONLY THOSE MEN WHO DON'T SHAVE THEMSELVES.

To me, the rule stated in the article seems to mean the following:

"For all man A, IF the barber shaves A THEN A does not shave himself."

And not:

"For all man A, the barber shaves A ONLY IF A does not shave himself."

Therefore, there would be no contradiction if the barber does not shave himself at all. 218.250.168.18 (talk) 13:39, 5 November 2008 (UTC)[reply]

Electrology?

If the Barber has had his beard removed by electrology then he would not need to shave. It appears that being clean shaven is somewhat compulsory in this town so removing hair permanently would save a lot of time and effort. Strangely, I don't think this causes any problems to the paradox; he still shaves all the men who do not shave themselves... What if they don't need to shave? Then they do not shave themselves and he must shave them, but they've no hair and so he can not! What does he do then? Kiffer.geo 10:38, 14 May 2007 (UTC)[reply]

wiki broken references

I just broke the references (visually). I don't know how to fix them properly. Somebody else do it please! Thanks. Jemmy Button 10:32, 28 September 2007 (UTC)[reply]

WikiProject class rating

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 03:48, 10 November 2007 (UTC)[reply]

True origin of the Barber paradox?

The intro. on the article page states:

"The Barber paradox is a puzzle (falsely) attributed to Bertrand Russell."

If the Barber paradox is falsely attributed to Bertrand Russell, then who is in fact the true originator of the paradox? I think it would be nice to see a reference rather than a mere assertion. PaaulG (talk) 14:43, 20 November 2007 (UTC)[reply]

Speaking of

Does anyone else find the disambiguation text at the top of the article to be a wry, if accidental, witticism? 137.190.86.211 18:01, 4 December 2007 (UTC)Jingles[reply]

Woman? (again)

I've heard a similarly-worded brainteaser (perhaps a derivation?) in which the barber's gender isn't specified, and the answer is that the barber's a woman. If this is well-known, it should be noted in the article. --68.161.161.206 (talk) 06:10, 17 April 2008 (UTC)[reply]

I've noted it as a variant now. Chuck Adams (talk) 19:55, 13 June 2008 (UTC)[reply]

My interpretation

Everyone seems to assume that people NEVER change between self-shave and no-self-shave. The way I see things, such a barber is possible -- but he shaved himself once, then either never shaved again, or grew a beard long enough to qualify as "not self-shaving" (at which point he sliced it off). -- DragonAtma 162.83.232.5 (talk) 18:01, 5 January 2009 (UTC)[reply]

Answer

He doesn't shave himself, he has someone else shave him. —Preceding unsigned comment added by 69.235.130.157 (talk) 03:18, 22 June 2009 (UTC)[reply]

Seems pretty clear to me

If we assume that the question poser is TRYING to say what it LOOKS LIKE he's trying to say, this seems to be yet another simple attempt at a proof of the existence of a paradox: It's possible to state something that sounds logical which can't be reasoned out logically. I say that because it's clear that they've tried to eliminate several logical solutions: first, the question specifically states that there is only one barber, eliminating the multiple-barber solution. Second, it states that in the village, all men are clean-shaven. This eliminates the possibility that the barber doesn't shave, the next easiest logical solution. Third, it specifically states that all shavers are male, thus eliminating the next most reasonable solution, that the barber is a woman (and hence doesn't need to shave...we'll ignore the fact that many women shave their legs/armpits/other parts of their body, and that some women even shave their faces).

But my contention would be that the question is soluble by an near-infinite variety of answers, which goes to show that it's a paradox only as long as the question poser refines his question. This is indicated by the specifics noted above....but it can go on indefinitely. Okay, I'll engage, it seems a simple game to play. Here's my first solution: The barber is a boy. The question states that there is "just one male barber" in the village, and that "every man in the town keeps himself clean-shaven." A boy is male, and is clean-shaven without the need for shaving. A barber who is a boy resolves the paradox, not just by dodging the semantics but by not needing to shave.

In anticipation of the next obvious restatement, that the barber in town is an "adult male" rather than just "male", let me offer the next solution: The barber has alopecia. He's an adult male who doesn't need to shave to keep himself clean-shaven.

Again I'll anticipate the next rephrasing: the town barber is "an adult male (or "a man") with no known diseases/afflictions." Okay...assuming that eliminates a genetic anomaly who simply has no hair (which might easily be considered a convenience rather than an affliction), let me ask the next question...."How long has the barber been in town, and how long can he go before he is no longer considered 'clean-shaven'?" Middlenamefrank (talk) 22:58, 25 July 2009 (UTC)[reply]

Semantics

Is this paradox an illustration of the difficulty of clearly and definitively defining a set? Are we maybe arriving at the conclusion that no language is sufficient to conclusively enough define a set to make a paradox like this bullet-proof? Are we saying that there is no set without 'fuzzy elements'? If so, is this merely a language-based conclusion or is it mathematically true? Perhaps EVERY set has 'fuzzy elements' which depend on how the set is defined, with the definition being literally impossible to nail down. Middlenamefrank (talk) 23:19, 25 July 2009 (UTC)[reply]

@@ Line 233: / Line 233: @@
 Again I'll anticipate the next rephrasing: the town barber is "an adult male (or "a man") with no known diseases/afflictions." Okay...assuming that eliminates a genetic anomaly who simply has no hair (which might easily be considered a convenience rather than an affliction), let me ask the next question...."How long has the barber been in town, and how long can he go before he is no longer considered 'clean-shaven'?" [[User:Middlenamefrank|Middlenamefrank]] ([[User talk:Middlenamefrank|talk]]) 22:58, 25 July 2009 (UTC)
 == Semantics ==
-Is this paradox an illustration of the difficulty of clearly and definitively defining a set? Are we maybe arriving at the conclusion that no language is sufficient to conclusively enough define a set to make a paradox like this bullet-proof? Are we saying that there is no set without 'fuzzy elements'? If so, is this merely a language-based conclusion or is it mathematically true? Perhaps EVERY set has 'fuzzy elements' which depend on how the set is defined, with the definition being literally impossible to nail down.
+Is this paradox an illustration of the difficulty of clearly and definitively defining a set? Are we maybe arriving at the conclusion that no language is sufficient to conclusively enough define a set to make a paradox like this bullet-proof? Are we saying that there is no set without 'fuzzy elements'? If so, is this merely a language-based conclusion or is it mathematically true? Perhaps EVERY set has 'fuzzy elements' which depend on how the set is defined, with the definition being literally impossible to nail down. [[User:Middlenamefrank|Middlenamefrank]] ([[User talk:Middlenamefrank|talk]]) 23:19, 25 July 2009 (UTC)