Talk:Barber paradox

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..." &mdash;The preceding unsigned comment was added by Brion VIBBER (talk &bull; 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. &mdash;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)
 * There aren't any men with facial hair in the town. The story states, "every man in the town keeps himself clean-shaven". AbuMaia (talk) 19:26, 20 November 2010 (UTC)

the complete sentence is: In this town, every man keeps himself clean-shaven by doing exactly one of two things:. this only sais that the means of shaving is one of two. yet it doesn't assert that they shave. it is same like saying "in this town the shaving is done in only 2 possible ways" - this doesn't coerce everyone is shaving.--Quatso (talk) 19:39, 14 April 2012 (UTC)

[The barber is the "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself?] The Philosophy of Logical Atomism, reprinted in The Collected Papers of Bertrand Russell, 1914-19, Vol 8., p. 228 Wiki, 19 August 2021

The statement is incomplete in not specifying if all residents shave, and contrived and misleading.

In a real world scenario, there are 4 classes of residents. U: unshaven S: shaven SS: shaved by self SB: shaved by the barber The barber, a member of U, does not shave himself, a true statement. Facial hair was common in the 1800's and 1900's. Phyti (talk) 16:12, 3 September 2021 (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)
 * Other possible solutions:
 * A woman shaves the barber.
 * The barber leaves town to shave himself or to be shaved.
 * DesertSteve 04:02 11 Jun 2003 (UTC)

No, because if a woman shaves the barber then he doesn't shave himself and therefore must shave himself. (The barber is said to be male, so my suggestion won't work either, BTW) -- Tarquin


 * The barber shaves every man who doesn't shave himself.


 * A = the set of men who shave themselves
 * B = the set of men who don't shave themselves
 * C = the barber


 * A = M ^ S
 * B = M ^ ~ S


 * Assuming the barber is a man,
 * C = (M ^ S) v (M ^ ~ S)


 * Tis a puzzlement. DesertSteve 04:26 12 Jun 2003 (UTC)

What are M and S? -- Tarquin 08:13 12 Jun 2003 (UTC)
 * M = Man
 * S = Shaves himself
 * (M ^ S) = man and shaves himself
 * (M ^ ~S) = man and not shaves himself
 * DesertSteve 04:18 13 Jun 2003 (UTC)

I don't understand what you're trying to say. Throwing M and S in doesn't really add anything new. Of course the barber must belong to set A or B. It is that which prevents him from existing, it's the question of whether he shaves himself or not -- Tarquin 09:03 13 Jun 2003 (UTC)

Not saying anything different, but making it clearer for myself using symbolic logic. Axiomatic set theory is supposed to solve the problem of the paradox, but I'm not sure how. -- DesertSteve 22:12 13 Jun 2003 (UTC)


 * ah... Sorry, we sometimes get people posting on talk pages about how they can "amazingly disprove theorem X" or "solve paradox Y" -- I'm afraid I mistakenly got the idea from your earlier post you were trying to resolve the paradox somehow. (go see the talk page for Relativity, for an example). But by all means, a formulation of the paradox in symbolic logic would be a good addition to the article. I suspect Axiomatic set theory just forbids the paradox from being stated in the first place. -- Tarquin 22:19 13 Jun 2003 (UTC)


 * No problem. If Bertrand Russell couldn't solve it, I don't think I will. :) I added the symbolic logic example to the article.  You're probably right about Axiomatic set theory. -- DesertSteve 23:18 13 Jun 2003 (UTC)

I removed the symbolic logic description again, since it did not contain the basic feature that makes the paradox work, namely the description of those people shaved by the barber. AxelBoldt 20:13 22 Jun 2003 (UTC)

The paradox says that the barber is male, not that the barber is a man. What if the barber is Spock? PsyMar 03:16, 16 December 2006 (UTC)

No, the paradox says that the town has one male barber, BUT it also states that everyone either shaves themselves or attends this barber, so technically any others are not important. —Preceding unsigned comment added by 86.154.46.250 (talk) 22:00, 2 September 2010 (UTC)

The paradox states, "Suppose there is a town with just one male barber..." It doesn't specifically state that the barber lives in town, or even has a permanent shop there. I propose that the barber is actually based in a nearby town, and includes this town in his territory. In this way, the town has just one male barber, who lives elsewhere and can be shaved by a different barber in his home town. AbuMaia (talk) 19:34, 20 November 2010 (UTC)

FYI: Using set theory, it can be shown that the resident barber can shave those and only those male residents who do not shave themselves if and only if the barber is not male. Danchristensen (talk) 17:00, 7 January 2017 (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 &mdash;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)

"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 &mdash;The preceding unsigned comment was added by Lee M (talk • contribs). , 1:56, May 16, 2004 (UTC)
 * I think thats the point...Talltim (talk) 22:27, 12 January 2018 (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 &mdash;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)

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. &mdash;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. &mdash;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. &mdash;The preceding unsigned comment was added by 67.160.30.127 (talk • contribs). , 23:09, January 13, 2006 (UTC)

If the man who is the barber shaves himself, then the barber (who is the man) doesn't shave himself. In fact, the barber does shave every man who does not shave himself, including himself, because the barber doesn't shave him--he shaves himself. o_o 71.35.220.152 (talk) 04:12, 8 March 2015 (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 &#9742; 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. &mdash;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 &mdash; it doesn't contribute anything. &mdash; Asbestos | Talk  10:38, 3 August 2005 (UTC)

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)


 * 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)

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)
 * You are changing the rules of the paradox. In the paradox "X shaves Y" is a relation which can be applied even if X and Y are the same (just like X<X and X<=X are both well-formed relations - a false and a true one, respectively). - Mike Rosoft (talk) 17:24, 25 January 2011 (UTC)

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)

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)

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)

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)

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

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)


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

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)

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)

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)

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)

okay...
Why can't the barber shave himself. It says nothing in the rule that he can't shave himself. —Preceding unsigned comment added by 97.122.196.127 (talk) 05:50, 16 November 2009 (UTC)
 * Every man either shaves himself, or is shaved by the barber. The barber only shaves those who do not shave themselves.  There is the rule you're looking for.  If he's extremely strict about the rule to only shave those who do not shave themselves, he cannot shave himself.  If he cannot shave himself, then as the barber he has to shave himself.  But since he has to shave himself, he cannot shave himself. AbuMaia (talk) 19:42, 20 November 2010 (UTC)

Function analysis
Since this paradox was constructed as a mechanism to evaluate the notion of a universal set including itself as a set, it's possible to evaluate this through functional analysis.

Using this approach it becomes immediately obvious the *function* fails by virtue of it querying itself irregardless of the conditional requirement that "IF the person shaves themselves I must not shave them" versus "IF the person doesn't shave themselves I must shave them."

The true nature of the paradox is, "Does the barber requery the actor to determine if the person shaves themselves or not?" If the barber does then so long as the answer is consistent he acts.

The problem is if he queries himself he can never stop.

typedef bool (Person)(bool, void *); bool NonBarber(bool x, Person f) { return x; /*Do I *NOT* shave myself?*/ } bool Barber(bool x, Person f ) { printf("The Barber is told the person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); if(f(x, f) == x) { printf("The Barber CONFIRMED the person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); return x;  } return false; } int _tmain(int argc, _TCHAR* argv[]) {  printf("NonBarber: Does the barber shave me? %s \n\n", Barber(true, (Person*) &NonBarber) ? "true" : "false"); printf("NonBarber: Does the barber shave me? %s \n\n", Barber(false, (Person*) &NonBarber) ? "true" : "false"); printf("Barber: Does the barber shave me? %s \n", Barber(false, (Person*) &Barber) ? "true" : "false"); return 0; }
 * 1) include 
 * 2) include 
 * 3) include 

Now if we take the paradox in its original format and add the conditional component to the Barber function we see it makes little to no difference because it's the self-reference that causes the problem:

bool Barber(bool x, Person f ) { printf("The Barber is told the person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); if(f == (Person*) &Barber) { if(x == true) //if the person DOESN'T shave their self I must shave them. {      x = false; //, but since the person is me I must shave myself. }    else //if the person DOES shave themselves I can't shave them. {      x = true; //, but since it's me I can't shave myself because I only shave men who don't shave themselves. }  }   if(f(x, f) == x) { printf("The Barber CONFIRMED the person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); return x;  } return false; }

All this does is cause the barber to switch back and forth because he's looking for a consistent answer, but can't find one because he's not allowing himself the autonomy to arbitrate. So he asks the question over and over again.

Put another way if one of the townsmen said, "I shave myself." Then the barber as a rule-based person would state, "I can't shave you. Are you sure?" The townsmen might recant, "Actually I don't shave myself" and the barber would then requery, "Oh ok, you're sure you don't shave yourself?" The townsmen as a joker would continue this skit and say, "Actually I do shave myself." This scenario loops indefinitely (just like the original paradox) because the townsmen is refusing to be consistent.

Likewise as an actor the barber too has to be arbitrary to decide if he shaves or not.

Meaning the whole paradox is to say anything that's self-referential that uses itself for the original input and checks against itself *must* arbitrarily choose a stopping point or it will continue forever. --Xtraeme (talk) 09:33, 14 March 2010 (UTC)

Also if the barber ever arbitrarily stops then his answer will depend on either when he stops, if he chooses to return the last answer or the original answer, and when he applies the conditional logic.

int g_count = 0; bool g_hitend = false; const int max_iters = 2; bool Barber(bool x, Person f ) { bool answer = false; if(g_count > 0 && f == (Person*) &Barber) { if(x == true) //if the person DOESN'T shave themselve I must shave them. {      x = false; //, but since the person is me I must shave myself. }    else //if the person DOES shave themselves I can't shave them. {      x = true; //, but since it's me I can't shave myself because I only shave men who don't shave themselves. }  }   printf("The Barber is told the person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); if((++g_count) < max_iters && (answer = f(x, f)) != x)  { printf("The Barber found person inconsistent, said %s & then %s shave himself...\n", x ? "DOESN'T": "DOES", answer ? "DOESN'T": "DOES"); }  if(g_count < max_iters && g_hitend != true) {    printf("The Barber CONFIRMED the person %s shave themselves ...\n", answer ? "DOESN'T": "DOES"); }  else {    if(g_count-- == max_iters) {      g_hitend = true; }    printf("The Barber gave up, assumed person %s shave themselves ...\n", x ? "DOESN'T": "DOES"); return x; //will always give an answer that's the same as the original query (due to initial conditional block) }  return answer; //ditto. }

another possibility that debunks this paradox
What happens if the barber has a disorder that prevents him from growing a beard??


 * Nothing changes. It doesn't matter whether he has a beard or not. If he has no beard and therefore does not shave, then he must shave himself, which he can't, not only because there is no beard to shave, but also because he only shaves those who do not shave. Skrofler (talk) 20:44, 1 December 2011 (UTC)

It is only a paradox via an unexpressed assumption
The paradox is such only because it assumes that the barber has never shaved himself. If we posit that the barber has shaved himself in the past (and that "shaved himself" only obtains when his past shave was fully complete), then there is no contradiction: he would not shave himself because he has, at least one time in the past, shaved himself and, as such, would fall within the set of those men who do shave themselves which preclude him from the class of men who do not shave themselves. The paradox demonstrates, in at least one way, the anomalies which can occur in logically abstract vacuums not temporally situated or conditioned

Functional Entities
The “Barber Paradox”, like all logically inconsistent statements, is a result of poor reasoning or an imperfect understanding of language. In this particular example, the author failed to understand that a ‘barber’ is merely a functional entity, and as such, co-exists alongside many other functional entities within one and the same human being, for example, the same man may at the same time be: ‘a villager’, ‘a husband’, ‘a father’, ‘a brother’, and ‘a barber’. The so-called paradox arises because we erroneously attribute to one functional entity (the barber), a function that rightfully belongs to another (the villager), the function in question being, “to shave oneself”. Now, it is the function of a barber to shave another, and generally for some sort of remuneration, however, when the same villager shaves himself, it is not as a barber that he performs the task, for if shaving oneself was the function of a barber, then every villager that shaved himself would also be rightfully called a barber. —Preceding unsigned comment added by RGGehue (talk • contribs) 02:26, 29 November 2010 (UTC)


 * Another solution to this is that Bertrand Russell knows what language is, but you don't know what logic is.
 * Logic is essentially an abstract language that is independent from human thought. Logic would still exist if there were no humans, but human language wouldn't. Human language is dependent on human thought. You are erroneously mixing the two together. While we must use human language to talk about logic, the language of logic doesn't change by this, and you cannot skew the language of logic by applying rules that only pertain to human language. Skrofler (talk) 20:40, 1 December 2011 (UTC)

It doesn't state the barber is always the barber
One possible solution i see is that when it is his turn, the barber (person) steps down and another person takes his place, he transfers his tittle, possibly temporarily, to another person. The barber(professional) shaves the ex-barber(person), or the currently non-barber shaves himself while not holding the title. --TiagoTiago (talk) 09:36, 1 November 2011 (UTC)
 * Oops, should've paid more attention to what others wrote, this has already been suggested. --TiagoTiago (talk) 09:38, 1 November 2011 (UTC)

Incorrect statement.
"1.Shaving himself, or 2.going to the barber.

Another way to state this is: The barber shaves only those men in town who do not shave themselves. "

Totally disagree with this statement and the article in general. In the first case as stated is a logical or, the second case is a logical xor.

Russell's paradox is really not a paradox. It's a trick of laguage. The fact is we use 'or' to mean both logical or and logical xor. You can't really know if the first way is either 'or' or 'xor', it depends on context. The trick is you think it's or but then Russell says oh no it's really xor. It's a trick of language rather than a paradox. — Preceding unsigned comment added by 192.35.156.11 (talk) 06:42, 13 January 2012 (UTC)


 * It is my opinion that the paradox arises because the statement is incomplete. It says that either a man is shaved by himself or by the barber. But there are two more groups: those who have no growth of beards, and the barber. We need no women or gorillas as barbers. In politics one hears similar errors often, incomplete pre-definitions. If A and B is different, and C is not A, then C is B. But there can be D and E also, omitted. In mathematics, if there is a paradox, the statement is often wrong or incomplete.BIL (talk) 06:25, 26 May 2019 (UTC)

Location
The wording of this paradox points out a keen flaw. It states that if he does not shave himself, he must go to the barber. However, this person is already the barber and, therefore, does not have to actually go anywhere, resulting in the second reason being automatically false and the first reason remaining true. -- Jahkayhla (talk) 00:59, 31 January 2012 (UTC)

Inaccuracy
The beginning of this article reads: "Another way to state this is: The barber shaves only those men in town who do not shave themselves." This is inaccurate and pointless. Pointless due to the fact that there is already a better definition two lines prior to this one. Inaccurate in that this phrasing of the paradox does not preclude the barber from simply growing a beard. In which case he would not need to be shaved. In which case there would be not paradox. Hence, "Another way to state..." must go. Oulipal (talk) 01:40, 22 February 2012 (UTC)

Women are the key sometimes

 * the answer is simple there is two barbers in the town one male, one female the male barber goes to the female barber to get shaved. this works because it states that their is just one male barber it says nothing about if there can be another barber that is female it only says there cant be 2 male barbers and that it also says all men Shave themselves, or go to the barber. so the male barber goes to the female barber to get clean-shaven. (edit on 1:41 Feb 27, 2012...MAGJR...) — Preceding unsigned comment added by 69.204.99.98 (talk) 06:54, 27 February 2012 (UTC)

The answer has been stated above by another
In plain English, the man shaves himself. The reason is because that when he is shaving himself, he isn't being a barber. The reason this appears as a paradoxical riddle (it isn't) is because we have been conditioned to think of people as their profession, which is the source of the confusion. There is no confusion when you realize this.

As suggested on this post by others, it is a slight misuse of the language to identify someone "as" their profession. A wife will tell a new acquantance that her husband is a lawyer, when it would be more responsible to say that "he works as a lawyer".

Also, I heard some guy on youtube solve this supposed 'paradox' by giving an example (no kidding this is the example he used, albeit a little crude, but effective): If a prostitute does herself, she is masturbating, but when a barber shaves himself, what is he doing? The man on youtube's point is that we trick ourselves with labels. You don't need a degree in philosophy to solve this.

Again, he isn't being a barber when he shaves himself...

Paradox incorrectly stated
The author writes: "The barber shaves only those men in town who do not shave themselves."

This is incorrectly stated. It should be: The barber is a man in town who shaves those and only those men in town who do not shave themselves.

The first-order logical equivalent would then be:

Man(barber) & For all x (Man(x) -> (Shaves(barber,x) <-> ~Shaves(x,x)))

where:

Man(x)     = x is a man in town

Shaves(x,y) = x shaves y

--Danchristensen (talk) 19:31, 14 August 2012 (UTC)

A Resolution
We obtain a contradiction if we postulate the existence of a man in town who shaves those and only those men in town who do not shave themselves. Therefore, no such man can existent. The paradox arises out of nothing more than a poorly phrased, self-contradictory definition of the role of the town barber.

--Danchristensen (talk) 20:25, 14 August 2012 (UTC)


 * Yes, in fact the symbolic statement given in the article contains an existence quantifier. If you negate it, then the whole thing goes away. It's like saying "There is a square triangle". The correct response is, "No there isn't". Or is there some other way to express this "paradox" symbolically, so that such a simple negation doesn't make it go away? 198.70.193.2 (talk) 00:48, 6 November 2012 (UTC)


 * Thanks, Danch, for expressing it better than I ever could. So if we're agreed that this is essentially an exaggerated logic system based on a simple impossibility, how is it a paradox, or even worthy of thought? --Sgtlion (talk) 08:28, 9 November 2013 (UTC)

Prolog?
The Prolog section seems completely out of place, but maybe I am missing something. Is it common for Wikipedia to express logic problems using Prolog? Is that really useful? Is the barber paradox a common Prolog exercise? If so, a reference would make this look less like original research. 173.172.70.38 (talk) 21:22, 20 March 2014 (UTC)
 * I agree, so I have moved it under the one for first-order logic. 86.127.138.234 (talk) 13:13, 21 February 2015 (UTC)

Non-Paradoxical Multiple Barber Scenarios
Suggested definition of the multiple barber scenario:

"For every men in the village, he does not shave himself if and only if there exists a man in the village (a barber) who does shave him ."

From this definition, if there is only one barber, we will always obtain a contradiction, as in the Russell's original BP.

If, however, there are exactly two barbers, B1 and B2, such that B1 shaves every man in the village and B2 shaves B1, then, contrary to the article, the paradox does not remain. No man shaves himself, and a barber shaves every man in the village.

Likewise if there are no barbers and every man in the village shaves himself, the paradox does not remain.

There are probably many more such non-paradoxical multiple barber scenarios.

--Danchristensen (talk) 19:55, 27 August 2014 (UTC)


 * Are there reliable sources which contain this? Paradoctor (talk) 21:06, 27 August 2014 (UTC)

Alternative for "In first-order logic?"
Informally, if the barber is a man in the town, then no matter who shaves whom among the men in town, we can show that it would be impossible for that barber to shave those and only those men in town who do not shave themselves.

To formally prove this, we begin by supposing that the barber is a man in the town:


 * $$Man(barber)$$

We suppose further that Shaves is a relation on the men in town:


 * $$\forall a,b: [Shaves(a,b)\rightarrow Man(a) \land Man(b)]$$

Now, we suppose to the contrary that the barber does indeed shave those and only those men in town who do not shave themselves:


 * $$\forall a:[Man(a) \rightarrow [Shaves(barber,a) \leftrightarrow \neg Shaves(a,a)]]$$

From these assumptions, we can trivially obtain the contradiction:


 * $$Shaves(barber,barber) \leftrightarrow \neg Shaves(barber,barber)$$

Therefore, by contradiction, we can generalize as follows:


 * $$\forall barber: [Man(barber) \land \forall a,b: [Shaves(a,b)\rightarrow Man(a) \land Man(b)]$$


 * $$\rightarrow \neg \forall a:[Man(a) \rightarrow [Shaves(barber,a) \leftrightarrow \neg Shaves(a,a)]]$$

In the notation of set theory:


 * $$\forall Man: \forall barber \in Man:\forall Shaves\subseteq Man \times Man: \neg \forall a\in Man:[(barber,a)\in Shaves \leftrightarrow \neg (a,a)\in Shaves]$$

where


 * $$Man$$ is the set of men in town


 * $$(x,y)\in Shaves$$ means $$x$$ shaves $$y$$

--Danchristensen (talk) 04:05, 18 March 2016 (UTC)

"Start Class" "Low Importance"
One of the guidelines is to be welcoming to new users. Another is that this Talk forum is not about the subject matter generally, but rather about the article specifically. I do not find either of those guidelines to be appropriately applicable to the particular instance of this particular article.

This Article Is Really Bad. It is "Start Class" For A Reason. Its being "Low Importance" is arguably tragic since Russell's Paradox is in fact very important.

Especially objectionable is the notion that this version is easier than the "real" Russell's paradox on sets. If you say that the set version "follows from plausible axioms", then it will be equally true that the (possible) existence of this barber seems initially plausible as well. Any man in the town could undertake to shave all&only those who don't shave themselves (while explicitly disdaining those who do). This produces no contradictions or difficulties at all EXCEPT FOR ONE person. Since hunting high and low throughout the community will NOT reveal this person to the barber, this possiblity will remain plausible. If he's skilled as an activist then he could mount a successful campaign to enact an ordinance granting him a legal monopoly insisting that he's the only barber in town and that everybody who wasn't shaving himself HAD to come to him (and that everyone who was, could not). That would all be well and good until he (belatedly) got around to asking, "Hmm, should I shave MYself?" He won't find the counter-example or the contradiction UNTIL he looks IN THE MIRROR. That he himSELF should be the impediment to achieving his OWN goal will ALWAYS be IMplausible, at least in advance -- to the naive.

More to the point, this paradox is paradoxical for all binary relations equally -- it never matters what the relation is. "Shaves" is NOT different from "is an element of", with respect to this paradox. There is no r that R's all and only those r's that don't R themselves -- if there were, would that r succeed or fail in R'ing itself? Pretending that some R's are more relevant than others here is the opposite of educational. — Preceding unsigned comment added by 2602:306:30CA:6270:1C3F:A888:4F37:7EB9 (talk) 13:58, 19 March 2016 (UTC)


 * The point here is that, if the barber is a man in town, then, no matter who shaves whom, that barber would not be shaving those and only those men in town who do not shave themselves, since this would result in the well known contradiction.


 * --Danchristensen (talk) 18:47, 19 March 2016 (UTC)

Russel's endorsement or lack thereof
The first paragraph states: "It was used by Bertrand Russell himself as an illustration of the paradox", while later in the article it says: "However, Russell denied that the Barber's paradox was an instance of his own" followed by a quote saying the latter. The first sentence seems misleading and should be removed and/or reworded.

Furthermore in the same two places it says: "he attributes it to an unnamed person who suggested it to him." and "It was suggested to him as an alternative form of Russell's paradox," the first stating the authorship as an assertion of Russel's, the second as a fact. Which should be preferred? -- Hiferator (talk) 12:15, 21 July 2017 (UTC)

question
Why doesn't he just shave himself when he's off the clock?Sarahmuffins (talk) 01:56, 18 June 2018 (UTC)

There is no paradox, just an ambiguity
I ask: "Is the barber one of the people of the town?" If "yes", then we can say "the barber doesn't" without encountering any paradox. If "no", then we say "The barber does" with no difficulty. Emehri (talk) 15:00, 18 June 2019 (UTC)

Reverted without reason
The edit at https://en.wikipedia.org/w/index.php?title=Barber_paradox&diff=prev&oldid=1039617866 and https://en.wikipedia.org/w/index.php?title=Barber_paradox&oldid=1039630498 revert my edits (and also a bot's edit) without a valid reason. --2001:56A:72E9:D900:795A:4EA2:35BC:319C (talk) 20:35, 19 August 2021 (UTC)
 * The reason is that the change was no improvement of the article. The paradox states that a male barber exists who shaves all man that do not shave themself. Siply claiming that he does not exist violates one of the premisses of the paradox and is therefore not a solution. Gial Ackbar (talk) 20:39, 19 August 2021 (UTC)
 * WP:DONTREVERT says "Do not revert unnecessary edits (i.e., edits that neither improve nor harm the article). For a reversion to be appropriate, the reverted edit must actually make the article worse." Therefore "no improvement" is an invalid reason. If you believe that the lack of existence of a barber is not a valid resolution for the paradox, then rename the section or reword it, rather than reverting a bunch of unrelated changes along with it. --2001:56A:72E9:D900:795A:4EA2:35BC:319C (talk) 20:42, 19 August 2021 (UTC)
 * The linked page is just an essay, not a policy page. Also, it did make the article worse. It brought in what appears to be Fringe theories in an article that should use established mathematicl facts. Furthermor, I would advide you to get faamilira with WP:BRD and especially the WP:3RR-rule. Gial Ackbar (talk) 20:50, 19 August 2021 (UTC)
 * The section on first-order logic uses established mathematical facts. How does it appear to be "fringe theories"? --2001:56A:72E9:D900:795A:4EA2:35BC:319C (talk) 20:56, 19 August 2021 (UTC)
 * That's not the part I'm having problems with. It is the part that claims that the "Solution" would be that the barber does not exist. However, I far as I have always known it, the paradox has no solution as it contradicts itself. Gial Ackbar (talk) 21:01, 19 August 2021 (UTC)
 * If that is the case, then it can be solved by rewording the text to say that there is no solution, rather than by reverting unrelated changes along with it. --2001:56A:72E9:D900:795A:4EA2:35BC:319C (talk) 21:04, 19 August 2021 (UTC)
 * I have not only remoed the parts claiming that this is the resolution. In fact, proving the nonexistence of the barber only proves that this is a paradox as the existence of the barber is also required. I hope everyone is hapy with that version. Gial Ackbar (talk) 21:09, 19 August 2021 (UTC)
 * Are you planning to write the "Non-paradoxical variations" section that the comment references? --2001:56A:72E9:D900:795A:4EA2:35BC:319C (talk) 21:13, 19 August 2021 (UTC)

Inconsistent axiom sets
The paradox can be stated as: 1/ There exists a town where all shaved men are shaved in one of two ways 2/ They are self shaved 3/They are shaved by a barber who only shaves those not self shaved =>a barber cannot shave himself 4/ There is only one barber

In this form it is simply an inconsistent axiom set ie two or more axioms conflict; fairly obviously 3/ and 4/ no ?

Consider the Liar's Paradox 1/ I am a Cretan 2/ "All Cretans are liars" 3/ A liar always tells the opposite of the truth

Again an inconsistent axiom set; ie two or more axioms conflict fairly obviously 1/ and 2/ no ?

Rhnmcl (talk) 01:13, 8 September 2021 (UTC)

Second try The paradox can be stated as: (a) 1/ There exists a town where all shaved men are shaved in one of two ways 2/ They are self shaved or 3/They are shaved by a barber, who only shaves those not self shaved =>a barber cannot shave himself 4/ There is only one barber 5/ Only the barber may shave men ,other than himself 3/,4/ & 5/ => the barber is unshaved

(b) 1/ There exists a town where all shaved men are shaved in one of two ways 2/ They are self shaved or 3/They are shaved by a barber, who only shaves those not self shaved =>a barber cannot shave himself 4/ There is only one barber 5/ Only the barber may shave men ,other than himself 6/ there are no unshaved men in the town 3/,4/, 5/ & 6/ => CONFLICTING AXIOMS => INCONSISTENT AXIOM SYSTEM yes ?

Consider the Liar's Paradox 1/ "I am a Cretan" 2/ "All Cretans are liars" 3/ A liar always tells the opposite of the truth 1/ & 2/ => CONFLICTING AXIOMS => INCONSISTENT AXIOM SYSTEM yes ?

Rhnmcl (talk) 06:50, 8 September 2021 (UTC)

Exception
Exception does not prove the rule. Exception disproves the rule 2600:100D:B149:9EA:E9C0:B9E0:FCE0:5A57 (talk) 15:51, 11 December 2021 (UTC)

Statement made about Martin Gardner...
I don't see in "Aha!" where Martin Gardner attributes the paradox directly to Russell. This should be clarified, or removed. Johnedwardmiller (talk) 19:39, 8 April 2023 (UTC)

Shave half a beard
Does it make a difference if the men shave half their beard? 199.247.64.167 (talk) 11:06, 11 May 2023 (UTC)