Talk:Barber paradox

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Contents 1 Question 2 Woman? 3 The oldest of logical paradoxes 4 "It's only a paradox because …" 5 barber paradoxon 6 The Barber paradox is not such a paradox … 7 Removed content which makes no sense to me 8 actual quote? 9 Human is not the same as Profession 10 Paradox resolves with attention to language.

[edit] 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)

[edit] 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)

[edit] 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)

[edit] "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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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.