Talk:Barber 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).
- 2. The conclusion is false (the rule cann´t be applied to the barber, as much as to the men in town who shave themselves, like myself).
My sophist conclusion is that if the barber was B. Russell, he turned wrong and bearded.
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..."
There can't be any bearded men in town. As stated, the barber shaves everyone who does not shave himself.
- 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
- 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 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
- that's not quite the same paradox -- Tarquin 12:18, 4 Aug 2003 (UTC)
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
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