The Barber Paradox.

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I got a desk copy of a new book sent to me - with a collection of thought experiments ("What if..." Pearson Longman Press) and read it. It is really cool.

What I thought is that I could use one of these a week for our discussions.

I will put the topic as it is written in the book - and tell you where it originally came from.

This one is from an unknown origin but was popularized in Russell's Principia Mathematica.

Here it goes:

"Imagine a village in which a barber (a man) is to shave all and only those men in the villiage who don't shave themselves. Does the barber shave himself?"

What, if any, is the solution?

TTF

p.s. Moderators - if this is lame or goes against good taste - let me know and I will not continue the practice.

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Might be thinking inside the box here, but I think everything's been said about it:

http://en.wikipedia.org/wiki/Barber_paradox

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Re: The Barber Paradox.

thethinkfactory wrote:

"Imagine a village in which a barber (a man) is to shave all and only those men in the villiage who don't shave themselves. Does the barber shave himself?"

Gramatically the question makes no sense to me. All and only? Perhaps it's just an expression I'm not familiar with but I didn't think you could say "all and only" and have it mean anything.

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No problem. The man could get another persion to shave him, thus removing himself from the equation.

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Yes, but ... he shaves all the men in the village and he lives in the village.

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JoeFX wrote:

Yes, but ... he shaves all the men in the village and he lives in the village.

Actually the question above only states that he operates his business in the village. Nothing said there would stop him from commuting in :wink:. (Yes, I realise it's implied but I'm a bastard when it comes to finding exceptions).

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Paradoxes are stupid.

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It's not a paradox. The premise is not logically valid, therefore it's simply a contradiction. The barber as described, cannot exist.

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Is there a paradox where that is not the case? They can all be reduced to contradictions, insofar as my experience with them goes - hence my above comment. And of course it's a paradox. It's a very famous paradox. If you Google "paradox," you'll more than likely see this one. Which is just more to my point: they're all stupid.

For God's sake, Zeno's says motion is impossible. Wow, what a brain-bender. <yawn>

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A contradiction cannot be resolved. A paradox, although appearing contradictory, can be resolved. The barber paradox is just a simple contradiction. It cannot be resolved, the barber cannot exist. The birthday paradox can be resolved. It is true, It just doesn't seem true.

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Adrian wrote:

A contradiction cannot be resolved. A paradox, although appearing contradictory, can be resolved.

I was not aware of that. ::takes notes:: Wink

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Don't take notes from me mate, I'm a liar. :wink:

(Is that a contradiction or a paradox?) Laughing

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I'll keep that in mind Wink

. I still say paradoxes are a waste of mental energy.

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Of course the barber can exist. But he's supposed to shave all males that don't shave themselves. The paradox is that he cannot do this, because if he doesn't shave himself, then he will be one of those who doesn't shave themselves, thus he should shave himself. But he can't because then he'll be shaving himself...

I think this was fun... Smile

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The existence of such a barber is simply impossible.
(Process of thinking is fun.)

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What about the women.

Anybody seen The Barber of Seville?

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Or what about a long-bearded barber?

I'm with satt_fs. He can't exist, either that or one of the statements made is false.

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Yes, if the barber was a woman we wouldn't have a problem...
But seriously..

The barber was supposed to shave all men who didn't shave themselves. There are two reasons for a man not to shave.
1. he goes to the barber
2. he wants his facial hair

We only have a paradox when the barbers reason to not shave is no 1. If it is no. 2 everything is dandy Smile

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Nietzche:

I don't think Paradoxes are a waste of time. In fact some philosophers (Kierkegarrd included) would say that truth IS a paradox.

Take this paradox. Conservative Christian Republican voters embrace both the death penalty and the right to life - both Christianity (gie up all you own and follow me - the meek shall enherit the earth - AND Maximizing profit as the best form of capitalism.

These are paradoxes the describe the reality of these beleivers. Paradoxes are truths that do not appear to be truths at the surface.

I don't think to deny that Zeno's paradox might describe ultimate truth is to deny whole sections of philosophical reality - such as Buddhist belief.

TTF

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You might say that Kierkegård was right. Think about this paradox:

If you help a friend in need you make him less capable of fending for himself, since he gets less practice. If you leave him to his troubles you make him more capable to fend for himself. What is the friendly thing to do?

A paradox is not a paradox until it encounters the rigidness of the philosophic mind. I have this notion in my head that the world is an equation constantly balancing itself out. The concept of a paradox is what we get when we try to percieve this as a still image. If you want to you can find paradoxes everywhere.

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The Barber Paradox.

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