Cuts will be needed
A hair-brained law.
In the Hindu Kush, the rulers decree that the town’s hairdresser has to cut everyone’s hair and that anyone whose hair hasn’t been cut after six months will have their heads cut off. (I’ve heard of a little off the top, but this is ridiculous.) Amateurs cannot cut anyone’s hair and the hairdresser may not cut their hair of anyone who does it themselves. If he does, there are a couple of guards who will chop his hands off.
It sounds like a good deal for the hairdresser who gets paid one piece of silver for each cut. It sounds like a good deal until he realises that there’s a slight flaw in all this and goes into hiding for twenty years.
What’s the problem?
The hairdresser falls into two categories. He’s the only person who can cut other’s hair and is banned from cutting the hair of people who do it themselves – which includes him.
The only way out of this paradox is a third party solution. He’d have to go to the rulers and explain the situation so that they could then emend the law (and perhaps fine the people in the legal department for not formulating the law more carefully). Actually, I suppose you could take an OT-style approach to the problem and say that the six month constraint outranks the ban on cutting the hair of people who cut their own hair. So long as the former constraint is satisfied, the latter has no effect. But this isn’t really a solution because if the hairdresser does cut his own hair and the law is then applied, he’ll be executed in six month’s time. Again, without recourse to a third party, the hairdresser can’t simply change the terms of the law.
In fact, there doesn’t seem to be a solution. If you get painted into a corner like this, the only way out is to walk on the paint. I’m inclined to agree with those who have declared these sorts of things to be meaningless. It’s a bit like saying that something is simultaneously completely black and completely white, but not a shade of grey.
The paradox illustrates Russell’s Paradox (wikipedia; it includes a more comprehensible illustration of the paradox than “the set of sets which are not members of themselves – is it a member of itself?”).
It sounds like a good deal for the hairdresser who gets paid one piece of silver for each cut. It sounds like a good deal until he realises that there’s a slight flaw in all this and goes into hiding for twenty years.
What’s the problem?
The hairdresser falls into two categories. He’s the only person who can cut other’s hair and is banned from cutting the hair of people who do it themselves – which includes him.
The only way out of this paradox is a third party solution. He’d have to go to the rulers and explain the situation so that they could then emend the law (and perhaps fine the people in the legal department for not formulating the law more carefully). Actually, I suppose you could take an OT-style approach to the problem and say that the six month constraint outranks the ban on cutting the hair of people who cut their own hair. So long as the former constraint is satisfied, the latter has no effect. But this isn’t really a solution because if the hairdresser does cut his own hair and the law is then applied, he’ll be executed in six month’s time. Again, without recourse to a third party, the hairdresser can’t simply change the terms of the law.
In fact, there doesn’t seem to be a solution. If you get painted into a corner like this, the only way out is to walk on the paint. I’m inclined to agree with those who have declared these sorts of things to be meaningless. It’s a bit like saying that something is simultaneously completely black and completely white, but not a shade of grey.
The paradox illustrates Russell’s Paradox (wikipedia; it includes a more comprehensible illustration of the paradox than “the set of sets which are not members of themselves – is it a member of itself?”).
Tomorrow, ravens and universals.
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