Saturday, July 25, 2009

The barber who shaved

I encountered this paradox online: “There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?”

Now, at face value, the paradox does indeed appear to be paradoxical. That is, we’d assume that the barber is a part of the village, and is therefore referenced as part of the villagers who either shave themselves, or the villagers who don’t. Obviously, if the barber is a villager, is himself, hasn’t shaved himself, and has no one to shave him, he will be unable to shave himself without violating the statement.

Yet there are a number of assumptions already in place. Moreover, it is not mentioned whether the statement is true across all time frames. The simplest solution would be that the barber simply shaves himself. Why? Because at the point of time at which the statement was made, the statement was true: he only shaves those who don’t shave themselves. However, since he’s a part of the group of non-self shavers, he’s obliged to shave himself, therefore violating the statement. Thereafter, the statement ceases to be true. QED.

Then we can consider that, perhaps, the barber wasn’t in the group of people who either shave or do not shave themselves. This can be true if:
1) The barber isn’t himself. He’s a RED spy.
2) We consider the barber to be outside the village (and therefore beyond those groups
3) We consider the barber (vocation) to be separate from barber (the person)
4) We consider that someone else is shaving the barber.

If 1 is true, we’d have to spycheck him, just in case.
If 2 is true, we’re assuming that both groups are from the village. Hence, he may not be a part of either group, enabling him to shave himself without violating the statement.
If 3 is true, he can also shave himself without violating the statement, since the vocation of barber is separate from the person of the barber.
If 4 is true, well, that greatly simplifies things, doesn’t it?

2 comments:

Freefall said...

Let x and b be members of set V. S denotes a relationship in set V.

Rule:
bSx, iff ~xSx

Therefore,
bSb, iff ~bSb

The paradox is "bSb, iff ~bSb".

English language is sufficiently ambiguous to obfuscate the fundamental paradox expressed as a scenario. There's a reason why lawyers make so much money.

Fenrir Nightwolf said...

When I grow up, I wana be a macadamia, or a lawyer, or a scam artist or a consultant. Strangely, they all sound pretty much the same...