Friday, January 13, 2012

Friday Paradox:

This one is from Bertrand Russell.

The Barber Paradox
A certain village has a barber named Saul. Saul is an affable fellow and is liked by everyone who knows him. But Saul has a peculiar practice from which he never waivers. He shaves all and only those adult male villagers who do not shave themselves. Now Saul is an adult male who lives in the village and he is clean-shaven. So an interesting question arises: Does he or does he not shave himself?

You might think that Saul does shave himself but this would contradict his practice of only shaving those individuals that do not shave themselves. Alternatively, you might think that Saul does not shave himself but this would contradict his practice of shaving all those individuals that do not shave themselves. Something has to give!?

* I should mention that Saul is a "normal" adult male and would have a beard if it were not for the fact that his face is regularly shaved.
(No cheating now... try to solve it on your own.)

6 comments:

BHFoster said...

Well this is actually simpiliar than what people are making it seem. Saul once shaved himself before his practice opened. Then at that point after he had never shaved himself again and had someone else do it or another alternative would be after his hours at the barber he would go back to his home were he then shaved himself because after leaving the practice would be void. Perhaps Saul is also not a full villager and which his practice wouldn't apply to himself. This is also known as a "Barber Paradox".

Bryce H. Foster

Jesse Steinberg said...

But if someone else shaves him now, then this violates the description of the case. The men that live in this town either shave themselves or get shaved by Saul. And Saul only shaves people that don't shave themselves. Given this, someone other than Saul can't shave Saul; but Saul can't shave himself either... thus the paradox. The key is to solve it without changing the case. But how do we do that?

I think your last suggestion also changes the case. Russell tells us that he is a villager.

Those of you math geeks out there might know about this same sort of puzzle in set theory (also from Russell). If you're stumped, you could check out what logicians have said about that form of the puzzle and see if it can be applied to the Barber Paradox. But I'd rather see what YOU think, than what you can find on wikipedia.

upshooter91 said...

Maybe Saul is a Substance Dualist who does not see his bodily self as "himself" but rather as the vessel that carries his real, essential self. His mind is the only "self" that he is aware of or can be aware of. He only has access to his mind. So, either Saul sees other people as other minds contained in vessels called "bodies", or maybe Saul is a skeptic and does not know if anyone he shaves is actually a "person" at all. So, Saul is really a mind that shaves its container, which is not himself. He shaves the other possible figments of his conscience in order to etch out a living in the village his mind seems to inhabit.

Anonymous said...

I am actually on the same page as Above^. Although I would wonder whether or not all the villagers are also Substance Dualists, in which case none of them would shave themselves meaning they shave their vessels and Saul would be a poor barber.

Another argument would make sense if you think of the universe along Big Bounce lines: every time he has to shave: he shaves. Existence cannot either be in a state of non-existence or not, it isn't anything.

-Matt

Jesse Steinberg said...

I have to confess that I'm at a total loss after reading the last two comments. It's not clear to me how one's theory of the relationship between mind and body (substance dualism, in this case) gets rid of the paradox. Saul still has a body and it is still clean-shaven. The question remains: Who shaves Saul? If you want to rephrase it, you could ask: Who shaves Saul's body?

So I need a bit more of an explanation.

Anonymous said...

I guess it comes down to a semantics match over what Saul considers to be himself. From his perspective Saul and Saul's Body are not the same thing. He shaves all and only those adult male villagers who do not shave themselves. To Saul, Saul's Body is a body: and organic mass. To Saul, Saul is an entity that does not grow facial hair. He does not shave himself, he shaves the object he inhabits, which is an object that I suppose he prefers to be shaven rather than bearded.

-Matt