Wednesday, September 30, 2009

So I heard this paradox today, thought I'd pass it on

So there's a barber in this town whom shaves everyone in town that doesn't shave themselves. So the question is, does he shave himself?

6 comments:

Peter H of Lebo said...

Yes, he shaves himself. I believe you forgot, "only those". In your premise he shaves everyone who doesn't shave but there is no restricting parameter on shaving people who shave. You need "only" to make it a Russell paradox.

It should read, "So there's a barber in this town whom shaves all and only those in town that doesn't shave themselves. So the question is, does he shave himself?"

Big Myk said...

This is not unlike the paradox George Carlin used to pose to the nuns in his parochial school:
"If God is all powerful, can He make a stone so big that He Himself can't lift it?"

For no extra charge, here's another line from George Carlin: The very existence of flamethrowers proves that some time, somewhere, someone said to themselves, "You know, I want to set those people over there on fire, but I'm just not close enough to get the job done."

Sean Harvey said...

but if he doesnt shave.... then he shaves himself... but he said he hadn't shaved in the first place

James R said...

I believe you forgot "who"--"who shaves everyone who doesn't shave". That is the type of paradox Douglas Hofstadter falls in love with in "Godel, Escher, Bach: An Eternal Golden Braid." I hadn't heard the term "Russell paradox" but it makes some sense as Hofstadter says that Godel's paradoxes and Incompleteness Theorem basically disproved Russell (and anyone else's future) attempt to create a self contained logical system.

It has no answer as in "Please answer this question truthfully? Is 'no' the answer to this question?

Peter H of Lebo said...

Repost, bad grammar on my part. Based on your post yes, he shaves himself, it is not a paradox. I believe you forgot, "only those". In your premise he shaves everyone who doesn't shave but there is no restricting parameter on shaving people who shave. The barber is allowed to shave people who shave. You need "only" to make it a Russell paradox.

It should read, "So there's a barber in this town who shaves only those in town who don't shave themselves. So the question is, does he shave himself?"

James R said...

Ah, I see now what Peter was saying. Nice catch! Indeed, without the 'only' it is not a paradox.
(He may be shaving himself in his spare time.)