If a barber shaves all and only those who do not shave themselves, does the barber shave himself?
You mean Shaggy Bob? Nah; he just doesn’t shave.
Such a barber cannot exist. It’s not possible to have exactly that pattern of behavior.
(It’s just like asking “If a barber shaves himself if and only if he doesn’t shave himself, does the barber shave himself?”)
The barber is a woman.
The women I hang out with usually shave (interpret that how you will).
And stop trying to fix the paradox, it doesn’t work and you’re ruining the fun.
He’s planning to shave himself just as soon as he’s finished shaving Schrodinger’s cat.
That doesn’t work; the barber is explicitly referred to as “himself”.
It’s not my fault if people don’t know who the barber is. Her name is Jane. She’s a really nice older woman, and will give you the best Damn shave you ever had. It’s a little pricey, which is why some of the menfolk shave themselves.
IIRC, Raymond Smullyan said the claim about the barber is pretty much like hearing that Al is taller than Bob, and Bob is taller than Al, and how do you explain that? (He goes on to add that the obvious answer is, of course, something along the lines of “Well, you’re either lying or mistaken.”)
“Good sir, I sell the finest spears in all the land! They punch right through any shield!”
“Fair enough, but I’m not in the market for a spear. Do you sell shields?”
“The finest in all the land! No spear can penetrate them!”
The barber used to be a man . . . or used to be a woman, whichever works.
Shaved a little too close, huh?
He could wax. Or pluck.
Alopecia sufferer.
Or he had electrolysis years ago when he got tired of people asking the question.
Good points. For some reason, though I’m familiar with Raymond Smullyan and his books touching on logical paradoxes and such matters, when I read the name in your post, somehow I mentally connected it to Rudyard Kipling. So I was startled at first, and then went, “Well, he’s a pretty bright guy, I could certainly imagine that somebody asked him about the barber paradox and he was able to come up with something intelligent to say about it, even if it’s not really his wheelhouse.”
All the same, something was nagging me about ‘either lying or mistaken’, which is something Smullyan uses fairly often in his books to describe a character who has claimed something logically impossible or contradictory.
The barber isn’t old enough to shave yet…
Yeah, the answer to the barber paradox is simply that such a barber can’t exist. That, in itself, isn’t really that big a woop. The paradox is only interesting (well, for certain values of “interesting”) because it’s an illustration of Russel’s paradox (and used as such by Russel himself), which again proves that set theory, as developed by Frege and Cantor, contains contradictions. This, apparently, shakes the foundations of mathematics, although precisely why and how, I’ll admit that I haven’t a clue.
Part of it was because before Russell, mathematicians hoped (or assumed) that they could devise a perfect system of proofs, that would prove every true statement in whatever branch of mathematics they were interested. Kurt Gödel proved that for many important branches of mathematics, every system S of proofs has a ‘Barber statement’ - a statement that is true if and only if it is unprovable in S. Therefore every system is either flawed (proving a false statement) or incomplete (unable to prove a true statement.)
The barber is his mother.
I think the barber uses 40 K of g in an fpd.