Russell's Barber Paradox

twdavis13 · #1 07-25-2009, 08:08 PM

There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

This is a popular paradox by B. Russell, there have actually been Doctoral Dissertations written on this very paradox, and I have trying to figure it out. See if you can.

But first, here's my take on it:

If the barber is not a member of the people who are getting shaved by him, he must be a membe rof the group tha tis not getting shaved by him, which would be the group shaving himself. Soooo: He is a member of the group who shaves themselves, but at the same time, he is a member of the ones who do shave themselves because he doesnt.......uhhhhhh...hhhhhhhhmkmcm;sv

the barber shaves himself And Doesnt shave himself at the same time???

uhhhhhh

doctorjazz · #2 07-25-2009, 08:40 PM

It's a problem of causality, the issue being whether the non-shavers are non-shavers because they're shaved by the barber or whether they're shaved by the barber because they're non-shavers. If the first is true, the barber is a member of both groups: he shaves himself and is shaved by the barber. If the second is true, the situation is paradoxical.

TrooperFarva · #3 07-25-2009, 08:46 PM

The Barber has a beard

/thread

Thunderscreech · #4 07-25-2009, 08:49 PM

Quote:

Originally Posted by TrooperFarva

The Barber has a beard

/thread

twdavis13 · #5 07-25-2009, 09:00 PM

Quote:

Originally Posted by TrooperFarva

The Barber has a beard

/thread

+5

twdavis13 · #6 07-25-2009, 09:04 PM

Quote:

Originally Posted by doctorjazz

It's a problem of causality, the issue being whether the non-shavers are non-shavers because they're shaved by the barber or whether they're shaved by the barber because they're non-shavers. If the first is true, the barber is a member of both groups: he shaves himself and is shaved by the barber. If the second is true, the situation is paradoxical.

This.

I believe it is the latter because that is the only way it could be a paradox.

I'm still having difficulty understanding it though.

doctorjazz · #7 07-25-2009, 09:12 PM

Yep. And if you make the exclusivity of both groups a condition of the hypothesis, both outcomes become paradoxical.

If you want a slightly more off-the-wall solution, there is no literal, singular barber. Everyone becomes a "barber" in the moment that he is shaving himself or someone else.

twdavis13 · #8 07-25-2009, 09:27 PM

Quote:

Originally Posted by doctorjazz

Yep. And if you make the exclusivity of both groups a condition of the hypothesis, both outcomes become paradoxical.

If you want a slightly more off-the-wall solution, there is no literal, singular barber. Everyone becomes a "barber" in the moment that he is shaving himself or someone else.

Ohhhhh. I didn't think about it that way, but in other words, the barber, since you become a barber once you shave yourself, would be everyone who wasnt shaved by the barber.......wait, you culd actually say that instead of two groups, it's only one?? So there's no logical answer.......

TrooperFarva · #9 07-25-2009, 09:43 PM

The barber is a woman

/thread again

Rumzini · #10 07-25-2009, 09:49 PM

I read this with Spock's voice in my head.

Quote:

Originally Posted by twdavis13

Ohhhhh. I didn't think about it that way, but in other words, the barber, since you become a barber once you shave yourself, would be everyone who wasnt shaved by the barber.......wait, you culd actually say that instead of two groups, it's only one?? So there's no logical answer.......

doctorjazz · #11 07-25-2009, 10:00 PM

Quote:

Originally Posted by twdavis13

Ohhhhh. I didn't think about it that way, but in other words, the barber, since you become a barber once you shave yourself, would be everyone who wasnt shaved by the barber.......wait, you culd actually say that instead of two groups, it's only one?? So there's no logical answer.......

It's kind of an "essence precedes existence" argument, which I usually don't jive with but whatever. Still, it operates on the terms of the hypothesis as stated for barbers, I'm not sure that it falls within the conditions of Russell's Paradox proper.

hbarcat · #12 07-26-2009, 12:45 AM

It is a paradox because the question itself defines the conditions to be nonsensical and the conditions have no objective reality apart from the word problem.

Another example:

An all powerful being can do anything. Can he make an object so heavy that he himself can't lift it?

The problem is there is no objective meaning behind what defines an all powerful being. Such a thing only exists as a construct of our own words and so it's meaningless to try to find holes in the logic of what a being like this can or can't do if it really existed.

Similarly, the barber story exists only as a word problem and so the only definition of what it means to be a barber and the rules regarding who may shave whom are limited to the word problem itself and can't be checked against a valid, objective reality.

Stripped to its most simplistic form, the barber paradox is really the same thing as this problem:

The rock in my left hand is heavier than the rock in my right hand. The rock in my right hand is heavier than the rock in my left hand. Which rock is heavier?

bongomania · #13 07-26-2009, 01:04 AM

Quote:

Originally Posted by hbarcat

Which rock is heavier?

The one containing metal.

bongomania · #14 07-26-2009, 01:06 AM

Oh, and I agree completely that paradoxes which are merely arbitrary language constructs are nothing but fake problems, which only a sap lost in academic thought would waste more than a casual minute on. "How many angels can dance on the head of a pin?" Yes, dozens -maybe hundreds- of scholars have spent long hours debating that one in all seriousness.

hbarcat · #15 07-26-2009, 01:20 AM

Quote:

Originally Posted by bongomania

The one containing metal.

hbarcat · #16 07-26-2009, 01:24 AM

Quote:

Originally Posted by bongomania

Oh, and I agree completely that paradoxes which are merely arbitrary language constructs are nothing but fake problems, which only a sap lost in academic thought would waste more than a casual minute on. "How many angels can dance on the head of a pin?" Yes, dozens -maybe hundreds- of scholars have spent long hours debating that one in all seriousness.

Duuuuude . . . what if every atom in the universe was actually a complete universe itself and what if our universe was actually an atom in a much larger universe? Whoaaaaa, duuuuuuude . . . .

Alright, put down the bong and get back to studying.

**bassybill** · #17 07-26-2009, 07:25 AM

Quote:

Originally Posted by hbarcat

Duuuuude . . . what if every atom in the universe was actually a complete universe itself and what if our universe was actually an atom in a much larger universe? Whoaaaaa, duuuuuuude . . . .

Alright, put down the bong and get back to studying.

Then isn't the barber thing a words within worlds paradox?

i_got_a_mohawk · #18 07-26-2009, 07:36 AM

The barbour gets his face waxed or is in ZZ Top.

Pfft, simple!

TrooperFarva · #19 07-26-2009, 07:48 AM

Quote:

Originally Posted by twdavis13

There is a village where the barber shaves all those and only those who do not shave themselves. Who shaves the barber?

As it's stated here, it does not mention that the people who shave themselves exclusively shave themselves. So the Barber could he shaved by any of the people he doesn't shave.

MJ5150 · #20 07-26-2009, 10:44 AM

Are you looking for some help selecting a barber in your town or something?

-Mike