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Barber Paradox
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Tank123



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Post: #1
Barber Paradox

Here is an interesting mathematical paradox for those interested in Mathematics or in general:

The paradox involves a male barber in a town, who everyday shaves every man who does not shave himself, does the barber shave himself?


The paradox seems to demand that the barber shave himself if and only if he does not shave himself!  This paradox was proposed by Mathematician and Philosopher Bertrand Russel.  It still has not been solved today, but nevertheless it forced a modification to set theory in Mathematics.


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04-11-2011 12:17 AM
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skyblue1
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Post: #2
RE: Barber Paradox

not much of a paradox, especially if the barber wore a beard.


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04-11-2011 12:47 AM
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Vampslord



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RE: Barber Paradox

And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.

04-11-2011 12:50 AM
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Tank123



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RE: Barber Paradox

skyblue1  Wrote:
not much of a paradox, especially if the barber wore a beard.


In a mathematical paradox, there is no double meaning behind the statements.  It is a paradox because it implies that the barber shave himself if and only if he does not shave himself.


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04-11-2011 01:10 AM
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Tank123



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RE: Barber Paradox

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


First they ignore you
Then they laugh at you
Then they fight you
Then you win

-Mahatma Gandhi
04-11-2011 01:11 AM
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d_olson27
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RE: Barber Paradox

Tank123 Wrote:

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


Where does it say that?


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04-11-2011 01:38 AM
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skyblue1
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RE: Barber Paradox

Tank123 Wrote:

skyblue1  Wrote:
not much of a paradox, especially if the barber wore a beard.


In a mathematical paradox, there is no double meaning behind the statements.  It is a paradox because it implies that the barber shave himself if and only if he does not shave himself.


there is no math involved


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04-11-2011 02:11 AM
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142857



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RE: Barber Paradox

I can see the value in this as a thought experiment, and even though I don't have a lot of knowledge of higher mathematics I can see how it would affect set theory.

What it shows is that a simple "either/or" statement can actually imply 3 categories, not just 2.

You have to move beyond the idea that there are two types of men in the town, as implied by the original statement - those who shave themselves and those who are shaved by the barber. The barber himself is obviously a 3rd category not covered by the statement.

I don't think that there is much point trying to "solve" it, though, as there is about as much chance of solving this one as there is of solving definitively "which came first, the chicken or the egg?".

04-11-2011 02:57 AM
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142857



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RE: Barber Paradox

skyblue1  Wrote:
there is no math involved


Not directly. But it does have implications for set theory, which is part of mathematics.

04-11-2011 02:58 AM
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d_olson27
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RE: Barber Paradox

142857 Wrote:
I don't think that there is much point trying to "solve" it, though, as there is about as much chance of solving this one as there is of solving definitively "which came first, the chicken or the egg?".


If you believe in evolution, obviously the egg came first.


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04-11-2011 03:21 AM
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Tank123



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Post: #11
RE: Barber Paradox

d_olson27 Wrote:

Tank123 Wrote:

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


Where does it say that?


It doesn't have to say that.  Within a mathematical context such as this, what is said is all that is allowed to be worked with.  In other words, there can be no one else that shaves the barber, for example.


First they ignore you
Then they laugh at you
Then they fight you
Then you win

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04-11-2011 03:27 AM
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d_olson27
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RE: Barber Paradox

Tank123 Wrote:

d_olson27 Wrote:

Tank123 Wrote:

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


Where does it say that?


It doesn't have to say that.  Within a mathematical context such as this, what is said is all that is allowed to be worked with.  In other words, there can be no one else that shaves the barber, for example.


Source?


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04-11-2011 03:35 AM
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142857



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RE: Barber Paradox

d_olson27 Wrote:

142857 Wrote:
I don't think that there is much point trying to "solve" it, though, as there is about as much chance of solving this one as there is of solving definitively "which came first, the chicken or the egg?".


If you believe in evolution, obviously the egg came first.


So something that was not a chicken laid an egg that had a chicken inside it - and what hatched out was the first true chicken?

Actually you are right - in evolutionary terms, the egg has to come first.

04-11-2011 03:45 AM
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Tank123



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Post: #14
RE: Barber Paradox

d_olson27 Wrote:

Tank123 Wrote:

d_olson27 Wrote:

Tank123 Wrote:

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


Where does it say that?


It doesn't have to say that.  Within a mathematical context such as this, what is said is all that is allowed to be worked with.  In other words, there can be no one else that shaves the barber, for example.


Source?


Mathematics is my source.  Mathematical language is much more specific meaning than everyday, ordinary language.  When something is stated or implied, there are no double meanings at all involved.


First they ignore you
Then they laugh at you
Then they fight you
Then you win

-Mahatma Gandhi
04-11-2011 04:09 AM
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d_olson27
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RE: Barber Paradox

Tank123 Wrote:

d_olson27 Wrote:

Tank123 Wrote:

d_olson27 Wrote:

Tank123 Wrote:

Vampslord Wrote:
And it does not implies that he shave only the man who dont shave. Only that he shave all the man who dont.


There is no double meaning behind this paradox.


Where does it say that?


It doesn't have to say that.  Within a mathematical context such as this, what is said is all that is allowed to be worked with.  In other words, there can be no one else that shaves the barber, for example.


Source?


Mathematics is my source.  Mathematical language is much more specific meaning than everyday, ordinary language.  When something is stated or implied, there are no double meanings at all involved.


But your statement is not mathematical in nature. As soon as your language becomes removed from mathematics in any way, there are multiple ways it can be interpreted. In this case, the question does not exclude the possibility of the barber shaving himself and being shaved by the barber.


Friends will let you be who you are. Best friends will never let you forget it. I'm just trying to be everyone's best friend.
04-11-2011 04:16 AM
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