What is Bertrand Russels Barber Paradox?

Показать описание

Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we naturally assume that an answer must exist. In the case of Bertrand Russell's Barber Paradox, a solution does exist, but it becomes even less obvious than other statements like it.

Proposed by Bertrand Russell in the early 1900s, the barber paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves. These statements may seem simple at first, but a paradoxical proposition arises: who shaves the barber?

Let's take a look and see just what's going on in this puzzling paradox...

All images courtesy of Creative Commons or protected under Fair Use. For questions or concerns about the use of any media, please contact the page directly.

Concerning Reality

Рекомендации по теме

Комментарии

Calling it paradox is the same as as calling sentence "2 is 3" paradox. I can't get why are people calling it paradox, you explanation is great!

lukassmida

Fun fact: Using some elementary set theory, we can prove that, in an village with a resident barber, that barber can shave those and only those men in the village who do not shave themselves if and only if that barber is NOT a man. A female barber could, without any contradiction, shave every man in the village. This arrangement would meet the stated requirements of the job. A male barber simply could NOT meet those requirements.

dcproof

A similar false paradox would be "what happens when an irresistible force meets an immovable object?" It's not real; because either an irresistible force, or an immovable object, exists but not both. I believe we live in the first universe because gravity would appear to be an irresistible force. I don't want to get into an argument here about the definition of force, just consider it something that affects other things. Also keep in mind that the effect on certain objects may be very tiny, yet still exist.

stevenc.

The barber paradox is not Bertrand Russell's! It's _based_ on his own paradox about set theory, but the barber form of the paradox was suggested to him by someone else.

NoriMori

Noise without meaning nails it, didn't knew what were the intentions of his paradox but it makes sense now

atzmut

"This paradox does not compile"

brainwater

Nonsense. This is "not" the resolution. Here is the resolution. In this paradox, there was a town in which all men were required to be beardless. In this town, there was a set of men who shaved themselves and another separate set who did not shave themselves. For that latter set of men there was a barber who posted a sign which instructed that he only shaved men who did not shave themselves. The paradoxical aspect becomes visible when considering who would shave the barber, there being only two sets of men to which he could be a member by virtue of whether or not he did or did not shave himself. He had to be beardless so he had to shave himself but his sign instructed that he did not shave men who shaved themselves, thus the paradox. Though confusing to some, the resolution is clear and simple. The two sets of men were defined as such by virtue of only one, unique criterion, i.e., for the one that they shaved themselves and for the other that they did not but rather visited the barber. Each set of men shared three other criteria for membership which were identical. In each they were men. In each they lived in town and in each they had to be beardless. The only means of the definition of their membership into the two separate sets of men (the deciding factor) was the inclusion of their respective relationships to shaving. That being the case, the barber would necessarily have to be defined as a member of a third set of men, i.e., those who shaved others. Consider, he too was a man, lived in town and had to be beardless and like the first two sets of men, if the same logic were to hold throughout the paradox (which it must), was designated a member of a separate, third set of men by his unique relationship to shaving, the only defining factor in the first two and thus necessarily for the third. Deny this and you deny the very means by which the first two groups of men were defined as members of their separate sets and the paradox fails. Accept this and the paradox fails. That is because it is not a paradox.

Comments? Opinions?

jamestagge

Bertrand Russell in this video exposes the limits of logic. During his time and together with David Hilbert, there was hope that logic would provide the foundational framework of mathematics. What was mathematics but rules in how to manipulate numbers and symbols. They failed in this endeavor so it was not just noise without meaning. Mathematics was fundamentally either incomplete or inconsistent.

rockprime

This is a true paradox, not a false paradox to some at sometime, under some other circumstances. It's typical of all truth and all paradoxes.

May the love and the peace of Jesus be with us.

jwu

Barber paradox is a valid paradox, it just appears to be "arguable". An inarguable paradox would be "this statement is false"

FlowerKlam

It seems that the barber shaves himself. All that was stated was that there was a barber in the town. It didn't say the barber was a resident of the town.

roadknight

You can make anything a paradox if you create rules to make it a paradox.

freddykruger

Absolutes are unattainable but isn't that an absolute statement which contradicts the previous statement of absolutes being unattainable in this universe so there's always exceptions to the rule and the barber is the exception to the rule

cherkas

There is indeed an answer, and it's quite simple.

There is no proof that anyone shaves himself until after he has shaved himself, at which point it is too late to not shave himself.

So the barber shaves everyone but himself, and because there is no proof that he shaves himself until he has shaved himself, he also shaves himself.

So there is no paradox, but rather, the supposed paradox is produced by deficient category definitions which fail to distinguish between action and state.

lawrence

You stick the barber in Schrodinger's box and give him a barbers razor. If you never open the box then he can be in a superposition of shaving himself and not shaving himself at the same time. That is the solution.
Ask Bertrand Russell if an electron has to pass through the left or the right slit in the double slit experiment and he will tell you it had to pass through only one slit. He would say it would be impossible to pass through both slits at the same time. We all know that electrons can pass through both slits at the same time.

I really think all these math problems stem from the same thing and that is using the fake classical universe in the thought process behind math development. In Quantum Mechanics, things can be true and false at the same time.
In the double slit experiment I can say, it is true the electron went through the right slit and it is true that the electron did not go through the right slit. Both are valid if you don't disturb the wave function.

All of these self referral paradoxes that pop up are related to the fact that quantum mechanic is not incorporated into the though process of the math development.

jeffbguarino