The barber paradox solved
The barber shaves those and only those who do not shave themselves
So there are perhaps people who do not shave themselves whom he does not shave. And those who shave themselves he does not shave. But he can't shave himself because he shaves only those who do not shave themselves. So anyone can shave the barber except himself
Solved?
So there are perhaps people who do not shave themselves whom he does not shave. And those who shave themselves he does not shave. But he can't shave himself because he shaves only those who do not shave themselves. So anyone can shave the barber except himself
Solved?
Comments (47)
Apparently not anyone.
Also. This thread in a nutshell.
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Therefore he does not shave himself, making him the kind of person who he does shave.
Therefore he does shave himself, making him the kind of person who he does not shave.
Therefore he does not shave himself ...
That's why this is a paradox.
"Therefore he does not shave himself, making him the kind of person who he does shave." He shaves others
"Therefore he does shave himself, making him the kind of person who he does not shave." No he doesn't shave himself. He can't because of the paradox
The trick in the sentence is that it implies its talking about people other than himself. If we put the true intention of the sentence together we get:
The barber only shaves others who do not shave themselves.
Now, if we add in the idea that this also includes him, there is no paradox, we just realize the sentence contains a contradiction.
The barber only shaves others who do not shave themselves. The barber also shaves himself, because he does not shave himself.
The first sentence makes sense. The second sentence, which was attempted to be placed implicitly within the OP's sentence, reveals itself to be a nonsense statement when made implicit. If you combine the first and the second sentence together, then the contradictory part of the second sentence makes the combined sentence false, but not a paradox.
There is no paradox, but contradiction instead? Nop. He does not shave himself because he shaves only those who not shave themselves. The paradox is one sentence: the barber shaves those and only those who do not shave themselves.
The difference between a paradox and a poorly constructed sentence can be tricky. A paradox would be the result of a logical concept taken to its conclusion. For example, someone is able to time travel, and ends up accidently killing their mother before they were born. A paradox denotes something can happen, but if something is done within that action, it could negate the possibility of being able to do that action to begin with. This is a contradiction, but it is a contradiction that states limits within action A that do not allow it to do action B.
A poorly constructed sentence is written as a contradiction. Poor sentences often come about because there is implicit cultural understanding that confuses the issue. That's why I broke the sentences down into explicit parts, removing the implicit assumptions that muddy the waters.
If you are saying that he shaves everyone who doesn't shave themselves, and also himself, then its fine. If you say that he shaves everyone who doesn't shave themselves, and himself, even though he doesn't shave himself, then its a contradiction. We can remove the first part about "other people", because its unnecessary. You cannot both shave, and not shave yourself. That's the contradiction, not a paradox. If you include a contradiction with extra sentence combinations, it still doesn't negate the fact of the contradiction.
Paradoxes are contradictions. They're just often not obviously so.
Quoting Srap Tasmaner
Let S be the set of all men who don't shave themselves.
P is a member of S.
To be a member of R, you have to shave all the members of S.
Since P is a member of S, to be a member of R he would have to shave himself.
But he doesn't.
Therefore P is not a member of R.
Every person who shaves himself is named John. Every person who does not shave himself is named James. The barber shaves every person named James and doesn't shave anyone named John.
What is the barber's name?
No, not solved. Also a poor framing of the original problem.
There is a town. It has two laws about Barbers.
First law; Everyone has to be shaved by the barber.
Second law; No one can shave himself.
The solution is simple. The barber shaves himself. First law states "Everyone".
By way of the first law, the barber shaves no man who shaves himself, except himself because he is ultimately still accounted for when the word "Everyone" is used. He's by law logically exempt from the second law because he's the only barber in the town.
Now it's solved. It's just a logic puzzle.
Your latest post is illogical. It has me have a "mad laugh" . I know what I need to know about logic. I have a full vision of it. Are you into math or just logic? Math is too tedious but I have a full vision of it too.
The barber shaves every person named James (as per the third rule), and so if his name is James then he shaves himself. But if he shaves himself then his name is John (as per the first rule).
BS
Dude, if you have one group doing something and another doing something, they are doing something. I didn't know you'd play a game that's idiotic
Dear gods people listen to Gregory! Gregory knows, be more like Gregory. Make it a fucking meme.
Still though Gregory, you could have framed it a little better for them.
I couldn't have
Part of your reply seems to be missing.
Which of these do you disagree with?
1. The barber shaves himself because his name is James
2. The barber's name is John because he shaves himself
Thusly because you went with them in trying to force a contradiction
I'm not sure what you mean but you seem nice. I always try my hardest
A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. For example mathematical reasonings where every step is valid in an explanation of how 2+2 could possibly equal 5 is a mathematical paradox.
You're right about the logic, but you've made the mistake of treating a language game like a numbers game. The rules aren't the same. So neither is the definition of a paradox.
For example, a paradox in time, where you travel in time and encounter a past or future version of you is a mathematical paradox.
If time travel is possible in a given universe and you encounter another version of you then what should normally be 1, becomes 2. Mathematical paradox.
To explain the problem of the barber mathematically, it's just algebra.
Symbol for Barber, Symbol for everyone, Symbol for rules of culture on who gets to cut who's hair or shave who's beard.
Let me put it this way. If all Bs are a part of E and only B gets to do S, B must do S to E, because B is equal to E, B must also do S to B.
B is Barber
E is everyone
S is shave
Does that make a bit more sense? I hope I haven't made it more confusing for you.
@Gregory Did you feel threatened at all by this comment from this extremely new account? I've sent a message to the moderators and this account. If anyone said this to my face I'd probably act pre-emptively. Way too dark and not funny if it's meant as a joke either.
The contradiction is in claiming that there can be any such barber. There cannot. Just because you can string words together grammatically doesn't mean you're describing something that can actually be.
That's why I like framing the problem as figuring out who would be in the set of all such barbers. You find that such a set is necessarily empty because the conditions for being a member are inconsistent. You might as well define a set of all the numbers equal to 4 and equal to 5. There's no contradiction in that; you've just defined a set that's necessarily empty.
First things first, some things need to be clarified:
Are B, T and M each categorized/defined (for example when M is categorized as one who shaves himself), before the hypotetical shavings are done or after they are done? I'll asume first that it is after the shavings are done:
If M shaves himself, he shaves himself and can't be a member.
Does «The philosopher does not shave himself» mean: He hasn't shaved himself until know and never will? If so, by definition he can't ever shave himself, and therefore can never be a member since he can never shave someone who does not shave himself.
Since Srap says that the implication: if the philosopher shaved himself, then he would be a member is true, we'd have to say: if he shaved himself he would shave someone who does not shave himself. But if it were possible for him to shave himself, then he would in that case have shaved someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore he would not be a member. So the implication can't be true if P shaves himself.
However, it's impossible for him to shave himself by definition, and therefore he can never be a member. This means the implication «If he shaved himself, he would be a member» is true, since it could only be false if he both shaved himself and wasn't a member, which can never happen since the antecedent is impossible. So what Srap says up to this point appears correct if we interpret it like this.
Or does it mean: He hasn't shaved himself until know, but may shave himself in the future? If so, he would shave someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore not be a member. So this can't be what it means if Srap is right.
As for the barber: If he shaves himself he will shave someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore not be a member.
If he shaves M, if M already shaved himself before, then the barber would shave someone who shaves himself, and not be a member. If M hasn't shaved himself yet, then he would shave someone who doesn't shave himself, and be a member. So it must be the case that M already shaved himself in the past if Srap is right.
If B shaves P, then he shaves someone who doesn't shave himself, and is therefore a member of R.
This is problematic, because according to this interpretation since P does not shave himself, the barber would shave someone who does not shave himself, and therefore the barber would be a part of R, which contradicts what Srap says: that R is empty.
Nonetheless, this interpretation does show that if he shaves himself, he would not be a member of R.
Let's now assume they are caracterized *before* any of the hypotetical shavings used in the previous reasonings happen:
If M shaves himself, then if M shaved himself in the past, then he shaves someone who shaves himself and is not a member. This must be the case if Srap is right.
If he hasn't, then he shaves someone who doesn't shave himself (yet) and therefore is a member. This can't be right if Srap is right.
If P shaves himself, then he shaves someone who doesn't shave himself (yet) and therefore is a member. According to Srap, this too can't be the case.
Unless we include in the definition of P that he never will shave himself, in which case it's impossible for him to shave someone who does not shave himself, and therefore he can never be a member of R, and the implication “if P shaves himself, he would shave someone who doesn't shave himself (yet)” would once again be true because the ground/ antecedent is by definition always false. This must be right if Srap is right.
If the barber shaves himself, and if he hasn't shaved himself in the past, then he would be shaving someone who does not shave himself, since before he shaves himself he hasn't shaved himself. Therefore, he would be a member. This can't be the case if Srap is right.
If the barber shaves himself but has also shaved himself in the past, then he shaves someone who shaves himself, and is therefore not a member. This must be so, according to Srap.
If the barber shaves M, then if M shaved himself in the past, then he shaves someone who shaves himself and is not a member. This must be the case if Srap is right.
If M hasn't shaved himself in the past, then the barber would be shaving someone who does not shave himself, and therefore would be a member, which can't be the case according to Srap.
If B shaves P, then he shaves someone who doesn't shave himself, and is therefore a member of R.
And so we have the same problem as before.
So it seems that in either case R is not empty because the barber belongs to R.
Unless I made a mistake somewhere, of course.