I see you made other threads with titles like this, but I'm too lazy to check them.

Anyway, in modern mathematics Russell's Paradox isn't so much "solved" as it is avoided. The Unrestricted Comprehension Scheme allows for this paradox , despite Frege thinking it to have been "self-evident". Russell tried to get away from it but the whole motivation behind this, Logicism, died with Gödel's Incompleteness Theorems.

But really, it's an open question. The Incompleteness Theorems didn't so much destroy Logicism as much as it made the lay of the landscape clear. If you want to endorse Logicism, your mathematical system must be inconsistent. If you want to avoid triviality (e.g. proving all sentences are true) then you have to adopt a Paraconsistent logic to go with your inconsistent set theory. But if you want to keep consistency, you cannot accept Logicism. Of course for those like the Intuitionists this isn't an issue for their view. They never accepted Logicism.

Probably why foundationalism died a horrible death for mathematicians and logicians. There's a whole panoply of options for constructing mathematical and logical systems which are equally open to interesting and valid mathematical investigation.

Anyway, I simply accept the paradox. Nothing has gone wrong with it, it's a veridical argument.

Good God Almighty. Russell's paradox was resolved in 1922 by the axiom schema of specification.

Great, then tell me, does the barber shave himself?

The barber is shaved by Occam's razor.

The definitive reply. I'm still laughing.

The town barber, who is a man, shaves exactly every man in the town who does not shave himself. Does the barber shave himself? — Jeremiah

Hello. I can see that the first statement is logically impossible, because whether the barber shaves himself or not, the statement contains a contradiction. But why call it a paradox, as opposed to a mere impossibility?

If the paradox has been resolved, as you said, then you should be able to fully and clearly answer the question. Unless of course the paradox was never really resolved. . .

It is not even the right application for Occam's Razor.

What is it you think is impossible?

Good God Almighty. Russell's paradox was resolved in 1922 by the axiom schema of specification. — fishfry

As I say, that's a somewhat naive view. The specification scheme allows one to avoid the paradox, but it doesn't necessarily solve the paradox. The whole point of regimenting set theory this way was to make make math consistent (or at least not provably inconsistent). But it comes with well known issues, like a number of unsolved questions that have known answers in other systems (e.g. Continuum Hypothesis).

It's kind of like saying you solve the Liar paradox by simply disallowing self-reference in your language. It's true in a sense (you can no longer articulate the paradox) but the debate is in the merits and justification in doing so. It's simply incorrect to say the see foundational issues were solved; no one studying modern fundamental mathematics would say it with such certainty, in any case.

Contradictions are impossible.
The statement “the town barber ...” contains a contradiction either way we look at it.
Therefore the statement is impossible.

I am asking what specifically is impossible. It is an easy enough question. If you can't tell me what is impossible, then how can you say it is impossible?

“The town barber, who is a man, shaves exactly every man in the town who does not shave himself.”
Either the barber shaves himself or not. If he does, then he does not only shave men who do not shave themselves. If he does not, then he does not shave all men who do not shave themselves. The statement is therefore impossible.

But the barber is psychically cable of shaving himself or not, our problem is with the group. Does he fit the group, or not? That is where the paradox is, and in the meantime look up the meaning of a paradox.

But the barber is psychically cable of shaving himself or not, our problem is with the group. Does he fit the group, or not? — Jeremiah

He fits in the group and does not fit in the group, but only in a fiction can it obtain, even for metaphysical dialetheists. To motivate anything more you'd have to show such a barber does exist. So even if you're like me and think certain aspects of.reality might be inconsistent, the Barber Paradox doesn't show there is or can be such a barber.

A paradox is an apparent, but not real, contradiction. The barber can shave himself or not, and the group as defined can exist, but the barber cannot fit the group without contradiction. Now you claim it is a paradox and not a contradiction. Why is the contradiction not real?

Here is another simpler example for clarity:
A triangle exists in a world where all shapes have four sides. A triangle is possible, and a world where all shapes have four sides is possible, but the triangle cannot exist in the world without contradiction.

It is not even the right application for Occam's Razor. — Jeremiah

Oh but it is. Perhaps you are unable to see your unnecessary, superfluous, psychological baggage that you pile upon these threads of yours.

You are trolling, that's the only reason you even join my threads. You never contribute. You are trying to bait me.

Stay on topic

The barber can exist, that is not the question. The question is if he shaves himself.

Far more often than you.

I'm saying that even as metaphysical dialetheist I do not believe a "barber who shaves all and only those who do not shave themselves" cant exist. Obviously vanilla barbers can exist.

https://en.oxforddictionaries.com/definition/paradox

You do realize this has been a recognized paradox since 1901?

It does not actually say he shaves all. It is every man who does not shave himself, it is a set condition.

The set condition is the paradox, it is very important to understand that difference.

It does not actually say he shaves all. It is every man who does not shave himself, — Jeremiah

That's is literally what I said. My post:

I'm saying that even as metaphysical dialetheist I do not believe a "barber who shaves all and only those who do not shave themselves" cant exist. — Me

I already said I accept the paradox as a valid argument, but unlike most that's because I accept naive set theory. In ZFC, the set is not a valid one, sets cannot contain themselves in ZFC.

And that is not the paradox in the OP. Which is my point.

The town barber, who is a man, shaves exactly every man in the town who does not shave himself. — Jeremiah

This statement is false.

If we are working with a logic that allows proof by contradiction, it is false because it allows deduction of contradictory propositions.

If we are not, we can in any case deduce the negation of the sentence.

This case is not the same as Russell's Paradox. Russell's Paradox arises from the inconsistency of the axioms of Naïve Set Theory, whereas this statement is meaningful and false in any reasonable logic.

Since the barber statement is false, the answer to the question 'who shaves the barber' is 'anybody, including the barber, could shave the barber, but we don't know who does it'.

And that is not the paradox in the OP. Which is my point. — Jeremiah

Are you serious? Your OP:

The town barber, who is a man, shaves exactly every man in the town who does not shave himself. — Jeremiah

I have to assume there's some communication issue here. I accept Russell's Paradox, but the Barber doesn't seem difficult: no such barber exists, problem solved. If the barber is tangential to your question, fine. But you did in fact bring it up.

This is exactly Russell's Paradox.