"Does a set of all sets contain itself?" is NOT a paradox.

[she cyka on my oro til i blyat]

Mathematically speaking, every set is a subset of itself (ACA), meaning that every set contains itself.

[Turambar]

Not at all, from a logical point of view.

[G-man]

That logical point of view is just afraid of infinite iterations of all sets within.

[Khorps]

Originally posted by G-man:

That logical point of view is just afraid of infinite iterations of all sets within.

which is why it's a paradox...

a paradox is something that loops in on itself

for example a time paradox is when someone changes something in time, then their future self does not have a reason to go back in time to change that and so it doesn't get changed thus they would have a reason to go back in time to change it then their future self etc...

basically there is no answer, you can repeat the same logic infinitely

[Khorps]

which is why, yes "Does a set of all sets contain itself?" is a paradox

[she cyka on my oro til i blyat]

This sentence assumes that every element of the set does not contain itself, which is not included. In an anegdotal format, it was presented like this:

A hairdresser cuts the hair of everyone who doesnt cut it themselves. Does the hairdresser cut his hair?

[Turambar]

Originally posted by Magné:

This sentence assumes that every element of the set does not contain itself, which is not included. In an anegdotal format, it was presented like this:

A hairdresser cuts the hair of everyone who doesnt cut it themselves. Does the hairdresser cut his hair?

You are missing the idea compleatly, man, what you said hasn't nothing to do with the portal sentence, and there are not any nonsense or paradox at your sentence.

A set of everything, can't cointan itself, therefore it can't exist a set of everything. That is the paradox, is like when you say "I am a liar". If you are saying the truth your are lying at the same time, but if you are saying a lie, you are not saying the truth.

[she cyka on my oro til i blyat]

The assumption that a set cannot contain itself is not included. The Russel paradox regards only those sets. He wrote the hairdresser analogy himself, notice how the additional condition must be put seperately.

[Turambar]

Originally posted by Magné:

The assumption that a set cannot contain itself is not included. The Russel paradox regards only those sets. He wrote the hairdresser analogy himself, notice how the additional condition must be put seperately.

That is very cute kiddo, but the fact is that for those AIs such paradox can destroy their brains for sure. And that is nothing to do with reality, is with logical statements, try to learn a little about the "Truth tables" and you will convince you by yourself.

[Turambar]

By the way you even doesn't understand the hairdresser thing, you miss the most important part of the sentence:

one who shaves all those, and those only, who do not shave themselves.

that "all" and that "those only" creates the paradox in that case, what you said wasn't a paradox at all. Because in those sentences that kind of words are the most important part: All, or, if... At your sentence, "everyone" doesn't include the animals.

And yeah, in that example you put the question at other place.

But that doesn't means nothing, you don't need set, in all cases, one conditicion followed by one question to create a paradox.

In the question from portal 2, the afirmative concept inside the question is a paradox itself. To avoid the paradox you should say "A set of all sets can no contain itself". IS not assumption, is "logic". And for sure there are other ways to create thoughts and statments, and with other rules, this sentence couldn't not be a paradox. For sure in Maths there are cases where 2+2 is not equal to 4.

But is evident that GLaDOS and Atlas and P-body, works under the logic rules. And they just can't concive a set that contains itself, so they can't understand even the question.

Sure that question itself in that form is not a paradox, but I repeat that its afirmative idea it is. So the question itself is enought to destroy the robots because that question incudes a paradox.

[Zammy]

Just go check math-people argue over this:
http://math.stackexchange.com/questions/162/why-is-the-set-of-all-sets-a-paradox

Most of that is way over my head. I just enjoyed the game and believed the ingame board that told me to know my paradoxes in case of rogue AI

[Turambar]

Originally posted by G-man:

That logical point of view is just afraid of infinite iterations of all sets within.

It Is not afraid of nothing, dude, logic can't feel, is just a tool for us to set the rules that will rule our statments to make them understable for others. And those rules are not perfect, that's all.

[Turambar]

Another thing, the paradox in the hairdresser case is avoided if the sentence was:

One, but when he is a barber, who shaves all those, and those only, who do not shave themselves. Does the barber shave himself?

[G-man]

But men, who use it, do feel. I heard they had a sence of humor too.

Anyway, since you're making a free-for-all lection out of this, I would like to contribute that paradoxes are bounded with the logic you're operating in. They are dealing with statements and situations, that are or appear to be outside the logic's boundaries. So, it must be made clear what logic is used, to determine whether the statement is paradox or not. Otherwise, logic can be changed to justify the statement, making some other paradoxical instead.

[Kyzer]

Sigh. Pinhead's determined to get his way. I (most likely) will not reply to this discussion again.

A Set of All Sets contains itself because a set of all sets contains all existing sets.

"This sentence is false" is not a paradox either, because nothing would change it from being false. There is nothing to make it true, and it would always be false; hense it has no counter-arguement, which is necessary for paradoxes. Easily why neither GLaDOS nor Wheatley got fried during being exposed to it.

"This sentence is true" is not a paradox either, since nothing exists to make it false. It has no counter-arguement.

A paradox is defined by something that has an answer that is not logically acceptable. A counter-arguement is required to get an answer.

[Styx]

no,really,if it does,THAT would be a paradox .