Russell's Paradox - a simple explanation of a profound problem

I always tell the truth and I tell you that I always lie.

Mentions of LeBron so many times became a distraction. Is that what you wanted?

This reminiscent of Schrodinger's cat and Goedel's theorem.

Everything I write is a lie.

Hm... I still don't really get what the huff is about then. I mean.. ok, we got contradictions, but why does this make adults faint?

Its like the old barber in the village that shaves the beard of everyone who does not shave himself - does he shave himself? paradox. So what?

Enormous is the measurement not the pile

I thought a number is a measurement of objects or ideas.

Predocates taste like chicken

I have just a a brain fart. 🤪 I got about half way and the word “set” broke me. 😫

Languages are meant to enslave and control That's why they were designed in the first place.

Might as well Just steady condums while you're at it

It's all your own mind perception. Some people are capable to tap into a wider range of perception.

Until I saw this video, I was convinced that I was set in my ways.

To quote The Guard, "Bertrand Russel was Welsh"

Futility. Useless information, only in my opinion. I have a set of guitar strings. There are six strings. So what?
Has this info evolved humanity?

Take a shot everytime he says "set"

Set

i use sets all the time in programming, thanks

Wow. I think you just broke me.

I can't see why there must be correspondence between predicates and set theory.

My father was F.W. Lawvere, who recently passed away, and I have always wanted to understand his branch of math better. Would you consider doing a video on Category theory?

A rule is a restriction. Saying something "can be" is not a rule. It's a possibility which itself contains two possible outcomes, as well as all possible outcomes. A thing either is or isn't something, and... uh oh. Quantum theory. I am surprised that with all that talk about cats, Schrödinger's name didn't crop up. What a great presentation though. I really enjoy your explanation and communication skills!

A couple thoughts on this:
Perhaps I missed it, but in what way were all 11 rules derived from the concept of predication? It just seems like you're applying the rules of set theory because they happen to work with predication, not due to some fundamental emergence of rules. You're effectively still only making up rules, in which case they can just be wrong or incorrectly formed.

Rule 11 is that they "can" contain or be true of themselves, not that they must. Whether they do, or do not, does not break the rule. Technically, these paradoxical sets are only breaking the logic used to generate their contents, they are not breaking the concept of sets or predicates.

If the paradox must be resolved, instead of removing Rule 11, you could modify Rule 1 to exclude sets that impose restrictions on self-referential sets. You could also add some Rule 12 to alleviate the issue such as: There can exist paradoxical sets that only contain themselves when they don't, and vice versa. (I would personally call these "harmonic" sets)

Im not sure that the three words “is a cat” are necessarily a predicate since they could also be used in a question “is a cat fun?” So “is a cat” are three dangling words with no context. In order to declare that they are a predicate, you would need to say “I have a predicate, and that predicate is “is a cat.”” But then you throw it in a sentence “is a cat is a cat” and say that sentence is a predicate of a predicate and yet now it is the subject, but a predicate at the same time? Where is my nobel prize? No autographs.

Real life Sheldon?

I wonder how the followers of "Set" will receive this? Said Ra as he ran the numbers.

Somewhere some calculus student is really flipping out and just writing 0 on all their math tests

As a mathematician, I believe that math is made up to describe what we see or sense. We make it make sense by definition. There are numerous paradoxes, such as zero to the zero power.

Holy fuckin holy fuck

Much ado about nothing.

"Self-referential" is self-referential. But is "non self-referential" non self-referential?

Another simple paradox I could solve in my sleep. And I have.

I shouldn't have clicked on this at 8pm. 2 minutes in I woke up in the morning having not gotten anything done I needed to.

But why? How do sets help mankind?

This just seems like quantum mechanics manifesting in foundational mathematics. I don't know if that sentence makes sense, but this video reminds me of all the wonky things in quantum mechanics.

This was so boring

Remarkable of the set of Sh..t that some people can think with out having a computer!

I have a problem with this. A predicate that is turned around and used as a subject is no longer the original predicate, but becomes an alias used to refer to the predicational usage of the original predicate. "Is a cat" is not the same as the predicate of the "Garfield is a cat" sentence. It goes back to the original statement that "4", the Arabic numeral used as an alias for a 4-member set, is not 4 things, just an alias.

How 'bout this Mr. Kaplan: "The following statement is true. The previous statement is false."

I prefer sex to sects.

The solution to the "paradox" must surely be, for all rules to apply we will need an infinite amount of rules.
That is the core of theoretical mathematics and, in my opinion, its misinterpretation is why mathematicians takes paradoxes like Schrödinger's cat too literally. Hence, a paradox is merely a lazy solution to a problem or cause we don't understand. If I don't understand basic maths, 1x2 will always be a paradox.

I really was enjoying the video until the 8th time I heard LeBron James, then I couldn't take any more and punched out.

Is this apply on what is a woman ?

I think Kaplan confuses convention and logic. Logic is subordinate to convention. And if convention permits infinite possibilities, then the logic has infinite possibilities.

I don't understand. Why does the set with all non-self-containing sets have to contain itself

NUMBER 4 IS NOT A THEORY, IT IS A FACT,,,,,,,,AND IF YOU SELL ONE OF YOUR 4 EGGS YOU ARE LEFT WITH 3 EGGS,,,,,,,,,,THATS NOT A THEORY , ITS A FACT. NO PROBLEM AT ALL.
IF YOUR THEORY DOESNT WORK THEN ITS A MISTAKE NOT A THEORY.

I didn't get why it is a paradox, can somebody explain me it please?

What I get is that the paradox should be the problem that a set{x:x is a set that does not contain itself} should be in itself, but when it does, it would be a paradox.
Wouldn't a set which does not contain itself be a set of everything else but itself?
Just because a set can contain itself doesn't mean it has to. Rule #11 says can which does not imply have to.
So when you say you build a set of sets which doesn't contain itself, than you build a set of sets which doesn't contain itself. Rule #1 only lets the possibility of each combination.
When you have two groups of sets a set b which contains itself and a set c which does not, then the moment set c would contain itself it would switch to the group in which set b is. But per definition of set you are not required to include the set itself in itself, because rule #11 says "... can contain itself".
How I understand it, the problem is more in the language. Trying with limited word to describe a abstract concept for that this words never really intended for this type of explanation.

Perhaps an other why to explain my thoughts is you have a set a which does not contain itself, in the moment you contain the set a in itself, the original set a becomes b containing the set a (rule #2, because the sets are not equal), which does not contain itself, in the moment you contain b in itself, the original set b becomes c containing the sets a and b, and so on... per definition of the sets content "it does not contain itself" it will never contain itself. I would describe this as a set containing a infinitive number of sets which are not itself. And by rules you are never forced to include the set itself. Rule #1 only describes the basic behaviour of sets and is overwritten at the moment you say "I have a set{x:x is a set that does not contain itself}", at this moment you set a restriction for the set.

Well this is how I understand the definition of sets, I could be wrong cause math is my archenemy since it started to use characters and symbols instead of numbers. So when somebody could explain me why my thoughts are wrong, that would be nice.

I'm sorry for my bad translation. I'm not sure if I could write down my thoughts that well in a foreign language, that somebody could understand what I wanted to describe.