[zeroca]

Originally Posted by harmonygirl

okay, I may be missing something, why would the realization of a zero set "solve" Russells paradox? It doesn't address the set of all sets contain itself question...

Originally Posted by <<>>

For Zeroca, the idea of binary set which he develops and wabout which I have big doubts leads to the set of all empty sets contains the set of all sets that don't contain itself and therefore is a set of empty set's, sub interprets this is also being an empty set

Originally Posted by subversion

wow! Good job zeroca. That's the exact same solution I came up with in my post Russell's Paradox no more. Essentially I said that Russell's paradox is a question about the empty set and it is irrelevant to ask whether or not the empty set contains itself, which is the same thing that you just said but in different terms. That must mean that our solution is correct! I give us both a pat on the back. I don't know why my thread was moved to the your toe theory section. Can we put it under mathematics please?

I think I was misinterpreted:
----I didn’t say that empty set is the solution of Russel’s paradox. I say that empty set isn’t the solution of Russel’s paradox. The set, which doesn’t contain itself isn’t empty set: for instance the set, called “unity”, the name of which is described with five letters and is the set of names described with four letters (i.e. the set-“unity” doesn’t contain itself) isn’t empty set, but is the set of elements: “mama”, “papa”, “home” etc… And the set of all such sets can’t be empty set, as it isn’t collection of empty sets, but is collection of sets, each of which isn’t empty.
--But I pointed out the ground for solution of paradox, when mentioned, that the possible answer must be of a binary nature like an empty set, and it wasn’t me who adopted a conception of a binary set. I was one of them, who noticed a binary nature of empty set: empty set doesn’t contain itself, as it doesn’t contain elements, but at the same time it contains itself, as it (as consisting element) is empty.
---I also noticed that at the stage of definition of sets mutually exclusive suppositions were made:
1. A set can be thought of as any collection of distinct things considered as a whole.
2. Empty set is the unique set which contains no elements.
I think that conception of empty set needs to be revised. I’ll try to explain on the example of universe: if universe was defined as something that consists of one, or infinite number of elementary particles, then the universe ceases to exist at once when there isn’t even any single elementary particle. We can not say – empty universe to characterize such state, i.e. complete absence of elementary particles, i.e. complete absence of universe can’t be called empty universe, so
I wanted to show that wrong definitions lead to wrong conclusions.
Anyway, under a present condition of sets’ definition, we can seek solution of paradox, i.e. under present conditions it is solvable.
Russel’s paradox, as I understood, consists in following:
If the set-A of all sets-B (each of which is “self-not-contained”) doesn’t contain itself, then we must include A among other B sets; if we include A among others, then it becomes the set, which contains itself, so we must exclude it from the list of B sets.
I’ll try to solve paradox with illustrative examples:
At starting stage let’s take a set of all possible sets, all possible variants of sets and call it universal set. As you see, universal set contains in itself all existing sets (infinite variants of sets).
----Let’s take a set A, which is collection of all names, each of which consists of four letters, and let’s call this set “Home”. Home is example of the set, which contains itself as element, because its name also is composed of four letters.
----Let’s take a set B, which is the collection of all names, composed of four letters, and let’s call it “Unity”. “Unity” is the example of the set, which doesn’t contain itself as element, as mandatory for including within itself is that its name must be composed of four letters.
----Let’s take a set B1, which is the collection of all names, composed of five letters, and let’s call it “Unito”. “Unito” is the example of the set, which contains itself, and at same time “Unito” contains the set B, called “Unity”, as the name of latter is composed of five letters (and which is self-not-contained).
----Let’s take a set A2, which is the collection of names, composed of five letters, and call it “Mama”. “Mama” is the example of sets, which doesn’t contain itself, but it contains the set “Unito”, as it’s the collection of all five-letter names (and which is self-contained).
I.e. any set within universal set is represented in two forms: when it is consisting part of self-comtained and part of self-not-contained sets. The “trick” of Russel’s paradox consists in following: when you take the set of all sets, each of which doesn’t contain itself, you take at the same time all sets, each of which contains itself:
In our example:
When you are collecting all self-not-contained sets and take a set “Unity” (which is the example of the set, which doesn’t contain itself), you should remember that “Home” is consisting element of “Unity” (and “Home” is the example of the set, which contains itself and you can’t “touch” it, in spite of the fact that you need it, as it is consisting element of “unity”), you can’t as well “touch” the set “Mama”, as you take at once all its consistent five-letter-named sets, each of which are self-contained i.e.
You can not take separately a set of all sets, each of which doesn’t contain itself; you at once infringe the right of all sets (or parts of them), each of which contains itself, as they both are organic consisting parts of each-other.
I.e. any set (be it self-contained, or self-not-contained) is represented in two different forms of sets within universal set: within some sets- as part of self-contained, within another sets- as part of self-not-contained (for instance, the set “Mama” is the part of “home”, which is self-contained, but the same “Mama” ” is the part of “Unity”, which is self-not-contained)
I.e. Set of all set’s (each of which doesn’t contain itself)=Set of all sets (each of which contains itself)=Universal set. As universal set has the binary nature, so it can serve as a solution of Russel’s paradox.
I.e. the solution of Russel’s paradox can be:
You can’t collect all self-not-contained sets separately within one set, as you at once take all self-contained sets together with them, as they are consisting parts of each-other.