Russell's Paradox

[zeroca]

Yes, I read your post and enjoyed discussion. Empty set is only one example of binary sets; the second one could be given by Guille above example:

Let's consider that set A is the set of all the sets that can be described with less than 10 words. I have described set A with 16 words, which is more than 10 words, and so, it doesn't enters the requiermnets of itself (being described with more than 10 words) and so it doesn't contains itself. Now, let's consider set R the set of all sets that don't contain themselves. Such as the set of all dogs (which isn't itself a dog) or the set previously described (set A). Then, doesn R contain itself? If it contains itself, it must not contain itself, and if it doesn't contain itself, it must contain itself.

i.e. the set, that contains all sets, each of which doesn't contain iself, is the example of binary set according to the definition above.
All this is too vague...

[Guille]

Yes, I read your post and enjoyed discussion. Empty set is only one example of binary sets; the second one could be given by Guille above example:

i.e. the set, that contains all sets, each of which doesn't contain iself, is the example of binary set according to the definition above.
All this is too vague...

I agree and understand what you say. But why is this all too vague?

[zeroca]

I like everything to be too clear to me. I always fight with myself and strain all my abilities until I have subject clear to me. I know, when I can not explain things the way, that every part of explanation is logical and simple for everybody, it means that subject is unclear to me. The same is with the example above, the truth I didn’t intend to solve Russel’s paradox - I have restricted capabilities. Only wanted to relax and switch on different subject. Accepted by me binary set was something composed on the spur of the moment to explain the faults of definitions quickly.

[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...

[Guille]

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...

For sub, it's that the set of all sets that odn't contain themselves is an empty set for all sets contain themselves and the question whether an empty set contains itself for not is irelevant.

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.

But still I believe Russell's paradox is not solved. The accepted solution of the paradox by mathematicians and logicians is that there is not set of sets, for these are called type, and then they went into classes, groups... Too many complications for being the foundations of mathematical logic.

[subversion]

Yes you are right, and thank you for stating my solution correctly. Also I want to say that I think that Zeroca's solution and my solution are really the same thing and I'll say why in a minute but first I want to talk about the (in my opinion false) accepted solution that Guille mentioned.

Basically I was talking to my friend Owney who is a math major and he said that modern mathemeticians don't really solve the paradox, but rather they go around it by making up a false idea, which is what GUille said, the idea of a type, a type being different then a set. Now I'm not totally sure but the definition of a type is that it is like a set but it can be allowed to be the set of all sets that do not contain themselves. The problem is this does not really exist. It is the empty set and emptiness is not a type at all, it is a lack of type. Hence I say false idea because we are equating nothing with something which it is not.

Here's why and here's where I get into the fact that Zeroca's proof and my proof are the same in my opinion. Let's take an example. Let's say this is the set that contains all sets that can not be described by words. Therefore that sentence is not one of the sets, but the sentence still describes itself, because all sentences describe themselves by being sentences. Another way to put this is that all things contain themselves in order to exist. So even though the sentence which we use to label the set of all sets which are not described by words is itself not something not described by words, it still refers to a set which contains itself in order to exist. In this manner the proof that something exists is that something must contain itself. Anything which does not necessarely contain itself must not exist. Therefore anything which does not contain itself is what we call the empty set, or simply just 0. Therefore I say that any binary set has to be the empty set because something has to be itself in order to exist but the empty set is nothing so it is not necessarely itself or not. That's why I'm saying that mine and zeroca's proof are the same because I'm saying that the empty set is the only binary set, or rather that any binary set must be the empty set. But perhaps someone else would like to offer comment.

ps. Owney described the empty set to me as all things which are not themselves, which to me must be nothing

[harmonygirl]

Let's say this is the set that contains all sets that can not be described by words. Therefore that sentence is not one of the sets, but the sentence still describes itself, because all sentences describe themselves by being sentences.

I am not sure I agree with your conclusion. All sentences exist by being sentences, but that does not mean they describe themselves. The word 'sentence' is just a label to which we have arbitrarily ascribed meaning.Are you saying that each manifestation of 'reality' describes itself by existing?

[subversion]

Are you saying that each manifestation of 'reality' describes itself by existing?

yes, everything which exists serves as it's own description.

[harmonygirl]

but only by language and labels that we have imposed, not by any intrinsic meaning. What, after all, is a sentence?

[Guille]

yes, everything which exists serves as it's own description.

Really? If the TOE exists, and I belief it exists, and I belief you belief also that it exists, then it should show itself directly, we wouldn't have to make any effort. Such a world would be so easy-going... Bad luck I guess, we have to live in this one.