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Originally Posted by <<>> Sub,
It's an original approach but I logicworld is incompatible with originalityworld. There is a difference between being and containing. Containing is an external relationship, if something contains itself it is from an external condition, just as if it contains any other thing. But being is the thing itself, it is nothing if it doesn't be, it is to be, that's all. |
Good point Guille, the proof does rely on the definition that something always contains itself and that nothing is irrelevant to the notion of contents. In other words, whether nothing contains itself or not is an irrelevant and meaningless question according to the definition of nothing which is that it has no value and no contents. For clarity, we should arbitrarily say that nothing does not contain itself, because something does contain itself and this way we define the two "things" as different. However we always remember that in reality you cannot truely answer the question of whether nothing contains itself or not because the question is irrelevant to the definition of nothing.
Furthermore I think it is a good definition of something to say that something is something that exists and since it exists that means it is it's own contents. Therefore it does contain itself in a very technical sense. The definition of containing would be that for something to contain something most efficiently (i.e. with the least wasted space) it must be the same thing. This is a special case of containing in which the container is more than infinitely close to it's contents because they are the same thing. So if we accept these definitions, and I do think they are good definitions, then we have a solution to Russell's Paradox and we also have a new definition of set theory.
Here is the new definition: Sets are defined as something which contain themselves. The empty set is the one set that does not necessarily contain itself and thus the empty set is really a false set and should not be defined as a set but as a not set. Defining the empty set as a true set was a mistake by Set theorists and if they adopt this new definition of set it will probably help them out. Not that they'll ever read this but you know, I try.