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Originally Posted by WithoutMe Ok... how can u solve a paradox? If its a Paradox, then its unsolvable, & if u have solved, then it means that u have solved something that corresponds to the idea that u have of the problem in the paradox, but not the paradox itself, coz "by solving a paradox" wud mean that the paradox is solvable, so how come it is a paradox.... so if anyone claims that s/he demystefied a mystery, it just cannot be a true, coz all such talk of INVERTING, like "demystefied the mytery", "solving a paradox", "talking the untalkable" & all such will but always be a greater paradox... a sort of metaparadox, i.e., the paradox of the paradox being a paradox but simultaneously being able to be no more a paradox (coz its being solved now)!!!!
Similarly, the meta-paradox will have another paradox of its own... thus, existence in its very nature is like the scales of a Onion, with paradoxes reeling on on another -- paradox with the meta-paradox, the meta-paradox with the meta-meta-paradox.... ad infinitum!
Hell! If any of you reading this have been able to understand any but & have been able to solve the mystery (which I am trying uselessly) of existence by reading abt this "meta-meta-...-paradox...ad infitum", then that wud mean that the idea is not a paradox, hence another paradox. Now, if u try to avoid it, then that wud mean that it is avoidable, again a paradox, & if u accept it, u'll have a jump to the next level of "meta"-paradox..... thus, paradoxes all the way, even in the way I am expressing myself!!!! |
It is a paradox because we can not know whether the empty set contains itself or not. We know that the empty set does not contain what it is not, because then it would not be empty. However, we can't decide if the empty set theoretically contains itself or not. So I have simplified RUssell's Paradox to show that all sets which do not necessarily contain themselves form the empty set, and we can not tell whether the empty set contains itself or not. Luckily, we don't have to worry about Russell's Paradox anymore because we can realize that it is an irrelevant question about nothing (literally the empty set). That is why I say I have solved the Paradox, because I have shown it's irrelevancy.
However, in simplifying the paradox, I have discovered it's other half. The other half of the paradox states that the full set does contain itself (this is the solution to Russell's other paradox) but that we cannot tell if it contains the empty set or not. In other words, we can not tell if the complete set contains what it is not, but we can tell that it contains what it is. Again, the original part is that we know that nothing cannot contain what it is not, but we cannot tell if it contains what it is.
Basically the entire paradox is asking the question, is the empty set a true set, and if so is the complete set complete without it? The answer is that the answer is irrelevant.