Ripheus23
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"The set of all sets," is a paradox because we interpret it as, "The set that results from the last use of the powerset operation." But there is no last powerset operation. Accordingly, the concept of the set of all sets doesn't violate the powerset operation, but is founded differently, as in class or category or type or what-have-you theory...
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Because our sense of sets depends on the notation, we would think "{all sets}" as the set of all sets. But we know that we can make {{all sets}}, {{{all sets}}}, and so on, so... Arguably, the idea would have to be in this case that the mere notation of }}} and {{{, used here, adverts back to the American English phrase "all sets," that is the two sets(!) of symbols have the same meaning...
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