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| quote: | Originally posted by Noisician
well, if you want to get all technical about that, then the answer really depends on which set theory you base your explanation upon. for example, in zermelo-fraenkel set theory (the one adopted almost universally), the expression "set of all sets" makes no sense whatsoever because in zf such a thing simply does not exist. there's only the CLASS of all sets, and it actually happens to be a proper class (i.e. it's NOT a set). therefore, it cannot be a member of itself because a proper class is NOT an object. this is a direct consequence of the axiom of separation (aka axiom of subsets). for the same reason the entire universe of discourse cannot possibly be a set. it's a proper class as well. and for that matter, we can also prove that the class of all ordinals is not a set. etc. |
Nice explanation. I should study some set theory. In any case, it's not interesting for the same reason that Russell's Paradox is.
As for the continued debate for the chicken vs. egg... it's already solved. Depending on how you define an egg (something that gives birth to a chicken or something that a chicken lays), the problem vanishes immediately. If one defines a chicken egg to be "an egg that yields a chicken," then yes, the egg came before the chicken by definition. The silly question "but then what laid THAT egg" becomes moot. Either a chicken laid it, in which case the chicken came from the egg (by defn), or something else laid it, in which case there's still no paradox. If you define it to be "something that a chicken lays," then the chicken came first.
It's a purely logical argument that sidesteps evolution.
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