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On 17/02/2014 06:21, Steven D'Aprano wrote: > On Mon, 17 Feb 2014 11:54:45 +1300, Gregory Ewing wrote: >> [...] >> >> [1] Mathematicians tried this. "Everything is a set!" Yeah, right... > > No, that's okay. You only get into trouble when you have self-referential > sets, like "the set of all sets that don't contain themselves". Actually there's nothing wrong with self-referential sets per se. For example set theory with Aczel's anti-foundation axiom instead of the axiom of foundation is consistent if ZF is; see e.g. http://en.wikipedia.org/wiki/Non-well-founded_set_theory The trouble comes not with self-reference, but with unrestricted comprehension.

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