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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