Explanation of list reference

Rotwang sg552 at hotmail.co.uk
Mon Feb 17 19:24:35 CET 2014


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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