Talk:Set is Not Element of Itself

It needs to be pointed out that this result is true only in axiomatic structures of set theory which specifically include the Axiom of Foundation.

Ongoing, we will need to be precise about the exact axiomatic framework into which these statements are made. (This one is clearly a direct result of AoF, of corse.)

I mention this because there is something called "non-standard set theory" which is mentioned by Devlin in his The Joy Of Sets (I got bogged down when I started working through this by philosophical discussions that I was not confident enough to continue with) in which the Axiom of Foundation is not one of the axioms -- it's a version of Set Theory which has applications to graph theory. --prime mover (talk) 18:36, 8 May 2017 (EDT)


 * Unless it's something that isn't in ZF, I don't like specifying the use of axioms. Things like Foundation and the Law of Excluded Middle are used so often that it would get kind of annoying to do that for everything that uses it.


 * However, if what you say is true and there are applications of negating Foundation in Computer Science and stuff like that then I agree with you wholeheartedly. It should also be mentioned when one rejects the axiom, but I don't think there is any material on this site like that. At least not yet anyway. --HumblePi (talk) 19:03, 8 May 2017 (EDT)


 * "I don't like specifying the use of axioms" -- I'm sorry, but in this case it needs to be done.


 * I see you have added that AoF template, which is a start -- but there's something more that needs to be done, the name of the page would need to be amended so as to distinctly state that the limitations of the result. --prime mover (talk) 01:33, 9 May 2017 (EDT)