Full Idea
There are some proposals for non-well-founded set theory (tolerating cases of self-membership and membership circularities).
Gist of Idea
Maybe set theory need not be well-founded
Source
Achille Varzi (Mereology [2003], 2.1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.5
A Reaction
[He cites Aczel 1988, and Barwise and Moss 1996]