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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 Ref
'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]
| 10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
| 10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
| 10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
| 10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
| 10653 | Maybe set theory need not be well-founded [Varzi] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
| 10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| 10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
| 10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |