Full Idea
Given the theory of part and whole, the member-singleton relation may replace membership generally as the primitive notion of set theory.
Gist of Idea
We can replace the membership relation with the member-singleton relation (plus mereology)
Source
David Lewis (Parts of Classes [1991], Pref)
Book Reference
Lewis,David: 'Parts of Classes' [Blackwell 1991], p.-3
A Reaction
An obvious question is to ask what the member-singleton relation is if it isn't membership.
Related Idea
Idea 15496 We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis]