### Single Idea 15497

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets]

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]**