Single Idea 15496

[catalogued under 4. Formal Logic / F. Set Theory ST / 1. Set Theory]

Full Idea

The notion of a singleton, or unit set, can serve as the distinctive primitive of set theory. The rest is mereology: a class is the fusion of its singleton subclasses, something is a member of a class iff its singleton is part of that class.

Gist of Idea

We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton


David Lewis (Parts of Classes [1991], Pref)

Book Reference

Lewis,David: 'Parts of Classes' [Blackwell 1991], p.-4

A Reaction

This is a gloriously bold proposal which I immediately like, because it cuts out the baffling empty set (which many people think 'exists'!), and gets mathematics back to being about the real world of entities (as the Greeks thought).