### Single Idea 10191

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

Lewis has shown that set theory may be reduced to a mereological theory in which singletons are the only atoms.

Gist of Idea

Set theory reduces to a mereological theory with singletons as the only atoms

Source

report of David Lewis (Parts of Classes [1991]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.80

Book Reference

-: 'Bulletin of Symbolic Logic' [-], p.80

A Reaction

Presumably the axiom of extensionality, that a set is no more than its members, translates into unrestricted composition, that any parts will make an object. Difficult territory, but I suspect that this is of great importance in metaphysics.