Single Idea 15500

[catalogued under 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST]

Full Idea

A class divides exhaustively into subclasses in many different ways; whereas a class divides exhaustively into members in only one way.

Gist of Idea

Classes divide into subclasses in many ways, but into members in only one way


David Lewis (Parts of Classes [1991], 1.2)

Book Reference

Lewis,David: 'Parts of Classes' [Blackwell 1991], p.5

Related Ideas

Idea 13443 ∈ relates across layers, while ⊆ relates within layers [Hart,WD]

Idea 13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]

Idea 12337 There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]

Idea 15499 A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]