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
Source
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]