Full Idea
Lesniewski distinguished the part-whole relationship from class membership. Membership is not transitive: if s is an element of t, and t of u, then s is not an element of u, whereas a part of a part is a part of the whole.
Gist of Idea
Class membership is not transitive, unlike being part of a part of the whole
Source
report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7
Book Reference
'A Companion of Philosophical Logic', ed/tr. Jacquette,Dale [Blackwell 2002], p.45
A Reaction
If I am a member of a sports club, and my club is a member of the league, I am not thereby a member of the league (so clubs are classes, not wholes). This distinction is clearly fairly crucial in ontology.