Full Idea
On my view, sets are positions in certain patterns.
Gist of Idea
Sets are positions in patterns
Source
Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5)
Book Reference
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.218
A Reaction
I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties.