more from Michael D. Resnik

Single Idea 6303

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

On my view, sets are positions in certain patterns.

Gist of Idea

Sets are positions in patterns


Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [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.