more from Michael D. Resnik

### Single Idea 6300

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

Full Idea

In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern.

Gist of Idea

Mathematical constants and quantifiers only exist as locations within structures or patterns

Source

Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [OUP 1999], p.201

A Reaction

This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns.