more from Michael D. Resnik

Single Idea 6302

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism]

Full Idea

An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points.

Gist of Idea

Structuralism must explain why a triangle is a whole, and not a random set of points

Source

Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [OUP 1999], p.213


A Reaction

This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns.