more from Michèle Friend

### Single Idea 8696

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / c. Nominalist structuralism]

Full Idea

According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines.

Gist of Idea

Structuralist says maths concerns concepts about base objects, not base objects themselves

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1)

Book Reference

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.82

A Reaction

This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world.