### Single Idea 8921

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

Full Idea

With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do.

Gist of Idea

Structuralism is now common, studying relations, with no regard for what the objects might be

Source

Geoffrey Hellman (Structuralism [2007], §1)

Book Reference

'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.537

A Reaction

Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed.