more from Geoffrey Hellman

Single Idea 8922

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism]

Full Idea

There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'.

Gist of Idea

Maybe mathematical objects only have structural roles, and no intrinsic nature

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

This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics.