### Single Idea 13417

#### [catalogued under 7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems]

Full Idea

If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics.

Gist of Idea

If a mathematical structure is rejected from a physical theory, it retains its mathematical status

Source

Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)

Book Reference

-: 'Philosophia Mathematica' [-], p.224

A Reaction

This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course.