### Single Idea 9558

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

Full Idea

If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.

Gist of Idea

All scientific tests will verify mathematics, so it is a background, not something being tested

Source

Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.128

A Reaction

This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.