more from Willard Quine

Single Idea 18198

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics]

Full Idea

The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems,

Gist of Idea

Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted

Source

Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.105


A Reaction

The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted?

Related Idea

Idea 18200 Very large sets should be studied in an 'if-then' spirit [Putnam]