Single Idea 18199

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

Full Idea

We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.

Gist of Idea

Indispensability strongly supports predicative sets, and somewhat supports impredicative sets

Source

Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2

Book Reference

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


Related Ideas

Idea 18135 If mathematics rests on science, predicativism may be the best approach [Bostock]

Idea 8747 Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro]

Idea 18134 Predicativism makes theories of huge cardinals impossible [Bostock]