### Single Idea 8757

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

There is one and only one serious argument for the existence of mathematical entities, and that is the Indispensability Argument of Putnam and Quine.

Clarification

The argument is that science requires mathematics

Gist of Idea

The Indispensability Argument is the only serious ground for the existence of mathematical entities

Source

Hartry Field (Science without Numbers [1980], p.5), quoted by Stewart Shapiro - Thinking About Mathematics 9.1

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.227

A Reaction

Personally I don't believe (and nor does Field) that this gives a good enough reason to believe in such things. Quine (who likes 'desert landscapes' in ontology) ends up believing that sets are real because of his argument. Not for me.