Single Idea 8741

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

Full Idea

All numbers must be numbers of something: there are no such things as numbers in the abstract.

Gist of Idea

Numbers must be of something; they don't exist as abstractions

Source

John Stuart Mill (System of Logic [1843], p.245?), quoted by Stewart Shapiro - Thinking About Mathematics 4.3

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.95


A Reaction

This shows why the concept of 'abstraction' is such a deep problem. Numbers can't be properties of objects, because two boots can become one boot without changing the surviving boot. But why should abstractions have to 'exist'?