Single Idea 8751

[catalogued under 6. Mathematics / C. Sources of Mathematics / 7. Formalism]

Full Idea

It is applicability alone which elevates arithmetic from a game to the rank of a science.

Gist of Idea

Only applicability raises arithmetic from a game to a science

Source

Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.147


A Reaction

This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism.