Single Idea 6104

[catalogued under 6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics]

Full Idea

Numbers are classes of classes, and classes are logical fictions, so that numbers are, as it were, fictions at two removes, fictions of fictions.

Gist of Idea

Numbers are classes of classes, and hence fictions of fictions

Source

Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII)

Book Reference

Russell,Bertrand: 'Russell's Logical Atomism', ed/tr. Pears,David [Fontana 1972], p.129


A Reaction

This summarises the findings of Russell and Whitehead's researches into logicism. Gödel may have proved that project impossible, but there is now debate about that. Personally I think of numbers as names of patterns.