more from Gottlob Frege

### Single Idea 9856

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

In standard set theory, Frege's cardinals could not be members of classes, and his proof of the infinity of natural numbers fails. Nowadays they are defined as sets each representative of its cardinality, comprising ordinals of lower cardinality.

Gist of Idea

Frege's account of cardinals fails in modern set theory, so they are now defined differently

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.14

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.168

A Reaction

Pinning something down in a unique way is not the same as telling you its intrinsic nature. But a completely successful definition seems to have locked on to some deep truth about its target.