more from Gottlob Frege

Single Idea 13897

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

Full Idea

In Frege's definition of numbers, each number, except 0, is defined as the number belonging to the concept under which just its predecessors fall.

Gist of Idea

Each number, except 0, is the number of the concept of all of its predecessors


report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 4.xvii

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.136

A Reaction

This would make the numbers dependent on all of the predecessors, just as Dedekind's numbers do. Dedekind's progression has to continue, but why should Frege's? Frege's are just there, where Dedekind's are constructed. Why are Frege's ordered?