Single Idea 10028

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

Full Idea

Frege defines 'the number of F's' as the extension of the concept 'equinumerous with F'. The extension of such a concept will be a collection of first-level concepts, namely, just those that are equinumerous with F.

Gist of Idea

For Frege the number of F's is a collection of first-level concepts

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.30


A Reaction

This must be reconciled with Frege's platonism, which tells us that numbers are objects, so the objects are second-level sets. Would there be third-level object/sets, such as the set of all the second-level sets perfectly divisible by three?