more from Gottlob Frege

### Single Idea 9956

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle]

Full Idea

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

Gist of Idea

'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F'

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

Presumably this means equinumerous with 'instances' of F, if F is a predicate. The problem of universals looms. I was clear about this idea until I tried to draw a diagram illustrating it. You try!