more from Gottlob Frege

Single Idea 18181

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

Full Idea

My definition is as follows: the Number which belongs to the concept F is the extension of the concept 'equal to the concept F' [note: I believe that for 'extension of the concept' we could simply write 'concept'].

Gist of Idea

The Number for F is the extension of 'equal to F' (or maybe just F itself)


Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 68)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.79

A Reaction

The note has caused huge discussion [Maddy 1997:24]. No wonder I am confused about whether a Fregean number is a concept, or a property of a concept, or a collection of things, or an object. Or all four. Or none of the above.

Related Idea

Idea 18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]