more on this theme     |     more from this thinker     |     more from this text

Single Idea 9564

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero ]

Full Idea

In Frege's system 'concept' and 'extension of a concept' are primitive notions; whereas 'zero' and 'successor' are defined.

Gist of Idea

For Frege 'concept' and 'extension' are primitive, but 'zero' and 'successor' are defined

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Charles Chihara - A Structural Account of Mathematics 7.5

Book Ref

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.204

A Reaction

This is in contrast to the earlier Peano Postulates for arithmetic, which treat 'zero' and 'successor' as primitive. Interesting, given that Frege is famous for being a platonist.