Single Idea 8640

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

We cannot define number by the generalized concept of a series. Positions in the series cannot be the basis on which we distinguish the objects, since they must already have been distinguished somehow or other, for us to arrange them in a series.

Gist of Idea

We cannot define numbers from the idea of a series, because numbers must precede that

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §42)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.54


A Reaction

You can arrange things in a line without the use of numbers. You need prior mastery of counting, though, to say where an item comes in the line. And yet... why shouldn't you define counting by the use of some original primitive line? Numbers map onto it.