more from George Cantor

Single Idea 8631

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism]

Full Idea

Cantor calls mathematics an empirical science in so far as it begins with consideration of things in the external world; on his view, number originates only by abstraction from objects.

Gist of Idea

Cantor says that maths originates only by abstraction from objects


report of George Cantor (works [1880]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) 21

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.27

A Reaction

Frege utterly opposed this view, and he seems to have won the day, but I am rather thrilled to find the great Cantor endorsing my own intuitions on the subject. The difficulty is to explain 'abstraction'.