more from Gottlob Frege

Single Idea 9890

[catalogued under 18. Thought / E. Abstraction / 3. Abstracta by Ignoring]

Full Idea

From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity.

Gist of Idea

The modern account of real numbers detaches a ratio from its geometrical origins


Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], 159), quoted by Michael Dummett - Frege philosophy of mathematics

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.262

A Reaction

Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid.