more from Gottlob Frege

Single Idea 9886

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number]

Full Idea

The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity.

Gist of Idea

Cardinals say how many, and reals give measurements compared to a unit quantity


Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], 157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.246

A Reaction

We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals.