more from Gottlob Frege

Single Idea 9889

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton).

Gist of Idea

Real numbers are ratios of quantities


report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.261

A Reaction

If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'?