Single Idea 9831

[catalogued under 6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics]

Full Idea

The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.

Gist of Idea

Geometry appeals to intuition as the source of its axioms

Source

Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.68


A Reaction

Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.