more from Immanuel Kant

Single Idea 8740

[catalogued under 6. Mathematics / A. Nature of Mathematics / 2. Geometry]

Full Idea

Were it not for the connection to intuition, geometry would have no objective validity whatever, but be mere play by the imagination or the understanding.

Gist of Idea

Geometry would just be an idle game without its connection to our intuition


Immanuel Kant (Critique of Pure Reason [1781], B298/A239), quoted by Stewart Shapiro - Thinking About Mathematics 4.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.90

A Reaction

If we pursue the idealist reading of Kant (in which the noumenon is hopelessly inapprehensible), then mathematics still has not real application, despite connection to intuition. However, Kant would have been an intuitionist, and not a formalist.