Single Idea 16930

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

Full Idea

No principle of pure geometry is analytic. That the straight line beween two points is the shortest is a synthetic proposition. For my concept of straight contains nothing of quantity but only of quality.

Gist of Idea

Geometry is not analytic, because a line's being 'straight' is a quality

Source

Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 269)

Book Reference

Kant,Immanuel: 'Prolegomena to Any Future Metaphysic', ed/tr. Lucas,Peter G. [Manchester UP 1971], p.20


A Reaction

I'm not sure what his authority is for calling straightness a quality rather than a quantity, given that it can be expressed quantitatively. It is a very nice example for focusing our questions about the nature of geometry. I can't decide.