more from Immanuel Kant

Single Idea 3343

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

The possible denial of the parallel lines postulate does not entail that Kant was wrong in considering Euclid's the only viable geometry. If the denial issued in a contradiction, then the postulate would be analytic, and Kant would be refuted.

Gist of Idea

Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction

Source

comment on Immanuel Kant (Critique of Pure Reason [1781]) by Josť A. Benardete - Metaphysics: the logical approach Ch.18

Book Reference

Benardete,Josť A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.133