The Euclidean nature of our imagination led Kant to say that although the denial of the axioms of Euclid could be conceived without contradiction, our intuition is limited by the form of space imposed by our own minds on the world. While it is not uncommon to find claims that the very existence of non-Euclidean geometry refutes Kant's theory, such a view fails to take into account the meaning of the term "synthetic," which is that a synthetic proposition can be denied without contradiction. Leonard Nelson realized that Kant's theory implies a prediction of non-Euclidean geometry, not a denial of it, and that the existence of non-Euclidean geometry vindicates Kant's claim that the axioms of geometry are synthetic [Leonard Nelson, "Philosophy and Axiomatics," Socratic Method and Critical Philosophy, Dover, 1965; p.164].
But the axioms of geometry were suppose to be synthetic a priori which means they necessarily must be true. GRRRRRRRR!
Does he talk more about space in the transcendental logic section?
