Does the existence of non-euclidean geometry annihilates Kants theory?
This is a great question (and, I might add, asked in the right section of Yahoo! Answers). I don’t believe that the existence of non-Euclidean geometry annihilates Kant’s theories. It is true that he died before it was demonstrated that consistent non-Euclidean systems of geometry were possible. Had he been alive a half century or so later, he would no doubt have taken a keen interest in these discoveries and it probably would have influenced his discussions about epistemology. As you note, Kant believed that the postulates of Euclidean geometry were a priori synthetic statements. In laymen’s terms, we know that they are true by intuition or, in other words, we can “see” that they are true. Kant made the point however that our a priori synthetic judgements are not judgements about “things in themselves”. This could even be considered one of his greatest contributions to philosophy. People hold certain things to be self-evident because their minds are constituted in a certain way, not w
