Everyone once in a while I run across the opinion that non-Euclidean presents a serious problem for Kantian epistemology. While I've rebutted this notion before, it's common enough that I thought I'd have another go at explaining why it's a misconception. For Kant we can't know the universe to be spatial "in itself" (as in "things-in-themselves"), Euclidean or Non-Euclidean Continue Reading …
Schopenhauer on Euclid’s Geometry
One point on our Schopenhauer episode that we didn't take much time to get into was his attitude towards geometric demonstration, which was of course the model for all philosophy for thinkers like Descartes. Here's a short selection from section 39 of the Fourfold Root, which illustrates his idea that our knowledge of geometry is founded on our intuition of space ("knowledge Continue Reading …