Abstract: Imagine a carpenter, who, in her spare time, enjoys doing elementary mathematical exercises. She works through a proof of the Pythagorean theorem, and then, emerging from her study into her workshop, she sees a set of wooden beams that have been arranged into a right triangle. Having performed the proof, the carpenter will now expect a particular relation to hold among the lengths of the beams she is looking at. The beams are objects of the carpenter’s perceptual awareness – they show up in her experience of the world. But she takes her knowledge of right triangles—knowledge that would appear to be a product of her a priori mathematical reasoning—to be directly applicable to those empirical objects. Such applications of our seemingly a priori geometrical concepts to empirical objects are mysterious – why would we take the physical world to be subject to the results of our purely abstract reasoning? This question has led many theorists to conclude that our geometrical concepts are not, in fact, a priori, and must, instead, be derived from experience. Against this, I argue that our use of spatial concepts in Euclidean geometry shows that they cannot be derived from experience. So we are left with the task of explaining why we take our genuinely a priori concepts to be applicable to the material world we encounter in visual perception. In the last part of the talk, I sketch an account of spatial experience according to which our geometrical concepts, though not derived from experience, do nevertheless feature in our visual representations.
February 2, 2018 @ 3:30 pm – 5:30 pm America/Toronto Timezone