Foundations and Philosophy

The Univalent Foundations (UF) of mathematics take the point of view that spatial notions (e.g. “point” and “path”) are fundamental, rather than derived, and that all of mathematics can be encoded in terms of them. We will argue that this new point of view has important implications for philosophy, and especially for those parts of analytic philosophy that take set theory and first-order logic as their benchmark of rigor. To do so, we will explore the connection between foundations and philosophy, outline what is distinctive about the logic of UF, and then describe new philosophical theses one can express in terms of this new logic