University of South Carolina
Not quite yet a hazy limbo of mystery: Intuition in Russell's An Essay on the Foundations of Geometry
Here I examine how Russell's forms of externality take over the role of Kant's forms of Intuition in Bertrand Russell's early An Essay on the Foundations of Geometry. Specifically, here Russell, like Kant, maintains that mathematics must be grounded on knowledge of bare numerical difference, where the intellect alone cannot provide a concept of this difference. What we will see is that while the intellect on both views affords knowledge of qualities and qualitative differences, on both we can imagine two qualitatively identical things that we can nonetheless distinguish, like, say two qualitatively identical raindrops, or two one-inch cubes. It is because Russell agrees with Kant that mathematics must be built on this kind of knowledge of bare numerical difference that I will argue the account of Foundations is deeply Kantian.