My work revolves around the question: what got lost with the advent of the new mathematical logic of Frege and Russell? Although mathematically probably not much—I don’t officially have a view—philosophically, I think quite a bit. I see a venerable tradition in the philosophy of mathematics that ends with Russell, but traces its roots back through Kant to Euclid, Eudoxus, and Aristotle, on which geometry was the preeminent mathematical science, fundamentally grounded in space. With the rejection of space as the foundation of mathematical knowledge, and the attempt to ground it in logic or thought alone, a tectonic transformation within the order of knowledge took place. In many respects, its subtle repercussions for virtually all parts of philosophy would be hard to overstate. Much of my work attempts to peer back through the Fregean looking glass and bring back into focus insights and questions from the earlier tradition that have become occluded or distorted, firmly planted as we now are on the other side of the Fregean revolution. 

At the Center I will be working with Stephanie Grüne on her project about Kant and the bounds of human understanding (a topic which I address in some of my published work). I will also be working on two of my own projects. In one I argue that if we keep in mind that “function” was a technical early modern Latin translation of energeia (ἐνέργεια), then we can shed new light on some of the most obscure claims concerning functions in Kant’s metaphysical and transcendental deductions of the categories. In the other I examine Russell's view of space in his 1897 An Essay on the Foundations of Geometry and argue that his "forms of externality" neither have the structure of Kant's intuitions nor Kant's concepts but are something in-between, and that they instead have the structure of Sigwart's collective concepts.