Phenomenology of Mathematics: Seminar on Special Topics (PHIL690)
Professor Kyle Banick
Tuesdays · 7:00pm–9:45pm · LA2–203
This seminar will consider Husserl’s phenomenological philosophy in relation to mathematics. Phenomenology and mathematics have a deep bilateral interchange: Husserl’s early training in mathematics gave shape to his conception of how philosophy can and should be done; and his phenomenological reflection also provides a method capable of elucidating and criticizing mathematical concepts and practices. Up for grabs are phenomenological analyses yielding insight into the nature of abstract objects, cognitive access to the infinite, the relation of mathematics to embodied perception of the physical world, and the meaning of mathematical practice itself as a human cultural tradition.
The course will be centered around Mirja Hartimo’s cutting edge new book, Husserl and Mathematics, which uses hitherto unpublicized archival evidence to flesh out Husserl’s pluralistic and evolving conception of mathematics. Husserl was situated in the middle of the wide-ranging mathematical innovations of the early 20th century. He engaged in personal correspondence with the likes of Hilbert, Brouwer, Weyl, etc., leading Husserl to intriguing changes of view as he responded in real-time to the emerging mathematics of the day. Husserl’s resulting partial embrace of a variety of seemingly incompatible foundational frameworks makes his view impossible to pigeonhole, providing for a puzzling but intellectually rewarding knot to untie. We shall also investigate Hartimo’s claim that much of Husserl’s later philosophical developments in the 1930s were related to advancements in mathematics (e.g., Gödel’s incompleteness theorems, Löwenheim-Skolem theorem) that throw into a new light the limits of the wider philosophical ambitions of phenomenology.
The course does not presuppose any background in mathematics, logic, or phenomenology. We will attend primarily to philosophical issues and leave the technical issues in the background, except where technical points are absolutely required to grasp the sense of Husserl’s philosophical stance. The significance of this material ramifies into a host of philosophical topics, and is not restricted to those with an interest in the philosophy of mathematics or those with technical backgrounds. Moreover, students will have the opportunity to gain some background in developments in mathematics and mathematical logic that will serve them well in deepening their understanding of philosophy as it stands today.