Student Spotlight: Sean Walsh, Ph.D. in Mathematics and Philosophy

Author: Mary Hendriksen

Sean Walsh, a graduate of Notre Dame’s departments of philosophy and mathematics, was awarded a Kurt Gödel Research Prize Fellowship — one of the most prestigious honors in the field of logic. He was one of five pre-and post-doctoral winners.

The Kurt Gödel Society, named for the late mathematical logician and philosopher, awards the fellowships to support original research that carries on his legacy.

A native of Fairbanks, Alaska, Sean completed a joint doctoral degree in logic and foundations of mathematics in January 2011 under the direction of Michael Detlefsen, McMahon-Hank Professor of Philosophy, and Peter Cholak, professor of mathematics. He says he is “deeply humbled and grateful” to receive such recognition for his work on “The Limits of Arithmetical Definability.”

Currently a post-doctoral fellow in the philosophy department at Birkbeck, University of London, Sean studies the philosophy of mathematics, mathematical logic, and the intersection of the two.

“Some parts of my research are pure philosophy—I ask and try to answer questions about the nature of mathematical objects and the possibility of mathematical knowledge,” Sean explains. “Other parts of my research are pure mathematics: I try to formulate conjectures and prove them, availing myself of known proof techniques from different parts of mathematics and different parts of mathematical logic. Perhaps what is most distinctive about my research is that I attempt to combine these two things.”

Sean’s award-winning paper is representative of this type of interdisciplinary approach. Specifically, he used tools from contemporary mathematical logic to gauge the strength of the logical resources needed to effect one traditional reduction of arithmetic to logic.

“Such a reduction played a central role in Gottlob Frege’s logicism,” he says, “one key idea of which was that mathematical knowledge does not require an appeal to intuition or other quasi-perceptual resources, as had been claimed by [Immanuel] Kant in his famous Critique of Pure Reason.”

In addition to the distinction of publishing his paper in the Annals of Pure and Applied Logic, Sean gave a lecture at the 2011 “New Trends in Logic” conference in Vienna, Austria. He says, “I plan to use some of the resources afforded by the prize fellowship to run seminars on topics at the intersection of philosophy of mathematics and mathematical logic; and in particular, to use these resources to host external speakers and some workshops.” [For a detailed description of the seminar Sean is teaching in the Autumn 2011 term, read more].

As for his post-doctoral fellowship, he says: “It is associated with a grant funded by the European Research Council, which is ‘vertically integrated’ in the way common now in Europe. Thus, in addition to a senior investigator, there are two post-docs and two Ph.D. students, and in addition to working on our individual but thematically-linked projects, we jointly run various seminars and conferences that involve and are open to the larger academic community. For instance, this last year I was teaching courses on set theory and its philosophy, and this past summer, we organized a summer school jointly with the University of Notre Dame and the University of Munich.”

Some portions of this article were originally published by the Notre Dame Office of Public Affairs and Information (