Congratulations to Andrew Y. Lee, who emerged from a highly competitive field as the winner of the 2024 Marc Sanders Prize in Metaphysics with his essay “A Puzzle about Sums.” The biennial Sanders Prize is an essay competition open to scholars within 15 years of receiving their doctoral degree, as well as to students currently enrolled in a graduate program. Winning pieces receive a cash prize and will appear in the journal Oxford Studies in Metaphysics.
“Most people think of me as a philosopher of consciousness,” Lee says, “but I’m secretly interested in almost every topic in contemporary analytic philosophy, and I’ve aimed to let my research be guided by whatever strikes my curiosity.” A few years ago he became interested in a philosophical puzzle associated with Riemann’s Rearrangement Theorem, a mathematical theorem stating that the sum of an infinite series of numbers can sometimes depend on the order in which those numbers occur. While his winning article is framed around that philosophical puzzle, its bigger ambition, Lee asserts, “is to motivate some general ideas about the metaphysics of quantities and locations. Those ideas are applicable not only to the puzzle at the heart of the paper, but also to questions concerning infinite ethics, infinite decision theory, and some classic paradoxes concerning ‘supertasks.'”
Lee has expressed particular gratitude for having some of his work outside of consciousness recognized with the Sanders Prize.
The paper’s abstract reads as follows: “A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard to believe. A puzzle then arises: How do we interpret the metaphysical significance of this mathematical theorem? I first argue that prior solutions to the puzzle lead to implausible consequences. Then I develop my own solution, where the basic idea is that the weight of a collection of items is equal to the limit of the weights of its finite subcollections contained within ever-expanding regions of space. I show how my solution is intuitively plausible and philosophically motivated, how it reveals an underexplored line of metaphysical inquiry about quantities and locations, and how it elucidates some classic puzzles concerning supertasks, including the Ross-Littlewood Paradox and Thomson’s Lamp.”
Runners-up in the essay competition were
- “Distinctions with a Difference,” by Alexander Roberts (Wisconsin)
- “Permeating Properties,” by Erica Shumener (Syracuse)
- “Matter and Mereology,” by Jeremy Goodman (Johns Hopkins)
