University Seminar- Computability, Complexity, and Algebraic Structure: Ratio, Analysis, and the Delian Problem: Insights from Plato's Meno

Time: Wednesday, April 22, 5:00–6:00 pm

Place: Phillips Hall, Room 108

Speaker: Peter Ulrickson, The Catholic University of America

Title: Ratio, Analysis, and the Delian Problem: Insights from Plato's Meno

Abstract:  Important mathematical developments during Plato’s lifetime shaped his philosophical writing. Plato’s dialogue Meno draws on these developments, using mathematics as a way to discuss learning and virtue. One difficult passage in Meno involving geometry has drawn much scholarly attention. I will offer a new interpretation of this passage, presenting a connection of the text with the Delian problem, the problem of doubling a cube. Along the way, I will discuss ancient theories of ratio and the classical geometrical method of analysis. My approach will be one in which philosophy and the history of mathematics are reciprocally informative; mathematical details clarify fundamental themes of the philosophical work, while global features of the dialogue illuminate local obscurities in the mathematical text.