Lecture: How Many Points are in a Line Segment? From Grosseteste to Numerosities
Guest Lecturer: Professor Paolo Mancosu, Department of Philosophy, University of California.
Can we count the uncountable?
The Institute of Advanced Studies is honored to host Professor Paolo Mancosu as part of the Lowy Distinguished Guest Professors program. As part of the “Logic in Philosophy” Distinguished Lecture Series in Memory of Ruth Manor, Professor Mancosu will deliver a lecture titled “How Many Points Are in a Line Segment? From Grosseteste to Numerosities.”
In his commentary on Aristotle’s Physics, the medieval scholar Robert Grosseteste proposed that the numerosity of points in a finite line segment varies proportionally with its length. His view sparked significant debate in the 13th century, particularly after Richard Fishacre introduced a one-to-one correspondence between points on line segments of different lengths.
In this lecture, Professor Mancosu will reconstruct key aspects of this medieval discussion, connect it to later developments in the thought of Bolzano and Cantor, and present recent results from the modern theory of numerosities. These results show that counting points in a line segment, while preserving the part–whole principle, can be made compatible with Lebesgue measure, offering a surprising mathematical framework in which Grosseteste’s intuitions find coherent expression.
Wednesday, 10 December 2025, 16:00
Where: Room 449, Gilman Building
The lecture will be conducted in English and is open to the public.
Light refreshments will be served before the lecture.
Click here to see the invitation >
