Talk by Daniel Sutherland (UIC) this Friday, February 28th at 4 pm:
“Bridging the Gap Between Mereology and Mathematics: The General Theory of Pure Concrete Measurement in Euclid and Kant”
Abstract:
It was common place in Kant’s time to describe mathematics as the science of magnitudes and their measurement. This is not just an antiquated manner of expression, but reflects a very different understanding of mathematics prior to its arithmetization in the 19th century, an understanding whose origins are rooted in the rich mathematical theory of magnitudes found in Euclid’s Elements. Yet Kant’s own account of magnitudes is mereological, and falls short of the Euclidean mathematical notion of magnitude. I argue that Euclid’s implicit definition of magnitude tacitly assumes a general theory of pure concrete measurement, which crucially presupposes the relation of equality. I argue that Kant also tacitly assumes the general theory of pure concrete measurement, but is nevertheless aware of the limitations of bare mereology, and explicitly defines greater than and less than for magnitudes in terms of part-whole relations and equality, which bridges the gap between his mereological account of magnitude and Euclid’s mathematical notion of magnitude.
The talk will be held in the John Hope Franklin Room, which is located in the Social Science Research Building, Room 224. (The Fishbein Center (SS 205-208) is located across the hall. The street address is 1126 E. 59th Street, Chicago, IL 60637.)