Paolo Mancosu (University of California, Berkeley)
Ciclo “Lectures on Infinity—From Classical Antiquity to the Middle Ages” (FLUL, 26 e 28 de Maio de 2026)
Conferência/Seminário (Seminário HPhil)
Nos próximos dias 26 de Maio (10h30-12h00, FLUL, Sala B112.E) e 28 de Maio (17h00-18h30, FLUL, Sala Matos Romão) o Professor Paolo Mancosu, Willis S. and Marion Slusser Professor of Philosophy da Universidade da California (Berkeley), apresentará duas sessões dedicadas ao tema do infinito na Antiguidade Clássica e Tardia e na Idade Média.
O Professor Paolo Mancosu (Ph.D., Stanford University) tem-se dedicado ao estudo da filosofia da matemática e da sua história, da filosofia da lógica e da lógica matemática. As suas últimas publicações debruçaram-se sobre os temas da filosofia da prática matemática e do infinito matemático. Publicou recentemente “Infini, logique, géométrie” (Vrin, Paris, 2015) (Prémio Jean Cavaillès 2018), “Abstraction and Infinity” (Oxford University Press, 2017), “Moscow Has Ears Everywhere. New Investigations on Pasternak and Ivinskaya” (Hoover Press, Stanford, 2019); em coautoria com S. Galvan e R. Zach, “An Introduction to Proof Theory. Normalization, Cut-Elimination, and Consistency Proofs” (Oxford University Press, Oxford, 2021) (Prémio Shoenfield 2022); e, com M. Mugnai, “Syllogistic Logic and Mathematical Proof” (Oxford University Press, 2023).
As sessões resultam de uma colaboração entre o Centro de Estudos Clássicos e o Centro de Filosofia da Faculdade de Letras da Universidade de Lisboa.
Abstract:
In his commentary on Aristotle’s Physics, Robert Grosseteste (ca. 1175-1253), Oxford theologian and Chancellor of the University, wrote: “Moreover, [God] created everything by number, weight, and measure, and He is the first and most accurate Measurer. By infinite numbers which are finite to Him, he measured the lines which He created. By some infinite number which is fixed and finite to Him, He measured and numbered the one-cubit line; and by an infinite number twice that size, He measured the two-cubit line; and by an infinite number half that size, He measured the half-cubit line.” In Grosseteste’s account the numerosity of the points in a finite line segment covaries with the length of the line segment. This position gave rise to an interesting number of debates in the XIIIth century especially as a consequence of a challenge raised by the Oxford theologian Richard Fishacre (1205-1248) who set up a one to one correspondence between the points in line segments of different lengths. I will reconstruct some aspects of this medieval debate, connect it to later intuitions (Bolzano and Cantor), and then discuss recent results from the theory of numerosities to the effect that the counting of points in a line segment preserving the part-whole principle is compatible with Lebesgue measure. I conclude that Grosseteste’s intuitions can find a suitable mathematical implementation.