Séminaire – Mathématiques 19e-21e, histoire et philosophie

Cette séance est annulé

Séance sur la notion de co-algèbre

Jeffrey Elawani (University McMaster et Université Paris Cité)
Measurement and numbers in Leibniz. A coalgebraic approach to continuous quantities ?

Résumé :
In his important works on the evolution of the concept of ratio in Renaissance and early modern time, Antoni Malet points out that many early modern scholars assumed a concept of continuous numbers that is at best ill-grounded relative to the traditional Euclidean conception of ratios and at worst plainly circular. At first sight, the conception of numbers and ratios found in Leibniz is open to these same critiques.
On the contrary, I argue in this talk that Leibniz developed a conception of number that is free of the circularity criticized by Malet. Moreover, although it is not without difficulties, I hint that the conception is based on valuable and (for the time) commendable foundational insights. I end the talk by a discussion of some aspects of contemporary coalgebraic characterizations of the continuum that, I believe, are relevant for the appreciation of Leibniz’s own conception.
The Leibnizian concept of number I discuss is based on the measurement of continuous quantities. In Leibniz, this measurement consists in a procedure of iterative division that yields a sequence of repetitions of parts. Following (Costantini, F. and Elawani, J. (2024)), I argue that this procedure involves no notion of abstract numbers. Abstract numbers are rather the common feature shared by all the different measurement procedures, be they measurement of lines, surfaces, forces etc.

Graham Leach-Krouse (Software engineer et auparavant à Kansas University)
Coalgebras for philosophers

Résumé :
In this talk, I introduce F-algebras and F-coalgebras, with some familiar examples of each. I make the case for both the intrinsic philosophical interest of coalgebras (for example, as potential sources of insight into the intuitive concept of the continuum) and for the significance of the algebra/coalgebra duality.

Lieu : Salle Malevitch (483A) bâtiment Condorcet