Mouvement et origine du calcul infinit\'esimal Philosophie et continuit\'e

TL;DR

This paper explores the philosophical and mathematical foundations of movement and infinitesimal calculus, focusing on their historical development and conceptual diversity across disciplines.

Contribution

It provides an interdisciplinary analysis of the philosophical background and foundational questions related to movement and infinitesimal calculus.

Findings

Highlights the philosophical debates on the one and the multiple

Examines the concepts of discreet and continuous in history and philosophy

Prepares for a subsequent study on the relation between movement and calculus

Abstract

This article has his origin in some lectures given at the University of Bologna, inside an interdisciplinary program of mathematics, history of science, physics and philosophy. Since they are at the junction of these fields, movement and infinitesimal calculus are good instances to understand some fundamental questions in history of sciences, the diversity of the conceptions stretching across it and more generally the philosophy background of theses researches. It is the field where the 'struggle of giants' takes place. In this article we consider the general foundations needed for this study, in particular its philosophical background. While the principal question concerns 'the one and the multiple' it is treated through the study of the 'discreet and the continuous' considered under both his philosophical and mathematical aspect. In a second article we will consider the relation between the theorization of the movement and the infinitesimal calculus, and their historical background where they were able to grow