The Difficulty of being simple

International audienceThe aim of this paper is to explore some aspects of the connection between mathematics and philosophy in Leibniz’s thought, and in particular the role that a certain model of logical analysis played in it. In a first section, I will briefly recall the central role ascribed very early by Leibniz to analysis of notions (analysis notionum) and to the constitution of an “alphabet of human thoughts”, from which all true knowledge was to be recovered by some form of “combinations”. I will then give some testimonies of the doubts raised by Leibniz himself against this program as early as 1675–1676. In order to understand better how these doubts arose, and the change that they induced in Leibniz’s philosophical orientations, I will consider the influence played in this evolution by his mathematical practice. In particular, I will emphasize the role played by some demonstrations of impossibility elaborated at the beginning of the stay in Paris and mentioned in later philosophical texts. As a conclusion, I will sketch how this evolution of Leibniz’s philosophical ideas, which was provoked by mathematics, had a ricochet effect on his mathematical practice. This will provide evidence in a simple case of how mathematics and philosophy really did interact in Leibniz’s thought. I will claim that this form of interaction is quite different from the one generally reconstructed by commentators in the past