La notion d’expression et ses origines mathématiques

Abstract

The notion of “expression”, which infuses the whole Leibnizian thought, originates, at least partially, from mathematics, for it appears explicitly in the corpus of the author, after his Parisian initiation to modern mathematics. The crucial point then consists in drawing the path that leads Leibniz from his first mathematical works about quadrature of the circle, differential calculus and series, and his discovery of perspective projection, to the notion of “expression”. Then, many mathematical elements seem to be inscribed in the very nature of “expression”: the idea of transformation and preservation, of relationship between finite and infinite, or still of envelopment and development. Now, it turns out that these elements, if they are considered merely in their mathematical dimension, are sometimes more problematic than enlightening when the question is grasping what “expression” means in its metaphysical instances, and consequently that “expression” cannot be reduced to a mere mathematical notion.