Le tome II de La Philosophie de l’algèbre. Dossier documentaire

Abstract

Here is the as yet unpublished critical edition of the general conclusion to the two volumes of La Philosophie de l’Algèbre. Vuillemin first describes the two successive revolutions that occurred in algebra : the transition—as described in Volume I—from the Cartesian Algebra of equations to the Algebra of structures as exemplified by Galois’ theory, then the transition from the latter to the Algebra of algebra in the work of Dedekind and Birkhoff. A parallel renewal can thus be expected in theoretical philosophy : after the mathesis universalis of the classical age which transposed the methods of classical mathematics then that of phenomenology which brought the idea of structure into philosophy, a new revolution is awaited in philosophy which bases the analysis of structures on a prior critique of reason. This text is followed by a document record by Gudrun Vuillemin-Diem describing the manuscripts of the second part of La Philosophie de l’algèbre.