This book reconstructs, both from the historical and theoretical points of view, Leibniz's geometrical studies, focusing in particular on the research Leibniz ...

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

Sa gloire projetée tantôt sur l'un, tantôt sur l'autre de ses thèmes -harmonie préétablie, optimisme, monade, etc. - Leibniz n'a jamais donné lieu à une de ces agressivités idéologiques qui lancent une mode dans l'intelligentsia. Moderniste? Non. Moderne? Oui. Aujourd'hui, de plus en plus notre contemporain. Son immense savoir - en progrès sur celui de la Renaissance - semble préfigurer l'Encyclopédie du monde actuel. Ne multiplions pas des exemples. Son algorithme infinitésimal, la dyatique, l'art combinatoire sont à la base de (...) notre Mécanique, de nos ordinateurs et par là, sans doute, d'une notion d'ordre qui a cessé d'être linéaire. Pour formuler ses nouveaux calculs en mathématiques et en logique - raisonner, c'est aussi calculer - et suivre les migrations des peuples au cours de l'histoire, il médite sur le langage. Il l'interprète selon la théorie de l'expression et non plus sur celles des signes. Il nous rapproche de nos préoccupations linguistiques, il déplace l'épistémologie vers la philosophie analytique : presque notre contemporain. En politique et morale, il projetait Société des Nations et Conciles : peut-être son souci de tout concilier l'a-t-il trop limité à une morale de bon sens difficilement compatible avec l'amoralisme de nos grands Etats. Mais que l'on n'oublie pas de savourer le style (en français) de Leibniz : grenu, familier, soutenu d'exemples, clair-profond. (shrink)

Gonzalo Rodriguez-Pereyra presents an original study of the place and role of the Identity of Indiscernibles in Leibniz's philosophy. The Principle of the Identity of Indiscernibles rules out numerically distinct but perfectly similar things; Leibniz derived it from more basic principles and used it to establish important philosophical theses. Rodriguez-Pereyra aims to establish what Leibniz meant by the Principle of Identity of Indiscernibles, what his arguments for and from it were, and to assess those arguments and Leibniz's claims about the (...) Principle of Identity of Indiscernibles. He argues that Leibniz had a very strong version of the principle, according to which no possibilia are intrinsically perfectly similar, where this excludes things that differ in magnitude alone. The book discusses Leibniz's arguments for the Identity of Indiscernibles in the Meditation on the Principle of the Individual, the Discourse on Metaphysics, Notationes Generales, Primary Truths, the letter to Casati of 1689, the correspondence with Clarke, as well as the use of the Identity of Indiscernibles in Leibniz's arguments against the Cartesian conception of the material world, atoms, absolute space and time, the Lockean conception of the mind as a tabula rasa, and freedom of indifference. Rodriguez-Pereyra argues that the Identity of Indiscernibles was a central but inessential principle of Leibniz's philosophy. (shrink)

Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...) practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz’s philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance. (shrink)

In the famous Correspondence with Clarke, which took place during the last year of Leibniz's life, Leibniz advanced several arguments purporting to refute the absolute theory of space and time that was held by Newton and his followers. The main aim of this book is to reassess Leibniz's attack on the Newtonian theory in so far as he relied on the principle of the identity of indiscernibles. The theological side of the controversy is not ignored but isolated and discussed in (...) the last three chapters, which deal with problems connected with the notions of omnipotence and omniscience. (shrink)

Depuis Léon Brunschvicg s’est établie une sorte de lieu commun de l’interprétation de la métaphysique de Leibniz, dont la cohérence serait compromise par la contradiction entre la monade, pour qui l’espace est idéal, et la « monadologie » ou système de toutes les monades coexistantes, qui présupposerait un réalisme de l’espace. Dans cet article, l’argument de Brunschvicg est reconstitué, puis critiqué par la restitution de la pensée réelle de Leibniz sur les rapports entre monade et espace : on ne doit (...) en aucun cas se représenter la pluralité des monades comme une multiplicité spatiale – l’espace est un ordre non des substances simples, mais des phénomènes, – seule l’union constante et universelle de chaque monade à un corps organique permet de parler d’un « point de vue », qui n’est autre que la localisation de ce corps parmi les autres et non de la monade qui, en tant que telle, n’a pas de lieu. (shrink)