ALEMBERT Jean Baptiste LE ROND D’—a philosopher, mathematician, and physicist, b. November 15, 1717 in Paris, d. Oxtober 29, 1783 in Paris.

D’Alembert completed studies at the Jansenist Collège de Quatre-Nations (College Mazarin), then studied law at the Academy of Legal Science where he earned a bachelor’s degree in the arts and a licenciate in law. He studied mathematics and mechanics on his own from the works of Varignon, L’Hospital, and Newton. At the beginning of this period his teacher was the historian of mathematics, J. E. Montucla. In the years 1739–1740, d’Alembert presented his treatises on the motion of rigid bodies in a a fluid and on integral calculus before the Paris Academy of Sciences. In May 1741 he was made a member of the Academy (in 1746 he received the title of associé géometre, in 1756 he became an academic, and in 1764 he becanme a foreign member of the Petersburg Academy).

His best known work on theoretical mechanics, Traité de la dynamique, appeared in Paris in 1743. The work presents what has come to be known as d’Alembert’s principle, which provided a general method for reducing the dynamic problems of the motion of a constrained system to a problem of statics. In this work we find, among other things, a solution to the great controversy of the seventeenth and eighteenth century concerning the analytic and algebraic expression of kinetic energy (vis viva). In his philosophical introduction, d’Alembert fully accepts the sensualistic epistemology initiated by Locke and developed by Condillac that proposes that all knowledge is derived from sense experience. He follows Descartes in holding that the criterion of truth is clear and distinct ideas, although these are not innate ideas. According to d’Alembert, the most fundamental ideas are those of time and space, and he speaks of treating time as a fourth dimension (in the article Dimension, in volume 4 of the Encyclopédie). Thereby he may be considered a precursor of the special theory of relativity.

According to d’Alembert, the idea of motion is a complex idea and as such must be defined by the categories of time and space. In the first part of the Traité he presents his own laws of motion wherein he presents the famous principles of Newton’s dynamics in algebraic and analytic form. He tries to reduce the first two laws to strict mathematics (analysis and geometry).

In connection with his studies of the problem of a vibrating string, and the discussion of the nature of the functions that occur in integers of the equations of mathematical physics, he developed a new area of mathematical analysis—the theory of partial differential equations (the method of integral difference). He also made an important contribution in the formulation of mathematical problems that have philosophical consequences. In the articles Différentiel, (Encyclopédie, vol. 4, 1759) and Limite, (ibid., vol 9, 1765), he addresses one of the most important problems in eighteenth-century mathematics, the problems of whether infinitesimally small or infinitely big quantities exist. He sees the solution to the problem in the concept of limit. D’Alembert presents one of the first definitions of this concept.

Starting in 1750, he played an active role in Diderot’s Great French Encyclopedia. D’Alembert became one of the founders, an editor and an author. In the Discours préliminaire de l’Encyclopédii, he presented some of his philosophical views.

In another philosophical work called Essai sur les éléments de philosophie […] (published in Mélanges de littérature, d’histoire et de philosophie, P 1759, vol. 4; critical edition, C. Kintzler, P 1986), d’Alembert developed and refined his earlier views. He also presented his own diagnosis of the eighteenth century and called it an age of philosophy because of the great changes that took place in philosophy. In his philosophical works he began positivism and so had an important influence on the further development of philosophy. D’Alembert’s aim was a thorough reform of science. One of the methods of reform was to limit science’s claims and to show the sociological and biological conditions that affect science. One of d’Alembert’s proposals was to eliminate all metaphysical statements (both spiritualistic and materialistic) from science, and to limit science to propositions concerning external facts. According to d’Alembert, the task of science is only to gather external data (facts) and see their relations (to present the facts in sequence, to arrive at the laws that govern them). The object of philosophy, on the other hand, is the synthesis of the facts developed by the particular sciences. According to this conception, philosophy should be meta-science, i.e., it should be a science concerning the principles of the sciences, where these principles are conceived as facts of a part type, as simple and generally recognized facts (faits simples et reconnus). According to d’Alembert, the development of philosophy was possible only in strict association with the particular sciences, since only then could we guarantee that philosophy would be in touch with experience, and this would protect philosophy from going down the path of speculation. According to d’Alembert, human knowledge is a collective undertaking and is inevitably fragmentary in character. We cannot foresee the future limits or growth of human knowledge. Therefore human knowledge cannot be developed in the form of a system, especially an a priori and deductive system. The unity of human knowledge can be guaranteed only by way of induction and history. In practice, this means that we should recognize the biological genesis of human knowledge and we should replace systematic ordering of knowledge with encyclopedic ordering. In this context, the problem of the classification of the sciences would become especially important . D’Alembert set forth a classification that was developed on the basis of genetic principles, i.e., he organized the science in the order in which they actually develop (in order of increasing abstraction). The new approach in classification resembled in part the classifications of Hugh of St. Victor and Robert Kilwardby, but owed the most to Bacon and Diderot. D’Alembert’s classification was presented in the first volume of the Enyclopedia which contained an extensive introductory article by him on the origins and development of the sciences. D’Alembert followed Bacon when he present memory, common sense, and imagination as intellectual powers. He also made a division of human knowledge where he connected history with memory, philosophy with common sense, and poetry with imagination. Comte later developed this classification and adapted it to his own philosophical system.

L. Kunz, Die Erkenntnistheorie d’Alembert, AGPh 20 (1907), 96–126; J. Halpern, Rzekoma i prawdziwa klasyfikacja wiedzy d’Alemberta [Alleged and true classification of knowledge of d’Alembert], PF 21 (1918), 1–33; M. Muller, Essai sur la philosophie de Jean d’Alembert, P 1926; F. Venturi, D’Alembert. Discours préliminaire de l’Encyclopédie 1751, Ox 1955; J. M. Briggs, D’Alembert: Mechanics, Matter, and Morals, NY 1962; H. Jarret, D’Alembert and the Encyclopédie, Durham 1962; J. N. Pappas, Voltaire and d’Alembert, Bloomington 1962; T. L. Hankins, Jean d’Alembert, Science and the Enlightenment, Ox 1970; G. Klaus, Philosophiehistorische Abhandlungen. Kopernikus, D’Alembert, Condillac, Kant, B 1977; A. Schober, D'Alembert, der vermeintliche Vater des Positivismus. Eine historisch-systematische Untersuchung, Nü 1982; R. G. van Oss, D’Alembert and the Fourth Dimension, Historia Mathematica 10 (1983), 455–457; P. Casini, D’Alembert: L’economia dei principi e la ‘metafisica della scienze’, Rivista di Filosofia 75 (1984), 45–62; M. Naumann, Artikel aus der von Diderot und d’Alembert herausgegebenen Enzykopädie, L 1984; J. N. Pappas, Inventaire de la correspondance de d’Alembert, Studies on Voltaire and the Eightenneth Century 245 (1986), 131-276; Z. G. Swijtink, D’Alembert and the Maturity of Chances, Studies in History and Philosophy of Science 17(1986), 327–349; C. Kintzler, D’Alembert, les Éléments de philosophie et leurs ‘Éclaircissements’: Une pensée en éclats, Corpus 4 (1987), 117–141; F. de Gandt, D’Alembert et la chaîne des sciences, Revue de Synthèse 115 (1994), 39–53; D’Alembert and the Encyclopédie, Transactions of the International Congress on the Enlightenment 9 (1995), 685–713; P. Bailhache, Deux mathématiciens musicies: Euler et d’Alembert, Physis 32 (1995), 1–35; E. J. Hobart, The Analytical Vision and Organisation of Knowledge in the Encyclopédie, Studies on Voltaire and the Eighteenth Century 327 (1995), 153–181; A. Firode, Les lois du choc et la rationalité de la mécanique selon D’Alembert, Recherches sur Diderot et sur l’Encyclopédie, ibid., 99–112; V. La Ru, La méthode des éléments de D’Alembert dans l’Encyclopédie, ibid., 91–97; Jean Le Rond d’Alembert, Einleitung zur Enczyklopädie. Durchgesehen und mit einer Einleitung, H 1997; M. Paty, D&srquo;Alembert, ou La raison physico-mathématique au siècle des Lumières, P 1998.

Zenon E. Roskal

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