Jean Le Rond D'Alembert

D’Alembert, Jean Le Rond (1717–83)

Mathematician, scientist and man of letters, Jean D’Alembert is a central figure of the French Enlightenment. As a young man he made significant contributions to the refinement of mathematical techniques, and later was actively engaged in the theoretical controversies which surrounded the gradual assimilation of Newtonian mechanics into the mainstream of European science. For twelve years (1746–58) he was co-editor, with Denis Diderot, of the Encyclopedia, the serial publication of which was one of the defining events of the Enlightenment period as a whole. D’Alembert frequented the various Paris salons where much of the intellectual fervour and high-spiritedness of the age was cultivated and given shape. As Secretary of the French Academy he worked assiduously to advance the cause of human knowledge.

D’Alembert’s philosophy is characterized by an abiding commitment to the clarity and precision which attends mathematical abstraction. He believed that in its essence the natural order is internally structured by laws whose operation can be articulated under the principles of geometry. All natural phenomena are to be explained under the terms of those basic mathematical principles that govern the scientific domain in which they are located (chemistry or astronomy for example), and all scientific domains could be brought ultimately to perfect consistency and systematic order within a comprehensive theory. The events and processes which constitute the natural order reflect the reality of the mathematical structure which underlies them. As he says in the Preliminary Discourse (1751) to the Encyclopedia (1751–65), ‘The universe would only be one fact and one great truth for whoever knew how to embrace it from a single point of view’.

1 Life and works

D’Alembert was the illegitimate son of Mme de Tencin and the chevalier Louis-Camus Destouches. Shortly after his birth he was left by his mother at the steps of the church St Jean Le Rond in Paris, a circumstance which gave the boy his name. While never formally acknowledging paternity, the father took a devoted interest in his son and provided for his education. Jean was enrolled in the Jansenist Collège des Quatre Nations under the name of Dalemberg, which was later altered to the form by which he is known to history. The boy’s intellectual gifts were apparent from the start; he was encouraged to pursue a career in theology, though he never expressed any great interest in it, studied law and medicine for three years, but was increasingly drawn to mathematics. Though his formal instruction in mathematics was limited, by 1739 D’Alembert had attained a sufficient mastery of the subject to submit a paper to the Academy of Sciences in which he pointed out some errors in a popular textbook of the time. On the strength of this and several other mathematical papers he was elected to the Academy of Sciences in 1741.

In 1743 D’Alembert published his Traité de dynamique (Treatise on Dynamics), a book which attracted the attention of the leading scientific authorities and helped secure his reputation as a most promising young savant. In this, his first major publication, he attempted to reconstruct the science of motion (mechanics) on a purely formal and mathematical basis, proscribing appeals to any such quasi-metaphysical notions as force or gravity and assigning observation and experiment to the subordinate role of confirming the basic principles of the theory. The axioms of geometry, together with the assumption of the impenetrability of the objects constituting a system, were all that was needed to establish the precision and certainty that should attend the study of motion. By this time Newtonian mechanics was well on its way toward gaining the ascendancy over the vestiges of Cartesian physics, and D’Alembert was in compliance with the best scientific opinion of the day in rejecting Descartes’ theory of vortices and his conception of nature as a plenum. In certain fundamental respects, however, D’Alembert retained a decided preference for a rigorous, Cartesian rationalism in his approach to scientific theorizing as opposed to the meticulous empirical observation and data-gathering which characterize Newton’s own researches (see EMPIRICISM; RATIONALISM). For D’Alembert priority should always be accorded to the strict logical formulation of the basic principles which grounded any scientific inquiry, and he maintained that such principles could be articulated independently of experience. While many of his contemporaries were impressed by the extent to which D’Alembert had apparently succeeded in preserving and carrying through to completion the best features of the Cartesian approach to physical science, others raised the suspicion that his attempts to mathematicize the foundations of mechanics were based on a confusion regarding the ineluctably empirical dimension of basic mechanical principles. In any case, the Traité de dynamique is secure in its place in the history of science for having clarified the central theoretical issues which remained to be addressed in working out the details of the Newtonian programme, preparing the way, in particular, for the later researches of Lagrange (see DESCARTES, R.; NEWTON, I.).

Over the next few years D’Alembert produced a series of scientific monographs in which he applied the principles worked out in the Traité de dynamique to specific problems including the behaviour of fluids, the cause of the winds, precise calculations for the incidence of the equinoxes and the vibration of strings, all impressive scientific achievements in their own right. Beginning in 1746, however, D’Alembert’s intellectual energies began to move away from such narrowly focused scientific investigations towards a more literary engagement with the broader currents of the Enlightenment movement that were gaining momentum across Europe. This year marks D’Alembert’s earliest involvement in the tempestuous history of the publication of the Encyclopedia which he was to co-edit with Denis DIDEROT for the next twelve years. In 1751 he produced the Preliminary Discourse to the Encyclopedia, the work for which he is best known; he would ultimately contribute, or make substantial editorial additions to some 1,500 articles on an enormous range of topics from mathematics and physics (which make up the largest part of his contribution) to music, philosophy and religion. In many of these articles D’Alembert is unabashedly partisan in his support of the philosophical campaign to secure the claims of science and enlightenment against the resistance of the political authorities and the chauvinism of the religious establishment. By his polemical zeal, for example, in his contentions against the unflagging hostility of the Jesuits to the whole Encyclopedia project, he makes known his willingness to be counted among the ranks of the philosophes who, in turn, were more than happy to have his considerable reputation as a scientist joined to their cause. The depth of D’Alembert’s commitment to the cause was challenged, however, when his article ‘Genève’ appeared in 1757 in the seventh volume of the Encyclopedia. He had intended to present a flattering view of the atmosphere of religious tolerance in Geneva at the time by imputing to the authorities there an advocacy of various doctrines associated with SOCINIANISM, such as the denial of the divinity of Christ. The Genevans were neither flattered nor amused. In the firestorm of criticism and vituperation that came down on his head in the months after his article appeared, D’Alembert resigned his position as editor and withdrew from the public controversies altogether, much to the disappointment of his more vociferous comrades including, notably, Voltaire. His further contributions to the Encyclopedia would be confined to relatively uncontroversial topics dealing with scientific matters with which he was especially conversant.

In 1754 D’Alembert was elected to the French Academy, and if the high profile and protracted controversies of the Encyclopedia project were too much for D’Alembert’s tastes, his membership in the Academy provided the ideal setting for his continued advocacy of the natural sciences. For some years prior to his election, the reputation of the Academy had been diminished in the public’s estimation by the perception that its members were perhaps too much beholden to the interests of the political establishment. With D’Alembert things changed. By virtue of his own reputation for scholarly achievement and personal integrity he was able to improve contacts with scientific establishments across Europe and cultivate friendly relations with foreign heads of state. Internally, he worked assiduously in the cause of progressive ideas by setting agendas and seeking to advance the careers of like-minded colleagues. In his speeches before the assembly and public addresses he championed the cause of the philosophic spirit and argued the material and moral advantages to a society in which it was permitted to flourish. In ways that were unprecedented he brought the affairs and proceedings of the Academy before the public and thereby enhanced the reputation of the Academy itself while raising at the same time the status and the influence of scientific and philosophic research. In 1772 he acceded to the office of permanent secretary of the Academy in which capacity he continued to serve until his death.

Throughout this period D’Alembert continued to write and publish books and essays on scientific and philosophical topics. In 1759 he published the Essai sur les éléments de philosophie; in the aftermath of the Jesuit expulsion from France in 1762 he published the highly polemical essay Sur la destruction des Jésuites en France (1765), in which he argued, in effect, that it was the rising tide of enlightenment which precipitated the downfall of this remaining bastion of religious obscurantism. His technical works in mathematics and physics were published in eight volumes as Opuscules mathématiques between 1761 and 1780. His voluminous correspondence, his many speeches and elegies were collected and published posthumously.

2 Philosophical outlook and the Preliminary Discourse

D’Alembert’s philosophy is of decisive importance to anyone who would understand the Enlightenment in its intellectual and theoretical (as distinct from its social and political) dimension because it manifests, more clearly perhaps than any other author’s, the delicate combination of French rationalism in the tradition of Descartes and Malebranche and British empiricism as represented by Newton and Locke (see Malebranche, N.; Locke, J.). As a mathematician of the very first rank, D’Alembert was entirely sympathetic to Descartes’ insistence upon the clarity and precision of basic principles and the need for rigorous deductive logic in establishing the linkages between one theoretical proposition and any others which might be linked with it. Like virtually all his contemporaries, D’Alembert was hugely impressed by the power of Newtonian mechanics to explain and integrate vast tracts of natural phenomena and predict future events, and by the extent to which observational and experimental data could be incorporated into a system constituted at its core by mathematical principles. To understand D’Alembert himself, and to appreciate his importance as a signal representative of the thought of this watershed period in human history, the relationship between the Cartesian and empirical strands of his work must be made out.

D’Alembert was unequivocal in his rejection of metaphysical principles as constituting an appropriate base for inquiry in the natural sciences. He repudiated the Cartesian doctrine of innate ideas and denied that Descartes’ Cogito had any value as a starting point in constructing the system of human knowledge. Appeals to divine intervention in the natural order had no place in trying to explain the connection between events or the relation between natural objects and the human perception of them. In this respect, D’Alembert adhered closely to the principles of Lockean epistemology as these were modified and expanded in the works of his friend and colleague, CONDILLAC. With Locke and Condillac, D’Alembert insisted that all knowledge begins by attending to the facts and that the way those facts appear to us is as close as we can ever hope to get to their reality. But the facts which present themselves to our experience are only isolated and fragmentary pieces of a greater systematic structure in which they are embedded, and for the full articulation of that structure one must have recourse to the principles of mathematics – specifically those of geometry – in order to represent the orderliness of natural events and processes. The basic principles of any science should consist in perfectly unambiguous and precise mathematical formulas together with whatever basic assumptions are necessary to secure their attachment to the objects which constitute the domain under investigation. The various discrete facts disclosed to our observations can then be expressed as formal propositions which could in turn be fitted into the deductive chain of formulas derivable from the basic principles.

D’Alembert rejected Descartes’ notion of the universe as a plenum because it was infected by the unwarranted metaphysical doctrine of substances. In his own conception of the universe, however, D’Alembert maintained that all parts of nature are systematically interrelated in a comprehensive structure of laws which evinces the same integrity, consistency and formal precision as any of the more extended and elegant proofs in geometry. Like Descartes, D’Alembert believed that the methodical and painstaking implementation of human reason would gradually serve to disclose this rational structure, and that, as it came into view, the empirical facts could find their place within it and thereby attain theoretical clarity. By setting his first priority on the articulation of the rational structure which informed all of nature, D’Alembert comports with the most fundamental aspects of Cartesian methodology and reaffirms the optimistic faith of his great precursor in the autonomous power of human reason.

In the Preliminary Discourse to the Encyclopedia D’Alembert presents an interpretation of the contemporary state of scientific research in which his own rationalistic conception of the structure of human knowledge forms the core. The Encyclopedia itself is conceived as a compendium of all the scientific truths so far achieved, but the greater utility and value of the work is found to consist precisely in its capacity to arrange and integrate these results so as to facilitate further research by revealing both the systematic interrelations between seemingly remote domains and the lacunas which remained to be filled in. D’Alembert compares the Encyclopedia to a road map: certain areas of the terrain of human knowledge are well understood and laid out in careful detail while the expanses between these areas are marked out only by the most rudimentary traces which might none the less provide a researcher with his theoretical bearings as he laboured to extend the boundaries of knowledge ever deeper into the realm of terra incognita. All of the articles in the Encyclopedia were to be knit together by an extensive network of cross-references so that an arbitrarily selected topic would lead the reader eventually to a comprehensive view of the whole structure in all its intricacies. The Encyclopedia, as the systematic embodiment of the whole vast range of human knowledge, would thus reflect the rational structure which constituted the natural order itself.

D’Alembert invokes a second metaphor in the Discourse, inspired by the prescient writings of the great English philosopher of science Francis Bacon, in which the ‘tree of human knowledge’, rooted in such fundamental disciplines as mathematics and logic, branches out into the various scientific subregions and extends ever further to include the most narrowly defined and detailed subject matter. Reconfiguring the Baconian conception of knowledge in accordance with the general principles of epistemology worked out by Condillac, D’Alembert recognizes three essential functions of the human mind: memory, reason and imagination. Under these three rubrics all domains of human inquiry, including history (sacred, civil and natural), literature and art, can be systematically interrelated. This second metaphor expresses D’Alembert’s view of knowledge as an organic unity, as something which grows from within when all of the various parts derive their sustenance from the flourishing of the others and contribute in turn to the flourishing of the whole.

To D’Alembert’s way of thinking there was no area of human inquiry which could not be incorporated into this unified and integrated structure of knowledge, and in this respect the Preliminary Discourse gives powerful and eloquent expression to one of the guiding inspirations of the Enlightenment period as a whole. In his own researches he made significant contributions toward bringing the study of language and aesthetics under the purview of science, and believed that ultimately even politics and morality should have to be subsumed under its methodology if there were to be progress. But here, D’Alembert’s attachment to rationalistic principles becomes deeply problematic, in that the more inscrutable and ambiguous aspects of human nature seem unamenable to anything like the geometrical precision that he made the hallmark of all true science. If from our historical vantage point his own philosophical commitments should appear somewhat dogmatic and unwarranted, we must at least acknowledge that the issues concerning the relationships between the various domains of human knowledge to which he was so acutely sensitive continue into our own day, reflected in the uneasy division within institutions of higher learning between the humanities and the ‘hard sciences’.

3 Reputation and influence

D’Alembert continues to enjoy a rightly prominent role in virtually all historical treatments of the Enlightenment period. He is one of only a few philosophes to have achieved the very highest standing as both a scientist and man of letters. His contributions to mathematics and physics stand as significant landmarks in the history of both disciplines. His indefatigable labours as secretary of the French Academy were profoundly efficacious in advancing the cause of enlightenment across Europe. Some of the most important historical figures of the age, including Voltaire, Frederick the Great and David Hume were proud to count him among their friends, a testament to both his high reputation and the warmth and integrity of his personality. His philosophical work was influential in the world of practical affairs as well, for example, in the formation of economic policy under the ministries of Quesnay and Turgot. And it is by no means the least of his contributions to have served as mentor to and helped to advance the careers of some of the brightest young minds of the rising generation such as Laplace, Lagrange and Condorcet. A close study of D’Alembert’s life and works provides an excellent point of entry into the world of the European Enlightenment.