SOURCE: Hayes, Julie Candler. “Physics and Figuration in Du Châtelet's ‘Institutions de physique.’” In Reading the French Enlightenment: System and Subversion, pp. 86-110. Cambridge: Cambridge University Press, 1999.

For philosophers and scientists as well as the non-specialist reading public, Newtonian science presented a model of conceptual clarity and methodological purity. Even if Newton's prestige was not enough to save the word “système” from its negative connotations, for d'Alembert, Newton “gave Philosophy the form it should preserve.” To the notion that Newton had brought philosophy to definitive perfection one can frame several sorts of replies, and for a number of commentators, aspects of his method and textual practice are problematic, especially as they intersect with specific historical circumstances and institutions. Margaret C. Jacobs goes so far as to assert that “the Newtonian version of the Enlightenment looks increasingly like a vast holding operation against a far more dangerous rendering of Enlightenment ideals.”¹ In France, Newton's experimentalism achieved high prestige, but other emphases shifted. French thinkers tended to adopt Newton's insights in mechanics and optics, but tried to fit them into other conceptual frameworks. One can find the effect of what I. B. Cohen calls “the Newtonian style,” or mathematicization of the natural world, in Condillac and d'Alembert, but the lingering influence of Descartes, among other factors, prompted a greater tolerance for hypothetical thinking and a continuing concern with explanatory principles in natural philosophy, as opposed to an acceptance of the inexplicable functioning of phenomena.² There are few philosophical “purists” in eighteenth-century France. Instead, a number of writers engage in various sorts of projects integrating the aims and insights of Descartes, Newton, and Leibniz, and through such integration, find new vectors and potentials within their work.

Such a project is Emilie du Châtelet's Institutions de physique of 1740. As she explains in the Avant-propos, one of her goals is to “make Newton's system known, to show you the extent of its consistency and verisimilitude, and how phenomena can be explained by the hypothesis of attraction.”³ The association of Newton's name with “hypothesis” is a mark of Du Châtelet's revisionism, which becomes further evident in an entire section defending hypothesis, but the extent to which her version of Newton's system varies from the canonical becomes evident a few pages later when she offers Leibnizian metaphysics as an introduction to Newtonian physics, calling the principle of sufficient reason “a compass capable of leading us through the quicksand” of metaphysics (13). It is not my purpose here to decide whether or not Du Châtelet was successful in reconciling such bitter antagonists as Newton and Leibniz. Nor shall I go very far in establishing her intellectual genealogy by sorting out which threads of her argument lead to Leibniz, Wolff, Newton, Clarke, Descartes, or Maupertuis.⁴ Du Châtelet presents herself at the outset as a kind of cartographer, one of those who “draw the blueprints” of physics (12). Her cartography involves more than simply outlining the shapes of things already known, however. Just as map-making has always been fraught with semiological and ideological difficulties, so too Du Châtelet's particular way of charting the borderlands between physics and metaphysics is highly significant.

My interest in the Institutions lies in seeing how Du Châtelet comes to terms with a number of the issues that we have seen arising within the discourse on and of systematicity, inasmuch as both its physics and metaphysics are geared to explicating relations, both logical and phenomenal. In her project, the split between sequential or discursive and synoptic order that plagued d'Alembert is reconfigured: the terms retain their separateness, but no longer appear incommensurable. The Institutions offer relationality as a conceptual mode adequate to the demands of both science and philosophy, and, it is implied, other areas as well. Despite a stringent official program of authorial self-effacement, part of the work's agenda is to construct its author as a member of the scientific community, and to give her a significant voice in dialogue with other voices. Thus simultaneity and sequence, motion, force, and relation, and the institution of a dialogue create sectors of textual activity which mutually reinforce one another.

The term I use for these multiple, yet interrelated, activities is “figuration,” understood in its etymological, rhetorical, and philosophical senses. The earliest meanings of figura concern a shape imposed on substance, plastic form; gradually the meaning shifted from the substantial to the abstract: shape, model, image.⁵ In ordinary French, figure can refer to the geometric illustrations accompanying the text; it can also mean “face.” To a great extent, I see the motor behind Du Châtelet's enterprise to be an active self-fashioning or self-configuration, in which both materials taken from elsewhere and her own insights are woven together in a double project of self-education and self-presentation. “Se figurer” means to imagine or picture something, and is a common enough expression in Du Châtelet's French as well as in contemporary usage. Du Châtelet se figure, or (con)figures herself, however, in a particularly literal way through this text, where she imposes a shape, attributes an identity, and situates herself in a system of relationships.

I will explore this process by looking at specific passages in the Institutions, organizing the reading in terms of a series of general issues: the question of authorial self-presentation and its relation to the tension between abstract and concrete language; the larger question of abstraction with respect to space and time; and the role of divisibility and porosity in the concept of matter and “figure.” In the final section of the chapter, we will consider Du Châtelet's foray into the public scientific debate over vis viva at the end of the Institutions, and her subsequent pamphlet exchange with Dortous de Mairan.

Many of these issues are already implicit in the opening pages of the Institutions. In the Avant-propos, the relation between pedagogy, interlocution, and self-fashioning is already apparent. Indeed, the pedagogical bent of the work is evoked in the slightly antiquated use of institutions in the title. Dedicating the work to her young son Louis-Marie, Du Châtelet begins by instituting a discourse aimed at a specific interlocutor, defining a je and a vous whose identities remain constant throughout the twenty chapters of the treatise. Her simultaneous inaugural gesture is to situate the text in time, even in several time-frames at once.

J'ai toujours pensé que le devoir le plus sacré des Hommes étoit de donner à leurs Enfans une éducation qui les empêchât dans un âge plus avancé de regreter leur jeunesse …

(1)

[I have always thought that Men's most sacred duty was to give their children an education that would prevent them at a later age from regretting their youth …]

Du Châtelet elaborates the anticipatory retrospection by imagining possibilities for the way in which her son will look back on his childhood and youth; the project begins almost on a note of carpe diem. There are other temporal framework: the material time required for Du Châtelet to write the treatise (5), the specifics of past developments in the lives of her son and herself.⁶ She also evokes the historical context in which she writes, both microscopically—no one has attempted to write a work of basic physics in French since Rouhault's 1671 Traité de physique—and macroscopically, in the larger intellectual renewal that she traces from Descartes to Huyghens, Newton, and Leibniz (5-7). The preface exists simultaneously in these different temporal sequences, from the longue durée of intellectual history, to the ephemeral existence in Louis-Marie's memory of conversations at Cirey, to the several possibilities his future may hold. This is already a textual instantiation of her (Leibnizian) opposition to (Newtonian) absolute time. Time, like space, is relational and ideal.

In addition to weaving the time of her work, and her son's and her own vécu into the progress of intellectual and scientific achievement, Du Châtelet begins to define herself in other ways. Her descriptions of her project are, however, overtly self-effacing:

… je n'ai point chargé ce livre de citations, je n'ai point voulu vous séduire par des autorités; & de plus, il y en auroit trop eu; je suis bien loin de me croire capable d'écrire un Livre de Physique sans consulter aucun livre …

(11-12)

[… I have not burdened this book with quotations as I did not want to persuade you with authorities; and in any case, there would have been too many; I am far from considering myself capable of writing a book on physics without consulting a single book …]

Increasingly, the references to what Du Châtelet is not writing become assertions regarding what she is writing. The question of authorship skirts the issue of originality in a way typical of the period: the Institutions is an assemblage of sorts, but is nevertheless new, and fills a gap in knowledge. Du Châtelet may not be a “physicist,” but her role is indispensable to the shared intellectual project.⁷

Du Châtelet reins in her style. “I have not sought to be witty [avoir de l'esprit], but to be right [avoir raison]” (12), she states, and goes on to eschew the “foreign flowers” [fleurs étrangères] of rhetoric. The Institutions explicitly abstains from the usual devices of vulgarization—dialogue, anecdote, lively writing. While the norms of scientific writing currently in force were still coming into usage in Du Châtelet's day, this self-imposed restriction is one of the strongest assertions of authorial “seriousness” in the Avant-propos. Du Châtelet maintains tighter control on her style and presentation than does Voltaire in a comparable, if less scientifically thorough or rigorous, work, his Elémens de la philosophie de Neuton,⁸ or even, as we shall see, Condillac in his eminently serious Traité des systèmes.

There cannot be, of course, any entirely successful exclusion of rhetoric or metaphor from scientific or philosophical discourse. Du Châtelet's exclusion offers itself in a metaphor and, as I have suggested, rhetorical figuration is an integral part of the Institutions' structure. The denial of the figurative in the Avant-propos is a necessary performance that is part of the identification of the writer as a philosopher; another part of that performance, initially, is identifying the writer as male, or at least effacing any overt suggestion to the contrary. The jealousy of a former mathematics tutor, Koenig, had led him to spread rumors prior to publication that she had plagiarized his work, thus destroying her anonymity. Her name appeared on the title page of the second edition, an edition which furthermore included the exchange with Mairan, in which gender became a not-so-subtle issue. Nevertheless, the effort to erase gender as a category for interpreting the work occurred early on. In the manuscript version of the Avant-propos, the first sentence reads, “Jai toujours pensé que le devoir le plus sacré des mères et pères étoit de donner à leurs Enfants une éducation …” [“I have always believed that the most sacred duty of mothers and fathers was to give their children an education …”].⁹ The substitution of Hommes for mères et pères removes not only the woman, but also the affectivity of all parental relationships, from view.

The retreat of the author from the preface, the restrictions placed on her presence, underscore the paradox of the Institutions' task: Du Châtelet's attempt to gain a voice, to show her face in the scientific community, is predicated on a kind of dissolution of the identifiable woman. Two striking analogies for this evaporation occur in Chapter 7, “Des Elemens de la matiere,” where she is primarily concerned with elucidating the relations between the phenomenal world and “simple substances” or monads. In the first, Du Châtelet performs a striking dispersion of the here-and-now of her own act of writing.

Qu'une infinité de représentations obscures accompagnent nos idées les plus claires, c'est ce dont nous ne pouvons disconvenir, si nous faisons un peu d'attention sur nous-mêmes. J'ai une idée claire, par exemple, de ce papier, sur lequel j'écris, & de la Plume dont je me sers: cependant, combien de représentations obscures sont enveloppées & cachées, pour ainsi dire, dans cette idée claire; car il y a une infinité des choses dans la tissure de ce papier, dans l'arrangement des fibres qui le composent, dans la différence & la ressemblance de ces fibres que je ne distingue point, & dont j'ai cependant une représentation obscure …

(153)

[That an infinity of obscure representations accompany our clearest ideas cannot be denied, if we heed ourselves. For example, I have a clear idea of this paper on which I write, and of this pen that I use; and yet so many obscure representations are enveloped and hidden, so to speak, in this clear idea; for there is an infinity of things in the make of this paper, in the arrangement of the fibers of which it is composed, in the differences and resemblances among fibers that I do not distinguish individually, yet of which I have an obscure representation.]

As she also says in her chapter on time, Du Châtelet here explains that the condition of our continued orderly perception of reality is obscurity, inattention, or forgetfulness. A few pages later, she explains that extension exists in the blurred perception of certain relations as a form of abstraction: “la même confusion, qui est dans mes organes, & qui fait que la ressemblance d'un visage humain resulte de l'assemblage de plusieurs portions de matiere différemment mues, dont aucune n'a de rapport au Phénomène …” [“the same confusion that is in my organs, and that causes the resemblance of a human face to result from the assemblage of various, differently prompted portions of matter, none of which has a direct connection with the phenomenon”] (157). Displaced into a passing analogy and subjected to a solvent that equates perception with “confusion,” the recognizable human face loses contact with reality. Under the analytic lens in each of these examples, that which is the most present, the most personal, dissipates into obscurity. Such is the odd poetry of analogy in the most rhetorically restrained forms of philosophic writing.¹⁰ This is the other side of the paradox as well, of course, in that the images of dissipation maintain our sense of the writer's inventiveness and control.

Her situation as author parallels the analogy of the face, where the resemblance results, not from internal identity, but from disparity. While the effect of Du Châtelet's syntax is to disperse the known into the unknown, unlike, and incommensurable (“ressemblance” to “aucun … rapport au Phénomène”), it remains nevertheless the case that the “phenomenon” thus produced is a recognizable face. Du Châtelet uses the word “visage,” but “figure” hovers as a usable synonym. Disparity, anonymity, and the obligations of abstraction will not curtail the conversation that she envisages. It is instructive to consider Du Châtelet's strategies of figuration in the light of the analysis of “faciality,” visagéité, in Deleuze and Guattari's Mille Plateaux, where the face and the voice emanating from it provide a focussing, exclusionary device that works to impede open signifying processes.¹¹ There is in Du Châtelet's text a tension between infinite dissipation, both in such mathematical problems as the labyrinth of the continuum and in the implications of philosophical abstraction that we have seen, and the necessity to arrest such dissipation. To what extent do such limitations imply a curtailment of the play of meaning in her system? The question is significant, for although there is clearly a strategic need for Du Châtelet to gain a voice by constructing certain arguments within the scientific conversation, her victory is hollow if she only succeeds in replicating the dominating gestures that have repressed her. I hope to show through the analysis of the Institutions' internal arguments and in the subsequent exchange with Mairan, that this is not the case.

Let us consider the equilibrium between abstraction and materiality at the level of Du Châtelet's language. Despite moments of stylistic aridity that remind one of current norms for “scientifically neutral” writing, where the je/vous relation of the Avant-propos becomes occulted by impersonal constructions and passive voice, the concrete specificity of the examples (carriages, ships, objects dropped from a tower, etc) nonetheless anchors the sentence. Significantly, it is in the final chapters of the Institutions on Newtonian mechanics, where the examples are the most abstract (line A-B, body C, inclined plane D, etc), that the rhetorical relation between Du Châtelet and her son comes the most frequently into the text: “as I told you,” “as you have seen,” “as I am showing you,” etc. Or in a more explicit reference to their shared experience:

Vous avez vu l'explication de cette loi dans les Elémens de la philosophie de Newton, que nous avons lus ensemble …

(305)

[You have already seen the explanation of this law in the Elements of the Philosophy of Newton, which we read together …]

The conscious staging of the text's communicative and pedagogical functions, the evocation of life at Cirey, the virtual presence of Voltaire, recuperate the abstraction of the text. Even the most unrelievedly abstract demonstrations are granted materiality, through figures, both the traditional schematic line drawings representing bodies, planes, vectors, and so forth, as well as the “figurative” headpieces, allegorical engravings at the beginning of each chapter. Chapter 9, “De la divisibilité de la Matière,” for example, offers a Mediterranean countryside where Achilles pursues the Tortoise in the foreground. Chapter 18, “De l'Oscillation des Pendules,” describes “Corps P suspendu à un fil BP,” but its illustration shows an eighteenth-century French interior, and a large ornate clock on one wall; the pendulum is not visible, but among the clock's embellishments is the figure of a nude, semi-reclining woman, who offers herself to the gaze of a male geometer and gives form to the uncertain and searching expression of both scientific inquiry and male desire.

The connection between abstraction and the phenomenal world is at the heart of Du Châtelet's discussion in the chapters on space and time, of “how we come to form our ideas of extension, space, and continuity” (101). Like Locke, she believes that we arrive at the idea of space from our experience of extension. The path taken is different, however. Locke touches on the notion of space in the context of his discussion of solidity (Essay Book 1, Chapter 4); and as he summarizes the simple process in a later chapter, “we get the Idea of Space, both by our Sight, and Touch” (Essay, Book 2, Chapter 13, § 2). Du Châtelet's intricate construction of the process starts from perceptions of difference and exteriority; the frequent repetition of the verb se représenter underscores the mediated, even fictive, quality of experience.

Du Châtelet argues against the existence of absolute space by showing its derivation from the notion of extension through the process of abstraction. She further shows that the notion of extension, taken to the requisite level of abstraction, enters into conflict with the principle of the identity of indiscernibles (103). She pauses, however, over the question of abstraction itself. We imagine (“nous nous figurons,” 104) that ideal entities such as space, extension, etc, have a real existence because we are able to strip qualities away from certain entities and apply them to others.

… il nous semble que nous portons toutes ces choses dans cet Etre idéal, que nous les y logeons, & que l'étendue les reçoit & les contient, comme un vase reçoit la liqueur qu'on y verse.

(104)

[… it appears to us that we carry all these things into an ideal entity, that we lodge them there, and that the extended substance receives and contains them as a vase receives the liquid one pours into it.]

The prominent features of the process are the stripping away of qualities, dépouillement, and their transportation and relocation within the new structure (porter, transporter, loger). As Paul de Man commented on similar passages in Condillac's 1746 Essai sur l'origine des connaissances humaines and Rousseau's Second Discourse, abstraction is here constructed as metaphor, or more broadly, as the process of figuration itself.¹² In Du Châtelet's other “figurations,” the process involves both substitution and definition. The simultaneity and indeterminacy of experience can be given a repeatable structure, and that structure in turn offers form to experience and makes it available to reflection. Du Châtelet constantly reminds us, however, that this is a mental activity, a function of thought and perception in their interaction with the world, not the world as brute fact. Her analysis pursues the reasons why space must appear to be, as the Newtonians argue, empty, penetrable, immutable, and infinite—but also why it is not so.

Like Condillac, Du Châtelet uses her epistemological genealogies as a critical weapon: “Cette explication, de la façon dont nous formons l'idée de l'espace et de ces prétendues propriétés, fait tomber tous les raisonnemens que l'on a coutume d'en tirer pour prouver la possibilité du vuide” (110). Genealogy unmasks error. Despite its potential for spurious uses, however, abstraction's necessity is also clear in this part of the discussion. Du Châtelet will go on in the final pages of the chapter to a series of definitions of related abstract concepts (Lieu, Place, Situation), whose status she indicates by concluding the abstraction with explicit reflections on the links between abstraction in mathematics and science and other works of the imagination: “ces sortes de fictions, qui sont un des plus grands secrets de l'art d'inventer …” (111). Figuration/fiction, once recognized for what it is, is not to be abolished from science or philosophy; like hypothesis, this is a necessary constituent of knowledge, although it is not to be taken from the actual physical world. She thus situates her concluding definitions within the conceptual sphere by which the world is made intelligible to us. They also mark the transformation of the subject at hand from the title, “space,” to a discussion of relation.

Du Châtelet defines space in Leibniz's terms, as the “order of coexistents” (105). These beings coexist in total continuity, since there is no empty space, no vacuum, “de façon qu'il n'est pas possible de mettre rien de nouveau dans l'Univers” (107). There is no “in between” or entre-deux; the coexisting beings surpass mere contiguity inasmuch as they “cohere” or are held in place by relationships of force (106). This definition explains the importance of the debate on force that Du Châtelet will take up in her final chapters; it also shows the necessity of the careful definitions of the nuances of “place” with which the chapter ends. Within the plenum, relation is the key to perception and reason.

Du Châtelet's basic terms, and her argument from the principles of sufficient reason, indiscernibles, and continuity, are clear reminders of the extent to which the Institutions is intended as an exposition of Leibniz's thought. A reading of the source she foregrounds in Chapter 5, the Leibniz-Clarke correspondence, however, is an equal reminder that her work has its own vectors and zones of intensity. The examination of abstraction is one such area, indicating interests in interiority and the psychology of perception and ideation that have roots in the Cartesian intellectual tradition, and furthering the process by which her text actively constructs a thinking subject engaged in dialogue with the world.¹³

As Du Châtelet points out at the beginning of Chapter 6, “Du Tems,” Leibniz's definition of time has “beaucoup d'analogies” with his account of space. As space is the order of coexistents, so time is the “order of successions.” So thorough is the analogy that she proceeds to demonstrate in parallel manner to the previous chapter why, through the process of abstraction, time must appear to be uniform, independent of objects, and eternal, and why, nonetheless, it should be understood as none of those things. Stylistically, the organization of the chapter on space foregrounds narrative linearity; that on time, repetition, as the basic definition occurs in a series of contexts, each with slightly different analogies and emphases. Repetition, accompanied by change, produces the effect of temporality. Yet, as Du Châtelet indicates, spatial and temporal representations—for abstraction is representation—function analogously. In Leibnizian thought, temporality and simultaneity are projected onto one another through their parallel structure of relationality. In the Monadology, each simple substance mirrors the totality, just as the totality exists in terms of its relation to each monad, the resulting labyrinth of relations is both spatial and temporal: “every body responds to all that happens in the universe, so that he who saw all, could read in each one what is happening everywhere, and even what has happened and what will happen” (Monadology, § 61, p. 265).¹⁴

The Leibnizian model is a powerful one, not merely because of its role in physics, as historically influential as that was, but also because it responds to a problem we have seen elsewhere, notably in d'Alembert's Discours préliminaire, the problem of reconciling two apparently disparate and incommensurable orders of knowledge, the synoptic or systematic—“coexistent”—and the discursive or “successive.” The Leibnizian chiasmus rearticulates the orders by foregrounding the spatial aspect of the discursive, and the temporal dimension (through repetition) of the synoptic. Du Châtelet circumvents d'Alembert's problem by showing both orders to be construals of relationships, and by arguing for the usefulness of different constructions or explanatory schemes in different contexts. Her guiding figure is the non-canonical trope of analogy (rather than metaphor or metonymy). Analogy enables multi-directional correspondences based on shifting points of resemblance and continguity, and providing not a single model, but instead a series of connections. The ability to see the correspondence between space and time parallels the overall work of the Institutions, which is to see connections and intersections of metaphysics and physics.¹⁵

Thus on several fronts, we see how Du Châtelet arrests the dissipative effects of abstraction through connections and “figurations” of various sorts. The question comes to the fore in the chapters that serve to explicate the Leibnizian view of matter. Here, Du Châtelet examines the potential for infinite regress lurking within the Leibnizian principle of continuity (because of matter's theoretically infinite divisibility into “imperceptible gradations”). Leibniz himself referred to this problem as the “labyrinth of the continuum.” His arguments against the Newtonian vacuum invoke the continuity of the plenum as one of the implications of the principle of sufficient reason: “what reason can anyone assign for confining nature in the progression of subdivision? There are fictions merely arbitrary, and unworthy of true philosophy.”¹⁶ That “progression of division” led to other problems, however. As Du Châtelet explains:

nous sommes naturellement portés à croire que si nous pouvions étendre nos divisions jusqu'à l'infini, nous trouverions toujours de quoi diviser, ce qui entraine nécessairement dans ce labirinte de la composition, & de la division infinie du continu dans lequel on ne peut jamais trouver, ni le dernier terme de la division, ni le premier terme de la composition, & dont les Etres simples peuvent seuls nous tirer …

(194-95)

[we are naturally led to believe that if we could extend our divisions infinitely, we would always have more to divide, thus bringing us into the labyrinth of the composition and infinite divisibility of the continuum, in which we can never find either division's final term, nor composition's first term. Only simple substances can lead us out …]

Her distinction between the (infinitely divisible) geometrical body and the (composite, finite) physical body simplifies Leibniz's distinctions among the geometrical, the physical, and the phenomenal.¹⁷ Du Châtelet also tends to emphasize the extent to which the infinite underscores the ultimate unknowability of the world. Speaking of recent experiments with the microscope, she asserts that an infinity of smaller entities (corpuscules) escape our senses (197), rendering indispensable the simple substances which stand as the limit of divisibility. A marginal note in the manuscript puts it well:

… il devient tous les jours plus vraisemblable que la nature nagit que par developmens, or si chaque grain de bled contient le germe de tous les bleds qu'il doit produire il faut necessairement que les divisions actuelles de la matiere ayent des bornes, quoique ces bornes soyent imaginables pour nous.

(ms 158 verso, marginal addition)

[… every day it appears more likely that nature works developmentally, so, if each grain of wheat contains the germ of all the wheat it will produce, it follows necessarily that the actual divisions of matter must have limits, although these limits are (only) imaginable for us.]

The manuscript passage does not appear in the 1742 edition of the Institutions, where Du Châtelet emphasizes that our powerlessness to perceive and know the mechanical causes of phenomena does not hamper our ability to offer different schemas of explanation that enable us to function in the world. Du Châtelet is not persuaded that in order for science to proceed it is necessary to close off questions with over-hasty answers. Even though certitude is not available, careful hypotheses and delimiting of the needed explanatory register offer sufficient material “to satisfy our desire to know, when we know how to regulate it” (205).¹⁸ Du Châtelet negotiates a path between knowledge and skepticism, the endless proliferation and infinite divisibility of phenomena, and a term at which one can begin to construct an account of the world. Despite the limitations on what we may know, knowledge is still possible within the labyrinth of the continuum.

Thus, while the labyrinth continues to be an emblem of the insoluble, it no longer presents the kind of menace it holds for d'Alembert or others. Du Châtelet's Leibnizian universe of dynamic complexity and connectivity has its labyrinthine aspects, but is not overwhelmed by them. Du Châtelet uses the word in a conventional sense, but still gives it a different twist, when in Chapter 1 she affirms that the principle of sufficient reason preserves us from “ces labirinthes d'erreur que l'esprit humain s'est bâtis pour avoir le plaisir de s'y perdre” (27). Certainly the potential for pleasure in the vertiginous proliferation of possibilities has not been particularly remarked on before. There is no total dissolution of structure or meaning, needless to say. The dissipative tendencies of the labyrinthine are balanced by the shapes in which inquiry, identity, perception, and desire may be channelled or “figured.” The universe is infinitely complex, but absolutely harmonious.

Du Châtelet follows her discussion on infinite divisibility with a chapter that shows its relation to the qualities of matter: porosity, solidity, and of course “figure.” Here she defines figure, not simply as an attribute of finite extended bodies, their “configuration,” but rather as having “sa raison suffisante dans les Corps environans” [“its sufficient reason in the surrounding bodies”] (207). “Figure” is thus neither imposed from without nor perfectly innate; it is a function of dynamic relations among particles.¹⁹ In this chapter, which provides part of the transition between the “metaphysics” and “physics” halves of the Institutions, Du Châtelet considers the labyrinthine potential of matter itself, asserting that all bodies are penetrable and that they contain “une infinité de pores,” and remarking that our senses belie their appearance of unity and correspondence by a real incommensurability: “la main ne jugera jamais des sons, ni l'oreille des couleurs” [“the hand will never judge sounds, nor the ear colors”] (212). The schism among the senses suggests a kind of unanchored multiplicity in the reality they communicate; Du Châtelet's image of a being with only one sense at a time contrasts with the progressive accumulation of sensory and mental faculties in Condillac's well-known statue. One finds a kindred intuition in Walter Benjamin's essay on Naples, where “porosity is the inexhaustible law of the city, reappearing everywhere.”²⁰

The stamp of the definite is avoided. No situation appears intended forever, no figure asserts its “thus and not otherwise.”

(166)

Although similarly destabilizing, neither the “separateness” of the senses, however, nor the permeable universe of objects shot through with “matiere étrangere” provokes quite the sense of unease that we find in Benjamin. This is a world of relations and movement, of infinite penetrability without loss of identity, of disparate phenomena and substance, in which all that appears solid would melt into air but for the constant dynamic forces in matter which enable us to perceive cohesion in mere contiguity.

Universal harmony maintains balance within the system; hypotheticalism allows for knowledge within contingency; simple substances make the physical world finite and graspable within an endless network of relations. Yet even as she recognizes throughout her exposition the interdependence of the various components of Leibniz's system—the principles of contradiction and sufficient reason, continuity and the plenum—her awareness of the system's complexity is accompanied, especially in the manuscripts, by the occasional desire to speculate beyond the system.²¹ In the chapter on divisibility, for example, she returns to the principle of the identity of indiscernibles; i.e., that no two entities are ever identical. Her earlier discussion of this notion in Chapter 1 included the oft-cited anecdote of Leibniz's stroll through the gardens of Herrenhausen with Princess Sophia, to whom he explained that amidst the myriad of leaves around them, no two would ever be alike. In the margins of her discussion on divisibility and indiscernibles, Du Châtelet wonders aloud: “pourroit il y avoir quelquun entierement semblable a moi dans un autre monde” [“could there be someone exactly like me in another world”] (ms 180 verso). The answer is obvious, within the Leibnizian scheme wherein the possibility of two entities differing in number only is resolutely denied, and so the published text affirms (“personne ne doute que la suite des idées d'une Ame quelconque, ne soit différente de la suite des idées de toutes les autres Ames qui existent” [“no one doubts that the sequence of ideas of any person are different from the sequence of ideas of all other existing persons”], 145).²² The question's poignancy, however, remains. It suggests, among other things, that there is no such similar being in this world. The momentary marginal reflection hovers as a ghostly presence in the printed version. There is no one quite like Emilie du Châtelet; the Institutions de physique give her solitude a deeper meaning and lend it a purpose. Hence the vital importance of establishing a voice.

“Voice,” as we usually conceive of it, is related to identity, and as we have seen, the problem of preventing “identity” from dissolving into the continuum is of prime importance. On the one hand, everything in the plenum coheres along the cognitively infinite gradations of the labyrinthus continui, and is held in place by the harmony of sufficient reason. Like metaphor, such relations suggest a stable, ahistorical identity. On the other hand, the dynamic forces at work within the system, the metonymic insistence on the relations of each to all and all to each, leave a space for contingency and constant change.²³ And our perception, Du Châtelet explains, contains elements of both. As we saw earlier in the discussion of divisibility, the totality of objects, relations, and gradations is not available to perception—if it were, phenomena would dissipate into unintelligibility. We perceive continuity, but only because of gaps, memory loss.

… rien ne peut nous assûrer qu'entre deux perceptions qui paroissent se suivre immédiatement, il ne s'en est pas écoulé une infinité dont nous avons perdu le souvenir, & que des temps immenses séparent.

(131)

[… nothing can assure us that between two perceptions that appear to be in immediate succession, there has not flowed an infinity that we have forgotten, separated by immense periods of time.]

It is the work of analogy that constitutes our experience, a kind of cognitive bricolage weaving resemblance, contiguity, identity, and change into the constant narrative of perception. Such is the work of hypothesis.

Furthermore, as I have been arguing all along, this bricolage is emblematic of the textual work of authorial self-construction, or figuration, that provides a large measure of the impetus for the Institutions de physique. As she explains in the chapter on “figure,” form finds its sufficient reason in its environment, les Corps environans, just as, in later chapters, she will discuss gravity in relation to its effect on the shape of the earth (“la figure de la terre,” 322-8), and explain force in terms of its effects among elastic bodies.²⁴ The elasticity of form is crucial to the understanding of vis viva or force vive (now understood as kinetic energy), since force is legible only in “restitution,” reaction, and re-configuration (475). Textually, Du Châtelet herself takes shape, first, through the encounter with two bodies of work, Leibniz's and Newton's, and in the search for points of coordination; second, as she finds herself narrating, and eventually being drawn into, the scientific debate—becoming a voice.

The place of the Institutions in intellectual history is due to a large extent to its twenty-first chapter, “De la force des Corps,” which marks Du Châtelet's foray into the controversy over force vive or vis viva. The significance of that debate is still subject to discussion, but twentieth-century commentators have generally moved away from d'Alembert's pronouncement (in his 1743 Traité de dynamique) that the entire debate was a mere dispute over words. Both the Leibnizian and Newtonian notions of force have become part of modern physics.²⁵ Du Châtelet comes down squarely on Leibniz's side. In so doing, she criticizes various other accounts of force, among them that of Jean-Jacques Dortous de Mairan, Perpetual Secretary of the Academy of Sciences. The ensuing exchange in many ways realizes the authorial trajectory of the Institutions; the impression that it functions as a continuation of Du Châtelet's text is heightened by her decision to include both Mairan's reply and her rejoinder in the 1742 edition.

Du Châtelet's chapter on force begins with a strategic footnote:

Quoique l'Auteur des Institutions ait fait beaucoup de changemens à son Ouvrage pour cette seconde Edition, elle n'en a fait aucun à ce Chapitre XXI (on a seulement ajouté quelques mots au §582 pour l'éclaircir), afin que le Lecteur le trouve ici tel qu'il étoit, lorsque la dispute publique qu'elle a eue avec Mr. de Mairan, au sujet des Forces Vives, a commencé. On joint à cette Edition la Lettre de Mr. de Mairan à l'Auteur des Institutions, & la Réponse qu'elle lui a faite, ce sont jusqu'à présent les deux seules pièces que cette dispute ait produites.

(435-6n.)

[Although the author of the Institutions has made a number of changes for this second edition, she has made none to this Chapter 21 (other than adding a few words to §582 for the sake of clarity), in order that the reader may find it as it was when the public dispute with M. de Mairan on the subject of vis viva began. We have included M. de Mairan's Letter to the Author of the Institutions, as well as her reply. To date these are the only pieces produced by the dispute.]

This note retrospectively illuminates the care taken earlier by Du Châtelet in various footnotes (for example, 373n) to show her willingness to listen to new arguments and modify her views. The note will also be revealed some pages later to be a reply to Mairan's remark—chronologically anterior, but necessarily later in its placement in the book—that he has made no changes in the reprinting of his 1728 work on force motrice that she attacked in her chapter 21 (477).²⁶ The proliferation of reprints indicates the hardening of the opponents' positions. Judgements have varied as to the relative effectiveness of Du Châtelet's and Mairan's arguments,²⁷ and contemporary reactions, while generally favorable to the marquise, were sometimes marked by personal allegiances or a reluctance to become involved. In certain respects, however, the simple fact of Mairan's public reply achieved an important aim of the Institutions. As Du Châtelet wrote to Argental, “I am very honored to have such an adversary. Even to fail at this juncture would be fine, but I hope not to fail” (March 22, 1741).²⁸

The tone of Chapter 21 is quite different from the preceding ones. Du Châtelet begins with an expansive recapitulation that both situates the argument in a direct line from her basic principles and recalls its discursive location: “Vous avez vu dans le Chapitre prémier, que le principe de continuité, fondé sur celui de la raison suffisante, ne souffre point de saut dans la nature …” [“You saw in the first chapter that the principle of continuity, founded on that of sufficient reason, tolerates no leaps in nature …”] (435). The renewed foregrounding of the I-you relation between the writer and her son sets the stage for an increasingly prominent use of the first person pronoun as she inserts herself more and more into the debate. Du Châtelet recalls to her son the work by Mairan that they have read together and that she now proposes to examine in some detail in order to refute it. This is the most extended piece of close reading and criticism in the Institutions; its significance is underlined at the outset by another sign-posting footnote:

Voiez à la suite de ce Chapitre la Lettre de Mr. de Mairan à l'Auteur des Institutions, & la Réponse de l'Auteur à cette Lettre.

(453n.)

[See following this chapter the Letter from M. de Mairan to the author of the Institutions, and the author's response.]

The readers—since “voiez” and the third person suddenly evoke an audience other than young Louis-Marie—are thus enjoined to observe the debate, a debate in which they will be called upon as judges by both sides.

The citations from Mairan's treatise that Du Châtelet first comments on reveal much of the fundamental differences between their positions.

Mr. de Mairan dit, No 38 & 40 de son Memoire: “Qu'il ne faut pas estimer la force des corps par les espaces parcourus par le mobile dans le mouvement retardé, ni par les obstacles surmontés, les ressorts fermés, & c mais par les espaces non parcourus, par les parties de matières non déplacées, les ressorts non fermés, ou non aplatis: or dit-il, ces espaces, ces parties de matière, & ces ressorts sont comme la simple vitesse.”

(453)

[M. de Mairan says in parts 38 and 40 of his book: “That a body's force cannot be estimated by the space traversed by a moving object in retarded motion, nor by obstacles overcome or springs closed, etc; but by the spaces not traversed, by the particles of matter not disturbed, the springs not closed or flattened; for, he says, these spaces, these particles of matter, and these springs are like simple velocity.”]

As Carolyn Iltis observes, “Mairan was analyzing nature not as it was, but as it was not.”²⁹ The passage chosen by Du Châtelet to begin her refutation underscores this problem by its remarkable insistence on negation and non-engagement. As we have already seen, the position Du Châtelet espouses demands connection, activity, and reciprocity, through “restitution” and elasticity.³⁰ The Newtonian Mairan instead viewed matter as inert, acted on from without, devoid of internal activity or force.

In a sense, the two models inform the textual activity of the ensuing exchange. In her reading of Mairan in Chapter 21, Du Châtelet quotes extensively and couches her comments in the first person. Her remarks do not spare Mairan, whose work she presents as “the most ingenious attack on vis viva to date” (453), and she is clearly aiming at provocation in the final lines of her commentary, where she assumes the role of protective mother guarding her impressionable young son against the “seductions” of bad physics. To have his arguments described as séduisans (457) rankled with Mairan in the extreme and would haunt his reply, as if it had exerted its etymological power to divert his argument off course, away from the technical weight of Du Châtelet's analysis and onto her rhetorical model. There are dangers in his approach. Although he will score a few points on form, his irritation causes him to neglect much of the substance of the argument, leaving her the last word.

Mairan's reply is in the form of a letter—a typical gesture in many public “quarrels” of the period—which, typographically and textually, has the effect of foregrounding his institutional position and her gender and class.

LETTRE
DE
MR. DE MAIRAN,
Secrétaire Perpetuel de l'Académie Royale
des Sciences, & c. A Madame la Marquise
DU CHATELET.

With Mairan's opening words, “the Public shall judge,” several things happen. The Institutions shifts onto an entirely new communicational plane: je and vous are re-identified, Du Châtelet's son disappears, and both interlocutors will call upon le Public as arbiter of their debate. The act of publication becomes significant; Mairan calls attention to the new (but emphatically unrevised) edition of his Dissertation, which he “includes” with his letter, although Du Châtelet does not reprint it in her 1742 edition; she thanks him ceremoniously (505) and marks her mastery of his text by citing pages from both his 1728 edition and the new one.

Mairan's header underlines their respective social status: his important function in the nation's primary scientific institution, and her role as “society lady,” however influential or singled-out for note by the very fact of his acknowledgment. Much of Du Châtelet's dilemma as an intellectual is present in these lines: she may have been able to help her male friends achieve election to the Academy which remained closed to her, but she must spend her life distinguishing herself from the various amateur marquises who inhabit the popularizing scientific works of Algarotti and Fontenelle.³¹

Mairan's main line of attack—and his error—is to accuse her of not having read his work. He is at pains to cast her in the light of a gullible amateur, given to whims, easily influenced, and not disciplined enough to read primary texts. He refers to Leibniz as her “hero,” on whose “altar” he, Mairan, has been sacrificed. This is the language of sexual intrigue, not science. His flattering references to Du Châtelet's native intelligence are offered only so that he may claim that she is no more than the tool, or dupe, of “the Partisans of vis viva” (478-9). The assumption is that Du Châtelet's intelligence exists purely as “natural light,” vos propres lumières, incapable of withstanding corrupting outside influences. Most of his reply is couched in similarly condescending terms. Had she only “reflected a little,” she would have better understood the weakness of the arguments she put forth; had she read him at all, she would not have attacked him. Mairan's letter is shot through with requests to be read, for an “attentive and disinterested reading” (480). He claims that her quotations are wrong, and insinuates that she is not responsible for them.

C'est, Madame, que vous y paroissez toujours citer mes propres paroles, & que ce ne sont pourtant que les vôtres, ou celles d'un autre que vous avez citées, ou de simples résumés que vous y avez transcrits.

(483)

[You appear, Madam, always to cite my own words, and yet they are your own, or those of someone else whom you are quoting, or simple paraphrases that you have transcribed.]

Mairan's bitterness shows through in his italicized borrowings of words and phrases from the Institutions (“séduisans” and “subterfuge” for example), and in his constant insinuations that Du Châtelet has neither done her reading nor intended what she wrote (498).

Mairan both protects himself and shows his non-engagement with his interlocutor, by repeatedly emphasizing that his reply is a schematic one, neither “a complete Treatise” nor “a formal Refutation” (485). Tellingly, it is after having ironically qualified one of her arguments as ad hominem (by which he apparently means, unanswerable) that he permits himself one of his most brutal dismissals, but without addressing his criticisms to her directly.

Mais que diroit-on d'un homme, … dans la fausse persuasion que le double de tout nombre entier, ou rompu, est égal à son quarré … ? Ne lui répondroit-on point sur le champ, que 3 & 3 font 6, & que le quarré de 3 est pourtant 9; … ou plutôt se donneroit-on la peine de lui répondre?

(486-7)

[But what would one say of a man … under the false impression that the double of any whole number or fraction is equal to its square … ? Wouldn't one simply say that 3 and 3 are 6, and that the square of 3 is 9; … or would one even bother to respond?]

Although Mairan has referred to the proof in question as having come from Du Châtelet's acknowledged source, Herman, the passage still has the effect of achieving the sleight-of-hand (and truly ad hominem!) transformation of Du Châtelet into “un homme” just long enough for Mairan to gesture toward “his” foolishness and unworthiness as an interlocutor; even as he suggests that he cannot permit himself this level of boorishness with Madame la Marquise, he nevertheless succeeds in passing the message through rhetorical deflection.

Even when he does not claim to correct her argument, Mairan belittles her examples as “fortuitous” and “equivocal.” In his final paragraphs, he enlarges his perspective and situates the vis viva controversy in the contexts of the struggle between lumière and obscurité, unreflective nationalism, and the misfortunes brought about by “presuppositions, prejudice, recourse to authorities, and bias” (500). Having gone to at least some trouble to respond to them, he then claims that Du Châtelet's arguments contain nothing new (500), and recapitulates and enlarges his earlier insinuations that Leibniz is no more than a fad, a “hero” to “les Partisans des Forces Vives” in general, and to one would-be woman intellectual in particular. His final words politely tell us just what he thinks of her.

Je me flat[t]e, Madame, que vous regarderez toutes ces réflexions comme une preuve du cas que je fais de vos lumières, & de ce bon esprit qui ne sauroit vous permettre de résister au Vrai, quand il se présentera à vous sans nuage.

(504)

[I flatter myself, Madam, that you will regard these reflections as proof of my high opinion of your insight, and of the excellent mind that will not allow you to resist Truth when it is presented to you clearly.]

Whatever her philosophic allegiance may be or become, the marquise remains in Mairan's discourse an unresisting female awaiting revelation from beyond, from his own incarnation of the Truth.

Truth, Du Châtelet points out in the final pages of her reply, is certainly more important than the nouveauté or originality that he sees lacking in the Institutions, but it is not necessarily in his possession for all that.

… je me flatte, du moins, d'y avoir démontré, que votre façon d'estimer la force des corps, n'a pas l'avantage de la vérité, & je ne cherche pas à vous disputer celui de la nouveauté.

(541)

[… I flatter myself, at least, that I have demonstrated that your manner of calculating the force of bodies does not have the advantage of truth; I do not seek to dispute you that of novelty.]

As the italicized terms from Mairan's text suggest, Du Châtelet makes extensive use of his technique of ironic quotation. As he had shown himself to be nettled by her use of séduisans, she rises to the challenge of his injunction that she should lire et relire: “but I can assure you that the more I read and reread, the more I am confirmed in my opinion” (508).

“Reading” is in some ways at the heart of the matter. As Du Châtelet said in her preface, one could hardly write such a work as the Institutions without consulting others. Thus what is at stake is not her originality as such, but rather her ability to read, to comprehend, and to judge. Her first step in the demonstration of her abilities is to provide a scathing close reading of Mairan's letter, in which no indirect insult or insinuation goes unnoticed, any more than do the challenges to her proofs. Just as Mairan was pleased to paint himself as the purveyor of truth and the voice of Enlightenment, so Du Châtelet, having called attention to his tactics by echoing him, casts herself as the defender of scientific neutrality and seriousness (513, 516, 526, etc.). She calls attention to her procedure by affecting to abandon it, noting that “it is in spite of myself, and only to follow you, that I depart from the severe style” of philosophic debate (529-30). She subtly casts Mairan as the non-serious, unengaged dilettante, a role that his assertions that he was not offering a “full” reply only reaffirm.

Part of Du Châtelet's defense includes maintaining her position as someone who is open to new ideas, without appearing to be driven by whim. In effect she goes between the horns of the dilemma posed by Mairan, who criticized her for having changed her mind regarding his work, on the one hand; and for being subject to prejudice and authority, on the other: she would thus be both vacillating and obstinate, and in either case incapable of rational judgement. As we have seen in her use of footnotes, Du Châtelet presents herself as open to new ideas and hardly inflexible. But in her reply to his account of the writing and printing of the Institutions, she emphasizes the fact that her ideas on vis viva are not as recent, or as sudden, as he implies. As she narrates it, her work thus bears the mark of the successive stages in her ongoing process of self-education and figuration. It remains for her to indicate that she has correctly understood Mairan, and has not “tronqué et défiguré” his text as he claims.

To what extent has she “truncated and disfigured” Mairan? Here it is she who calls on the reader to judge the evidence presented in the double columns where she compares her Chapter 21 quotations and Mairan's 1728 text (510). It is in fact the case, as Mairan had said, that she has offered her readers a paraphrase, not a quotation. The paraphrase is syntactically marked as such by the use of indirect discourse, but the use of quotation marks (which appear on every line in the original) gives the passage the visual appearance of direct citation. Mairan protests that such “resumés” are not the same as his text (484). Unlike Mairan—or Leibniz, for that matter—Du Châtelet believes in synonymy, and she defends her paraphrases (which are, in fact, extremely close) by identifying them as his own words, “your very own” (513), as he would have recognized, she adds ironically, had he only “read closely.”³² The real issue is the question of authority, not authorship, although Mairan would like for the two to coincide.

Mairan's actual words, however, are not his personal property. Du Châtelet demonstrates this both by pointing out the adequacy of her paraphrases and, more insidiously, by adopting his technique of ironic italicized quotation. She had made it clear in her Avant-propos that she had no particular stake in “original authorship” as such. Her inaugural gesture of dispossession renders possible the authorial bricolage throughout the Institutions, gives her a place to stand, and makes the public debate possible. She appropriates or puts to use texts, without possessing them. As she observes in the opening lines of her reply, the significance of a text derives to a certain extent from its circulation in the world and its interaction with other texts:

je commence à croire véritablement les Institutions de Physique un Livre d'importance, depuis qu'elles ont procuré au Public la Lettre à laquelle je vais repondre …

(505)

[I have begun to believe the Institutions to be a truly important work ever since it procured the Public the letter to which I am about to reply …]

The exchange between Du Châtelet and Mairan offers two models of knowledge, each of which shows parallels with the philosophical positions of the two interlocutors. In Mairan's account, Du Châtelet's mind is like matter in Newtonian theory: inert and subject to external agency (Mairan's identification with le vrai puts him in the structurally same position with respect to Du Châtelet as God is in with respect to the world). He furthermore attempts to reassert control over a text that has slipped from his hands, both by reprinting his 1728 thesis without changes, and by claiming that any refutation of Du Châtelet's must be based on a misreading.

Du Châtelet's model for knowledge is the process I have been referring to as “figuration.” While denying herself absolute authority, she is free to pursue connections and variously structured analogies among texts, and to construct an intellectual position in which relations and encounters determine significance, and in which every element contains its possibilities for change: a mental monadology. As Steven Shapin has observed, if Newtonian matter-theory suggests a “hierarchy-justifying” model, then a hylozoist, intrinsically active model offers a position “available to groups resisting domination by a hierarchy.”³³ Despite the privileges of her social position, it is not difficult to see why such a model might appeal to Du Châtelet, who was keenly aware of the restrictions imposed by her sex. Du Châtelet is also part of a larger movement of integrative work in natural philosophy, as was Mairan himself. But her work on Leibniz and Newton goes beyond a simple catalog of useful concepts from either; it gives form, or “figure,” to those insights. The face-off with Mairan and the figurative strategies of the entire treatise enable us to understand how she can find a voice and face her public, without being liable to the critique Deleuze and Guattari level at visagéité. The figures of her discourse are not coercive impositions of a single name or interpretation on malleable and indeterminate reality, but instead negotiations based on the mutual interaction of “les Corps environans.” This same mobility and adaptability allows her to see the analogy between temporal/sequential and spatial/synoptic orders, where others, less able to maintain an equilibrium among differing interpretive schemas, founder on the shoals of incommensurability.

There is a sense in which Du Châtelet's Chapter 4 on hypothesis best represents this equilibrium in her writing. The chapter explicitly counters the Newtonian dictum, hypotheses non fingo.³⁴ Instead, Du Châtelet argues for the usefulness of hypothesis, which she examines in terms that emphasize its in-between status: between past and future, as it articulates what we know and what we don't yet know; between a priori and a posteriori truths, as it weaves existing schemas together with the potential changes wrought by experience. Du Châtelet acknowledges the danger of overextending one's hypotheses, but, like Descartes, she likens the technique to “the pathway leading to truth” (79).

By properly gauging their degree of probability, Du Châtelet asserts, one can prevent hypothesis from falling into “une fiction indigne d'un Philosophe” (“a fiction unworthy of a Philosopher”) (92). One might turn the phrase around to say that, properly used, hypothesis can provide une fiction digne d'un(e) Philosophe. As I. B. Cohen and others have noticed, the fingo of Newton's famous phrase can be rendered by either “frame,” as Andrew Motte translated it, or “feign,” which was Newton's usage. “Feign” brings out the etymological relation to “fiction,” a path provided by the common stem of fingere and figura. “Framing” is “feigning”; the hypothetical or “figurative” act posits, ultimately, that we construct reality in order to understand it in the dialogic process of perception. “Je me figure …” as Du Châtelet often says, is a common enough equivalent for “je pense,” but in her implicit version of the cogito, “thinking” has become a tool for framing—or feigning—a self and projecting it into the world. Even if there is only a negative answer to her marginal question,

Could there be someone just like me in another world?

the task of self-creation has produced results, through change and the apprehension of relations. In that act of apprehension, Du Châtelet finds her voice.

Notes

1. Margaret C. Jacobs, The Radical Enlightenment: Pantheists, Freemasons, and Republicans (London: George Allen and Unwin, 1981), 94. See also Steven Shapin, “Social Uses of Science,” in G. S. Rousseau and R. Porter, eds., The Ferment of Knowledge: Studies in the Historiography of Eighteenth-Century Science (Cambridge University Press, 1980), 93-109, and “Of Gods and Kings: Natural Philosophy and Politics in the Leibniz-Clarke Disputes,” Isis 72 (1981): 187-215. Steven Shapin and Simon Schaffer offer an exemplary case study of the intersection of sociopolitical regulation and the development of science in their Leviathan and the Air Pump, Hobbes, Boyle, and the Experimental Life (Princeton University Press, 1985). Charles Bazerman has shown how Newton deploys mathematical proof in order to eliminate discussion and “reduce disagreement to error,” in Shaping Written Knowledge: The Genre and Activity of the Experimental Article in Science (Madison: University of Wisconsin Press, 1988), 115-17. Robert Markley asserts that “the fiction of objectivity” allows the Royal Society to subsume disagreement “by furnishing a means to ground scientific fact in shared religious and sociopolitical beliefs.” Fallen Languages: Crises of Representation in Newtonian England, 1640-1740 (Ithaca: Cornell University Press, 1993), 98-99.

2. I. Bernard Cohen, The Newtonian Revolution (Cambridge University Press, 1980). See Rupert Hall, “Newton in France: A New View,” History of Science 13 (1975): 233-50. Aram Vartanian, Diderot and Descartes: A Study in Scientific Naturalism in the Enlightenment (Princeton University Press, 1953). See esp. chapter 3 on scientific method, 203-88. As Ellen McNiven Hine observes, “By the 1730s, it was no longer possible to be either a strict Cartesian or a strict Newtonian.” “Dortous de Mairan, the ‘Cartonian,’” Studies on Voltaire and the Eighteenth Century 266 (1989): 178.

3. Gabrielle-Emilie Le Tonnelier de Breteuil, Marquise du Châtelet, Institutions physiques, nouvelle edition (1742). Facsimile edition reprinted in vol. 28 of Christian Wolff, Gesammelte Werke Materialien and Dokumente, ed. J. Ecole et al. (Heldesheim, Zurich, New York: Georg Olms, 1988) 28:7. The page numbers remain those of the 1742 edition of the Institutions.

4. For a detailed analysis of the developments of Du Châtelet's thought as she revised the Institutions, see Linda Gardiner Janik, “Searching for the Metaphysics of Science: The Structure and Composition of Madame du Châtelet's Institutions de physique, 1737-1740,” Studies in Voltaire and the Eighteenth Century 201 (1982): 85-113. Carolyn Iltis assesses certain arguments and discusses the status of integrative projects in “Mme du Châtelet's Metaphysics and Mechanics,” Studies in History and Philosophy of Science 8 (1977): 29-48; W.H. Barber situates Du Châtelet in the context of Leibnizianism in France in “Mme Du Châtelet and Leibnizianism: The Genesis of the Institutions de physique,” in The Age of Enlightenment, ed. Barber et al. (Edinburgh: Oliver and Boyd, 1967) and in his broad study, Leibniz in France from Arnauld to Voltaire: A Study in French Reaction to Leibnizianism, 1670-1760 (Oxford: Clarendon Press, 1955), 135-40 and 182-86. Erica Harth examines Du Châtelet's Cartesianism in the Institutions and other writings, in Cartesian Women, 189-213. For biographical treatments, see Elisabeth Badinter, Emilie, Emilie: L'ambition féminine au XVIIIe siècle (Paris: Flammarion, 1983) and René Vaillot, Madame du Châtelet (Paris: Albin Michel, 1978).

5. My discussion, needless to say, is indebted to Erich Auerbach's superb essay, “Figura, originally published in 1944 and reprinted in Scenes from the Drama of European Literature (Minneapolis: University of Minnesota Press, 1984), 11-76.

6. As when, for example, she refers to the “celebrated Wolf, whom you used to hear me talking about with one of his disciples who was with us for a while and sometimes gave me excerpts from his work (13). The disciple is Du Châtelet's tutor Koenig; one may suppose that this indirect reference to his limited assistance is her response to his accusation that she had plagiarized his work. (See Janik, “Searching for the Metaphysics” 96-97).

7. See also the discussion of the role in her preface to her translation of Mandeville's Fable of the Bees, in which she contends with both the subordination of translators to authors and that of women to men. “Mme du Châtelet's Translation of the ‘Fable of the Bees,’” ed. Ira O. Wade, Studies on Voltaire, with Some Unpublished Papers of Mme du Châtelet (Princeton University Press, 1947), 131-87.

8. See Hugh M. Davidson, “Voltaire Explains Newton: An Episode in the History of Rhetoric,” in The Dialectic of Discovery, ed. John Lyons and Nancy Vickers (Lexington, KY: French Forum, 1984), 72-82.

9. Du Châtelet, manuscript of the Institutions de physique. BN (Bibliothèque Nationale) f.fr. 12265 (p. 2).

10. See Paul de Man's comments on the “curious choice of examples” in Locke's Essay. “The Epistemology of Metaphor,” Critical Inquiry 5 (1978): 13-30; also Milton Wilson, “Reading Locke and Newton as Literature,” University of Toronto Quarterly 57 (1988): 471-83, especially his remarks on “negative narration” in conditional or hypothetical statements, pp. 480-82.

11. “Faces … delimit a field that neutralizes in advance any expressions or connections unamenable to the appropriate significations.” Gilles Deleuze and Félix Guattari, A Thousand Plateaus (168). See also the discussion 115-16.

12. De Man, “Epistemology,” 22-23.

13. For a useful contrast, see Leibniz's fifth paper in the correspondence with Clarke (L 5.47), for his version of “how men come to form to themselves the notion of space” (p. 63).

14. Michel Serres offers an extended reading of the Monadology's reconceptualizing of system as complexity and multiple relations (from the individual to the whole, and from the whole to each individual) as a key to his work. Le Système de Leibniz et ses modèles mathématiques (Paris: PUF, 1968), esp. 620-31.

15. A similar technique for maintaining a connection between space and time is offered by the medieval practice of “figural interpretation.” In Erich Auerbach's words, “Figural prophecy implies the interpretation of one worldly event through another; the first signifies the second, the second fulfills the first.” “Figura,” 58. The events or persons so related maintain their historical concreteness, but their signification is apprehended in a transhistorical, spiritual act, in which they are “viewed primarily in immediate vertical connection with a divine reality” (72). Thus are (temporal) sequence and (spatial) simultaneity projected onto one another.

16. Leibniz's fourth paper, The Leibniz-Clarke Correspondence, with Extracts from Newton's Principia and Opticks, ed. H. G. Alexander (Manchester University Press, 1956), 44-45.

17. See Leibniz's letter XXIII to Arnauld of Oct 6, 1687. Discourse on Metaphysics, Correspondence with Arnauld, Monadology, trans. George R. Montgomery (1902; reprint, La Salle, IL: Open Court, 1973), 222-23. For a discussion of the problem of the continuum in Leibniz, see J. E. McGuire, “‘Labyrinthus continui’: Leibniz on Substance, Activity, and Matter,” in P. K. Machamer and R. G. Turnbull, eds., Motion and Time, Space and Matter (Columbus: Ohio State University Press, 1976), 290-326.

18. Laurens Laudan discusses the shift from a similar, implicitly Cartesian, hypotheticalism in Boyle and Glanville to the later belief of Newton and others that improved instrumentation and patient experimentation would unlock all of nature's secrets. “The Clock Metaphor and Probabilism: The Impact of Descartes on English Methodological Thought, 1650-1665,” Annals of Science 22 (1966): 73-104. It is interesting to note that, although Du Châtelet makes a case similar to Descartes's in arguing that there is no way of knowing which of any number of possible mechanical explanations of a phenomenon is correct (just as we can hypothesize about the internal organization of a clock, but not see inside), her watch analogy makes a different point about the autonomy of explanatory registers.

19. Locke, on the other hand, defines “figure” in terms of the visual perception of boundaries “that really exist in the coherent masses of Matter.” An Essay concerning Human Understanding, ed. Peter H. Nidditch (Oxford: Clarendon Press, 1975), 168.

20. Walter Benjamin, Reflections: Essays, Aphorisms, Autobiographical Writings, ed. Peter Demetz, trans. Edmund Jephcott (New York: Harcourt, Brace, Jovanovich, 1978), 168.

21. In Deleuze's account of Leibniz, such desiring speculation is produced by the system's own dynamics, its emphasis on variety within unity. Le Pli: Leibniz et le baroque (Paris: Minuit, 1988), 78.

22. Leibniz claimed that this principle of “the identity of indiscernibles,” according to which any two individuals in whom the predicates are entirely the same are indiscernible from one another and are in fact one and the same, was one of the mainstays of his system. As we shall see below, it is also extremely important in Condillac's logic and has strong resonances in Diderot's work. See section 9 of the Discourse on Metaphysics as well as Leibniz's Letter 8 to Arnauld (May, 1686) Discourse on Metaphysics, Correspondence with Arnauld, Monadology, 14-15, 111.

23. On metaphor as necessity and metonymy as contingency, see Paul de Man, Allegories of Reading (New Haven: Yale University Press, 1979), 14-15, 63.

24. For a useful account of the theories of force that Du Châtelet takes over from Leibniz, see Richard S. Westfall, Force in Newton's Physics: The Science of Dynamics in the Seventeenth Century (New York and London: Elsevier and Macdonald, 1971), esp. Chapter 6, “Leibnizian Dynamics,” 283-322.

25. Westfall, Force, 505. See also H. G. Alexander's introduction to the Leibniz-Clarke correspondence, xxix-xxxii. A different turn on the outcome is offered by David Papineau, who sees it as a revision of physical thought resulting in “the repudiation of both.” “The Vis viva Controversy: Do Meanings Matter?” Studies in History and Philosophy of Science 8 (1977): 142. See also Thomas Hankins, “Eighteenth-Century Attempts to Resolve the Vis Viva Controversy,” Isis 56 (1965): 281-97. Carolyn Iltis discusses Leibniz's and Du Châtelet's participation in various stages of the debate, and examines the means by which theological, metaphysical, and emotional commitments within the scientific community precluded real debate or objective analysis of the data. “Leibniz and the Vis viva Controversy,” Isis 62 (1971): 21-35; “The Leibnizian-Newtonian Debates: National Philosophy and Social Psychology,” British Journal of the History of Science 6 (1973): 343-77; and “Madame du Châtelet's Metaphysics and Mechanics,” Studies in History and Philosophy of Science 8 (1977): 29-48.

26. Jean Jacques Dortous de Mairan, Dissertation sur l'estimation et la mesure des forces motrices des corps (1728; rpt. Paris, 1741). Ellen McNiven Hine discusses Mairan's own integrative tendencies in “Dortous de Mairan, the ‘Cartonian,’” Studies on Voltaire and the Eighteenth Century 266 (1989): 163-79.

27. Without venturing into the physics of the matter himself, René Taton claims that Du Châtelet's quarrel with Mairan and Jurin “exceeded her competence” (and he is also at some pains to minimize her role in Voltaire's Eléments and even in her own translation of Newton). “Madame du Châtelet, traductrice de Newton,” Archives internationales d'histoire des sciences 22 (1969): 185-210. In a more thorough discussion of the scientific issues, however, C. Iltis shows that Du Châtelet “proceeded to reduce the arguments of Jean-Jacques Mairan … to non-sense.” “Mme du Châtelet's Metaphysics and Mechanics,” 40.

28. On this episode see Badinter, 324-43; Vaillot, 208-11.

29. Iltis, “Metaphysics and Mechanics,” 41.

30. R. S. Westfall sees the analysis of imperfectly elastic bodies in Leibniz's Essay on Dynamics “the cornerstone of the ultimate principle of the conservation of energy.” Force, 295.

31. Erica Harth ably characterizes Du Châtelet's frustration and her complex relationships with male mentors, the Academy of Science, and the gendering of “popular science” as feminine, Cartesian Women, 199-208.

32. Du Châtelet claims that there is no other difference between the passages “que la différence numérique des mots” (511), a strategically useful assertion, but hardly in keeping with the principle of the identity of indiscernibles!

33. Shapin, “Social Uses of Science,” in Rousseau and Porter, Ferment, 135-36.

34. Newton's position on hypothesis hardened over time, as Bernard Cohen's study of the revisions of the Principia shows. Introduction to Newton's ‘Principia’ (Cambridge: Harvard University Press, 1971) 241-45. According to Cohen, the final version, “Hypothesis non fingo,” is an “absolutely pejorative expression.” See also his comparison of Newton and Descartes, The Newtonian Revolution, 99-109.