In Chapter 7  (Chapter 10 in the manuscript) Du Châtelet examines the question of the origin of matter. Aristotle believed that there were four elements that everything was made up of: earth, water, air, and fire. He thought that these elements were simples and not resolvable into each other. Du Châtelet speaks of these elements as principles (which is omitted in the German translation)  and maintains that it was the idea of Aristotle that the mixture of these four principles resulted in all that surrounds us.

Comparing Aristotle with Descartes, Du Châtelet concludes that “for Aristotle’s four principles Descartes substituted three kinds of small bodies of different sizes and shapes, these small bodies, or elements, resulted, according to him, from the original divisions of matter, and were formed by their combination: fire, water, earth, air, and all the bodies that surround us” (InstPhy, § 118).  Most philosophers have abandoned this view and hold the opinion that matter is simple mass (InstPhy, § 118):

La plûpart des Philosophes d’aujourd’hui ont abandonné les trois Elemens de Descartés, & conçoivent simplement la Matiére comme une masse uniforme & similaire, sans aucune différence interne. (Amsterdam 1742)

Most philosophers today have abandoned Descartes’ three elements and conceive of matter simply as a mass, uniform and similar, with no internal difference. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

The theory that matter is made up of atoms, which are the smallest particles of matter and which have such diversified forms and sizes that the infinite variety existing in this universe can result from them, goes back to Epicurus and was revived by Pierre Gassendi. Du Châtelet contrasts this kind of atomism with Leibniz’s concept of monads which rests on the idea that the reason for the extension of matter might be found in parts which are not extended (InstPhys, § 119):

Mr. de Leibníts qui ne perdoit jamais de vue le principe de la raison suffisante, trouva que ces Atomes ne lui donnoient point la raison de l’étendue de la Matière, et cherchant à découvrir cette cette raison, il crut voir qu’elle ne pouvoit être dans des parties non étendues, et c’est ce qu’il appelle des Monades. (Amsterdam 1742)

M. de Leibnits, who never lost sight of the principle of sufficient reason, believed that atoms did not give him the reason for the extension of matter, and endeavoring to discover this reason, he thought that this reason might be found in a different idea of particles, those without extension, (in parts which are not extended), and this is what he called monads. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Du Châtelet notes that little is known about Leibniz’s monadology, especially in France. The same holds for Christian Wolff’s work and his interpretation of Leibniz’s philosophy. She therefore aims to present Leibniz’s system, which took a totally new form in Wolff’s hands (InstPhy, § 119):

Peu de gens en France connaissent autre chose de cette opinion de M. de Leibnits que le mot des Monades; les livres du célèbre Wolff, dans lesquels il explique avec tant de clarté & d’éloquence le système de Mr. de Leibnits, qui a pris entre ses mains une forme toute nouvelle, ne sont point encore traduits dans notre Langue: je vais donc tâcher de vous faire comprendre les idées de ces deux grands Philosophes sur l’origine de la Matière; une opinion que la moitié de l’Europe savante a embrassèe, mérite bien qu’on s’applique à la connaitre. (Amsterdam 1742)

Few people in France know anything of this opinion of M. Leibniz’s but the word, monads; the books of the famous Wolff, in which he explains so clearly and eloquently M. Leibniz’s system, which, in his hands, took a totally new form, have not yet been translated into our language. So, I am going to try to explain the ideas of these two great philosophers on the origin of matter; an opinion, which half of learned Europe has embraced, which deserves serious attention. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Simple beings cannot be represented by imagination. Only understanding («entendement») can conceive of them. If someone asked why there were watches, he certainly would not be content if he was answered, it is because there are watches; it would be necessary to come to things that were not watches, this is to say, to springs, to cogwheels, to pinions, to the chain, etc. Analogous, if one says there are bodies with extension because there are atoms, it is as if one said: “there is extension, because there is extension.” This is in effect saying nothing at all. Consequently, just as the sufficient reason for a compound number can only be found in a noncompound number, that is to say, in a unit, the sufficient reason for extended and composed beings can only be in simple beings. So, it must be admitted there are simple beings, since there are compound beings; and compound, extended beings exist because there are simple beings (InstPhy, § 120):

Si l’on veut satisfaire à ce principe sur l’origine de l’étendue, il faut en venir enfin à quelque chose de non-étendu, & qui n’aît point de parties, pour rendre raison de ce qui est étendu, & qui a des parties: or une Etre non étendu & sans parties, est une Etre simple. Donc les composés, les Etres étendus éxistent, parce qu’il y a des Etres simples. (Amsterdam 1742)

if one wants to fulfill this principle about the origin of extension, it is necessary to come in the end to something that is without extension, that has no particles, to give a reason for that which is extended and has particles. Now, a being without extension and without particles is a simple being; so, compounds, extended beings, exist because there are simple beings. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

The analogy of a watch composed of springs and wheels in order to explain and justify the existence of substantial units, or simple beings, can be found in Leibniz’s Système nouveau de la nature et de la communication des substances (first published in Journal des Sçavans 1695, 27 Juin 1695, p. 294—300, 4 Juillet, p. 301—306). Simple beings are indivisible (i.e., without parts), therefore they are not separable; they are unextended, therefore without shape (for shape is the limitation of extension); for the same reason they have no magnitude («grandeur»), fill no space, and have no internal motion; thus, a simple being cannot originate from a compound being nor from another simple being. It follows that the reason, or cause of simple beings must be in a necessary being, this is to say, in God, the immediate reason for simple beings. Further, no simple being can identical with another simple being, because simple beings must have intrinsic determinations, enabling us to understand why the compounds that result from them are such as they are (consequence of the principle of indiscernibles).

Although simple beings cannot be seen, touched, or represented in imagination, perpetual change can be observed in compound beings. This enables us to assume a principle of action («principe de action») in simple beings.  This principle, which contains the sufficient reason for the actuality of an action (l’actualité d’une action),  is called force (InstPhy, § 126):

On observe dans les composés un changement perpétuel; rien ne demeure dans l’état où il est; tout tend au changement dans la nature; or puisque la raison prémiere de ce qui arrive dans les composés se doit enfin trouver dans les simples, dont les composés resultent, il doit y avoir dans les Etres simples un principe d’action capable de produire ces changemens perpétuels, & par lequel on puisse comprendre pourquoi les changemens se sont dans ul tel tems, plutôt que dans tout autre, & d’une telle manière, plutôt qu’autrement. (Amsterdam 1742)

Perpetual change can be observed in compounds; nothing stays in the same state; all tends to change in nature. Now, since the primary cause for what happens in compounds must ultimately be found in simple beings, from which the compounds resulted, there must be found in simple beings a principle of action capable of producing these perpetual changes, and by which may be understood why the changes happen in such a time, rather than in any other, and in such a manner, rather than in any other. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Du Châtelet distinguishes between the actuality and the possibility (ability) of an action, or force. By contrast to the simple power or ability to act, the actuality of a force depends on whether there is a resistance which prevents force from acting. At this point Du Châtelet refers to the role of  “energy” as follows (InstPhy, § 126):

Les êtres simples sont donc doués d’une force, quelle qu’elle puisse être, par l’énergie de laquelle ils tendent à agir, et agissent en effet dès qu’il n’y a point de résistance. (Amsterdam 1742)

So, simple beings are endowed with a force, whatever it may be, as a result of whose energy they tend to act, and act indeed as soon as there is no point of resistance. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

The principle of energy conservation is clearly stated here, although not in the form known today. It is linked to another conservation principle, i.e. the conservation of matter (matter remains the same while it takes different forms). In this rudimentary form of conservation principles the concept of substance is redefined and linked with the principle of invariance: substance is that which conserves (keeps constant) essential determinations, whereas attributes as its modes vary and succeed one another.

One can specify the series (succession) of the states of simple beings by distinguishing between actual, precedent and antecedent states. They correspond to the timelike order of successions, i.e. present, past and future states. Given the supposition that “there must be a sufficient reason why such a state is actual, and why, rather in such a time than in any other. Now, this reason can only be found in the preceding state, and the reason for that will be in the state antecedent to it, and so on back to the first” (InstPhy, § 129). Du Châtelet concludes (InstPhy, § 131):

tous les états de tous les Elémens ont une rélation à l’état présent qui doit coéxister avec eux, aux états passés dont cet état présent est une suite, & aux états qui le suivront, & dont il est la cause. Ainsi, dans le systême de Mr. de Leibnits on peut proposer ce problême: l’état d’un Elément étant donné, en déterminer l’état passé, présent, & futur de tout l’Univers: la solution de ce problême est, à la vérité, réservée à l’éternel Géomètre. (Amsterdam 1742)

all future states of the elements will also have a relation to the present state that must coexist with them, to past states from which this present state results, and to the states that will follow it, and of which it is the cause. Thus, it can be said that in M. Leibniz’s system, it is a metaphysical- geometric problem, the state of an element being given, to determine the past state, present, and future of all the universe. The solution of this problem is reserved to the Eternal Geometrician. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Leibniz thought that the state of each element contains a relation to the present state of the entire universe, to all the states that will be born from the present state, just as in a well-made machine the least part has a relation to all the others. This idea, culminating in Leibniz’s project of a characteristica universalis, would afford a direct insight in all possible relations of the whole universe and would turn metaphysics into an analysis of universal algebra. Du Châtelet remains skeptical regarding the success of this project (InstPhy, § 135):

peur-être quelque jour trouvera-t-on un calcul pour les vérités Métaphysiques, par le moyen duquel par la seule substitution des caractéres, on parviendra à des vérités comme dans dans l’Algebre. Mr. de Leibnits croyoit l’avoir trouvé; mais par malheur il est mort sans communiquer sur cela ses idées, qui du moins nous auroient mis sur la voie, si elle n’avoient pas donné tout ce que le nom d’un aussi grand homme promettoit. (Amsterdam 1742)

Perhaps some day a calculus for metaphysical truths will be found, by means of which, merely by the substitution of characters, one will arrive at truths as in algebra. M. Leibniz believed he had found it; but sadly, he died without imparting his ideas on this, which at least would have put us on the right path, even if they had not yielded all that the name of such a great man promised. (Copyright © 2009 BZ)

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Chapter 7 ends with a sceptical attitude, which nevertheless entails an optimistic note. Du Châtelet questions the possibility to gain knowledge of simple beings, or monads by experiments and experience (InstPhy, § 136):

Il ne m’appartient pas de décider si les Monades de M. de Leibnits sont dans le même cas: mais soit qu’on les admette, ou qu’on les refute, nos recherches sût la nature des chofès n’en seront pas moins sures; car nous né parviendrons jamais dans nos expériences jusqu’à ces premiers Elemens qui composent les Corps. (Amsterdam 1742)

It does not rest with me to decide if the monads of M. Leibniz are of the same case; but whether they are accepted or rejected, our research on the nature of things will be no less certain; for, in our experiments we never will arrive at these first elements of which bodies are composed.

[ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ]

Interestingly, the Paris edition of 1740 contains an additional remark that was deleted in the Amsterdam edition of 1742, namely the following addition:

& les Atomes physiques (§ 172.), quoique composés encore d’Etres simples, sont que suffisans, pour exercer le desir que nous avons de connoître. (Paris 1740)

and the physical atoms (§.172), although still composed of simple Beings, are more than sufficient to exercise our desire for knowledge. (Copyright © 2009 BZ)

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The manuscript [ Manuscript Bibliotheque nationale de France (Paris), Fonds français 12265 ] contains further additions which have been integrated into Chapter 8, § 162 in the edited versions.

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