This chapter opens with a discussion of the Cartesian doctrine that the essence of a body, or matter, is  extension. This doctrine was also shared by Nicolas Malebranche and others. The argument for this assertion is as follows: Essential is what is inseparable from matter. The following attributes are eligible: shape, divisibility, impenetrability, and extension. Shape, divisibility, and impenetrability presuppose extension. Extension does not presuppose anything. Once extension is given, shape, impenetrability, and divisibility are given as well. Consequently, extension is the essence of bodies. According to this definition, matter is a passive substance; it can never become active by any possible modifications. The only excuse the Cartesians have is the recourse to the will of God in order to explain active force.

However, given the principle of sufficient reason, matter is inhomogeneous (dissimilar) and distinguished by internal qualities. The consequence is as follows (InstPhy, § 139):

Ainsi l’essence du Corps ne peut consister dans la simple étenduë, puisqu’il est nécessaire, pour satisfaire au principe de la raison suffisante qu’il n’y ait point de différences internes dans les parties de la Matière, & que par conséquent les différences ayent leur fondement dans l’essence de la Matière, & naissent de quelques-unes de ces propriétés. (Amsterdam 1742)

Thus the essence of Body cannot consist in simple extension since it is necessary, in order to satisfy the principle of sufficient reason, that there are no internal differences in the parts of the Matter, & that consequently the differences have their foundation in the essence of the Matter, & arise from some of these properties. (Copyright © 2018 KB)

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

Paragraphs 139 and 140 of the Paris edition do not agree word for word with the Amsterdam edition, nor with the manuscript. For example, in the Amsterdam edition, and also in the manuscript, the analogy between body and machine is missing. Despite these small deviations, the line of argument is the same: Matter in motion presupposes force. Force is therefore as necessary to the essence of bodies as extension (InstPhy, § 141):

L’étendue qui résulte de la composition n’est donc pas la seule propriété qui convienne au Corps et qui compose son essence, il y faut ajouter encore le pouvoir d’agir: ainsi la force qui est principe de l’action se trouve répandue dans toute la Matière, et il ne sautoir y avoir de Matière sans force motrice, ni de force motrice sans Matière, comme quelques Anciens forte l’avoient sort bien reconnu. (Amsterdam 1742)

The extension that results from the composition is therefore not the only property that is suited to odies; the power to act must also be added. Thus, the force that is the principle of action finds itself spread throughout all Matter, and there cannot be any Matter without motive force, nor a motive force without Matter, just as some Ancients recognized so well. (Copyright © 2018 KB)

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

Annother property of bodies is that of resistance, or inertia (InstPhy, § 142):

Cette force résistante a été exprimée par Képler d’une manière fort significative par les mots de vis inertie, force d’inertie. Sans cette force, aucune des loix du mouvement ne pourroit subfifter, & tous les mouvemens se seroient sans suffisante: car dès qu’on admettroit que la Matiere fût sans résistance, ou force d’inertie, il n’y auroit plus de proportion entre la cause & l’effet. (Amsterdam 1742)

Kepler expressed this resistant force in a significant way by the words vis inertia, force of inertia. Without this force, none of the laws of motion could subsist, and all motions would be without sufficient reason. For were we to admit that Matter was without resistance, or force of inertia, there would be no proportion between cause and effect. (Copyright © 2018 KB)

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

Instead of referring to Newton’s definition of inertia as vis insita, or innate force of matter, i.e., the power of resisting (see Definitio III, Principia 1726), Du Châtelet mentions Johannes Kepler who has introduced the term “inertia” in his Epitome Astronomiae Copernicanae (published in three parts from 1617–1621). Kepler understood inertia as a property that inhibits motion and represents an impediment to it.

Considering that bodies are inert, matter is a heavy mass without action; and we call extension matter, insofar as we regard it as something passive. That sounds very much like Newton’s concept of matter. However, Du Châtelet disagrees with Newton regarding the concept “body,” or “matter.” According to Du Châtelet the essence of a body consists in (i) extension («étendue»), (ii) inertial force («force d’inertie»), and (iii) moving/motive force («force motrice») (InstPhy, § 143):

Inertial force is characerized as a passive force, moving force as  an active force. In striking difference to Newton, Du Châtelet refers to the principle of the sufficient reason in order to explain and to justify why matter is determined by these three essential properties. Her argument is as follows: The principle of sufficent reason is the principle of complete determination. Any theory regarding the laws of motion has to fulfill the principle of complete determination, i.e., it has to fulfill the criteria of completeness, including consistency and independence. Both, extension and inertia, are necessary conditions for the possibility (ability) of a body to move, but not sufficient for the actualization of the (potential) motion of a body. The force of inertia is here a kind of selection principle for distinguishing between the possibility and the actualization of motion. Moving force, on the other hand, contains the sufficient reason of the actuality of the changes in the bodies. Thus, it is needed in order to explain why a body really (actually) moves (InstPhy, § 147):

Ces trois principes, savoir, l’etendue, la force passive, & la force motrice, ne dépendent point l’un de l’autre; car ce sont les essentielles du Corps, & on a vu que les essentielles ne se déterminent point mutuellement, mais qu’elles peuvent seulement sûbsister ensemble sans se détruire. Ainsi, la force active & la force passive ne découlent point de l’étendue, & ces deux forces ne sont point une suite l’une de l’autre, ni l’origine de la propriété qu’on nomme étendue. (Amsterdam 1742)

These three principles, that is to say extension, passive force, and motive force, do not depend at all upon each other; for these are the essentials of Body, and we saw that the essentials do not mutually determine each other, but that each is able to subsist with the others without destroying one another. Thus, active force and passive force do not arise from extension, and these two forces neither follow one from the other, nor are they the origin of the property we call extension. (Copyright © 2018 KB)

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

Insofar as extension, passive force (inertia) and active force (moving force) are essential determinations of a body, which are independent from each other, they must seem to us to be substances, i.e., durable and modifiable subjects. In fact, neither extension nore force (i.e., active and passive force) are truly substances, but phenomena (InstPhys, § 152):

Ce ne sont que des Phénomènes qui résultent de la confusion, qui regne dans nos perceptions. (Amsterdam 1742)

They are only Phenomena that result from the confusion that reigns in our organs and in our perceptions. (Copyright © 2018 KB)

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

In the corresponding manuscript-paragraph the notions “confusion,” and “perceptions” are missing. Instead, the term “abstraction” is used. In any case, if we understand by phenomena imagintions, or appearances that originate from the confusion (abstraction) of realities called simple beings, the three essential properties of bodies are phenomena, or, to be precise, substantial phenomena (InstPhy, § 156):

Les trois propriétés qui font l’essence du Corps, sont donc des Phénomènes, mais on peut dire que ce sont des Phénomènes, mais on peut dire que ce sont des Phénomenes substantiés, comme les appelle M. Wolf, c’est-à-dire, des Phénomènes qui nöus paraissent des substances, mais qui n’en font cependant pas. (Amsterdam 1742)

The three properties that make the essence of Body are therefore Phenomena, but we can say that they are Substantial Phenomena, as Mr. Wolff calls them, that is to say Phenomena that seem substances to us, but that nevertheless are not; for there are no true substances except simple Beings. (Copyright © 2018 KB)

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

The distinction between the phenomenal and the real world leads Du Châtelet to the distinction between two kinds of moving forces in a Leibnizian sense: primitive and derivative forces (InstPhy, § 158):

Il y a deux fortes de forces actives. Mr. de Leibnits appelle la force qui se trouve dans tous les Corps, & dont la raison est dans les Elérnens , force primitive , & celle qui tombe sous nos sens , & qui nait dans le choc des Corps du conflict de toutes les forces primitives des Elémens, force derivative; cette dernière force dérive de la prémière, & n’est qu’un Phénomène, comme je vous l’ai expliqué plus haut. (Amsterdam 1742)

There are two sorts of motive force; Mr. Leibnitz calls the force that is found in all Bodies, and the reason for which is in the elements, primitive force; and that which falls under our senses and originates in the collision of Bodies, from the conflict of all the primitive forces of the Elements, derivative force. (Copyright © 2018 KB)

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

According to Leibniz the so called primitive force is inherent in every substantial unity, the monad. Leibniz also called the monad a substantial form or first entelechy, i.e. the principle and source of activity. The primitive force always remains constant; derivative forces, on the other hand, arise as modifications of primitive forces through the collision of bodies with one another. Du Châtelet remarks: We cannot know anything about the primitive force. We can explain only the phenomena, therefore derivative forces, which arises from the collision of bodies. With this statement she positions herself between Leibniz and Robert Boyle. The difference between both turned on the question of the limitation of God’s power with respect to the creation of nature. In Leibniz’s view Divine reason and Divine will goes hand in hand such that no choice is entirely indifferent: it must be the best possible choice rationally considered. Robert Boyle’s voluntarist theology, on the other hand, denies that God must have a sufficient reason for creation, holding that he is absolutely free to create any world he so chooses by an arbitrary fiat of Divine will. Boyle rejected substantial forms, and real qualities as mere names. He also rejected nature conceived as a truly self-sufficient entity. In The Sceptical Chymist: or Chymico-Physical Doubts & Paradoxes (1661) Boyle presented his famous hypothesis that matter consisted of atoms and clusters of atoms in motion and that every phenomenon was the result of collisions of particles in motion. In this later treatise, The Christian Virtuoso (1690), Boyle presented the view of nature as a clocklike mechanism and expressed reservation about the principle of conservation. Du Châtelet counters this view by emphasizing that we must admit our ignorance, when the possibility of our explanations surpasses our powers. As an example of this ignorance she mentions the gravitational force for which the mechanical cause is unknown.

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