A being, in the most general sense, is comprised of three different types of determinations: essentials, attributes, and modes. Chapter 3 is devoted to this distinction. When we consider things which surround us, we observe that a stone, for example, is sometimes hot and sometimes cold, but it is always hard, composed of parts, and heavy. That means that some determinations characterizing an object are variable, others are constant (InstPhy, § 36). Another example: A triangle has three straight line segments joined at their endpoints. These determinations are essential, i.e., they hold true for each triangle, whether it be equilateral, isosceles, large or small. Essential determinations are always and necessarily the same, i.e., they do not vary; they are constant (invariant). Any Being has both constant and variable determinations. Du Châtelet calls the first class “essentials,” and the second “attributes.”

Essential determinations must fulfill the following criteria: Firstly, they must fulfill the criterion of consistency. For instance, a triangle cannot have four sides. This is impossible. Impossible is that which implies a contradiction; contradictory propositions cannot both be true in the same sense at the same time. Consequently, one and the same triangle cannot be defined as having three and four lines at the same time (InstPhy, § 39). Here, the principle of contradiction comes into play, which Du Châtelet has introduced in the first chapter. Secondly, essential determinations must fulfill the criterion of independence in the sense that they are not the consequence of each other (InstPhy, § 38):

In order to conceive the possibility of some being, we cannot posit its constant determinations as consequences of others that precede them; for as we want to know how this being is possible, and on what its possibility depends, it is necessary to assemble those determinations of that being that neither contradict each other nor follow from any other antecedent determinations. (my own translation)

On ne point non plus poser, pour concevoir la possibilité de cet Etre, les déterminations constantes qui sont elles-mêmes déterminées par d’autres déterminations qui les précèdent; car on veut sçavoir ici comment l’Etre est possible, & ce qui le rend possible: il faut donc assembler les déterminations de cet Être qui ne se répugnent point l’une à l’autre, et qui ne sont point des suites nécessaires d’autres déterminations antécédentes. (Amsterdam 1742)

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

Thirdly, essential determinations must fulfill the criterion of completeness. If all three criteria are fulfilled, the principle of the immutability, or invariance of essences is fulfilled. Attributes are called determinations that are not essentials. As essential determinations vary, the attributes or properties necessarily vary as well; they are the unknowns of a problem, which must have their sufficient reason in what is given, since if that weren’t the case it would be impossible to solve the problem and to determine them. Consequently, attributes have their sufficient reason in essential determinations (InstPhy, § 42):

It is evident from this that the properties or attributes have their sufficient reason in the essential determinations; for since once these essentials are posited the properties also are, one can understand by the nature of these essential determinations why the attributes or properties are as they are, rather than otherwise. (Copyright © 2018 KB)

Il est évident par là que les propriétés ou attributs, ont leur raison suffisante dans les essentielles; car puisque ces essentielles étant posées, les propriétés le sont aussi, on peut comprendre par la nature des déterminations essentielles pourquoi les attributs ou propriétés, sont plutôt telles, que tout autrement. (Amsterdam 1742)

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

It is through its “essentials” that a being is possible. Attributes are determined by its essentials. Whereas essentials and attributes are both necessary properties of a thing, modes are contingent, or accidental properties. They are the properties of a thing that may or may not be exist.

For example, a triangle would continue to be a triangle, even if its color changed. The essentials of a being make many modes possible. An equilateral triangle, as a possibility, is undetermined as to the length of its sides, for example. The filling out of the undetermined mode is the actualization of a thing, i.e. the full determination of a being, the “completion (fulfillment) of possibility.” Thus, modes are quite different from both essentials and attributes, in that they are dependent on other beings. While the essentials make modes possible, their actuality depends on the relation of the being to another being or beings. An equilateral triangle, as a possibility, is undetermined as to the length of its sides, for example. The filling out of the undetermined mode is the actualization of a thing.

Attributes (as such) are perhaps best understood as necessary accidents, since they are determined by and necessarily follow from a thing’s essentials. Modes, in contrast, are only contingent accidents of substance. More precisely, the possible presence of any given mode follows from a substance’s essentials, but the actual presence of a given mode is the result of something outside the substance’s essence.

Du Châtelet assigns a special role to the so-called principle of the immutability, or invariance of essence. This principle does not just refute the “celebrated idea of Locke about the possibility of thinking matter,” but also Descartes’ opinion that essences were arbitrary, depending on God’s will (InstPhy, § 50). For if things were possible only because God willed it thus, they would become impossible if he willed otherwise – that is to say, that everything would be possible and impossible at the same time, which is a contradiction (InstPhy, § 48). In general, the principle of the immutability (invariance) of essence banishes every precarious hypothesis from philosophy, among them the primitive forces of the Scholastics which were found in matter, without any other reason than the will of God. Such would be attraction if one wished to make out of it an inherent property of matter.

For the same reason common definitions of “substance” given by the Scholastic philosophers, by Descartes and by Locke turn out to be wrong. The Scholastics defined “substance” as Ens quod per se subsistit et sustinet accidentia, that is to say, a being which subsists by itself and is the “soutien” of accidents. But it’s not clear at all, what it is to subsist by itself (InstPhy, § 51). Descartes defined “substance” as a being which exists such that it does not need any other being for its existence. Now, one sees well, Du Châtelet says, that this returns to the untenable Scholastic definition of “substance,” and that further, if one takes this definition rigorously, he will have God as the only one true Substance. After all, also Locke’s definition of “substance” is misguided for another reason (InstPhy, § 51):

Locke himself stops at the imaginary notion of Substance, such that the senses and the imagination give it to the common man, he says: that the Substance is no other thing than a subject which we do not know, which we suppose to be the support of qualities whose existence we discover, and which we do not believe to be able to subsist, sine re substante, without some thing which sustains them, and that we give to this support the name of Substance which, translated clearly in French means, that which is below, or that which supports. One easily sees that this notion of Substance is entirely confused, as M. Locke admits himself, and which is nothing other than a kind of comparison which has some resemblance with the true notion. (Copyright © 2018 KB)

Mr. Loke lui-même s’arrête à la notion imaginaire de la Substance, telle que les sens & imagination la donnent au vulgaire, il dit que la Substance n’est autre chose qu’un sujet que nous ne connoissons pas, et que nous supposons être le soutien des qualités dont nous découvrons l’éxistence, et que nous ne croyons pas pouvoir subsister, sine re substante, sans quelque chose qui les soutienne, & que nous donnons à de soutien le nom de Substance qui, rendu nettement en François, veut dire ce qui est dessous, ou ce qui soutient. On voit aisément que cette notion de la Substance est entièrement confuse, comme Mr. Locke l’avoue lui-même, qu’elle n’est autre chose qu’une espèce de comparaison qui a quelque ressemblance avec la notion véritable. (Amsterdam 1742)

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

The punch line of Du Châtelet’s own definition of “substance” is very interesting and deserves special attentions: One can explain by the principle of the immutability, or invariance of essences what a substance is (InstPhy, § 52):

one can define Substance like this: that which conserves [preserves] the essential determinations and constant attributes, while the modes in it vary and succeed one another​. (Copyright © 2018 KB)

l’on peut définir la Substance, ce qui conserve des déterminations essentielles, & des attributs constans, pendant que les modes y varient & se succèdent. (Amsterdam 1742)

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

Substance is, therefore, a subject which is perdurable and modifiable (“un sujet durable et modifiable”); essence is the force (source) of attributes and of the possibility of modes (InstPhy, § 52):

Thus, since essence is the force (source) of attributes and the possibility of modes, it is as a support and pillar (“substratum”) for everything which is suitable for being. (my own translation)

Ainsi, l’essence etant la force des attributs & de la possibilité des modes, elle est comme se support & le soutien de tout ce qui peut convenir a l’Etre. (Amsterdam 1742)

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

Compare, at this point, Christian Wolff, who writes in his Ontologia: “Subiectum perdurabile et modificabile dicitur substantia” (Wolff 1730, § 768). Substance means: “substantia est subiectum determinationum intrinsecarum constantium atque variabilium” (Wolff 1730, § 769); or: “Quod in se continet principium mutationum, substantia est” (Wolff 1730, § 872). Substance is the “durable and modifiable subject,” namely that which “conserves” and “keeps constant” essentials and attributes as its modes vary and succeed one another. The immutability of essences rejects “all precarious hypotheses and all the monsters that came out of imagination of men who have long delayed the progress of sciences and human spirit” (InstPhy, § 50).

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