Right at the beginning of the sixth chapter, Du Châtelet notes that there is an analogy between space and time insofar as space is the order of coexisting things and time is the order of successive things. The common notion of time as a necessary and absolute Being, immutable, eternal, and subsisting by itself, is misleading. To substantiate this claim, Du Châtelet refers to Leibniz’s famous question why God had not created the universe thousand years earlier or later (InstPhy, § 96):

From this idea of time M. Clarke put the famous question to M. Leibniz: why God had not created the universe six thousand years earlier or later. M. Leibniz had no trouble countering this objection of the English doctor and his opinion on the nature of time by the principle of sufficient reason; he only needed to use M. Clarke’s own objection on the time of the creation. For if time is an absolute being consisting in a uniform flow, the question of why God did not create the world six thousand years earlier or later becomes a meaningless question, and forces one to acknowledge that something happened without sufficient reason. For the same succession of beings in the universe being kept, God could make the world begin earlier or later, without thereby causing any disturbance. Now since all instants are equal, when only succession is attended to there is nothing in them that could have led to a preference for one over another, to the extent that no diversity in the world would have been caused by this choice. Thus, one instant would have been chosen in preference to another to make this world actual without sufficient reason, which cannot be accepted. (Copyright © 2009 BZ)

C’est de cette idée qu’on se forme du Tems qu’est venue la fameuse question que Mr. Clarke faisoit à M. Leibnitz: pour quoi Dieu n’avoit pas créé l’Univers six mille ans plutôt, ou plus tard. Mr. de Leibnitz n’eut pas de peine à renverser cette objection du Docteur Anglois, & son opinion sur la nature du Tems par le principe de la raison suffisante; il n’eut besoin pour y parvenir que de l’objection même de Mr. Clarke sur le tems de la creation: car si le Tems est un Etre absolu qui consiste dans un flux uniforme, la question pourquoi Dieu n’a pas créé le Monde six mille ans plutôt ou plus tard devient réelle, & force à reconnoître qu’il est arrivé quelque chose sans raison suffisante. En effet, la même succession des êtres de l’univers étant conservée, Dieu pouvoit faire commencer le monde plutôt ou plus tard, sans causer le moindre dérangement. Or, puisque tous les instans sont égaux, quand on ne fait attention qu’à la simple succession, il n’y a rien en eux qui eût pû faire préférer l’un à l’autre, dès qu’aucune diversité ne seroit parvenue dans le monde par ce choix. Ainsi un instant auroit été choisi par Dieu préférablement à un autre, pour donner l’existence à ce monde sans raison suffisante; ce qu’on ne peut point admettre. (Amsterdam 1742)

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

Compare Leibniz’s third letter to Clarke:

Il en est de même du temps. Supposé que quelqu’un demande pourquoi Dieu n’a pas tout créé un an plus tôt, et que ce même personnage veuille inférer de là que Dieu a fait quelque chose dont il n’est pas possible qu’il y ait une raison pourquoi il l’a faite ainsi plutôt qu’autrement, on lui répondrait que son illation serait vraie si le temps était quelque chose hors des choses temporelles; car il serait impossible qu’il y eût des raisons pourquoi les choses eussent été appliquées plutôt à de tels instants qu’à d’autres, leur succession demeurant la même. Mais cela même prouve que les instants hors des choses ne sont rien et qu’ils ne consistent que dans leur ordre successif; lequel demeurant le même, I’un des deux états, comme celui de l’anticipation imaginée, ne différerait en rien, et ne saurait être discerné de l’autre qui est maintenant. (Des Maizeaux 1720, § 6, p. 33)

The case is the same with respect to time. Supposing anyone should ask why God did not create everything a year sooner, and the same person should infer from this that God has done something concerning which it is not possible that there should be a reason why he did it so and not otherwise; the answer is that his inference would be right, if time was anything distinct from things existing in time. For it would be impossible that there should be any reason why things should be applied to such particular instants rather than to others, their succession continuing the same. But then the same argument proves that instants, considered without the things, are nothing at all and that they consist only in the successive order of things; this order remaining the same, one of the two states, namely, that of a supposed anticipation, would not at all differ, nor could be discerned from the other which now is. (Third letter to Clarke, § 6 [Feb 25, 1716])

For one posits temporal relations as existing of instants among absolute time, that is independently of things and their states, there is no way of deciding which instants they occupy. Implicitly, Leibniz is appealing here to the Principle of the Identity of Indiscernibles. Instants, i.e. temporal units, or points, cannot be distinguished from one another. Thus, any point of time is identical to any other point in time, only distinguishable by the things placed within it. If time is a substance, then it would matter when God decided to create the world at a particular instant of time and one could ask what sufficient reason God had for creating at the time he chose rather than creating earlier or later. God’s creation itself must have a final cause which helps to actualize the best of all possible worlds which is lacking if the creative act have occurred earlier or later. If the substantivalists are unable to provide such a sufficient reason for the timing of creation, their theory is at an explanatory loss, Leibniz argued. Clarke, who claimed to agree with the principle of sufficient reason, replied that “thus sufficient reason is often times no other than the mere will of God” (LC 2.1). Leibniz felt misunderstood. God’s will should be always in accordance with the principle of the sufficient reason. God can never act without sufficient reason.

As in the case of space, Du Châtelet interprets Leibniz’s argument as a critique of the deification of time. Neither space nor time are attributes or affections of God. In case of time: it is neither a substance nor an accident of things, but a simple mode or exterior relationship, which depends on the mind (»esprit«) (InstPhy, § 97). Thus, there is no time without true, successive beings arranged in a continuous sequence; and there is time as soon as such beings exist (InstPhy, § 103):

Thus, there is time when things are, it is removed when one removes these things. (Copyright © 2009 BZ)

ainsi, il y a du Tems dès qu’il a des choses successives, & on l’ôte, lors qu’on ôte ces choses. (Amsterdam 1742)

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

At this point, Du Châtelet again takes up the analogy with numbers: Space is not the extension of a thing, any more than duration is its time. Like the number is different from the numbered thing, time is different from the measured thing. While extension and duration, therefore, must always belong to some actual things, space and time are relations of possible things. Space and time express possibilities. Thus, possible coexistences constitute space, successive existences constitute time (InstPhy, § 105). Following reflections on the constitution of time, Du Châtelet addresses the question of how time is represented and measured (InstPhy, § 106):

Time is usually represented by the uniform movement of a point that describes a straight line, because the point is there a successive being, present successively at different points, creating by its flow a continuous succession to which we attach the idea of time. We also measure time by the uniform movement of an object. (Copyright © 2009 BZ)

On représente ordinairement le tems par le mouvement uniforme d’un point qui décrit une ligne droite, parce que le point est l à l’Etre successif, present successivement à différens points, & engendrant par la fluxion une succession continue à laquelle nous attachons l’idée de Tems. Nous mesurons aussi le Tems par le mouvement uniforme d’un objet. (Amsterdam 1742)

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

Uniform motion, i.e., motion in a straight line, plays a crucial role for the geometrical representation and construction of a body’s motion in space and time. By means of motion time is measurable. Du Châtelet reminds of traditional methods of time measurement, e.g. through the movement of celestial bodies, and highlights Christiaan Huygens’ construction of pendulum clocks as a milestone on the way to a more precise time measurement (InstPhy, § 107):

Astronomers’ efforts to find a uniform motion, which put them in reach of measuring time exactly, are well known, and it is what M. Huygens found with pendulums, of which he is the inventor, and which will be discussed further on. (Copyright © 2009 BZ)

On connoît les efforts que les Astronomes ont faits pour trouver un mouvement uniforme qui les mît à portée d’en mesurer exactement le Tems, & c’est ce que M. Huyghens a trouvé par le moyen des pendules. (Amsterdam 1742)

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

Motion, Du Châtelet says, is far from giving us the idea of duration.  Jean-Pierre Crousaz wrongly presupposed this assumption in his prize essay Commentaire sur l’Analyse des infiniment petits (1721). Time, which is an ideal being, has to be distinguished from motion, which is something real (InstPhy, § 109). The reason why motion and time have been confused is that time has not been carefully enough distinguished from its measurement (InstPhy, § 111). The measurement of time is taken from exterior bodies, the idea of time from the succession of our ideas (InstPhy, § 108).

The measurement of time allows us to distinguish past, present, and future events and to give to ourselves and others an idea of what we mean by such a portion of time, e.g., the annual and daily course of the Sun, the vibrations of a pendulum (which are, of all measurements, the most accurate), minutes, hours, days, and years; but it is quite possible that other things have been used as measurements by other peoples. The only one that might be universal is what is called an instant, i.e., an infinitesimal moment (InstPhy, § 114):

It is easy to grasp that measurements of time can be different for different peoples, the annual and daily course of the Sun, the vibrations of a pendulum (which are, of all measurements, the most accurate) have provided us with those of minutes, hours, days, and years; but it is quite possible that other things have been used as measurements by other peoples. The only one that might be universal is what is called an instant; for all men necessarily know this portion of time, which flows while a single idea stays in our mind. (Copyright © 2009 BZ)

On sent aisément que les mesures du Tems peuvent être différentes chez les différens Peuples, le cours annuel & journalier du Soleil, les vibrations dune Pendule (qui sont de toutes les mesures la plus juste) nous ont sourni celles de Minutes, d’Heures, de Jours , & d’Années: mais il est très possible que d’autres choses ayent tenu lieu de mesures à d’autres Peuples. La seule qui soit universelle, c’est celle que l’on appelle un instant; car tous les hommes connaissent récesfairement cette portion de Tems, qui s’écoule pendant qu’une seule idée reste dans notre esprit. (Amsterdam 1742)

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

The measurement of time requires the specification of units, but there are many different units of time, some of which may be more appropriate in certain circumstances than others. However, according to Du Châtelet, an instant of time is universal. What is that supposed to mean? Leibniz’s differential calculus and Newton’s method of fluxions were both methods of calculating the motion of an object; both methods presuppose and require the notion of a finite rate of change, or fluxion, at each instant. This is analogous to the notion that a moving body has an instantaneous velocity at a given moment in time. Under this conception, every motion is conceived of as beginning from a point, or instantaneous moment, and ending at another point, or instantaneous moment. Against this background, Du Châtelet concludes that all measurements of time are founded only on the duration of our being, and on that of the beings that coexist with us and whose existence we view in terms of our own (IntPhy, § 115). This consideration also explains how we acquire the idea of eternity (InstPhy, § 116):

if we remove its beginning and its end from the idea that we have of the duration of finite beings, the duration will become the eternity of God, for only God can be eternal a parte post, and a parte ante, that is to say, have neither beginning nor end. (Copyright © 2009 BZ)

sa fin, la durée deviendra lEternité de Dieu, car il n’y a que Dieu qui puisse être Eternel à parte post, & a parte ante, c’est-à-dire, n’avoir ni commencement, ni fin. (Amsterdam 1742)

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

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See also the entry TEMS, s. m. (Métaphysique.) in d’Alembert’s and Diderot’s Encyclopédie. See also the entry “Temps” in: Johann Heinrich Samuel Formey (ed.): Dictionnaire instructif, où l’on trouve les principaux termes des sciences et des arts dont l’explication peut être utile ou agréable aux personnes qui n’ont pas fait des études approfondies. Halle: Gebauer 1767.

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