There must be an alternate history in which Émilie du Châtelet (Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet) is a well-known 18th century philosopher. In our past, Du Châtelet collaborated with Voltaire (who was also her lover) and carried out correspondences with Leonhard Euler, Frederick the Great, and Pierre Louis Moreau du Maupertuis, as well as with the Bernoullis. Kant appreciated her intellect, but couldn’t comprehend that it was a woman’s, crudely commenting that she “might as well have a beard”. Du Châtelet was an early advocate of Newton’s physics over that of Descartes, which until then was popular in the France of her time. In her later life, she translated Newton’s Principia from Latin into French – a translation which is still in use to this day. Despite all these feats her magnum opus, the Institutions de Physique (Foundations of Physics), was only fully translated into English a few years ago through the laudable work of Katherine Brading’s group at Notre Dame. Part of the reason for this long neglect, surely, is the fact that Du Châtelet was a woman. Her early death at the age of 42 is probably another. But her philosophy has seen renewed attention in recent years, and some of her writings are being scrutinised by contemporary analytic philosophers for the very first time.
The topics of the Foundations range from the straightforwardly scientific (‘Of the Motion of Projectiles’) and methodological (‘Of Hypotheses’) to the religious (‘Of the Existence of God’). But one of Du Châtelet’s most intriguing contributions concerns metaphysics, or, more accurately, ‘natural philosophy’. Chapter 5 of the Foundations is devoted to the nature of space, and particularly extension; it is among those chapters that had never been translated into English before, and so analytic philosophers have only quite recently started to explore Du Châtelet’s views on this issue. The aim of this essay is to introduce these views, which Brading describes as “interesting and highly unusual”. As we will see, Du Châtelet’s physics-inspired account of extension is very different from those of her most influential predecessors, Gottfried Wilhelm Leibniz and Christian Wolff. This essay will offer a glimpse into a time when both physics and philosophy were at a crossroads between Newton’s empirical science on the one hand and Leibniz’s rationalist philosophy on the other. Du Châtelet admirably aims to balance these two perspectives.
The physics of Du Châtelet’s time was concerned with ‘bodies’: matter moving and colliding, from billiard balls and sailing boats to the planets and the Earth. The question that was on many natural philosophers’ minds was: what are these bodies? In a sense, this query is not too dissimilar from present-day theoretical physicists’ quest for the fundamental particles that make up the objects that we see around us (are they composed of protons? quarks? strings?).
An essential quality of bodies is their extension, that is, the property of occupying a certain volume in space. Put differently, what it means for bodies to be extended is that they ‘take up space’. The crucial question then becomes: how does matter become extended in this way? A few decades before Du Châtelet, Leibniz argued that the answer couldn’t consist simply of smaller bits of extension, which were called atoms. This is so because one can always imagine that an atom is made up of a bunch of even smaller atoms, until there is no extension left: there is no natural ‘stopping point’ for this process of division. Du Châtelet agreed, arguing that one cannot explain a phenomenon in terms of itself. She illustrates this with an analogy:
If someone asked why there were watches, he certainly would not be content if he was answered, it is because there are watches; but in order to give sufficient reasons and ones that satisfy the questioner about the possibility of a watch, 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.
Just as with watches, in order to account for extension one has to come up with a cause that is itself not extended.
As a solution to this problem, Leibniz posited what he called monads instead of atoms. Monads are ‘simple’ elements with no extension whatsoever. Leibniz is famous for the quite bizarre suggestion that all these monads are minds or souls, and so perceive and represent the world. In modern terminology, it’s as if the quarks and electrons that comprise matter are all conscious! In his system, extension is a ‘well-founded phenomenon’ that exists in the common perceptions of all these monads. In other words, the monads all see themselves and each other as extended, even though in fact they are not. But this does not mean that extension is a complete illusion: the monads’ perceptions are supposed to reflect, in some mysterious way, the internal structure of the monads themselves. However, many commentators agree that Leibniz left it quite unclear in what way extension reflects this underlying structure.
One of those commentators was Leibniz’ younger contemporary, Christian Wolff. The latter’s dissatisfaction with Leibniz’s system led him to come up with physical monads which, unlike Leibniz’s mental monads, have no powers of perception. Instead, physical monads are similar to the particles of classical mechanics: they are non-extended points without any parts that continually interact with each other. Nevertheless, like Leibniz’s monads Wolff’s physical monads are not located in space, but instead ‘live’ in some more mysterious metaphysical realm. Instead, Wolff argued that both extension and space (which for Wolff were virtually equivalent) arise from a certain order amongst his physical monads. “Now when many things exist at the same time… a certain order among them thereby arises,” he wrote, “and as soon as we represent this order to ourselves, we represent space”. But it is not clear that Wolff can avoid the objection he levelled at Leibniz, for it seems equally unclear how extension arises from an unspecified ‘order’ amongst simples. Wolff’s contemporary Crusius criticised that on this account even a piece of music counts as a space—after all, a melody contains many distinct elements next to each other in a certain order! Therefore, neither Leibniz’s and Wolff’s can satisfactorily explain the origin of extension.
Enter Du Châtelet. Du Châtelet admired Leibniz, but the philosopher Marius Stan has convincingly argued that her views on many issues are actually closer to Wolff’s. Du Châtelet believes in the existence of what she called ‘Simple Beings’. These are much the same as Wolff’s physical monads: Simple Beings causally interact with each other, but unlike Leibniz’s monads they are not able to ‘see’ the world around them. Nevertheless, Du Châtelet’s solution to the problem of bodies was radically different from both Leibniz and Wolff’s solutions, as we will now see.
Du Châtelet starts with the Leibniz-Wolffian idea that extension arises from collections of many Simple Beings. But to this, she adds the notion of unity. When we represent a collection of simples as a unity, she says, extension arises: “We cannot represent to ourselves several different things as being one, without this resulting in a notion that is attached to this diversity and union, and this notion we call Extension”. In other words, imagine a few Simple Beings, which are “external to [distinct from – CJ] each other”. So far, this is simply a collection of points. But, Du Châtelet claims, if we instead consider this collection as a whole it becomes extended. Du Châtelet illustrates this with the example of a line: ‘Thus we give extension to a line, insofar as we pay attention to several distinct parts which we see as existing externally to one another, which are united together and which are for this reason a single whole’. Of course, you may well wonder why we must unify bunches of simples into extended bodies; I’ll come back to this question below.
Although this story is not airtight, I believe that it is not so vague as Wolff’s concept of ‘order’. We can easily see how extension is at once a unity and a multiplicity. Think, for example, of the water in a glass. On the one hand, the liquid occupies a certain volume: its extension. This is why we think of the liquid as a single object. On the other hand, the water ultimately consists of many point-like particles, which we may idealise as non-extended. Extension, in other words, is a way of reconciling the multiplicity of a collection of Simple Beings with the unity of the physical bodies we see around us.
Nevertheless, Du Châtelet doesn’t seem to explain why we must represent multiplicities of simples as a unity. Why not represent each simple on its own, one-by-one, with no further attempt at unification? You might even think that such a representation is more truthful to the world as it is in itself. In response to this worry, Du Châtelet essentially admits to the fact that extension is an illusion. In her words, it is a confusion. As Marius Stan notes, this is somewhat of a pun, since ‘con-fusere’ is also Latin for fusing together. The reason that we con-fuse multiplicities of simples into bodies, Du Châtelet argues, is that our senses are faulty: extension arises from the “confusion that reigns in our organs and in our perceptions”. Indeed, “if we could see distinctly all that composes extension, this appearance of extension… would disappear”. This claim is decidedly different from Leibniz’s account on which extension is also a phenomenon that exists in our perceptions, but one that is ‘well-founded’ in the underlying world of monads. For Du Châtelet, on the other hand, the perception of extension is not well-founded, but merely confused.
Du Châtelet offers a handful of excellent analogies that help us understand how the senses confuse extension into being. In the Preface of the Foundations, Du Châtelet explains that it is written as a textbook for her son, which is why she took great care in accompanying the book’s complex ideas with clear illustrations. For example, Du Châtelet considers the way in which painters mix their colours:
for blue and yellow mixed together give us green, but this Phenomenon that was only an appearance disappears when we use a Microscope […]; for the Phenomenon of green exists only through this confusion, and there is in reality only the particles of blue and yellow placed next to one another.
Unlike colours, however, there is no microscope that allows us to distinctly perceive Simple Beings (although Du Châtelet never rules this out as a possibility for future science). In a sense, the reason that we perceive matter as extended is that our vision is ‘low-resolution’. Similarly, Du Châtelet compares extension with the sound of a choir. From the centre of the theatre, all their voices mix together into a pleasing whole. But “when we are very close to the Choristers’ Voices, we distinguish each one individually and we lose the beauty made by the ensemble”. Again, though, individual Simple Beings are impossible for us to perceive, unlike the individual singers of a choir.
This, then, is Du Châtelet’s solution to the problem of bodies: our confused sense organs mistakenly perceive collections of multiple simples as extended wholes. But recall that the problem of bodies was so important because bodies are the subject matter of physics. So if extension is merely an illusion, does that mean that all of physics is false? Surely, that is not a welcome conclusion to a philosopher as scientifically-minded as Du Châtelet.
In response, note first that Du Châtelet’s Simple Beings do constrain our observations of extended bodies. Extension is an illusion, but it is not a hallucination. While a hallucination is entirely unrelated to what’s happening around us, an illusion is a misperception that is still based on reality. Nevertheless, Du Châtelet’s system gives significant autonomy to physics over philosophy: the physical world of extended bodies in a sense ‘floats free’ on top of the metaphysical world of monadic simples. This naturally leads to a form of dualism, according to which the world has two distinct yet related ‘levels’. Again, Du Châtelet acknowledges this implication of her views; she admits that it is not the business of science to enquire into the most basic metaphysical reason for natural phenomena. As she writes, “the feeble extent of our minds and the present state of the Sciences do not permit it”. (As I mentioned before, this leaves the tantalising possibility that a future science can draw metaphysical conclusions – and who knows what Du Châtelet would say of modern particle physics?)
This conclusion may seem disappointing, but it also helps Du Châtelet to reconcile her philosophical views with Newton’s empirical theories. Specifically, the universal force of gravitation posed a long-standing problem for the Leibniz-inspired type of metaphysics that Du Châtelet was involved with. The force of gravity acts instantaneously at a distance; for example, the Earth immediately feels the gravitational attraction of the sun, even though it is millions of miles away. This action-at-a-distance is incompatible with the so-called ‘Principle of Sufficient Reason’ (PRS), which was a cornerstone of Leibniz’s overall philosophical system. Du Châtelet followed Leibniz in assuming the PRS, but she also appreciated the empirical success of Newton’s theory of universal gravitation. In order to reconcile these conflicting points of view, she argued that gravitation exists at the phenomenal level of bodies, one step removed from the fundamental level of monads. In this way, she could appeal to gravitation in order to explain physical phenomena without a commitment to its existence as a truly fundamental force of nature. In a sense, gravity is also an illusion, just as the extended bodies that it acts on are. Therefore, the fact that science ‘floats free’ from metaphysics allowed Du Châtelet to synthesise Newton’s empiricism with Leibniz’s rationalism, albeit at the cost of relegating gravity to the status of a ‘mere’ phenomenon.
I am not the first to note that this streak of phenomenalism brings Du Châtelet close to the later Kant. For Kant too, space, time and causality were imposed on our perceptions by the mind. Recent scholarship has explored this idea of Du Châtelet as the ‘missing link’ between Leibniz and Wolff on the one hand, and Kant on the other. But Du Châtelet’s material also deserves our philosophical attention in its own right. Here is a thinker who wrote at a crucial point in time for the development of so-called natural philosophy, yet whose work is barely familiar to present-day philosophers. I recommend anyone with even the smallest interest in the history and philosophy of science to read parts of the Foundations and witness an important document in the development of 18th century natural philosophy.
Caspar Jacobs  is a DPhil student in Philosophy at Magdalen College, Oxford.