Émilie Du Châtelet’s Foundations of Physics

Émilie Du Châtelet’s Foundations of Physics (Institutions de physique 1740/42) have recently been attracting increasing interest from analytical philosophy in the Anglophone world. A controversial issue concerns the question whether and in what sense Du Châtelet was a space-time idealist. I argue, firstly, that the current debate underestimates the modal approach and epistemological turn of Du Châtelet’s view on space and time. Seen from this perspective, Du Châtelet was both, an idealist and realist. Secondly, I give a historical outlook that underlines the significance of this turning point. This prospect focuses on Abraham Gotthelf Kästner’s criticism and Jean Henry Samuel Formey’s plagiarism of Du Châtelet. Against this background I revisit Leonhard Euler’s space-time realism and its influence on Immanuel Kant.

My paper on that subject will be published in 2021:

“On Space and Time. From Émilie Du Châtelet to Immanuel Kant.” In: A-L. Rey, ed.: L'épistémologie et à la philosophie des sciences d'Emilie du Châtelet. (Revue d'histoire des sciences).

A fictive dialogue

Once upon a time long ago, three children were playing with a bucket of water. Their names were: Émilie, Leonhard and Immanuel. They filled a bucket with water and suspended it from a fixed point with a rope. When the rope had taken all the twisting that it can take, they hold the bucket steady and let the water settle, then let go. What happened? The bucket started to rotate because of the twisted rope. At first the water in the bucket did not rotate with the bucket but remained fairly stationary. Its surface remained flat. Slowly, however, the water began to rotate with the bucket and as it did so the surface of the water became concave. Soon the spin of the bucket slowed as the rope began to twist in the opposite direction. The water was now spinning faster than the bucket and its surface remained concave. The three children wondered: Why did the surface of the water became concave?

Leonhard: That is an easy question – the surface becomes concave since the water is spinning.

Émilie: Is the shape of the surface of the water determined by the spin of the water relative to the bucket?

Leonhard: The water is spinning with respect to absolute space.

Émilie: Really? It is a matter of great difficulty to discover and effectually to distinguish the true motions of bodies from the apparent, because the parts of that immovable space in which these motions are performed do by no means come under the observations of our senses. I remind you of Leibniz who argued that there is a difference between absolute true motion of a body and a mere relative change of its situation with respect to another body.

Immanuel: Could you explain this?

Émilie: Space and time, far from being a substance, are not even things in-themselves. Space is a possible order, like time: space is an order of possible coexistences, as time is an order among beings that are not together. Potential beings lack individuality and action. This is the reason why motion differs from space and time. Motion is real and actual. For time to exist there must be some changes (in motion), and for space to exist, there must be some bodies, but not all moments and places must be occupied by events or bodies.

Leonhard: As so indubitably established, these two truths, namely the law of inertia and the law of the moving force, must be absolutely grounded upon the nature of bodies; and as it is metaphysics which is concerned with the study of the nature and properties of bodies, the awareness of these truths will be able to serve as a guide in these thorny investigations. Therefore this shall also be the case for the principles of mechanics that are intertwined with the ideas of space and time, i.e. real ideas. To better situate our ideas, let us suppose that body A is in still water and let us consult the experiment that teaches us that a body at rest in still water will be put into motion as soon as the water begins to ow. This seems to favor the rule as it is conceived metaphysically. But mechanics shows very clearly that the body does not follow the water current so much as it is struck by the water particles, and consequently an outside force puts the body in motion. Therefore without this force the body would remain at rest in owing water as it does in still water, and thus the body in the conservation of its state of rest does not follow the bodies that immediately surround it. From this it follows that what is called position in mechanics does not allow the explanation offered by metaphysics which claims that position is nothing but the relationship of the body with respect to other bodies that surround it. So, One should conclude that both absolute space and time, as mathematicians represent them, are real things that exist beyond our imagination, since it would be absurd to support the idea that pure imagination could serve as a foundation for real principles of mechanics. With this view I agree that the idea of time only exists in our imagination. But we have reason to ask whether or not the idea of time and time itself are different from one another. And it seems to me that the metaphysicians, in doing away with the reality of time, have confused time with the notion of it.

Émilie: I’m afraid that the physicist, in doing away with the ideality of time, have confused the potential order of time with actual and real motion.

Kant: I think we should better ask for the conditions of the possibility of experience than of ideal and real possibilities as such. The point is that instead of assuming that the objects have a pre-given structure in themselves and then asking how we can come to know it, we should pursue the hypothesis that there are structures of knowledge that are necessary for the very experience of any object. We can know a priori of things only what we ourselves put into them. From this perspective, space and time, subjectively considered, are forms of sensibility; but in order to form a concept of them as objects of pure intuition (without which nothing whatever could be said of them), an a priori concept of a composite, hence of the composition (synthesis) of the manifold, is required, and thus synthetic unity of apperception in the combination of this manifold.

Leonhard: This might be a brilliant approach, but it seems to me that one crucial problem remains open: How to determine true, i.e. real motion from apparent motion? A person moving along a road has real motion; while the change of position he observes in the trees, houses, etc, is only an apparent or relative motion of these objects. In this sense, apparent motion is where the stars appear to be moving because we are on the Earth and the Earth is moving. The actual motion of the stars is how they actually move in relationship to each other and the planets. This is the true motion of the stars. Is this true motion absolute or relative? It seems to me that we are faced back to the problem with the rotating bucket filled with water.


My doctoral dissertation and book on Émilie Du Châtelet was published by Springer in 2016 and received very positive international responses (e.g., C. Carus, Mathematical Intelligencer 2018: "Reichenberger's extremely well researched book is an omnium gatherum of interesting historical and contextual facts."). I have also written an Online Reading Guide on Émilie Du Châtelets Foundations of Physics (A project within the Center for the History of Women Philosophers and Scientist HWPS, Paderborn University).

Further readings:

2020 “Du Châtelet and Newton.” In: D. Jalobeanu and C. T. Wolfe, eds.: Encyclopedia of Modern Philosophy and Science. Springer 2020. DOI: https://doi.org/10.1007/978-3-319-20791-9_26-1.

2019 Die Rolle der Familie Keyserlingk und des Gottsched-Kreises für Kants Du Châtelet-Rezeption.“ In: R. Hagengruber u. H. Hecht, Hgg.: Émilie Du Châtelet und die deutsche Aufklärung. Wiesbaden: Springer, 245–271.

2018 “Émilie Du Châtelet’s Interpretation of the Laws of Motion in the Light of 18th Century Mechanics.” Studies in History and Philosophy of Science Part A 69 (June), 1–11.

2012 “Leibniz’s Quantity of Force: A Heresy? Émilie du Châtelet’s Institutions in the Context of the Vis Viva Controversy.” In: R. Hagengruber, ed.: Emilie du Châtelet between Leibniz und Newton (= International Archives of the History of Ideas / Archives internationales d’histoire des idées 205), Dordrecht et. al.: Springer, 157–171.