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Gabrielle-Émilie le Tonnelier de Breteuil; Marquise Du Châtelet-Laumont

Introduction

Of the many outstanding female philosophers of the European Enlightenment, Emilie Du Châtelet excelled as a physicist, a philosopher, and a mathematician, as well as a Bible critic. She was famous in her lifetime and was not completely forgotten thereafter. Among her admirers, correspondents and friends were the most acknowledged scholars of her time, including Voltaire, Clairault, Maupertuis, Diderot, Helvetius, La Mettrie, Buffon, Christian Wolff, Leonard Euler, and Johann II Bernoulli. Her philosophical work enjoyed high reputation and her opus magnum, the Institutions physiques, was translated into Italian and German and proved her to be an intellectual of European stature. Its defense of living forces and its implied forecast into dynamics as well as her methodological grounding of scientific knowledge as hypothetical, impacted philosophy and science. Reality must by nature escape us. What we perceive are phenomena. Du Châtelet explains the function of space and time to trace us back to the origin of phenomena. Her influence on Kant is evident. Next to her writings in physics, mathematics, philosophy, language, and logic, she contributed to morality and ethics. Du Châtelet left an opus of quite systematic breadth. This impressive publishing activity excels in the amount of its scientific and philosophical production to which a vast collection of manuscripts must be added.

She argued against prejudice and idolatry in philosophy and science. Science is a cooperative undertaking over history and beyond nations. Her moral writings align with ideas of the French materialists. Du Châtelet translated and commented on Newton’s Principia, preparing thus the fertile soil of the generation of physicists to come in France.

Life and Writings

Gabrielle-Émilie le Tonnelier de Breteuil, marquise Du Châtelet was born into a highly ranking aristocratic family on 17 December, 1706. In 1725, she married Florent Claude, marquis Du Châtelet-Lomont (1695–1765), a member of the old aristocracy. She gave birth to four children. For a long period in her life, she was the companion of Voltaire and also collaborated with him in literature and science. Maupertuis and Clairault taught her in mathematics. Du Châtelet died in Lorraine on September 10, 1749, a few days after she had given birth to her fourth child.

Educated in an open-minded environment, Du Châtelet was educated with her brothers. Well acquainted with Horace, Virgil, Lucretius, Cicero, Plato, and Aristotle, she excelled in a whole range of subjects. Dedicated to music and poetry, she rehearsed the plays of Voltaire and sung operas. When Voltaire was forced to flee from Paris, the Du Châtelet family gave shelter to him in the abandoned castle of Cirey, where she joined him in 1735. With Voltaire, she made the castle of Cirey into a petite académie, where a scientific laboratory with the most sophisticated instruments was maintained and the most important scientific literature was at hand. Among the visitors and friends, renowned scholars came to discuss and to collaborate, and the likes of Maupertuis, Bernoulli, and Algarotti passed by.

Du Châtelet’s influence on Voltaire’s scientific production during that period is well documented in the Saint Petersburg Manuscripts, a compilation of over 400 papers, collected from Voltaire’s estate, bought by Catherine the Great after he died (Du Châtelet 2020). The manuscripts stem from this earlier period in her life that she shared with Voltaire in Cirey. Du Châtelet made clear that it was she who took on the scientific element. In a letter from 1735, she writes to the Italian Algarotti, “I have a pretty nice library. Voltaire has a whole bunch of anecdotes; mine is all (of) philosophy” (Correspondence 2018). Du Châtelet was open to supporting Voltaire in his interest in becoming a member of the French Academy. They worked together to respond to a prize question on the nature of fire, but their interests soon diverged greatly and Du Châtelet submitted her own response.

When Voltaire was about to draft his Elements de la philosophie de Neuton, he praised her support for him in public and in private. To the crown prince Frederic, he wrote: “Minerva dictated and I wrote,” a remark evidenced in the frontispiece showing Du Châtelet transmitting the spiritual light from Newton for Voltaire’s inspiration (1738). Du Châtelet’s reading differed extensively from Voltaire’s. In the same year he published his Elements, 1738, Du Châtelet presented the first draft of her Institutions de physique, to the royal censor, who confirmed: “This publication exposes the principles of the philosophy of Leibniz and Newton” (1740).

Du Châtelet’s Dissertation on the nature and propagation of fire, published by the French Academy along with Voltaire’s and the prize-winner’s, was the first text the French Academy ever published by a female scholar. Its reference to Mairan, who had become the secretary of the French Academy, was the start of a famous dispute with him (1741a, b). Du Châtelet’s independent attitude as a philosopher can be observed from her early studies onwards, for instance in her drafts on Optics (Gesell 2019). A complete essay on optics was found in the Bernoulli Archive in Basel (Nagel 2011). In 1745, the translation of Newton’s Principia was ready for publishing. In 1749, two further commentaries had been added, all published for the first time completely in 1759. In 1779, her Discours sur le Bonheur was published for the first time.

An impressive amount of philosophical writing circulated in the form of manuscripts and was published posthumously. The manuscripts in the Saint Petersburg collection mentioned above, include the Commentary on Mandeville’s Fable of the Bees, a translation of Woolston’s Miracles of Jesus, as well as a Reasoned Grammar, chapter drafts for the Institutions, on Colours and on Liberty, and corrections, margins, and writings adding and contributing to Voltaire’s legacy, such as his Treatise on metaphysics (Brown and Kölving 2003). In 2011, the thousand-page Examination of the Bible was identified as having been written by her. In 2010, more manuscripts were discovered, including ones on optics, physics, mathematics, and more private material stemming from her lawsuits in Brussels. A vivid part of Du Châtelet’s intellectual production must be retraced in her correspondence, of which parts had even been published during her lifetime (Kölving and Brown 2018a).

The Institutions of Physics (Foundations of Physics)

The Institutions physiques is not an ontological foundation of physical entities, but a contribution to secure how what we know, be it about the preconditions of our understanding, be it about phenomena, matter and physics can be found and secured. In its time, it was a ground-breaking presentation of how to tackle the divides in philosophy and science, represented in the figures of Descartes, Leibniz, and Newton. Du Châtelet’s Institutions contributes to epistemology and scientific reasoning. Going beyond Voltaire and Locke, an intensive study of the Leibniz-Clarke Correspondence formed her ideas. She had a profound knowledge of Leibniz’s writings, as well as the work of Wolff, Huygens, Bernoulli, and the followers of Newton’s Gravesande, Musschenbroek, Raphson, Keill, and Pemberton.

In a time when philosophy was divided, Du Chatelet holds, one has to acknowledge both sides; since both are also wrong (IP 2009, vi ff.). Her methodology is crucial for overcoming that divide, insisting though that physics is based on metaphysics and cannot surpass it. Du Châtelet confirms that any physical appearance, as well as any knowledge about it, is dependent on the mental formation of perception. There is no law in nature, it is the principles of our understanding without which there would be no chain of knowledge and no reasoning about it at all. Rank and reliability of hypotheses, the nature of space and the measuring of forces were among the topics Du Châtelet advanced. In 1742, an authorized and extended version of the book was released including her portrait, slightly changing the title Institutions de physique to Institutions physiques. Various journals reviewed and mentioned her book, such as the Journal des savants, the Mémoires de Trévoux, and more (Kölving and Courcelle 2008, 341 ff.). This second edition was published the following year in Italian and German and also contained her dispute with Mairan.

On Hypotheses

Du Châtelet’s epistemology shatters the notion of secured knowledge and offers a different method in how to decide on scientific claims; her methodology is set against both reveries and rejections of hypotheses (IP 4.55). All scientific knowledge is hypothetical and the utmost reliability is a truthlike one. While the Cartesians denied Newton’s law of attraction to be any more than a hypothesis, the Newtonians likewise dismissed the hypothetical reasoning of Descartes as obscure. Locke’s epistemology did not provide a sufficient criterion of proof, as she held that “the true causes of natural effects and of the phenomena we observe are often so far from the principles on which we can rely and the experiments we can do that one is obliged to be content with probable reasons to explain them” (IP 2009, 4.53).

Du Châtelet criticized Descartes for his unsecured reasoning and likewise rebutted the Newtonian scholars, who held that mathematics was an absolute language of science and that with it the validity of Newton’s law could be deduced. Numbers as well as scientific laws are based on hypotheses, since they are the only means to find new insights and truth and without it, there would never have been a discovery. As there must be a beginning and this beginning must always be a very imperfect and often unsuccessful attempt, any attempt to gain new knowledge is built upon hypothesis.

Hypotheses are between a priori insights and a posteriori experiments and they help science to grow (IP 2009, 4.60). The rules to follow and the pitfalls to avoid are found in how one must proceed when making a hypothesis. Hypotheses may not be in contradiction with the principles laid out in the first chapter of Institutions. One’s knowledge of the facts has to be exhaustive, understood in its degree of probability. A hypothesis cannot be proven by one experiment, but can be rejected by only one contradiction. It may be questioned in part or as a whole and its probability is greater the more consequences can be proven coherent to it (IP 2009, 4.66).

Du Châtelet’s endeavor to overcome the divide between Leibniz and Newton by integrating them into a new basis of scientific reasoning and to tackle the most challenging features of that divide, also contributed to her fame. Her findings influenced Euler, d’Alembert and have been influential up to Poincaré.

The Principles of Knowledge

Hypotheses, Du Châtelet says, are not necessarily true and therefore, require methods to be used correctly. Wolff would not agree with Du Châtelet to erect scientific insights on all phenomena as hypothetical (Blank 2019). The principles of knowledge clarified the methodological approach to any scientific reasoning, based on self-evident principles that could “not even be denied by the Pyrrhonniens” (IP 2009, 1.4). Two such principles are the Principle of Non-contradiction and the Principle of Sufficient Reason. While the principle of non-contradiction is the first a priori principle of any scientific finding, a self-evident principle that does not require proof and cannot be subjected to proof, the second Principle of Sufficient Reason is the condition of any rational understanding of what occurs (Moriarty 2006, Detlefsen 2014). Without it, there is no chain of reasoning and we could not differentiate dreams from reality:

For example I declare that all is still in my room in the state in which I left it, because I am certain that no one has entered since I left; but if the principle of sufficient reason does not apply, my certainty becomes a chimera, since everything could have been thrown into confusion in my room, without anyone having entered who was able to turn it upside down.(IP 2009 1.8)

The absurdities that would result if one negated that principle would lead us into a world of dreams.

Phenomena in Space

From Du Châtelet’s chapter on hypotheses, we learn how to build knowledge, though the true causes of things are not open to us. As all perception of realities must escape us by nature (IP 2018b, 5.86), what we perceive are phenomena. Du Châtelet explains the function of space and time to trace us back to the origin of phenomena. Though this is “not easy to understand,” it is indispensable to know how we unlock the world via imaginary beings, such as space and time. Everything we perceive is perceived in a spatial mode, is presented within a spatial representation. Space is an imaginary being, she holds, that allows us to peep at reality through the form of space. Eberhard pointed out that Du Châtelet claimed to trace back phenomena to its origin, and referred to her as a precursor of Kant’s epistemology (Hagengruber 2019).

Science is built upon imaginary beings as we access the world through phenomena. Real and coexisting things are accessed through space, always and intrinsically in a spatial or “shaped” manner. Like all imaginary beings, space connects us to reality, but it also deceives us about reality. Nevertheless, it is through these imaginary concepts such as space that we understand and are able to retrace a phenomenon to “its origin” (IP 2018b, 8.154). Our understanding of the world via these concepts is limited, as it is experienced through this imaginary being that unlocks the world for us, but also deceives us about what is there. As all we perceive is in space, space must be conceived of as a plenum and relative. “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” (IP 2018b, 5.77). All things stand in spatial relation to each other. Space is the order of coexisting things, like time is the order of successive beings (IP 2009, 6.102).

Newton and Leibniz’s disagreement on space is a decisive point in the development of Du Châtelet’s epistemology, brought to a new level. Du Châtelet rebuts Locke’s concept of space as a container and as a trivialization of the meaning of essence and substance. This concept of space cannot explain either the form or the place of a body. Leibniz’ relativist stance on space is based on the concept of location (Lat. situs). The perceived phenomenon of the world is a plenum and the extension of anybody in it is according to the active forces of the other bodies (Hecht 2019).

Matter and Forces

As reality must by nature escape us, we are not able to perceive the world as it is. Nothing remains to us but the confused ideas that we have of each of these simple Beings, which is an idea of several coexisting things, linked together without us knowing distinctly how they are linked. Though “Philosophers from all times have exerted themselves about the origin of matter, and the elements,” Du Châtelet crucially distances her own approach from that of the atomists but also from Leibniz (IP 2018b, 7.117). Matter in its simple form cannot be an atom, as an atom pretends to be indivisible but extended, which contradicts the first law of our understanding. Consequently, it has to be concluded that the first kind of matter must be presumed without extension. Descartes, though, is not right. Investigating what Leibniz calls monads, she states, “It must be confessed that this conclusion astonishes the imagination, simple beings are not within its province” (7.119). We cannot grasp simple beings, being the very beginning and being not matter. But these simple beings are endowed with a force, which cannot be stopped nor broken nor destroyed (7.127). These simple non-extended beings give reason for all that happens in composed bodies. However, Du Chatelet’s definition differs from that of Leibniz, whose monads are purely metaphysical and do not act upon each other, but present the order of the universe in its pre-established harmony. She retorted that, “this solution to this problem is indeed reserved for the Eternal Geometrician,” but will always be impossible for finite beings, except “then they would become God …” she ironically added (7.131).

We cannot trace back the impressions to that kind of beginning. We only perceive what affects our organs with a certain force, though there is an infinity of dim representations, and that also accompanies our ideas, though it cannot be grasped clearly. This interrelatedness “between our soul and the entire universe comes from the union of the elements among themselves” (7.133). Extension is the assemblage of diverse, coexisting things and not substances, as Descartes had claimed. The great fault in Descartes and his followers was to define the essence of a body as extended and thereby to “remove all force and all activity from creatures” (8.138), while its essence must also entail a reason for why it is different to any other matter. This can only have its origin in an internal force, a force tending toward motion in all matter and diversifying to infinity. The essence of matter is force, active force and passive force and extension, all three attributes independent from each other. The diversity of any matter results from its specific force. Being without any motion, all parts would be similar (8.139). There is not matter without force, nor force without matter. Essence is not defined solely by active force and extension but also by its resistance, as it is the resisting force that creates the proportion between cause and effect; would there not be this force, the largest and the smallest body could be moved by the same force, if there were no inertia. It is these three essential and independent attributes that define what matter is. And all that happens in matter can be reduced to these three principles (8.145, Brading 2019).

Dead and Living Forces

When the Institutions de physique was first published in 1740, there was a full chapter on the living forces. This chapter included a rebuttal of Mairan’s critique of living forces, which Du Châtelet had still defended in her Dissertation. Mairan attacked Du Châtelet in a public letter, mocking her “change of thoughts” (1741a, b). Du Châtelet delivered a quick reply, the Response of the marquise to the letter of M. Mairan, permanent secretary of the Royal Academy of Science, he wrote on February 18, 1741. Only months later the dispute was published by Luise Gottsched, introducing a German audience to Du Châtelet’s work, which would eventually gain wide reception in Germany. It was this paper that Immanuel Kant discussed in his first Dissertation on the living forces. His interest in Du Châtelet continued throughout his entire life (Winter 2019).

Du Châtelet’s ideas on dynamics were based on her reading of Leibniz’ Brevis demonstration erroribus memorabilis Cartesii, which she refers to at the beginning of 1738 in her letters. She questioned the Cartesian concept of the conservation of motion as well as the Cartesian quantity of motion and reflected on the advantage given by the living forces. Dead forces measured the empirical phenomenon (mv) of any movement. The derivative forces that caused this action hereby modified the primitive forces and allowed quantification of the action. One was not meant to replace the other, rather it was a more embracing explanation of motive activity, as the metaphysical concept of living forces attempted to understand the beginning and the end of motion, the quarrel about it was a dispute over words (Rey 2019).

Moreover, the metaphysical concept of living forces responded to a further pressing question that arose in Du Châtelet. Du Châtelet, who strictly rebutted any reference to God as a reference in physics, was challenged to respond to the question of free will. How could one understand that the physical world, explained by laws, was compatible with free human action? Did this kind of physics not rebut any claim for human freedom? “If humans do not have the power to set something in motion, they are not free,” Du Châtelet claimed (2018, letter from April 4, 38). In this letter, she asserted that though the causal chain of the physical world was incompatible with human freedom, the living forces seemed to reconcile this, as she emphatically claimed, that hereby Leibniz had lifted “one of the greatest secrets of our creator” (Jorati 2019).

Newton’s Principia and Du Châtelet’s Translation

Du Châtelet’s laws differ from those presented in Newton’s Principia (Reichenberger 2020). Hecht’s claim that Du Châtelet’s laws of motion are general laws of motion, for which Newton’s laws are a special case, is delivered in the first Law (Hecht 2020). In Du Châtelet, Newton’s impressed force is presented more generally as cause, since “there must be a cause that sets a body in motion,” which is not reducible to a force impression, but could also be due to the absence of a former active force (IP 2018b, 11.227).

On December 9, 1745, the translation of Newton’s Principia was submitted to the administration of the book trade and announced by Voltaire in May 1746. Du Châtelet’s translation is based on the latest edition of the Principia published in London in 1726. Her manuscript was sent to the royal Library the day she died (Hutton 2004). It has the stamp of September 10, 1749, the day after her death. Between 1745 and 1749, two commentaries were added. The first presented mathematical results and problems as Analytical solution of problems concerning the system of the world. The second, A short exposition of the world and explication of the principles according to Mr. Newton, that became part of the 1759 edition, which still serves as the relevant reference in France today (Cohen 1968). In the spring of 1749, she wrote to Jacquier that she was going to write her Short Exposition of Newton’s system “without figures and without algebra,” to show Mr. Newton’s sequence of principles. In a second piece of her Analytic Commentary, she wanted to “put something on the form of the Earth and on the theory of the Moon and comets, including the findings of Mr. Clairaut” (Toulmonde 2015). The Short Exposition tells the history of astronomical models, from the Babylonians and Pythagoras up to Newton’s death, while the Analytic Solution is an algebraic presentation of disputed topics from the Principia that brings Newton up to date. Given the fact that Newton had written in the seventeenth century, various assumptions had since been confirmed. Finally, the return of Halley’s comet pressed the publication in 1759.

As Toulmonde confirms, Du Châtelet’s careful transformation of Newton’s fluxion calculus contributed to a much easier access to Newton’s Principia (2008). Instead of Newton’s geometric method, analytical formulas are used, based on Leibniz’s differential calculus along the lines of Johann Bernoulli, Euler, d’Alembert, and others. According to Smith, Du Châtelet’s aim with her commentary was not to provide a commentary on Newton’s Principia but rather on the system of the world “according to Newtonian principles.” She wanted to give readers access to the state of Newton’s theory of the system of the world at the time, which indeed, they could not readily find elsewhere. As Smith explains further, there are also passages that are not in keeping with the historical situation of the Principia, as when she referred to Kepler’s account of planetary motion. Interestingly, Du Châtelet not only also cites Hooke, “but quotes in full the three hypotheses and following paragraphs from the end of his An Attempt to prove the Motion of the Earth from Observations of 1674, which is the very passage Hooke subsequently invoked as the basis for his claim to priority over Newton” (Smith 2021).

Moral Writings

The Individual in Society: From Politics to Happiness

The Mandeville Commentary

In early 1735, Du Châtelet undertook a partial translation of and commentary on Mandeville’s Fable of the Bees, that she had described as the best ethics ever written. This work marks her starting point in becoming a philosopher. There, we find her first and seminal critique of the philosophy of Locke, extensive elaborations on the good in society as well as a variety of introductions blaming society’s mistreatment of women. It was not published, though we may assume that her manuscripts circulated, given the various overlap with other writers, their relations and references to her, including La Mettrie and Diderot (Gottmann 2012). She concedes to Mandeville’s analysis that morality results from politics and is nothing more than an invention “to lead the many.” Societal order emerges from generations that are forced to care for the offspring. The Epicurean concept of self-deprivation as a means to happiness is relevant, and those who best adapt to this are successful. These rules vary, since they depend on local, temporal, and cultural circumstances. Greece and Rome, or Paris and Constantinople are examples of this virtue-relativism, she explains. One may even find that the various definitions of vice and virtue contradict each other, as different societies and climates diverge in their positions on which behaviors are desirable for the good of society (Du Châtelet 2020). Beyond this relativist approach to morality, the prosperity of any society can only be attained by knowledge and truth, by investigation and scientific experiments. Every rule must be subjected to the truth, for the good of any society always rests on truth, which is the only criterion for virtue (Hagengruber 2011).

Discourse on Happiness

The Reflections on Happiness, published as Discourse on Happiness, were drafted according to Zinsser during a longer period from the thirties to the forties. Interesting similarities to and differences from La Mettrie’s Anti-Seneque had been detected early. The publication of the Discourse was planned in 1769, but only carried out in 1779. La Mettrie provides a sharp profile to be compared with the writings of Du Châtelet. He referenced her Dissertation on Fire, dedicated a 12-page letter on the Nature of the soul to her and recalls her and her ideas in several writings, though to this day it is unknown if they ever met. Challenges of moral materialism are responded to, parallels to Epicurus’ writings can be observed, and a literal intercourse with the French philosophes was evident (Mauzi 1961). Rodrigues claims a utilitarian stance since the pursuit of happiness and even the pursuit of passion and illusions, is a central topic in her morals (Rodrigues 2019).

Women in Science and Society

The Prize-winning Dissertation on Fire (1739) and her Dispute with Marain (1740) as well as her Institutions made Du Châtelet famous in her time. In 1745, the Pinacotecarum Scriptorium illustrissimum, edited by Jacob Brucker presented Du Châtelet alongside Luise Gottsched and Laura Bassi, praising them as the most famous people of the epoch. In April 1746, Du Châtelet was elected as a member of the Academy of Bologna and also elected to the Accademia dell’Arcadia in Rome.

Regardless of her own success, Du Châtelet speaks critically about the roles women have to play in society. As the manuscripts of Saint Petersburg and other writings show, women’s dedication to care for “hair and teeth” and ostracizing from education and science is condemned in many ways.

For those who are not familiar with Du Châtelet’s scientific method, it may be strange to find her pronouncement of women’s subjection as a contradiction. “I feel the full weight of prejudice that excludes us (women) so universally from the sciences, this being one of the contradictions of this world which has always astonished me, as there are great countries whose laws allow us to decide their destiny, but none where we are brought up to think” (Du Châtelet, Selected Writings 2009, 44). Consistent with her ideas about the principles of understanding and her commentary on society’s betrayal on women, it is understood as a failure from comprehending what is good for any society. At the center of her writings, it is all about identifying the contradictions in our thought that lead us “astray” in our conduct and reasoning. The denial of women’s right to participate in society, education, etc. is such a contradiction and hinders society’s prosperity.

Examination of the Bible

The Examinations of the Bible was found in three manuscript versions and was published in 2011 (Schwarzbach). The examination of the Bible was originally ascribed to Voltaire, who, as its editor, Schwarzbach, maintains, only contributed “banal references to the Holy Scriptures” in comparison to Du Châtelet. Schwarzbach identified Du Châtelet as the author. He also demonstrates Du Châtelet’s impact on clandestine literature and her participation in that movement. As Seguin (2020) points out, the Biblical criticism resulted from the philosophical rationalism that marks the enlightened early eighteenth century.

The text contributes to the Biblical critiques of the period, which are not unique among the Libertines regarding the questioning of revelation, prophecies, and miracles. What is different and unique throughout Du Châtelet’s opus, is that she examined the subjects in the Holy Book, text by text, through a rational reading that derives its arguments, not from earlier polemical works, but from the strict application of well-informed historical and scientific facts. The principle of contradiction was the most employed methodological instrument in doing so and historical data was considered unreal. This vast volume contributed to the European Enlightenment and was still present among the enlightened philosophers of the revolution.

Legacy

Du Châtelet may rightly be seen as a famous figure of the French Enlightenment. Her scholarship was unsurpassed and her reputation spread across Europe. As in many cases, those who outperform are the most criticized. This was surely true for Du Châtelet. Neither she nor her writings fell into complete oblivion. Articles taken from Du Châtelet’s Institutions have been copied directly, either referring to her or simply copying her, in total or in part. In Diderot’s and d’Alembert’s Encyclopédie her work was copied for important entries such as continuity, space, hypothesis, movement, weight, rest, and time. The entry on fire was taken from her Dissertation and the entry “Newtonianism” from her commentary of the Principia. D’Alembert, Euler, Poincaré, and Bachelard resorbed her ideas on hypotheses; Kant must be seen as a well-informed reader of her texts.

Cross-References