Criticizing Locke and the debate on thinking matter In her writings, du Châtelet criticized
John Locke's philosophy. She emphasizes the necessity of the
verification of knowledge through experience: "Locke's idea of the possibility of
thinking matter is […] abstruse". Her critique on Locke originated in her commentary on Bernard de Mandeville's
The Fable of the Bees. She resolutely favored universal principles that precondition human knowledge and action, and maintained that this kind of law is innate. Du Châtelet claimed the necessity of a universal presupposition, because if there were no such beginning, all our knowledge is relative. In that way, Du Châtelet rejected Locke's aversion to innate ideas and prior principles. She also reversed Locke's negation of the principle of contradiction, which would constitute the basis of her methodic reflections in the
Institutions. On the contrary, she affirmed her arguments in favor of the necessity of prior and universal principles. "Two and two could then make as well 4 as 6 if prior principles did not exist." References by Pierre Louis Moreau de Maupertuis and Julien Offray de La Mettrie to du Châtelet's deliberations on motion, free will,
thinking matter, numbers, and the way to conduct
metaphysics are a sign of the importance of her reflections. She rebuts the claim to finding truth by using mathematical laws, and argues against Maupertuis.
Fire, heat, and combustion In 1737, the Royal Academy of Science in Paris (now
French Academy of Sciences) announced an essay competition on the question of the nature and propagation of fire, to be awarded the following year.
Voltaire, who was then working with Du Châtelet at her estate in Cirey, entered the competition. Eventually, Du Châtelet decided to enter herself, though without informing Voltaire, with whom she had significant theoretical disagreements. While neither of them won the competition, their essays were judged to be of sufficient quality to be published in the collections of the Academy, alongside the winning essays. Her
Dissertation sur la nature et la propagation du feu thus appeared in 1739, the first time the Academy published a work written by a woman. Du Châtelet's essay takes the position that fire is a distinctive type of matter, a common view in the period, and sought to use mechanical theory to understand its properties. For instance, she argued that it is a massless particle, whereas Voltaire had claimed fire had weight. She also speculated that there may be colors in other suns that are not found in the spectrum of sunlight on Earth.
Institutions de Physique Her book
Institutions de Physique ("Lessons in Physics") was published in 1740; it was presented as a review of new ideas in science and philosophy to be studied by her 13-year-old son, but it incorporated and sought to reconcile complex ideas from the leading thinkers of the time. The book and subsequent debate contributed to her becoming a member of the
Academy of Sciences of the Institute of Bologna in 1746. Du Châtelet originally preferred anonymity in her role as the author, because she wished to conceal her gender. Ultimately, however,
Institutions was convincing to salon-dwelling intellectuals in spite of the commonplace sexism.
Institutions discussed, refuted, and synthesized many ideas of prominent mathematicians and physicists of the time. In particular, the text is famous for discussing ideas that originated with G. W. Leibniz and Christian Wolff, and for using the principle of sufficient reason often associated with their philosophical work. This main work is equally famous for providing a detailed discussion and evaluation of ideas that originated with Isaac Newton and his followers. That combination is more remarkable than it might seem now, since the ideas of Leibniz and Newton were regarded as fundamentally opposed to one another by most of the major philosophical figures of the eighteenth century. In chapter I, du Châtelet included a description of her rules of reasoning, based largely on Descartes’s principle of contradiction and Leibniz’s principle of sufficient reason. In chapter II, she applied these rules of reasoning to metaphysics, discussing God, space, time, and matter. In chapters III through VI, du Châtelet continued to discuss the role of God and his relationship to his creation. In chapter VII, she broke down the concept of matter into three parts: the macroscopic substance available to sensory perception, the atoms composing that macroscopic material, and an even smaller constituent unit similarly imperceptible to human senses. However, she carefully added that there was no way to know how many levels truly existed. The remainder of
Institutions considered more metaphysics and classical mechanics. Du Châtelet discussed the concepts of space and time in a manner more consistent with modern relativity than her contemporaries. She described both space and time in the abstract, as representations of the relationships between coexistent bodies rather than physical substances. This included an acknowledgement that "absolute" place is an idealization and that "relative" place is the only real, measurable quantity. Du Châtelet also presented a thorough explanation of Newton’s laws of motion and their function on earth.
Forces Vives In 1741, du Châtelet published a book entitled
Réponse de Madame la Marquise du Chastelet, a la lettre que M. de Mairan.
D'Ortous de Mairan, secretary of the Academy of Sciences, had published a set of arguments addressed to her regarding the appropriate mathematical expression for
forces vives ("living forces"). Du Châtelet presented a point-by-point rebuttal of de Mairan's arguments, causing him to withdraw from the controversy.
Immanuel Kant's first publication in 1747, '
Thoughts on the True Estimation of Living Forces' (
Gedanken zur wahren Schätzung der lebendigen Kräfte), focused on du Châtelet's pamphlet rebutting the arguments of the secretary of the French Academy of Sciences, Mairan. Kant's opponent,
Johann Augustus Eberhard, accused Kant of taking ideas from du Châtelet. In his
Observations on the Feeling of the Beautiful and Sublime, Kant wrote
ad hominem and sexist critiques of learned women of the time, including Mme. du Châtelet, rather than writing about their work. Kant stated: "A woman who has a head full of Greek, like
Mme. Dacier, or who conducts disputations about mechanics, like the Marquise du Châtelet might as well also wear a beard; for that might perhaps better express the mien of depth for which they strive."
Advocacy of kinetic energy Although in the early eighteenth century the concepts of force and
momentum had been long understood, the idea of energy as being transferable between different systems was still in its infancy, and would not be fully resolved until the nineteenth century. It is now accepted that the total mechanical momentum of a system is conserved and that none is lost to friction. Simply put, there is no 'momentum friction', and momentum cannot transfer between different forms, and particularly, there is no 'potential momentum'. In the twentieth century,
Emmy Noether proved this to be true for all problems where the initial state is
symmetric in generalized coordinates. E.g., mechanical energy, either kinetic or potential, may be lost to another form, but the total is conserved in time. Du Châtelet's contribution was the hypothesis of the conservation of total energy, as distinct from momentum. In doing so, she became the first to elucidate the concept of energy as such, and to quantify its relationship to mass and velocity based on her own empirical studies. Inspired by the theories of
Gottfried Leibniz, she repeated and publicized an experiment originally devised by
Willem 's Gravesande in which heavy balls were dropped from different heights into a sheet of soft clay. Each ball's
kinetic energy – as indicated by the quantity of material displaced – was shown to be proportional to the square of the
velocity: She showed that if two balls were identical except for their mass, they would make the same size indentation in the clay if the quantity mv^2 (then called
vis viva) were the same for each ball. Newton's work assumed the exact conservation of only mechanical momentum. A broad range of mechanical problems in physics are soluble only if energy conservation is included. The collision and scattering of two point masses is one example.
Leonhard Euler and
Joseph-Louis Lagrange established a more formal framework for mechanics using the results of du Châtelet.
Translation and commentary on Newton's Principia In 1749, the year of du Châtelet's death, she completed the work regarded as her outstanding achievement: her translation into French, with her commentary, of Newton's
Philosophiae Naturalis Principia Mathematica (often referred to as simply the
Principia), including her derivation of the notion of
conservation of energy from its principles of mechanics. Despite modern misconceptions, Newton's work on his
Principia was not perfect. Du Châtelet took on the task of not only translating his work from Latin to French, but adding important information to it as well. Her commentary was as essential to her contemporaries as her spreading of Newton's ideas. Du Châtelet's commentary was very extensive, comprising almost two-thirds of volume II of her edition. To undertake a formidable project such as this, du Châtelet prepared to translate the
Principia by continuing her studies in
analytic geometry, mastering
calculus, and reading important works in experimental physics. Her rigorous preparation afforded her commentary a wealth of substantive, accurate information, derived from her own research as well as from the work of other scientists she studied or worked alongside. She was one of only 20 or so people in the 1700s who could understand such advanced math and apply the knowledge to other works. This helped du Châtelet greatly, not only with her work on the
Principia but also in her other important works like the
Institutions de Physique. Du Châtelet made very important corrections in her translation that helped support Newton's theories about the universe. Newton, based on the theory of fluids, suggested that gravitational attraction would cause the poles of the earth to flatten, thus causing the earth to bulge outwards at the
equator. In
Clairaut's
Memoire, which confirmed Newton's hypothesis about the shape of the Earth and gave more accurate approximations, Clairaut discovered a way to determine the shape of the other planets in the
Solar System. Du Châtelet used Clairaut's proposal that the planets had different
densities in her commentary to correct Newton's belief that the Earth and the other planets were made of
homogeneous substances. Du Châtelet used the work of
Daniel Bernoulli, a Swiss mathematician and physicist, to further explain Newton's theory of the
tides. This proof depended upon the
three-body problem which still confounded even the best mathematicians in 18th century Europe. Using Clairaut's hypothesis about the differing of the planets' densities, Bernoulli theorized that the moon was 70 times denser than Newton had believed. Du Châtelet used this discovery in her commentary of the
Principia, further supporting Newton's theory about the
law of gravitation. Published ten years after her death, today du Châtelet's translation of the
Principia is still the standard translation of the work into French, and remains the only complete rendition in that language. Her translation was so important that it was the only one in any language used by
Newtonian expert
I. Bernard Cohen to write his own English version of Newton's
Principia. Du Châtelet not only used the works of other great scientists to revise Newton's work, but she added her own thoughts and ideas as a scientist in her own right. Her contributions in the French translation made Newton and his ideas look even better in the
scientific community and around the world, and recognition for this is owed to du Châtelet. This enormous project, along with her
Foundations of Physics, proved du Châtelet's abilities as a great mathematician. Her translation and commentary of the
Principia contributed to the completion of the
Scientific Revolution in France and to its acceptance in Europe. ===Possible Influence on
Immanuel Kant=== Kant mostly engaged with
Georg Friedrich Meier’s Excerpts from the Doctrine of Reason (1752) in his logic lectures. It is highly plausible that du Châtelet’s presence was recognized by contemporaries such as Baumgarten, which alludes to a connection that might have broader implications for Kant’s knowledge of du Châtelet. Notably, Meier’s involvement in the publication of
Christine Ziegler (later Unzer)’s work,
Grundriss einer Weltweisheit für das Frauenzimmer (A Sketch of a World Wisdom for Women), suggests a potential linkage to du Châtelet’s philosophical ideas. Hence, du Châtelet’s name held certain significance within Meier’s sphere of influence. The immediate translation of the Institutions into German following its release also implies its likely role in paving the philosophical path for Kant’s later endeavors. == Illusions and happiness ==