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Du Châtelet on the Need for Mathematics in Physics

Published online by Cambridge University Press:  01 January 2022

Aaron Wells
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Abstract

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches.

Type
Physical and Mathematical Sciences
Information
Philosophy of Science , Volume 88 , Issue 5 , December 2021 , pp. 1137 - 1148
Copyright
Copyright 2021 by the Philosophy of Science Association. All rights reserved.

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Footnotes

†

I am grateful to Katherine Brading, Corey Dyck, Ashton Green, Qiu Lin, Andrea Reichenberger, Marius Stan, Paul Tran-Hoang, and audience members at the 2020 Central Division Meeting of the American Philosophical Association for helpful discussions. I would like to especially thank Monica Solomon for outstanding written comments on an earlier draft of this article.

References

Arnauld, Antoine, and Nicole, Pierre. 1996. Logic or the Art of Thinking. ed. Buroker, Jill Vance. New York: Cambridge University Press.CrossRefGoogle Scholar
Baker, Alan. 2009. “Mathematical Explanation in Science.” British Journal for the Philosophy of Science 60 (3): 611–33.CrossRefGoogle Scholar
Blay, Michel. 1986. “Deux moments de la critique du calcul infinitésimal: Michel Rolle et George Berkeley.” Revue d’histoire des sciences 39:223–53.CrossRefGoogle Scholar
Brading, Katherine. 2019. Emilie Du Chaâtelet and the Foundations of Physical Science. New York: Routledge.CrossRefGoogle Scholar
Buchenau, Stefanie. 2011. “Notions directrices et architectonique de la métaphysique.” Astérion 9. https://doi.org/10.4000/asterion.2136.Google Scholar
Carson, Emily. 2004. “Metaphysics, Mathematics and the Distinction between the Sensible and the Intelligible in Kant’s Inaugural Dissertation.” Journal of the History of Philosophy 42 (2): 165–94.CrossRefGoogle Scholar
Chareix, Fabien. 2010. “Geometrization or Mathematization: Christiaan Huygens’s Critiques of Infinitesimal Analysis in His Correspondence with Leibniz.” In The Practice of Reason, ed. Dascal, Marcelo, 33–50. Amsterdam: Benjamins.CrossRefGoogle Scholar
Cohen, I. Bernard. 1980. The Newtonian Revolution. Cambridge: Cambridge University Press.Google Scholar
Dear, Peter. 1995. Discipline and Experience. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Detlefsen, Karen. 2019. “Du Châtelet and Descartes on the Roles of Hypothesis and Metaphysics in Natural Philosophy.” In Feminist History of Philosophy, ed. O’Neill, Eileen and Lascano, Marcy, 97–128. Cham: Springer.Google Scholar
Du Châtelet, Emilie. 1738. “Lettre sur les Eléments de la Philosophie de Newton.” Journal des Sçavans, September, 534–41.Google Scholar
Du Châtelet, Emilie. 1740. Institutions de Physique. Paris: Prault.Google Scholar
Du Châtelet, Emilie. 1742. Institutions Physiques: Nouvelle Edition. Amsterdam.Google Scholar
Du Châtelet, Emilie. 1759. “Exposition Abregée du Systême du Monde.” In Principes Mathématiques de la Philosophie Naturelle, by Isaac Newton, Vol. 2, trans. with commentary by Madame la Marquise Du Chastellet. Paris: Gabay.Google Scholar
Du Châtelet, Emilie. 2009. Selected Philosophical and Scientific Writings. ed. Zinsser, Judith and Bour, Isabelle. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Du Châtelet, Emilie. 2018. La Correspondance d’Émilie Du Châtelet. Ferney-Voltaire: Centre international d’étude du XVIIIe siècle.Google Scholar
Dunlop, Katherine. 2013. “Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff.” Studies in History and Philosophy of Science A 44 (3): 457–69.Google Scholar
Dyck, Corey, ed. 2020. Early Modern German Philosophy, 1690–1750. New York: Oxford University Press.Google Scholar
[Furetière, Antoine]. 1690. Dictionaire Universel … Diviseé en trois Tomes. Rotterdam: Arnout & Renier Leers.Google Scholar
Gava, Gabriele. 2018. “Kant, Wolff, and the Method of Philosophy.” In Oxford Studies in Early Modern Philosophy, Vol. 7, ed. Dan Garber and Don Rutherford, 271–304. Oxford: Oxford University Press.Google Scholar
George, Albert. 1938. “The Genesis of the Académie des Sciences.” Annals of Science 3 (4): 372–401.CrossRefGoogle Scholar
Gingras, Yves. 2001. “What Did Mathematics Do to Physics?” History of Science 39 (4): 383–416.CrossRefGoogle Scholar
Greenberg, John. 1996. “Isaac Newton and the Problem of the Earth’s Shape.” Archive for History of Exact Sciences 49 (4): 371–91.CrossRefGoogle Scholar
Hagengruber, Ruth. 2012. “Emilie du Châtelet between Leibniz and Newton: The Transformation of Metaphysics.” In Emilie du Châtelet between Leibniz and Newton, ed. Hagengruber, Ruth, 1–60. Dordrecht: Springer.CrossRefGoogle Scholar
Hankins, Thomas. 1985. Jean d’Alembert: Science and the Enlightenment. Cambridge: Cambridge University Press.Google Scholar
Koyré, Alexandre. 1968. Metaphysics and Measurement. London: Chapman & Hall.Google Scholar
Lear, Jonathan. 1982. “Aristotle’s Philosophy of Mathematics.” Philosophical Review 91 (2): 161–92.CrossRefGoogle Scholar
Locke, John. 1975. An Essay Concerning Human Understanding. ed. Nidditch, Peter Harold. Oxford: Clarendon.Google Scholar
Maglo, Koffi. 2008. “Madame Du Châtelet, l’Encyclopédie, et la philosophie des sciences.” In Emilie Du Châtelet: Éclairages et documents nouveaux, ed. Kölving, Ulla and Courcelle, Olivier, 255–66. Paris: Centre international d’étude du XVIIIe siècle.Google Scholar
Maier, Annelise. 1968. Zwei Grundprobleme der Scholastischen Naturphilosophie. Rome: Edizioni di Storia e Letteratura.Google Scholar
Mancosu, Paolo. 1992. “Aristotelian Logic and Euclidean Mathematics.” Studies in History and Philosophy of Science 23 (2): 241–65.CrossRefGoogle Scholar
McKenzie, Kerry. 2020. “A Curse on Both Houses: Naturalistic versus A Priori Metaphysics and the Problem of Progress.” Res Philosophica 97 (1): 1–29.CrossRefGoogle Scholar
McMullin, Ernan. 1985. “Galilean Idealization.” Studies in History and Philosophy of Science 16 (3): 247–73.CrossRefGoogle Scholar
Neumann, Hanns-Peter. 2014. “Der preußische Kronprinz Friedrich und die französische Übersetzung der Deutschen Metaphysik Christian Wolffs im Jahr 1736.” Forschungen zur Brandenburgischen und Preußischen Geschichte 24 (1): 35–68.CrossRefGoogle Scholar
Rey, Anne-Lise. 2013. “Le leibnizo-newtonianisme: La construction d’une philosophie naturelle complexe dans la première moitié du 18e siècle.” Dix-huitième siècle 45 (1): 115–29.CrossRefGoogle Scholar
Rutherford, Donald. 2004. “Idealism Declined: Leibniz and Christian Wolff.” In Leibniz and His Correspondents, ed. Lodge, Paul, 214–37. Cambridge: Cambridge University Press.Google Scholar
Saatsi, Juha. 2011. “The Enhanced Indispensability Argument: Representational versus Explanatory Role of Mathematics in Science.” British Journal for the Philosophy of Science 62:143–54.CrossRefGoogle Scholar
Shank, John Bennett. 2018. Before Voltaire: The French Origins of “Newtonian” Mechanics, 1680–1715. Chicago: University of Chicago Press.Google Scholar
Smith, George. 2002. “The Methodology of the Principia.” In The Cambridge Companion to Newton, ed. Cohen, I. Bernard, 187–228. Cambridge: Cambridge University Press.Google Scholar
Stan, Marius. 2018. “Emilie du Châtelet’s Metaphysics of Substance.” Journal of the History of Philosophy 56 (3): 477–96.CrossRefGoogle Scholar
Sylla, Edith. 1973. “Medieval Concepts of the Latitude of Forms: The Oxford Calculators.” Archives d’histoire doctrinale et littéraire du moyen âge 40:223–83.Google Scholar
Wolff, Christian. 1737a. Der Anfangsgründe aller mathematischen Wissenschaften. Frankfurt.Google Scholar
Wolff, Christian. 1737b. Philosophia prima, sive Ontologia. Verona.Google Scholar
Wolff, Christian. 1983. Vernünfftige Gedancken von den Absichten der natürlichen Dinge. ed. Arndt, Hans Werner et al. Hildesheim: Olms.Google Scholar
Wolff, Christian. 1996. Discursus praeliminaris de philosophia in genere. ed. Gawlick, Gunter and Kreimendahl, Lothar. Stuttgart: Frommann-Holzboog.Google Scholar
Wolff, Christian. 2001. Deutsche Schriften. ed. École, Jean et al. Hildesheim: Olms.Google Scholar
Wolff, Christian. 2019. Briefwechsel zwischen Christian Wolff und Ernst Christoph von Manteuffel. 3 vols., ed. Stolzenberg, Jürgen et al. Hildesheim: Olms.Google Scholar
Zinsser, Judith, and Courcelle, Olivier. 2003. “A Remarkable Collaboration: The Marquise Du Châtelet and Alexis Clairaut.” Studies on Voltaire and the Eighteenth Century 12:107–20.Google Scholar