Arguments for the Continuity of Matter in Kant and Du Châtelet
-
Aaron Wells
Abstract
In the Metaphysical Foundations of Natural Science, Kant attempts to argue a priori from the indefinite divisibility of space to the indefinite metaphysical divisibility of matter. This is one type of argument from the continuity of space – purportedly established by Euclidean geometry – to the continuity of matter. I compare Kant’s argument to parallel reasoning in Du Châtelet, whose work he knew. Both philosophers appeal to idealism about matter in their reasoning, yet also face difficulties in explaining why continuity, though not some other properties from geometry, applies to matter. Both also risk inconsistency in adopting potentialist accounts of material parts, while also committing to realism about infinitesimals. An important difference between them is that Du Châtelet deploys at least three definitions of continuity; only one of these, amounting to indefinite divisibility, is shared with Kant.
Acknowledgments
I owe special thanks to Stephen Howard, Jeff McDonough, Rudolf Meer, Lorenzo Spagnesi, Marius Stan, and an editor at Kant-Studien for written comments on earlier versions; to Emily Carson for correspondence that inspired several ideas; and to Silvia De Bianchi for giving me the opportunity to present some of this material at the University of Milan’s PROTEUS seminar. For helpful exchanges, I am also indebted to Joe Anderson, Laura Follesa, Rima Hussein, Laura Marongiu, William Marsolek, Andrea Reichenberger, Anat Schechtman, and Jan-Willem van Holten.
Works cited
Arthur, R. T. W. (2018). Monads, Composition, and Force. Oxford.10.1093/oso/9780198812869.001.0001Suche in Google Scholar
Brading, K. and M. Stan (2024). Philosophical Mechanics in the Age of Reason. Oxford.10.1093/oso/9780197678954.001.0001Suche in Google Scholar
Büchel, G. (1987). Geometrie und Philosophie. Berlin/New York.10.1515/9783110857511Suche in Google Scholar
Cajori, F. (1926). “Madame Du Châtelet on fluxions”. The Mathematical Gazette 13, 252.10.2307/3604156Suche in Google Scholar
Carson, E. (1997). “Kant on Intuition in Geometry”. Canadian Journal of Philosophy, 27 (4), 489–512.10.1080/00455091.1997.10717483Suche in Google Scholar
Castelli, L. (2018). Aristotle: Metaphysics Book Iota. Oxford.10.1093/oseo/instance.00258620Suche in Google Scholar
Coissard, G. (2021). “Du Châtelet entre monadisme et atomisme: La matière dans les Institutions de physique”. Revue d’histoire des sciences 74 (2), 297–329.10.3917/rhs.742.0297Suche in Google Scholar
De Risi, V. (2019). “Leibniz on the Continuity of Space”. In Leibniz and the Structure of Sciences, ed. by V. De Risi. Cham, 111–170.10.1007/978-3-030-25572-5_4Suche in Google Scholar
De Risi, V. (2021a). Gapless Lines and Gapless Proofs: Intersections and Continuity in Euclid’s Elements. Apeiron 54 (2), 233–259.10.1515/apeiron-2019-0012Suche in Google Scholar
De Risi, V. (2021b). “Has Euclid Proven Elements I, 1? The Early Modern Debate on Intersections and Continuity”. In Reading Mathematics in Early Modern Europe, ed. by P. Beeley, Y. Nasifoglu, and B. Wardhaugh. London, 12–32.10.4324/9781003102557-2Suche in Google Scholar
Du Châtelet, E. (1740). Institutions de Physique. First edition. Paris.Suche in Google Scholar
Du Châtelet, E. (1742). Institutions Physiques. Second edition. Paris.Suche in Google Scholar
Euler, L. (1768). Lettres à un Princesse d’Allemagne sur divers sujets de physique & de philosophie. Three volumes. St. Petersburg.Suche in Google Scholar
Friedman, M. (2010). “Synthetic History Reconsidered.” In Discourse on a New Method, ed. by M. Domski and M. Dickson. Chicago, 571–813.Suche in Google Scholar
Heath, T. L. (1908). The Thirteen Books of Euclid’s Elements. Cambridge.Suche in Google Scholar
Goldenbaum, U. (2021). “How Kant was Never a Wolffian, or, Estimating Forces to Enforce Influxus Physicus”. In Leibniz and Kant, ed. by B. C. Look. Oxford, 27–56.10.1093/oso/9780199606368.003.0002Suche in Google Scholar
Jankowiak, T. (2020). “Kant on the Continuity of Alterations”. Canadian Journal of Philosophy 50 (1), 49–66.10.1017/can.2019.6Suche in Google Scholar
Jauernig, A. (2022). “The Labyrinth of the Continuum: Leibniz, the Wolffians, and Kant on Matter and Monads”. In The Sensible and Intelligible Worlds, ed. by K. Schafer and N. F. Stang. Oxford, 185–216.10.1093/oso/9780199688265.003.0009Suche in Google Scholar
Keill, J. (1733). Introduction to Natural Philosophy. Fourth edition. London.Suche in Google Scholar
Leibniz, G. W. (1849–1863). Leibnizens mathematische Schriften. (C. I. Gerhardt, Ed.). Halle: Schmidt.Suche in Google Scholar
McNulty, M. B. (2019). “Continuity of change in Kant’s dynamics”. Synthese, 196, 1595–1622.10.1007/s11229-017-1527-4Suche in Google Scholar
Moretto, A. (1995). “La rilevanza matematica della discussione sui concetti di continuo e di funzione nella filosofia tedesca dell’età dell’illuminismo”. Fenomenologia e società, 18/2–3, 109–153.Suche in Google Scholar
Pasini, E. (1994). “La prima recezione della Monadologia”. Studi settecenteschi XIV, 107–163.Suche in Google Scholar
Pelayo, A. (2023). “Certitude et loi de continuité dans les Institutions de physique d’Émilie du Châtelet”. Les études philosophiques 146 (3), 7–22.10.3917/leph.233.0007Suche in Google Scholar
Pfeiffer, C. (2018). Aristotle’s Theory of Bodies. Oxford.10.1093/oso/9780198779728.001.0001Suche in Google Scholar
Pollok, K. (2001). Kants ‘Metaphysische Anfangsgründe der Naturwissenschaft’: Ein Kritischer Kommentar. Hamburg.Suche in Google Scholar
Sattler, B. (2020). The Concept of Motion in Ancient Greek Thought. Cambridge.10.1017/9781108775199Suche in Google Scholar
Stan, M. (2015). “Kant and the object of determinate experience”. Philosophers’ Imprint 15 (33), 1–19.Suche in Google Scholar
Stan, M. (2023). “Newtonianism and the Physics of Du Châtelet’s Institutions de Physique”. In Collected Wisdom of the Early Modern Scholar, ed. by A.M. Roos and G. Manning. Cham, 277–297.10.1007/978-3-031-09722-5_13Suche in Google Scholar
Sutherland, D. (2021). “Continuity and Intuition in Eighteenth-Century Analysis and in Kant”. In The History of Continua, ed. by S. Shapiro and G. Hellman. Oxford, 123–158.10.1093/oso/9780198809647.003.0008Suche in Google Scholar
Sutherland, D. (2022). Kant’s Mathematical World. Cambridge.Suche in Google Scholar
van Strien, M. (2017). “Continuity in Nature and in Mathematics: Du Châtelet and Boscovich”. In EPSA15 Selected Papers, ed. by M. Massimi et al. Dordrecht, 71–81.10.1007/978-3-319-53730-6_7Suche in Google Scholar
Wells, A. (2023). “‘In Nature as in Geometry’: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects”. In Between Leibniz, Newton, and Kant, ed. by W. Lefèvre, 2nd ed. Dordrecht, 69–98.10.1007/978-3-031-34340-7_4Suche in Google Scholar
Wilson, C. (2019). “The Reception of Newton’s Theory of Matter and his Atomism”. In The Reception of Isaac Newton in Europe vol. II, ed. by H. Pulte and S. Mandelbrote. London, 433–450.Suche in Google Scholar
Wilson, M. (2022). Imitation of Rigor. Oxford.10.1093/oso/9780192896469.001.0001Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Titelseiten
- Abhandlungen
- Kant’s Spies
- Heideggers Zuflucht bei Kant
- Berichte und Diskussionen
- Introduction
- Monads, Solidity and the Metaphysics of Bodies
- Arguments for the Continuity of Matter in Kant and Du Châtelet
- “Also setzen alle mechanischen Gesetze die dynamischen voraus”: Kant and his German Predecessors on Dynamical and Mechanical Forces
- The Penetrability of Matter: Mechanical and Chemical
- Physik und Metaphysik. Zur Umkehrung ihres Verhältnisses am Beispiel von Trägheitsgesetz und Raum bei Newton, Euler und Kant
- Buchbesprechungen
- Kant, Immanuel: Crítica de la raó pura [katalanische Übersetzung der Kritik der reinen Vernunft], Übersetzung und Anmerkungen von Miquel Montserrat Capella; von Salvi Turró und Josep Monserrat revidiert, mit einer Einführung von Salvi Turró versehen. Barcelona: Universitat de Barcelona, 2024. 582 Seiten. ISBN 978-84-10-50006-8.
- Antoine Grandjean: Métaphysiques de l’expérience : empirisme et philosophie transcendantale selon Kant. Paris: Vrin 2022. 448 p. ISBN 978-2-7116-3025-7
- Hope and the Kantian Legacy: New Contributions to the History of Optimism. Edited by Katerina Mihaylova and Anna Ezekiel. New York: Bloomsbury, 2023. 328 pp. ISBN 9781350238107
- Mitgliederversammlung der Kant-Gesellschaft
Artikel in diesem Heft
- Titelseiten
- Abhandlungen
- Kant’s Spies
- Heideggers Zuflucht bei Kant
- Berichte und Diskussionen
- Introduction
- Monads, Solidity and the Metaphysics of Bodies
- Arguments for the Continuity of Matter in Kant and Du Châtelet
- “Also setzen alle mechanischen Gesetze die dynamischen voraus”: Kant and his German Predecessors on Dynamical and Mechanical Forces
- The Penetrability of Matter: Mechanical and Chemical
- Physik und Metaphysik. Zur Umkehrung ihres Verhältnisses am Beispiel von Trägheitsgesetz und Raum bei Newton, Euler und Kant
- Buchbesprechungen
- Kant, Immanuel: Crítica de la raó pura [katalanische Übersetzung der Kritik der reinen Vernunft], Übersetzung und Anmerkungen von Miquel Montserrat Capella; von Salvi Turró und Josep Monserrat revidiert, mit einer Einführung von Salvi Turró versehen. Barcelona: Universitat de Barcelona, 2024. 582 Seiten. ISBN 978-84-10-50006-8.
- Antoine Grandjean: Métaphysiques de l’expérience : empirisme et philosophie transcendantale selon Kant. Paris: Vrin 2022. 448 p. ISBN 978-2-7116-3025-7
- Hope and the Kantian Legacy: New Contributions to the History of Optimism. Edited by Katerina Mihaylova and Anna Ezekiel. New York: Bloomsbury, 2023. 328 pp. ISBN 9781350238107
- Mitgliederversammlung der Kant-Gesellschaft
