Abstract
In the mid-eighteenth century, it was usually taken for granted that all curves described by a single mathematical function were continuous, which meant that they had a shape without bends and a well-defined derivative. In this paper I discuss arguments for this claim made by two authors, Emilie du Châtelet and Roger Boscovich. I show that according to them, the claim follows from the law of continuity, which also applies to natural processes, so that natural processes and mathematical functions have a shared characteristic of being continuous. However, there were certain problems with their argument, and they had to deal with a counterexample, namely a mathematical function that seemed to describe a discontinuous curve.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
This fragment was later copied in the entry on the law of continuity in the Encyclopédie of Diderot and D’Alembert, without mention of the source (in Van Strien 2014, I have discussed this fragment without attributing it to Du Châtelet).
References
Bernoulli, Johann. 1727. Discours sur les loix de la communication du mouvement. In Johann Bernoulli, Opera omnia, vol. 3 (1742), 1–107. Lausanne, Genève: Bousquet.
Boscovich, R.J. 1754/2002. De continuitatis lege/Über das Gesetz der Kontinuität. Transl. J. Talanga. Heidelberg: Winter.
———. 1763/1922. A theory of natural philosophy. Chicago/London: Open court publishing company.
Bottazzini, Umberto. 1986. The higher calculus: A history of real and complex analysis from Euler to Weierstrass. New York: Springer.
Du Châtelet, Emilie. 1740. Institutions de physique. Paris: Prault.
Guzzardi, Luca. 2016. Article on Boscovich’s law, the curve of forces, and its analytical formulation (draft).
Heimann, P.M. 1977. Geometry and nature: Leibniz and Johann Bernoulli’s theory of motion. Centaurus 21 (1): 1–26.
Koznjak, Boris. 2015. Who let the demon out? Laplace and Boscovich on determinism. Studies in history and philosophy of science 51: 42–52.
Maupertuis, Pierre-Louis Moreau de. 1750. Essay de cosmologie. In Oeuvres de Maupertuis, 3–54. Dresden: Walther. 1752.
Schubring, Gert. 2005. Conflicts between generalization, rigor, and intuition: Number concepts underlying the development of analysis in 17th-19th century France and Germany. New York: Springer.
Truesdell, C. 1960. The rational mechanics of flexible or elastic bodies. Introduction to Leonhardi Euleri Opera Omnia, 2nd series, (11)2. Zürich: Orell Füssli.
Van Strien, Marij. 2014. On the origins and foundations of Laplacian determinism. Studies in History and Philosophy of Science 45 (1): 24–31.
Wilson, Mark. 1991. Reflections on strings. In Thought experiments in science and philosophy, ed. T. Horowitz and G. Massey. Lanham: Rowman & Littlefield.
Youschkevitch, A.P. 1976. The concept of function up to the middle of the nineteenth century. Archive for History of Exact Sciences 16: 37–85.
Acknowledgements
Many thanks to Katherine Brading, Tal Glezer, Luca Guzzardi, Boris Kožnjak and others for helpful comments and discussion.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
van Strien, M. (2017). Continuity in Nature and in Mathematics: Du Châtelet and Boscovich. In: Massimi, M., Romeijn, JW., Schurz, G. (eds) EPSA15 Selected Papers. European Studies in Philosophy of Science, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-53730-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-53730-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-53729-0
Online ISBN: 978-3-319-53730-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)