Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T20:37:00.842Z Has data issue: false hasContentIssue false
  • English
  • Français

From Jurisprudence to Mechanics: Jacobi, Reech, and Poincaré on Convention

Published online by Cambridge University Press:  31 May 2018

María de Paz
María de Paz*
Affiliation:
Department of Philosophy, Logic and Philosophy of Science, Universidad de Sevilla Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Argument

This paper aims at understanding the concept of convention in mechanics as a notion transferred from the field of jurisprudence. This enables us to clarify it as a new epistemic category having a pertinent role in the transformation of mechanics in the nineteenth century. Such understanding permits a separation from linguistic and arbitrary conventions, thus highlighting its epistemic features and not transforming fundamental principles into mere arbitrary agreements. After addressing the main references in the literature discussing the role of convention in mechanics, we analyze its classical use as a concept originating from law. Then we explain its use by Carl G. Jacobi, Ferdinand F. Reech, and J. Henri Poincaré. Here we also show how their uses conform to the features analyzed regarding conventions in jurisprudence. Finally, we try to explain how the use of this concept, among other factors, contributed to the transformation of mechanics.

Type
Research Article
Information
Science in Context , Volume 31 , Issue 2 , June 2018 , pp. 223 - 250
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrade, Jules. 1898. Leçons de mécanique physique. Paris: Société d’éditions scientifiques.Google Scholar
Archibald, Thomas. 2001. “Images of Applied Mathematics in the German Mathematical Community.” In Changing Images in Mathematics, edited by Bottazzini, Umberto and Dalmedico, Amy Dahan, 49–67. Paris: Routledge.Google Scholar
Belhoste, Bruno. 2001. “The École Polytechnique and Mathematics in Nineteenth Century France.” In Changing Images in Mathematics, edited by Bottazzini, Umberto and Dalmedico, Amy Dahan, 15–30. Paris: Routledge.Google Scholar
Ben-Menahem, Yemima. 2001. “Convention: Poincaré and Some of His Critics.” British Journal for Philosophy of Science 52:471–513.CrossRefGoogle Scholar
Bertin, Auguste. 1867. Rapport sur les progrès de la thermodynamique en France. Paris: Imprimerie Impérial.Google Scholar
BosHenk, J. M. Henk, J. M. 1980. “Mathematics and Rational Mechanics.” In The Ferment of Knowledge, edited by Rousseau, George S. and Porter, Roy, 327–355. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Bottazzini, Umberto. 2001. “From Paris to Berlin: Contrasted Images of Nineteenth-Century Mathematics.” In Changing Images in Mathematics, edited by Bottazzini, Umberto and Dalmedico, Amy Dahan, 31–47. Paris: Routledge.Google Scholar
Bottazzini, Umberto, and Dalmedico, Amy Dahan. 2001. Changing Images in Mathematics, Paris: Routledge.Google Scholar
Carnap, Rudolf. [1937] 2002. The Logical Syntax of Language. Translated by Amethe Smeaton. Chicago: Open Court Press.Google Scholar
D'Argis, Antoine, and Boucher, Gaspar. 1751. “Contrat.” In Encyclopédie, edited by Diderot, Denis et D'Alembert, Jean, 1st ed., vol. 4, 122–127. Paris: Briasson et al.Google Scholar
D'Argis, Antoine, and Boucher, Gaspar et al. 1751. “Convention”, .” In Encyclopédie, edited by Diderot, Denis et D'Alembert, Jean, 1st ed., vol. 4, 161–164. Paris: Briasson et al.Google Scholar
Delon, Michel. 2001. Encyclopedia of the Enlightenment. Vol. 1. London & New York: Routledge.Google Scholar
Demopoulos, William. 2000. “On the Origin and Status of Our Conception of Number.” Notre Dame Journal of Formal Logic 41:210–226.CrossRefGoogle Scholar
de Paz, María. 2014. “The Third Way Epistemology: A Re-characterization of Poincaré’s Conventionalism.” In Poincaré, Philosopher of Science: Problems and Perspectives, edited by de Paz, María and DiSalle, Robert, 47–65. Western Ontario Series in the Philosophy of Science, 79. New York: Springer.CrossRefGoogle Scholar
de Paz, María. 2015. “Poincaré’s Classification of Hypotheses and Their Role in Natural Science.” International Studies in the Philosophy of Science 29 (4):369–382.CrossRefGoogle Scholar
de Paz, María. 2016. Henri Poincaré: Del Convencionalismo a la Gravitación. London: College Publications.Google Scholar
Diderot, Denis. 1754. Pensées sur l'interprétation de la nature. Paris, Garnier.Google Scholar
DiSalle, Robert. 2006. Understanding Space-Time: The Philosophical Developments of Physics from Newton to Einstein. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
DiSalle, Robert. 2014a. “Conventionalism.” In The Routledge Companion to the Philosophy of Science, edited by Psillos, Stathis and Curd, Martin, 2nd ed., 3–14. London: Routledge.Google Scholar
DiSalle, Robert. 2014b. “Poincaré on the Construction of Space-Time.” In Poincaré, Philosopher of Science: Problems and Perspectives, edited by de Paz, María and DiSalle, Robert, 167–183. Western Ontario Series in the Philosophy of Science, 79. New York: Springer.CrossRefGoogle Scholar
Duhem, Pierre. 1892. “Quelques réflexions au sujet des théories physiques.” Revue des questions scientifiques 31:139–177.Google Scholar
During, Elie. 2001. La Science et l'Hypothèse: Poincaré. Paris: Ellipse.Google Scholar
Epple, Moritz. 1994. “Das bunte Geflecht der mathematischen Spiele.” Mathematische Semesterberichte 41:113–133.CrossRefGoogle Scholar
Ferreirós, José. 1999. Labyrinth of Thought. Basel: Springer.CrossRefGoogle Scholar
Ferreirós, José. 2006. “The Rise of Pure Mathematics as Arithmetic with Gauss.” In The Shaping of Arithmetic: Number Theory after Carl Friedrich Gauss's Disquisitiones Arithmeticae, edited by Goldstein, Catherine, Schappacher, Norbert, and Schwermer, Joachim, 206–240. Berlin: Springer.Google Scholar
Folina, Janet. 2014. “Poincaré and the Invention of Convention.” In Poincaré, Philosopher of Science: Problems and Perspectives, edited by de Paz, María and DiSalle, Robert, 25–45. Western Ontario Series in the Philosophy of Science, 79. New York: Springer.CrossRefGoogle Scholar
Friedman, Michael. 1999. Reconsidering Logical Positivism. Cambrige: Cambrige University Press.CrossRefGoogle Scholar
Galison, Peter. 2003. Einstein's Clocks, Poincaré’s Maps: The Empires of Time. New York: Norton.Google Scholar
Giedymin, Jerzy. 1977. “On the Origin and Significance of Poincaré’s Conventionalism.” Studies in History and Philosophy of Science 8 (4):271–301.CrossRefGoogle Scholar
Giedymin, Jerzy. 1982. Science and Convention: Essays on Henri Poincaré’s Philosophy of Science and the Conventionalist Tradition. Oxford: Pergamon Press.Google Scholar
Giedymin, Jerzy. 1991. “Geometrical and Physical Conventionalism of Henri Poincaré in Epistemological Formulation.” Studies in History and Philosophy of Science 22 (1):1–22.CrossRefGoogle Scholar
Heinzmann, Gerhard. 2010. “Conventions in Geometry and Pragmatic Reconstruction in Poincaré: A Problematic Reception in Logical Empiricism.” https://halshs.archives-ouvertes.fr/halshs-00529135/document, last accessed February 11, 2018.Google Scholar
Hertz, Heinrich Rudolf. 1894. Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt. Leipzig: Barth.Google Scholar
Ivanova, Milena. 2015. “Conventionalism, Structuralism and Neo-Kantianism in Poincaré’s Philosophy of Science.” Studies in History and Philosophy of Modern Physics 52:114–122.CrossRefGoogle Scholar
Jacobi, Carl Gustav 1996. Vorlesungen über analytische Mechanik. Berlin 1847/48. Braunschweig/Wiesbaden: F. Vieweg & Sohn.CrossRefGoogle Scholar
Jungnickel, Christa, and McCormmach, Russell. 1986. Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein. Volume I: The Torch of Mathematics. 1800–1870. Chicago: University of Chicago Press.Google Scholar
Klein, Martin Jesse. 1973. “Mechanical Explanation at the End of the Nineteenth Century.” Centaurus 17 (1):58–82.CrossRefGoogle Scholar
Lange, Ludwig. 1885. “Ueber die wissenschaftliche Fassung des Galilei'schen Beharrungsgesetzes.” Wundt's Philosophische Studien 2:266–297.Google Scholar
Lagrange, Joseph Louis. [1797] 1813. Théorie des fonctions analytiques. Paris: Bachelier.Google Scholar
Lewis, David. 1969. Convention. Cambridge: Harvard University Press.Google Scholar
Lützen, Jesper. 2009. “Review of Helmut Pulte's Axiomatik und Empirie.” Historia Mathematica 36:87–89.CrossRefGoogle Scholar
Mach, Ernst. [1883] 1912. Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt, 7th ed. Leipzig: Brockhaus.Google Scholar
Mortier, Roland. 1954. Diderot en Allemagne (1750-1850). Paris: Presses Universitaires de France.Google Scholar
Milhaud, Gaston. 1896. “La science rationnelle.” Revue de métaphysique et de morale 4:280–302.Google Scholar
Plato. 1997. “Cratylus.” Translated by C. D. C. Reeve. In Complete Works, edited by Cooper, John. Indianapolis: Hackett.Google Scholar
Poincaré, Henri. 1891a. “Les géométries non euclidiennes.” Revue générale des sciences pures et appliquées 2:769–774.Google Scholar
Poincaré, Henri. 1891b. La thermodynamique. Paris: G. Carre & C. Naud.Google Scholar
Poincaré, Henri. 1897. “Les idées de Hertz sur la mécanique.” Revue générale des sciences pures et appliquées 8:734–743.Google Scholar
Poincaré, Henri. 1898. “On the Foundations of Geometry.” The Monist IX:1–43.Google Scholar
Poincaré, Henri. 1900. “La théorie de Lorentz et le principe de réaction.” Recueil de Travaux offerts par les auteurs à H. A. Lorentz, professeur de Physique à l'Université de Leiden à l'occasion du 25° anniversaire de son Doctorat, le 11décembre 1900. Archives néerlandaises des sciences exactes et naturelles, 2e série, t. 5, 252–278. In Poincaré, Henri. Oeuvres, 1916–1956. Paris: Gauthier-Villars IX:464–488.Google Scholar
Poincaré, Henri. 1901. “Sur les principes de la mécanique”. Actes du Congrès International de Philosophie III:457–591.Google Scholar
Poincaré, Henri. [1902] 1968. La science et l'hypothèse. Paris: Flammarion.Google Scholar
Poincaré, Henri. 1905 /1970. La valeur de la science. Paris: Flammarion.Google Scholar
Poincaré, Henri. 1906. “Sur la dynamique de l’électron.” Rendiconti del Circolo matematico di Palermo 21:129–176. Also in Oeuvres, 1916–1956, by Henri Poincaré. Paris: Gauthier-Villars. IX:494–550.CrossRefGoogle Scholar
Poincaré, Henri. 1908a. Science et Méthode. Paris: Flammarion, 1908. Cahier Spécial 3:1998-1999. Reed. Philosophia Scientiae.Google Scholar
Poincaré, Henri. 1908b. “La dynamique de l’électron.” Revue générale de Sciences pures et appliquées 19:386–402.Google Scholar
Poisson, Siméon Denis. 1829. “Mémoire sur l’équilibre et le mouvement des corps élastiques.” Mémoires de l'Académie des sciences de l'Institut de France 357–569.Google Scholar
Psillos, Stathis. 2014. “Conventions and Relations in Poincaré’s Philosophy of Science.” Methode. Analytic perspectives 4:98–140.Google Scholar
Pulte, Helmut. 1994. “C. G. J. Jacobis Vermächtnis einer ‘konventionalen’ analytischen Mechanik: Vorgeschichte, Nachschriften und Inhalt seiner letzten Mechanik-Vorlesung.” Annals of Science 51 (5):487–517.CrossRefGoogle Scholar
Pulte, Helmut. 1998. “Jacobi's Criticism of Lagrange: The Changing Role of Mathematics in the Foundations of Classical Mechanics.” Historia Mathematica 25 (2):154–184.CrossRefGoogle Scholar
Pulte, Helmut. 2000. “Beyond the Edge of Certainty: Reflections on the Rise of Physical Conventionalism.” Philosophia Scientiae 4 (1):47–68.Google Scholar
Pulte, Helmut. 2005. Axiomatik und Empirie: Eine wissenschaftstheoriegeschichtliche Untersuchung zur Mathematischen Naturphilosophie von Newton bis Neumann. Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
Pulte, Helmut. 2009. “From Axioms to Conventions and Hypotheses: The Foundations of Mechanics and the Roots of Carl Neumann's ‘Principles of the Galilean-Newtonian Theory’.” In The Significance of the Hypothetical in the Natural Sciences, edited by Heidelberger, Michael and Schiemann, Gregor, 77–98. Berlin: de Gruyter.CrossRefGoogle Scholar
Pulte, Helmut. 2012. “Rational Mechanics in the Eighteenth Century: On Structural Developments of a Mathematical Science.” Berichte zur Wissenschaftsgeschichte 35:183–199.CrossRefGoogle ScholarPubMed
Pulte, Helmut. 2016. “Johannes von Kries's Objective Probability as a Semiclassical Concept: Prehistory, Preconditions and Problems of a Progressive Idea.” Journal for General Philosophy of Science 47:109–129.CrossRefGoogle Scholar
Quine, Willard van Orman. [1936] 1976. “Truth by Convention.” Reprinted in The Ways of Paradox, 2nd ed., 70–99. Cambridge: Harvard University Press.Google Scholar
Reech, Fréderic Ferdinad. 1852. Cours de mécanique d'après la nature généralement flexible et élastique des corps. Paris: Carilian-Goeury et Vor Dalmnont, Librairies des corps des ponts et chaussées et des mines.Google Scholar
Rescorla, Michael. 2015. “Convention.” The Stanford Encyclopedia of Philosophy (Summer 2015 Edition), edited by Zalta, Edward N. https://plato.stanford.edu/archives/sum2015/entries/convention/ last accessed February 12, 2018.Google Scholar
Riemann, Bernhard. 1876. “Neue mathematische Principien der Naturphilosophie.” In Gesammelte Mathematische Werke und wissenschaftlicher Nachlass, edited by Weber, Heinrich and Dedekind, Richard, 502–506, Leipzig: Teubner.Google Scholar
Roseveare, N. T. 1982. Mercury's Perihelion from Le Verrier to Einstein. Oxford: Clarendon Press.Google Scholar
Schalk, Fritz. 1951. “Le rayonnement de l'Encyclopédie en Allemagne.” Cahiers de l'Association internationale des études françaises, 1–2: 85–91.CrossRefGoogle Scholar
Schiemann, Gregor. 1997. Hermann von Helmholtz's Mechanism: The Loss of Certainty, Archimedes 17. New York: Springer.Google Scholar
Schmaus, Warren. 2017. “Poincaré and Renouvier on Conventions: Or, How Science is like Politics.” HOPOS: The Journal of the International Society for the History of Philosophy of Science, 7 (2): 182–198.Google Scholar
Spree, Ulrike. 2000. Das Streben nach Wissen. Eine vergleichende Gattungsgeschichte der populären Enzyklopädie in Deutschland und Grossbritannien im 19. Jahrhundert. Tübingen: Niemeyer.Google Scholar
Stump, David. 1989. “Henri Poincaré’s Philosophy of Science.” Studies History and Philosophy of Science 20:335–63.CrossRefGoogle Scholar
Stump, David. 2015. Conceptual Change and the Philosophy of Science. New York: Routledge.CrossRefGoogle Scholar
Torretti, Roberto. 1978. Philosophy of Geometry from Riemann to Poincaré. Dordrecht: Reidel Publishing Company.CrossRefGoogle Scholar
Truesdell, Clifford. 1974. “How to Understand and Teach the Logical Structure and the History of Classical Thermodynamics.” In Proceedings of the International Congress of Mathematicians, edited by James, Ralph D., 577–586. Vancouver: ICM.Google Scholar
Truesdell, Clifford. 1980. The Tragicomical History of Thermodynamics 1822–1854. New York: Springer.CrossRefGoogle Scholar
Varzi, Achille. 2011. “Boundaries, Conventions, and Realism.” In Carving Nature at Its Joints: Natural Kinds in Metaphysics and Science, edited by Campbell, Joseph Keim, O'Rourke, Michael, and Slater, Matthew H., 129–153. Cambridge MA: MIT Press.CrossRefGoogle Scholar
Young, John Radford. 1841. Mathematical Dissertations, for the Use of Students in the Modern Analysis. London: John Souter.Google Scholar
Zahar, Ellie. 2001. Poincaré’s Philosophy. From Conventionalism to Phenomenology. Chicago: Open Court.Google Scholar