Can the Principle of Least Action Be Considered a Relativized A Priori?

  • Michael Stöltzner
Part of the The Western Ontario Series In Philosophy of Science book series (WONS, volume 74)


Hardly another principle of classical physics has to a larger extent nourished hopes into a universal theory and has simultaneously been plagued by mathematical counterexamples than the Principle of Least Action (PLA). I investigate whether the PLA can be interpreted as a historically relativized constitutive a priori principle of mathematical physics along the lines Michael Friedman has drawn in Dynamics of Reason, using the example of relativity theory. Such an interpretation suggests itself, historically, because two main advocates of the PLA, Max Planck and David Hilbert, considered relativity theory as a case in point for the PLA. But they were also aware of the mathematical pitfalls and that without physical specification the PLA only represented an empty form. I argue that the different levels required for a consistent application of the PLA in mathematical physics induce a stratification that bears close parallels to the one by which Friedman intends to overcome the joint challenges of epistemological holism and a relativist reading of Kuhnian incommensurability. Yet, two differences remain. First, the mathe matical and physical levels of the PLA are more intertwined than in Friedman's case. Second, although the PLA has survived quite a few scientific revolutions, so has the formulation of physical theories in terms of differential equations.


Physical Theory Axiom System Scientific Revolution Logical Empiricist Regulative Principle 
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  1. Carnap, R. (1950), “Empiricism, Semantics, and Ontology”, Revue internationale de philosophie, 4, 20–40.Google Scholar
  2. Friedman, M. (2001), Dynamics of Reason, Stanford: CSLI Publications.Google Scholar
  3. Hilbert, D. (1900), “Mathematische Probleme”, Göttinger Nachrichten. Mathematisch-Physikalische Klasse, 253–297. English translation in Bulletin of the American Mathematical Society, 8 (1902), 437–479.Google Scholar
  4. Hilbert, D. (1916), “Die Grundlagen der Physik (Erste Mitteilung)”, Göttinger Nachrichten. Mathematisch-Physikalische Klasse, 395–407.Google Scholar
  5. Hilbert, D. (1917), “Die Grundlagen der Physik (Zweite Mitteilung)”, Göttinger Nachrichten. Mathematisch-Physikalische Klasse, 53–76.Google Scholar
  6. Hilbert, D. (1918), “Axiomatisches Denken”, Mathematische Annalen, 78, 405–415. English translation in W. Ewald (ed.), From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. II. Oxford: Clarendon Press, 1996, 1105–1115.CrossRefGoogle Scholar
  7. Hilbert, D. (1924), “Die Grundlagen der Physik”, reprinted in Hilbertiana–Fünf Aufsätze von David Hilbert, Darmstadt: Wissenschaftliche Buchgesellschaft, 1964, 47–78.Google Scholar
  8. Hilbert, D. (1930), “Naturerkennen und Logik”, Die Naturwissenschaften, 18, 959–963. English translation in W. Ewald (ed.), op.cit., vol. II., 1157–1165.CrossRefGoogle Scholar
  9. Kuhn, Thomas S. (1962), The Structure of Scientific Revolutions, Chicago, IL: University of Chicago Press.Google Scholar
  10. Mach, E. (1989), The Science of Mechanics. Account of Its Development, La Salle, IL: Open Court.Google Scholar
  11. Planck, M. (1910), “Zur Theorie der Wärmestrahlung”, in: Physikalische Abhandlungen und Vorträge, Braunschweig, Vieweg, 1958, vol. II, 237–247.Google Scholar
  12. Planck, M. (1944), Wege zur physikalischen Erkenntnis. Reden und Vorträge, Leipzig: S. Hirzel.Google Scholar
  13. Reichenbach, H. (1920), Relativitätstheorie und Erkenntnis A Priori, Berlin: Springer; English translation, Los Angeles: University of California Press, 1965Google Scholar
  14. Rowe, D.E. (2001), “Einstein Meets Hilbert: At the Crossroads of Physics and Mathematics”, Physics in Perspective, 3, 379–424.CrossRefGoogle Scholar
  15. Sauer, T. (1999), “The Relativity of Discovery: Hilbert's First Note on the Foundations of Physics”, Archive for the History of Exact Sciences, 53, 529–575.Google Scholar
  16. Stöltzner, M. (2000), “Le principe de moindre action et les trois ordres de la téléologie formelle dans la Physique”, Archives de Philosophie, 63, 621–655.Google Scholar
  17. Stöltzner, M. (2003), “The Least Action Principle as the Logical Empiricist's Shibboleth”, Studies in History and Philosophy of Modern Physics, 34, 285–318.CrossRefGoogle Scholar
  18. Stöltzner, M. (2005), “Drei Ordnungen formaler Teleologie. Ansichten des Prinzips der kleinsten Wirkung”, in M. Stöltzner and P. Weingartner (eds.), Formale Teleologie und Kausalität, Paderborn: Mentis, 199–241.Google Scholar
  19. Von Helmholtz, H. (1886), “Über die physikalische Bedeutung des Princips der kleinsten Wirkung”, in: Wissenschaftliche Abhandlungen, Leipzig, 1895, vol. III, 203–248.Google Scholar

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© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Michael Stöltzner
    • 1
  1. 1.Department of PhilosophyUniversity of South CarolinaColumbiaUSA

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