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

Abstract

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.