Tuesday, 23 March 2004
Formal Teleology, Modality or Structural Realism?
On What We Can Still Learn from the Principle of Least Action
Michael Stöltzner
University of Bielefeld and Notre Dame
12:05 pm, 817R Cathedral of Learning

Abstract: In contrast to the years 1880-1920, the principle of least action (PLA) is currently attracting little attention. This is quite surprising in view of the fact that it provides a simple scheme to formulate the basic laws of many physical theories. Yet, to rigorously turn the PLA into the correct dynamics requires considerable mathematical care and a specification of the respective physical set-up. Neglecting these subtleties has led to a plethora of misunderstandings after which the PLA became a shibboleth to most philosophers of science standing in the empiricist tradition.

In the present paper, I argue that the PLA provides an independent justification of a scientific theory above and beyond the mere statement of the differential equations. Setting out from the mathematical relationship between the PLA and the corresponding differential equations, I first distinguish three types of such formal teleological arguments that characterize the interpretations of the PLA put forward by Ernst Mach, Max Planck and David Hilbert respectively. Second, I investigate how these orders of formal teleology relate to the Lewisian modality that Jeremy Butterfield has identified in the whole of analytical mechanics. Third, while Planck claimed that the PLA was able to survive scientific revolutions, Hilbert closely associated it with the architectural foundations of a physical theory. This suggests viewing the PLA as an instance of some kind of structural realism. Moreover, while zeroth order teleology is unavoidable even for an empiricist as a necessary supplement of causal explanations, the higher orders of formal teleology seem to require the assumption of some kind of structural realism.