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 18801920, 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 setup. 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.
