Identity, Equivalence and Reduction

In this chapter we will attempt to use our understanding of the logical structure of the empirical claims in theories of mathematical physics — the account developed in the first five chapters — to clarify some other questions about these theories. First, we will attempt to say, as precisely as we can, just what a theory of mathematical physics is. That is, we will attempt to give some general, and precise characterization of theories of mathematical physics. Once we have developed this characterization, we will employ it to investigate the properties of two relations — equivalence and reduction — that are commonly alleged to hold between some theories of mathematical physics. In the course of this discussion, we will have occasion to examine the Lagrangian and Hamiltonian formulations of particle mechanics as examples of theories of mathematical physics that are, in some sense, equivalent to the Newtonian formulation of particle mechanics. We shall also examine rigid body mechanics as an example of a theory which reduces to particle mechanics.