Classical Particle Mechanics

Thus far we have considered some simple examples of set-theoretic predicates to illustrate various alternative ways that such a predicate might be used to elucidate the logical structure of a scientific theory. We want now to see how these alternatives fare when we attempt to use them in providing a logical reconstruction of a real theory of mathematical physics. The theory to be considered is classical, or Newtonian, particle mechanics. Our procedure will be roughly this. We will settle upon a likely candidate for a set-theoretic predicate to characterize the mathematical structure of this theory. Then we will try to use this predicate to render the empirical content of this theory in each of the ways discussed in the preceding four chapters. This will serve to illustrate, in a more concrete way, the difficulties with some of these methods, and ultimately to provide at least a sketch of an adequate logical reconstruction of this theory. This sketch, together with the notion of Ramsey eliminability, will provide a means of treating in a systematic and perspicuous way some frequently raised questions about the status of the concepts of mass and force. It will also serve to illuminate questions about the measurability of masses and forces and the status of specific force laws in measuring forces.