This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincaré group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms is associated with the theory of general relativity as its local dynamical symmetry group, while the Poincaré group is associated with a special relativistic theory as both its global dynamical (...) symmetry group and its geometrical symmetry group. It is argued that the two groups are of equal significance as symmetry groups of their associated theories. (shrink)

A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the status of Newton's Law of (...) Inertia are critically examined including these: the Law of Inertia is not an empirical law but a definition; it is not a law simpliciter but a family of schemata; it is a convention and gravitational forces exist only by convention; it is (or is not) redundant; the concepts it embodies can be dispensed with in favor of operationally defined entities; it is unique for a given theory. More generally, the paper demonstrates the importance of space-time structure for the philosophy of space and time and provides support for a realist interpretation of space-time theories. (shrink)