Since Leibniz it has become clearer and clearer that a priori judgment is inadequate to establish the presence of exact symmetries in the physical laws, and the exact conservation laws which flow from them. The latest example has been the Yang-Lee demonstration of the failure of mirror invariance in the weak interactions. It is possible to conjecture that even the kinematical symmetries under continuous transformations which give energy-momentum conservation may be inexact; their failure may be expressed, for example, in the spontaneous creation of nucleons postulated by Bondi and Gold. Still further, one may at least raise the question of the exactness of general relativity, or rather of the principle of equivalence between acceleration and a uniform gravitational field. If this equivalence is regarded as an approximate consequence of the predominance of matter over antimatter in our environment, it is possible to frame a consistent scheme which predicts large-scale symmetry between matter and antimatter, but at the expense of introducing gravitational repulsion. Conceptual experiments are constructed to show the consistency of this picture at least in the Newtonian limit; certain specified conditions on the gravitational behavior of various types of inertial mass must be satisfied.