  Arguing from his "hole" thought experiment, Einstein became convinced that,
in cases in which the energy-momentum-tensor source vanishes in a spacetime
hole, a solution to his general relativistic field equation cannot be uniquely
determined by that source. After reviewing the definition of active
diffeomorphisms, this paper uses them to outline a mathematical proof of
Einstein's result. The relativistic field equation is shown to have multiple
solutions, just as Einstein thought. But these multiple solutions can be
distinguished by the different physical meaning that each metric solution
attaches to the local coordinates used to write it. Thus the hole argument,
while formally correct, does not prohibit the subsequent rejection of spurious
solutions and the selection of a physically unique metric. This conclusion is
illustrated using the Schwarzschild metric. It is suggested that the Einstein
hole argument therefore cannot be used to argue against substantivalism.
