Since we do not have a third kind of device to specify the spatio-temporal location of the devices measuring the spacetime geometry, we do not have any further operationally defined, maybe non-dynamical background, just in accordance with the principle of equivalence. If there were some non-dynamical background metric g0ab on M, then by requiring g0ab = f*g0ab we could reduce the almost arbitrary diffeomorphism f (essentially four arbitrary functions of four variables) to a transformation depending on at most ten parameters.