  A model for quantized gravity coupled to matter in the form of a single
scalar field is investigated in four dimensions. For the metric degrees of
freedom we employ Regge's simplicial discretization, with the scalar fields
defined at the vertices of the four-simplices. We examine how the continuous
phase transition found earlier, separating the smooth from the rough phase of
quantized gravity, is influenced by the presence of scalar matter. A
determination of the critical exponents seems to indicate that the effects of
matter are rather small, unless the number of scalar flavors is large. Close to
the critical point where the average curvature approaches zero, the coupling of
matter to gravity is found to be weak. The nature of the phase diagram and the
values for the critical exponents suggest that gravitational interactions
increase with distance. \vspace{24pt} \vfill
