Paramagnets on the border of ferromagnetism at low temperatures are more subtle and complex than anticipated by the conventional theory of quantum critical phenomena. Could quantum criticality theory be more relevant in the corresponding case of quantum paraelectrics on the border of ferroelectricity? To address this question we have investigated the temperature dependence of the dielectric function of the displacive quantum paraelectrics SrTiO 3 , oxygen-18 substituted SrTiO 3 and KTaO 3 . In all of these materials on the border of ferroelectricity we observe non-classical T 2