We show that the ubiquitous formula for ponderomotive forces due to a distribution of a polarized substance implies a non-vanishing self-force. This constitutes a striking paradox since this prediction is in startling contrast with observed phenomena. A recorded lecture on the paradox can be found on the authors' website. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).