In the early days of research on visual imagery, it was believed that visual images are like pictures in one's head. Only as the field matured did it come to be appreciated that visual images do not bear a first-order isomorphic relation to visual percepts. Now that the early days of research on motor imagery are coming to an end, it is important to ask whether motor images bear a first-order isomorphic relation to movements. We asked whether they do by focusing on internal simulations for motor planning. Our participants indicated which of two possible actions they preferred either by performing the preferred action or by indicating which action they would prefer to perform. We reasoned that if internal simulations of physical actions bear a first-order isomorphic relation to actual physical actions, the choices would be the same in the two conditions. They were not. We discuss the reasons for this outcome, including the adaptive advantage of a representational system for action which, like the representational system for vision, does not bear a first-order isomorphic relation to its external analog. (Contains 6 figures.)