 The problem with this line of reasoning, however, is that it only works if one presupposes that the two bodies are approaching one another, and this is not a feature of the system that can be captured by sole reference to the contiguous neighborhood of each individual body. Even if there is reciprocity of transfer between a body and its neighborhood, it is still not possible to determine which collision rule the impact will fall under, or if the bodies will even collide at all, unless some reference frame is referred to that can compute the motion of both bodies relative to one another. Suppose, for instance, that a certain spatial distance separates two bodies, and that one of the bodies is, and the other is not, undergoing a translation relative to its neighboring bodies. Given this scenario, it is not possible to determine if; (i) the translating body is approaching the non-translating body, or (ii) the spatial interval between them remains fixed and the translating body simply undergoes a change of neighborhood (i.e., the neighborhood moves relative to a stationary body). In short, Descartes’ reciprocity of transfer thesis underdetermines the outcome of his bodily collisions, as well as the capacity to apply, and make predictions from, the Cartesian collision rules. The context of the collision rules also supports the view that the motions of the impacting bodies are determined from an external reference frame, rather than from the local translation of their contiguous neighborhoods. In elucidating the fourth rule, for instance, Descartes states that B could never move C “no matter how great the speed at which B might approach C” (Pr II 49)—and only an external perspective, not linked to the bodily reciprocity of transfer, could determine that B “approaches” C. Such admissions make it very difficult to reconcile Descartes’ physics with a strict relational theory of space and motion, although it may be compatible with weaker forms of relationism that can countenance various external reference frames, structures, or other methods for determining the individual states of bodily motion. These weaker relationist strategies (or even non-relational, absolutist interpretations) of Descartes’ physics come at a high price, however, since the reciprocity of transfer thesis must be abandoned. For these reasons, it is more likely that Descartes’ reciprocity of transfer thesis is intended to counter any interpretation that regards motion as caused by a bodily property, as some Scholastics had held (such as Buridan), rather then defend relational motion (see Maier 1982 on these earlier views of motion). That is, if there is nothing in the moving body that differs from its neighborhood of contiguous bodies (see Pr II 30), then a body’s motion is not due to it possessing a special property that its neighborhood lacks.