 Nevertheless, Descartes’ hypothesis of motion may sanction a species of relative motion, since his phrase, “considered at rest”, implies that the choice of which bodies are at rest or in motion is purely arbitrary. According to the “relational” theory (or at least the more strict versions of relationism), space, time, and motion are just relations among bodies, and not separately existing entities or properties that are in any way independent of material bodies. Motion only exists as a “relative difference” among bodies: that is, the bodies do not possess individual, determinate properties of speed, velocity, acceleration (e.g., body C has the speed property of “5 miles per hour”); rather, all that really exists is a difference in their relative speed, velocity, and acceleration (e.g., there is a speed difference among bodies C and B of “5 miles per hour”). Several passages in Descartes’ analysis of motion seem to support this strong variety of relationism: “we cannot conceive of the body AB being transported from the vicinity of the body CD without also understanding that the body CD is transported from the vicinity of the body AB” (Pr II 29). Hence, “all the real and positive properties which are in moving bodies, and by virtue of which we say they move, are also found in those [bodies] contiguous to them, even though we consider the second group to be at rest” (Pr II 30). This form of relational motion has been dubbed the “reciprocity of transfer” in the recent literature. Yet, as will be discussed in a later section, Descartes also holds that rest and motion are different bodily states, a view that is incompatible with a strict relationism as regards motion. Therefore, Cartesian reciprocity of transfer only satisfies relationism (along with its ban on individual bodily states of motion) for moving bodies (i.e., when there is a translation manifest between a body and its contiguous neighborhood). Many of the difficulties associated with Cartesian physics can be traced to the enormous ontological burden that Descartes places on his hypothesis of motion. In a later section we will examine the problem of integrating his account of motion with the Cartesian laws of nature, but a brief discussion of the apparent circularity of Descartes’ definitions of motion and body is required at this point. After describing motion as the transference of a body from the surrounding neighborhood of bodies, Descartes states that by “one body, or one part of matter, I here understand everything which is simultaneously transported” (Pr II 25). The problem, of course, is that Descartes has defined motion as a change of contiguous bodies, and then proceeds to define body as that which moves (translates, transports). Although this circularity threatens the entire edifice of Cartesian physics, it is possible that Descartes intended both motion and body to possess an equal ontological importance in his theory, such that neither is the more fundamental notion (which serves as the basis for constructing or defining the other notion). Yet, their intrinsic interrelationship entails that any attempted definition of one must inevitably incorporate the other. The problem with this reconstruction of Descartes’ reasoning, however, is that Descartes explicitly deems motion to be a “mode” of extension; where a mode is a lesser ontological category that, roughly, can be understood as a way that extension manifests itself, or as a “property” of extension (Pr I 53; shape is also mentioned as a mode of extension). Finally, another difficulty implicit in Descartes’ theory is the fact that a resting body, according to the definition of body and place, would seem to “blend” into the surrounding plenum: that is, if a body is “everything which is simultaneously transported”, then it is not possible to discern a resting body from the surrounding plenum matter that forms the external place of that resting body. In addition, Descartes rejects any explanation of the solidity of a body that employs a bond among its particles (since the bond itself would be either a substance or property, and thus the solidity of the bond would presumably need to be explained; Pr II 55). A macroscopic material body is, essentially, held together just by the relative rest of its constituent material parts. This raises the obvious difficulty that the impact of such bodies should result in their dispersion or destruction (for there is nothing to hold them together). These sorts of complications prompted many later natural philosophers, who were generally sympathetic to Descartes’ mechanical philosophy, to search for an internal property of matter that could serve as a type of individuating and constitutive principle for bodies; e.g., Leibniz’ utilization of “force”.