  Weyl’s view that there must be an inertial structure field  on spacetime, which governs material bodies in free motion, follows from the mathematical nature of the  coordinate-transformation laws for acceleration. In a world equipped  with only a differential structure, it is possible to do calculus;  one can define curves and paths and differentiate, etc. However, as  was already pointed out, in such a world, the world of Weyl’s  plasticine example, there would be no preferred curves or paths.  Consequently, the motion of material bodies would not be predictable. However, experience overwhelmingly indicates that  the acceleration of a massive body cannot be freely chosen. In  particular, consider a simple type of particle, a monopole  (unstructured) particle. Experience overwhelmingly tells us that such a particle is characterized by the fact that at any event on its  world line, its velocity at that event is sufficient to determine its acceleration at that event. Predictability of motion, therefore,  entails that corresponding to every type of massive monopole, there  exists a geometric structure field, or what Weyl calls a  Strukturfeld that governs the motion of that type of  particle. The basic reason which explains this brute fact of  experience is a simple mathematical fact about how the acceleration  of bodies transforms under a coordinate transformation. Moreover,  this simple mathematical fact, involving no more than the basic  techniques of partial differentiation, holds in all relativistic,  non-relativistic, curved or flat, dynamic or non-dynamic spacetime  theories that are based on a local differential topological  structure, the minimal structure required for the possibility of  assigning arbitrary local coordinates on a differential manifold. 