Despite the success of these theories in making accurate numerical predictions of a wide range of phenomena, these laws were generally seen as deficient as natural philosophies of mechanics, since they were all essentially action-at-a-distance mechanisms. In the context of the development of field theory, the fact that a function could be written to give the force per unit mass, charge, or current for each point in space was just a mathematical construct. It was seen as untenable on metaphysical grounds that a force be exerted across empty space, and hence these force laws were assumed to be merely descriptive and not explanatory.