Leibniz Differentiates the Problem on Principle

The differentiation of the problem was, on principle, achieved by Leibniz. . . . . First of all, he located the crucial point of the difficulty by differentiating between geometry and phoronomy [a Kantian term: a theory of motion deducible from a priori conceptions] on the one side and mechanics on the other. The relativity of position and motion is indisputable as long as we deal with them as 'purely mathematical" problems. Nature, however, does not offer the spectacle of abstractly shoving bodies that change their relative positions chaotically. It offers the spectacle of a calculable order in the relative movements.

This order in the movements cannot be explained within the realm of geometry. For the purpose of its interpretation we have to go beyond the purely mathematical principles and introduce a "metaphysical" principle ["metaphysics" meant to Leibniz the general science of principles excluding only mathematics and geometry.]. Whether we call this principle Form, or Entelechy, or Force, is irrelevant as long as we remember that only the notion of forces will express it intelligibly. . . . Moreover, by localizing the difficulty in the theory of dynamics, Leibniz correctly marked the direction in which the solution had to be sought and ultimately was found, that is, the geometrization of physics.

. . . . The localization of the difficulty is the first step toward a solution, but it is not the solution itself. . . . the introduction of force is immediately followed by the differentiation into vis primitiva and vis derivativa , that is, into force in the sense of an inherent quality of substance and force in the phenomenal sense. Primitive force (whether active or passive) is substantial force, and its problems belong to metaphysics in the narrower sense. This primitive force belongs among the “general causes” that “are insufficient for the explanation of phenomena.” Derivative force arises “as it were through a limitation of primitive force through the interaction ( conflictus ) of bodies in various ways.”

The differentiation of primitive and derivative force, and in particular the definition of phenomenal force, is the decisive achievement of Leibniz. The problem of absoluteness is eliminated through the definition of phenomenal force as force in relation to other forces. Phenomenal force is relative force by definition; and only this phenomenal force is the object of physics. Force has no meaning beyond the meaning that is contained in the differential equations of physics.

. . . . The third step in Leibniz's analysis is the clarification of the ideas of space and time. His most mature formulation of this problem is to be found in the correspondence with Clarke, which was an indirect correspondence with Newton because the latter collaborated with Clarke in the answers. . . . "I have stressed more than once that I consider space something purely relative, just as time; it is an order of coexistences, just as time is an order of successions. For space signifies, in terms of possibility, an order of things that exist at the same time, insofar as they exist together, without determining their particular way of existing."

. . . . Space and time of physics, thus, are not qualities of reality; they are orders that the mind applies to the interpretation of phenomena. The problem of absolute space cannot arise if space is understood as an ideal form that constitutes the order of phenomena. This solution not only eliminates the Newtonian problem of absolute space critically, it also gives a positive answer to the question of “objectivity” in science. We do not have to search for the “absolute” validity of propositions in an absolute reality because the objectivity of science has its source in the order of the mind.

Chapter 4, The English Quest for the Concrete
§ 3, Absolute Space and Relativity, pp199-203.