Hans Jonas, Philosophical Essays, “Seventeenth Century and After: The Meaning of the Scientific and Technological Revolution”
VI
It only remains to draw one last inference so as to have this account of the conceptual revolution terminate in a full-fledged mechanics of nature. To use abridged labels, it means completing the Galilean with the Newtonian record. There recurred in our account one term which is obviously crucial but is not a geometrical term and not resolvable into purely geometrical, i.e., space-time, terms; the concept of “force.” It lurks in the concepts of both acceleration and inertia. We may define (measure) a force by the magnitude of acceleration which it can impart to a given body; or we may define the inertia of a body (i.e., its “force” of resisting a change in its state of motion or rest) by the magnitude of acceleration that can be imparted to it by a given force. In either case we have geometrized the action of force through the concept of acceleration, which is constituted of space-time magnitudes purely, and have thereby “defined” the force in question — acting force in one case, resisting force in the other. But in either case we have a non-geometrical referent in the definition as a primitive datum (a given body) alternative to its counterpart in the other definition (a given force): what remains primitive datum (definiens) in one is defined in the other, and vice versa; and We cannot geometrize both data together in one definition without falling into an empty circle. In other words, the dynamic account is incomplete without a concept of the “intensive” order added to those of the “extensive” order. This clearly concerns the mysterious concept of force, and more particularly, in the case of inertia, the seat of force. The slowly emerging concept of mass filled the desideratum. Although Newton simply defined it as “the quantity of matter,” it actually denotes in its physical function a dynamic quantity, viz., the quantity of inertia — a magnitude independent (not a variable) of size, shape, place, motion, temperature or any of the variables by which we may otherwise determine the being of a body “Mass” in short denotes a power somehow identical with the essence of matter — which thus becomes an ens realissimum in its own right, with respect to whose stubborn, primary invariance all other determinations become shifting and secondary. This is worlds apart from the Aristotelian scheme of substantial forms, qualities, accidents (etc.) determining an indifferent “prime matter” which becomes “real” only insofar as thus determined. It also is vastly different from ancient atomism which, lacking in its concept of matter this dynamic aspect of “mass,” could never evolve into a physics.
Since inertia (= “quantity of matter”), when conjoined with motion, yields momentum, i.e. kinetic energy, it follows that mass, space, and time — or, with the last two united in one term, mass and acceleration — are the sufficient terms for a mechanics of impact; and through the equation of mass with weight also for a mechanics of attraction, viz., of terrestrial motions involving free fall. This joint mechanics is thus constituted by two geometrical (formal) quantities, space and time, and one non-geometrical quantity, mass, the last of which represents the core reality; but all three are quantities, subject to the simple law of numerical addition.
What Newton then achieved by transforming the merely terrestrial concept of “weight” (as a force directed to the center of the earth) into the universal concept of “gravitation” (as a force acting between all bodies in strict correlation with mass and distance) was to extend the unitary mechanics of “mass and acceleration” to the limits of the universe. “Mass” here assumed a doubly dynamical meaning, matter thus becoming the seat of two forces — inertia and gravitation — whose conjunction and equivalence in one entity (so that one can alternate with the other in defining a given mass) remained the unexplained mystery of Newtonian physics. But mystery or not, by its irrefutable evidence the celestial orbits were assimilated to the trajectories of terrestrial missiles: astronomy and ballistics had become branches of one and the same science. For the epistemologist we may add that this science of nature represented the union of a priori with a posteriori elements: while space, time, and motion in abstracto present a pure mathematical manifold for a priori construction, inertia and gravity, the dynamical ingredients of mass (and the same goes for the electromagnetic forces discovered later) fall as to their existence and their actual values in the realm of irreducible empirical fact; the gravitational constant, e.g., is a purely empirical magnitude. Insofar was Descartes’ excessive rationalism rectified. But those empirical constants operate in the mathematical continuum, their values expressible in its terms, and so physics could be mathematized with these rationally recalcitrant facts.