This formula contains the repudiation of a belief which had blocked the progress of physics for two thousand years. It also deals with a fundamental concept which is essential to scientific theory; I mean, the concept of an ideally isolated system. This conception embodies a fundamental character of things, without which science, or indeed any knowledge on the part of finite intellects, would be impossible. The ‘isolated’ system is not a solipsist system, apart from which there would be nonentity. It is isolated as within the universe. This means that there are truths respecting this system which require reference only to the remainder of things by way of a uniform systematic scheme of relationships. Thus the conception of an isolated system is not the conception of substantial independence from the remainder of things, but of freedom from casual contingent dependence upon detailed items within the rest of the universe. Further, this freedom from casual dependence is required only in respect to certain abstract characteristics which attach to the isolated system, and not in respect to the system in its full concreteness. The first law of motion asks what is to be said of a dynamically isolated system so far as concerns its motion as a whole, abstracting from its orientation and its internal arrangement of parts. Aristotle said that you must conceive such a system to be at rest. Galileo added that the state of rest is only a particular case, and that the general statement is ‘either in a state of rest, or of uniform motion in a straight line.’ Accordingly, an Aristotelean would conceive the forces arising from the reaction of alien bodies as being quantitatively measurable in terms of the velocity they sustain, and as directively determined by the direction of that velocity; while the Galilean would direct attention to the magnitude of the acceleration and to its direction. This difference is illustrated by contrasting Kepler and Newton. They both speculated as to the forces sustaining the planets in their orbits. Kepler looked for tangential forces pushing the planets along, whereas Newton looked for radial forces diverting the directions of the planets’ motions.