THE PROBLEM OF INSTANTANEOUS MOTION

Among Aristotle's arguments denying the possibility of motion in a vacuum (see Chapter 1), none was viewed as more fundamental than the deduction that such motions would be instantaneous. As Aristotle expressed it, the speeds of bodies moving in a void would be “beyond any ratio”; or, to put it another way, a body would occupy the termini of its motion, and all intervening points, simultaneously. Before describing the subsequent history of this powerful argument, it will be well to take note of a paradoxical feature that was implicit in many discussions of it. Did the assumption of instantaneous motion in a vacuum categorize one as a proponent of motion in a vacuum, even though that motion is instantaneous or of infinite velocity? Or rather, did the assumption of instantaneous motion imply that its proponent actually denied motion in a vacuum because the very concept of instantaneous motion is absurd and impossible? One can scarcely doubt that Aristotle was of the latter opinion. For him, the consequence that motion in a vacuum would be instantaneous was equivalent to a denial of motion. Thus instantaneous motion in a vacuum is no motion at all. But already in the thirteenth century, Roger Bacon distinguished between those motions in a void that were instantaneous (and presumably nontemporal) and those that were successive (and therefore finite and temporal).