>>14572624
But it is this very conception of motion that is in error, for it amounts in short to regarding the continuous as if it were composed of points, or of final, indivisible elements, like the notion according to which bodies are composed of atoms; and this would amount to saying that in reality there is no continuity, for whether it is a question of points or atoms, these final elements can only be discontinuous; furthermore, it is true that without continuity there would be no possible motion, and this is all that the argument actually proves. The same goes for the argument of the arrow that flies and is nonetheless immobile, since at each instant one sees only a single position, which amounts to supposing that each position can in itself be regarded as fixed and determined, and that the successive positions thus form a sort of discontinuous series.
It is further necessary to observe that it is not in fact true that a moving object is ever viewed as if it occupied a fixed position, and that quite to the contrary, when the motion is fast enough, one will no longer see the moving object distinctly, but only the path of its continuous displacement; thus for example, if a flaming ember is whirled about rapidly, one will no longer see the form of the ember, but only a circle of fire; moreover, whether one explains this by the persistence of retinal impressions, as physiologists do, or in any other way, it matters little, for it is no less obvious that in such cases one grasps the continuity of motion directly, as it were, and in a perceptible manner. What is more, when one uses the expression 'at each instant' in formulating such arguments, one is implying that time is formed from a sequence of indivisible instants, to each of which there corresponds a determined position of the object; but in reality, temporal continuity is no more composed of instants than spatial continuity is of points, and as we have already pointed out, the possibility of motion presupposes the union, or rather the combination, of both temporal and spatial continuity. It is also argued that in order to traverse a given distance, it is first necessary to traverse half this distance, then half of the remaining half, then half of the rest, and so on indefinitely, (1) such that one would always be faced with an indefinitude that, envisaged in this way, is indeed inexhaustible.
(1) This corresponds to the successive terms of the indefinite series 1/1 + 1/2 + 1/4 + 1/8 + ... = 2, used by Leibnitz as an example in a passage already cited above.