First. If a body moves, it moves where it is, not where it is not. But it cannot move where it is; for to move implies not to remain where it is, and therefore bodies cannot move. The answer is, that bodies neither move where they are nor where they are not, but from the place where they are to the place where they are not.
Second. A material element cannot describe a line in space between two points without gliding through all the intermediate ubications. But the intermediate ubications are infinite, as infinite points can be designated in any line; and the infinite cannot be passed over. The answer is that an infinite multitude cannot be measured by one of its units; and for this reason the infinite multitude of ubications which may be designated between the terms of a line cannot be measured by a unit of the same kind. Nevertheless, a line can be measured by movement—that is, not by the ubication itself, but by the flowing of an ubication; because the flowing of the ubication is continuous, and involves continuous quantity; and therefore it is to be considered as containing in itself its own measure, which is a measure of length, and which may serve to measure the whole line of movement. If the length of a line were an infinite sum of ubications—that is, of mathematical points—the objection would have some weight; but the length of the line is evidently not a sum of points. The line is a continuous quantity evolved by the flowing of a point. It can therefore be measured by the flowing of a point. For as the line described can be divided and subdivided without end, so also the time employed in describing it can be divided and subdivided without end. Hence the length of a line described in a finite length of time can be conceived as an infinite virtual multitude of infinitesimal lengths, just in the same manner as the time employed in describing it can be conceived as an infinite multitude of infinitesimal instants. Now, the infinite can measure the infinite; and therefore it is manifest that an infinite multitude of infinitesimal lengths can be measured by the flowing of a point through an infinite multitude of infinitesimal instants.[161]
Third. The communication of movement, as we know by experience, requires time; and yet time arises from movement, and cannot begin before the movement is communicated. How, then, will movement be communicated? The answer is that time and movement begin together, and evolve simultaneously in the very act of the communication of movement. It is not true, then, that all communication of movement requires time. Our experience regards only the communication of finite movement, which, of course, cannot be made except the action of the agent continue for a finite time. But movement is always communicated by infinitesimal degrees in infinitesimal instants; and thus the beginning of the motive action coincides with the beginning of the movement, and this coincides with the beginning of its duration.
And here we end. The considerations which we have developed in our articles on space, duration, and movement have, we think, a sufficient importance to be regarded with interest by those who have a philosophical turn of mind. The subjects which we have endeavored so far to investigate are scarcely ever examined as deeply as they deserve by the modern writers of philosophical treatises; but there is no doubt that a clearer knowledge of those subjects must enable us to extricate ourselves from many difficulties to be met in other parts of metaphysics. It is principally in order to solve the sophisms of the idealists and of the transcendental pantheists that we need an exact, intellectual notion of space and of time. We see how Kant, the father of German idealism and pantheism, was led into numerous errors by his misconception of these two points, and how his followers, owing to a like hallucination, succeeded in obscuring the light of their noble intellects, and were prompted to deny and revile the most certain and fundamental principles of human reasoning. In fact, a mistaken notion of space lies at the bottom of nearly all their philosophical blunders. If we desire to refute their false theories by direct and categorical arguments, we must know how far we can trust the popular language on space, and how we can correct its inaccuracies so as to give precision to our own phraseology, lest by conceding or denying more than truth demands we furnish them with the means of retorting against our argumentation. This is the main reason that induced us to treat of space, duration, and movement in a special series of articles, as we entertained the hope that we might thus help in cutting the ground from under the feet of the pantheist by uprooting the very germ of his manifold errors.
NOT YET.
Methought the King of Terrors came my way:
Whom all men flee, and none esteem it base.
But lo! his smile forbidding me dismay,