We reply that this reason is even less plausible than the preceding one. To form the abstract notion of extension, we must first directly perceive some extension in the concrete, in the same manner as we must perceive concrete humanity in individual men before we conceive humanity in the abstract. But in all sensible movements we directly perceive extension through space and time. Therefore from sensible movements, without a previous knowledge of extension, we can form the notion of extension in general. Is there any one who can find in this a vicious circle?
This answer might suffice. But we will further remark that the argument may be retorted against its author. For if we cannot conceive movement as extending in space without a previous knowledge of extension, how can we conceive matter as extending in space without a previous knowledge of extension? And how can we conceive matter as continuous without a previous knowledge of continuity, or time as enduring without a previous knowledge of duration? To these questions the author of the argument can give no satisfactory answer without solving his own objection. Space, distance, and [pg 279] movement, says he, involve extension; and therefore they cannot be known “without a previous knowledge of what extension is.” It is evident that this conclusion is illogical; for if space, distance, and movement imply extension, we cannot perceive space, distance, and movement without directly perceiving extension; and, since the direct perception of a thing does not require a previous knowledge of it, the logical conclusion should have been that, to perceive space, distance, and movement, no previous knowledge of extension is needed.
On the other hand, while our senses perceive the extension of continuous movement in space, they are not competent to perceive material continuity in natural bodies. Hence it is from movement, and not from matter, that our notion of continuous extension is derived. In fact, to form a conception of the dimensions of a body, we survey it by a continuous movement of our eyes from one end of it to the other. In this movement the eye glides over innumerable pores, by which the material particles of the body are separated. If our conception of the geometric extension of the body depended on the continuity of its matter, these pores, as not consisting of continuous matter, should all be thrown away in the measurement of the body. Why, then, do we consider them as contributing with their own dimensions to form the total dimensions of the body? Merely because the geometric dimensions are estimated by movement, and not by matter.
Nor is it in the least strange that we should know extension from movement, and not from matter. For no one can perceive extension between two terms, unless he measures by continuous movement the space intercepted between them. The local relation between two terms cannot, in fact, be perceived otherwise than by referring the one term to the other through space; hence no one ever perceives a distance between two given terms otherwise than by drawing, at least mentally, a line from the one to the other—that is, otherwise than by measuring by some movement the extent of the movement which can take place between the two given terms. And this is what the very word extension conveys. For this word is composed of the preposition ex, which connotes the term from which the movement begins, and of the verb tendere, which is a verb of motion. And thus everything shows that it is from motion, and not from continuous matter, that our first notion of extension proceeds.
A sharp opponent, however, might still object that before we can perceive any movement we need to perceive something movable—that is, visible matter. But no matter is visible unless it be extended. Therefore extension must be perceived in matter itself before we can perceive it in local movement.
But we answer, first, that although nothing can be perceived by our senses unless it be extended, nevertheless we can see extended things without perceiving their extension. Thus we see many stars as mere points in space, and yet we can perceive their movement from the east to the west. Hence, although matter is not visible unless it be extended, it does not follow that extension must be first perceived in matter itself.
Secondly, we answer that when we perceive the movable matter as extended, we do not judge of its [pg 280] extension by its movement, but by the movement which we ourselves have to make in going from one of its extremities to the other. This is the only way of perceiving extension in space. For how could we conceive anything as extended, if we could not see that it has parts outside of parts? And how could we pronounce that anything has parts outside of parts, if we did not see that between one part and another there is a possibility of local movement? On the other hand, as soon as we perceive the possibility of local movement between distinct parts, we have sufficient evidence of geometric extension. And thus we have no need of continuous matter in order to perceive the volume of bodies.
Before we dismiss this subject, we must add that the advocates of continuous matter, while fighting against us, shield themselves with two other arguments. If matter is not continuous, they say, bodies will consist of mere mathematical points acting at a distance; but actio in distans is the extreme of absurdity, and therefore bodies cannot consist of mathematical points. They also allege that nature abhors a vacuum, and therefore all space must be filled up with matter; which would be impossible, were not matter continuous. That nature abhors a vacuum was once considered a physical axiom; but, since science has destroyed the physical grounds on which the pretended axiom rested, metaphysics has in its turn been appealed to, that the time-honored dictum may not be consigned to complete oblivion. It has therefore been pretended that space without matter is a mere delusion, and consequently that to make extension dependent on empty intervals of space imagined to intervene between material points is to give a chimerical solution of the question of material extension.
The first of these two arguments we have fully answered in our last article, and we shall not again detain our readers with it. Let us notice, however, that when the elements of matter are called “mathematical” points, the sense is not that they are not physical, but only that those physical points are mathematically, or rigorously, unextended.
The second argument assumes that space void of matter is nothing. As we cannot enter here into a detailed examination of the nature of absolute space, we shall content ourselves with the following answer: 1st. All real relations require a real foundation. Real distances are real relations. Therefore real distances have a real foundation. But their foundation is nothing else than absolute space; and therefore absolute space is a reality. 2d. If empty space is nothing, then bodies were created in nothing, occupy nothing, and all spaces actually occupied are nothing. To say, as so many have said, that empty space is nothing, and that space occupied by matter is a reality, is to say that the absolute is nothing until it becomes relative—a proposition which is the main support of German pantheism, and which every man of sense must reject. 3d. Of two different recipients, the greater has a greater capacity independently of the matter which it may contain; for, whether it be filled with the rarest gas or with the densest metal, its capacity does not vary. It is therefore manifest that its capacity is not determined by the matter it contains, but only by the space intercepted between its [pg 281] limits. In the same manner the smaller recipient has less capacity, irrespective of the matter it may contain, and only in consequence of the space intercepted. If, therefore, space, prescinding from the matter occupying it, is nothing, the greater capacity will be a greater nothing, and the less capacity a less nothing. But greater and less imply quantity, and quantity is something. Therefore nothing will be something.