the body fills: the inner place and size of the body are therefore identical.1 Against the position that body and quantity of space (extension) are identical, two doubts arise, based on the rarefaction of bodies, and empty space. If body and extension were identical, the same body would have to occupy the same extension all the time, and could not be extended, now more, now less, which is the case in the rarefaction and condensation of bodies. But the supposition upon which the objection rests is not true. Rarefaction is not increased extension, since extension, or matter, consists in the multitude of parts; but rarefaction does not consist in increasing the parts of bodies, but in enlarging the spaces between them, or in other bodies entering into them. Thus, the sponge which is filled with water does not increase in size because its parts increase in number, but because there is more water than before in the spaces between them. The rarefaction and condensation of bodies does not, therefore, consist in their increased or decreased extension, but in the enlargement or diminution of their pores.2 But empty pores are empty space: this is extension without body, and is, therefore, an actual proof that body and extension are not identical. This objection also is invalid, and rests on confused concepts. Empty space is either understood relatively or absolutely: in the first case it is not empty, in the second it is without meaning. A waterpitcher, a cauf, and a trading-vessel are said to be empty when the first is empty of water, the second of fish, and the third of goods, although they are always filled with other bodies. We call the space empty which does not contain certain bodies which we expected to find there, or which in general are capable of being perceived by the senses. This customary (relative) concept of empty space has, however, led to the philosophical (absolute) concept. There is no necessary connection between a vessel and its contents; it 2 Ib., ii. secs. 5-7. 1 Princ., ii. secs. 10-15. can contain air, water, sand, and also nothing; and when every content is lacking, it is absolutely empty. Absolute emptiness is nothing, space is something; and there is just as little an empty space as a something which is nothing. A vessel can be empty of this or that thing, but not absolutely empty, since in that case it could not exist. In absolute emptiness, there would be literally nothing to separate the concave walls of a vase from each other; and these would have to fall together, and there would be no configuration and no vessel. In truth, there is no emptiness, but only the appearance of emptiness. Every body is extended, and is full in the same proportion as it is extended: it cannot be more or less extended, therefore not more or less full than it is whether it is filled with gold or lead or water or air, or whether it seems to be empty.' II. THE MATERIAL WORLD. Body and extension are identical: there is nothing empty. Where space is, there are bodies and only bodies; these stretch through the whole of space, however far it extends; it extends as far as extension. Within extension, there is nothing which is unextended or indivisible. There are no atoms the smallest parts of bodies are always still divisible, therefore not atoms, but molecules or corpuscles. And just as little can extension anywhere cease or be bounded; for with this boundary, the unextended would have to begin, and the boundary itself could therefore no longer be extended. It is, therefore, absolutely impossible to enclose extension within bounds: it is absolutely boundless. Therefore the material world is infinite. Since extension can nowhere be empty, or cease at any place, it is continuous, and forms a continuum. There are, therefore, not different kinds of extension or matter, therefore, also, not different material worlds. The material world is merely extended, boundless, and one. Beyond thought, there is no other world than the material. 1 Princ., ii. secs. 16-19. when H CHAPTER VIII. THE PHILOSOPHY OF NATURE. (8) THE MECHANICAL PRIN- I. MOTION AS THE FUNDAMENTAL PHENOMENON OF THE MATERIAL WORLD. 1. Motion as a Mode of Extension. ALL the phenomena or events of the inner world are Α modifications of thought: all the phenomena and modifications of the outer world are modifications of extension, which, we have seen, is the attribute of material substance. Now, if extension is infinitely divisible, its parts can be united and separated, and thus different formations or forms of matter result. This union and separation take place through the approach and removal of the parts; i.e., through motion. Extension is therefore divisible, capable of form, and movable. Its possible changes consist in division, formation, and motion: there are no other modifications of extension. With the following declaration, Descartes concludes the second part of his "Principles:" "I frankly avow that I acknowledge in the nature of bodies no other matter than that which can be divided, formed, and moved in a great variety of ways, that which mathematicians call magnitude (quantity); that in this matter I consider merely its divisions, figures, and motions, and accept nothing as true that does not follow from these principles as evidently as the certainty of mathematical propositions. In this way all the phenomena of nature can be explained. I think, therefore, that no other principles in physics than those here expounded are necessary or admissible." 1 1 Princ., ii. sec. 64. These principles can be simplified. All division and formation of matter takes place through motion. All the modifications of matter can, therefore, be analyzed into motion. The changes in the material world are all phenomena of motion: every change in matter and all the dif ferences of its forms are dependent upon motion. The stand-point of the Cartesian philosophy of nature is now perfectly clear: the nature of bodies consists in quantity of space and their changes in motion; that is conceived mathematically, this mechanically. Descartes' explanation of nature, therefore, rests completely on mathematical-mechanical principles. 2. Motion as Change of Place. - All motion consists in a spatial change. Now, the space which a body takes up in relation to other bodies is its place, or position. If a body moves, it changes its place: all motion is, therefore, change of place. "It is the action by means of which a body passes from one place into another." 2 This concept must be more precisely determined that it may be guarded against the objection that the same body in the same time can be both moved and not moved. A body can change its place while it rests, as a man sitting in a ship which is moving with the current of the stream. He is changing his place with reference to the banks of the stream, but not with reference to the ship in which he is sitting; he remains in the same position with reference to the bodies that immediately surround him; i.e., he rests. Since motion can be considered only as a mode of a moving body, or as a change peculiar to it, it cannot be predicated of a body that changes its place without its own action. A body or (since all bodies are parts of one and the same matter) a part of matter moves only when it changes its place in relation to the immediately surrounding bodies; i.e., when it is transported from the vicinity of the bodies that directly touch it to the vicinity of others. Now, that change of place which has the character of such a transposition or translation (transport) from one place to another is motion in the strict sense of the word. But this concept also requires a yet more precise determination, that it may meet the above objection from a new point of view. Change of place is always relative. If a body A changes its place in relation to the immediately neighboring parts of the matter B, B also changes its place in relation to A. It is possible that both bodies are active and in motion at the same time. But there are cases in the change of place of immediately neighboring parts of matter, in which only one of the bodies moves. Two bodies, A and B, move on the surface of the earth directly towards each other. This motion is reciprocal, and belongs to each of the two in like manner. Both bodies change their places at the same time in relation to the parts of the surface of the earth that immediately surround them: this change of place is also reciprocal, and the earth also must be considered to move in relation to A and B; i.e., it must at the same time move in two opposite directions, which is impossible. The bulk of the earth is, therefore, considered as resting in relation to the bodies of the earth and so many smaller bodies that move here and there on its surface. From this it is evident that a body is moved when it passes from the vicinity of those parts of matter that directly touch it, and which, in relation to it, are considered at rest. A ship that is urged forward by the stream, and backwards by the wind, with the same force, remains opposite to the same place on the bank: it does not change its place on the earth, but rests, while the particles of water and air which surround it are in constant motion. "If we would know," says Descartes, "what motion really is, in order to determine it precisely, we must explain it as the translation of place (transport) of one part of matter or of one body from the vicinity of those bodies which directly touch it, and are considered at rest, into the vicinity of others." "By a body, or a part of matter, |