第10章

will produce the motion in BF in the time C.Thus the finite and infinite effect the same alteration in equal times.But this is impossible; for the assumption is that the greater effects it in a shorter time.It will be the same with any time that can be taken, so that there will no time in which the infinite can effect this movement.And, as to infinite time, in that nothing can move another or be moved by it.For such time has no limit, while the action and reaction have.

(3.There is no interaction between infinites.) Nor can infinite be acted upon in any way by infinite.Let A and B be infinites, CD

being the time of the action A of upon B.Now the whole B was modified in a certain time, and the part of this infinite, E, cannot be so modified in the same time, since we assume that a less quantity makes the movement in a less time.Let E then, when acted upon by A, complete the movement in the time D.Then, as D is to CD, so is E to some finite part of B.This part will necessarily be moved by A in the time CD.For we suppose that the same agent produces a given effect on a greater and a smaller mass in longer and shorter times, the times and masses varying proportionately.There is thus no finite time in which infinites can move one another.Is their time then infinite? No, for infinite time has no end, but the movement communicated has.

If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is impossible that an infinite body should be perceptible.All bodies, however, that occupy place are perceptible.There is therefore no infinite body beyond the heaven.Nor again is there anything of limited extent beyond it.And so beyond the heaven there is no body at all.For if you suppose it an object of intelligence, it will be in a place-since place is what 'within' and 'beyond' denote-and therefore an object of perception.But nothing that is not in a place is perceptible.

The question may also be examined in the light of more general considerations as follows.The infinite, considered as a whole of similar parts, cannot, on the one hand, move in a circle.For there is no centre of the infinite, and that which moves in a circle moves about the centre.Nor again can the infinite move in a straight line.For there would have to be another place infinite like itself to be the goal of its natural movement and another, equally great, for the goal of its unnatural movement.Moreover, whether its rectilinear movement is natural or constrained, in either case the force which causes its motion will have to be infinite.For infinite force is force of an infinite body, and of an infinite body the force is infinite.So the motive body also will be infinite.(The proof of this is given in our discussion of movement, where it is shown that no finite thing possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move unnaturally, there will be two infinites, one which causes, and another which exhibits the latter motion.Again, what is it that moves the infinite? If it moves itself, it must be animate.But how can it possibly be conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that which moves and that which is moved, differing in their form and power.

If the whole is not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated by void, there must necessarily be one movement of all the multitude.They are distinguished, we are told, from one another by their figures; but their nature is one, like many pieces of gold separated from one another.But each piece must, as we assert, have the same motion.

For a single clod moves to the same place as the whole mass of earth, and a spark to the same place as the whole mass of fire.So that if it be weight that all possess, no body is, strictly speaking, light: and if lightness be universal, none is heavy.

Moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region.But this is impossible while the world is conceived as infinite.And, generally, that which has no centre or extreme limit, no up or down, gives the bodies no place for their motion; and without that movement is impossible.A thing must move either naturally or unnaturally, and the two movements are determined by the proper and alien places.Again, a place in which a thing rests or to which it moves unnaturally, must be the natural place for some other body, as experience shows.

Necessarily, therefore, not everything possesses weight or lightness, but some things do and some do not.From these arguments then it is clear that the body of the universe is not infinite.