Chapter 7

Every body must necessarily be either finite or infinite, and if infinite, either of similar or of dissimilar parts. If its parts are dissimilar, they must represent either a finite or an infinite number of kinds. That the kinds cannot be infinite is evident, if our original presuppositions remain unchallenged. For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple body is simple, and the simple movements are finite, and every natural body must always have its proper motion. Now if the infinite body is to be composed of a finite number of kinds, then each of its parts must necessarily be infinite in quantity, that is to say, the water, fire, &c., which compose it. But this is impossible, because, as we have already shown, infinite weight and lightness do not exist. Moreover it would be necessary also that their places should be infinite in extent, so that the movements too of all these bodies would be infinite. But this is not possible, if we are to hold to the truth of our original presuppositions and to the view that neither that which moves downward, nor, by the same reasoning, that which moves upward, can prolong its movement to infinity¹. For it is true in regard to quality, quantity, and place alike that any process of change is impossible which can have no end. I mean that if it is impossible for a thing to have come to be white, or a cubit long, or in Egypt, it is also impossible for it to be in process of coming to be any of these. It is thus impossible for a thing to be moving to a place at which in its motion it can never by any possibility arrive. Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all these scattered² particles, say, of fire, is infinite. But body we saw to be that which has extension every way. How can there be several dissimilar elements, each infinite? Each would have to be infinitely³ extended every way.

It is no more conceivable, again, that the infinite should exist as a whole of similar parts. For, in the first place, there is no other (straight) movement beyond those mentioned: we must therefore give it one of them. And if so, we shall have to admit either infinite weight or infinite lightness. Nor, secondly⁴, could the body whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible.

Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either naturally or by constraint⁵: and if by constraint, it possesses also a natural motion, that is to say, there is another place, infinite like itself, to which it will move. But that is impossible.

That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as follows.

(1. The infinite cannot be acted upon by the finite.) Let A be an infinite, B a finite, C the time of a given movement produced by one in the other. Suppose, then, that A was heated, or impelled⁶, or modified in any way, or caused to undergo any sort of movement whatever, by in the time C. Let D be less than B; and, assuming that a lesser⁷ agent moves a lesser patient in an equal time, call the quantity thus modified by D, E. Then, as D is to B, so is E to some finite quantum. We assume that the alteration⁸ of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion which obtains between the agents, greater and less. If so, no movement can be caused in the infinite by any finite agent in any time whatever. For a less agent will produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will be a finite quantity, since no proportion holds between finite and infinite.

(2. The infinite cannot act upon the finite.) Nor, again, can the infinite produce a movement in the finite in any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that motion in a patient less than B, say F. Then take E, bearing the same proportion to D as the whole BF bears to F. E 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 acting⁹ 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 unnatural¹⁰ movement. Moreover, whether its rectilinear movement is natural or constrained¹¹, 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 motive¹² 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 unnaturally¹³, 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 animate¹⁴. 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 distinguished¹⁵, 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, strictly¹⁶ 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 determined¹⁷ 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.

1 infinity   

n.无限，无穷，大量

参考例句：

• It is impossible to count up to infinity.不可能数到无穷大。
• Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。

2 scattered   

adj.分散的，稀疏的；散步的；疏疏落落的

参考例句：

• Gathering up his scattered papers,he pushed them into his case.他把散乱的文件收拾起来，塞进文件夹里。

3 infinitely   

adv.无限地，无穷地

参考例句：

• There is an infinitely bright future ahead of us.我们有无限光明的前途。
• The universe is infinitely large.宇宙是无限大的。

4 secondly   

adv.第二，其次

参考例句：

• Secondly,use your own head and present your point of view.第二，动脑筋提出自己的见解。
• Secondly it is necessary to define the applied load.其次，需要确定所作用的载荷。

5 constraint   

n.(on)约束，限制；限制(或约束)性的事物

参考例句：

• The boy felt constraint in her presence.那男孩在她面前感到局促不安。
• The lack of capital is major constraint on activities in the informal sector.资本短缺也是影响非正规部门生产经营的一个重要制约因素。

6 impelled   

v.推动、推进或敦促某人做某事( impel的过去式和过去分词 )

参考例句：

• He felt impelled to investigate further. 他觉得有必要作进一步调查。
• I feel impelled to express grave doubts about the project. 我觉得不得不对这项计划深表怀疑。 来自《简明英汉词典》

7 lesser   

adj.次要的，较小的；adv.较小地，较少地

参考例句：

• Kept some of the lesser players out.不让那些次要的球员参加联赛。
• She has also been affected,but to a lesser degree.她也受到波及，但程度较轻。

8 alteration   

n.变更，改变；蚀变

参考例句：

• The shirt needs alteration.这件衬衣需要改一改。
• He easily perceived there was an alteration in my countenance.他立刻看出我的脸色和往常有些不同。

9 acting   

n.演戏，行为，假装；adj.代理的，临时的，演出用的

参考例句：

• Ignore her,she's just acting.别理她，她只是假装的。
• During the seventies,her acting career was in eclipse.在七十年代，她的表演生涯黯然失色。

10 unnatural   

adj.不自然的；反常的

参考例句：

• Did her behaviour seem unnatural in any way?她有任何反常表现吗？
• She has an unnatural smile on her face.她脸上挂着做作的微笑。

11 constrained   

adj.束缚的,节制的

参考例句：

• The evidence was so compelling that he felt constrained to accept it. 证据是那样的令人折服，他觉得不得不接受。
• I feel constrained to write and ask for your forgiveness. 我不得不写信请你原谅。

12 motive   

n.动机，目的；adv.发动的，运动的

参考例句：

• The police could not find a motive for the murder.警察不能找到谋杀的动机。
• He had some motive in telling this fable.他讲这寓言故事是有用意的。

13 unnaturally   

adv.违反习俗地；不自然地；勉强地；不近人情地

参考例句：

• Her voice sounded unnaturally loud. 她的嗓音很响亮，但是有点反常。 来自《简明英汉词典》
• Her eyes were unnaturally bright. 她的眼睛亮得不自然。 来自《简明英汉词典》

14 animate   

v.赋于生命，鼓励；adj.有生命的，有生气的

参考例句：

• We are animate beings,living creatures.我们是有生命的存在，有生命的动物。
• The girls watched,little teasing smiles animating their faces.女孩们注视着，脸上挂着调皮的微笑，显得愈加活泼。

15 distinguished   

adj.卓越的，杰出的，著名的

参考例句：

• Elephants are distinguished from other animals by their long noses.大象以其长长的鼻子显示出与其他动物的不同。
• A banquet was given in honor of the distinguished guests.宴会是为了向贵宾们致敬而举行的。

16 strictly   

adv.严厉地，严格地；严密地

参考例句：

• His doctor is dieting him strictly.他的医生严格规定他的饮食。
• The guests were seated strictly in order of precedence.客人严格按照地位高低就座。

17 determined   

adj.坚定的；有决心的

参考例句：

• I have determined on going to Tibet after graduation.我已决定毕业后去西藏。
• He determined to view the rooms behind the office.他决定查看一下办公室后面的房间。