Book XII Chapter 8

It is clear, then, why these things are as they are. But we must not ignore the question whether we have to suppose one such substance or more than one, and if the latter, how many; we must also mention, regarding the opinions expressed by others, that they have said nothing about the number of the substances that can even be clearly stated. For the theory of Ideas has no special discussion of the subject; for those who speak of Ideas say the Ideas are numbers, and they speak of numbers now as unlimited¹, now as limited by the number 10; but as for the reason why there should be just so many numbers, nothing is said with any demonstrative exactness. We however must discuss the subject, starting from the presuppositions and distinctions we have mentioned. The first principle or primary being is not movable either in itself or accidentally, but produces the primary eternal and single movement. But since that which is moved must be moved by something, and the first mover must be in itself unmovable, and eternal movement must be produced by something eternal and a single movement by a single thing, and since we see that besides the simple spatial² movement of the universe, which we say the first and unmovable substance produces, there are other spatial movements-those of the planets-which are eternal (for a body which moves in a circle is eternal and unresting; we have proved these points in the physical treatises), each of these movements also must be caused by a substance both unmovable in itself and eternal. For the nature of the stars is eternal just because it is a certain kind of substance, and the mover is eternal and prior to the moved, and that which is prior to a substance must be a substance. Evidently, then, there must be substances which are of the same number as the movements of the stars, and in their nature eternal, and in themselves unmovable, and without magnitude, for the reason before mentioned. That the movers are substances, then, and that one of these is first and another second according to the same order as the movements of the stars, is evident. But in the number of the movements we reach a problem which must be treated from the standpoint of that one of the mathematical sciences which is most akin³ to philosophy-viz. of astronomy; for this science speculates about substance which is perceptible but eternal, but the other mathematical sciences, i.e. arithmetic and geometry, treat of no substance. That the movements are more numerous than the bodies that are moved is evident to those who have given even moderate attention to the matter; for each of the planets has more than one movement. But as to the actual number of these movements, we now-to give some notion of the subject-quote what some of the mathematicians⁴ say, that our thought may have some definite number to grasp; but, for the rest, we must partly investigate for ourselves, Partly learn from other investigators⁵, and if those who study this subject form an opinion contrary to what we have now stated, we must esteem⁶ both parties indeed, but follow the more accurate.

Eudoxus supposed that the motion of the sun or of the moon involves, in either case, three spheres, of which the first is the sphere of the fixed⁷ stars, and the second moves in the circle which runs along the middle of the zodiac, and the third in the circle which is inclined across the breadth of the zodiac; but the circle in which the moon moves is inclined at a greater angle than that in which the sun moves. And the motion of the planets involves, in each case, four spheres, and of these also the first and second are the same as the first two mentioned above (for the sphere of the fixed stars is that which moves all the other spheres, and that which is placed beneath this and has its movement in the circle which bisects the zodiac is common to all), but the poles of the third sphere of each planet are in the circle which bisects the zodiac, and the motion of the fourth sphere is in the circle which is inclined at an angle to the equator of the third sphere; and the poles of the third sphere are different for each of the other planets, but those of Venus and Mercury are the same.

Callippus made the position of the spheres the same as Eudoxus did, but while he assigned the same number as Eudoxus did to Jupiter and to Saturn⁸, he thought two more spheres should be added to the sun and two to the moon, if one is to explain the observed facts; and one more to each of the other planets.

But it is necessary, if all the spheres combined are to explain the observed facts, that for each of the planets there should be other spheres (one fewer than those hitherto assigned) which counteract⁹ those already mentioned and bring back to the same position the outermost¹⁰ sphere of the star which in each case is situated¹¹ below the star in question; for only thus can all the forces at work produce the observed motion of the planets. Since, then, the spheres involved in the movement of the planets themselves are — eight for Saturn and Jupiter and twenty-five for the others, and of these only those involved in the movement of the lowest-situated planet need not be counteracted¹² the spheres which counteract those of the outermost two planets will be six in number, and the spheres which counteract those of the next four planets will be sixteen; therefore the number of all the spheres — both those which move the planets and those which counteract these — will be fifty-five. And if one were not to add to the moon and to the sun the movements we mentioned, the whole set of spheres will be forty-seven in number.

Let this, then, be taken as the number of the spheres, so that the unmovable substances and principles also may probably be taken as just so many; the assertion of necessity must be left to more powerful thinkers. But if there can be no spatial movement which does not conduce to the moving of a star, and if further every being and every substance which is immune from change and in virtue¹³ of itself has attained¹⁴ to the best must be considered an end, there can be no other being apart from these we have named, but this must be the number of the substances. For if there are others, they will cause change as being a final cause of movement; but there cannot he other movements besides those mentioned. And it is reasonable to infer this from a consideration of the bodies that are moved; for if everything that moves is for the sake of that which is moved, and every movement belongs to something that is moved, no movement can be for the sake of itself or of another movement, but all the movements must be for the sake of the stars. For if there is to be a movement for the sake of a movement, this latter also will have to be for the sake of something else; so that since there cannot be an infinite regress, the end of every movement will be one of the divine bodies which move through the heaven.

(Evidently there is but one heaven. For if there are many heavens as there are many men, the moving principles, of which each heaven will have one, will be one in form but in number many. But all things that are many in number have matter; for one and the same definition, e.g. that of man, applies to many things, while Socrates is one. But the primary essence has not matter; for it is complete reality. So the unmovable first mover is one both in definition and in number; so too, therefore, is that which is moved always and continuously; therefore there is one heaven alone.) Our forefathers¹⁵ in the most remote ages have handed down to their posterity¹⁶ a tradition, in the form of a myth, that these bodies are gods, and that the divine encloses the whole of nature. The rest of the tradition has been added later in mythical¹⁷ form with a view to the persuasion¹⁸ of the multitude and to its legal and utilitarian¹⁹ expediency²⁰; they say these gods are in the form of men or like some of the other animals, and they say other things consequent on and similar to these which we have mentioned. But if one were to separate the first point from these additions and take it alone-that they thought the first substances to be gods, one must regard this as an inspired utterance²¹, and reflect that, while probably each art and each science has often been developed as far as possible and has again perished, these opinions, with others, have been preserved until the present like relics²² of the ancient treasure. Only thus far, then, is the opinion of our ancestors and of our earliest predecessors²³ clear to us.

1 unlimited   

adj.无限的，不受控制的，无条件的

参考例句：

• They flew over the unlimited reaches of the Arctic.他们飞过了茫茫无边的北极上空。
• There is no safety in unlimited technological hubris.在技术方面自以为是会很危险。

2 spatial   

adj.空间的，占据空间的

参考例句：

• This part of brain judges the spatial relationship between objects.大脑的这部分判断物体间的空间关系。
• They said that time is the feeling of spatial displacement.他们说时间是空间位移的感觉。

3 akin   

adj.同族的，类似的

参考例句：

• She painted flowers and birds pictures akin to those of earlier feminine painters.她画一些同早期女画家类似的花鸟画。
• Listening to his life story is akin to reading a good adventure novel.听他的人生故事犹如阅读一本精彩的冒险小说。

4 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

5 investigators   

n.调查者，审查者( investigator的名词复数 )

参考例句：

• This memo could be the smoking gun that investigators have been looking for. 这份备忘录可能是调查人员一直在寻找的证据。
• The team consisted of six investigators and two secretaries. 这个团队由六个调查人员和两个秘书组成。 来自《简明英汉词典》

6 esteem   

n.尊敬，尊重；vt.尊重，敬重；把…看作

参考例句：

• I did not esteem him to be worthy of trust.我认为他不值得信赖。
• The veteran worker ranks high in public love and esteem.那位老工人深受大伙的爱戴。

7 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

8 Saturn   

n.农神，土星

参考例句：

• Astronomers used to ask why only Saturn has rings.天文学家们过去一直感到奇怪，为什么只有土星有光环。
• These comparisons suggested that Saturn is made of lighter materials.这些比较告诉我们，土星由较轻的物质构成。

9 counteract   

vt.对…起反作用，对抗，抵消

参考例句：

• The doctor gave him some medicine to counteract the effect of the poison.医生给他些药解毒。
• Our work calls for mutual support.We shouldn't counteract each other's efforts.工作要互相支持，不要互相拆台。

10 outermost   

adj.最外面的，远离中心的

参考例句：

• He fired and hit the outermost ring of the target.他开枪射中了靶子的最外一环。
• The outermost electron is shielded from the nucleus.原子核对最外层电子的作用受到屏蔽。

11 situated   

adj.坐落在...的，处于某种境地的

参考例句：

• The village is situated at the margin of a forest.村子位于森林的边缘。
• She is awkwardly situated.她的处境困难。

12 counteracted   

对抗，抵消( counteract的过去式 )

参考例句：

• This can be counteracted only by very effective insulation. 这只能用非常有效的绝缘来防止。
• The effect of his preaching was counteracted by the looseness of his behavior. 他讲道的效果被他放荡的生活所抵消了。

13 virtue   

n.德行，美德；贞操；优点；功效，效力

参考例句：

• He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
• You need to decorate your mind with virtue.你应该用德行美化心灵。

14 attained   

（通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况）

参考例句：

• She has attained the degree of Master of Arts. 她已获得文学硕士学位。
• Lu Hsun attained a high position in the republic of letters. 鲁迅在文坛上获得崇高的地位。

15 forefathers   

n.祖先，先人；祖先，祖宗( forefather的名词复数 )；列祖列宗；前人

参考例句：

• They are the most precious cultural legacy our forefathers left. 它们是我们祖先留下来的最宝贵的文化遗产。 来自《简明英汉词典》
• All of us bristled at the lawyer's speech insulting our forefathers. 听到那个律师在讲演中污蔑我们的祖先，大家都气得怒发冲冠。 来自《简明英汉词典》

16 posterity   

n.后裔，子孙，后代

参考例句：

• Few of his works will go down to posterity.他的作品没有几件会流传到后世。
• The names of those who died are recorded for posterity on a tablet at the back of the church.死者姓名都刻在教堂后面的一块石匾上以便后人铭记。

17 mythical   

adj.神话的；虚构的；想像的

参考例句：

• Undeniably,he is a man of mythical status.不可否认，他是一个神话般的人物。
• Their wealth is merely mythical.他们的财富完全是虚构的。

18 persuasion   

n.劝说；说服；持有某种信仰的宗派

参考例句：

• He decided to leave only after much persuasion.经过多方劝说，他才决定离开。
• After a lot of persuasion,she agreed to go.经过多次劝说后，她同意去了。

19 utilitarian   

adj.实用的，功利的

参考例句：

• On the utilitarian side American education has outstridden the rest of the world.在实用方面美国教育已超越世界各国。
• A good cloth coat is more utilitarian than a fur one.一件优质的布外衣要比一件毛皮外衣更有用。

20 expediency   

n.适宜；方便；合算；利己

参考例句：

• The government is torn between principle and expediency. 政府在原则与权宜之间难于抉择。 来自《简明英汉词典》
• It was difficult to strike the right balance between justice and expediency. 在公正与私利之间很难两全。 来自辞典例句

21 utterance   

n.用言语表达，话语，言语

参考例句：

• This utterance of his was greeted with bursts of uproarious laughter.他的讲话引起阵阵哄然大笑。
• My voice cleaves to my throat,and sob chokes my utterance.我的噪子哽咽，泣不成声。

22 relics   

[pl.］n.遗物，遗迹，遗产；遗体，尸骸

参考例句：

• The area is a treasure house of archaeological relics. 这个地区是古文物遗迹的宝库。
• Xi'an is an ancient city full of treasures and saintly relics. 西安是一个有很多宝藏和神圣的遗物的古老城市。

23 predecessors   

n.前任( predecessor的名词复数 )；前辈；（被取代的）原有事物；前身

参考例句：

• The new government set about dismantling their predecessors' legislation. 新政府正着手废除其前任所制定的法律。 来自《简明英汉词典》
• Will new plan be any more acceptable than its predecessors? 新计划比原先的计划更能令人满意吗？ 来自《简明英汉词典》