Book I Chapter 5

Contemporaneously with these philosophers and before them, the so-called Pythagoreans, who were the first to take up mathematics, not only advanced this study, but also having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being-more than in fire and earth and water (such and such a modification¹ of numbers being justice, another being soul and reason, another being opportunity-and similarly almost all other things being numerically expressible); since, again, they saw that the modifications³ and the ratios of the musical scales were expressible in numbers;-since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent. E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth — the ‘counter-earth’. We have discussed these matters more exactly elsewhere.

But the object of our review is that we may learn from these philosophers also what they suppose to be the principles and how these fall under the causes we have named. Evidently, then, these thinkers also consider that number is the principle both as matter for things and as forming both their modifications and their permanent states, and hold that the elements of number are the even and the odd, and that of these the latter is limited, and the former unlimited⁴; and that the One proceeds from both of these (for it is both even and odd), and number from the One; and that the whole heaven, as has been said, is numbers.

Other members of this same school say there are ten principles, which they arrange in two columns of cognates-limit and unlimited, odd and even, one and plurality, right and left, male and female, resting and moving, straight and curved, light and darkness, good and bad, square and oblong. In this way Alcmaeon of Croton seems also to have conceived the matter, and either he got this view from them or they got it from him; for he expressed himself similarly to them. For he says most human affairs go in pairs, meaning not definite contrarieties such as the Pythagoreans speak of, but any chance contrarieties, e.g. white and black, sweet and bitter, good and bad, great and small. He threw out indefinite suggestions about the other contrarieties, but the Pythagoreans declared both how many and which their contraricties are.

From both these schools, then, we can learn this much, that the contraries are the principles of things; and how many these principles are and which they are, we can learn from one of the two schools. But how these principles can be brought together under the causes we have named has not been clearly and articulately stated by them; they seem, however, to range the elements under the head of matter; for out of these as immanent parts they say substance is composed and moulded.

From these facts we may sufficiently⁵ perceive the meaning of the ancients who said the elements of nature were more than one; but there are some who spoke⁶ of the universe as if it were one entity⁷, though they were not all alike either in the excellence⁸ of their statement or in its conformity⁹ to the facts of nature. The discussion of them is in no way appropriate to our present investigation¹⁰ of causes, for. they do not, like some of the natural philosophers, assume being to be one and yet generate it out of the one as out of matter, but they speak in another way; those others add change, since they generate the universe, but these thinkers say the universe is unchangeable. Yet this much is germane¹¹ to the present inquiry¹²: Parmenides seems to fasten on that which is one in definition, Melissus on that which is one in matter, for which reason the former says that it is limited, the latter that it is unlimited; while Xenophanes, the first of these partisans¹³ of the One (for Parmenides is said to have been his pupil), gave no clear statement, nor does he seem to have grasped the nature of either of these causes, but with reference to the whole material universe he says the One is God. Now these thinkers, as we said, must be neglected for the purposes of the present inquiry-two of them entirely¹⁴, as being a little too naive¹⁵, viz. Xenophanes and Melissus; but Parmenides seems in places to speak with more insight. For, claiming that, besides the existent, nothing non-existent exists, he thinks that of necessity one thing exists, viz. the existent and nothing else (on this we have spoken more clearly in our work on nature), but being forced to follow the observed facts, and supposing the existence of that which is one in definition, but more than one according to our sensations, he now posits¹⁷ two causes and two principles, calling them hot and cold, i.e. fire and earth; and of these he ranges the hot with the existent, and the other with the non-existent.

From what has been said, then, and from the wise men who have now sat in council with us, we have got thus much-on the one hand from the earliest philosophers, who regard the first principle as corporeal¹⁸ (for water and fire and such things are bodies), and of whom some suppose that there is one corporeal principle, others that there are more than one, but both put these under the head of matter; and on the other hand from some who posit¹⁶ both this cause and besides this the source of movement, which we have got from some as single and from others as twofold.

Down to the Italian school, then, and apart from it, philosophers have treated these subjects rather obscurely, except that, as we said, they have in fact used two kinds of cause, and one of these-the source of movement-some treat as one and others as two. But the Pythagoreans have said in the same way that there are two principles, but added this much, which is peculiar¹⁹ to them, that they thought that finitude and infinity²⁰ were not attributes of certain other things, e.g. of fire or earth or anything else of this kind, but that infinity itself and unity² itself were the substance of the things of which they are predicated. This is why number was the substance of all things. On this subject, then, they expressed themselves thus; and regarding the question of essence they began to make statements and definitions, but treated the matter too simply. For they both defined superficially and thought that the first subject of which a given definition was predicable was the substance of the thing defined, as if one supposed that ‘double’ and ‘2’ were the same, because 2 is the first thing of which ‘double’ is predicable. But surely to be double and to be 2 are not the same; if they are, one thing will be many-a consequence which they actually drew. From the earlier philosophers, then, and from their successors we can learn thus much.

1 modification   

n.修改，改进，缓和，减轻

参考例句：

• The law,in its present form,is unjust;it needs modification.现行的法律是不公正的，它需要修改。
• The design requires considerable modification.这个设计需要作大的修改。

2 unity   

n.团结，联合，统一；和睦，协调

参考例句：

• When we speak of unity,we do not mean unprincipled peace.所谓团结，并非一团和气。
• We must strengthen our unity in the face of powerful enemies.大敌当前，我们必须加强团结。

3 modifications   

n.缓和( modification的名词复数 )；限制；更改；改变

参考例句：

• The engine was pulled apart for modifications and then reassembled. 发动机被拆开改型，然后再组装起来。 来自《简明英汉词典》
• The original plan had undergone fairly extensive modifications. 原计划已经作了相当大的修改。 来自《简明英汉词典》

4 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。

5 sufficiently   

adv.足够地，充分地

参考例句：

• It turned out he had not insured the house sufficiently.原来他没有给房屋投足保险。
• The new policy was sufficiently elastic to accommodate both views.新政策充分灵活地适用两种观点。

6 spoke   

n.（车轮的）辐条；轮辐；破坏某人的计划；阻挠某人的行动 v.讲，谈（speak的过去式）；说；演说；从某种观点来说

参考例句：

• They sourced the spoke nuts from our company.他们的轮辐螺帽是从我们公司获得的。
• The spokes of a wheel are the bars that connect the outer ring to the centre.辐条是轮子上连接外圈与中心的条棒。

7 entity   

n.实体，独立存在体，实际存在物

参考例句：

• The country is no longer one political entity.这个国家不再是一个统一的政治实体了。
• As a separate legal entity,the corporation must pay taxes.作为一个独立的法律实体，公司必须纳税。

8 excellence   

n.优秀，杰出，(pl.)优点，美德

参考例句：

• His art has reached a high degree of excellence.他的艺术已达到炉火纯青的地步。
• My performance is far below excellence.我的表演离优秀还差得远呢。

9 conformity   

n.一致，遵从，顺从

参考例句：

• Was his action in conformity with the law?他的行动是否合法？
• The plan was made in conformity with his views.计划仍按他的意见制定。

10 investigation   

n.调查，调查研究

参考例句：

• In an investigation,a new fact became known, which told against him.在调查中新发现了一件对他不利的事实。
• He drew the conclusion by building on his own investigation.他根据自己的调查研究作出结论。

11 germane   

adj.关系密切的，恰当的

参考例句：

• He asks questions that are germane and central to the issue.他问了一些与论点有密切关系的重要问题。
• Fenton was a good listener,and his questions were germane.芬顿听得聚精会神，提问也切中要害。

12 inquiry   

n.打听，询问，调查，查问

参考例句：

• Many parents have been pressing for an inquiry into the problem.许多家长迫切要求调查这个问题。
• The field of inquiry has narrowed down to five persons.调查的范围已经缩小到只剩5个人了。

13 partisans   

游击队员( partisan的名词复数 )； 党人； 党羽； 帮伙

参考例句：

• Every movement has its partisans. 每一运动都有热情的支持者。
• He was rescued by some Italian partisans. 他被几名意大利游击队员所救。

14 entirely   

ad.全部地，完整地；完全地，彻底地

参考例句：

• The fire was entirely caused by their neglect of duty. 那场火灾完全是由于他们失职而引起的。
• His life was entirely given up to the educational work. 他的一生统统献给了教育工作。

15 naive   

adj.幼稚的，轻信的；天真的

参考例句：

• It's naive of you to believe he'll do what he says.相信他会言行一致，你未免太单纯了。
• Don't be naive.The matter is not so simple.你别傻乎乎的。事情没有那么简单。

16 posit   

v.假定，认为

参考例句：

• If she needs salvation,she will posit a savior.如果她需要救助，她就会设想一个救助者。
• Other historians posit that she died of old age around 550 BC.别的史学家则认为她一直活到公元前550年左右才寿终正寝。

17 posits   

v.假定，设想，假设( posit的第三人称单数 )

参考例句：

• If a book is hard going, it ought to be good. If it posits a complex moral situation, it ought to be even better. 如果一本书很难读，那么它应该是一本好书；如果它提出了一个复杂的道德状况，那么它就更应该是本好书了。 来自《简明英汉词典》
• Ray posits that this miracle is an object lesson for the disciples. 雷把这个奇事当作教训信徒们的事件。 来自互联网

18 corporeal   

adj.肉体的，身体的；物质的

参考例句：

• The body is the corporeal habitation of the soul.身体为灵魂之有形寓所。
• He is very religious;corporeal world has little interest for him.他虔信宗教，对物质上的享受不感兴趣。

19 peculiar   

adj.古怪的，异常的；特殊的，特有的

参考例句：

• He walks in a peculiar fashion.他走路的样子很奇特。
• He looked at me with a very peculiar expression.他用一种很奇怪的表情看着我。

20 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。