Book XIV Chapter 5

If, then, it is equally impossible not to put the good among the first principles and to put it among them in this way, evidently the principles are not being correctly described, nor are the first substances. Nor does any one conceive the matter correctly if he compares the principles of the universe to that of animals and plants, on the ground that the more complete always comes from the indefinite and incomplete-which is what leads this thinker to say that this is also true of the first principles of reality, so that the One itself is not even an existing thing. This is incorrect, for even in this world of animals and plants the principles from which these come are complete; for it is a man that produces a man, and the seed is not first.

It is out of place, also, to generate place simultaneously¹ with the mathematical solids (for place is peculiar² to the individual things, and hence they are separate in place; but mathematical objects are nowhere), and to say that they must be somewhere, but not say what kind of thing their place is.

Those who say that existing things come from elements and that the first of existing things are the numbers, should have first distinguished³ the senses in which one thing comes from another, and then said in which sense number comes from its first principles.

By intermixture? But (1) not everything is capable of intermixture, and (2) that which is produced by it is different from its elements, and on this view the one will not remain separate or a distinct entity⁴; but they want it to be so.

By juxtaposition⁵, like a syllable⁶? But then (1) the elements must have position; and (2) he who thinks of number will be able to think of the unity⁷ and the plurality apart; number then will be this-a unit and plurality, or the one and the unequal.

Again, coming from certain things means in one sense that these are still to be found in the product, and in another that they are not; which sense does number come from these elements? Only things that are generated can come from elements which are present in them. Does number come, then, from its elements as from seed? But nothing can be excreted from that which is indivisible. Does it come from its contrary, its contrary not persisting? But all things that come in this way come also from something else which does persist. Since, then, one thinker places the 1 as contrary to plurality, and another places it as contrary to the unequal, treating the 1 as equal, number must be being treated as coming from contraries. There is, then, something else that persists, from which and from one contrary the compound is or has come to be. Again, why in the world do the other things that come from contraries, or that have contraries, perish (even when all of the contrary is used to produce them), while number does not? Nothing is said about this. Yet whether present or not present in the compound the contrary destroys it, e.g. ‘strife’ destroys the ‘mixture’ (yet it should not; for it is not to that that is contrary).

Once more, it has not been determined⁸ at all in which way numbers are the causes of substances and of being-whether (1) as boundaries (as points are of spatial⁹ magnitudes). This is how Eurytus decided¹⁰ what was the number of what (e.g. one of man and another of horse), viz. by imitating the figures of living things with pebbles¹¹, as some people bring numbers into the forms of triangle and square. Or (2) is it because harmony is a ratio of numbers, and so is man and everything else? But how are the attributes-white and sweet and hot-numbers? Evidently it is not the numbers that are the essence or the causes of the form; for the ratio is the essence, while the number the causes of the form; for the ratio is the essence, while the number is the matter. E.g. the essence of flesh or bone is number only in this way, ‘three parts of fire and two of earth’. And a number, whatever number it is, is always a number of certain things, either of parts of fire or earth or of units; but the essence is that there is so much of one thing to so much of another in the mixture; and this is no longer a number but a ratio of mixture of numbers, whether these are corporeal¹² or of any other kind.

Number, then, whether it be number in general or the number which consists of abstract units, is neither the cause as agent, nor the matter, nor the ratio and form of things. Nor, of course, is it the final cause.

1 simultaneously   

adv.同时发生地，同时进行地

参考例句：

• The radar beam can track a number of targets almost simultaneously.雷达波几乎可以同时追着多个目标。
• The Windows allow a computer user to execute multiple programs simultaneously.Windows允许计算机用户同时运行多个程序。

2 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。

3 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。

4 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。

5 juxtaposition   

n.毗邻，并置，并列

参考例句：

• The juxtaposition of these two remarks was startling.这两句话连在一起使人听了震惊。
• It is the result of the juxtaposition of contrasting colors.这是并列对比色的结果。

6 syllable   

n.音节；vt.分音节

参考例句：

• You put too much emphasis on the last syllable.你把最后一个音节读得太重。
• The stress on the last syllable is light.最后一个音节是轻音节。

7 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。

8 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。

9 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。

10 decided   

adj.决定了的，坚决的；明显的，明确的

参考例句：

• This gave them a decided advantage over their opponents.这使他们比对手具有明显的优势。
• There is a decided difference between British and Chinese way of greeting.英国人和中国人打招呼的方式有很明显的区别。

11 pebbles   

[复数]鹅卵石； 沙砾； 卵石，小圆石( pebble的名词复数 )

参考例句：

• The pebbles of the drive crunched under his feet. 汽车道上的小石子在他脚底下喀嚓作响。
• Line the pots with pebbles to ensure good drainage. 在罐子里铺一层鹅卵石，以确保排水良好。

12 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。