Book X Chapter 1

WE have said previously¹, in our distinction of the various meanings of words, that ‘one’ has several meanings; the things that are directly and of their own nature and not accidentally called one may be summarized under four heads, though the word is used in more senses. (1) There is the continuous, either in general, or especially that which is continuous by nature and not by contact nor by being together; and of these, that has more unity² and is prior, whose movement is more indivisible and simpler. (2) That which is a whole and has a certain shape and form is one in a still higher degree; and especially if a thing is of this sort by nature, and not by force like the things which are unified³ by glue or nails or by being tied together, i.e. if it has in itself the cause of its continuity. A thing is of this sort because its movement is one and indivisible in place and time; so that evidently if a thing has by nature a principle of movement that is of the first kind (i.e. local movement) and the first in that kind (i.e. circular movement), this is in the primary sense one extended thing. Some things, then, are one in this way, qua continuous or whole, and the other things that are one are those whose definition is one. Of this sort are the things the thought of which is one, i.e. those the thought of which is indivisible; and it is indivisible if the thing is indivisible in kind or in number. (3) In number, then, the individual is indivisible, and (4) in kind, that which in intelligibility⁴ and in knowledge is indivisible, so that that which causes substances to be one must be one in the primary sense. ‘One’, then, has all these meanings-the naturally continuous and the whole, and the individual and the universal. And all these are one because in some cases the movement, in others the thought or the definition is indivisible.

But it must be observed that the questions, what sort of things are said to be one, and what it is to be one and what is the definition of it, should not be assumed to be the same. ‘One’ has all these meanings, and each of the things to which one of these kinds of unity belongs will be one; but ‘to be one’ will sometimes mean being one of these things, and sometimes being something else which is even nearer to the meaning of the word ‘one’ while these other things approximate to its application. This is also true of ‘element’ or ‘cause’, if one had both to specify⁵ the things of which it is predicable and to render the definition of the word. For in a sense fire is an element (and doubtless also ‘the indefinite’ or something else of the sort is by its own nature the element), but in a sense it is not; for it is not the same thing to be fire and to be an element, but while as a particular thing with a nature of its own fire is an element, the name ‘element’ means that it has this attribute, that there is something which is made of it as a primary constituent⁶. And so with ‘cause’ and ‘one’ and all such terms. For this reason, too, ‘to be one’ means ‘to be indivisible, being essentially⁷ one means a “this” and capable of being isolated⁸ either in place, or in form or thought’; or perhaps ‘to be whole and indivisible’; but it means especially ‘to be the first measure of a kind’, and most strictly⁹ of quantity; for it is from this that it has been extended to the other categories. For measure is that by which quantity is known; and quantity qua quantity is known either by a ‘one’ or by a number, and all number is known by a ‘one’. Therefore all quantity qua quantity is known by the one, and that by which quantities are primarily known is the one itself; and so the one is the starting-point of number qua number. And hence in the other classes too ‘measure’ means that by which each is first known, and the measure of each is a unit-in length, in breadth, in depth, in weight, in speed. (The words ‘weight’ and ‘speed’ are common to both contraries; for each of them has two meanings-’weight’ means both that which has any amount of gravity and that which has an excess of gravity, and ‘speed’ both that which has any amount of movement and that which has an excess of movement; for even the slow has a certain speed and the comparatively light a certain weight.)

In all these, then, the measure and starting-point is something one and indivisible, since even in lines we treat as indivisible the line a foot long. For everywhere we seek as the measure something one and indivisible; and this is that which is simple either in quality or in quantity. Now where it is thought impossible to take away or to add, there the measure is exact (hence that of number is most exact; for we posit¹⁰ the unit as indivisible in every respect); but in all other cases we imitate this sort of measure. For in the case of a furlong or a talent or of anything comparatively large any addition or subtraction¹¹ might more easily escape our notice than in the case of something smaller; so that the first thing from which, as far as our perception goes, nothing can be subtracted, all men make the measure, whether of liquids or of solids, whether of weight or of size; and they think they know the quantity when they know it by means of this measure. And indeed they know movement too by the simple movement and the quickest; for this occupies least time. And so in astronomy a ‘one’ of this sort is the starting-point and measure (for they assume the movement of the heavens to be uniform and the quickest, and judge the others by reference to it), and in music the quarter-tone (because it is the least interval), and in speech the letter. And all these are ones in this sense — not that ‘one’ is something predicable in the same sense of all of these, but in the sense we have mentioned.

But the measure is not always one in number — sometimes there are several; e.g. the quarter-tones (not to the ear, but as determined¹² by the ratios) are two, and the articulate sounds by which we measure are more than one, and the diagonal of the square and its side are measured by two quantities, and all spatial¹³ magnitudes reveal similar varieties of unit. Thus, then, the one is the measure of all things, because we come to know the elements in the substance by dividing the things either in respect of quantity or in respect of kind. And the one is indivisible just because the first of each class of things is indivisible. But it is not in the same way that every ‘one’ is indivisible e.g. a foot and a unit; the latter is indivisible in every respect, while the former must be placed among things which are undivided to perception, as has been said already-only to perception, for doubtless every continuous thing is divisible.

The measure is always homogeneous with the thing measured; the measure of spatial magnitudes is a spatial magnitude, and in particular that of length is a length, that of breadth a breadth, that of articulate sound an articulate sound, that of weight a weight, that of units a unit. (For we must state the matter so, and not say that the measure of numbers is a number; we ought indeed to say this if we were to use the corresponding form of words, but the claim does not really correspond-it is as if one claimed that the measure of units is units and not a unit; number is a plurality of units.)

Knowledge, also, and perception, we call the measure of things for the same reason, because we come to know something by them-while as a matter of fact they are measured rather than measure other things. But it is with us as if some one else measured us and we came to know how big we are by seeing that he applied¹⁴ the cubit-measure to such and such a fraction of us. But Protagoras says ‘man is the measure of all things’, as if he had said ‘the man who knows’ or ‘the man who perceives’; and these because they have respectively knowledge and perception, which we say are the measures of objects. Such thinkers are saying nothing, then, while they appear to be saying something remarkable¹⁵.

Evidently, then, unity in the strictest sense, if we define it according to the meaning of the word, is a measure, and most properly of quantity, and secondly¹⁶ of quality. And some things will be one if they are indivisible in quantity, and others if they are indivisible in quality; and so that which is one is indivisible, either absolutely or qua one.

1 previously   

adv.以前，先前（地）

参考例句：

• The bicycle tyre blew out at a previously damaged point.自行车胎在以前损坏过的地方又爆开了。
• Let me digress for a moment and explain what had happened previously.让我岔开一会儿，解释原先发生了什么。

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 unified   

(unify 的过去式和过去分词)； 统一的； 统一标准的； 一元化的

参考例句：

• The teacher unified the answer of her pupil with hers. 老师核对了学生的答案。
• The First Emperor of Qin unified China in 221 B.C. 秦始皇于公元前221年统一中国。

4 intelligibility   

n.可理解性，可理解的事物

参考例句：

• Further research on the effects of different characteristics on intelligibility is necessary. 不同的特征对字码可懂度的影响力的进一步研究是必要的。 来自互联网
• Demand concisely intelligibility, word number 30 or so thanks! 要求简洁明了，字数30左右谢谢啦！ 来自互联网

5 specify   

vt.指定，详细说明

参考例句：

• We should specify a time and a place for the meeting.我们应指定会议的时间和地点。
• Please specify what you will do.请你详述一下你将做什么。

6 constituent   

n.选民；成分，组分；adj.组成的，构成的

参考例句：

• Sugar is the main constituent of candy.食糖是糖果的主要成分。
• Fibre is a natural constituent of a healthy diet.纤维是健康饮食的天然组成部分。

7 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。

8 isolated   

adj.与世隔绝的

参考例句：

• His bad behaviour was just an isolated incident. 他的不良行为只是个别事件。
• Patients with the disease should be isolated. 这种病的患者应予以隔离。

9 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。

10 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。

11 subtraction   

n.减法，减去

参考例句：

• We do addition and subtraction in arithmetic.在算术里,我们作加减运算。
• They made a subtraction of 50 dollars from my salary.他们从我的薪水里扣除了五十美元。

12 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。

13 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。

14 applied   

adj.应用的；v.应用，适用

参考例句：

• She plans to take a course in applied linguistics.她打算学习应用语言学课程。
• This cream is best applied to the face at night.这种乳霜最好晚上擦脸用。

15 remarkable   

adj.显著的，异常的，非凡的，值得注意的

参考例句：

• She has made remarkable headway in her writing skills.她在写作技巧方面有了长足进步。
• These cars are remarkable for the quietness of their engines.这些汽车因发动机没有噪音而不同凡响。

16 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。