Book XIV Chapter 2

We must inquire generally, whether eternal things can consist of elements. If they do, they will have matter; for everything that consists of elements is composite. Since, then, even if a thing exists for ever, out of that of which it consists it would necessarily also, if it had come into being, have come into being, and since everything comes to be what it comes to be out of that which is it potentially (for it could not have come to be out of that which had not this capacity, nor could it consist of such elements), and since the potential can be either actual or not,-this being so, however everlasting¹ number or anything else that has matter is, it must be capable of not existing, just as that which is any number of years old is as capable of not existing as that which is a day old; if this is capable of not existing, so is that which has lasted for a time so long that it has no limit. They cannot, then, be eternal, since that which is capable of not existing is not eternal, as we had occasion to show in another context. If that which we are now saying is true universally-that no substance is eternal unless it is actuality-and if the elements are matter that underlies² substance, no eternal substance can have elements present in it, of which it consists.

There are some who describe the element which acts with the One as an indefinite dyad, and object to ‘the unequal’, reasonably enough, because of the ensuing difficulties; but they have got rid only of those objections which inevitably³ arise from the treatment of the unequal, i.e. the relative, as an element; those which arise apart from this opinion must confront even these thinkers, whether it is ideal number, or mathematical, that they construct out of those elements.

There are many causes which led them off into these explanations, and especially the fact that they framed the difficulty in an obsolete⁴ form. For they thought that all things that are would be one (viz. Being itself), if one did not join issue with and refute the saying of Parmenides:

‘For never will this he proved, that things that are not are.’

They thought it necessary to prove that that which is not is; for only thus-of that which is and something else-could the things that are be composed, if they are many.

But, first, if ‘being’ has many senses (for it means sometimes substance, sometimes that it is of a certain quality, sometimes that it is of a certain quantity, and at other times the other categories), what sort of ‘one’, then, are all the things that are, if non-being is to be supposed not to be? Is it the substances that are one, or the affections and similarly the other categories as well, or all together-so that the ‘this’ and the ‘such’ and the ‘so much’ and the other categories that indicate each some one class of being will all be one? But it is strange, or rather impossible, that the coming into play of a single thing should bring it about that part of that which is is a ‘this’, part a ‘such’, part a ‘so much’, part a ‘here’.

Secondly⁵, of what sort of non-being and being do the things that are consist? For ‘nonbeing’ also has many senses, since ‘being’ has; and ‘not being a man’ means not being a certain substance, ‘not being straight’ not being of a certain quality, ‘not being three cubits long’ not being of a certain quantity. What sort of being and non-being, then, by their union pluralize the things that are? This thinker means by the non-being the union of which with being pluralizes the things that are, the false and the character of falsity. This is also why it used to be said that we must assume something that is false, as geometers assume the line which is not a foot long to be a foot long. But this cannot be so. For neither do geometers assume anything false (for the enunciation⁶ is extraneous⁷ to the inference), nor is it non-being in this sense that the things that are are generated from or resolved into. But since ‘non-being’ taken in its various cases has as many senses as there are categories, and besides this the false is said not to be, and so is the potential, it is from this that generation proceeds, man from that which is not man but potentially man, and white from that which is not white but potentially white, and this whether it is some one thing that is generated or many.

The question evidently is, how being, in the sense of ‘the substances’, is many; for the things that are generated are numbers and lines and bodies. Now it is strange to inquire how being in the sense of the ‘what’ is many, and not how either qualities or quantities are many. For surely the indefinite dyad or ‘the great and the small’ is not a reason why there should be two kinds of white or many colours or flavours or shapes; for then these also would be numbers and units. But if they had attacked these other categories, they would have seen the cause of the plurality in substances also; for the same thing or something analogous⁸ is the cause. This aberration⁹ is the reason also why in seeking the opposite of being and the one, from which with being and the one the things that are proceed, they posited¹⁰ the relative term (i.e. the unequal), which is neither the contrary nor the contradictory¹¹ of these, and is one kind of being as ‘what’ and quality also are.

They should have asked this question also, how relative terms are many and not one. But as it is, they inquire how there are many units besides the first 1, but do not go on to inquire how there are many unequals besides the unequal. Yet they use them and speak of great and small, many and few (from which proceed numbers), long and short (from which proceeds the line), broad and narrow (from which proceeds the plane), deep and shallow (from which proceed solids); and they speak of yet more kinds of relative term. What is the reason, then, why there is a plurality of these?

It is necessary, then, as we say, to presuppose for each thing that which is it potentially; and the holder¹² of these views further declared what that is which is potentially a ‘this’ and a substance but is not in itself being-viz. that it is the relative (as if he had said ‘the qualitative’), which is neither potentially the one or being, nor the negation¹³ of the one nor of being, but one among beings. And it was much more necessary, as we said, if he was inquiring how beings are many, not to inquire about those in the same category-how there are many substances or many qualities-but how beings as a whole are many; for some are substances, some modifications¹⁴, some relations. In the categories other than substance there is yet another problem involved in the existence of plurality. Since they are not separable from substances, qualities and quantities are many just because their substratum becomes and is many; yet there ought to be a matter for each category; only it cannot be separable from substances. But in the case of ‘thises’, it is possible to explain how the ‘this’ is many things, unless a thing is to be treated as both a ‘this’ and a general character. The difficulty arising from the facts about substances is rather this, how there are actually many substances and not one.

But further, if the ‘this’ and the quantitative¹⁵ are not the same, we are not told how and why the things that are are many, but how quantities are many. For all ‘number’ means a quantity, and so does the ‘unit’, unless it means a measure or the quantitatively¹⁶ indivisible. If, then, the quantitative and the ‘what’ are different, we are not told whence or how the ‘what’ is many; but if any one says they are the same, he has to face many inconsistencies.

One might fix one’s attention also on the question, regarding the numbers, what justifies¹⁷ the belief that they exist. To the believer in Ideas they provide some sort of cause for existing things, since each number is an Idea, and the Idea is to other things somehow or other the cause of their being; for let this supposition be granted them. But as for him who does not hold this view because he sees the inherent objections to the Ideas (so that it is not for this reason that he posits¹⁸ numbers), but who posits mathematical number, why must we believe his statement that such number exists, and of what use is such number to other things? Neither does he who says it exists maintain that it is the cause of anything (he rather says it is a thing existing by itself), nor is it observed to be the cause of anything; for the theorems of arithmeticians will all be found true even of sensible things, as was said before.

1 everlasting   

adj.永恒的，持久的，无止境的

参考例句：

• These tyres are advertised as being everlasting.广告上说轮胎持久耐用。
• He believes in everlasting life after death.他相信死后有不朽的生命。

2 underlies   

v.位于或存在于（某物）之下( underlie的第三人称单数 )；构成…的基础（或起因），引起

参考例句：

• I think a lack of confidence underlies his manner. 我认为他表现出的态度是因为他缺乏信心。 来自《简明英汉词典》
• Try to figure out what feeling underlies your anger. 努力找出你的愤怒之下潜藏的情感。 来自辞典例句

3 inevitably   

adv.不可避免地；必然发生地

参考例句：

• In the way you go on,you are inevitably coming apart.照你们这样下去，毫无疑问是会散伙的。
• Technological changes will inevitably lead to unemployment.技术变革必然会导致失业。

4 obsolete   

adj.已废弃的，过时的

参考例句：

• These goods are obsolete and will not fetch much on the market.这些货品过时了，在市场上卖不了高价。
• They tried to hammer obsolete ideas into the young people's heads.他们竭力把陈旧思想灌输给青年。

5 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。

6 enunciation   

n.清晰的发音；表明，宣言；口齿

参考例句：

• He is always willing to enunciate his opinions on the subject of politics. 他总是愿意对政治问题发表意见。> enunciation / I9nQnsI5eIFn; I9nQnsI`eFEn/ n [C, U]。 来自辞典例句
• Be good at communicating,sense of responsibility,the work is careful,the enunciation is clear. 善于沟通，责任心强，工作细致，口齿清晰。 来自互联网

7 extraneous   

adj.体外的；外来的；外部的

参考例句：

• I can choose to ignore these extraneous thoughts.我可以选择无视这些外来的想法。
• Reductant from an extraneous source is introduced.外来的还原剂被引进来。

8 analogous   

adj.相似的；类似的

参考例句：

• The two situations are roughly analogous.两种情況大致相似。
• The company is in a position closely analogous to that of its main rival.该公司与主要竞争对手的处境极为相似。

9 aberration   

n.离开正路，脱离常规，色差

参考例句：

• The removal of the chromatic aberration is then of primary importance.这时消除色差具有头等重要性。
• Owing to a strange mental aberration he forgot his own name.由于一种莫名的精神错乱，他把自己的名字忘了。

10 posited   

v.假定，设想，假设( posit的过去式和过去分词 )

参考例句：

• Several writers have posited the idea of a universal consciousness. 有几个作者都假设存在普遍意识。 来自辞典例句
• All cash receipts should be recorded and de-posited daily. 所有的现金收据应该被每日记录和存放。 来自互联网

11 contradictory   

adj.反驳的，反对的，抗辩的；n.正反对，矛盾对立

参考例句：

• The argument is internally contradictory.论据本身自相矛盾。
• What he said was self-contradictory.他讲话前后不符。

12 holder   

n.持有者，占有者；(台，架等)支持物

参考例句：

• The holder of the office of chairman is reponsible for arranging meetings.担任主席职位的人负责安排会议。
• That runner is the holder of the world record for the hundred-yard dash.那位运动员是一百码赛跑世界纪录的保持者。

13 negation   

n.否定；否认

参考例句：

• No reasonable negation can be offered.没有合理的反对意见可以提出。
• The author boxed the compass of negation in his article.该作者在文章中依次探讨了各种反面的意见。

14 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》

15 quantitative   

adj.数量的，定量的

参考例句：

• He said it was only a quantitative difference.他说这仅仅是数量上的差别。
• We need to do some quantitative analysis of the drugs.我们对药物要进行定量分析。

16 quantitatively   

adv.数量上

参考例句：

• With the ease, radiation detectors can be used semi-quantitatively in the field. 使用射线探测器可以很方便地进行野外半定量测定。 来自辞典例句
• In other words, you are to analyze them quantitatively and qualitatively. 换句话说，你们要对它们进行量和质的分析。 来自辞典例句

17 justifies   

证明…有理( justify的第三人称单数 )； 为…辩护； 对…作出解释； 为…辩解（或辩护）

参考例句：

• Their frequency of use both justifies and requires the memorization. 频繁的使用需要记忆，也促进了记忆。 来自About Face 3交互设计精髓
• In my judgement the present end justifies the means. 照我的意见，只要目的正当，手段是可以不计较的。

18 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