Chapter 5

If Water, Air, and the like are a ‘matter’ of which the natural bodies consist, as some thinkers in fact believe, these ‘clements’ must be either one, or two, or more. Now they cannot all of them be one-they cannot, e.g. all be Air or Water or Fire or Earth-because ‘Change is into contraries’. For if they all were Air, then (assuming Air to persist) there will be ‘alteration’ instead of coming-to-be. Besides, nobody supposes a single ‘element’ to persist, as the basis of all, in such a way that it is Water as well as Air (or any other ‘element’) at the same time. So there will be a certain contrariety, i.e. a differentiating¹ quality: and the other member of this contrariety, e.g. heat, will belong to some other ‘element’, e.g. to Fire. But Fire will certainly not be ‘hot Air’. For a change of that kind (a) is ‘alteration’, and (b) is not what is observed. Moreover (c) if Air is again to result out of the Fire, it will do so by the conversion² of the hot into its contrary: this contrary, therefore, will belong to Air, and Air will be a cold something: hence it is impossible for Fire to be ‘hot Air’, since in that case the same thing will be simultaneously³ hot and cold. Both Fire and Air, therefore, will be something else which is the same; i.e. there will be some ‘matter’, other than either, common to both.

The same argument applies to all the ‘elements’, proving that there is no single one of them out of which they all originate. But neither is there, beside these four, some other body from which they originate-a something intermediate, e.g. between Air and Water (coarser than Air, but finer than Water), or between Air and Fire (coarser than Fire, but finer than Air). For the supposed ‘intermediate’ will be Air and Fire when a pair of contrasted qualities is added to it: but, since one of every two contrary qualities is a ‘privation’, the ‘intermediate’ never can exist-as some thinkers assert the ‘Boundless’ or the ‘Environing’ exists-in isolation⁴. It is, therefore, equally and indifferently any one of the ‘elements’, or else it is nothing.

Since, then, there is nothing-at least, nothing perceptible-prior to these, they must be all. That being so, either they must always persist and not be transformable into one another: or they must undergo transformation⁵-either all of them, or some only (as Plato wrote in the Timacus).’ Now it has been proved before that they must undergo reciprocal transformation. It has also been proved that the speed with which they come-to-be, one out of another, is not uniform-since the process of reciprocal transformation is relatively⁶ quick between the ‘elements’ with a ‘complementary factor’, but relatively slow between those which possess no such factor. Assuming, then, that the contrariety, in respect to which they are transformed, is one, the elements’ will inevitably⁷ be two: for it is ‘matter’ that is the ‘mean’ between the two contraries, and matter is imperceptible and inseparable from them. Since, however, the ‘elements’ are seen to be more than two, the contrarieties must at the least be two. But the contrarieties being two, the ‘elements’ must be four (as they evidently are) and cannot be three: for the couplings’ are four, since, though six are possible, the two in which the qualities are contrary to one another cannot occur.

These subjects have been discussed before:’ but the following arguments will make it clear that, since the ‘elements’ are transformed into one another, it is impossible for any one of them-whether it be at the end or in the middle-to be an ‘originative source’ of the rest. There can be no such ‘originative element’ at the ends: for all of them would then be Fire or Earth, and this theory amounts to the assertion that all things are made of Fire or Earth. Nor can a ‘middle-element’ be such an originative source’-as some thinkers suppose that Air is transformed both into Fire and into Water, and Water both into Air and into Earth, while the ‘end-elements’ are not further transformed into one another. For the process must come to a stop, and cannot continue ad infinitum in a straight line in either direction, since otherwise an infinite number of contrarieties would attach to the single ‘element’. Let E stand for Earth, W for Water, A for Air, and F for Fire. Then (i) since A is transformed into F and W, there will be a contrariety belonging to A F. Let these contraries be whiteness and blackness. Again (ii) since A is transformed into W, there will be another contrariety: for W is not the same as F. Let this second contrariety be dryness and moistness, D being dryness and M moistness. Now if, when A is transformed into W, the ‘white’ persists, Water will be moist and white: but if it does not persist, Water will be black since change is into contraries. Water, therefore, must be either white or black. Let it then be the first. On similar grounds, therefore, D (dryness) will also belong to F. Consequently F (Fire) as well as Air will be able to be transformed into Water: for it has qualities contrary to those of Water, since Fire was first taken to be black and then to be dry, while Water was moist and then showed itself white. Thus it is evident that all the ‘elements’ will be able to be transformed out of one another; and that, in the instances we have taken, E (Earth) also will contain the remaining two ‘complementary factors’, viz. the black and the moist (for these have not yet been coupled).

We have dealt with this last topic before the thesis we set out to prove. That thesis-viz. that the process cannot continue ad infinitum-will be clear from the following considerations. If Fire (which is represented by F) is not to revert⁸, but is to be transformed in turn into some other ‘element’ (e.g. into Q), a new contrariety, other than those mentioned, will belong to Fire and Q: for it has been assumed that Q is not the same as any of the four, E W A and F. Let K, then, belong to F and Y to Q. Then K will belong to all four, E W A and F: for they are transformed into one another. This last point, however, we may admit, has not yet been proved: but at any rate it is clear that if Q is to be transformed in turn into yet another ‘element’, yet another contrariety will belong not only to Q but also to F (Fire). And, similarly, every addition of a new ‘element’ will carry with it the attachment⁹ of a new contrariety to the preceding elements’. Consequently, if the ‘elements’ are infinitely¹⁰ many, there will also belong to the single ‘element’ an infinite number of contrarieties. But if that be so, it will be impossible to define any ‘element’: impossible also for any to come-to-be. For if one is to result from another, it will have to pass through such a vast number of contrarieties-and indeed even more than any determinate number. Consequently (i) into some ‘elements’ transformation will never be effected-viz. if the intermediates are infinite in number, as they must be if the ‘elements’ are infinitely many: further (ii) there will not even be a transformation of Air into Fire, if the contrarieties are infinitely many: moreover (iii) all the ‘elements’ become one. For all the contrarieties of the ‘elements’ above F must belong to those below F, and vice¹¹ versa: hence they will all be one.

1 differentiating   

[计] 微分的

参考例句：

• They succeed in differentiating the most commodity-like products. 在最通用的日用产品方面，它们也能独树一帜标新立异。
• The simplest and most effective method of differentiating areas is to use different colours. 区别面状要素最简单而又行之有效的办法，是使用不同的颜色。

2 conversion   

n.转化，转换，转变

参考例句：

• He underwent quite a conversion.他彻底变了。
• Waste conversion is a part of the production process.废物处理是生产过程的一个组成部分。

3 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。

4 isolation   

n.隔离，孤立，分解，分离

参考例句：

• The millionaire lived in complete isolation from the outside world.这位富翁过着与世隔绝的生活。
• He retired and lived in relative isolation.他退休后，生活比较孤寂。

5 transformation   

n.变化；改造；转变

参考例句：

• Going to college brought about a dramatic transformation in her outlook.上大学使她的观念发生了巨大的变化。
• He was struggling to make the transformation from single man to responsible husband.他正在努力使自己由单身汉变为可靠的丈夫。

6 relatively   

adv.比较...地，相对地

参考例句：

• The rabbit is a relatively recent introduction in Australia.兔子是相对较新引入澳大利亚的物种。
• The operation was relatively painless.手术相对来说不痛。

7 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。

8 revert   

v.恢复，复归，回到

参考例句：

• Let us revert to the earlier part of the chapter.让我们回到本章的前面部分。
• Shall we revert to the matter we talked about yesterday?我们接着昨天谈过的问题谈，好吗？

9 attachment   

n.附属物，附件；依恋；依附

参考例句：

• She has a great attachment to her sister.她十分依恋她的姐姐。
• She's on attachment to the Ministry of Defense.她现在隶属于国防部。

10 infinitely   

adv.无限地，无穷地

参考例句：

• There is an infinitely bright future ahead of us.我们有无限光明的前途。
• The universe is infinitely large.宇宙是无限大的。

11 vice   

n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的

参考例句：

• He guarded himself against vice.他避免染上坏习惯。
• They are sunk in the depth of vice.他们堕入了罪恶的深渊。