Book III Chapter 5

(14) A question connected with these is whether numbers and bodies and planes and points are substances of a kind, or not. If they are not, it baffles us to say what being is and what the substances of things are. For modifications¹ and movements and relations and dispositions² and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a ‘this’. And as to the things which might seem most of all to indicate substance, water and earth and fire and air, of which composite bodies consist, heat and cold and the like are modifications of these, not substances, and the body which is thus modified alone persists as something real and as a substance. But, on the other hand, the body is surely less of a substance than the surface, and the surface than the line, and the line than the unit and the point. For the body is bounded by these; and they are thought to be capable of existing without body, but body incapable³ of existing without these. This is why, while most of the philosophers and the earlier among them thought that substance and being were identical with body, and that all other things were modifications of this, so that the first principles of the bodies were the first principles of being, the more recent and those who were held to be wiser thought numbers were the first principles. As we said, then, if these are not substance, there is no substance and no being at all; for the accidents of these it cannot be right to call beings.

But if this is admitted, that lines and points are substance more than bodies, but we do not see to what sort of bodies these could belong (for they cannot be in perceptible bodies), there can be no substance.-Further, these are all evidently divisions of body,-one in breadth, another in depth, another in length. Besides this, no sort of shape is present in the solid more than any other; so that if the Hermes is not in the stone, neither is the half of the cube in the cube as something determinate; therefore the surface is not in it either; for if any sort of surface were in it, the surface which marks off the half of the cube would be in it too. And the same account applies to the line and to the point and the unit. Therefore, if on the one hand body is in the highest degree substance, and on the other hand these things are so more than body, but these are not even instances of substance, it baffles us to say what being is and what the substance of things is.-For besides what has been said, the questions of generation and instruction confront us with further paradoxes⁴. For if substance, not having existed before, now exists, or having existed before, afterwards does not exist, this change is thought to be accompanied by a process of becoming or perishing; but points and lines and surfaces cannot be in process either of becoming or of perishing, when they at one time exist and at another do not. For when bodies come into contact or are divided, their boundaries simultaneously⁵ become one in the one case when they touch, and two in the other-when they are divided; so that when they have been put together one boundary does not exist but has perished, and when they have been divided the boundaries exist which before did not exist (for it cannot be said that the point, which is indivisible, was divided into two). And if the boundaries come into being and cease to be, from what do they come into being? A similar account may also be given of the ‘now’ in time; for this also cannot be in process of coming into being or of ceasing to be, but yet seems to be always different, which shows that it is not a substance. And evidently the same is true of points and lines and planes; for the same argument applies, since they are all alike either limits or divisions.

1 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》

2 dispositions   

安排( disposition的名词复数 )； 倾向； （财产、金钱的）处置； 气质

参考例句：

• We got out some information about the enemy's dispositions from the captured enemy officer. 我们从捕获的敌军官那里问出一些有关敌军部署的情况。
• Elasticity, solubility, inflammability are paradigm cases of dispositions in natural objects. 伸缩性、可缩性、易燃性是天然物体倾向性的范例。

3 incapable   

adj.无能力的，不能做某事的

参考例句：

• He would be incapable of committing such a cruel deed.他不会做出这么残忍的事。
• Computers are incapable of creative thought.计算机不会创造性地思维。

4 paradoxes   

n.似非而是的隽语，看似矛盾而实际却可能正确的说法( paradox的名词复数 )；用于语言文学中的上述隽语；有矛盾特点的人[事物，情况]

参考例句：

• Contradictions and paradoxes arose in increasing numbers. 矛盾和悖论越来越多。 来自辞典例句
• As far as these paradoxes are concerned, the garden definitely a heterotopia. 就这些吊诡性而言，花园无疑地是个异质空间。 来自互联网

5 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。