Chapter 4

The next question to consider is whether the elements are finite or infinite in number, and, if finite, what their number is. Let us first show reason or denying that their number is infinite, as some suppose. We begin with the view of Anaxagoras that all the homoeomerous bodies are elements. Any one who adopts this view misapprehends the meaning of element. Observation shows that even mixed bodies are often divisible into homoeomerous parts; examples are flesh, bone, wood, and stone. Since then the composite cannot be an element, not every homoeomerous body can be an element; only, as we said before, that which is not divisible into bodies different in form. But even taking ‘element’ as they do, they need not assert an infinity¹ of elements, since the hypothesis of a finite number will give identical results. Indeed even two or three such bodies serve the purpose as well, as Empedocles’ attempt shows. Again, even on their view it turns out that all things are not composed of homocomerous bodies. They do not pretend that a face is composed of faces, or that any other natural conformation is composed of parts like itself. Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved. This is the common demand of mathematicians², who always assume as principles things finite either in kind or in number. Again, if body is distinguished³ from body by the appropriate qualitative⁴ difference, and there is a limit to the number of differences (for the difference lies in qualities apprehended⁵ by sense, which are in fact finite in number, though this requires proof), then manifestly there is necessarily a limit to the number of elements.

There is, further, another view-that of Leucippus and Democritus of Abdera-the implications of which are also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by their combination and involution. Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning. And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so far to allot⁶ the sphere to fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element. Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate⁷ no other alteration⁸ in their theory. Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity. Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement. They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated⁹ by the relative sizes of their atoms, since then they could not be generated out of one another. The extrusion¹⁰ of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation of water, air, and earth from one another. Again, even on their own presuppositions it does not seem as if the clements would be infinite in number. The atoms differ in figure, and all figures are composed of pyramids, rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have their principles, and, whether these are one or two or more, the simple bodies must be the same in number as they. Again, if every element has its proper movement, and a simple body has a simple movement, and the number of simple movements is not infinite, because the simple motions are only two and the number of places is not infinite, on these grounds also we should have to deny that the number of elements is infinite.

1 infinity   

n.无限，无穷，大量

参考例句：

• It is impossible to count up to infinity.不可能数到无穷大。
• Theoretically,a line can extend into infinity.从理论上来说直线可以无限地延伸。

2 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

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 qualitative   

adj.性质上的，质的，定性的

参考例句：

• There are qualitative differences in the way children and adults think.孩子和成年人的思维方式有质的不同。
• Arms races have a quantitative and a qualitative aspects.军备竞赛具有数量和质量两个方面。

5 apprehended   

逮捕，拘押( apprehend的过去式和过去分词 )； 理解

参考例句：

• She apprehended the complicated law very quickly. 她很快理解了复杂的法律。
• The police apprehended the criminal. 警察逮捕了罪犯。

6 allot   

v.分配；拨给；n.部分；小块菜地

参考例句：

• The government is ready to allot houses in that area.政府准备在那个地区分配住房。
• Who will she allot the easy jobs to?她把轻活儿分给谁呢？

7 necessitate   

v.使成为必要，需要

参考例句：

• Your proposal would necessitate changing our plans.你的提议可能使我们的计划必须变更。
• The conversion will necessitate the complete rebuilding of the interior.转变就必需完善内部重建。

8 alteration   

n.变更，改变；蚀变

参考例句：

• The shirt needs alteration.这件衬衣需要改一改。
• He easily perceived there was an alteration in my countenance.他立刻看出我的脸色和往常有些不同。

9 differentiated   

区分，区别，辨别( differentiate的过去式和过去分词 )； 区别对待； 表明…间的差别，构成…间差别的特征

参考例句：

• The development of mouse kidney tubules requires two kinds of differentiated cells. 小鼠肾小管的发育需要有两种分化的细胞。
• In this enlargement, barley, alfalfa, and sugar beets can be differentiated. 在这张放大的照片上，大麦，苜蓿和甜菜都能被区分开。

10 extrusion   

n.挤出；推出；喷出；赶出

参考例句：

• The dough was formed into tubular grains by extrusion. 药团通过挤压而成管状药。 来自辞典例句
• Some other materials are added to facilitate extrusion and other manufacturing operations. 添加其它的一些物质是为了使挤压和别的加工过程更为方便。 来自辞典例句