This is indeed the first question we have to ask: is generation a fact or not? Earlier speculation6 was at variance7 both with itself and with the views here put forward as to the true answer to this question. Some removed generation and destruction from the world altogether. Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of movement, but if so they belong to another and a higher inquiry than the study of nature. They, however, had no idea of any form of being other than the substance of things perceived; and when they saw, what no one previously8 had seen, that there could be no knowledge or wisdom without some such unchanging entities9, they naturally transferred what was true of them to things perceived. Others, perhaps intentionally10, maintain precisely11 the contrary opinion to this. It has been asserted that everything in the world was subject to generation and nothing was ungenerated, but that after being generated some things remained indestructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers12, but afterwards outside his circle by the earliest natural philosophers. But what these thinkers maintained was that all else has been generated and, as they said, ‘is flowing away, nothing having any solidity, except one single thing which persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus and many others. And some subject all bodies whatever to generation, by means of the composition and separation of planes.
Discussion of the other views may be postponed13. But this last theory which composes every body of planes is, as the most superficial observation shows, in many respects in plain contradiction with mathematics. It is, however, wrong to remove the foundations of a science unless you can replace them with others more convincing. And, secondly14, the same theory which composes solids of planes clearly composes planes of lines and lines of points, so that a part of a line need not be a line. This matter has been already considered in our discussion of movement, where we have shown that an indivisible length is impossible. But with respect to natural bodies there are impossibilities involved in the view which asserts indivisible lines, which we may briefly15 consider at this point. For the impossible consequences which result from this view in the mathematical sphere will reproduce themselves when it is applied16 to physical bodies, but there will be difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and physics with a more concrete object. There are many attributes necessarily present in physical bodies which are necessarily excluded by indivisibility; all attributes, in fact, which are divisible. There can be nothing divisible in an indivisible thing, but the attributes of bodies are all divisible in one of two ways. They are divisible into kinds, as colour is divided into white and black, and they are divisible per accidens when that which has them is divisible. In this latter sense attributes which are simple are nevertheless divisible. Attributes of this kind will serve, therefore, to illustrate17 the impossibility of the view. It is impossible, if two parts of a thing have no weight, that the two together should have weight. But either all perceptible bodies or some, such as earth and water, have weight, as these thinkers would themselves admit. Now if the point has no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body has weight. It is, further, manifest that their point cannot have weight. For while a heavy thing may always be heavier than something and a light thing lighter18 than something, a thing which is heavier or lighter than something need not be itself heavy or light, just as a large thing is larger than others, but what is larger is not always large. A thing which, judged absolutely, is small may none the less be larger than other things. Whatever, then, is heavy and also heavier than something else, must exceed this by something which is heavy. A heavy thing therefore is always divisible. But it is common ground that a point is indivisible. Again, suppose that what is heavy or weight is a dense19 body, and what is light rare. Dense differs from rare in containing more matter in the same cubic area. A point, then, if it may be heavy or light, may be dense or rare. But the dense is divisible while a point is indivisible. And if what is heavy must be either hard or soft, an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it cannot; and if it can be pressed in it is divisible.
Moreover, no weight can consist of parts not possessing weight. For how, except by the merest fiction, can they specify20 the number and character of the parts which will produce weight? And, further, when one weight is greater than another, the difference is a third weight; from which it will follow that every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points will superior in weight to it, a thing which has weight. But the difference between weight and weight must be a weight, as the difference between white and whiter is white. Here the difference which makes the superior weight heavier is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight.
Further, to assume, on the one hand, that the planes can only be put in linear contact would be ridiculous. For just as there are two ways of putting lines together, namely, end to and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end. But if, similarly, in putting the lanes together, superficial contact is allowed as an alternative to linear, that method will give them bodies which are not any element nor composed of elements. Again, if it is the number of planes in a body that makes one heavier than another, as the Timaeus explains, clearly the line and the point will have weight. For the three cases are, as we said before, analogous21. But if the reason of differences of weight is not this, but rather the heaviness of earth and the lightness of fire, then some of the planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earthplane, I mean, will be heavier than the fire-plane. In general, the result is either that there is no magnitude at all, or that all magnitude could be done away with. For a point is to a line as a line is to a plane and as a plane is to a body. Now the various forms in passing into one another will each be resolved into its ultimate constituents22. It might happen therefore that nothing existed except points, and that there was no body at all. A further consideration is that if time is similarly constituted, there would be, or might be, a time at which it was done away with. For the indivisible now is like a point in a line. The same consequences follow from composing the heaven of numbers, as some of the Pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight.
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1
alterations
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| n.改动( alteration的名词复数 )；更改；变化；改变 | |
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2
transformations
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| n.变化( transformation的名词复数 )；转换；转换；变换 | |
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3
inquiry
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| n.打听，询问，调查，查问 | |
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4
inspection
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| n.检查，审查，检阅 | |
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5
remains
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| n.剩余物，残留物；遗体，遗迹 | |
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6
speculation
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| n.思索，沉思；猜测；投机 | |
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7
variance
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| n.矛盾，不同 | |
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8
previously
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| adv.以前，先前（地） | |
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9
entities
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| 实体对像； 实体，独立存在体，实际存在物( entity的名词复数 ) | |
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10
intentionally
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| ad.故意地，有意地 | |
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11
precisely
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| adv.恰好，正好，精确地，细致地 | |
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12
followers
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| 追随者( follower的名词复数 )； 用户； 契据的附面； 从动件 | |
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13
postponed
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| vt.& vi.延期，缓办，（使）延迟vt.把…放在次要地位；[语]把…放在后面（或句尾）vi.（疟疾等）延缓发作（或复发） | |
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14
secondly
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| adv.第二，其次 | |
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15
briefly
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| adv.简单地，简短地 | |
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16
applied
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| adj.应用的；v.应用，适用 | |
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17
illustrate
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| v.举例说明，阐明；图解，加插图 | |
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18
lighter
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| n.打火机，点火器；驳船；v.用驳船运送；light的比较级 | |
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19
dense
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| a.密集的，稠密的，浓密的；密度大的 | |
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20
specify
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| vt.指定，详细说明 | |
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21
analogous
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| adj.相似的；类似的 | |
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22
constituents
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| n.选民( constituent的名词复数 )；成分；构成部分；要素 | |
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