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Book XI Chapter 10
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The infinite is either that which is incapable1 of being traversed because it is not its nature to be traversed (this corresponds to the sense in which the voice is ‘invisible’), or that which admits only of incomplete traverse or scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited; further, a thing may be infinite in respect of addition or of subtraction2, or both. The infinite cannot be a separate, independent thing. For if it is neither a spatial3 magnitude nor a plurality, but infinity4 itself is its substance and not an accident of it, it will be indivisible; for the divisible is either magnitude or plurality. But if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this, nor are we examining this sort of infinite, but the infinite as untraversable. Further, how can an infinite exist by itself, unless number and magnitude also exist by themselvess-since infinity is an attribute of these? Further, if the infinite is an accident of something else, it cannot be qua infinite an element in things, as the invisible is not an element in speech, though the voice is invisible. And evidently the infinite cannot exist actually. For then any part of it that might be taken would be infinite (for ‘to be infinite’ and ‘the infinite’ are the same, if the infinite is substance and not predicated of a subject). Therefore it is either indivisible, or if it is partible, it is divisible into infinites; but the same thing cannot be many infinites (as a part of air is air, so a part of the infinite would be infinite, if the infinite is substance and a principle). Therefore it must be impartible and indivisible. But the actually infinite cannot be indivisible; for it must be of a certain quantity. Therefore infinity belongs to its subject incidentally. But if so, then (as we have said) it cannot be it that is a principle, but that of which it is an accident-the air or the even number.

This inquiry5 is universal; but that the infinite is not among sensible things, is evident from the following argument. If the definition of a body is ‘that which is bounded by planes’, there cannot be an infinite body either sensible or intelligible6; nor a separate and infinite number, for number or that which has a number is numerable. Concretely, the truth is evident from the following argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body, since the elements are limited in multitude. For the contraries must be equal and no one of them must be infinite; for if one of the two bodies falls at all short of the other in potency8, the finite will be destroyed by the infinite. And that each should be infinite is impossible. For body is that which has extension in all directions, and the infinite is the boundlessly9 extended, so that if the infinite is a body it will be infinite in every direction. Nor (b) can the infinite body be one and simple-neither, as some say, something apart from the elements, from which they generate these (for there is no such body apart from the elements; for everything can be resolved into that of which it consists, but no such product of analysis is observed except the simple bodies), nor fire nor any other of the elements. For apart from the question how any of them could be infinite, the All, even if it is finite, cannot either be or become any one of them, as Heraclitus says all things sometime become fire. The same argument applies to this as to the One which the natural philosophers posit7 besides the elements. For everything changes from contrary to contrary, e.g. from hot to cold.

Further, a sensible body is somewhere, and whole and part have the same proper place, e.g. the whole earth and part of the earth. Therefore if (a) the infinite body is homogeneous, it will be unmovable or it will be always moving. But this is impossible; for why should it rather rest, or move, down, up, or anywhere, rather than anywhere else? E.g. if there were a clod which were part of an infinite body, where will this move or rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole place, then? And how? (This is impossible.) What then is its rest or its movement? It will either rest everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still. But (b) if the All has unlike parts, the proper places of the parts are unlike also, and, firstly, the body of the All is not one except by contact, and, secondly10, the parts will be either finite or infinite in variety of kind. Finite they cannot be; for then those of one kind will be infinite in quantity and those of another will not (if the All is infinite), e.g. fire or water would be infinite, but such an infinite element would be destruction to the contrary elements. But if the parts are infinite and simple, their places also are infinite and there will be an infinite number of elements; and if this is impossible, and the places are finite, the All also must be limited.

In general, there cannot be an infinite body and also a proper place for bodies, if every sensible body has either weight or lightness. For it must move either towards the middle or upwards11, and the infinite either the whole or the half of it-cannot do either; for how will you divide it? Or how will part of the infinite be down and part up, or part extreme and part middle? Further, every sensible body is in a place, and there are six kinds of place, but these cannot exist in an infinite body. In general, if there cannot be an infinite place, there cannot be an infinite body; (and there cannot be an infinite place,) for that which is in a place is somewhere, and this means either up or down or in one of the other directions, and each of these is a limit.

The infinite is not the same in the sense that it is a single thing whether exhibited in distance or in movement or in time, but the posterior among these is called infinite in virtue12 of its relation to the prior; i.e. a movement is called infinite in virtue of the distance covered by the spatial movement or alteration13 or growth, and a time is called infinite because of the movement which occupies it.

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1 incapable w9ZxK     
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。
2 subtraction RsJwl     
n.减法,减去
参考例句:
  • We do addition and subtraction in arithmetic.在算术里,我们作加减运算。
  • They made a subtraction of 50 dollars from my salary.他们从我的薪水里扣除了五十美元。
3 spatial gvcww     
adj.空间的,占据空间的
参考例句:
  • This part of brain judges the spatial relationship between objects.大脑的这部分判断物体间的空间关系。
  • They said that time is the feeling of spatial displacement.他们说时间是空间位移的感觉。
4 infinity o7QxG     
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。
5 inquiry nbgzF     
n.打听,询问,调查,查问
参考例句:
  • Many parents have been pressing for an inquiry into the problem.许多家长迫切要求调查这个问题。
  • The field of inquiry has narrowed down to five persons.调查的范围已经缩小到只剩5个人了。
6 intelligible rbBzT     
adj.可理解的,明白易懂的,清楚的
参考例句:
  • This report would be intelligible only to an expert in computing.只有计算机运算专家才能看懂这份报告。
  • His argument was barely intelligible.他的论点不易理解。
7 posit nPHxx     
v.假定,认为
参考例句:
  • If she needs salvation,she will posit a savior.如果她需要救助,她就会设想一个救助者。
  • Other historians posit that she died of old age around 550 BC.别的史学家则认为她一直活到公元前550年左右才寿终正寝。
8 potency 9Smz8     
n. 效力,潜能
参考例句:
  • Alcohol increases the drug's potency.酒精能增加这种毒品的效力。
  • Sunscreen can lose its potency if left over winter in the bathroom cabinet.如果把防晒霜在盥洗室的壁橱里放一个冬天,就有可能失效。
9 boundlessly 4bc433b7008dfa4c13e8a09bc3946d1f     
adv.无穷地,无限地
参考例句:
10 secondly cjazXx     
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。
11 upwards lj5wR     
adv.向上,在更高处...以上
参考例句:
  • The trend of prices is still upwards.物价的趋向是仍在上涨。
  • The smoke rose straight upwards.烟一直向上升。
12 virtue BpqyH     
n.德行,美德;贞操;优点;功效,效力
参考例句:
  • He was considered to be a paragon of virtue.他被认为是品德尽善尽美的典范。
  • You need to decorate your mind with virtue.你应该用德行美化心灵。
13 alteration rxPzO     
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。


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