INFINITY.

Who will give me a clear idea of infinity¹? I have never had an idea of it which was not excessively confused — possibly because I am a finite being.

What is that which is eternally going on without advancing — always reckoning without a sum total — dividing eternally without arriving at an indivisible particle?

It might seem as if the notion of infinity formed the bottom of the bucket of the Dana?des. Nevertheless, it is impossible that infinity should not exist. An infinite duration is demonstrable.

The commencement of existence is absurd; for nothing cannot originate something. When an atom exists we must necessarily conclude that it has existed from all eternity²; and hence an infinite duration rigorously demonstrated. But what is an infinite past? — an infinitude which I arrest in imagination whenever I please. Behold³! I exclaim, an infinity passed away; let us proceed to another. I distinguish between two eternities, the one before, the other behind me.

When, however, I reflect upon my words, I perceive that I have absurdly pronounced the words: “one eternity has passed away, and I am entering into another.” For at the moment that I thus talk, eternity endures, and the tide of time flows. Duration is not separable; and as something has ever been, something must ever be.

The infinite in duration, then, is linked to an uninterrupted chain. This infinite perpetuates⁴ itself, even at the instant that I say it has passed. Time begins and ends with me, but duration is infinite. The infinite is here quickly formed without, however, our possession of the ability to form a clear notion of it.

We are told of infinite space — what is space? Is it a being, or nothing at all? If it is a being, what is its nature? You cannot tell me. If it is nothing, nothing can have no quality; yet you tell me that it is penetrable⁵ and immense. I am so embarrassed, I cannot correctly call it either something or nothing.

In the meantime, I know not of anything which possesses more properties than a void. For if passing the confines of this globe, we are able to walk amidst this void, and thatch⁶ and build there when we possess materials for the purpose, this void or nothing is not opposed to whatever we might choose to do; for having no property it cannot hinder any; moreover, since it cannot hinder, neither can it serve us.

It is pretended that God created the world amidst nothing, and from nothing. That is abstruse⁷; it is preferable to think that there is an infinite space; but we are curious — and if there be infinite space, our faculties⁸ cannot fathom⁹ the nature of it. We call it immense, because we cannot measure it; but what then? We have only pronounced words.
Of the Infinite in Number.

We have adroitly¹⁰ defined the infinite in arithmetic by a love-knot, in this manner ∞; but we possess not therefore a clearer notion of it. This infinity is not like the others, a powerlessness of reaching a termination. We call the infinite in quantity any number soever, which surpasses the utmost number we are able to imagine.

When we seek the infinitely¹¹ small, we divide, and call that infinitely small which is less than the least assignable quantity. It is only another name for incapacity.
Is Matter Infinitely Divisible?

This question brings us back again precisely¹² to our inability of finding the remotest number. In thought we are able to divide a grain of sand, but in imagination only; and the incapacity of eternally dividing this grain is called infinity.

It is true, that matter is not always practically divisible, and if the last atom could be divided into two, it would no longer be the least; or if the least, it would not be divisible; or if divisible, what is the germ or origin of things? These are all abstruse queries¹³.
Of the Universe.

Is the universe bounded — is its extent immense — are the suns and planets without number? What advantage has the space which contains suns and planets, over the space which is void of them? Whether space be an existence or not, what is the space which we occupy, preferable to other space?

If our material heaven be not infinite, it is but a point in general extent. If it is infinite, it is an infinity to which something can always be added by the imagination.
Of the Infinite in Geometry.

We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads. It means, however, nothing more than that a square larger than any assignable square, surpasses a line larger than any assignable line, and bears no proportion to it.

It is a mode of operating, a mode of working geometrically, and the word infinite is a mere¹⁴ symbol.
Of Infinite Power, Wisdom, Goodness.

In the same manner, as we cannot form any positive idea of the infinite in duration, number, and extension, are we unable to form one in respect to physical and moral power.

We can easily conceive, that a powerful being has modified matter, caused worlds to circulate in space, and formed animals, vegetables, and metals. We are led to this idea by the perception of the want of power on the part of these beings to form themselves. We are also forced to allow, that the Great Being exists eternally by His own power, since He cannot have sprung from nothing; but we discover not so easily His infinity in magnitude, power, and moral attributes.

How are we to conceive infinite extent in a being called simple? and if he be uncompounded, what notions can we form of a simple being? We know God by His works, but we cannot understand Him by His Nature. If it is evident that we cannot understand His nature, is it not equally so, that we must remain ignorant of His attributes?

When we say that His power is infinite, do we mean anything more than that it is very great? Aware of the existence of pyramids of the height of six hundred feet, we can conceive them of the altitude of 600,000 feet.

Nothing can limit the power of the Eternal Being existing necessarily of Himself. Agreed: no antagonists¹⁵ circumscribe¹⁶ Him; but how convince me that He is not circumscribed¹⁷ by His own nature? Has all that has been said on this great subject been demonstrated?

We speak of His moral attributes, but we only judge of them by our own; and it is impossible to do otherwise. We attribute to Him justice, goodness, etc., only from the ideas we collect from the small degree of justice and goodness existing among ourselves. But, in fact, what connection is there between our qualities so uncertain and variable, and those of the Supreme¹⁸ Being?

Our idea of justice is only that of not allowing our own interest to usurp¹⁹ over the interest of another. The bread which a wife has kneaded out of the flour produced from the wheat which her husband has sown, belongs to her. A hungry savage²⁰ snatches away her bread, and the woman exclaims against such enormous injustice²¹. The savage quietly answers that nothing is more just, and that it was not for him and his family to expire of famine for the sake of an old woman.

At all events, the infinite justice we attribute to God can but little resemble the contradictory²² notions of justice of this woman and this savage; and yet, when we say that God is just, we only pronounce these words agreeably to our own ideas of justice.

We know of nothing belonging to virtue²³ more agreeable than frankness and cordiality, but to attribute infinite frankness and cordiality to God would amount to an absurdity²⁴.

We have such confused notions of the attributes of the Supreme Being, that some schools endow Him with prescience, an infinite foresight²⁵ which excludes all contingent²⁶ event, while other schools contend for prescience without contingency²⁷.

Lastly, since the Sorbonne has declared that God can make a stick divested²⁸ of two ends, and that the same thing can at once be and not be, we know not what to say, being in eternal fear of advancing a heresy²⁹. One thing may, however, be asserted without danger — that God is infinite, and man exceedingly bounded.

The mind of man is so extremely narrow, that Pascal has said: “Do you believe it impossible for God to be infinite and without parts? I wish to convince you of an existence infinite and indivisible — it is a mathematical point — moving everywhere with infinite swiftness, for it is in all places, and entire in every place.”

Nothing more absurd was ever asserted, and yet it has been said by the author of the “Provincial Letters.” It is sufficient to give men of sense the ague.

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 eternity   

n.不朽，来世；永恒，无穷

参考例句：

• The dull play seemed to last an eternity.这场乏味的剧似乎演个没完没了。
• Finally,Ying Tai and Shan Bo could be together for all of eternity.英台和山伯终能双宿双飞，永世相随。

3 behold   

v.看，注视，看到

参考例句：

• The industry of these little ants is wonderful to behold.这些小蚂蚁辛勤劳动的样子看上去真令人惊叹。
• The sunrise at the seaside was quite a sight to behold.海滨日出真是个奇景。

4 perpetuates   

n.使永存，使人记住不忘( perpetuate的名词复数 )；使永久化，使持久化，使持续

参考例句：

• Giving these events a lot of media coverage merely perpetuates the problem. 媒体大量地报道这些事件只会使问题持续下去。 来自《简明英汉词典》
• Lack of water perpetuates poverty, increases the risk of political instability, and affects global prosperity. 水资源短缺导致贫穷，使政局不稳，且影响全球的繁荣。 来自互联网

5 penetrable   

adj.可穿透的

参考例句：

• soil that is easily penetrable with a fork 能轻易下耙的土壤
• Perhaps the most aspect of this technology is that it is intellectually penetrable. 这个技术最重要的地方在于它是可以被理解贯通的。 来自互联网

6 thatch   

vt.用茅草覆盖…的顶部；n.茅草(屋)

参考例句：

• They lit a torch and set fire to the chapel's thatch.他们点着一支火把，放火烧了小教堂的茅草屋顶。
• They topped off the hut with a straw thatch. 他们给小屋盖上茅草屋顶。

7 abstruse   

adj.深奥的，难解的

参考例句：

• Einstein's theory of relativity is very abstruse.爱因斯坦的相对论非常难懂。
• The professor's lectures were so abstruse that students tended to avoid them.该教授的课程太深奥了，学生们纷纷躲避他的课。

8 faculties   

n.能力( faculty的名词复数 )；全体教职员；技巧；院

参考例句：

• Although he's ninety, his mental faculties remain unimpaired. 他虽年届九旬，但头脑仍然清晰。
• All your faculties have come into play in your work. 在你的工作中，你的全部才能已起到了作用。 来自《简明英汉词典》

9 fathom   

v.领悟，彻底了解

参考例句：

• I really couldn't fathom what he was talking about.我真搞不懂他在说些什么。
• What these people hoped to achieve is hard to fathom.这些人希望实现些什么目标难以揣测。

10 adroitly   

adv.熟练地，敏捷地

参考例句：

• He displayed the cigarette holder grandly on every occasion and had learned to manipulate it adroitly. 他学会了一套用手灵巧地摆弄烟嘴的动作，一有机会就要拿它炫耀一番。 来自辞典例句
• The waitress passes a fine menu to Molly who orders dishes adroitly. 女服务生捧来菜单递给茉莉，后者轻车熟路地点菜。 来自互联网

11 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。

12 precisely   

adv.恰好，正好，精确地，细致地

参考例句：

• It's precisely that sort of slick sales-talk that I mistrust.我不相信的正是那种油腔滑调的推销宣传。
• The man adjusted very precisely.那个人调得很准。

13 queries   

n.问题( query的名词复数 )；疑问；询问；问号v.质疑，对…表示疑问( query的第三人称单数 )；询问

参考例句：

• Our assistants will be happy to answer your queries. 我们的助理很乐意回答诸位的问题。
• Her queries were rhetorical,and best ignored. 她的质问只不过是说说而已，最好不予理睬。 来自《简明英汉词典》

14 mere   

adj.纯粹的；仅仅，只不过

参考例句：

• That is a mere repetition of what you said before.那不过是重复了你以前讲的话。
• It's a mere waste of time waiting any longer.再等下去纯粹是浪费时间。

15 antagonists   

对立[对抗] 者，对手，敌手( antagonist的名词复数 )； 对抗肌； 对抗药

参考例句：

• The cavalier defeated all the antagonists. 那位骑士打败了所有的敌手。
• The result was the entire reconstruction of the navies of both the antagonists. 双方的海军就从这场斗争里获得了根本的改造。

16 circumscribe   

v.在...周围划线，限制，约束

参考例句：

• Please circumscribe the words which are wrongly spelled.请将拼错的词圈出来。
• The principal has requested all teachers to circumscribe failures in red on the report cards.这项规定要求，所有老师均要在报告卡用红笔上标出错误所在。

17 circumscribed   

adj.[医]局限的：受限制或限于有限空间的v.在…周围划线( circumscribe的过去式和过去分词 )；划定…范围；限制；限定

参考例句：

• The power of the monarchy was circumscribed by the new law. 君主统治的权力受到了新法律的制约。
• His activities have been severely circumscribed since his illness. 自生病以来他的行动一直受到严格的限制。 来自《简明英汉词典》

18 supreme   

adj.极度的，最重要的；至高的，最高的

参考例句：

• It was the supreme moment in his life.那是他一生中最重要的时刻。
• He handed up the indictment to the supreme court.他把起诉书送交最高法院。

19 usurp   

vt.篡夺，霸占；vi.篡位

参考例句：

• Their position enabled them to usurp power.他们所处的地位使其得以篡权。
• You must not allow it to usurp a disproportionate share of your interest.你不应让它过多地占据你的兴趣。

20 savage   

adj.野蛮的；凶恶的，残暴的；n.未开化的人

参考例句：

• The poor man received a savage beating from the thugs.那可怜的人遭到暴徒的痛打。
• He has a savage temper.他脾气粗暴。

21 injustice   

n.非正义，不公正，不公平，侵犯（别人的）权利

参考例句：

• They complained of injustice in the way they had been treated.他们抱怨受到不公平的对待。
• All his life he has been struggling against injustice.他一生都在与不公正现象作斗争。

22 contradictory   

adj.反驳的，反对的，抗辩的；n.正反对，矛盾对立

参考例句：

• The argument is internally contradictory.论据本身自相矛盾。
• What he said was self-contradictory.他讲话前后不符。

23 virtue   

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。

24 absurdity   

n.荒谬，愚蠢；谬论

参考例句：

• The proposal borders upon the absurdity.这提议近乎荒谬。
• The absurdity of the situation made everyone laugh.情况的荒谬可笑使每个人都笑了。

25 foresight   

n.先见之明，深谋远虑

参考例句：

• The failure is the result of our lack of foresight.这次失败是由于我们缺乏远虑而造成的。
• It required a statesman's foresight and sagacity to make the decision.作出这个决定需要政治家的远见卓识。

26 contingent   

adj.视条件而定的；n.一组，代表团，分遣队

参考例句：

• The contingent marched in the direction of the Western Hills.队伍朝西山的方向前进。
• Whether or not we arrive on time is contingent on the weather.我们是否按时到达要视天气情况而定。

27 contingency   

n.意外事件，可能性

参考例句：

• We should be prepared for any contingency.我们应该对任何应急情况有所准备。
• A fire in our warehouse was a contingency that we had not expected.库房的一场大火是我们始料未及的。

28 divested   

v.剥夺( divest的过去式和过去分词 )；脱去（衣服）；2。从…取去…；1。（给某人）脱衣服

参考例句：

• He divested himself of his jacket. 他脱去了短上衣。
• He swiftly divested himself of his clothes. 他迅速脱掉衣服。 来自《简明英汉词典》

29 heresy   

n.异端邪说；异教

参考例句：

• We should denounce a heresy.我们应该公开指责异端邪说。
• It might be considered heresy to suggest such a notion.提出这样一个观点可能会被视为异端邪说。