BOOK III. OF INDUCTION. CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.

 § 1. The portion of the present inquiry¹ upon which we are now about to enter, may be considered as the principal, both from its surpassing in intricacy all the other branches, and because it relates to a process which has been shown in the preceding Book to be that in which the investigation² of nature essentially³ consists. We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions⁵, and the interpretation⁶ of inductions: that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction⁴ is, therefore, and what conditions render it legitimate⁷, cannot but be deemed the main question of the science of logic⁸—the question which includes all others. It is, however, one which professed⁹ writers on logic have almost entirely¹⁰ passed over. The generalities of the subject have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for induction itself what the rules of the syllogism¹¹ are for the interpretation of induction: while those by whom physical science has been carried to its present state of improvement—and who, to arrive at a complete theory of the process, needed only to generalize, and adapt to all varieties of problems, the methods which they themselves employed in their habitual¹² pursuits—never until very lately made any serious attempt to philosophize on the subject, nor regarded the mode in which [Pg 314]they arrived at their conclusions as deserving of study, independently of the conclusions themselves.

 

§ 2. For the purposes of the present inquiry, Induction may be defined, the operation of discovering and proving general propositions. It is true that (as already shown) the process of indirectly¹³ ascertaining¹⁵ individual facts, is as truly inductive as that by which we establish general truths. But it is not a different kind of induction; it is a form of the very same process: since, on the one hand, generals are but collections of particulars, definite in kind but indefinite in number; and on the other hand, whenever the evidence which we derive¹⁶ from observation of known cases justifies¹⁷ us in drawing an inference respecting even one unknown case, we should on the same evidence be justified¹⁸ in drawing a similar inference with respect to a whole class of cases. The inference either does not hold at all, or it holds in all cases of a certain description; in all cases which, in certain definable respects, resemble those we have observed.

 

If these remarks are just; if the principles and rules of inference are the same whether we infer general propositions or individual facts; it follows that a complete logic of the sciences would be also a complete logic of practical business and common life. Since there is no case of legitimate inference from experience, in which the conclusion may not legitimately¹⁹ be a general proposition; an analysis of the process by which general truths are arrived at, is virtually an analysis of all induction whatever. Whether we are inquiring into a scientific principle or into an individual fact, and whether we proceed by experiment or by ratiocination²⁰, every step in the train of inferences is essentially inductive, and the legitimacy²¹ of the induction depends in both cases on the same conditions.

 

True it is that in the case of the practical inquirer, who is endeavouring to ascertain¹⁴ facts not for the purposes of science but for those of business, such for instance as the advocate or the judge, the chief difficulty is one in which the principles of induction will afford him no assistance. It lies not in making his inductions, but in the selection of them; in choosing from [Pg 315]among all general propositions ascertained²² to be true, those which furnish marks by which he may trace whether the given subject possesses or not the predicate in question. In arguing a doubtful question of fact before a jury, the general propositions or principles to which the advocate appeals are mostly, in themselves, sufficiently²³ trite²⁴, and assented²⁵ to as soon as stated: his skill lies in bringing his case under those propositions or principles; in calling to mind such of the known or received maxims²⁶ of probability as admit of application to the case in hand, and selecting from among them those best adapted to his object. Success is here dependent on natural or acquired sagacity, aided by knowledge of the particular subject, and of subjects allied²⁷ with it. Invention, though it can be cultivated, cannot be reduced to rule; there is no science which will enable a man to bethink himself of that which will suit his purpose.

 

But when he has thought of something, science can tell him whether that which he has thought of will suit his purpose or not. The inquirer or arguer must be guided by his own knowledge and sagacity in the choice of the inductions out of which he will construct his argument. But the validity of the argument when constructed, depends on principles and must be tried by tests which are the same for all descriptions of inquiries²⁸, whether the result be to give A an estate, or to enrich science with a new general truth. In the one case and in the other, the senses, or testimony²⁹, must decide on the individual facts; the rules of the syllogism will determine whether, those facts being supposed correct, the case really falls within the formul? of the different inductions under which it has been successively brought; and finally, the legitimacy of the inductions themselves must be decided³⁰ by other rules, and these it is now our purpose to investigate. If this third part of the operation be, in many of the questions of practical life, not the most, but the least arduous³¹ portion of it, we have seen that this is also the case in some great departments of the field of science; in all those which are principally deductive, and most of all in mathematics; where the inductions themselves are few in number, and so obvious and elementary that they seem to stand in no need of the evidence of experience, while to combine them so as to [Pg 316]prove a given theorem or solve a problem, may call for the utmost powers of invention and contrivance with which our species is gifted.

 

If the identity of the logical processes which prove particular facts and those which establish general scientific truths, required any additional confirmation³², it would be sufficient to consider that in many branches of science, single facts have to be proved, as well as principles; facts as completely individual as any that are debated in a court of justice; but which are proved in the same manner as the other truths of the science, and without disturbing in any degree the homogeneity of its method. A remarkable³³ example of this is afforded by astronomy. The individual facts on which that science grounds its most important deductions³⁴, such facts as the magnitudes of the bodies of the solar system, their distances from one another, the figure of the earth, and its rotation³⁵, are scarcely any of them accessible to our means of direct observation: they are proved indirectly, by the aid of inductions founded on other facts which we can more easily reach. For example, the distance of the moon from the earth was determined³⁶ by a very circuitous³⁷ process. The share which direct observation had in the work consisted in ascertaining, at one and the same instant, the zenith distances of the moon, as seen from two points very remote from one another on the earth's surface. The ascertainment³⁸ of these angular distances ascertained their supplements; and since the angle at the earth's centre subtended by the distance between the two places of observation was deducible by spherical³⁹ trigonometry from the latitude⁴⁰ and longitude⁴¹ of those places, the angle at the moon subtended by the same line became the fourth angle of a quadrilateral of which the other three angles were known. The four angles being thus ascertained, and two sides of the quadrilateral being radii⁴² of the earth; the two remaining sides and the diagonal, or in other words, the moon's distance from the two places of observation and from the centre of the earth, could be ascertained, at least in terms of the earth's radius⁴³, from elementary theorems of geometry. At each step in this demonstration⁴⁴ we take in a [Pg 317]new induction, represented, in the aggregate⁴⁵ of its results, by a general proposition.

 

Not only is the process by which an individual astronomical⁴⁶ fact was thus ascertained, exactly similar to those by which the same science establishes its general truths, but also (as we have shown to be the case in all legitimate reasoning) a general proposition might have been concluded instead of a single fact. In strictness, indeed, the result of the reasoning is a general proposition; a theorem respecting the distance, not of the moon in particular, but of any inaccessible⁴⁷ object: showing in what relation that distance stands to certain other quantities. And although the moon is almost the only heavenly body the distance of which from the earth can really be thus ascertained, this is merely owing to the accidental circumstances of the other heavenly bodies, which render them incapable⁴⁸ of affording such data as the application of the theorem requires; for the theorem itself is as true of them as it is of the moon.[1]

 

 

We shall fall into no error, then, if in treating of Induction, we limit our attention to the establishment of general propositions. The principles and rules of Induction as directed to this end, are the principles and rules of all Induction; and the logic of Science is the universal Logic, applicable to all inquiries in which man can engage.

1 inquiry   

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。

2 investigation   

n.调查，调查研究

参考例句：

• In an investigation,a new fact became known, which told against him.在调查中新发现了一件对他不利的事实。
• He drew the conclusion by building on his own investigation.他根据自己的调查研究作出结论。

3 essentially   

adv.本质上，实质上，基本上

参考例句：

• Really great men are essentially modest.真正的伟人大都很谦虚。
• She is an essentially selfish person.她本质上是个自私自利的人。

4 induction   

n.感应，感应现象

参考例句：

• His induction as a teacher was a turning point in his life.他就任教师工作是他一生的转折点。
• The magnetic signals are sensed by induction coils.磁信号由感应线圈所检测。

5 inductions   

归纳（法）( induction的名词复数 )； （电或磁的）感应； 就职； 吸入

参考例句：

6 interpretation   

n.解释，说明，描述；艺术处理

参考例句：

• His statement admits of one interpretation only.他的话只有一种解释。
• Analysis and interpretation is a very personal thing.分析与说明是个很主观的事情。

7 legitimate   

adj.合法的，合理的，合乎逻辑的；v.使合法

参考例句：

• Sickness is a legitimate reason for asking for leave.生病是请假的一个正当的理由。
• That's a perfectly legitimate fear.怀有这种恐惧完全在情理之中。

8 logic   

n.逻辑(学)；逻辑性

参考例句：

• What sort of logic is that?这是什么逻辑？
• I don't follow the logic of your argument.我不明白你的论点逻辑性何在。

9 professed   

公开声称的，伪称的，已立誓信教的

参考例句：

• These, at least, were their professed reasons for pulling out of the deal. 至少这些是他们自称退出这宗交易的理由。
• Her manner professed a gaiety that she did not feel. 她的神态显出一种她并未实际感受到的快乐。

10 entirely   

ad.全部地，完整地；完全地，彻底地

参考例句：

• The fire was entirely caused by their neglect of duty. 那场火灾完全是由于他们失职而引起的。
• His life was entirely given up to the educational work. 他的一生统统献给了教育工作。

11 syllogism   

n.演绎法，三段论法

参考例句：

• The ramifications or the mystery of a syllogism can become a weariness and a bore.三段论证法的分歧或者神秘会变成一种无聊、一种麻烦。
• The unexpected bursts forth from the syllogism.三段论里常出岔子。

12 habitual   

adj.习惯性的；通常的，惯常的

参考例句：

• He is a habitual criminal.他是一个惯犯。
• They are habitual visitors to our house.他们是我家的常客。

13 indirectly   

adv.间接地，不直接了当地

参考例句：

• I heard the news indirectly.这消息我是间接听来的。
• They were approached indirectly through an intermediary.通过一位中间人，他们进行了间接接触。

14 ascertain   

vt.发现，确定，查明，弄清

参考例句：

• It's difficult to ascertain the coal deposits.煤储量很难探明。
• We must ascertain the responsibility in light of different situtations.我们必须根据不同情况判定责任。

15 ascertaining   

v.弄清，确定，查明( ascertain的现在分词 )

参考例句：

• I was ascertaining whether the cellar stretched out in front or behind. 我当时是要弄清楚地下室是朝前还是朝后延伸的。 来自辞典例句
• The design and ascertaining of permanent-magnet-biased magnetic bearing parameter are detailed introduced. 并对永磁偏置磁悬浮轴承参数的设计和确定进行了详细介绍。 来自互联网

16 derive   

v.取得；导出；引申；来自；源自；出自

参考例句：

• We derive our sustenance from the land.我们从土地获取食物。
• We shall derive much benefit from reading good novels.我们将从优秀小说中获得很大好处。

17 justifies   

证明…有理( justify的第三人称单数 )； 为…辩护； 对…作出解释； 为…辩解（或辩护）

参考例句：

• Their frequency of use both justifies and requires the memorization. 频繁的使用需要记忆，也促进了记忆。 来自About Face 3交互设计精髓
• In my judgement the present end justifies the means. 照我的意见，只要目的正当，手段是可以不计较的。

18 justified   

a.正当的，有理的

参考例句：

• She felt fully justified in asking for her money back. 她认为有充分的理由要求退款。
• The prisoner has certainly justified his claims by his actions. 那个囚犯确实已用自己的行动表明他的要求是正当的。

19 legitimately   

ad.合法地；正当地，合理地

参考例句：

• The radio is legitimately owned by the company. 该电台为这家公司所合法拥有。
• She looked for nothing save what might come legitimately and without the appearance of special favour. 她要的并不是男人们的额外恩赐，而是合法正当地得到的工作。 来自英汉文学 - 嘉莉妹妹

20 ratiocination   

n.推理；推断

参考例句：

• There's no difference of Win or lose,or good or bad in ratiocination.推理是没有胜负、好坏之分的。
• Your thesis is short for the accurate ratiocination to suppose your argument.你的论文缺少能证明你的论点的正确推理。

21 legitimacy   

n.合法，正当

参考例句：

• The newspaper was directly challenging the government's legitimacy.报纸直接质疑政府的合法性。
• Managing from the top down,we operate with full legitimacy.我们进行由上而下的管理有充分的合法性。

22 ascertained   

v.弄清，确定，查明( ascertain的过去式和过去分词 )

参考例句：

• The previously unidentified objects have now been definitely ascertained as being satellites. 原来所说的不明飞行物现在已证实是卫星。 来自《简明英汉词典》
• I ascertained that she was dead. 我断定她已经死了。 来自《简明英汉词典》

23 sufficiently   

adv.足够地，充分地

参考例句：

• It turned out he had not insured the house sufficiently.原来他没有给房屋投足保险。
• The new policy was sufficiently elastic to accommodate both views.新政策充分灵活地适用两种观点。

24 trite   

adj.陈腐的

参考例句：

• The movie is teeming with obvious and trite ideas.这部电影充斥着平铺直叙的陈腐观点。
• Yesterday,in the restaurant,Lorraine had seemed trite,blurred,worn away.昨天在饭店里，洛兰显得庸俗、堕落、衰老了。

25 assented   

同意，赞成( assent的过去式和过去分词 )

参考例句：

• The judge assented to allow the prisoner to speak. 法官同意允许犯人申辩。
• "No," assented Tom, "they don't kill the women -- they're too noble. “对，”汤姆表示赞同地说，“他们不杀女人——真伟大！

26 maxims   

n.格言，座右铭( maxim的名词复数 )

参考例句：

• Courts also draw freely on traditional maxims of construction. 法院也自由吸收传统的解释准则。 来自英汉非文学 - 行政法
• There are variant formulations of some of the maxims. 有些准则有多种表达方式。 来自辞典例句

27 allied   

adj.协约国的；同盟国的

参考例句：

• Britain was allied with the United States many times in history.历史上英国曾多次与美国结盟。
• Allied forces sustained heavy losses in the first few weeks of the campaign.同盟国在最初几周内遭受了巨大的损失。

28 inquiries   

n.调查( inquiry的名词复数 )；疑问；探究；打听

参考例句：

• He was released on bail pending further inquiries. 他获得保释，等候进一步调查。
• I have failed to reach them by postal inquiries. 我未能通过邮政查询与他们取得联系。 来自《现代汉英综合大词典》

29 testimony   

n.证词；见证，证明

参考例句：

• The testimony given by him is dubious.他所作的证据是可疑的。
• He was called in to bear testimony to what the police officer said.他被传入为警官所说的话作证。

30 decided   

adj.决定了的，坚决的；明显的，明确的

参考例句：

• This gave them a decided advantage over their opponents.这使他们比对手具有明显的优势。
• There is a decided difference between British and Chinese way of greeting.英国人和中国人打招呼的方式有很明显的区别。

31 arduous   

adj.艰苦的，费力的，陡峭的

参考例句：

• We must have patience in doing arduous work.我们做艰苦的工作要有耐性。
• The task was more arduous than he had calculated.这项任务比他所估计的要艰巨得多。

32 confirmation   

n.证实，确认，批准

参考例句：

• We are waiting for confirmation of the news.我们正在等待证实那个消息。
• We need confirmation in writing before we can send your order out.给你们发送订购的货物之前，我们需要书面确认。

33 remarkable   

adj.显著的，异常的，非凡的，值得注意的

参考例句：

• She has made remarkable headway in her writing skills.她在写作技巧方面有了长足进步。
• These cars are remarkable for the quietness of their engines.这些汽车因发动机没有噪音而不同凡响。

34 deductions   

扣除( deduction的名词复数 )； 结论； 扣除的量； 推演

参考例句：

• Many of the older officers trusted agents sightings more than cryptanalysts'deductions. 许多年纪比较大的军官往往相信特务的发现，而不怎么相信密码分析员的推断。
• You know how you rush at things,jump to conclusions without proper deductions. 你知道你处理问题是多么仓促，毫无合适的演绎就仓促下结论。

35 rotation   

n.旋转；循环，轮流

参考例句：

• Crop rotation helps prevent soil erosion.农作物轮作有助于防止水土流失。
• The workers in this workshop do day and night shifts in weekly rotation.这个车间的工人上白班和上夜班每周轮换一次。

36 determined   

adj.坚定的；有决心的

参考例句：

• I have determined on going to Tibet after graduation.我已决定毕业后去西藏。
• He determined to view the rooms behind the office.他决定查看一下办公室后面的房间。

37 circuitous   

adj.迂回的路的，迂曲的，绕行的

参考例句：

• They took a circuitous route to avoid reporters.他们绕道避开了记者。
• The explanation was circuitous and puzzling.这个解释很迂曲，让人困惑不解。

38 ascertainment   

n.探查，发现，确认

参考例句：

• Part 1 introduces the ascertainment of key stuff in state-owned commercial banks. 第1部分介绍了国有商业银行核心员工的界定。 来自互联网
• IV The judicial ascertainment and criminal liability of involuntary dangerous crime. 过失危险犯的司法认定及刑事责任。 来自互联网

39 spherical   

adj.球形的；球面的

参考例句：

• The Earth is a nearly spherical planet.地球是一个近似球体的行星。
• Many engineers shy away from spherical projection methods.许多工程师对球面投影法有畏难情绪。

40 latitude   

n.纬度，行动或言论的自由(范围)，(pl.)地区

参考例句：

• The latitude of the island is 20 degrees south.该岛的纬度是南纬20度。
• The two cities are at approximately the same latitude.这两个城市差不多位于同一纬度上。

41 longitude   

n.经线，经度

参考例句：

• The city is at longitude 21°east.这个城市位于东经21度。
• He noted the latitude and longitude,then made a mark on the admiralty chart.他记下纬度和经度，然后在航海图上做了个标记。

42 radii   

n.半径；半径（距离）( radius的名词复数 )；用半径度量的圆形面积；半径范围；桡骨

参考例句：

• Hence, the damage radii can not be determined from overpressure alone. 因此，破坏半径不能单单由超压力大小来决定。 来自辞典例句
• It is now necessary to introduce a sign convention for radii of curvature. 现在必须介绍曲率半径的正负号规则。 来自辞典例句

43 radius   

n.半径，半径范围；有效航程，范围，界限

参考例句：

• He has visited every shop within a radius of two miles.周围两英里以内的店铺他都去过。
• We are measuring the radius of the circle.我们正在测量圆的半径。

44 demonstration   

n.表明，示范，论证，示威

参考例句：

• His new book is a demonstration of his patriotism.他写的新书是他的爱国精神的证明。
• He gave a demonstration of the new technique then and there.他当场表演了这种新的操作方法。

45 aggregate   

adj.总计的，集合的；n.总数；v.合计；集合

参考例句：

• The football team had a low goal aggregate last season.这支足球队上个赛季的进球总数很少。
• The money collected will aggregate a thousand dollars.进帐总额将达一千美元。

46 astronomical   

adj.天文学的，（数字）极大的

参考例句：

• He was an expert on ancient Chinese astronomical literature.他是研究中国古代天文学文献的专家。
• Houses in the village are selling for astronomical prices.乡村的房价正在飙升。

47 inaccessible   

adj.达不到的，难接近的

参考例句：

• This novel seems to me among the most inaccessible.这本书对我来说是最难懂的小说之一。
• The top of Mount Everest is the most inaccessible place in the world.珠穆朗玛峰是世界上最难到达的地方。

48 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。