The Art of Logical
Thinking
逻辑思维的艺术
Chapter I.
Reasoning.
第一章 推理
“Reasoning” is defined as: “The act, process or art of exercising the faculty of reason; the act or faculty of employing reason in argument; argumentation, ratiocination; reasoning power; disputation, discussion, argumentation.” Stewart says: “The word reason itself is far from being precise in its meaning. In common and popular discourse it denotes that power by which we distinguish truth from falsehood, and right from wrong, and by which we are enabled to combine means for the attainment of particular ends.”
“推理”被定义为“行使推理能力的行为、过程或艺术；在论证过程中使用推理的行为和能力；论证推理；思辨能力；以及争论、讨论和论证。”思图尔特（Stewart）说：“推理一词本身并无精确之意。在我们普遍谈论中，它指的是我们用以区分真假、明辨是非并借此可以结合多种途径从而获得特殊目的的能力。”
By the employment of the reasoning faculties of the mind we compare objects presented to the mind as percepts or concepts, taking up the “raw materials” of thought and weaving them into more complex and elaborate mental fabrics which we call abstract and general ideas of truth. Brooks says: “It is the thinking power of the mind; the faculty which gives us what has been called thought knowledge, in distinction from sense knowledge. It may be regarded as the mental architect among the faculties; it transforms the material furnished by the senses … into new products, and thus builds up the temples of science and philosophy.” The last mentioned authority adds: “Its products are twofold, ideas and thoughts. An idea is a mental productwhich when expressed in words does not give a proposition; a thought is a mental product which embraces the relation of two or more ideas. The ideas of the understanding are of two general classes; abstract ideas and general ideas. The thoughts are also of two general classes; those pertaining to contingent truth and those pertaining to necessary truth. In contingent truth, we have facts, or immediate judgments, and general truths including laws and causes, derived from particular facts; in necessary truth we have axioms, or self evident truths, and the truths derived from them by reasoning, called theorems.”
通过采用思维推理能力，我们从呈现在脑海中的事物中形成知觉和概念。同时，我们使用思想的“原材料”进行复杂而精心的编织，从而形成我们谓之有关事实的抽象而普遍的概念。布鲁克（Brooks）说：“这是我们的思维能力，这种能力赋予我们思想的知识，与我们的感觉知识有别。这种能力可以被称为诸多能力中的思想构建能力。它把我们感官所提供的素材转化成了新的事物，从而构筑了科学和哲学的殿堂。”他又说：“思想的产物是两个层面的：概念和想法。概念是一种用语言表达无法给出命题的思想产物。而想法是包含两种或两种以上概念关系的思想产物。关于理解的概念总的可以分为两大类，抽象概念和普遍概念；想法也分为两大类，与偶然事实相关的想法和与必然事实相关的想法。偶然事实包含真相或直觉判断；普遍事实包含从特定事实中衍生出的规律和原因；必然事实包含公理、或者自圆其说的事实和通过推理从以上事实中获取的事实，我们谓之真理。”
In inviting you to consider the processes of reasoning, we are irresistibly reminded of the old story of one of Moliere’s plays in which one of the characters expresses surprise on learning that he “had been talking prose for forty years without knowing it.” As Jevons says in mentioning this: “Ninety nine people out of a hundred might be equally surprised on hearing that they had been converting propositions, syllogizing, falling into paralogisms, framing hypotheses and making classifications with genera and species. If asked whether they were logicians, they would probably answer, No! They would be partly right; for I believe that a large number even of educated persons have no clear idea of what logic is. Yet, in a certain way, everyone must have been a logician since he began to speak.”
在我们邀请你思考推理步骤时，我们势必会想到莫里哀（Moliere）剧本中的一个人物，当他了解到他 “四十年来一直在谈论无聊的议论却不自知”时表示了惊讶。提到此，杰文斯（Jevons）说：“当听说他们也曾经历转化命题，三段论证，陷入谬论，形成假说和分门别类的推理过程，99%的人也可能同样感到惊讶。如果问他们是不是逻辑学者，答案有可能是否。他们并不全错，因为我相信，很多即便受过教育的人也不清楚什么是逻辑。然而，从某种意义上来讲，每个人自他开始说话以来势必曾今是一个逻辑学家。”
So, in asking you to consider the processes of reasoning we are not assuming that you never have reasoned—on the contrary we are fully aware that you in connection with every other person, have reasoned all your mature life: ‘That is not the question. While everyone reasons, the fact is equally true that the majority of persons reason incorrectly. Many persons reason along lines far from correct and scientific, and suffer therefor and thereby. Some writers have claimed that the majority of persons are incapable of even fairly correct reasoning, pointing to the absurd ideas entertained by the masses of people as a proof of the statement. These writers are probably a little radical in their views and statements, but one is often struck with wonder at the evidences of incapacity for interpreting facts and impressions on the part of the general public. The masses of people accept the most absurd ideas as truth, providing they are gravely asserted by someone claiming authority. The most illogical ideas are accepted without dispute or examination, providing they are stated solemnly and authoritatively. Particularly in the respective fields of religion and politics do we find this blind acceptance of illogical ideas by the multitude. Mere assertion by the leaders seems sufficient for the multitude of followers to acquiesce.
所以在要求你思考推理步骤的时候，我们的假设并非你从未推理过。相反，我们充分知晓与任何其他人息息相关的你已就你的生活进行了仔细的思考和推理：毫无疑问，每个人都推理，而事实是大多数人的推理并不正确。很多人沿着远不正确和科学的思路推理并因此影响结论。有些作家声称大部分人甚至不能进行合理的推理。他们抱有荒谬的观点并以此为证据或论点。这些作家在表达观点和提出论点的时候可能有些偏激，然而，对于普通大众不能解释事物及其印象的事实证据，我们都会感到疑惑。只要某个声称权威的人严肃断定某事，大多数人就把这最最荒诞的想法归结为事实。只要有人庄重权威地阐明某些观点，那么即便是最无逻辑的思想也被毫无争议、不经检验地接纳。尤其在宗教和政治的各自领域里，我们发现大众对毫无逻辑的思想的盲目接受。似乎只要领导的断言就足以让大批追随者默许认可。
In order to reason correctly it is not merely necessary to have a good intellect. An athlete may have the proper proportions, good framework, and symmetrical muscles, but he cannot expect to cope with others of his kind unless he has learned to develop those muscles and to use them to the best advantage. And, in the same way, the man who wishes to reason correctly must develop his intellectual faculties and must also learn the art of using them to the best advantage. Otherwise, he will waste his mental energy and will be placed at a disadvantage when confronted with a trained logician in argument or debate. One who has witnessed a debate or argument between two men equally strong intellectually, one of whom is a trained logician and the other lacking this advantage, will never forget the impression produced upon him by the unequal struggle. The conflict is like that of a powerful wrestler, untrained in the little tricks and turn of the science, in the various principles of applying force in a certain way at a certain time, at a certain place, with a trained and experienced wrestler. Or of a conflict between a muscular giant untrained in the art of boxing, when confronted with a trained and experienced exponent of “the manly art.” The result of any such conflict is assured in advance. Therefore, everyone should refuse to rest content without a knowledge of the art of reasoning correctly, for otherwise he places himself under a heavy handicap in the race for success,and allows others, perhaps less well equipped mentally, to have a decided advantage over him.
正确推理不仅仅需要智慧。一个好的运动员可能身材比例合适，体形矫健，肌肉匀称，但除非他学会了如何发展并最好地使用他的肌肉，否则并不能指望他能够对付其他类似的运动员。同样，一个人希望正确推理，那么他必须开发他的智力能力并学会最佳使用此能力的艺术。否则，在论证或辩论过程中，面对一个训练有素的逻辑学者，他会浪费他的智慧力量并被置于劣势地位。见证过一场两个智力相当的人之间的辩论或争论，其中一人是一个训练有素的逻辑学者，另一人却缺乏这一优势，那么他就永远不会忘记这场并非势均力敌的较量带给他的印象。这样的较量就如同一个强大的摔跤运动员，未经有关小技巧，科学转身以及怎样在某个时间，某个地点以某种方式使用力量的不同准则的训练，去对阵一个有训练有经验的摔跤高手。或者是未经拳击艺术训练的肌肉猛男去面对一个有训练有经验的“男子气概”的典范。任何此类较量的结果早已预知。因此，任何一个人，在没有掌握正确推理的艺术知识时不应该盲目自足。否则，在角逐成功的过程中，他会置自己于重大困难中，而让别人，或许思想装备并不如他充分的人，取得决定性的胜利
Jevons says in this connection: “To be a good logician is, however, far more valuable than to be a good athlete; because logic teaches us to reason well, and reasoning gives us knowledge, and knowledge, as Lord Bacon said, is power. As athletes, men cannot for a moment compare with horses or tigers or monkeys. Yet, with the power of knowledge, men tame horses and shoot tigers and despise monkeys. The weakest framework with the most logical mind will conquer in the end, because it is easy to foresee the future, to calculate the result of actions, to avoid mistakes which might be fatal, and to discover the means of doing things which seemed impossible. If such little creatures as ants had better brains than men, they would either destroy men or make them into slaves. It is true that we cannot use our eyes and ears without getting some kind of knowledge, and the brute animals can do the same. But what gives power is the deeper knowledge called Science. People may see, and hear, and fool all their lives without really learning the nature of things they see. But reason is the mind’s eye, and enables us to see why things are, and when and how events may be made to happen or not to happen. The logician endeavors to learn exactly what this reason is which makes the power of men. We all, as I have said, must reason well or ill, but logic is the science of reasoning and enables us to distinguish between the good reasoning which leads to truth, and the bad reasoning which every day betrays people into error and misfortune.”
在这个关系中，杰文斯（Jevons）说：“要成为一个好的逻辑学者却远比成为一个好的运动员来得有价值。因为逻辑教会我们很好地推理，推理给予我们知识，而正如洛德.培根（Lord Bacon）所说，知识就是力量。作为运动员，人类永远不能跟马、老虎或者猴子比较。而有了知识的力量，人类却驯马，猎虎并凌驾于猴子之上。最薄弱的框架，加上最具逻辑的思维就会最后征服一切。因为如此就容易预见未来，计算行动的结果，避免潜在的、致命的错误，从而发现看似不可能的做事方法。如果像蚂蚁这样的生物拥有比人类还智慧的脑袋，他们就会摧毁或奴役人类。我们使用耳目势必获得某种知识，动物禽兽也能如此。而能够给予力量的是深度的科学知识。人们或许看、听，却未必真正学到他们所见事物的本质而愚昧无知虚度一生。但是推理是我们思想的眼睛，使我们看到事物的由来，看到何时，以怎样的方式，事物得以发生。”逻辑学者努力想要准确找到给予人类力量的推理能力。正如我说的，我们大家肯定有推理得好的也有坏的，但逻辑学是有关推理的科学，它使得我们能够区分好的推理和不好的推理。好的推理引领我们走向真理，而不好的推理每天却背叛我们，陷我们于错误和不幸中。”
In this volume we hope to be able to point out the methods and principles of correctly using the reasoning faculties of the mind, in a plain, simple manner, devoid of useless technicalities and academic discussion. We shall adhere, in the main, to the principles established by the best of the authorities of the old school of psychology, blending the same with those advanced by the best authorities of the New Psychology. No attempt to make of this book a school text book shall be made, for our soleobject and aim is to bring this important subject before the general public composed of people who have neither the time nor inclination to indulge in technical discussion nor academic hair splitting, but who desire to understand the underlying working principles of the Laws of Reasoning.
通过此书，我们希望能够以简单、平实的方式而不使用无用的技术和学术讨论找出正确使用人类推理能力的方法和原则。我们将主要秉承由最好的老的心理学权威群体所建立的原则，并结合由新的心理学权威群体所加强提升的原则。此书编写并不想要按照教科书的要求。我们唯一的目标是把这一重要课题介绍给那些普遍大众，他们即没有时间也没有打算去沉溺于技术讨论或学术思考但却想理解推理法则的根本工作原理。
