三段论(Syllogism)是现代科学推理的核心基础, 可以追根于亚里士多德 (Aristotle)。 一个完美的推理, 用英文表示为 “Sound”, 如果仅仅从逻辑的角度分析, 一个符合逻辑的推理,用英文表示为valid。 英文单词syllogism就词的构成而言是syn- + logizersthai, 起源于古希腊语, syn-表示合成, 而后半部分来自于拉丁语logos 表示 “思考, 思想, 推理”等意思。 Syllogism 中的logos和单词LEGEND有着历史的渊源。 中古英语就有silogisme的词汇, 到了十四世纪演变为现代的syllogism的形式。 韦氏字典解释该词为: “正式论证中的演绎推理形式, 包含大小前提和结论。 ( a deductive scheme of a formal argument consisting of a major and a minor premise and a conclusion)。 在大英百科全书中, 对三段论的解释比较详细, 英文原文如下:
In logic, a valid deductive argument having two premises and a conclusion. The traditional type is the categorical syllogism in which both premises and the conclusion are simple declarative statements that are constructed using only three simple terms between them, each term appearing twice (as a subject and as a predicate): “All men are mortal; no gods are mortal; therefore no men are gods.” The argument in such syllogisms is valid by virtue of the fact that it would not be possible to assert the premises and to deny the conclusion without contradicting oneself.
这一段是GMAT考生不得不看懂的内容, 否则很难理解逻辑的本质。 从而无法提高解题的速度和精确程度。 我现在把这段文字翻译如下:
在逻辑学中, 有效的演绎推理有两个前提和一个结论。 传统的形式是直言三段论。 在直言三段论中, 两个前提和一个结论是简单的陈述, 其构成仅仅包含三个项, 每个项要出现两次, 例如: 所有的人都是要死的, 神是不朽的, 因此没有人是神。 在这样一个三段论中, 推理是有效的, 结论成立。
因此, 考生应非产清楚, 一个三段论中有两个前提, 一个结论, 用公式表示为:
1. 所有的A 都是 B
2. 因为C 是 A
3. 所以C 是 B
1是大前提Assumption 或者叫做Major;2是小前提 minor;3 是结论conclusion。
GMAT的逻辑考试就是考核这个公式的应用, 根据这个公式, 进行命题, 无论命题的内容是什么, 考生不应为逻辑题中陈述的具体内容纷扰, 而是要找出命题中的三个项分别在哪里。就是用最简单的ABC 标志出来。答案一目了然。
The fewer restrictions there are on the advertising of legal services, the more lawyers there are who advertise their services, and the lawyers who advertise a specific service usually charge less for that service than lawyers who do not advertise. Therefore, if the state removes any of its current restrictions, such as the one against advertisements that do not specify fee arrangements, overall consumer legal costs will be lower than if the state retains its current restrictions.
If the statements in the passage are true, which of the following must be true?
A.
B.
C. If the restriction against advertisement that do not specify fee arrangements is removed, more lawyers will advertise their services.
D. If more lawyers advertise lower prices for specific services, some lawyers who do not advertise will also charge less than they currently charge for those services.
E. If the only restrictions on the advertising of legal services were those that apply to every type of advertising, most lawyers would advertise their services.
不少人在求解这个题目的时候绞尽脑汁也没有明白怎么回事, 还有不少人把题目全部翻译了一遍, 两遍, 甚至是八遍, 还是弄不明白到底是怎么回事。
我们把命题处理一下, 命题是传统的IF结构, 在命题开始, 用了个比较结构说: restrictions on advertising of legal services越少, lawyers who advertise their service就越多。 这个表达记为A 越少, B就越多。 用符号表达为A→B。 然后命题中用了个THEREFORE衔接, 如果没有A, 那么 overall consumer legal costs will be lower这个表示为C。 所以therefore后面的内容为if A 那么C, 符号表示为A→C。 我们看出, 命题实际上是两部分构成:
A = Restrictions on advertising of legal services
B= lawyers who advertise their services
C= overall consumer legal costs
命题既然说A→B ; A→C ,又问哪个是正确的, 当然只能是A→B 或者A→C 是正确的。
而备选项C 说: “如果没有A, 那么B” 其实这个选项就是A→B 所以这个选项 显然是正确的答案。