第一章 批判性推理的基础知识

本章你将了解：

● GMAT中的逻辑是什么

● GMAT批判性推理题目的简介

● 批判性推理题目的问题问法和解法是否有关

● 如何区分前提和结论

● 如何将题目分类，如何解题

1.1 逻辑概述

GMAT考生经常称“GMAT批判性推理”这类题型为“逻辑”。虽然这个称谓不甚严谨，但也基本上概括了这种题型的特点。逻辑是一门研究推理、论证之原则、规范和方法的学问，焦点是正确的推理或论证的条件。

狭义上，逻辑推理可以分成两类：演绎推理和归纳推理。所谓演绎推理，又称必然推理，其特点是前提必然包含结论。通俗点说，所谓演绎推理，是一种若前提正确，结论必然正确的推理，例如：

前提1：小明周三一定会穿衬衫。

前提2：今天是周三。

结论：小明今天会穿衬衫。

由本例可知，若前提1和前提2均是正确的，那么结论必然是正确的。实际上，在演绎推理中，前提永远包含结论。但是，生活中的推理往往不是演绎推理，我们面对的信息不完全，由这些不完全的信息做出的推论经常是有漏洞的，不准确的。为了寻求人类推理的奥秘，特别是推理的因果规律，人们构建了另一类逻辑——归纳推理。所谓归纳推理，又称或然推理，是一种与观察、经验、实验、比较概括、检验等一系列活动相联系的推理方法。它要面对信息不完全、主观偏差、实际条件制约、预见等因素，因而具有不确定性。并且我们可以对其他人做出的归纳推理做出自己的评估，例如：可以削弱或加强他人的归纳推理，例如：

前提：美国1935～1940年的汽油消耗由于世界大战期间采取了配额限制而下降了35%，与此同时，患肺癌的美国白人人数也下降了几乎相同的百分比。1941～1950年因肺癌死亡的人数增加了19倍，而同一时期汽油的消耗量也增加了相同的比率。

结论：汽油消耗是造成美国人患肺癌的重要原因。由本例可知，就算前提正确，结论也不一定是正确的。在归纳推理中，前提不包含结论。

在批判性推理这类考题中，演绎推理和归纳推理均有涉及。考查归纳推理的题目数量占据题目总数量的将近90%，剩下的将近10%的题目则考查演绎推理。

1.2 GMAT批判性推理题目初探

首先回顾一下绪论中讲到的批判性推理的题目形式。

例题

The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution.Therefore,just as the Earth exists life,so the Moon exists life.Which of the following,if true,most seriously weakens the conclusion above?

（A） The Moon’s environment being tough,there can be no biological existence.

（B） The Moon’s temperature is quite different from the Earth’s.

（C） Rotation and revolution have little effect on some kinds of life.

（D） There are no signs of life on the Moon by far.

（E） lt is easy for human beings to survey the Moon using the advanced technology.

任意一道批判性推理的题目均由一个推理文段、一个问题和五个选项组成。不同题目的推理文段和五个选项均不相同，但是问题的问法却很有规律，甚至可以被归类为五大种类。

这五大类分别为：

（1） Which of the following,if true,most seriously weakens the conclusion above?

（2） Which of the following,if true,most strengthens the argument above?

（3） Which of the following is an assumption on which the argument depends?

（4） Which of the following would it be most useful for the clinic to establish in order to make its decision?

（5） lf the statements above are true,which of the following must also be true?

这五种问法简称为：削弱、加强、假设、评估、演绎问法。

1.3 不同问法的相同考法

正是由于问法的趋同性，很多GMAT考生会将不同的问法归类在一起，然后分别针对不

同的问法做训练，以期找到每种问法的解决方案，甚至为不同的问法总结出不同的解题方法。但是，实际上，这些不同的问法只是GMAT使用的障眼法。不同的问法在原理上没有任何区别，下面我们给出此现象的解释。

假设D是一个事件，它有可能成立，也有可能不成立。如果不成立，其不成立的原因能且仅能是A、B或C，如下图：

由上述假设易知，若问如何来削弱事件D，那么我们提出的事件A、B或C均可以回答这个问题。因此我们可以称事件A、B或C为对事件D的削弱。下面我们来讨论什么是对事件D的加强。实际上，要想加强事件D很简单，令事件A、B、或C在当前情况下一定不存在即可。

简单证明如下：

我们用事件A来举例，事件B和C同理。对“A一定不存在”这个情况取“极限”，即假设在当前情况下，A、B、C这三个事件均不存在，那么根据最初的假设，当前事件D一定是成立的（若事件D不成立，那么是且仅是由于事件A、B或C导致的。

若这三个事件均不存在，那么事件D必定成立。）。如果我们仅仅指出A、B、C只有A不存在，虽然不能保证事件D成立，但是至少可以加强事件D成立的可能性。

由此可知，若A是D的削弱，那么not A是D的加强（请注意，这里的not A不是指除了A以外的所有都是加强，而是对A的取非，表示A一定不存在）。这个概念可能会和我们现有的知识体系有所不同，我们总认为可以“直接加强”，而不用绕着弯子地去“对削弱取非”。但是在逻辑学中，根本不存在“直接加强”，甚至可以说不存在所谓的“加强”，所有的“加强”都是“对削弱取非”后的结果。

由此可知，加强问法和削弱问法本质上是相同的。

什么是“假设”呢？假设其实也是加强，例如：

（a） 1+X=4

（b） X=3

我们可以称（b）是（a）成立的一个假设。显然，（b）也肯定算是（a）的一个加强。因此，我们可以将“假设”称为“重要的加强（Key Support）”。

由此可知，假设问法和加强问法在本质上是相同的。

那么“评估”呢？在逻辑学中，评估一个论证只有一种方法，那就是“提问题”。例如：我做出如下推理：为了减肥，我决定不吃饭了。小明对我的这个推理提出了一个问题：“你不吃饭真的可以减肥吗？”如果我能完美地回答这个问题，例如：“可以啊，不吃饭可以减少脂肪的摄入，如果保持每天的代谢量不变，那么就可以减肥”。显然，我的推理被加强了；如果这个问题问得我哑口无言，不知道该怎么回答，那么，我的推理就已经被削弱了。因此，提问题是评估推理的唯一方法。在GMAT考试中，一般“评估题”的选项都是一般疑问句，例如：

Whether the principles on which the machine operates have been known to science for a long time?

若我们对这个一般疑问句回答“Yes”可以加强推理文段，回答“No”可以削弱推理文段；或者回答“Yes”可以削弱推理文段，回答“No”可以加强推理文段，那么该选项即为评估题型的答案。

由此可知，评估问法和削弱/加强问法本质上是相同的。

最后一种“演绎问法”我们将会在第七章进行单独讨论，此处不做赘述。

对上述内容总结如下：

削弱：A/B/C

加强：not A/not B/not C

假设：not A/not B/not C

评估：A和not A/B和not B/C和not C

值得注意的是，有两种问法看起来和上述问法均不相同：

（1）The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution. Therefore,just as the Earth exists life,so the Moon exists life,since____.

实际上，（1）的这种问法和“加强问法”完全相同。让我们给出结论产生的“原因”，就是问如何“加强”推理文段。

（2）The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution.However,although the Earth exists life,the Moon does not exist life.

Which of the following,if true,does most to explain the apparently surprising result?

（A） The Moon’s environment being tough,there can be no biological existence.

（B） The Moon’s temperature is quite different from the Earth’s.

（C） Rotation and revolution have little effect on some kinds of life.

（D） There are no signs of life on the Moon by far.

（E） lt is easy for human beings to survey the Moon using the advanced technology.

在GMAT中，较为常见的题型是：A→B，之后问我们如何削弱该推理。现在的这种问法属于反其道而行之，即A,however,not B，之后问我们如何解释结论中not B这个情况。实际上，两种问法在原则上完全相同。试想，如果我们有能力削弱A→B，那么自然可以解释为什么“A不能推出B”，即A,however,not B。因此，（2）和原例题完全相同，依然相当于问如何来削弱A→B，答案也依然是（B）。

因此，所有不同的问法实际上没有本质区别，只要我们能找到A/B/C，就可以找到所有问法的答案了。那么，既然问题问法没有本质区别，那什么是有区别的呢？关于这个问题，我们必须得从推理文段的结构说起。

1.4 正确区分前提和结论

批判性推理，要考生批判的是推理的文段，而不是选项，更不是问题，因此，我们必须更加仔细地研究题目中的推理文段。正如绪论中讲到的，几乎每一个推理文段都可以分成两个部分，即前提和结论。如何区分“前提”和“结论”呢？我们给出如下两种方法：

1.4.1结论信号词

在很多GMAT批判性推理的考题中，结论的前面会出现一个信号词。当出现这类信号词时，后面必出现该推理文段的结论。这类信号词包括：therefore,consequently,clearly,thus等等。例题中用了结论信号词therefore。

The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution.Therefore,just as the Earth exists life,so the Moon exists life.

Therefore之后为例题推理文段的结论句部分（虽然最后的小半句才是真正的结论句，但是找到therefore，也就基本找到结论句了）。

1.4.2 被支持的句子

有些GMAT考题中没有结论信号词，抑或是我们人为地将例题中的therefore去掉，例如：

The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution.Just as the Earth exists life,so the Moon exists life.

进行如此操作后，结论句依然为粗体字部分。由此观之，信号词本身并不影响我们对于结论句的选取。实际上，若题目中没有结论信号词，我们就需要从语义上判断结论。在整个推理文段中，一定有且仅有一句话是被其他句子所支持的，而其他的句子都是为这句话服务的。这个被支持的句子就是“结论句”；其他句子都是“前提句”。在例题中，显然the Moon exists life是被Just as the Earth exists life以及其他句子所支持的，因此它就是结论句。

值得注意的是，从经验上来讲，在GMAT批判性推理考题中，很多题目的结论句都出现在推理文段的末尾。因此，我们需要对末尾的句子更加留心。

练习

判断下列推理文段的前提和结论。

1. A program instituted by a state government to raise money allows homeowners to prepay their future property taxes at the current rate.Even if the government were to raise the tax rate in a subsequent year,any prepaid taxes would allow the homeowner to maintain taxes at the lower rate,lowering the overall property tax burden overtime. For this reason,homeowners should participate in the program.

2. A recent report by the Press Club determined that although only eight percent of those members entering the Club were in fact correspondent members as opposed to non-correspondent members,these members represented fifteen percent of all the members entering the club.Clearly,correspondent members are more likely to enter the Press Club on a regular basis than non-correspondent members.

3. lt costs much less to grow an acre of grapes in California than it costs to grow an acre of watermelons in Oklahoma.This fact should be obvious to anyone who reads last year’s annual farm report,which clearly shows that many millions of dollars more were spent last year growing watermelons in Oklahoma than were spent growing grapes in California.

4. Editorial:To stem the influx of illegal immigrants,the government is planning to construct a wall along our entire border with Country Y.This wall,however,will do little to actually reduce the number of illegal immigrants.Because few economic opportunities exist in Country Y,individuals will simply develop other creative ways to enter our nation.

5. Advertising Executive:More than 10 million households now own digital video recorders that can fast-forward over television commercials;approximately 75%of these households fast-forward over at least one commercial per 30-minute program. Because television commercials are not as widely watched as they used to be,they are much less cost-effective today.

6. The Smithtown Theatre,which stages old plays,has announced an expansion that will double its capacity along with its operating costs.The theatre is only slightly profitable at present.ln addition,all of the current customers live in Smithtown,and the population of the town is not expected to increase in the next several years.Thus,the expansion of the Smithtown Theatre will prove unprofitable.

7. The cutback in physical education is the primary contributing factor to North High School’s increasing failure rate on the year-end physical fitness examination.Last year,when students participated in gym class on a daily basis,85 percent of the school’s seniors passed the test.Clearly,fewer sessions of gym class lead to reduced fitness.

8. Over the past decade,many companies have begun using automated telephone services;callers hear a machine-generated voice and are able to select options using the numbers on the telephone keypad.Research shows that callers are more patient when the machine-generated voice is that of a woman.Thus,smaller companies that cannot afford an automated service should consider hiring women,rather than men,to interact with customers by phone.

9. One fast-acting tablet contains twice the pain reliever found in a tablet of regular Aspirin.A consumer will have to take two Aspirin tablets in order to get the relief provided by one fast-acting tablet.Since a bottle of fast-acting Aspirin costs the same as a bottle of regular Aspirin,consumers can be expected to switch to fast-acting Aspirin.

10. ln a newly released book Decline of the Novelist,the author argues that novelists today lack technical skills that were common among novelists during the past century.ln this regard,the book might be right,since its analysis of 200 novels—100 contemporary and 100 non-contemporary—demonstrates convincingly that few contemporary novelists exhibit the same skill level as that of non-contemporary novelists.

答案及解析

判断下列推理文段的前提和结论。

1. A program instituted by a state government to raise money allows homeowners to prepay their future property taxes at the current rate.Even if the government were to raise the tax rate in a subsequent year,any prepaid taxes would allow the homeowner to maintain taxes at the lower rate,lowering the overall property tax burden overtime.For this reason,homeowners should participate in the program.

2. A recent report by the Press Club determined that although only eight percent of those members entering the Club were in fact correspondent members as opposed to non-correspondent members,these members represented fifteen percent of all the members entering the club.Clearly,correspondent members are more likely to enter the Press Club on a regular basis than non-correspondent members.

3. lt costs much less to grow an acre of grapes in California than it costs to grow an acre of watermelons in Oklahoma.This fact should be obvious to anyone who reads last year’s annual farm report,which clearly shows that many millions of dollars more were spent last year growing watermelons in Oklahoma than were spent growing grapes in California.

4. Editorial:To stem the influx of illegal immigrants,the government is planning to construct a wall along our entire border with Country Y.This wall,however,will do little to actually reduce the number of illegal immigrants,because few economic opportunities exist in Country Y,individuals will simply develop other creative ways to enter our nation.

5. Advertising Executive:More than 10 million households now own digital video recorders that can fast-forward over television commercials;approximately 75%of these households fast-forward over at least one commercial per 30-minute program.Because television commercials are not as widely watched as they used to be,they are much less cost-effective today.

6. The Smithtown Theatre,which stages old plays,has announced an expansion that will double its capacity along with its operating costs.The theatre is only slightly profitable at present.ln addition,all of the current customers live in Smithtown,and the population of the town is not expected to increase in the next several years.Thus,the expansion of the Smithtown Theatre will prove unprofitable.

7. The cutback in physical education is the primary contributing factor to North High School’s increasing failure rate on the year-end physical fitness examination.Last year,when students participated in gym class on a daily basis,85 percent of the school’s seniors passed the test.Clearly,fewer sessions of gym class lead to reduced fitness.

8. Over the past decade,many companies have begun using automated telephone services;callers hear a machine-generated voice and are able to select options using the numbers on the telephone keypad.Research shows that callers are more patient when the machine-generated voice is that of a woman.Thus,smaller companies that cannot afford an automated service should consider hiring women,rather than men,to interact with customers by phone.

9. One fast-acting tablet contains twice the pain reliever found in a tablet of regular Aspirin.A consumer will have to take two Aspirin tablets in order to get the relief provided by one fast-acting tablet.Since a bottle of fast-acting Aspirin costs the same as a bottle of regular Aspirin,consumers can be expected to switch to fast-acting Aspirin.

10. ln a newly released book Decline of the Novelist,the author argues that novelists today lack technical skills that were common among novelists during the past century.ln this regard,the book might be right,since its analysis of 200 novels—100 contemporary and 100 non-contemporary—demonstrates convincingly that few contemporary novelists exhibit the same skill level as that of non-contemporary novelists.

也可以认为the book might be right是本题的结论。

1.5 按照推理方式给题目分类

正如绪论中讲到的那样，推理的本质是一个从前提到结论的过程，它强调的是前提和结论的逻辑关系。在GMAT批判性推理题目中，我们应该按照前提和结论的逻辑关系来给题目进行分类。在逻辑学中，前提和结论不同的逻辑关系被称为不同的推理方式。不同的推理方式有它自己固定的评估方向。也就是说，只要我们能判断清楚推理文段的推方式，那么其评估的方向就是固定的。通俗点说，在给定的推理方式下，答案选项基本是确定的。若某个选项符合该推理文段的评估方向，则该选项能成为答案；反之，若某个选项不符合该推理文段的评估方向，则该选项不能成为答案，可以直接排除。接下来的章节中我们将着重对GMAT考试中出现的六种推理方式分别做详细的介绍，这六种推理方式为：

（1）类比/枚举推理

（2）方案推理

（3）相关→因果推理

（4）果因推理

（5）因果推理

（6）演绎推理

批判性问题

刚才我们讲到，不同的推理方式具有它自己固定的评估方向。在“1.3不同问法的相同考法”这个部分中已经讨论过，在逻辑学中，评估推理文段的方法只有一种，即用“提问题”的方式。当时举了一个非常实际的例子（减肥），现在我们将这个例子推而广之。对于不同的推理方式，可以提出不同的批判性问题。我们称这些能评估某种推理方式的问题为这种推理方式的“批判性问题集”。“批判性问题”是由英语Critical Question（简称CQ）直接翻译而来的。每一种推理方式会有自己的“批判性问题集”。每一个批判性问题揭示了评估这种推理方式的一个方向，通俗点说，若选项符合批判性问题所指出的方向，则该选项可以为答案；反之，该选项必须被排除。

例题

The Earth has many properties in common with the Moon.For example,each of them belongs to the solar system,is nonluminous,and has rotation and revolution.Therefore,just as the Earth exists life,so the Moon exists life.

Which of the following,if true,most seriously weakens the conclusion above?

（A） The Moon’s environment being tough,there can be no biological existence.

（B） The Moon’s temperature is quite different from the Earth’s.

（C） Rotation and revolution have little effect on some kinds of life.

（D） There are no signs of life on the Moon by far.

（E） lt is easy for human beings to survey the Moon using the advanced technology.

该例题的结论句为the Moon exists life。在接下来的章节中我们会讲到，这道例题的推理方式为“类比推理”。类比的对象为Earth和Moon。在逻辑学中，类比推理具有两个CQ：

CQ1：相似性问题：Earth和Moon真的相似么？是否存在某些重要差异？

CQ2：反案例问题：是否存在另一个案例C，它也相似于Earth/Moon，但是在C身上就没有生命？

若某一个选项符合两个CQ之一，则该选项为答案；反之，该选项必须排除。

显然，只有（B）提到了Earth和Moon的重要差异，属于CQ1（相似性问题）。其他的四个选项，均不符合两个CQ中的任意一个，因此均是无关选项，可以直接排除。

由于GMAT考试并不会告诉我们一道批判性推理题目究竟属于哪种推理方式，也不会告诉我们应该怎么评估，所以GMAT考试在批判性推理部分测试考生的三种能力：

（1） 论证（推理）的构建（argument construction）能力：所谓论证的构建，实际上是让考生去判断推理文段是由哪种推理方式构成的。说得直白点，即推理文段的推理方式是什么。

（2） 论证（推理）的评估（argument evaluation）能力：所谓论证的评估，实际上是考查考生是否掌握不同推理方式的不同评估方向。直白点说，即不同推理方式的CQ是什么。

（3） 规划并且评估一个计划（formulating and evaluating a plan of action）的能力：这种能力专门指代“方案推理”，在第三章中有详细的介绍。