The Value of Knowing Common Errors of Reasoning
In logic there are many more recognized forms of invalid argumentation than there are forms of valid argumentation. The test makers, being human (yes, it’s true), tend to repeat certain forms when creating stimuli and answer choices, and you can gain a demonstrable advantage by learning the forms most often used by the test makers. Applying the knowledge you acquire in this section will take two avenues:
1.Identifying errors of reasoning made in the stimulus
If you learn the mistakes that are often made by authors, then you will be able to quickly identify the error in the argument and accelerate through the answer choices to find the correct answer. Students without this knowledge will be forced to work more slowly and with less confidence.
2.Identifying answer choices that describe a common error of reasoning
In Flaw in the Reasoning questions, the test makers tend to use certain types of answers again and again. Depending on the reasoning used in the stimulus, these answers can describe the correct answer, but more often than not they are used as “stock” wrong answers. Familiarizing yourself with these answer choices will give you an advantage when you encounter similar answer choices in the future. For example, “attacking the source of an argument, not the argument itself” has appeared as the correct answer in several questions. But, it has appeared in many more questions as a wrong answer choice. If you are familiar with a “source” argument, you can then make an immediate determination as to whether that answer is correct or incorrect.
The paragraphs above help explain why test preparation works: the more you know about the exam before you walk in to take the test, the less time you have to waste during the exam thinking about these issues. Given the immense advantage you get by knowing the flawed reasoning that appears most frequently on the GMAT, the following section will detail a variety of errors of reasoning and provide examples of answer choices that describe the error under discussion. We strongly recommend that you spend a considerable amount of time learning these forms of flawed argumentation. It will definitely help you on the GMAT!
Please note that this discussion is not designed to include every possible error of reasoning, only those used most frequently by the makers of the GMAT.
Common Errors of Reasoning Explained
The following classic errors of reasoning appear with some frequency. The review is given in layman’s, not philosophical, terms:
Uncertain Use of a Term or Concept
As an argument progresses, the author must use each term in a constant, coherent fashion. Using a term in different ways is inherently confusing and undermines the integrity of the argument. Here is an example:
“Some people claim that the values that this country was built on are now being ignored by modern-day corporations. But this is incorrect. Corporations are purely profit-driven enterprises, beholden only to their shareholders, and as such they can only assess objects based on their value.”
The term “value” is used in the example above in two different senses: first in a moral or ethical sense and then in a monetary sense. This shift in meaning undermines the author’s position.
This type of answer choice appears more frequently as an incorrect answer than any other type. Here are examples of how this error of reasoning can be described in answer choices:
“depending on the ambiguous use of a key term”
“it confuses two different meanings of the word ‘solve’ ”
“relies on interpreting a key term in two different ways”
“equivocates with respect to a central concept”
“allows a key term to shift in meaning from one use to the next”
Also known as an ad hominem, this type of flawed argument attacks the person (or source) instead of the argument they advance. Because the GMAT is concerned solely with argument forms, a speaker can never validly attack the character or motives of a person; instead, a speaker must always attack the argument advanced by a person. Here is an example:
“The anti-smoking views expressed by Senator Smith should be ignored. After all, Smith himself is a smoker!”
A source argument can take different forms, including the following:
1.Focusing on the motives of the source.
2.Focusing on the actions of the source (as in the above example).
In the real world, you will often hear source arguments used by children and politicians (the two being alike in a number of ways, of course).
Here are examples of how this error of reasoning can be described in answer choices:
“makes an attack on the character of opponents”
“it is directed against the proponent of a claim rather than against the claim itself”
“he directs his criticism against the person making the argument rather than directing it against the argument itself”
“it draws conclusions about the merit of a position and about the content of that position from evidence about the position’s source”
“assuming that a claim is false on the grounds that the person defending it is of questionable character”
In circular reasoning the author assumes as true what is supposed to be proved. Consider the following example:
“This essay is the best because it is better than all the others.”
In this example the premise and the conclusion are identical in meaning. As we know, the conclusion should always follow from the premise. In the example above, the premise supports the conclusion, but the conclusion equally supports the premise, creating a “circular” situation where you can move from premise to conclusion, and then back again to the premise, and so on. Here is another example: “I must be telling the truth because I’m not lying.”
Here are examples of how this error of reasoning can be described in answer choices:
“it assumes what it seeks to establish”
“argues circularly by assuming the conclusion is true in stating the premises”
“presupposes the truth of what it sets out to prove”
“the argument assumes what it is attempting to demonstrate”
“it takes for granted the very claim that it sets out to establish”
“it offers, in place of support for its conclusion, a mere restatement of that conclusion”
Mistaken Cause and Effect
As discussed in Chapter Seven, arguments that draw causal conclusions are inherently flawed because there may be another explanation for the stated relationship. Because of the extreme causal assumption made by GMAT authors (that there is only one cause), any of the following answer choice forms could be used to describe an error of causality. Underneath each item are examples of how the error of reasoning can be described in answer choices.
1.Assuming a causal relationship on the basis of the sequence of events.
“mistakes the observation that one thing happens after another for proof that the second thing is the result of the first”
“mistakes a temporal relationship for a causal relationship”
2.Assuming a causal relationship when only a correlation exists.
“confusing the coincidence of two events with a causal relation between the two”
“assumes a causal relationship where only a correlation has been indicated”
3.Failure to consider an alternate cause for the effect, or an alternate cause for both the cause and the effect.
“fails to exclude an alternative explanation for the observed effect”
“overlooks the possibility that the same thing may causally contribute both to education and to good health”
4.Failure to consider that the events may be reversed.
“the author mistakes an effect for a cause”
Note the frequency with which the words “cause” or “effect” are used. This occurs because there are few substitutes for those two words, and thus the test makers are often forced to use those words to describe an argument containing causality. If you identify a stimulus with causal reasoning and are asked a Flaw question, quickly scan the answers for one that contains “cause,” “effect,” or both.
This error occurs when an author attempts to attack an opponent’s position by ignoring the actual statements made by the opposing speaker and instead distorts and refashions the argument, making it weaker in the process. In figurative terms, a “straw” argument is built up which is then easier for the author to knock down.
Often this error is accompanied by the phrase “what you’re saying is” or “if I understand you correctly,” which are used to preface the refashioned and weakened argument. Here is an example:
| “The platform proposed by my party calls for a moderate increase in taxes on those individuals making over $20,000 per year, and then taking that money and using it to rebuild the educational system.”
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| “But what you’re saying is that everyone should pay higher taxes, and so your proposal is unfair.”
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In the example above, Politician B recasts Politician A’s argument unfairly. Politician A indicated the tax increase would apply to those with incomes over $20,000 where Politician B distorts that to “everyone should pay higher taxes.”
To determine the error of reasoning, focus on the connection between the premises and the conclusion. Remember, GMAT authors are allowed to put forth virtually any premise when making an argument; the key is how those premises are used, not whether they are factually true.
Here are examples of how this error of reasoning can be described in answer choices:
“refutes a distorted version of an opposing position”
“misdescribing the student representative’s position, thereby making it easier to challenge”
“portrays opponents’ views as more extreme than they really are”
“distorts the proposal advocated by opponents”
Just a note: we did not make up the name “straw man.” The term is the proper name used in logic.
General Lack of Relevant Evidence for the Conclusion
Some GMAT authors misuse information to such a degree that they fail to provide any information to support their conclusion or they provide information that is irrelevant to their conclusion. Here is an example:
“Some critics claim that scientific progress has increased the polarization of society and alienated large segments of the population. But these critics are wrong because even a cursory glance at the past shows that society is always somewhat polarized and some groups are inevitably alienated.”
The author provides irrelevant evidence in an attempt to refute the claim that “scientific progress has increased the polarization of society and alienated large segments of the population.” Citing facts that such a situation has always existed does not help disprove that scientific progress has increased the severity of the situation.
Note the use of the construction “some critics claim...” As usual, the author’s main point is that the claim that the critics are making is wrong.
Here are examples of how this error of reasoning can be described in answer choices:
“The author cites irrelevant data.”
“draws a conclusion that is broader in scope than is warranted by the evidence advanced”
“It uses irrelevant facts to justify a claim about the quality of the disputed product.”
“It fails to give any reason for the judgment it reaches.”
“It introduces information unrelated to its conclusion as evidence in support of that conclusion.”
An internal contradiction (also known as a self-contradiction) occurs when an author makes conflicting statements. The example used was:
“Everyone should join our country club. After all, it’s an exclusive group that links many of the influential members of the community.”
The self-contradiction occurs when the speaker says “Everyone should join” and then follows that by saying that it is “an exclusive group.” Exclusive, by definition, means that some people are excluded.
The following show how this error of reasoning can be described in answer choices:
“bases a conclusion on claims that are inconsistent with each other”
“the author makes incompatible assumptions”
“introduces information that actually contradicts the conclusion”
“offers in support of its conclusion pieces of evidence that are mutually contradictory”
“some of the evidence presented in support of the conclusion is inconsistent with other evidence provided”
“assumes something that it later denies, resulting in a contradiction”
While there are a number of “appeal” fallacies that appear in traditional logic (Appeal to Fear, Appeal to Force, Appeal to Tradition, etc.), the following three are the most applicable to the GMAT:
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An Appeal to Authority uses the opinion of an authority in an attempt to persuade the reader. The flaw in this form of reasoning is that the authority may not have relevant knowledge or all the information regarding a situation, or there may a difference of opinion among experts as to what is true in the case. Here is an example:
“World-renowned neurologist Dr. Samuel Langhorne says that EZBrite Tooth Strips are the best for whitening your teeth. So, you know if you buy EZBrite you will soon have the whitest teeth possible!”
The primary defect in this argument is its use of a neurologist as an authority figure in an area of dentistry. While Dr. Langhorne can reasonably be appealed to in matters of the brain, dental care would be considered outside the scope of his expertise.
Here are examples of how this error of reasoning can be described in answer choices:
“the judgment of experts is applied to a matter in which their expertise is irrelevant”
“the argument inappropriately appeals to the authority of the mayor”
“it relies on the judgment of experts in a matter to which their expertise is irrelevant”
“accepts a claim on mere authority, without requiring sufficient justification”
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| Appeal to Popular Opinion/Appeal to Numbers
This error states that a position is true because the majority believe it to be true. As you know, arguments are created by providing premises that support a conclusion. An appeal to popular opinion does not present a logical reason for accepting a position, just an appeal based on numbers. Here is an example:
“A recent poll states that 75% of Americans believe that Microsoft is a monopoly. Antitrust law states that monopolies have a deleterious effect on the marketplace (with the exception of utilities), and therefore Microsoft should be controlled or broken into smaller pieces.”
The author uses the results of a poll that indicate many people think Microsoft is a monopoly to conclude that Microsoft is in fact a monopoly. This type of persuasion is often used in the arguments made by advertisements (“All the trend setters use EZBrite Tooth Strips”), politicians (“Everyone loves the environment. Vote for the Green Party!), and children (“C’mon, try this. Everyone does it.”).
This type of reasoning most often appears as an incorrect answer. Here are examples of how this error of reasoning can be described in answer choices:
“it treats popular opinion as if it constituted conclusive evidence for a claim”
“attempts to discredit legislation by appealing to public sentiment”
“a claim is inferred to be false merely because a majority of people believe it to be false”
“the argument, instead of providing adequate reasons in support of its conclusion, makes an appeal to popular opinion”
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An Appeal to Emotion occurs when emotions or emotionally-charged language is used in an attempt to persuade the reader. Here is an example:
“Officer, please do not give me a ticket for speeding. In the last month I’ve been fired from my job, kicked out of my apartment, and my car broke down. I don’t deserve this!"
Here are examples of how this error of reasoning can be described in answer choices:
“attempts to persuade by making an emotional appeal”
“uses emotive language in labeling the proposals”
“the argument appeals to emotion rather than reason”
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The makers of the GMAT believe that surveys, when conducted properly, produce reliable results. However, surveys can be invalidated when any of the following three scenarios arise:
1.The survey uses a biased sample.
Perhaps the most famous example of a biased survey occurred in 1936. The Literary Digest weekly magazine sent out ballots to some 10 million voters (2.3 million were returned), and returns indicated that a solid majority would vote for Republican candidate Alf Landon in the upcoming presidential election. On the basis of these results (and the size of the sample), the Literary Digest predicted that Landon would win easily. Of course, when the election was held Franklin Roosevelt won in a landslide. The Literary Digest erred by sending the ballots to groups such as telephone owners and automobile owners, groups that in that era (late Depression) tended to be among the wealthiest individuals and overwhelmingly Republican. The Literary Digest ended up polling a large number of Republicans and on that basis declared that the Republican candidate would win.
Note that a secondary error with the polling done by the Literary Digest is that the sample is self-selected; that is, the individuals being polled decided whether or not to respond. That opportunity introduces bias into the survey process because certain types of individuals tend to respond to surveys more often than others.
A similar type of sampling error occurred in 1948 when the Chicago Daily Tribune predicted Thomas Dewey would prevail over Harry Truman. The Tribune even went so far as to print the morning edition of the newspaper with that headline.
2.The survey questions are improperly constructed.
If a survey question is confusing or misleading, the results of the poll can be inaccurate.
Questions can be confusing, such as “Do you feel it is possible that none of the candidates would not vote to increase taxes?” (The question actually asks, “Do you feel it is possible that all of the candidates would vote to increase taxes?”). If a respondent cannot understand the question, how can they accurately answer the question?
Questions can also be misleading, such as “How soon should the U.S. government withdraw from the United Nations?” The question presumes that the United States should withdraw from the United Nations—a course of action that the respondent may not agree with.
3.Respondents to the survey give inaccurate responses.
People do not always tell the truth when responding to surveys. Two classic questions that often elicit false answers are “What is your age” and “how much money do you make each year?”
If respondents give false answers to survey questions, the results of the survey are skewed and inaccurate.
Here are examples of how the errors of reasoning above can be described in answer choices:
“uses evidence drawn from a small sample that may well be unrepresentative”
“generalizes from an unrepresentative sample”
“states a generalization based on a selection that is not representative of the group about which the generalization is supposed to hold true”
Exceptional Case/Overgeneralization
This error takes a small number of instances and treats those instances as if they support a broad, sweeping conclusion. Here is an example:
“Two of my friends were shortchanged at that store. Therefore, everyone gets shortchanged at that store. ”
This answer appears most frequently as an incorrect answer in Flaw questions, but as with any of the errors described in this section, occasionally it appears as a correct answer. Here are examples of how this error of reasoning can be described in answer choices:
“supports a universal claim on the basis of a single example”
“The argument generalizes from too small a sample of cases”
“Too general a conclusion is made about investing on the basis of a single experiment”
“bases a general claim on a few exceptional instances”
Errors of Composition and Division
Composition and division errors involve judgments made about groups and parts of a group.
An error of composition occurs when the author attributes a characteristic of part of the group to the group as a whole or to each member of the group. Here is an example:
“Every party I attend is fun and exciting. Therefore, my life is fun and exciting.”
Here are examples of how this error of reasoning can be described in answer choices:
“assuming that because something is true of each of the parts of a whole it is true of the whole itself”
“improperly infers that each and every scientist has a certain characteristic from the premise that most scientists have that characteristic”
“takes the view of one lawyer to represent the views of all lawyers”
An error of division occurs when the author attributes a characteristic of the whole (or each member of the whole) to a part of the group. Here is an example:
“The United States is the wealthiest country in the world. Thus, every American is wealthy.”
Here is an example of how this error of reasoning is described in GMAT answer choices:
“presumes, without providing justification, that what is true of a whole must also be true of its constituent parts”
An analogy is a comparison between two items. A False Analogy occurs when the author uses an analogy that is too dissimilar to the original situation to be applicable. Here is an example:
“Just as a heavy rainfall can be cleansing, the best approach to maintain a healthy relationship is to store up all your petty grievances and then unload them all at one time on your partner.”
The comparison in the example fails to consider that a heavy rainfall and an emotionally charged situation are fundamentally different.
Here are two examples of how a False analogy can be described in answer choices:
“treats as similar two cases that are different in a critical respect”
“treats two kinds of things that differ in important respects as if they do not differ”
A False Dilemma assumes that only two courses of action are available when there may be others. Here is an example:
“Recent accidents within the oil industry have made safety of operation a critical public safety issue. Because the industry cannot be expected to police itself, the government must step in and take action.”
The argument above falsely assumes that only two courses of action exist: industry self-policing or government action. But this ignores other courses of action, such as consumer watchdog groups.
Do not confuse a False Dilemma with a situation where the author legitimately establishes that only two possibilities exist. Phrases such as “either A or B will occur, but not both” can establish a limited set of possibilities, and certain real-world situations yield only two possibilities, such as “you are either dead or alive.”
Here is an example of how a False Dilemma can be described in answer choices:
“fails to consider that some students may be neither fascinated by nor completely indifferent to the subject being taught”
Errors in the Use of Evidence
Mis-assessing the force of evidence is a frequent error committed by GMAT authors. Each of the following describes an error of reasoning involving the force of evidence:
| Lack of evidence for a position is taken to prove that position is false.
Just because no evidence proving a position has been introduced does not mean that the position is false. Here is an example:
“The White House has failed to offer any evidence that they have reached a trade agreement with China. Therefore, no such agreement has been reached.”
In the example above the White House may have valid reasons for withholding information about the trade agreement. The lack of confirming evidence does not undeniably prove that a trade agreement has not been reached.
Here are two examples of how this error of reasoning can be described in answer choices:
“treats failure to prove a claim as constituting denial of that claim”
“taking a lack of evidence for a claim as evidence undermining that claim”
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| Lack of evidence against a position is taken to prove that position is true.
This error is the opposite of the previous error. Just because no evidence disproving a position has been introduced does not mean that the position is true. Here is a famous example:
“There has been no evidence given against the existence of God, so God must exist.”
The lack of evidence against a position does not undeniably prove a position. Here is an example of how this error of reasoning can be described in answer choices:
“treating the failure to establish that a certain claim is false as equivalent to a demonstration that the claim is true”
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| Some evidence against a position is taken to prove that position is false.
The introduction of evidence against a position only weakens the position; it does not necessarily prove the position false. Here is an example:
“Some historians claim that a lengthy drought preceded the fall of the Aztec empire. But we know from Aztec writings that in at least one year during the supposed drought there was minor flooding. Thus, the claim that there was a lengthy drought prior to the fall of the Aztec empire is false.”
The evidence offered in the example above weakens the claim that there was a lengthy drought, but it does not disprove it. A drought by definition is a prolonged period of unusually low rainfall, and thus it would be possible for flooding to occur on occasion, but not enough flooding to overcome the general drought conditions.
Here is an example of how this error of reasoning can be described in an answer choice:
“it confuses undermining an argument in support of a given conclusion with showing that the conclusion itself is false”
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| Some evidence for a position is taken to prove that position is true.
The introduction of evidence for a position only provides support for the position; it does not prove the position to be undeniably true. Here is an example:
“We know that the defendant was in the vicinity of the robbery when the robbery occurred. Therefore, the defendant is guilty of the robbery.”
As the above example proves, partial support for a position does not make the position invincible (especially in GMAT arguments, which are relatively short). As you might expect, partial evidence for a position can be outweighed by evidence against that position.
Here is an example of how this error of reasoning can be described in an answer choice:
“the argument takes evidence showing merely that its conclusion could be true to constitute evidence showing that the conclusion is in fact true”
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Although this error has a rather futuristic name, the mistake involves assuming that conditions will remain constant over time, and that what was the case in the past will be the case in the present or future.
“The company has always reimbursed me for meals when I’m on a business trip, so they will certainly reimburse me for meals on this business trip.”
Clearly, what has occurred in the past is no guarantee that the future will be the same. Yet, many GMAT authors make this assumption, especially when hundreds or thousands of years are involved. Here are examples of how this error of reasoning can be described in answer choices:
“treats a claim about what is currently the case as if it were a claim about what has been the case for an extended period”
“uncritically draws an inference from what has been true in the past to what will be true in the future”
Numbers and Percentages Errors
In Chapter Twelve of the Critical Reasoning Bible we discuss numbers and percentages problems in detail. Meanwhile, consider that many errors in this category are committed when an author improperly equates a percentage with a definite quantity, or when an author uses quantity information to make a judgment about the percentage represented by that quantity.
Here is an example of how this error of reasoning can be described in an answer choice:
“the argument confuses the percentage of the budget spent on a program with the overall amount spent on that program”
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发表于 2010-8-12 14:09:23
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