Test prep strategies for GMAT Arguments

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GMAT ARGUMENTS INTRODUCTION

An argument, as used on the GMAT, is a presentation of facts and opinions in order to support a position. Many arguments will be fallacious. And many correct answers will be false! This often causes students much consternation; they feel that the correct answer should be true. But the arguments are intended to test your ability to think logically. Now logic is the study of the relationships between statements, not of the truth of those statements. Being overly concerned with finding the truth can be ruinous to your GMAT argument score.

"2 OUT OF 5" RULE

Creating a good but incorrect answer-choice is much harder than developing the correct answer. For this reason, usually only one attractive wrong answer-choice is presented. This is called the "2 out of 5" rule. That is, only two of the five answer-choices will have any real merit. Hence, even if you don't fully understand an argument, you probably can still eliminate the three fluff choices, thereby greatly increasing your odds of answering the question correctly.

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LOGIC I

Although in theory the argument questions are designed to be answered without any reference to formal logic, the section is essentially a logic test. Some knowledge of the fundamentals of logic, therefore, will give you a definite advantage. Armed with this knowledge, you should quickly notice that the arguments are fundamentally easy and that most of them fall into a few basic categories. In this section, we will study the logical structure of arguments. In Logic II, we will symbolize and diagram arguments in much the same way as we did with games.

Conclusions

Most argument questions hinge, either directly or indirectly, on determining the conclusion of the argument. The conclusion is the main idea of the argument. It is what the writer tries to persuade the reader to believe. Most often the conclusion comes at the end of the argument. The writer organizes the facts and his opinions so that they build up to the conclusion. Sometimes, however, the conclusion will come at the beginning of an argument, rarely does it come in the middle, and occasionally, for rhetorical effect, the conclusion is not even stated.

Example:

The police are the armed guardians of the social order. The blacks are the chief domestic victims of the American social order. A conflict of interest exists, therefore, between the blacks and the police.--Eldridge Cleaver, Soul on Ice

Here the first two sentences anticipate or set up the conclusion. By changing the grammar slightly, the conclusion can be placed at the beginning of the argument and still sound natural:

A conflict of interest exists between the blacks and the police because the police are the armed guardians of the social order and the blacks are the chief domestic victims of the American social order.

The conclusion can also be forced into the middle:

The police are the armed guardians of the social order. So a conflict of interest exists between the blacks and the police because the blacks are the chief domestic victims of the American social order.

It is generally awkward, as in the previous paragraph, to place the conclusion in the middle of the argument because then it cannot be fully anticipated by what comes before nor fully explained by what comes after. On the rare occasion when a conclusion comes in the middle of an argument, most often either the material that comes after it or the material that comes before it is not essential.

In summary: To find the conclusion, check the last sentence of the argument. If that is not the conclusion, check the first sentence. Rarely does the conclusion come in the middle of an argument.

When determining the meaning of a conclusion, be careful not to read any more into it than what the author states. Although arguments are not worded as precisely as games, you still need to read them with more care than you would use in your everyday reading.

As with games, read the words and sentences of an argument precisely, and use their literal meaning.

For example, consider the meaning of some in the sentence "Some of Mary's friends went to the party." It would be unwarranted, based on this statement, to assume that some of Mary's friends did not go to the party. Although it may seem deceiving to say that some of Mary's friends went to the party when in fact all of them did, it is nonetheless technically consistent with the meaning of some.

Some means "at least one and perhaps all."

As mentioned before, the conclusion usually comes at the end of an argument, sometimes at the beginning, and rarely in the middle. Writers use certain words to indicate that the conclusion is about to be stated. Following is a list of the most common conclusion indicators:

Conclusion Indicators

Most often the conclusion of an argument is put in the form of a statement. Sometimes, however, the conclusion is given as a command or obligation.

Example:

All things considered, you ought to vote.

Here, the author implies that you are obliged to vote.

The conclusion can even be put in the form of a question. This rhetorical technique is quite effective in convincing people that a certain position is correct. We are more likely to believe something if we feel that we concluded it on our own, or at least if we feel that we were not told to believe it. A conclusion put in question form can have this result.

Example:

The Nanuuts believe that they should not take from Nature anything She cannot replenish during their lifetime. This assures that future generations can enjoy the same riches of Nature that they have. At the current rate of destruction, the rain forests will disappear during our lifetime. Do we have an obligation to future generations to prevent this result?

Here the author trusts that the power of her argument will persuade the reader to answer the question affirmatively.

Taking this rhetorical technique one step further, the writer may build up to the conclusion but leave it unstated. This allows the reader to make up his own mind. If the build-up is done skillfully, the reader will be more likely to agree with the author, without feeling manipulated.

Example:

He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet.

The unstated but obvious conclusion here is that none of the people has the right to cast the first stone.

When determining the conclusion's scope be careful not to read any more or less into it than the author states. GMAT writers often create wrong answer-choices by slightly overstating or understating the author's claim. Certain words limit the scope of a statement. These words are called quantifiers--pay close attention to them. Following is a list of the most important quantifiers:

Quantifiers

Example:

Whether the world is Euclidean or non-Euclidean is still an open question. However, if a star's position is predicted based on non-Euclidean geometry, then when a telescope is pointed to where the star should be it will be there. Whereas, if the star's position is predicted based on Euclidean geometry, then when a telescope is pointed to where the star should be it won't be there. This strongly indicates that the world is non-Euclidean.

Which one of the following best expresses the main idea of the passage?

(A) The world may or may not be Euclidean.
(B) The world is probably non-Euclidean.
(C) The world is non-Euclidean.
(D) The world is Euclidean.
(E) The world is neither Euclidean nor non-Euclidean.

Choice (A) understates the main idea. Although the opening to the passage states that we don't know whether the world is non-Euclidean, the author goes on to give evidence that it is non-Euclidean. Choice (C) overstates the main idea. The author doesn't say that the world is non-Euclidean, just that evidence strongly indicates that it is. In choice (B), the word "probably" properly limits the scope of the main idea, namely, that the world is probably non-Euclidean, but we can't yet state so definitively. The answer is (B).

Premises

Once you've found the conclusion, most often everything else in the argument will be either premises or "noise." The premises provide evidence for the conclusion; they form the foundation or infrastructure upon which the conclusion depends. To determine whether a statement is a premise, ask yourself whether it supports the conclusion. If so, it's a premise. Earlier we saw that writers use certain words to flag conclusions; likewise writers use certain words to flag premises. Following is a partial list of the most common premise indicators:

Premise Indicators

Example:

Since the incumbent's views are out of step with public opinion, he probably will not be reelected.

Here "since" is used to flag the premise that the incumbent's positions are unpopular.

Suppressed Premises

Most arguments depend on one or more unstated premises. Sometimes this indicates a weakness in the argument, an oversight by the writer. More often, however, certain premises are left tacit because they are too numerous, or the writer assumes that his audience is aware of the assumptions, or he wants the audience to fill in the premise themselves and therefore be more likely to believe the conclusion.

Example:

Conclusion: I knew he did it.

Premise: Only a guilty person would accept immunity from prosecution.

The suppressed premise is that he did, in fact, accept immunity. The speaker assumes that his audience is aware of this fact or at least is willing to believe it, so to state it would be redundant and ponderous. If the unstated premise were false (that is, he did not accept immunity), the argument would not technically be a lie; but it would be very deceptive. The unscrupulous writer may use this ploy if he thinks that he can get away with it. That is, his argument has the intended effect and the false premise, though implicit, is hard to find or is ambiguous. Politicians are not at all above using this tactic.

A common question on the GMAT asks you to find the suppressed premise of an argument. Finding the suppressed premise, or assumption, of an argument can be difficult. However, on the GMAT you have an advantage--the suppressed premise is listed as one of the five answer-choices. To test whether an answer-choice is a suppressed premise, ask yourself whether it would make the argument more plausible. If so, then it is very likely a suppressed premise.

Example:

American attitudes tend to be rather insular, but there is much we can learn from other countries. In Japan, for example, workers set aside some time each day to exercise, and many corporations provide elaborate exercise facilities for their employees. Few American corporations have such exercise programs. Studies have shown that the Japanese worker is more productive than the American worker. Thus it must be concluded that the productivity of American workers will lag behind their Japanese counterparts, until mandatory exercise programs are introduced.

The conclusion of the argument is valid if which one of the following is assumed?

(A) Even if exercise programs do not increase productivity, they will improve the American worker's health.
(B) The productivity of all workers can be increased by exercise.
(C) Exercise is an essential factor in the Japanese worker's superior productivity.
(D) American workers can adapt to the longer Japanese work week.
(E) American corporations don't have the funds to build elaborate exercise facilities.

The unstated essence of the argument is that exercise is an integral part of productivity and that Japanese workers are more productive than American workers because they exercise more. The answer is (C).

Counter-Premises

When presenting a position, you obviously don't want to argue against yourself. However, it is often effective to concede certain minor points that weaken your argument. This shows that you are open-minded and that your ideas are well considered. It also disarms potential arguments against your position. For instance, in arguing for a strong, aggressive police department, you may concede that in the past the police have at times acted too aggressively. Of course, you will then need to state more convincing reasons to support your position.

Example:

I submit that the strikers should accept the management's offer. Admittedly, it is less than what was demanded. But it does resolve the main grievance--inadequate health care. Furthermore, an independent study shows that a wage increase greater than 5% would leave the company unable to compete against Japan and Germany, forcing it into bankruptcy.

The conclusion, "the strikers should accept the management's offer," is stated in the first sentence. Then "Admittedly" introduces a concession; namely, that the offer was less than what was demanded. This weakens the speaker's case, but it addresses a potential criticism of his position before it can be made. The last two sentences of the argument present more compelling reasons to accept the offer and form the gist of the argument.

Following are some of the most common counter-premise indicators:

Counter-Premise Indicators

As you may have anticipated, the GMAT writers sometimes use counter-premises to bait wrong answer-choices. Answer-choices that refer to counter-premises are very tempting because they refer directly to the passage and they are in part true. But you must ask yourself "Is this the main point that the author is trying to make?" It may merely be a minor concession.

Logic II (Diagramming)

Most arguments are based on some variation of an if-then statement. However, the if-then statement is often embedded in other equivalent structures. Diagramming brings out the superstructure and the underlying simplicity of arguments.

_If-Then

A-->B

By now you should be well aware that if the premise of an if-then statement is true then the conclusion must be true as well. This is the defining characteristic of a conditional statement; it can be illustrated as follows:

A-->B
A
Therefore, B

This diagram displays the if-then statement "A-->B," the affirmed premise "A," and the necessary conclusion "B." Such a diagram can be very helpful in showing the logical structure of an argument.

Example: (If-then)

If Jane does not study for the GMAT, then she will not score well. Jane, in fact, did not study for the GMAT; therefore she scored poorly on the test.

When symbolizing games, we let a letter stand for an element. When symbolizing arguments, however, we may let a letter stand for an element, a phrase, a clause, or even an entire sentence. The clause "Jane does not study for the GMAT" can be symbolized as ~S, and the clause "she will not score well" can be symbolized as ~W. Substituting these symbols into the argument yields the following diagram:

~S-->~W
~S
Therefore, ~W

This diagram shows that the argument has a valid if-then structure. A conditional statement is presented, ~S-->~W; its premise affirmed, ~S; and then the conclusion that necessarily follows, ~W, is stated.

Embedded If-Then Statements

Usually, arguments involve an if-then statement. Unfortunately, the if-then thought is often embedded in other equivalent structures. In this section, we study how to spot these structures.

Example: (Embedded If-then)

John and Ken cannot both go to the party.

At first glance, this sentence does not appear to contain an if-then statement. But it essentially says: "if John goes to the party, then Ken does not."

Example: (Embedded If-then)

Danielle will be accepted to graduate school only if she does well on the GRE.

Given this statement, we know that if Danielle is accepted to graduate school, then she must have done well on the GRE. Note: Students often wrongly interpret this statement to mean:

"If Danielle does well on the GRE, then she will be accepted to graduate school."

There is no such guarantee. The only guarantee is that if she does not do well on the GRE, then she will not be accepted to graduate school.

"A only if B" is logically equivalent to "if A, then B."

Affirming the Conclusion Fallacy

A-->B
B
Therefore, A

Remember that an if-then statement, A-->B, tells us only two things: (1) If A is true, then B is true as well. (2) If B is false, then A is false as well (contrapositive). If, however, we know the conclusion is true, the if-then statement tells us nothing about the premise. And if we know that the premise is false (we will consider this next), then the if-then statement tells us nothing about the conclusion.

Example: (Affirming the Conclusion Fallacy)

If he is innocent, then when we hold him under water for sixty seconds he will not drown. Since he did not die when we dunked him in the water, he must be innocent.

The logical structure of the argument above is most similar to which one of the following?

(A) To insure that the remaining wetlands survive, they must be protected by the government. This particular wetland is being neglected. Therefore, it will soon perish.
(B) There were nuts in that pie I just ate. There had to be, because when I eat nuts I break out in hives, and I just noticed a blemish on my hand.
(C) The president will be reelected unless a third candidate enters the race. A third candidate has entered the race, so the president will not be reelected.
(D) Every time Melinda has submitted her book for publication it has been rejected. So she should not bother with another rewrite.
(E) When the government loses the power to tax one area of the economy, it just taxes another. The Supreme Court just overturned the sales tax, so we can expect an increase in the income tax.

To symbolize this argument, let the clause "he is innocent" be denoted by I, and let the clause "when we hold him under water for sixty seconds he will not drown" be denoted by ~D. Then the argument can be symbolized as

I-->~D
~D
Therefore, I

Notice that this argument is fallacious: the conclusion "he is innocent" is also a premise of the argument. Hence the argument is circular--it proves what was already assumed. The argument affirms the conclusion then invalidly uses it to deduce the premise. The answer will likewise be fallacious.

We start with answer-choice (A). The sentence

"To insure that the remaining wetlands survive, they must be protected by the government"

contains an embedded if-then statement:

"If the remaining wetlands are to survive, then they must be protected by the government."

This can be symbolized as S-->P. Next, the sentence "This particular wetland is being neglected" can be symbolized as ~P. Finally, the sentence "It will soon perish" can be symbolized as ~S. Using these symbols to translate the argument gives the following diagram:

S-->P
~P
Therefore, ~S

The diagram clearly shows that this argument does not have the same structure as the given argument. In fact, it is a valid argument by contraposition.

Turning to (B), we reword the statement "when I eat nuts, I break out in hives" as

"If I eat nuts, then I break out in hives." This in turn can be symbolized as N-->H.

Next, we interpret the clause "there is a blemish on my hand" to mean "hives," which we symbolize as H. Substituting these symbols into the argument yields the following diagram:

N-->H
H
Therefore, N

The diagram clearly shows that this argument has the same structure as the given argument. The answer, therefore, is (B).

Denying the Premise Fallacy

A-->B
~A
Therefore, ~B

The fallacy of denying the premise occurs when an if-then statement is presented, its premise denied, and then its conclusion wrongly negated.

Example: (Denying the Premise Fallacy)

The senator will be reelected only if he opposes the new tax bill. But he was defeated. So he must have supported the new tax bill.

The sentence "The senator will be reelected only if he opposes the new tax bill" contains an embedded if-then statement: "If the senator is reelected, then he opposes the new tax bill." (Remember: "A only if B" is equivalent to "If A, then B.") This in turn can be symbolized as R-->~T. The sentence "But the senator was defeated" can be reworded as "He was not reelected," which in turn can be symbolized as ~R. Finally, the sentence "He must have supported the new tax bill" can be symbolized as T. Using these symbols the argument can be diagrammed as follows:

R-->~T
~R
Therefore, T

[Note: Two negatives make a positive, so the conclusion ~(~T) was reduced to T.] This diagram clearly shows that the argument is committing the fallacy of denying the premise. An if-then statement is made; its premise is negated; then its conclusion is negated.

Transitive Property

A-->B
B-->C
Therefore, A-->C

These arguments are rarely difficult, provided you step back and take a bird's-eye view. It may be helpful to view this structure as an inequality in mathematics. For example, 5 > 4 and 4 > 3, so 5 > 3.

Notice that the conclusion in the transitive property is also an if-then statement. So we don't know that C is true unless we know that A is true. However, if we add the premise "A is true" to the diagram, then we can conclude that C is true:

A-->B
B-->C
A
Therefore, C

As you may have anticipated, the contrapositive can be generalized to the transitive property:

A-->B
B-->C
~C
Therefore, ~A

Example: (Transitive Property)

If you work hard, you will be successful in America. If you are successful in America, you can lead a life of leisure. So if you work hard in America, you can live a life of leisure.

Let W stand for "you work hard," S stand for "you will be successful in America," and L stand for "you can lead a life of leisure." Now the first sentence translates as W-->S, the second sentence as S-->L, and the conclusion as W-->L. Combining these symbol statements yields the following diagram:

W-->S
S-->L
Therefore, W-->L

The diagram clearly displays the transitive property.

DeMorgan's Laws

~(A & B) = ~A or ~B
~(A or B) = ~A & ~B

If you have taken a course in logic, you are probably familiar with these formulas. Their validity is intuitively clear: The conjunction A&B is false when either, or both, of its parts are false. This is precisely what ~A or ~B says. And the disjunction A or B is false only when both A and B are false, which is precisely what ~A and ~B says.

You will rarely get an argument whose main structure is based on these rules--they are too mechanical. Nevertheless, DeMorgan's laws often help simplify, clarify, or transform parts of an argument. They are also useful with games.

Example: (DeMorgan's Law)

It is not the case that either Bill or Jane is going to the party.

This argument can be diagrammed as ~(B or J), which by the second of DeMorgan's laws simplifies to (~B and ~J). This diagram tells us that neither of them is going to the party.

A unless B

~B-->A

"A unless B" is a rather complex structure. Though surprisingly we use it with little thought or confusion in our day-to-day speech.

To see that "A unless B" is equivalent to "~B-->A," consider the following situation:

Biff is at the beach unless it is raining.

Given this statement, we know that if it is not raining, then Biff is at the beach. Now if we symbolize "Biff is at the beach" as B, and "it is raining" as R, then the statement can be diagrammed as ~R-->B.

CLASSIFICATION

In Logic II, we studied deductive arguments. However, the bulk of arguments on the GMAT are inductive. In this section we will classify and study the major types of inductive arguments.

An argument is deductive if its conclusion necessarily follows from its premises--otherwise it is inductive. In an inductive argument, the author presents the premises as evidence or reasons for the conclusion. The validity of the conclusion depends on how compelling the premises are. Unlike deductive arguments, the conclusion of an inductive argument is never certain. The truth of the conclusion can range from highly likely to highly unlikely. In reasonable arguments, the conclusion is likely. In fallacious arguments, it is improbable. We will study both reasonable and fallacious arguments.

We will classify the three major types of inductive reasoning--generalization, analogy, and causal--and their associated fallacies.

Generalization

Generalization and analogy, which we consider in the next section, are the main tools by which we accumulate knowledge and analyze our world. Many people define generalization as "inductive reasoning." In colloquial speech, the phrase "to generalize" carries a negative connotation. To argue by generalization, however, is neither inherently good nor bad. The relative validity of a generalization depends on both the context of the argument and the likelihood that its conclusion is true. Polling organizations make predictions by generalizing information from a small sample of the population, which hopefully represents the general population. The soundness of their predictions (arguments) depends on how representative the sample is and on its size. Clearly, the less comprehensive a conclusion is the more likely it is to be true.

Example:

During the late seventies when Japan was rapidly expanding its share of the American auto market, GM surveyed owners of GM cars and asked them whether they would be more willing to buy a large, powerful car or a small, economical car. Seventy percent of those who responded said that they would prefer a large car. On the basis of this survey, GM decided to continue building large cars. Yet during the '80s, GM lost even more of the market to the Japanese.

Which one of the following, if it were determined to be true, would best explain this discrepancy.

(A) Only 10 percent of those who were polled replied.
(B) Ford which conducted a similar survey with similar results continued to build large cars and also lost more of their market to the Japanese.
(C) The surveyed owners who preferred big cars also preferred big homes.
(D) GM determined that it would be more profitable to make big cars.
(E) Eighty percent of the owners who wanted big cars and only 40 percent of the owners who wanted small cars replied to the survey.

The argument generalizes from the survey to the general car-buying population, so the reliability of the projection depends on how representative the sample is. At first glance, choice (A) seems rather good, because 10 percent does not seem large enough. However, political opinion polls are typically based on only .001 percent of the population. More importantly, we don't know what percentage of GM car owners received the survey. Choice (B) simply states that Ford made the same mistake that GM did. Choice (C) is irrelevant. Choice (D), rather than explaining the discrepancy, gives even more reason for GM to continue making large cars. Finally, choice (E) points out that part of the survey did not represent the entire public, so (E) is the answer.

Analogy

To argue by analogy is to claim that because two things are similar in some respects, they will be similar in others. Medical experimentation on animals is predicated on such reasoning. The argument goes like this: the metabolism of pigs, for example, is similar to that of humans, and high doses of saccharine cause cancer in pigs. Therefore, high doses of saccharine probably cause cancer in humans.

Clearly, the greater the similarity between the two things being compared the stronger the argument will be. Also the less ambitious the conclusion the stronger the argument will be. The argument above would be strengthened by changing "probably" to "may." It can be weakened by pointing out the dissimilarities between pigs and people.

Example:

Just as the fishing line becomes too taut, so too the trials and tribulations of life in the city can become so stressful that one's mind can snap.

Which one of the following most closely parallels the reasoning used in the argument above?

(A) Just as the bow may be drawn too taut, so too may one's life be wasted pursuing self-gratification.
(B) Just as a gambler's fortunes change unpredictably, so too do one's career opportunities come unexpectedly.
(C) Just as a plant can be killed by over watering it, so too can drinking too much water lead to lethargy.
(D) Just as the engine may race too quickly, so too may life in the fast lane lead to an early death.
(E) Just as an actor may become stressed before a performance, so too may dwelling on the negative cause depression.

The argument compares the tautness in a fishing line to the stress of city life; it then concludes that the mind can snap just as the fishing line can. So we are looking for an answer-choice that compares two things and draws a conclusion based on their similarity. Notice that we are looking for an argument that uses similar reasoning, but not necessarily similar concepts. In fact, an answer-choice that mentions either tautness or stress will probably be a same-language trap.

Choice (A) uses the same-language trap--notice "too taut." The analogy between a taut bow and self-gratification is weak, if existent. Choice (B) offers a good analogy but no conclusion. Choice (C) offers both a good analogy and a conclusion; however, the conclusion, "leads to lethargy," understates the scope of what the analogy implies. Choice (D) offers a strong analogy and a conclusion with the same scope found in the original: "the engine blows, the person dies"; "the line snaps, the mind snaps." This is probably the best answer, but still we should check every choice. The last choice, (E), uses language from the original, "stressful," to make its weak analogy more tempting. The best answer, therefore, is (D).

Causal Reasoning

Of the three types of inductive reasoning we will discuss, causal reasoning is both the weakest and the most prone to fallacy. Nevertheless, it is a useful and common method of thought.

To argue by causation is to claim that one thing causes another. A causal argument can be either weak or strong depending on the context. For example, to claim that you won the lottery because you saw a shooting star the night before is clearly fallacious. However, most people believe that smoking causes cancer because cancer often strikes those with a history of cigarette use. Although the connection between smoking and cancer is virtually certain, as with all inductive arguments it can never be 100 percent certain. Cigarette companies have claimed that there may be a genetic predisposition in some people to both develop cancer and crave nicotine. Although this claim is highly improbable, it is conceivable.

There are two common fallacies associated with causal reasoning:

1. Confusing Correlation with Causation.

To claim that A caused B merely because A occurred immediately before B is clearly questionable. It may be only coincidental that they occurred together, or something else may have caused them to occur together. For example, the fact that insomnia and lack of appetite often occur together does not mean that one necessarily causes the other. They may both be symptoms of an underlying condition.

2. Confusing Necessary Conditions with Sufficient Conditions.

A is necessary for B means "B cannot occur without A." A is sufficient for B means "A causes B to occur, but B can still occur without A." For example, a small tax base is sufficient to cause a budget deficit, but excessive spending can cause a deficit even with a large tax base. A common fallacy is to assume that a necessary condition is sufficient to cause a situation. For example, to win a modern war it is necessary to have modern, high-tech equipment, but it is not sufficient, as Iraq discovered in the Persian Gulf War.

SEVEN COMMON FALLACIES

Contradiction

A Contradiction is committed when two opposing statements are simultaneously asserted. For example, saying "it is raining and it is not raining" is a contradiction. Typically, however, the arguer obscures the contradiction to the point that the argument can be quite compelling. Take, for instance, the following argument:

"We cannot know anything, because we intuitively realize that our thoughts are unreliable."

This argument has an air of reasonableness to it. But "intuitively realize" means "to know." Thus the arguer is in essence saying that we know that we don't know anything. This is self-contradictory.

Equivocation

Equivocation is the use of a word in more than one sense during an argument. This technique is often used by politicians to leave themselves an "out." If someone objects to a particular statement, the politician can simply claim the other meaning.

Example:

Individual rights must be championed by the government. It is right for one to believe in God. So government should promote the belief in God.

In this argument, right is used ambiguously. In the phrase "individual rights" it is used in the sense of a privilege, whereas in the second sentence right is used to mean proper or moral. The questionable conclusion is possible only if the arguer is allowed to play with the meaning of the critical word right.

Circular Reasoning

Circular reasoning involves assuming as a premise that which you are trying to prove. Intuitively, it may seem that no one would fall for such an argument. However, the conclusion may appear to state something additional, or the argument may be so long that the reader may forget that the conclusion was stated as a premise.

Example:

The death penalty is appropriate for traitors because it is right to execute those who betray their own country and thereby risk the lives of millions.

This argument is circular because "right" means essentially the same thing as "appropriate." In effect, the writer is saying that the death penalty is appropriate because it is appropriate.

Shifting The Burden Of Proof

It is incumbent on the writer to provide evidence or support for her position. To imply that a position is true merely because no one has disproved it is to shift the burden of proof to others.

Example:

Since no one has been able to prove God's existence, there must not be a God.

There are two major weaknesses in this argument. First, the fact that God's existence has yet to be proven does not preclude any future proof of existence. Second, if there is a God, one would expect that his existence is independent of any proof by man.

Unwarranted Assumptions

The fallacy of unwarranted assumption is committed when the conclusion of an argument is based on a premise (implicit or explicit) that is false or unwarranted. An assumption is unwarranted when it is false--these premises are usually suppressed or vaguely written. An assumption is also unwarranted when it is true but does not apply in the given context--these premises are usually explicit.

Example: (False Dichotomy)

Either restrictions must be placed on freedom of speech or certain subversive elements in society will use it to destroy this country. Since to allow the latter to occur is unconscionable, we must restrict freedom of speech.

The conclusion above is unsound because

(A) subversives do not in fact want to destroy the country
(B) the author places too much importance on the freedom of speech
(C) the author fails to consider an accommodation between the two alternatives
(D) the meaning of "freedom of speech" has not been defined
(E) subversives are a true threat to our way of life

The arguer offers two options: either restrict freedom of speech, or lose the country. He hopes the reader will assume that these are the only options available. This is unwarranted. He does not state how the so-called "subversive elements" would destroy the country, nor for that matter, why they would want to destroy it. There may be a third option that the author did not mention; namely, that society may be able to tolerate the "subversives" and it may even be improved by the diversity of opinion they offer. The answer is (C).

Appeal To Authority

To appeal to authority is to cite an expert's opinion as support for one's own opinion. This method of thought is not necessarily fallacious. Clearly, the reasonableness of the argument depends on the "expertise" of the person being cited and whether she is an expert in a field relevant to the argument. Appealing to a doctor's authority on a medical issue, for example, would be reasonable; but if the issue is about dermatology and the doctor is an orthopedist, then the argument would be questionable.

Personal Attack

In a personal attack (ad hominem), a person's character is challenged instead of her opinions.

Example:

Politician: How can we trust my opponent to be true to the voters? He isn't true to his wife!

This argument is weak because it attacks the opponent's character, not his positions. Some people may consider fidelity a prerequisite for public office. History, however, shows no correlation between fidelity and great political leadership.

Reading

Data sufficiency

Math

Grammar