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Contradiction is the most glaring type of fallacy. It is committed when two opposing statements are simultaneously asserted.
For example, saying “it is raining and it is not raining” is a contradiction. If all contradictions were this basic, there would not be much need to study them. 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.

In the game of basketball, scoring a three-point shot is a skill that only those with a soft shooting touch can develop. Wilt Chamberlain, however, was a great player, so even though he did not have a soft shooting touch he would have excelled at scoring three point shots.

Which one of the following contains a flaw that most closely parallels the flaw contained in the passage?

  1. Eighty percent of the freshmen at Berkeley go on to get a bachelor’s degree. David is a freshman at Berkeley, so he will probably complete his studies and receive a bachelor’s degree.
  2. If the police don’t act immediately to quell the disturbance, it will escalate into a riot. However, since the police are understaffed, there will be a riot.
  3. The meek shall inherit the earth. Susie received an inheritance from her grandfather, so she must be meek.
  4. During the Vietnam War, the powerful had to serve along with the poor. However, Stevens’ father was a federal judge, so Stevens was able to get a draft deferment.
  5. All dolphins are mammals and all mammals breathe air. Therefore, all mammals that breathe air are dolphins.


The argument clearly contradicts itself. So look for an answer-choice that contradicts itself in like manner.


Choice (A) is not self-contradictory. In fact, it’s a fairly sound argument—eliminate it.


Choice (B), on the other hand, is not a very sound argument. The police, though understaffed, may realize the seriousness of the situation and rearrange their priorities. Nevertheless, (B) does not contain a contradiction—eliminate it. Choice (C), though questionable, does not contain a contradiction—eliminate it.


Choice (D), however, does contain a contradiction. It begins by stating that both the powerful and the poor had to serve in Vietnam and ends by stating that some powerful people—namely, Stevens—did not have to serve. This is a contradiction, so (D) is probably the answer.


Choice (E), like the original argument, is invalid but does not contain a contradiction—eliminate it.


The answer is (D).


Equivocation is the use of a word in more than one sense during an argument. It is often done intentionally.

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 correct or moral. The questionable conclusion is possible only if the arguer is allowed to play with the meaning of the critical word right.


Judy: Traditionally, Republican administrations have supported free trade. But the President must veto this free trade act because it will drain away American jobs to Mexico and lead to wholesale exploitation of the Mexican workers by international conglomerates.
Tina: I disagree. Exploitation of workers is the essence of any economic system just like the exploitation of natural resources.

Judy and Tina will not be able to settle their argument unless they

  1. Explain their opinions in more detail
  2. Ask an expert on international trade to decide who is correct
  3. Decide whose conclusion is true but irrelevant
  4. Decide whose conclusion is based on a questionable premise
  5. Define a critical word

Clearly, Judy and Tina are working with different definitions of the word exploitation. Judy is using the meaning that most people attribute to exploitation—abuse. We can’t tell the exact meaning Tina intends, but for her exploitation must have a positive, or at least neutral, connotation, otherwise she would be unlikely to defend it as essential. Their argument will be fruitless until they agree on a definition for exploitation.


Hence the answer is (E).

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.

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.


Democracy is the best form of government yet created. Therefore, we must be vigilant in its defense; that is, we must be prepared to defend the right to freedom. Because this right is fundamental to any progressive form of government, it is clear that democracy is better than any other form of government.

Which one of the following illustrates the same flawed reasoning as found in the passage?

  1. I never get a headache when I eat only Chinese food, nor when I drink only wine. But when I eat Chinese food and drink wine, I get a headache. So the combination of the two must be the cause of my headaches.
  2. The two times I have gone to that restaurant something bad has happened. The first time the waiter dropped a glass and it shattered all over the table. And after the second time I went there, I got sick. So why should I go there again—something bad will just happen again.
  3. I would much rather live a life dedicated to helping my fellow man than one dedicated to gaining material possessions and seeing my fellow man as a competitor. At the end of each day, the satisfaction of having helped people is infinitely greater than the satisfaction of having achieved something material.
  4. I’m obsessed with volleyball; that’s why I play it constantly. I train seven days a week, and I enter every tournament. Since I’m always playing it, I must be obsessed with it.
  5. In my academic studies, I have repeatedly changed majors. I decide to major in each new subject that I’m introduced to. Just as a bee lights from one flower to the next, tasting the nectar of each, I jump from one subject to the next getting just a taste of each.

The argument in the passage is circular (and filled with non-sequiturs). It is incumbent on the writer to give evidence or support for the conclusion. In this argument, though, the writer first states that democracy is the best government, the rest is merely “noise,” until he restates the conclusion.


Choice (A) is a reasonably valid causation argument—eliminate.


(B) argues by generalization. Although it is of questionable validity, it is not circular because the conclusion, “it will happen again,” is not stated, nor is it implicit in the premises—eliminate.


(C) is not circular because the conclusion is mentioned only once—eliminate.


(D) begins by stating, “I’m obsessed with volleyball.” It does not, however, provide compelling evidence for that claim: training seven days a week, rather than indicating obsession, may be required for, say, members of the Olympic Volleyball Team. Furthermore, the argument repeats the conclusion at the end. So it is circular in the same manner as the original.


Hence (D) is our answer.

Shifting the Burden of Proof

As mentioned before, it is incumbent upon 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.

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.


Reasoning by shifting the burden of proof is not always fallacious. In fact, our legal system is predicated on this method of thought. The defendant is assumed innocent until proven guilty. This assumption shifts the onus of proof to the state. Science can also validly use this method of thought to better understand the world—so long as it is not used to claim “truth.” Consider the following argument: “The multitude of theories about our world have failed to codify and predict its behavior as well as Einstein’s theory of relativity. Therefore, our world is probably Einsteinian.” This argument is strong so long as it is qualified with “probably”—otherwise it is fallacious: someone may yet create a better theory of our world.


Astronomers have created a mathematical model for determining whether life exists outside our solar system. It is based on the assumption that life as we know it can exist only on a planet such as our own, and that our sun, which has nine planets circling it, is the kind of star com­monly found throughout the universe. Hence it is projected that there are billions of planets with conditions similar to our own. So astronomers have concluded that it is highly probable, if not virtually certain, that life exists outside our solar system. Yet there has never been detected so much as one planet beyond our solar system. Hence life exists only on planet Earth.

Which one of the following would most weaken the above argument?

  1. Thousands of responsible people, people with reputations in the community to protect, have claimed to have seen UFOs. Statistically, it is virtually impossible for this many people to be mistaken or to be lying.
  2. Recently it has been discovered that Mars has water, and its equatorial region has temper­atures in the same range as that of northern Europe. So there may be life on Mars.
  3. Only one percent of the stars in the universe are like our sun.
  4. The technology needed to detect planets outside our solar system has not yet been developed.
  5. Even if all the elements for life as we know it are present, the probability that life would spontaneously generate is infinitesimal.

This argument implies that since no planet has been discovered outside our solar system, none exist and therefore no life exists elsewhere in the universe. Hence the burden of proof is shifted from the arguer to the astronomers.


Although choice (A) weakens the argument, it has a flaw: the UFOs may not be life forms.


Choice (B) is irrelevant. Although the argument states that the only life in the universe is on Earth, it is essentially about the possibility of life beyond our solar system.


Choice (C) also weakens the argument. However, one percent of billions is still a significant number, and it is not clear whether one percent should be considered “common.” Now, the underlying premise of the argument is that since no other planets have been detected, no others exist.


Choice (D) attacks this premise directly by stating that no planets outside our solar system have been discovered because we don’t yet have the ability to detect them. This is probably the best answer, but we must check all the choices.


Choice (E) strengthens the argument by implying that even if there were other planets it would be extremely unlikely that they would contain life.


The answer, therefore, is (D).

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. The varieties of unwarranted assumptions are too numerous to classify, but a few examples should give you the basic idea.
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

  1. subversives do not in fact want to destroy the country
  2. the author places too much importance on the freedom of speech
  3. the author fails to consider an accommodation between the two alternatives
  4. the meaning of “freedom of speech” has not been defined
  5. 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”; it may even be improved by the diversity of opinion they offer.


The answer is (C).

Example: (False Dichotomy)

When workers do not find their assignments challenging, they become bored and so achieve less than their abilities would allow. On the other hand, when workers find their assignments too difficult, they give up and so again achieve less than what they are capable of achieving. It is, therefore, clear that no worker’s full potential will ever be realized.

Which one of the following is an error of reasoning contained in the argument?

  1. mistakenly equating what is actual and what is merely possible
  2. assuming without warrant that a situation allows only two possibilities
  3. relying on subjective rather than objective evidence
  4. confusing the coincidence of two events with a causal relation between the two
  5. depending on the ambiguous use of a key term

This argument commits the fallacy of false dichotomy. It assumes that workers have only two reactions to their work—either it’s not challenging or it’s too challenging. Clearly, there is a wide range of reactions between those two extremes.


The answer is (B).


To score in the ninetieth percentile on the SAT, one must study hard. If one studies four hours a day for one month, she will score in the ninetieth percentile. Hence, if a person scored in the top ten percent on the SAT, then she must have studied at least four hours a day for one month.

Which one of the following most accurately describes the weakness in the above argument?

  1. The argument fails to take into account that not all test-prep books recommend studying four hours a day for one month.
  2. The argument does not consider that excessive studying can be counterproductive.
  3. The argument does not consider that some people may be able to score in the ninetieth percentile though they studied less than four hours a day for one month.
  4. The argument fails to distinguish between how much people should study and how much they can study.
  5. The author fails to realize that the ninetieth percentile and the top ten percent do not mean the same thing.

You may have noticed that this argument uses the converse of the fallacy “Confusing Necessary Conditions with Sufficient Conditions” mentioned earlier. In other words, it assumes that something which is sufficient is also necessary. In the given argument, this is fallacious because some people may still score in the ninetieth percentile, though they studied less than four hours a day for one month.


Therefore the answer is (C).


Of course Steve supports government sponsorship of the arts. He’s an artist.


Which one of the following uses reasoning that is most similar to the above argument?

  1. Of course if a person lies to me, I will never trust that person again.
  2. Conservatives in the past have prevented ratification of any nuclear arms limitation treaties with the Soviet Union (or Russia), so they will prevent the ratification of the current treaty.
  3. Mr. Sullivan is the police commissioner, so it stands to reason that he would support the NRA’s position on gun control.
  4. Following her conscience, Congresswoman Martinez voted against the death penalty, in spite of the fact that she knew it would doom her chances for reelection.
  5. You’re in no position to criticize me for avoiding paying my fair share of taxes. You don’t even pay your employees a fair wage.

This argument is fallacious—and unfair—because it assumes that all artists support government sponsorship of the arts. Some artists, however, may have reasons for not supporting government sponsorship of the arts.


For example, they may believe that government involvement stifles artistic expression. Or they may reject government involvement on purely philosophical grounds. The argument suggests a person’s profession taints his opinion.


Choice (C) does the same thing, so it is the answer.

True But Irrelevant

This tactic is quite simple: the arguer bases a conclusion on information that is true but not germane to the issue.

This pain relief product can be bought over the counter or in a stronger form with a prescription. But according to this pamphlet, for the prescription strength product to be effective it must be taken at the immediate onset of pain, it must be taken every four hours thereafter, and it cannot be taken with any dairy products. So it actually doesn’t matter whether you use the prescription strength or the over-the-counter strength product.

Which one of the following best identifies the flaw in the above argument?

  1. The fact that many people could not live a full life without the prescription strength prod­uct cannot be ignored.
  2. It cannot be concluded that just because the prescription strength product has certain guidelines and restrictions on its use that it is not more effective.
  3. It does not consider that complications may arise from the prescription strength product.
  4. It fails to consider that other products may be more effective in relieving pain.
  5. It is unreasonable to assume that the over-the-counter strength product does not have similar restrictions and guidelines for its use.

It is unreasonable to reject the effectiveness of a product merely because it has modest requirements for use. All medications have directions and restrictions.


Hence the answer is (B).


Don’t make the mistake of choosing (A). Although it is a good rebuttal, it does not address the flaw in the argument. Interestingly, it too is true but irrelevant.

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 he or 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.

The legalization of drugs is advocated by no less respectable people than William F. Buckley and federal judge Edmund J. Reinholt. These people would not propose a social policy that is likely to be harmful. So there is little risk in experimenting with a one-year legalization of drugs.

In presenting her position the author does which one of the following?

  1. Argues from the specific to the general.
  2. Attacks the motives of her opponents.
  3. Uses the positions of noted social commentators to support her position.
  4. Argues in a circular manner.
  5. Claims that her position is correct because others cannot disprove it.

The only evidence that the author gives to support her position is that respected people agree with her. She is appealing to the authority of others.


Thus, the answer is (C).

Personal Attack

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

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.


A reporter responded with the following to the charge that he resorted to tabloid journalism when he rummaged through and reported on the contents of garbage taken from the home of Henry Kissinger.


“Of all the printed commentary . . . only a few editorial writers thought to express the obvious point that when it comes to invasion of privacy, the man who as National Security Advisor helped to bug the home phones of his own staff members is one of our nation’s leading practitioners.”—Washington Monthly, October 1975

In defending his actions, the reporter does which one of the following?

  1. Attacks the character of Henry Kissinger.
  2. Claims Henry Kissinger caused the reporter to act as he did.
  3. Claims that “bugging” is not an invasion of privacy.
  4. Appeals to the authority of editorial writers.
  5. Claims that his actions were justified because no one was able to show otherwise.

The reporter justifies his actions by claiming that Kissinger is guilty of wrong doing. So, instead of addressing the question, he attacks the character of Henry Kissinger.


The answer is (A).

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