6. Fallacies

We have seen that the logical strength of an argument is the degree of support that its premises confer on its conclusion. In this chapter, we will continue our study of logical strength by examining fallacies. In the broadest sense of the term, a fallacy is any error in reasoning. But the term is normally restricted to certain patterns of errors that occur with some frequency, usually because the reasoning involved has a certain surface plausibility. To the unwary, the premises of a fallacious argument seem relevant to the conclusion, even though they are not; or the argument seems to have more strength than it actually does. This is why fallacies are committed with some frequency.

We are going to study fallacies now for two reasons. The first is to help you avoid them in your own thinking and identify them when they are used against you in debate. Forewarned is forearmed. The second reason is that understanding why these patterns of argument are fallacious will help us understand the nature of good reasoning. Every new disease that doctors identify tells them something about the nature of health, and the same is true of fallacies in logic.

The fallacies we're going to examine in this chapter should not be regarded as a complete list. The varieties of bad reasoning are too numerous to catalog here. I have included only the fallacies that are most common in everyday discussion, and that illustrate something about the nature of good reasoning. Many of these fallacies were identified and labeled by medieval logicians and thus have Latin names. In a few cases, the Latin name has become part of our vocabulary. In other cases the English name is more common, and I have put the Latin name in parentheses.

Subjectivist Fallacies

The cardinal virtue in reasoning is objectivity: a commitment to thinking in accordance with the facts and interpreting them logically, without bias or prejudice. The fallacies we'll examine in this section involve the rejection of objectivity in one way or another.


The first and most straightforward violation of objectivity is the fallacy of subjectivism. This fallacy is committed whenever we hold that something is true merely because we believe or want it to be true. Thus, if p is the proposition in question, subjectivism has the form:

I believe/want p to be true
p is true

In an argument of this sort, a subjective state — the mere fact that we have a belief or desire — is being used as evidence for the truth of a proposition. We can see what's wrong with this argument by identifying the implicit premise. To make this argument stronger, one would have to accept the premise that whatever I believe or want to be true is true. That is, subjectivism implicitly assumes that we are infallible. And of course we aren't. The thoughts and feelings that pass through our minds may or may not correspond to reality. That's why we need a logical method of discovering whether they are true; that's why objectivity is a virtue in the first place.

The fact that someone prefaces a statement with the words "I think" or "I feel" does not necessarily imply subjectivism. This is a conventional way of expressing a view, and the person may go on to offer a perfectly objective argument. Nor are statements about our thoughts and feelings necessarily subjective. Suppose I am trying to tell whether the emotion I am feeling is resentment or justifiable anger. My thought process may be either objective or subjective: objective if I am open to the evidence, subjective if I decide that it is justifiable anger merely because I can't bear to think of myself as resentful. In other words, subjectivism is not an issue of what a statement or conclusion is about; it's an issue of the kind of evidence one uses to support a conclusion. The fallacy is committed only when someone uses the mere fact that he believes or feels something as a reason for thinking it to be true.

It is unlikely that you will ever hear someone commit the fallacy of subjectivism in the pure form diagrammed above. As with most fallacies, the pure, textbook cases are too obviously fallacious for anyone to fall for them. In real life, the fallacies take more subtle and disguised forms. Here are some examples:

1. "I'll think about that tomorrow." This is Scarlett O'Hara's line from Gone with the Wind. It is her way of dealing with unpleasant facts. The point, of course, is that tomorrow never comes: she is simply putting the facts out of mind, on the implicit assumption that they will then cease to exist. Subjectivism is not only a way of adapting conclusions on subjective grounds, but also — and probably more often — a way of evading them. Some people have perfected the skill of ignoring what they don't want to see, and most of us indulge this habit occasionally. If the habit were put into words, it would take the form "I don't want to accept p, therefore p isn't true." That's subjectivism.

2. "I was just brought up to believe in X. " This statement typically occurs when people encounter challenges to their basic convictions. In a discussion of premarital sex, for example, someone might respond to arguments condoning this practice by saying "Well, I was just taught to believe it's wrong." The fact that one was brought up to believe something may explain how one came to have that belief, but it doesn't explain why one ought to believe it; it does not provide any reason for thinking that the belief is true. It simply reinforces the claim that one has that belief. This is not to say that you are irrational if you refuse to abandon a long-held belief just because you've heard an argument against it that you can't answer on the spot. Many of our beliefs—especially on fundamental issues of religion, ethics, and politics—are rooted in a lifetime of experience and reflection. We can't always put that experience and reflection into words right away, and we shouldn't throw out a well-rooted belief on the basis of a single counterargument. But we shouldn't ignore the counterargument, either. To dismiss it on the grounds that it's easier and less threatening not to reexamine our convictions is a type of subjectivism.

3. "That may he true for you, but it isn't true for me. " Suppose two people are discussing man's biological origins. Pat argues that our species arose by evolution; Mike, a creationist, says "Well, that may be true for you, but it's not for me." What does Mike mean when he says that something is (or is not) true for him? Perhaps he means simply that he does (or does not) believe it. In that case, the statement means: you may believe in evolution, but I don't. There's no fallacy here, just the recognition that a disagreement exists, without any claim as to which side is right. But if this is what he means, he should say so directly and not introduce the concept of truth. The point of introducing the concept of truth is usually to give an objective gloss to a belief without having to provide evidence for it or to paper over a disagreement by suggesting that both sides are legitimate, even though they contradict each other and cannot both be true. In either case, the concept of something as "true for me" contains an element of subjectivism: it attributes objective status to a proposition merely because one happens to believe it. At the very least, this concept ought to be a warning flag to keep an eye out for the fallacy.

Appeal to Majority

A newspaper commentary criticizes the Catholic Church for opposing birth-control measures even though "studies show that 90 percent of Catholics no longer consider birth control a sin" [Lawrence Lader, "The Family-Planning Ploy," New York Times, Op-ed, December 12, 1985]. The author, who approves of birth control, is appealing to majority opinion in support of his belief. This is a fallacy for essentially the same reason that subjectivism is. The argument has the form:

The majority (of people, nations, etc.) believe p
p is true

In this case, the subjective state of large numbers of people, not just a single person, is being used as evidence for the truth of a proposition. But the argument is still subjectivistic—and still fallacious. The implicit assumption is that majority opinion is infallible, but it isn't. At various times, majorities have believed that the earth is flat, that bathing is unsanitary, that certain women should be burned as witches.

The fallacy of appealing to the majority is committed whenever someone takes a proposition to be true merely because large numbers of people believe it (regardless of whether those people actually constitute a majority). This fallacy probably occurs more often in political debate than in any other area. One version is the argument from tradition—as in "I oppose socialized medicine because it is inconsistent with our tradition of private medical practice." To say that a principle or policy is traditional is merely to say that it was widely accepted by our predecessors, and the mere fact that they accepted it does not prove it correct. Another version of the fallacy might be called the "wave of the future" argument—as in "Every other progressive nation has already adopted a program of government-provided health care; the United States likewise should abandon its outmoded system of private medicine." To say that some principle or policy is the wave of the future is merely to say that many people or countries have already accepted it; so an appeal to their preferences in support of that principle or policy is, once again, an appeal to majority. The only difference between these opposing arguments is that they appeal to different majorities.

The fact that such an appeal is fallacious doesn't mean we should ignore majority opinion. Objectivity requires a willingness to consider the views of others. If large numbers of people have accepted a principle or policy, it may well be because the principle is true, the policy sound. The possibility is certainly worth exploring. When we explore it, however, we should look for objective evidence; mere popularity doesn't count.

Appeal to Emotion (Argumentum ad Populum)

This fallacy is the attempt to persuade someone of a conclusion by an appeal to emotion instead of evidence. A person who commits this fallacy is hoping that his listeners will adopt a belief on the basis of a feeling he has instilled in them: outrage, hostility, fear, pity, guilt, or whatever. In effect, he is hoping that they will commit the fallacy of subjectivism. The appeal to emotion may be quite explicit. In the 1964 U.S. presidential election, Barry Goldwater's supporters used the slogan, "In your heart you know he's right." More often, however, the appeal is less direct. It may take the form of rhetorical language that is heavily laden with emotive connotations, as in propaganda and other sorts of incendiary political speech. Indeed, medieval logicians called this fallacy argumenturn ad populum—appeal to the mob—because one of the clearest examples is the "rabble-rousing" language used by demagogues. The fallacy may also take the form of visual images that have a strong emotional impact. On television, for example, you can find examples of the fallacy not only in advertising but in news and documentary programs that use images to sway the viewer.

Rhetoric and other emotive devices are not fallacious per se. If you have a logical argument to back up a conclusion, there is nothing wrong with stating it in such a way that your audience will endorse it with their feelings as well as their intellects. Good writers and speakers combine logic and rhetoric to produce exactly that effect. Even in advertising, the emotional pitch may be accompanied by a bona fide reason to buy the product. The fallacy occurs only when rhetoric replaces logic, only when the intent is to make an audience act on emotion instead of rational judgment.

How can we tell when this intent is present? A good test is to translate the argument into neutral language. If the translation leaves a large gap between premises and conclusion, then there is reason to suspect that the emotive language (or visual image, as the case may be) was intended to make a nonrational appeal to the audience. Let's apply this test to some examples.

In a famous speech, Martin Luther King, Jr., said:

I have a dream that one day this nation will rise up and live out the true meaning of its creed: "We hold these truths to be self-evident—that all men are created equal." ... I have a dream that one day even the state of Mississippi, a desert state sweltering with the heat of injustice and oppression, will be transformed into an oasis of freedom and justice. I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin but by the content of their character.
[Quoted from Let the Trumpet Sound, by Stephen B. Oates]

This passage certainly makes an appeal to the emotions. But it is not fallacious, because King is also presenting a logical argument. In neutral language, the argument might be stated as follows: "America was founded on the principle that all men are created equal. This implies that people should not be judged by skin color, which is an accident of birth, but rather by what they make of themselves ('the content of their character'). To be consistent with this principle, America should treat black people and white people alike." The emotional devices in King's speech—the repetition of "I have a dream," the description of Mississippi as a "desert state," the reference to his children—do not compete with or replace his argument. They simply make the meaning of the abstract principles more concrete and vivid.

By way of contrast, let's look at an argument that does commit the fallacy. The following example is taken from a political advertisement by a state employees' union:


A long time ago, politicians hired private companies to do government work. They were mercenary ships, called privateers.

We know them as pirates.

Today, right here in New York State, politicians are trying to hoist the same old idea. This time around, calling it privatization.

Let them get away with it, and privateers will be loose again.

Privatization is a policy adopted by some state governments of hiring private companies to collect garbage, maintain parks, and so forth, rather than have these jobs performed by state employees. Some people argue that private companies do the job more efficiently and thus save the government money. Some people argue the opposite. But the passage quoted above can hardly be considered an argument at all. It relies solely on the negative emotions associated with the privateers, who were private sea-captains authorized by their governments to attack and loot the merchant ships of their enemies. In neutral language, the argument would be:

Governments once contracted with private interests to loot the ships of other nations.
New York State should not contract with private companies to collect garbage, maintain parks, and so forth.

This is an extremely weak argument, as we can see by noting the implicit premise required to link the stated premise with the conclusion. The implicit premise is that what was wrong with the privateers was that they were private. But surely what was wrong was that they engaged in looting. And looting would have been wrong even if done by the governments with their own ships and sailors. The authors of the advertisement are obviously hoping that the emotionally laden image of pirates will keep us from raising such objections.

Appeal to Force (Argumentum ad Baculum)

The eighteenth-century essayist Joseph Addison once wrote (with his tongue in his cheek):

There is a way of managing an Argument... which is made use of by States and Communities, when they draw up a hundred thousand Disputants on each side, and convince one another by dint of sword. A certain grand Monarch was so sensible of his strength in this way of Reasoning, that he writ upon his great Guns—Ratio Ultima Regum, The Logick of Kings.
[The Spectator,
No. 239, December 4, 1711]

Addison's remark is sarcastic: the use of force is not a type of reasoning, but is actually its antithesis. A threat is not an argument; a club (in Latin, baculum) is not a reason. If I "persuade" you of something by means of threats, I have not given you a reason for thinking the proposition is true; I have simply scared you into thinking, or at least into saying, it is true. In this respect, the appeal to force might be regarded as a form of the appeal to emotion.

An appeal to force may well involve direct coercion. When a government engages in censorship, for example, it uses force to prohibit the expression of certain ideas and to compel agreement with other ideas. The point of this control over verbal expression is to influence what people believe. But the fallacy need not involve actual physical force or violence. It is committed whenever any sort of threat is used, and nonphysical threats are probably more common than physical ones. When parents threaten to withdraw their support unless a child adopts their religious beliefs, when a teacher threatens a dissenting student with a lower grade, when someone "persuades" a friend by threatening the loss of affection—they are committing forms of this fallacy. As the examples illustrate, the fallacy is usually committed in the effort to breed conformity in belief, and society has many nonphysical means of intimidating people into accepting the conventional views. Dissenters may be held up to ridicule, threatened with moral disapproval ("Only a pig would believe that"), told they aren't "cool," and so on. Whenever intimidation of this sort replaces logic in an effort to persuade, it is no less fallacious than the use of actual force.

Summary Box 6.1

Subjectivist Fallacies

Subjectivism: using the fact that one believes or wants a proposition to be true as evidence of its truth.

Appeal to majority: using the fact that large numbers of people believe a proposition to be true as evidence of its truth.

Appeal to emotion (argumentum ad populum): trying to get someone to accept a proposition on the basis of an emotion one induces.

Appeal to force (argumentum ad baculum): trying to get someone to accept a proposition on the basis of a threat.


Practice Quiz 6.1

Identify which of the fallacies discussed in this section—subjectivism, appeal to majority, appeal to emotion, or appeal to force—is committed in the statements below.

1. Of course Jane is going to be successful. Everyone says so.

2. "Hank is a really sharp dresser."
"What about the purple plaid pants he wore last night?"
"I don't want to think about that."

3. How can you believe that John is innocent? I don't see how we can go on being friends if you believe that.

4. After the accident I was in, I was so upset I couldn't sleep for weeks; I'd wake up with my heart pounding, hearing the sound of the other car crushing the metal of my car door. Cars should be built more solidly than they are.

5. The Golden Rule is a sound moral principle, for it is basic to every system of ethics in every culture.

6. Foreign imports are wrecking our economy and savaging our workers, the backbone of this country. Buy American! Before you put your money on that Honda, think of the guy in Detroit whose kids may not eat tomorrow. Before you buy those Italian pumps, ask yourself whether a little glamour is worth the job of the shoemaker in Boston who's worked all his life to make an honest living.

7. You can argue all you want that democracy gives us only the illusion of control over the government, but I don't buy it. I was brought up to believe in the democratic system.

8. The most effective way to increase government revenues would be to raise the corporate income tax, since opinion polls show widespread support for this approach.

9. Teacher to student: "... and finally, in reconsidering your position, you might remember who gives the grades in this course."

10. "Fine. Go ahead and marry him. Why should you care about breaking your mother's heart? I guess you love him more than me—but why should I care? Who am I to complain? I'm only your mother. I only spent twenty years trying to make a good match for you, a nice boy, and now you run off. ..."


Fallacies Involving Credibility

We noticed at the beginning of Chapter 5 that we rely on information passed on by other people for much of what we know. Most of us lack firsthand knowledge of the evidence for the theory of relativity, the DNA model of genes, the link between smoking and lung cancer; we accept these and other scientific ideas because we accept, the authority oi experts m the various fields. We know about historical events largely through the records and memoirs left by our predecessors. We learn about current events from reading newspaper accounts by journalists. Courts of law rely on eyewitness testimony and expert witnesses. Indeed, we can extend the legal concept of testimonial evidence to cover all of these cases.

To evaluate of such evidence, we must weigh the credibility of the witness. When we accept a conclusion on the basis of someone's testimony, our reasoning can be diagrammed as follows:

X says p
p is true

If such an argument is to have any logical strength, two assumptions must be true. First, X must be competent to speak on the subject. If p is a statement in some technical area, then X must have some expertise in that area. If it is a statement about some event, X maust be someone who was in a position to know what happened. Second, X must be reporting what he knows objectively, without bias, distortion, or deceit. In other words, X must be someone who not only knows the truth, but who also tells the truth. Both conditions are essential for credibility. Ideally, we should have a positive reason to think that X is competent and objective. At the very least, we must not have any evidence that X is incompetent or nonobjective.

In this section, we'll look at two fallacies that involve a misuse of the standards for credibility.

Appeal to Authority (Argumentum ad Verecundiam)

An authority is someone whose word carries special weight, someone who can speak with authority, because of expertise in some area of knowledge such as law, science, or medicine. It is perfectly appropriate to rely on the testimony of authorities if the conditions of credibility are satisfied. If they are not satisfied, however, the appeal to authority is fallacious.

The first condition is that the alleged authority be competent—an expert on the subject matter in question. It is typically violated when people speak outside their fields of expertise. For example, advertisers often use celebrity endorsements—a basketball star praises his favorite brand of orange juice, a famous actor extols the virtues of a luxury car. If the role of the celebrity is merely to add glamour, there's no fallacy involved, because there's no attempt at logical argument. But the advertiser's point is usually to persuade you that the product is good because someone you respect says so. That's a fallacy. Skill on the basketball court does not imply a discriminating taste in orange juice, nor does acting ability give one expertise in judging cars. The same fallacy would be committed in a political argument if one cited the opinion of a scientist, or a rock star, or an eminent corporate executive. When people of talent or expertise speak on matters outside their fields, their opinion carries no more weight than that of any layman. That much ought to be obvious. But there is another, less obvious problem with the competence assumption.

It often happens that experts disagree. A criminal defendant is said to be insane by one psychiatrist, sane by another. One economist says that a change in the tax code will eliminate jobs, another says that it will create jobs. Across a wide array of issues—from the safety of nuclear power plants, to the causes of inflation, to the historical origins of human beings—specialists disagree. What should we do when we encounter such disagreements? The first thing to do, of course, is to make sure that we are dealing with a genuine dispute among experts and not simply an effort by some crackpot to challenge well-established principles or theories. If the dispute is a genuine one, then we have to take both sides into account. An argument that appeals only to one group of experts is fallacious. That's not because both sides are necessarily valid. It may be that one group of specialists are objectively right, and their opponents are mistaken or even irrational. But we are not in a position, as laymen, to make this judgment—otherwise we wouldn't have to rely on experts in the first place.

The second condition for credibility is that the alleged authority be objective. Since celebrities are paid to appear in advertisements, for example, they have an obvious motive for praising the product regardless of what they really think about it. In general, the condition of objectivity is violated when an expert has an emotional commitment or vested interest in an issue—even if it lies within his field of expertise. Professionals themselves recognize the dangers here: doctors do not operate on members of their own family; lawyers say that an attorney who represents himself in court has a fool for a client.

It is very difficult, however, to assess objectivity. For example, media coverage of technological risks, such as those at nuclear power plants or in chemical accidents, usually relies much more heavily on expert sources in government than on those in industry. The reporters' rationale is that industry experts have a vested interest in down-playing risks posed by the companies that employ them. But one could also argue that government experts have a vested interest in exaggerating risks, because that will increase support for government action and thus increase their job security.

The problem is that with enough imagination, and enough cynicism, we can find a reason to impugn anyone's objectivity. If we go to that extreme, however, then we lose all the advantages of having specialists in different fields; we lose the advantages of cooperation in the pursuit of knowledge. The cognitive division of labor, like any other social arrangement, depends to some extent on mutual trust. So it seems more reasonable to presume an expert innocent until proven guilty—that is, to presume he is objective unless we have good reason to doubt it. In any case, we should be even-handed. On economic issues, for example, government and industry experts should be judged by the same standard, regardless of whether we favor more or less government regulation.

The use of authorities, finally, is appropriate only when the issue in question requires specialized knowledge or skill that the ordinary person does not possess. If the issue is not a technical one—if it is a matter of common sense, or a value judgment, or a political view, or an observation about human nature—then the ordinary person is capable of understanding the evidence for it, and should not be asked to rely on someone else's judgment. Why should we settle for secondhand knowledge, when we could have firsthand knowledge? This distinction is especially important to keep in mind when we encounter an author who uses lots of quotations to back up his argument: he may well be trying to cover a hole in his argument by citing eminent people who happen to agree with him.

Ad Hominem

An ad hominem argument rejects or dismisses another person's statement by attacking the person rather than the statement itself. As we will see, there are many different forms of this fallacy, but all of them involve some attempt to avoid dealing with a statement logically, and in each case the method is to attempt to discredit the speaker by citing some negative trait. An ad hominem argument has the form:

(X says p) + (X has some negative trait)
p is false

This is a fallacy because the truth or falsity of the statement itself, or the strength of an argument for it, has nothing to do with the character, motives, or any other trait of the person who makes the statement or argument.

This principle is true even when we are concerned with testimonial evidence, but we have to keep a certain distinction in mind. If someone defends a position by citing an authority, as we have seen, then it is legitimate to consider evidence regarding the authority's competence and objectivity. In a trial where the jury is asked to accept the testimony of a witness, it is certainly legitimate for the opposing side to introduce evidence that the witness is dishonest or biased. But discrediting witnesses or authorities does not provide evidence that what they say is actually false; it merely eliminates any reason for thinking that what they say is true. So we go back to square one: we are left with no evidence one way or the other. In other contexts, where there is no issue of relying on authorities, the use of discrediting evidence about the person is always fallacious. If someone offers an argument for his position, then it doesn't matter how rotten or stupid he is. We have to evaluate the argument on its merits.

In its crudest form, the ad hominem fallacy involves nothing more than insults—calling one's opponent an idiot, slob, lowlife, airhead, fascist, pinko, nerd, fairy, bleeding heart, wimp, Neanderthal, and so on through the rich vocabulary of abuse our language offers. Unlike the other fallacies, moreover, this one is committed fairly often in its crude form. In personal disputes, disagreement often breeds anger, and angry people hit below the belt. In politics, ad hominem arguments are a common technique of propaganda and a common device of politicians who try to enlist support by attacking their enemies. But the fallacy can also take more sophisticated forms. Let's look at a few.

Suppose that someone criticizes you for telling a white lie. If your critic is himself a notorious liar, you would probably be tempted to say, "Look who's talking!" This response is certainly understandable—no one enjoys being censured by a moral inferior—but it is fallacious. It's a species of ad hominem known as the tu quoque ("you're another") argument. The fact that someone else is guilty of an accusation doesn't prove that you are innocent. It may be unseemly for the pot to call the kettle black, but the kettle is black nonetheless.

A related version of the ad hominem fallacy occurs when we attack someone's position by claiming that it is inconsistent with his practice or with his other positions. The classic example is the patient who says to his doctor: "How can you tell me I should stop smoking when you still smoke yourself?" The fact that a doctor doesn't take his own advice hardly means that it isn't good advice; a hypocrite may still say something true or make a valid argument.

A final version of ad hominem attempts to impugn someone's objectivity by claiming that he has a vested interest in the view he defends. Except in the case of someone being cited as an authority (as we discussed above), this tactic is fallacious, and it is usually done in a sneaky way. Here's an academic example:

In the constitutional struggles of the seventeenth century, the modern theory of natural law—the theory of individual rights—was eventually perfected. Stripped of the trappings which each particular theorist hung upon it, the bare theory was a simple pattern of ... assumptions which, in the opinion of the men whose interests they served, were as obviously true as the axioms of Euclid.
[Richard Schlatter, Private Property]

The natural law theory in politics said that individuals had certain inalienable rights that government could not violate, including the right to acquire and dispose of private property. This passage describes one aspect of the theory: that such rights were held to be self-evident, like axioms of geometry. The author clearly does not agree with this view. But instead of presenting a reasoned argument against it, he takes a shortcut: he implies that the principle of property rights seemed self-evident only because it served the political interests of those who were wealthy. This tactic is sometimes called "poisoning the well," and it is obviously fallacious.The fact that someone might have a nonrational motive for supporting a position does not mean the position is false, and it certainly does not mean we can decide ahead of time that all his arguments for the position can be dismissed.

In face-to-face disputes, poisoning the well usually takes the form of the statement, "You're just saying that because...." For example: "You're only supporting lulie for class president because she's your friend," or "You're just defending the draft because you know you'd get a medical exemption."

Statements of this type are fallacious: if you have given an argument for the draft, or in favor of Julie's candidacy, the soundness of your argument is unaffected by the existence of other motivations you may have for your position. Such statements are insulting. They say, in effect, "I won't even listen to what you have to say because I know ahead of time that you can't be objective; your reasoning is nothing more than a mouthpiece for your emotions and your vested interests." This is a particularly insidious form of the ad hominem fallacy, because it tries to undercut your confidence in your ability to think objectively; it breeds self-doubt and timidity. It's true that we have to be careful not to let our judgment be biased by subjective factors. But we should not accept undeserved accusations that we are guilty of this (or any other) logical sin.

Summary Box 6.2

Fallacies Involving Credibility

Appeal to authority (argumentum ad verecundiam): using testimonial evidence for a proposition when the conditions for credibility are not satisfied or the use of such evidence is inappropriate.

Ad hominem: using a negative trait of a speaker as evidence that his statement is false or his argument weak.


Practice Quiz 6.2

Identify which of the fallacies discussed in this section—appeal to authority or ad hominem—is committed in the statements below.

1.  1 think America should be more careful about the international organizations we join and the treaties we sign. After all, wasn't it George Washington himself who warned against "foreign entanglements"?

2.  Why should Congress consult the joint chiefs of staff about military funding? They are military men, so obviously they will want as much money as they can get.

3.  Mow can you say that animals have rights and should not be killed, when you eat meat?

4.  To solve our transportation problems, we have to put more money into mass transit. "CBS News" said so last night.

5.  TV commentators are always attacking big business for making "obscene profits," but the media companies they work for have higher profits than almost any other industry.


Fallacies of Context

Fallacies in this category include arguments that "jump to conclusions." There is a logical gap in these arguments because they fail to consider a wide enough context of information. The problem is not the premises per se: the premises are relevant to the conclusion; they do provide genuine evidence. But the evidence is simply inadequate or incomplete.

False Alternative

When we reason about the truth or falsity of a conclusion, we rarely consider the conclusion in a vacuum. Instead, we have in mind a range of other possible conclusions. When we think about whether to take a certain action, we weigh it against other options. When we consider a hypothesis to explain why something happened, we test it against other hypotheses. In short, thinking often involves a choice among alternatives. The fallacy of false alternatives occurs when we fail to consider all the relevant possibilities.

There are several common forms of the fallacy. One form occurs when we consider only the extreme points on a scale. If you told me that Diane is not rich, I would commit the fallacy if I inferred that she is poor. Rich and poor are the extremes on a scale that contains many intermediate degrees of wealth. Another common form of false alternative involves the polarization of positions. Fanatics sometimes say, "If you're not with us, you're against us," but there may be an alternative to these two positions. For example, one might agree with the fanatics' goals but disagree with their means. Yet another common example of the fallacy is the opinion poll that asks us to choose among a small number of possible viewpoints.

The most subtle examples of the fallacy are those in which relevant alternatives are excluded by some implicit, unspoken, and thus invisible assumption. Some political philosophers argue, for example, that as a society becomes more secular, it will tend to drift toward collectivism, because if people do not give meaning to their lives through service to God, they can find meaning only in service to the state. But why are these the only possibilities? The argument clearly assumes that the individual gives meaning to his life only through service to something outside himself, something "higher." It excludes the possibility that the individual can give meaning to his own life. It may be that the assumption is true; perhaps the latter possibility should be excluded. But this is not self-evident: some further argument would be required to justify the assumption. If the argument excludes an alternative without justification, it is fallacious.

The best safeguards against this fallacy are an open mind and a good imagination. No matter how certain we are of our conclusions and our arguments, it is always worthwhile to stop and ask: is there anything I've overlooked? could there be some other explanation for these facts? is there some other perspective one might take? When we can't find the solution to a problem, it is often because we are making an assumption that excludes alternative approaches. If we are not satisfied with any of the standard positions on a given issue, it may be because they all make some assumption that should be called into question, thus opening up other possible positions.

Post Hoc

The Latin name of this fallacy is short for post hoc ergo propter hoc: "after this, therefore because of this." The fallacy has to do with causality, and it has the structure:

A occurred before B
A caused B

Such reasoning is fallacious because many events that precede a given event have nothing to do with it, as in the old joke: "Why are you whistling?" "To keep the elephants away." "But there aren't any elephants around here." "See? It works."

The post hoc fallacy is probably the source of many superstitions. Someone, somewhere, had a run of bad luck and attributed it to breaking a mirror, walking under a ladder, stepping on a crack, or some other previous action. A student does well on an exam and thereafter always wears the same "lucky" sweater on exam days. More serious examples of the fallacy occur in situations where causal relationships are extremely complex and di fficult to identify. Stock market advisers, for instance, sometimes make predictions on the basis of a few indicators that happened to precede a previous rise or fall in prices. Post hoc reasoning can also occur in speculation about the causes of historical events such as the Civil War, the causes of economic phenomena such as the Great Depression, or the causes of sociological trends such as the increasing divorce rate.

It's certainly true that, if we want to know what caused an event or phenomenon B, we have to start by identifying the factors that preceded it. But we can't stop there. To show that some particular factor A was the cause, we have to find evidence that there is some stronger connection between A and B than just a temporal relationship. In Part Five, we will study in detail the types of argument that provide such evidence. For now, we will have to rely on our intuitive judgment. When someone presents an argument that A caused B, ask yourself: Could it be merely a coincidence that A happened just before B? Is A the kind of thing that could have an effect on B? Has the person offered any explanation of how A affected B?

Hasty Generalization

Each of the following is a general proposition, or generalization:

1. Water always flows downhill.
2. Large breeds of dogs have shorter lifespans than smaller ones.
3. People in France are not very friendly to tourists.
4. Italians are quick-tempered.
5. Stockbrokers drive BMWs.
6. Bill never gets anywhere on time.

Most general propositions make a claim about a category of things (water, dogs, Italians, etc.), attributing some characteristic to all members of the category. As statement 6 illustrates, however, a generalization may be about a particular individual; what makes it a generalization is that it attributes a general pattern of behavior to that individual.

General propositions play a vital role in reasoning. They allow us to reap the advantages of having concepts: we form a concept for a type of thing, and then generalize about the attributes and patterns of action shared by things of that type. This saves us the trouble of having to discover from scratch the features of every particular thing we encounter. Knowing about the lifespans of large versus small dogs, for example, can help us in choosing a pet.

General propositions are normally supported by observing particular cases. But we often draw conclusions too quickly, on the basis of insufficient evidence. This fallacy, known as hasty generalization, can take many forms. A single bad experience while traveling can prejudice our view of an entire city or country (as in 3 above). Most of us have stereotypes about ethnic groups, professions, or people from different regions of the country, based on our exposure to a few individuals (as in 4 and 5 above). Even a judgment about the character or personality of an individual is a generalization drawn from our observation of that person on specific occasions; here, too, we often jump to conclusions. And we can jump to conclusions about ourselves: we make a mistake, fail a test, have a problem in a relationship, and then draw a sweeping conclusion about our inadequacies.

In Part Five, we are going to study the proper methods and precautions for generalizing from particular cases. But the essence of the method is to ask ourselves whether we have considered a wide enough context. It is rarely if ever possible to draw a valid generalization from a single instance, or even from a few; we should consider a larger sample. I may have met a few stockbrokers who drive BMWs, for example, but if I asked around I would quickly find some who don't. We should also look at a variety of instances. For example, we might observe that Bill is late for work not just on one occasion but on many. It would still be hasty to conclude that he never gets anywhere on time. Is he also late for parties, dates, ball games? If so, we have much stronger evidence that his problem has to do with time in general rather than with work.

Composition and Division

The fallacy of composition consists in inferring that what is true of a part must be true of the whole. Of course, parts and wholes sometimes do have the same properties. Every page in a newspaper is flammable, and so is the newspaper as a whole. But not every property is like this. We commit the fallacy of composition when we jump to a conclusion about the whole without considering whether the nature of the property in question makes it reasonable. This fallacy is like hasty generalization, except that it is concerned with parts and wholes rather than with individuals and the general classes to which they belong. To see the difference, consider the radio in my car. The radio is a member of the general class of audio equipment. It would be hasty to generalize that all audio equipment is made by Motorola, just because my car radio is. The radio is also a part of my car. It would be a fallacy of composition to infer that my car as a whole was made by Motorola just because one part was.

The fallacy of division is the mirror image of composition: it is the inference that what is true of the whole must be true of the parts. The fact that my car gets 25 miles to the gallon does not mean that the radio gets 25 miles to the gallon—a statement that hardly even makes sense. The fact that my car was made by General Motors does not mean that GM made every part.

It isn't likely that anyone would commit these fallacies in the case of something like a car. The fallacies are more common when the relation between part and whole is more complicated, and especially when we are talking about social groups and the individuals of which they are composed. For example, a newspaper editorial defends government economic planning by asking, "Why is planning considered a good thing for individuals and business but a bad thing for the national economy?" The fact that individuals need to plan how they are going to earn a living and spend their income does not imply that society as a whole should plan how wealth should be produced and distributed throughout the economy. Whether national planning is a good idea depends on a host of other questions, such as whether government planners are capable of performing this task, and whether they have the right to supersede the decisions that individuals and businesses make about how to use their resources. In general, what is true of individuals may or may not be true of society as a whole.

The fallacies of composition and division are also committed frequently in the use of statistics. Consider the controversial issue of racial differences in intelligence. If such differences do exist, they are differences in the average IQ of racial groups. To infer that a given individual in one group is more intelligent than another individual in another group, just because his group's average is higher, would be a fallacy of division. Averages are computed from the scores of individuals who are distributed along the whole continuum of intelligence, so the group average tells us nothing about any individual.

Here's another example. The average person whose income is over $200,000 pays much more in taxes than the average person whose income is in the $50,000—200,000 range. But it would be a fallacy of composition to infer that the wealthier group as a whole pays more taxes than the middle-income group. In fact, they pay less, because there are many fewer people in the wealthier group.

Summary Box 6.3

Fallacies of Context

False alternative: excluding relevant possibilities without justification

Post hoc: using the fact that one event preceded another as sufficient evidence for the conclusion that the first caused the second

Hasty generalization: inferring a general proposition from an inadequate sample of particular cases

Composition: inferring that a whole has a property merely because its parts have that property

Division: inferring that a part has a property merely because the whole has that property


Practice Quiz 6.3

Identify which of the fallacies discussed in this section—false alternative, post hoc, hasty generalization, composition, and division—are committed in the statements on the next page.

1. Stock prices fell dramatically two years ago, after Congress raised tariffs, and they just raised tariffs again, so expect another crash in the market.

2. Everyone on the Dream Team is the best player in his position, so the Dream Team is the best team around.

3. Either Tom was telling the truth when he said his grade average was 3.7, or he was lying. But he wasn't telling the truth, since his average is actually 3.6, so he was lying.

4. Don't go down to River Road. I was down there once and got mugged. They're all thieves down there.

5. If she loved me, she would have called me back tonight. She didn't, so she must hate me.

6. Although I'm happy about the raise I got today, I'm also a little worried. The last time I got a raise my car got stolen the next morning.

7. On the basis of the rambling speech Madeleine gave at the school assembly last week, I would say she's not a good public speaker.

8. How can you say that you washed the car? Did you wash every part—under the hood, around the muffler, under the seats?

9. Congressman Jones denies that he's a liberal, so he must be a conservative. 10. Twenty-five years after graduation, Harvard alumni have incomes much higher than the average college graduate. A Harvard education must be the road to riches.


Fallacies of Logical Structure

In the previous sections, we examined arguments that are fallacious either because they introduce irrelevant considerations into the reasoning process (emotions, threats, personal traits) or because they fail to consider a wide enough context of information. In this section, we'll examine fallacies that involve more subtle logical errors within the argument itself.

Begging the Question (Circular Argument)

The phrase "begging the question" is often used rather loosely to mean any failure to address a certain issue. This is not necessarily a fallacy. In the strict and literal sense, however, begging the question is the use of a proposition as a premise in an argument intended to support that same proposition. This is fallacious. The point of reasoning is to throw light on the truth or falsity of a proposition (the conclusion) by relating it to other propositions (the premises) that we already have some basis for believing to be true. If our reasoning does nothing more than relate p to itself, then it hasn't gained us anything. Circular arguments are no more productive than circular definitions.

The most obvious way to commit the fallacy would be simply to restate the conclusion as a premise, in an argument of the form:


This usually occurs only when the proposition is formulated in two different ways, so that it is not immediately apparent that the person is simply restating the conclusion. For example: "[1] Society has an obligation to support the needy, because [2] people who cannot provide for themselves have a right to the resources of the community." Statement 2 expresses the same proposition as 1: "society" means the same thing as "community," "the needy" are the same class of people as "those who cannot provide for themselves," and the obligation mentioned in 1 is merely another way of expressing the right mentioned in 2. Both statements, therefore, should be given the same number, and the diagram would be:


People typically beg the question in this way when a proposition seems so obvious to them that they aren't sure what further evidence could be given for it, so they keep restating it in the hope that some formulation will strike a chord in the listener and lead him to agree.

A more subtle form of the fallacy occurs when the circle is enlarged to include more than one step: the conclusion p is supported by premise q, which in turn is supported by p (though there could be any number of intervening steps). Suppose I am arguing with an atheist about the existence of a supreme being. He asks why I believe that God exists, and I say, "Because the Bible says so." If he then asks why he should take the Bible's word for it, and I answer that the Bible is trustworthy because it is the Word of God, I am arguing in a circle: my premise assumes the existence of God, which was precisely the question at issue. As this example illustrates, circular reasoning of this type often occurs in debates when we try to answer an objection by falling back on the conclusion we are trying to establish.

Another common form of begging the question is known as the complex question. The classic example is the prosecutor who asks the witness, "Have you stopped beating your wife?" If the witness says "Yes," he has admitted that he was beating his wife, but if he answers "No," he seems to admit the same thing. The reason for this is obvious. Despite its appearance, the question is not simple but complex. There are really two questions here: has the man ever beaten his wife? and if so, has he stopped? We can't even raise the second question, much less answer it, until we have answered the first one. By not asking the first question, the prosecutor simply assumes that the answer to it is "Yes"—he begs that question. Most questions rest on certain assumptions. If we accept those assumptions, we can go ahead and answer the question. But if we reject those assumptions, then we should say so and refuse to answer the question. Thus the witness in the classic example should say, "Your question is invalid because I never started beating my wife."


We have seen that an argument links one or more propositions used as premises with a proposition that serves as the conclusion. We have also seen that what a proposition asserts depends (in part) on the words used to express it. The fallacy of equivocation occurs when a word switches meaning in the middle of the argument—when it expresses one concept in one premise and another concept in another premise or in the conclusion.

In Chapter 1, I used the example of two people talking past each other in discussing grades because one person is talking about letter grades and the other is referring to any form of evaluating student work. Suppose this difference in meaning occurred inside an argument:

[Letter] grades are a crude and mechanical device that does not measure the nuances of student performance
Student work should not be graded [evaluated]

The conclusion is not supported by the premise because the term "grade" has shifted its meaning. The claim that letter grades are a poor evaluation device hardly implies that student work should not be evaluated at all; if anything, it implies that we should find a better means for measuring performance.

In this example, the equivocation occurred because a word was used in both a narrower sense, to designate a species (letter grades) and in a wider sense to designate a genus (evaluation as such). This illustrates a common pattern in which a word's meaning is broadened in the course of an argument. One way in which this happens is by the metaphorical extension of a concept. The term "censorship," for example, refers to a restriction on someone's freedom of speech by a government, using the coercive threat of fines, jail, or worse. But the term is sometimes used metaphorically for other constraints on the ability to express oneself. It would be equivocation to switch between these meanings, as in the following argument:

1. Some newspapers censor speech by refusing to publish controversial authors + 2. Censorship violates the First Amendment
Some newspapers violate the First Amendment by refusing to publish controversial authors

In premise (1), the term "censor" is used in the metaphorical sense, since the newspapers are merely choosing not to publish certain authors rather than literally threatening them with legal sanctions. But in premise (2), the term is used in its literal meaning, so the conclusion does not follow.

As an argument employs more complex and abstract concepts, equivocation becomes more of a danger. The best way to avoid the danger is to use the techniques for clarifying and defining concepts that we studied in Part I.

Appeal to Ignorance (Argumentum ad Ignorantiam)

Suppose I accused you of cheating on an exam. "Prove it," you say. "Can you prove that you didn't?" I ask—and thereby commit the fallacy of appeal to ignorance. This fallacy consists in the argument that a proposition is true because it hasn't been proven false. To put it differently, it is the argument that a proposition is true because the opposing proposition hasn't been proven true. Using the symbol ~p to stand for the denial or negation of p, the fallacy has the structure:

~p has not been proven true
p is true

This is a fallacy because a lack of evidence for ~p does not imply that there is evidence for p. All it means is that we do not know that ~p is true. I can't prove that a storm is not brewing in the atmosphere of Jupiter, but that would hardly count as evidence that a storm is brewing. The absence of evidence usually means that we simply don't know enough to make a judgment. Such ignorance cannot be transmuted into knowledge, any more than brass can be transmuted into gold.

In the preceding examples of the fallacy, the proposition p was a positive claim: that you cheated, that a storm is brewing on Jupiter. But the fallacy can also be committed when p is a negative claim. The absence of evidence that you did cheat does not prove that you didn't, the absence of evidence that a storm is brewing doesn't prove that one isn't. In the diagram above, p may be either negative or positive, and ~p will have the opposite quality; the structure of the fallacy is the same in either case. Strictly speaking, there is a logical symmetry between positive and negative claims.

In practice, however, the fallacy is normally committed by those who assert the positive. The reason is that we rarely have occasion to make negative claims except in response to positive ones. We rarely have occasion to assert that something is not the case until someone has suggested that it is. Suppose I suddenly announced that there is an invisible leprechaun hovering over your left shoulder. Naturally, you would be skeptical, and you would ask what reason I had for believing this (we couldn't settle the matter by looking, since I said it was invisible). I'm the one making the assertion here, so I have to provide evidence. Apart from my statement, it would never occur to you to deny that there is an invisible leprechaun over your left shoulder. In the same way, it would not occur to you to deny that you cheated on the test unless someone accused you of it, and then the accuser has the burden of offering evidence.

As a rule, it is the positive claim that puts the ball in play, and the positive claim that carries the initial burden of proof. If someone makes an unsupported statement, therefore, the proper response is not to make an equally unsupported denial. Nor should you accept the burden of disproving the person's statement; if you do, you are cooperating in an implicit appeal to ignorance. (This is a trap that paranoid people often spring on their listeners: they make an arbitrary claim about a conspiracy against them and then take their claim to be vindicated unless others can disprove it.) The proper response is simply to point out that the claim is unsupported and ask the person to provide some evidence for it. If evidence is forthcoming, then the ball is in your court; if you do not find the evidence convincing, it is your responsibility to explain why.

One application of this rule is the legal principle that a person is innocent until proven guilty. To assert that someone is guilty is to make a positive claim: that he committed a certain act. Thus in a court of law, the burden of proof rests with the party who brings the charges. But we need to be careful here. The prosecution's failure to establish guilt on the part of the defendant does not prove that the defendant didn't commit the crime. We would commit the fallacy of appealing to ignorance if we thought so. In this respect, the legal rule goes beyond the burden of proof principle. It also reflects the ethical principle that it is better to let a guilty person go free than to punish an innocent one.


The fallacy of diversion consists in changing the issue in the middle of an argument. A prosecutor in a child abuse case might go on and on about the horrors of child abuse—the child's suffering and future psychological problems, statistics showing that the problem is a growing one, and so forth—when the real issue is whether the defendant is guilty of the crime. The argument would run:

1. The defendant is guilty of child abuse.
2. Child abuse is an awful crime.
3, 4, ... n. Statements concerning immediate and long-term effects on children, statistics on the extent of the problem, and other evidence.

The prosecutor's strategy is obvious. He is diverting attention from 1 to 2, because 2 is much easier to prove. Who could deny that child abuse is awful? At the same time, however, he is hoping that the jury will not notice the diversion and that the strength of the argument for conclusion 2 will carry over in their minds to 1, even though the defendant's guilt is a completely separate question. As the example illustrates, diversion often works hand in glove with the appeal to emotion: diversion works best when the nonrelevant conclusion arouses powerful emotions. For this reason, a nonrelevant issue is sometimes called a red herring—herring turns red when it is smoked, and a smoked fish has such a powerful smell that dragging it across the ground will throw a dog off the scent.

A common form of diversion occurs in regard to human actions and their consequences. Virtually any action has some effects that are not intended, and often not even foreseen. The fact that your action had a certain consequence, therefore, does not necessarily mean that you intended it, and I would commit the fallacy of diversion if I tried to prove your intent solely by showing that the action did have that consequence. Suppose you go to the library one evening and miss a call from your mother. There may have been no way to anticipate the call. Even if there was, you may have felt that doing work at the library was more important, and that missing the call would have to be an unfortunate by-product of going there. To prove that you were deliberately trying to avoid the call, we would need some positive evidence of that intent. It would be diversion to argue that you wanted to miss the call if the only evidence is that you did go to the library. In the same way, it would be fallacious to argue that the State Department is controlled by big business just because a foreign-policy decision turns out to be of benefit to large corporations; once again, we need evidence of intent, not merely of consequence.

Another form of diversion is called the straw man argument. This fallacy occurs in debate when someone distorts an opponent's position, usually stating it in an oversimplified or extreme form, and then refutes the distorted position, not the real one. For example, suppose you are a student in my class, and you come to me with the suggestion that I allow more class discussion. I would commit the straw man fallacy if I replied: "I don't want to give the entire class period over to an aimless bull session, because no one would learn anything." This may be an excellent argument against giving the entire class period over to an aimless bull session, but that is not what you suggested. (If you diagram this example, you will see that it fits the pattern of diversion.) Straw man arguments occur most often when issues are complex and emotions run high. Look for them especially in politics and in quarrels between friends and lovers.

We have now examined fifteen common fallacies; they are listed and defined in the summary box below. As indicated at the outset, this is not an exhaustive list of logical errors; it includes only the more common and more significant ones. It should also be emphasized that a given argument may commit more than one fallacy. If you encounter such an argument, in the exercises below or in real life, you should try to identify all the fallacies it commits.

Summary Box 6.4

Fallacies of Logical Structure

Begging the question (circular argument): trying to support a proposition with an argument in which that proposition is a premise.

Equivocation: using a word in two different meanings in the premises and/or conclusion.

Appeal to ignorance (argumentum ad ignorantiam): using the absence of proof for a proposition as evidence for the truth of the opposing proposition.

Diversion: trying to support one proposition by arguing for another proposition.


Practice Quiz 6.4

Each of the following arguments commits one or more of the fallacies of logical structure discussed in this section; identify them.

1.   No one has proved that global warming is actually occurring, so I'm sure it isn't.

2.   The federal government should save New York City from default, for New York deserves such aid.

3.   It would be a crime to let that dessert go to waste. Since I am a law-abiding citizen, I'd better eat it.

4.   Hard-core pornography is disgusting and offensive to any civilized person, so it cannot be included in the right to free speech.

5.   Only short poems, not long ones, can be good. Of course, many so-called poems, such as Paradise Lost, take up a large number of pages. But if they are any good, they must really be collections of short poems, because a long poem as such cannot be of any great value.

6.   Why are you so skeptical about ESP? Can you prove that it doesn't exist?

7.   "I don't see how you can support distribution requirements. Don't you want students to have any choice about their courses?"

8.   There can't be a law without a law-giver. But nature operates in accordance with laws, like the law of gravity, so there must be a Law-Giver above nature.

9.   Mary says she loves me. I don't know whether to believe her or not, but 1 guess I do, because I don't think she would lie to someone she loves about something that important.

10. The layoffs at Acme Corporation were obviously racist in intent, since over sixty percent of the people laid off were black or Puerto Rican.



A fallacy is an error in reasoning, an argument in which the premises do not in fact support the conclusion. This chapter covered a category of fallacies that occur fairly often in everyday thought and speech.

Subjectivist fallacies involve the attempt to support a conclusion by appealing to nonobjective, nonrational factors: one's desire to believe the conclusion, majority opinion, emotion, force.

Two other fallacies—appeal to authority and ad hominem—involve a misuse of the standards of credibility for evaluating testimonial evidence.

Fallacies of context—false alternative, post hoc, hasty generalization, composition, and division—jump to a conclusion without considering a large enough context of evidence.

The fourth subcategory includes more subtle fallacies of logical structure, errors involving the relation between premises and conclusion: begging the question, equivocation, appeal to ignorance, and diversion.

Summary Box 6.5


Note: each definition below gives only the differentia; the genus in each case is FALLACY.

Subjectivism: using the fact that one believes or wants a proposition to be true as evidence of its truth.

Appeal to majority: using the fact that large numbers of people believe a proposition to be true as evidence of its truth.

Appeal to emotion: trying to get someone to accept a proposition on the basis of an emotion one induces.

Appeal to force (argumentum ad baculum): trying to get someone to accept a proposition on the basis of a threat.

Appeal to authority (argumentum ad verecundiam): using testimonial evidence for a proposition when the conditions for credibility are not satisfied or the use of such evidence is inappropriate.

Ad hominem: using a negative trait of a speaker as evidence that his statement is false or his argument weak.

False alternative: excluding relevant possibilities without justification.

Post hoc. using the fact that one event preceded another as sufficient evidence for the conclusion that the first caused the second.

Hasty generalization: inferring a general proposition from an inadequate sample of particular cases.

Composition: inferring that a whole has a property merely because its parts have that property.

Division: inferring that a part has a property merely because the whole has that property.

Begging the question (circular argument): trying to support a proposition with an argument in which that proposition is a premise.

Equivocation: using a word in two different meanings in the premises and/or the conclusion.

Appeal to ignorance (argumentum ad ignorantiam): using the absence of proof for a proposition as evidence for the truth of the opposing proposition.

Diversion: trying to support one proposition by arguing for another proposition.