Fallacy

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A fallacy is an error in an argument. There are two main kinds of fallacies, corresponding to the distinction between formal and informal logic. If a formal argument is fallacious, it is invalid. If an informal argument is fallacious, its rational persuasive power is greatly reduced. It is often difficult to detect fallacies, for while they are not rationally persuasive, they may be psychologically persuasive, employing rhetorical strategies, emotional manipulation, or reasoning similar to valid forms, thus making the argument appear stronger than it is.

Since Aristotle's discussion in Sophistic Refutations, there have been many systems of classifying fallacies. In this article, the only classification is the distinction between formal and informal fallacies.

Formal fallacies

A formal fallacy involves an application of a fallacious rule of inference. Because of this, formal fallacies depend on a particular system of logic. There are, for example, fallacies of syllogism, propositional logic, and quantificational logic. Below are a few fallacies that occur frequently in contexts outside of strict logical proofs.

• Affirming the Consequent

One of the most basic rules of logic is called modus ponens. If you know that p and you know that if p then q, you can conclude q. The fallacy of affirming the consequent concludes p from the conditional and q (the consequent). For example,

“Everyone under 21 had orange juice. Gussie had orange juice, so he must be under 21.”

Gussie may be a 30-year old teetotaler. If the first sentence is true, then we can know what someone drank given that person’s age, but we cannot know how old a person is given what that person drank.

• Denying the Antecedent

This fallacy is similar to the fallacy of affirming the consequent. For example.

“Everyone under 21 had orange juice. Bertie is 30, so Bertie must not have had orange juice.”

Bertie may have simply chosen to have orange juice (perhaps out of camaraderie with Gussie). If the first sentence is true, we do know that anyone who has something other than orange juice must be over 21, but we do not know anything about what those over 21 had to drink.

• Quantifier fallacies

Quantifiers are words like ‘everyone,’ ‘something,’ and ‘no one.’ Quantifier fallacies involve improperly shuffling quantifiers. For example:

“Everyone is loved by someone or other. So someone loves everyone.”

It may of course be true that someone (God, perhaps) loves everyone, but this does not follow from the fact that everyone is loved by someone (everyone is loved by her mother, perhaps). The fallacy arises in lack of caution with the quantifiers ‘everyone’ and ‘someone.’ Notice, however, that the converse is not fallacious. If someone (God) loves everybody, then everybody is loved by somebody (namely, God). An incautious cosmological argument may commit this fallacy:

“Everything has a cause, so there must be something that is the cause of everything.”

Informal fallacies

There are many fallacious forms of reasoning. The following list is not exhaustive, containing only a few important or egregious fallacies. Often an assumption or way of thinking is called a fallacy without being a fallacy in the strict sense used here (for example, the genetic fallacy). The entries on the list are not mutually exclusive, since often a particular bad bit of reasoning may be an instance of more than one fallacy.

• Accident

The fallacy of accident occurs when one fails to take note that the “accidental” features of a specific example render a general claim inapplicable. Many general claims have exceptions or special cases in which they are not applicable. (All generalizations have exceptions, including this one.) This is often the case in moral arguments. Lying is wrong. But it would be a fallacy of accident to conclude from this rule that it would be wrong to lie in order to save someone’s life.

The converse fallacy is sometimes called “hasty generalization.” It is a kind of inductive argument, but the cases examined are too few or too atypical to warrant the generalization.

(Literally, “against the person”). An ad hominem argument responds to an argument by attacking the person who presented the argument, or by attacking that person’s right to present the argument. For example:

“Jim argues that there’s no God. Yet another self-styled intellectual making the same old claim.”

The response to Jim’s argument ignores the argument itself and instead attacks the person, in this case lumping him into a group whose arguments needn’t be heard. This type of ad hominem is often called “abusive,” but note that simple abuse (e.g., name-calling) does not make something a fallacy. One must argue that a given position is false because of some (irrelevant) fault of the person who holds the position.

Another example:

“Jane argues that God exists. But Jane is an employee of the church with an economic interest at stake.”

Here again, the response ignores the argument and directs the attention to the presenter of the argument. This response differs, however, in that it does not dismiss Jane entirely but instead questions her appropriateness or her vested interest in the outcome of the argument. This type of ad hominem is often called “circumstantial” or tu quoque. It should be distinguished from a non-fallacious caution that a person’s presentation of facts may be skewed because of vested interests.

• Amphiboly

In general, an amphiboly is a structural ambiguity. Often, a single sentence might be taken more than one way. This is common in headlines, with their need for space conservation, and in poetry, where the freer word order allows this ambiguous prophecy in Shakespeare’s Henry IV:

“The duke yet lives that Henry shall depose.”

It is ambiguous whether Henry shall depose the duke, or the duke shall depose Henry. As a premise in an argument, amphiboly would be fallacious if the plausibility of the premise required one reading, while the conclusion required another.

• Appeal to Authority

In general, it is not fallacious to appeal to authority. If the majority of cardiologists claim that aerobic exercise helps prevent heart disease, it is not fallacious to argue based on this assertion. However, if the majority of cardiologists claim that God does not exist, it is fallacious to argue based on this assertion. Appeal to authority is fallacious when the authority cited is not an authority in the field. Of course, even when the authority cited is a leading light in the field, appealing to this authority does not prove the case. Textbooks change every few years as new knowledge becomes available. Like nearly all informal arguments, a non-fallacious appeal to authority does not prove the conclusion, but it does lend it considerable weight.

• Appeal to Emotion

In an appeal to emotion, one presents an emotional, rather than rational, case for one’s conclusion. There are many kinds of appeals to emotion, including Appeal to fear:

“Believe in God or burn in Hell.”

Flattery:

“Surely someone as smart as you can see that there’s no God.”

Appeal to pity:

“Find him innocent, ladies and gentlemen of the jury, because he has a wife and three children.”

In a sense, many fallacies are appeals to emotion, since a fallacy often gets its appeal by psychological, rather than rational, persuasion.

• Appeal to novelty

In an appeal to novelty, one claims that one’s position is correct because it is modern and new. For example:

“It was quite right for our ancestors to believe in God, but this belief is out of place in our enlightened times.”

This is the flip side of an appeal to novelty. In an appeal to tradition, one claims that one’s position is correct because it has been believed for so long. For example:

“Our ancestors who founded our nation believed in God. Are we better than they were?”
• Appeal to ignorance

In an appeal to ignorance, one claims that a conclusion is true because it has not been proven false, or false because it has not been proven true. For example:

“Scientists and philosophers have been trying for centuries to prove that God exists. They have failed. So God does not exist.”

Like many fallacies, this is related to a good form of reasoning. Informal induction is a form of reasoning that progresses from the truth of something in some cases to its truth in general. If, say, a police search-and-rescue unit were looking for a shoe under a bed and did not find it, it would be compelling to assume the shoe was not there.

• Bandwagon

A bandwagon fallacy attempts to persuade based on the popularity of a claim. For example:

“70 percent of Americans believe in God. Why don’t you?”
• Begging the Question

(Sometimes called petitio principii; an argument that begs the question is often called “circular”.) One begs the question when one assumes what one is trying to prove. For example:

“God exists because the Bible says God exists, and the Bible is the word of God and so must be true.”
• Composition

A pair of fallacies are both known as the fallacy of composition. The first fallacy concludes that a whole has a certain property because each part of it has that property. For example, since a drop of water is smaller than a person, the ocean (which is made of drops of water) is smaller than a person. A subtler example is in Aristotle’s Nicomachean Ethics, in which he argues that since every part of a person (eye, hand, foot) has a function, a person also must have a function. The second fallacy is sometimes called the fallacy of division. It consists in concluding that every part has a property from the fact that the whole has that property. It would be hard to read every book in the New York Public Library. But it would be a fallacy of composition to conclude that city of God is difficult to read.

• Equivocation

Many words have more than one meaning. When an argument turns on two (or more) different meanings of a single word, the argument is equivocal. For example:

“The end of a thing is its perfect; death is the end of life; hence, death is the perfection of life.”

This argument confuses two senses of “end,” which can mean either “goal” or “conclusion.” The first premise takes “end” in the first sense; the second premise takes it in the second sense.

• False cause

Commonly called by its Latin name post hoc ergo propter hoc (literally, “after which therefore because of which”), one commits this fallacy in assuming that since X follows Y, X must cause Y. For example,

“Everyone who ate carrots before 1900 is dead. So carrots were poisonous before 1900.”
• Ignoratio Elenchi

(Sometimes called “irrelevant conclusion”). This fallacy occurs when one argues for a conclusion, but then presents a different conclusion as the result of the argument. For example:

“Fossil evidence shows that there has been life on the planet for millions of years, so God does not exist.”

The conclusion of this argument has little if any relation to the premises. In an example as obvious as this, the fallacy is very noticeable, but often the conclusion is slightly stronger than the evidence supports, and it takes a bit of thought to see that the argument does not support so strong a conclusion.

• Non sequiter

(literally, “it does not follow.”) This is a general term that can apply to any fallacy, to indicate that the conclusion does not follow from the premises. It is often applies to the fallacies of ignoratio elenchi and false cause.