Fallacies

AD HOC RESCUE

Psychologically, it is understandable that you would try to rescue a cherished belief from trouble. When faced with conflicting data, you are likely to mention how the conflict will disappear if some new assumption is taken into account. However, if there is no good reason to accept this saving assumption other than that it works to save your cherished belief, your rescue is an ad hoc rescue.

Example:
Yolanda: If you take four of these tablets of vitamin C every day, you will never get a cold.
Juanita: I tried that last year for several months, and still got a cold.
Yolanda: Did you take the tablets every day?
Juanita: Yes.
Yolanda: Well, I’ll bet you bought some bad tablets.

The burden of proof is definitely on Yolanda’s shoulders to prove that Juanita’s vitamin C tablets were probably “bad” — that is, not really vitamin C. If Yolanda can’t do so, her attempt to rescue her hypothesis (that vitamin C prevents colds) is simply a dogmatic refusal to face up to the possibility of being wrong.

AD HOMINEM

You commit this fallacy if you make an irrelevant attack on the arguer and suggest that this attack undermines the argument itself. It is a form of the Genetic Fallacy.

Example:
What she says about Johannes Kepler’s astronomy of the 1600’s must be just so much garbage. Do you realize she’s only fourteen years old?

This attack may undermine the arguer’s credibility as a scientific authority, but it does not undermine her reasoning. That reasoning should stand or fall on the scientific evidence, not on the arguer’s age or anything else about her personally.
If the fallacious reasoner points out irrelevant circumstances that the reasoner is in, the fallacy is a circumstantial ad hominem. Tu Quoque and Two Wrongs Make a Right are other types of the ad hominem fallacy.
The major difficulty with labeling a piece of reasoning as an ad hominem fallacy is deciding whether the personal attack is relevant. For example, attacks on a person for their actually immoral sexual conduct are irrelevant to the quality of their mathematical reasoning, but they are relevant to arguments promoting the person for a leadership position in the church. Unfortunately, many attacks are not so easy to classify, such as an attack pointing out that the candidate for church leadership, while in the tenth grade, intentionally tripped a fellow student and broke his collar bone.

AFFIRMING THE CONSEQUENT

If you have enough evidence to affirm the consequent of a conditional and then suppose that as a result you have sufficient reason for affirming the antecedent, you commit the fallacy of affirming the consequent. This formal fallacy is often mistaken for modus ponens, which is a valid form of reasoning also using a conditional. A conditional is an if-then statement; the if-part is the antecedent, and the then-part is the consequent. The following argument affirms the consequent that she does speaks Portuguese.

Example:
If she’s Brazilian, then she speaks Portuguese. Hey, she does speak Portuguese. So, she is Brazilian.

If the arguer believes or suggests that the premises definitely establish that she is Brazilian, then the arguer is committing the fallacy. See the non sequitur fallacy for more discussion of this point.

ANECDOTAL EVIDENCE

If you discount evidence arrived at by systematic search or by testing in favor of a few firsthand stories, you are committing the fallacy of overemphasizing anecdotal evidence.

Example:
Yeah, I’ve read the health warnings on those cigarette packs and I know about all that health research, but my brother smokes, and he says he’s never been sick a day in his life, so I know smoking can’t really hurt you.

APPEAL TO AUTHORITY

You appeal to authority if you back up your reasoning by saying that it is supported by what some authority says on the subject. Most reasoning of this kind is not fallacious. However, it is fallacious whenever the authority appealed to is not really an authority in this subject, when the authority cannot be trusted to tell the truth, when authorities disagree on this subject (except for the occasional lone wolf), when the reasoner misquotes the authority, and so forth. Although spotting a fallacious appeal to authority often requires some background knowledge about the subject or the authority, in brief it can be said that it is fallacious to accept the word of a supposed authority when we should be suspicious.

Example:
You can believe the moon is covered with dust because the president of our neighborhood association said so, and he should know.

This is a fallacious appeal to authority because, although the president is an authority on many neighborhood matters, he is no authority on the composition of the moon. It would be better to appeal to some astronomer or geologist. If you place too much trust in expert opinion and overlook any possibility that experts talking in their own field of expertise make mistakes, too, then you also commit the fallacy of appeal to authority.

Example:
Of course she’s guilty of the crime. The police arrested her, didn’t they? And they’re experts when it comes to crime.

APPEAL TO IGNORANCE

The fallacy of appeal to ignorance comes in two forms: (1) Not knowing that a certain statement is true is taken to be a proof that it is false. (2) Not knowing that a statement is false is taken to be a proof that it is true. The fallacy occurs in cases where absence of evidence is not good enough evidence of absence. The fallacy uses an unjustified attempt to shift the burden of proof. The fallacy is also called “Argument from Ignorance.”

Example:
Nobody has ever proved to me there’s a God, so I know there is no God.

This kind of reasoning is generally fallacious. It would be proper reasoning only if the proof attempts were quite thorough, and it were the case that if God did exist, then there would be a discoverable proof of this.

BLACK-OR-WHITE

The black-or-white fallacy is a false dilemma fallacy that unfairly limits you to only two choices.

Example:
Well, it’s time for a decision. Will you contribute $10 to our environmental fund, or are you on the side of environmental destruction?

A proper challenge to this fallacy could be to say, “I do want to prevent the destruction of our environment, but I don’t want to give $10 to your fund. You are placing me between a rock and a hard place.” The key to diagnosing the black-or-white fallacy is to determine whether the limited menu is fair or unfair. Simply saying, “Will you contribute $10 or won’t you?” is not unfair.

CUM HOC, ERGO PROPTER HOC

Latin for “with this, therefore because of this.” This is a false cause fallacy that doesn’t depend on time order (as does the post hoc fallacy), but on any other chance correlation of the supposed cause being in the presence of the supposed effect.

Gypsies live near our low-yield cornfields. So, gypsies are causing the low yield.

EQUIVOCATION

Equivocation is the illegitimate switching of the meaning of a term during the reasoning.

Brad is a nobody, but since nobody is perfect, Brad must be perfect, too.

The term “nobody” changes its meaning without warning in the passage.  So does the term “political jokes” in this joke: I don’t approve of political jokes. I’ve seen too many of them get elected.

FALSE ANALOGY

When reasoning by analogy, the fallacy occurs when the analogy is irrelevant or very weak or when there is a more relevant disanalogy. See also Faulty Comparison.

The book Investing for Dummies really helped me understand my finances better. The book Chess for Dummies was written by the same author, was published by the same press, and costs about the same amount.  So, this chess book would probably help me understand my finances.

INSUFFICIENT STATISTICS

Drawing a statistical conclusion from a set of data that is clearly too small.

A pollster interviews ten London voters in one building about which candidate for mayor they support, and upon finding that Churchill receives support from six of the ten, declares that Churchill has the majority support of London voters.

This fallacy is a form of the Fallcy of Jumping to Conclusions.

NON SEQUITUR

When a conclusion is supported only by extremely weak reasons or by irrelevant reasons, the argument is fallacious and is said to be a non sequitur. However, we usually apply the term only when we cannot think of how to label the argument with a more specific fallacy name. Any deductively invalid inference is a non sequitur if it also very weak when assessed by inductive standards.

Nuclear disarmament is a risk, but everything in life involves a risk. Every time you drive in a car you are taking a risk. If you’re willing to drive in a car, you should be willing to have disarmament.

The following is not an example: “If she committed the murder, then there’d be his blood stains on her hands. His blood stains are on her hands. So, she committed the murder.” This deductively invalid argument commits the fallacy of affirming the consequent, but it isn’t a non sequitur because it has significant inductive strength.

POST HOC

Suppose we notice that an event of kind A is followed in time by an event of kind B, and then hastily leap to the conclusion that A caused B. If so, we commit the post hoc fallacy. Correlations are often good evidence of causal connection, so the fallacy occurs only when the leap to the causal conclusion is done “hastily.” The Latin term for the fallacy is post hoc, ergo propter hoc (“After this, therefore because of this”). It is a kind of false cause fallacy.

Example:
I ate in that Ethiopian restaurant three days ago and now I’ve just gotten food poisoning. The only other time I’ve eaten in an Ethiopian restaurant I also got food poisoning, but that time I got sick a week later. My eating in those kinds of restaurants is causing my food poisoning.

Your background knowledge should tell you this is unlikely because the effects of food poisoning are felt soon after the food is eaten. Before believing your illness was caused by eating in an Ethiopian restaurant, you’d need to rule out other possibilities, such as your illness being caused by what you ate a few hours before the onset of the illness.

RED HERRING

A red herring is a smelly fish that would distract even a bloodhound. It is also a digression that leads the reasoner off the track of considering only relevant information.

Example:
Will the new tax in Senate Bill 47 unfairly hurt business? One of the provisions of the bill is that the tax is higher for large employers (fifty or more employees) as opposed to small employers (six to forty-nine employees). To decide on the fairness of the bill, we must first determine whether employees who work for large employers have better working conditions than employees who work for small employers.

Bringing up the issue of working conditions is the red herring.

REVERSING CAUSATION

Drawing an improper conclusion about causation due to a causal assumption that reverses cause and effect. A kind of false cause fallacy.

Example:
All the corporate officers of Miami Electronics and Power have big boats. If you’re ever going to become an officer of MEP, you’d better get a bigger boat.
The false assumption here is that having a big boat helps cause you to be an officer in MEP, whereas the reverse is true. Being an officer causes you to have the high income that enables you to purchase a big boat.

SCOPE

The scope fallacy is caused by improperly changing or misrepresenting the scope of a phrase.

Example:
Every concerned citizen who believes that someone living in the US is a terrorist should make a report to the authorities. But Shelley told me herself that she believes there are terrorists living in the US, yet she hasn’t made any reports. So, she must not be a concerned citizen.

The first sentence has ambiguous scope. It was probably originally meant in this sense: Every concerned citizen who believes (of someone that this person is living in the US and is a terrorist) should make a report to the authorities. But the speaker is clearly taking the sentence in its other, less plausible sense: Every concerned citizen who believes (that there is someone or other living in the US who is a terrorist) should make a report to the authorities. Scope fallacies usually are amphibolies.

STRAW MAN

You commit the straw man fallacy whenever you attribute an easily refuted position to your opponent, one that the opponent wouldn’t endorse, and then proceed to attack the easily refuted position believing you have undermined the opponent’s actual position. If the misrepresentation is on purpose, then the straw man fallacy is caused by lying.

Example (a debate before the city council):
Opponent: Because of the killing and suffering of Indians that followed Columbus’s discovery of America, the City of Berkeley should declare that Columbus Day will no longer be observed in our city.
Speaker: This is ridiculous, fellow members of the city council. It’s not true that everybody who ever came to America from another country somehow oppressed the Indians. I say we should continue to observe Columbus Day, and vote down this resolution that will make the City of Berkeley the laughing stock of the nation.

The speaker has twisted what his opponent said; the opponent never said, nor even indirectly suggested, that everybody who ever came to America from another country somehow oppressed the Indians.

UNDISTRIBUTED MIDDLE

In syllogistic logic, failing to distribute the middle term over at least one of the other terms is the fallacy of undistributed middle. Also called the fallacy of maldistributed middle.

Example:
All collies are animals.
All dogs are animals.
Therefore, all collies are dogs.

The middle term (“animals”) is in the predicate of both universal affirmative premises and therefore is undistributed. This formal fallacy has the logical form: All C are A. All D are A. Therefore, all C are D.

UNREPRESENTATIVE SAMPLE

If the means of collecting the sample from the population are likely to produce a sample that is unrepresentative of the population, then a generalization upon the sample data is an inference committing the fallacy of unrepresentative sample. A kind of hasty generalization. When some of the statistical evidence is expected to be relevant to the results but is hidden or overlooked, the fallacy is called suppressed evidence.

Example:
The two men in the matching green suits that I met at the Star Trek Convention in Las Vegas had a terrible fear of cats. I remember their saying they were from Delaware. I’ve never met anyone else from Delaware, so I suppose everyone there has a terrible fear of cats.

Most people’s background information is sufficient to tell them that people at this sort of convention are unlikely to be representative, that is, typical members of society.
Large samples can be unrepresentative, too.

Example:
We’ve polled over 400,000 Southern Baptists and asked them whether the best religion in the world is Southern Baptist. We have over 99% agreement, which proves our point about which religion is best.

Getting a larger sample size does not overcome sampling bias.

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