Appeal to the Consequences of a Belief
Argumentum Ad Consequentium
Category: Fallacies of Relevance (Red Herrings) → Distracting Appeals

The Appeal to the Consequences of a Belief is a fallacy that comes in the following patterns:

#1: X is true because if people did not accept X as being true, then there would be negative consequences.
#2: X is false because if people did not accept X as being false, then there would be negative consequences.

#3: X is true because accepting that X is true has positive consequences.
#4: X is false because accepting that X is false has positive consequences.

#5: I wish that X were true, therefore X is true. This is known as Wishful Thinking.
#6: I wish that X were false, therefore X is false. This is known as Wishful Thinking.

This line of "reasoning" is fallacious because the consequences of a belief have no bearing on whether the belief is true or false. For example, if someone were to say "If sixteen-headed purple unicorns don't exist, then I would be miserable, so they must exist", it would be clear that this would not be a good line of reasoning. It is important to note that the consequences in question are the consequences that stem from the belief. It is important to distinguish between a rational reason to believe (RRB) (evidence) and a prudential reason to believe (PRB) (motivation). A RRB is evidence that objectively and logically supports the claim. A PRB is a reason to accept the belief because of some external factor (such as fear, a threat, or a benefit or harm that may stem from the belief) that is relevant to what a person values but is not relevant to the truth or falsity of the claim. The nature of the fallacy is especially clear in the case of Wishful thinking. Obviously, merely wishing that something is true does not make it true. This fallacy differs from the Appeal to Belief fallacy in that the Appeal to Belief involves taking a claim that most people believe that X is true to be evidence for X being true.

Misleading Vividness
Category: Fallacies of Relevance (Red Herrings) → Distracting Appeals

Misleading Vividness is a fallacy in which a very small number of particularly dramatic events are taken to outweigh a significant amount of statistical evidence. This sort of "reasoning" has the following form:

1. Dramatic or vivid event X occurs (and is not in accord with the majority of the statistical evidence).
2. Therefore events of type X are likely to occur.

This sort of "reasoning" is fallacious because the mere fact that an event is particularly vivid or dramatic does not make the event more likely to occur, especially in the face of significant statistical evidence.

People often accept this sort of "reasoning" because particularly vivid or dramatic cases tend to make a very strong impression on the human mind. For example, if a person survives a particularly awful plane crash, he might be inclined to believe that air travel is more dangerous than other forms of travel. After all, explosions and people dying around him will have a more significant impact on his mind than will the rather dull statistics that a person is more likely to be struck by lightning than killed in a plane crash.

It should be kept in mind that taking into account the possibility of something dramatic or vivid occurring is not always fallacious. For example, a person might decide to never go sky diving because the effects of an accident can be very, very dramatic. If he knows that, statistically, the chances of the accident are happening are very low but he considers even a small risk to be unacceptable, then he would not be making an error in reasoning.

Poisoning the Well
Category: Fallacies of Relevance (Red Herrings) → Ad hominems (Genetic Fallacies)

This sort of "reasoning" involves trying to discredit what a person might later claim by presenting unfavorable information (be it true or false) about the person. This "argument" has the following form:

1. Unfavorable information (be it true or false) about person A is presented.
2. Therefore any claims person A makes will be false.

This sort of "reasoning" is obviously fallacious. The person making such an attack is hoping that the unfavorable information will bias listeners against the person in question and hence that they will reject any claims he might make. However, merely presenting unfavorable information about a person (even if it is true) hardly counts as evidence against the claims he/she might make. This is especially clear when Poisoning the Well is looked at as a form of ad Hominem in which the attack is made prior to the person even making the claim or claims. The following example clearly shows that this sort of "reasoning" is quite poor.

Appeal to Common Practice
Category: Fallacies of Relevance (Red Herrings)

The Appeal to Common Practice is a fallacy with the following structure:

1. X is a common action.
2. Therefore X is correct/moral/justified/reasonable, etc.

The basic idea behind the fallacy is that the fact that most people do X is used as "evidence" to support the action or practice. It is a fallacy because the mere fact that most people do something does not make it correct, moral, justified, or reasonable.

An appeal to fair play, which might seem to be an appeal to common practice, need not be a fallacy. For example, a woman working in an office might say "the men who do the same job as me get paid more than I do, so it would be right for me to get paid the same as them." This would not be a fallacy as long as there was no relevant difference between her and the men (in terms of ability, experience, hours worked, etc.). More formally:

1. It is common practice to treat people of type Y in manner X and to treat people of type Z in a different manner.
2. There is no relevant difference between people of type Y and type Z.
3. Therefore people of type Z should be treated in manner X, too.

This argument rests heavily on the principle of relevant difference. On this principle two people, A and B, can only be treated differently if and only if there is a relevant difference between them. For example, it would be fine for me to give a better grade to A than B if A did better work than B. However, it would be wrong of me to give A a better grade than B simply because A has red hair and B has blonde hair.

There might be some cases in which the fact that most people accept X as moral entails that X is moral. For example, one view of morality is that morality is relative to the practices of a culture, time, person, etc. If what is moral is determined by what is commonly practiced, then this argument:

1. Most people do X.
2. Therefore X is morally correct.

would not be a fallacy. This would however entail some odd results. For example, imagine that there are only 100 people on earth. 60 of them do not steal or cheat and 40 do. At this time, stealing and cheating would be wrong. The next day, a natural disaster kills 30 of the 60 people who do not cheat or steal. Now it is morally correct to cheat and steal. Thus, it would be possible to change the moral order of the world to one’s view simply by eliminating those who disagree.

Hasty Generalization
AKA Fallacy of Insufficient Statistics, Fallacy of Insufficient Sample, Leaping to A Conclusion, Hasty Induction
Category: Fallacies of Presumption

This fallacy is committed when a person draws a conclusion about a population based on a sample that is not large enough. It has the following form:

1. Sample S, which is too small, is taken from population P.
2. Conclusion C is drawn about Population P based on S.

The person committing the fallacy is misusing the following type of reasoning, which is known variously as Inductive Generalization, Generalization, and Statistical Generalization:

1. X% of all observed A's are B's.
2. Therefore X% of all A's are B's.

The fallacy is committed when not enough A's are observed to warrant the conclusion. If enough A's are observed then the reasoning is not fallacious.

Small samples will tend to be unrepresentative. As a blatant case, asking one person what she thinks about gun control would clearly not provide an adequate sized sample for determining what Canadians in general think about the issue. The general idea is that small samples are less likely to contain numbers proportional to the whole population. For example, if a bucket contains blue, red, green and orange marbles, then a sample of three marbles cannot possible be representative of the whole population of marbles. As the sample size of marbles increases the more likely it becomes that marbles of each color will be selected in proportion to their numbers in the whole population. The same holds true for things others than marbles, such as people and their political views.

Since Hasty Generalization is committed when the sample (the observed instances) is too small, it is important to have samples that are large enough when making a generalization. The most reliable way to do this is to take as large a sample as is practical. There are no fixed numbers as to what counts as being large enough. If the population in question is not very diverse (a population of cloned mice, for example) then a very small sample would suffice. If the population is very diverse (people, for example) then a fairly large sample would be needed. The size of the sample also depends on the size of the population. Obviously, a very small population will not support a huge sample. Finally, the required size will depend on the purpose of the sample. If Bill wants to know what Joe and Jane think about gun control, then a sample consisting of Bill and Jane would (obviously) be large enough. If Bill wants to know what most Australians think about gun control, then a sample consisting of Bill and Jane would be far too small.

People often commit Hasty Generalizations because of bias or prejudice. For example, someone who is a sexist might conclude that all women are unfit to fly jet fighters because one woman crashed one. People also commonly commit Hasty Generalizations because of laziness or sloppiness. It is very easy to simply leap to a conclusion and much harder to gather an adequate sample and draw a justified conclusion. Thus, avoiding this fallacy requires minimizing the influence of bias and taking care to select a sample that is large enough.

One final point: a Hasty Generalization, like any fallacy, might have a true conclusion. However, as long as the reasoning is fallacious there is no reason to accept the conclusion based on that reasoning.

Personal Attack
AKA Ad Hominem Abusive
Category: Fallacies of Relevance (Red Herrings) → Ad hominems (Genetic Fallacies)

A personal attack is committed when a person substitutes abusive remarks for evidence when attacking another person's claim or claims. This line of "reasoning" is fallacious because the attack is directed at the person making the claim and not the claim itself. The truth value of a claim is independent of the person making the claim. After all, no matter how repugnant an individual might be, he or she can still make true claims.

Not all ad Hominems are fallacious. In some cases, an individual's characteristics can have a bearing on the question of the veracity of her claims. For example, if someone is shown to be a pathological liar, then what he says can be considered to be unreliable.

However, such attacks are weak, since even pathological liars might speak the truth on occasion. In general, it is best to focus one’s attention on the content of the claim and not on who made the claim. It is the content that determines the truth of the claim and not the characteristics of the person making the claim.