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.

Slippery Slope
AKA The Camel's Nose
Category: Fallacies of Presumption → Casual Fallacies

The Slippery Slope is a fallacy in which a person asserts that some event must inevitably follow from another without any argument for the inevitability of the event in question. In most cases, there are a series of steps or gradations between one event and the one in question and no reason is given as to why the intervening steps or gradations will simply be bypassed. This "argument" has the following form:

1. Event X has occurred (or will or might occur).
2. Therefore event Y will inevitably happen.

This sort of "reasoning" is fallacious because there is no reason to believe that one event must inevitably follow from another without an argument for such a claim. This is especially clear in cases in which there are a significant number of steps or gradations between one event and another.

Appeal to Belief
Category: Fallacies of Relevance (Red Herrings)

Appeal to Belief is a fallacy that has this general pattern:

1. Most people believe that a claim, X, is true.
2. Therefore X is true.

This line of "reasoning" is fallacious because the fact that many people believe a claim does not, in general, serve as evidence that the claim is true.

There are, however, some cases when the fact that many people accept a claim as true is an indication that it is true. For example, while you are visiting Maine, you are told by several people that they believe that people older than 16 need to buy a fishing license in order to fish. Barring reasons to doubt these people, their statements give you reason to believe that anyone over 16 will need to buy a fishing license.

There are also cases in which what people believe actually determines the truth of a claim. For example, the truth of claims about manners and proper behavior might simply depend on what people believe to be good manners and proper behavior. Another example is the case of community standards, which are often taken to be the standards that most people accept. In some cases, what violates certain community standards is taken to be obscene. In such cases, for the claim "x is obscene" to be true is for most people in that community to believe that x is obscene. In such cases it is still prudent to question the justification of the individual beliefs.

Appeal to Popularity
Ad Populum
Category: Fallacies of Relevance (Red Herrings)

The Appeal to Popularity has the following form:

1. Most people approve of X (have favorable emotions towards X).
2. Therefore X is true.

The basic idea is that a claim is accepted as being true simply because most people are favorably inclined towards the claim. More formally, the fact that most people have favorable emotions associated with the claim is substituted in place of actual evidence for the claim. A person falls prey to this fallacy if he accepts a claim as being true simply because most other people approve of the claim.

It is clearly fallacious to accept the approval of the majority as evidence for a claim. For example, suppose that a skilled speaker managed to get most people to absolutely love the claim that 1+1=3. It would still not be rational to accept this claim simply because most people approved of it. After all, mere approval is no substitute for a mathematical proof. At one time people approved of claims such as "the world is flat", "humans cannot survive at speeds greater than 25 miles per hour", "the sun revolves around the earth" but all these claims turned out to be false.

This sort of "reasoning" is quite common and can be quite an effective persuasive device. Since most humans tend to conform with the views of the majority, convincing a person that the majority approves of a claim is often an effective way to get him to accept it. Advertisers often use this tactic when they attempt to sell products by claiming that everyone uses and loves their products. In such cases they hope that people will accept the (purported) approval of others as a good reason to buy the product.

This fallacy is vaguely similar to such fallacies as Appeal to Belief and Appeal to Common Practice. However, in the case of an Ad Populum the appeal is to the fact that most people approve of a claim. In the case of an Appeal to Belief, the appeal is to the fact that most people believe a claim. In the case of an Appeal to Common Practice, the appeal is to the fact that many people take the action in question.

This fallacy is closely related to the Appeal to Emotion fallacy, as discussed in the entry for that fallacy.

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.

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.