Begging the Question
Petitio Principii
AKA Circular Reasoning, Reasoning in a Circle
Category: Fallacies of Presumption

Begging the Question is a fallacy in which the premises include the claim that the conclusion is true or (directly or indirectly) assume that the conclusion is true. This sort of "reasoning" typically has the following form.

1. Premises in which the truth of the conclusion is claimed or the truth of the conclusion is assumed (either directly or indirectly).
2. Claim C (the conclusion) is true.

This sort of "reasoning" is fallacious because simply assuming that the conclusion is true (directly or indirectly) in the premises does not constitute evidence for that conclusion. Obviously, simply assuming a claim is true does not serve as evidence for that claim. This is especially clear in particularly blatant cases: "X is true. The evidence for this claim is that X is true."

Some cases of question begging are fairly blatant, while others can be extremely subtle.

Biased Generalization
AKA Biased Statistics, Loaded Sample, Prejudiced Statistics, Prejudiced Sample, Loaded Statistics, Biased Induction
Category: Fallacies of Presumption

This fallacy is committed when a person draws a conclusion about a population based on a sample that is biased or prejudiced in some manner. It has the following form:

1. Sample S, which is biased, 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 the sample of A's is likely to be biased in some manner. A sample is biased or loaded when the method used to take the sample is likely to result in a sample that does not adequately represent the population from which it is drawn.

Biased samples are generally not very reliable. As a blatant case, imagine that a person is taking a sample from a truckload of small colored balls, some of which are metal and some of which are plastic. If he used a magnet to select his sample, then his sample would include a disproportionate number of metal balls (after all, the sample will probably be made up entirely of the metal balls). In this case, any conclusions he might draw about the whole population of balls would be unreliable since he would have few or no plastic balls in the sample.

The general idea is that biased samples are less likely to contain numbers proportional to the whole population. For example, if a person wants to find out what most Americans thought about gun control, a poll taken at an NRA meeting would be a biased sample.

Since the Biased Sample fallacy is committed when the sample (the observed instances) is biased or loaded, it is important to have samples that are not biased making a generalization. The best way to do this is to take samples in ways that avoid bias. There are, in general, three types of samples that are aimed at avoiding bias. The general idea is that these methods (when used properly) will result in a sample that matches the whole population fairly closely. The three types of samples are as follows...

Random Sample: This is a sample that is taken in such a way that nothing but chance determines which members of the population are selected for the sample. Ideally, any individual member of the population has the same chance as being selected as any other. This type of sample avoids being biased because a biased sample is one that is taken in such a way that some members of the population have a significantly greater chance of being selected for the sample than other members. Unfortunately, creating an ideal random sample is often very difficult.

Stratified Sample: This is a sample that is taken by using the following steps: 1) The relevant strata (population subgroups) are identified, 2) The number of members in each stratum is determined and 3) A random sample is taken from each stratum in exact proportion to its size. This method is obviously most useful when dealing with stratified populations. For example, a person's income often influences how she votes, so when conducting a presidential poll it would be a good idea to take a stratified sample using economic classes as the basis for determining the strata. This method avoids loaded samples by (ideally) ensuring that each stratum of the population is adequately represented.

Time Lapse Sample: This type of sample is taken by taking a stratified or random sample and then taking at least one more sample with a significant lapse of time between them. After the two samples are taken, they can be compared for changes. This method of sample taking is very important when making predictions. A prediction based on only one sample is likely to be a Hasty Generalization (because the sample is likely to be too small to cover past, present and future populations) or a Biased Sample (because the sample will only include instances from one time period).

People often commit Biased Sample because of bias or prejudice. For example, a person might intentionally or unintentionally seek out people or events that support his bias. As an example, a person who is pushing a particular scientific theory might tend to gather samples that are biased in favor of that theory.

People also commonly commit this fallacy because of laziness or sloppiness. It is very easy to simply take a sample from what happens to be easily available rather than taking the time and effort to generate an adequate sample and draw a justified conclusion.

It is important to keep in mind that bias is relative to the purpose of the sample. For example, if Bill wanted to know what NRA members thought about a gun control law, then taking a sample at a NRA meeting would not be biased. However, if Bill wanted to determine what Americans in general thought about the law, then a sample taken at an NRA meeting would be biased.

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.

Guilt by Association
AKA Bad Company Fallacy, Company that You Keep Fallacy
Category: Fallacies of Relevance (Red Herrings) → Ad hominems (Genetic Fallacies)

Guilt by Association is a fallacy in which a person rejects a claim simply because it is pointed out that people she dislikes accept the claim. This sort of "reasoning" has the following form:

1. It is pointed out that person A accepts claim P.
2. Therefore P is false

It is clear that sort of "reasoning" is fallacious. For example the following is obviously a case of poor "reasoning": "You think that 1+1=2. But, Adolf Hitler, Charles Manson, Joseph Stalin, and Ted Bundy all believed that 1+1=2. So, you shouldn't believe it."

The fallacy draws its power from the fact that people do not like to be associated with people they dislike. Hence, if it is shown that a person shares a belief with people he dislikes he might be influenced into rejecting that belief. In such cases the person will be rejecting the claim based on how he thinks or feels about the people who hold it and because he does not want to be associated with such people.

Of course, the fact that someone does not want to be associated with people she dislikes does not justify the rejection of any claim. For example, most wicked and terrible people accept that the earth revolves around the sun and that lead is heavier than helium. No sane person would reject these claims simply because this would put them in the company of people they dislike (or even hate).

Gambler's Fallacy

The Gambler's Fallacy is committed when a person assumes that a departure from what occurs on average or in the long term will be corrected in the short term. The form of the fallacy is as follows:

1. X has happened.
2. X departs from what is expected to occur on average or over the long term.
3. Therefore, X will come to an end soon.

There are two common ways this fallacy is committed. In both cases a person is assuming that some result must be "due" simply because what has previously happened departs from what would be expected on average or over the long term.

The first involves events whose probabilities of occurring are independent of one another. For example, one toss of a fair (two sides, non‐loaded) coin does not affect the next toss of the coin. So, each time the coin is tossed there is (ideally) a 50% chance of it landing heads and a 50% chance of it landing tails. Suppose that a person tosses a coin 6 times and gets a head each time. If he concludes that the next toss will be tails because tails "is due", then he will have committed the Gambler's Fallacy. This is because the results of previous tosses have no bearing on the outcome of the 7th toss. It has a 50% chance of being heads and a 50% chance of being tails, just like any other toss.

The second involves cases whose probabilities of occurring are not independent of one another. For example, suppose that a boxer has won 50% of his fights over the past two years. Suppose that after several fights he has won 50% of his matches this year, that he his lost his last six fights and he has six left. If a person believed that he would win his next six fights because he has used up his losses and is "due" for a victory, then he would have committed the Gambler's Fallacy. After all, the person would be ignoring the fact that the results of one match can influence the results of the next one. For example, the boxer might have been injured in one match which would lower his chances of winning his last six fights.

It should be noted that not all predictions about what is likely to occur are fallacious. If a person has good evidence for his predictions, then they will be reasonable to accept. For example, if a person tosses a fair coin and gets nine heads in a row it would be reasonable for him to conclude that he will probably not get another nine in a row again. This reasoning would not be fallacious as long as he believed his conclusion because of an understanding of the laws of probability. In this case, if he concluded that he would not get another nine heads in a row because the odds of getting nine heads in a row are lower than getting fewer than nine heads in a row, then his reasoning would be good and his conclusion would be justified. Hence, determining whether or not the Gambler’s Fallacy is being committed often requires some basic understanding of the laws of probability.

Appeal to Emotion
Category: Fallacies of Relevance (Red Herrings) → Distracting Appeals

An Appeal to Emotion is a fallacy with the following structure:

1. Favorable emotions are associated with X.
2. Therefore, X is true.

This fallacy is committed when someone manipulates peoples' emotions in order to get them to accept a claim as being true. More formally, this sort of "reasoning" involves the substitution of various means of producing strong emotions in place of evidence for a claim. If the favorable emotions associated with X influence the person to accept X as true because they "feel good about X," then he has fallen prey to the fallacy.

This sort of "reasoning" is very common in politics and it serves as the basis for a large portion of modern advertising. Most political speeches are aimed at generating feelings in people so that these feelings will get them to vote or act a certain way. In the case of advertising, the commercials are aimed at evoking emotions that will influence people to buy certain products. In most cases, such speeches and commercials are notoriously free of real evidence.

This sort of "reasoning" is quite evidently fallacious. It is fallacious because using various tactics to incite emotions in people does not serve as evidence for a claim. For example, if a person were able to inspire in a person an incredible hatred of the claim that 1+1 = 2 and then inspired the person to love the claim that 1+1 =3, it would hardly follow that the claim that 1+1 = 3 would be adequately supported.

It should be noted that in many cases it is not particularly obvious that the person committing the fallacy is attempting to support a claim. In many cases, the user of the fallacy will appear to be attempting to move people to take an action, such as buying a product or fighting in a war. However, it is possible to determine what sort of claim the person is actually attempting to support. In such cases one needs to ask "what sort of claim is this person attempting to get people to accept and act on?" Determining this claim (or claims) might take some work. However, in many cases it will be quite evident. For example, if a political leader is attempting to convince her followers to participate in certain acts of violence by the use of a hate speech, then her claim would be "you should participate in these acts of violence." In this case, the "evidence" would be the hatred evoked in the followers. This hatred would serve to make them favorable inclined towards the claim that they should engage in the acts of violence. As another example, a beer commercial might show happy, scantily clad men and women prancing about a beach, guzzling beer. In this case the claim would be "you should buy this beer." The "evidence" would be the excitement evoked by seeing the beautiful people guzzling the beer.

This fallacy is actually an extremely effective persuasive device. As many people have argued, peoples' emotions often carry much more force than their reason. Logical argumentation is often difficult and time consuming and it rarely has the power to spurn people to action. It is the power of this fallacy that explains its great popularity and wide usage. However, it is still a fallacy.

In all fairness it must be noted that the use of tactics to inspire emotions is an important skill. Without an appeal to peoples' emotions, it is often difficult to get them to take action or to perform at their best. For example, no good coach presents her team with syllogisms before the big game. Instead she inspires them with emotional terms and attempts to "fire" them up. There is nothing inherently wrong with this. However, it is not any acceptable form of argumentation. As long as one is able to clearly distinguish between what inspires emotions and what justifies a claim, one is unlikely to fall prey to this fallacy.

As a final point, in many cases it will be difficult to distinguish an Appeal to Emotion from some other fallacies and in many cases multiple fallacies may be committed. For example, many Ad Hominems will be very similar to Appeals to Emotion and, in some cases, both fallacies will be committed. As an example, a leader might attempt to invoke hatred of a person to inspire his followers to accept that they should reject her claims. The same attack could function as an Appeal to Emotion and a Personal Attack. In the first case, the attack would be aimed at making the followers feel very favorable about rejecting her claims. In the second case, the attack would be aimed at making the followers reject the person's claims because of some perceived (or imagined) defect in her character.

This fallacy is related to the Appeal to Popularity fallacy. Despite the differences between these two fallacies, they are both united by the fact that they involve appeals to emotions. In both cases the fallacies aim at getting people to accept claims based on how they or others feel about the claims and not based on evidence for the claims.

Another way to look at these two fallacies is as follows
Appeal to Popularity

1. Most people approve of X.
2. So, I should approve of X, too.
3. Since I approve of X, X must be true.

Appeal to Emotion

1. I approve of X.
2. Therefore, X is true.

On this view, in an Appeal to Popularity the claim is accepted because most people approve of the claim. In the case of an Appeal to Emotion the claim is accepted because the individual approves of the claim because of the emotion of approval he feels in regards to the claim.