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.

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.

Circumstantial Ad Hominem
Category: Fallacies of Relevance (Red Herrings) → Ad hominems (Genetic Fallacies)

A Circumstantial ad Hominem is a fallacy in which one attempts to attack a claim by asserting that the person making the claim is making it simply out of self interest. In some cases, this fallacy involves substituting an attack on a person's circumstances (such as the person's religion, political affiliation, ethnic background, etc.). The fallacy has the following forms:

1. Person A makes claim X.
2. Person B asserts that A makes claim X because it is in A's interest to claim X.
3. Therefore claim X is false.

1. Person A makes claim X.
2. Person B makes an attack on A's circumstances.
3. Therefore X is false.

A Circumstantial ad Hominem is a fallacy because a person's interests and circumstances have no bearing on the truth or falsity of the claim being made. While a person's interests will provide them with motives to support certain claims, the claims stand or fall on their own. It is also the case that a person's circumstances (religion, political affiliation, etc.) do not affect the truth or falsity of the claim. This is made quite clear by the following example: "Bill claims that 1+1 =2. But he is a Republican, so his claim is false."

There are times when it is prudent to suspicious of a person's claims, such as when it is evident that the claims are being biased by the person's interests. For example, if a tobacco company representative claims that tobacco does not cause cancer, it would be prudent to not simply accept the claim. This is because the person has a motivation to make the claim, whether it is true or not. However, the mere fact that the person has a motivation to make the claim does not make it false. For example, suppose a parent tells her son that sticking a fork in a light socket would be dangerous. Simply because she has a motivation to say this obviously does not make her claim false.

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.

Special Pleading
Category: Fallacies of Relevance (Red Herrings)

Special Pleading is a fallacy in which a person applies standards, principles, rules, etc. to others while taking herself (or those she has a special interest in) to be exempt, without providing adequate justification for the exemption. This sort of "reasoning" has the following form:

1. Person A accepts standard(s) S and applies them to others in circumstance(s) C.
2. Person A is in circumstance(s) C.
3. Therefore A is exempt from S.

The person committing Special Pleading is claiming that he is exempt from certain principles or standards yet he provides no good reason for his exemption. That this sort of reasoning is fallacious is shown by the following extreme example:

1. Barbara accepts that all murderers should be punished for their crimes.
2. Although she murdered Bill, Barbara claims she is an exception because she really would not like going to prison.
3. Therefore, the standard of punishing murderers should not be applied to her.

This is obviously a blatant case of special pleading. Since no one likes going to prison, this cannot justify the claim that Barbara alone should be exempt from punishment.

The Principle of Relevant Difference
From a philosophic standpoint, the fallacy of Special Pleading is violating a well accepted principle, namely the Principle of Relevant Difference. According to this principle, two people can be treated differently if and only if there is a relevant difference between them. This principle is a reasonable one. After all, it would not be particularly rational to treat two people differently when there is no relevant difference between them. As an extreme case, it would be very odd for a parent to insist on making one child wear size 5 shoes and the other wear size 7 shoes when the children are both size 5.

It should be noted that the Principle of Relevant Difference does allow people to be treated differently. For example, if one employee was a slacker and the other was a very productive worker the boss would be justified in giving only the productive worker a raise. This is because the productivity of each is a relevant difference between them. Since it can be reasonable to treat people differently, there will be cases in which some people will be exempt from the usual standards. For example, if it is Bill's turn to cook dinner and Bill is very ill, it would not be a case of Special Pleading if Bill asked to be excused from making dinner (this, of course, assumes that Bill does not accept a standard that requires people to cook dinner regardless of the circumstances). In this case Bill is offering a good reason as to why he should be exempt and, most importantly, it would be a good reason for anyone who was ill and not just Bill.

While determining what counts as a legitimate basis for exemption can be a difficult task, it seems clear that claiming you are exempt because you are you does not provide such a legitimate basis. Thus, unless a clear and relevant justification for exemption can be presented, a person cannot claim to be exempt.

There are cases which are similar to instances of Special Pleading in which a person is offering at least some reason why he should be exempt but the reason is not good enough to warrant the exemption. This could be called "Failed Pleading." For example, a professor may claim to be exempt from helping the rest of the faculty move books to the new department office because it would be beneath his dignity. However, this is not a particularly good reason and would hardly justify his exemption. If it turns out that the real "reason" a person is claiming exemption is that they simply take themselves to be exempt, then they would be committing Special Pleading. Such cases will be fairly common. After all, it is fairly rare for adults to simply claim they are exempt without at least some pretense of justifying the exemption.

Middle Ground
AKA Golden Mean Fallacy, Fallacy of Moderation
Category: Fallacies of Ambiguity

This fallacy is committed when it is assumed that the middle position between two extremes must be correct simply because it is the middle position. this sort of "reasoning" has the following form:

1. Position A and B are two extreme positions.
2. C is a position that rests in the middle between A and B.
3. Therefore C is the correct position.

This line of "reasoning" is fallacious because it does not follow that a position is correct just because it lies in the middle of two extremes. This is shown by the following example. Suppose that a person is selling his computer. He wants to sell it for the current market value, which is $800 and someone offers him $1 for it. It would hardly follow that $400.50 is the proper price.

This fallacy draws its power from the fact that a moderate or middle position is often the correct one. For example, a moderate amount of exercise is better than too much exercise or too little exercise. However, this is not simply because it lies in the middle ground between two extremes. It is because too much exercise is harmful and too little exercise is all but useless. The basic idea behind many cases in which moderation is correct is that the extremes are typically "too much" and "not enough" and the middle position is "enough." In such cases the middle position is correct almost by definition.

It should be kept in mind that while uncritically assuming that the middle position must be correct because it is the middle position is poor reasoning it does not follow that accepting a middle position is always fallacious. As was just mentioned, many times a moderate position is correct. However, the claim that the moderate or middle position is correct must be supported by legitimate reasoning.