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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.

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18
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.

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12
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.

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29
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.

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21
Appeal to Fear
Ad Baculum

AKA Scare Tactics, Appeal to Force

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

The Appeal to Fear is a fallacy with the following pattern:

  1. Y is presented (a claim that is intended to produce fear).
  2. Therefore claim X is true (a claim that is generally, but need not be, related to Y in some manner).
This line of "reasoning" is fallacious because creating fear in people does not constitute evidence for a claim.

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. For example, it might be prudent to not fail the son of your department chairperson because you fear he will make life tough for you. However, this does not provide evidence for the claim that the son deserves to pass the class.

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4
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.

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