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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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1
Appeal to Novelty
AKA Appeal to the New, Newer is Better, Novelty

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

Appeal to Novelty is a fallacy that occurs when it is assumed that something is better or correct simply because it is new. This sort of "reasoning" has the following form:

  1. X is new.
  2. Therefore X is correct or better.
This sort of "reasoning" is fallacious because the novelty or newness of something does not automatically make it correct or better than something older. This is made quite obvious by the following example: Joe has proposed that 1+1 should now be equal to 3. When asked why people should accept this, he says that he just came up with the idea. Since it is newer than the idea that 1+1=2, it must be better.

This sort of "reasoning" is appealing for many reasons. First, "western culture" includes a very powerful commitment to the notion that new things must be better than old things. Second, the notion of progress (which seems to have come, in part, from the notion of evolution) implies that newer things will be superior to older things. Third, media advertising often sends the message that newer must be better. Because of these three factors (and others) people often accept that a new thing (idea, product, concept, etc.) must be better because it is new. Hence, Novelty is a somewhat common fallacy, especially in advertising.

It should not be assumed that old things must be better than new things (see the fallacy Appeal to Tradition) any more than it should be assumed that new things are better than old things. The age of a thing does not, in general, have any bearing on its quality or correctness (in this context).

Obviously, age does have a bearing in some contexts. For example, if a person concluded that his day old milk was better than his two‐month old milk, he would not be committing an Appeal to Novelty. This is because in such cases the newness of the thing is relevant to its quality. Thus, the fallacy is committed only when the newness is not, in and of itself, relevant to the claim.

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2
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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5
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.

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572
Confusing Cause and Effect
AKA Questionable Cause, Reversing Causation

Category: Fallacies of Presumption → Casual Fallacies

Confusing Cause and Effect is a fallacy that has the following general form:

  1. A and B regularly occur together.
  2. Therefore A is the cause of B. This fallacy requires that there not be, in fact, a common cause that actually causes both A and B.
This fallacy is committed when a person assumes that one event must cause another just because the events occur together. More formally, this fallacy involves drawing the conclusion that A is the cause of B simply because A and B are in regular conjunction (and there is not a common cause that is actually the cause of A and B). The mistake being made is that the causal conclusion is being drawn without adequate justification.

In some cases it will be evident that the fallacy is being committed. For example, a person might claim that an illness was caused by a person getting a fever. In this case, it would be quite clear that the fever was caused by illness and not the other way around. In other cases, the fallacy is not always evident. One factor that makes causal reasoning quite difficult is that it is not always evident what is the cause and what is the effect. For example, a problem child might be the cause of the parents being short tempered or the short temper of the parents might be the cause of the child being problematic. The difficulty is increased by the fact that some situations might involve feedback. For example, the parents' temper might cause the child to become problematic and the child's behavior could worsen the parents' temper. In such cases it could be rather difficult to sort out what caused what in the first place.

In order to determine that the fallacy has been committed, it must be shown that the causal conclusion has not been adequately supported and that the person committing the fallacy has confused the actual cause with the effect. Showing that the fallacy has been committed will typically involve determining the actual cause and the actual effect. In some cases, as noted above, this can be quite easy. In other cases it will be difficult. In some cases, it might be almost impossible. Another thing that makes causal reasoning difficult is that people often have very different conceptions of cause and, in some cases, the issues are clouded by emotions and ideologies. For example, people often claim violence on TV and in movies must be censored because it causes people to like violence. Other people claim that there is violence on TV and in movies because people like violence. In this case, it is not obvious what the cause really is and the issue is clouded by the fact that emotions often run high on this issue.

While causal reasoning can be difficult, many errors can be avoided with due care and careful testing procedures. This is due to the fact that the fallacy arises because the conclusion is drawn without due care. One way to avoid the fallacy is to pay careful attention to the temporal sequence of events. Since (outside of Star Trek), effects do not generally precede their causes, if A occurs after B, then A cannot be the cause of B. However, these methods go beyond the scope of this program.

All causal fallacies involve an error in causal reasoning. However, this fallacy differs from the other causal fallacies in terms of the error in reasoning being made. In the case of a Post Hoc fallacy, the error is that a person is accepting that A is the cause of B simply because A occurs before B. In the case of the Fallacy of Ignoring a Common Cause A is taken to be the cause of B when there is, in fact, a third factor that is the cause of both A and B. For more information, see the relevant entries in this program.

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8
Fallacy of Division
Category: Fallacies of Ambiguity

The fallacy of Division is committed when a person infers that what is true of a whole must also be true of its constituents and justification for that inference is not provided. There are two main variants of the general fallacy of Division:

The first type of fallacy of Division is committed when 1) a person reasons that what is true of the whole must also be true of the parts and 2) the person fails to justify that inference with the required degree of evidence. More formally, the "reasoning" follows this sort of pattern:

  1. The whole, X, has properties A, B, C, etc.
  2. Therefore the parts of X have properties A,B,C, etc.
That this line of reasoning is fallacious is made clear by the following case: 4 is an even number. 1 and 3 are parts of 4. Therefore 1 and 3 are even.

It should be noted that it is not always fallacious to draw a conclusion about the parts of a whole based on the properties of the whole. As long as adequate evidence is provided in the argument, the reasoning can be acceptable. For example, the human body is made out of matter and it is reasonable to infer from this that the parts that make up the human body are also made out of matter. This is because there is no reason to believe that the body is made up of non‐material parts that somehow form matter when they get together.

The second version of the fallacy of division is committed when a person 1) draws a conclusion about the properties of individual members of a class or group based on the collective properties of the class or group and 2) there is not enough justification for the conclusion. More formally, the line of "reasoning" is as follows:

  1. As a collective, group or class X has properties A,B,C, etc.
  2. Therefore the individual members of group or class X have properties A,B,C, etc.
That this sort of reasoning is fallacious can be easily shown by the following: It is true that athletes, taken as a group, are football players, track runners, swimmers, tennis players, long jumpers, pole vaulters and such. But it would be fallacious to infer that each individual athlete is a football player, a track runner, a swimmer, a tennis player, a swimmer, etc.

It should be noted that it is not always fallacious to draw a conclusion about an individual based on what is true of the class he/she/it belongs to. If the inference is backed by evidence, then the reasoning can be fine. For example, it is not fallacious to infer that Bill the Siamese cat is a mammal from the fact that all cats are mammals. In this case, what is true of the class is also true of each individual member.

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