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 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 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.

Appeal to Authority
Ad Verecundiam
AKA Fallacious Appeal to Authority, Misuse of Authority, Irrelevant Authority, Questionable Authority, Inappropriate Authority
Category: Fallacies of Relevance (Red Herrings) → Distracting Appeals

An Appeal to Authority is a fallacy with the following form:

1. Person A is (claimed to be) an authority on subject S.
2. Person A makes claim C about subject S.
3. Therefore, C is true.

This fallacy is committed when the person in question is not a legitimate authority on the subject. More formally, if person A is not qualified to make reliable claims in subject S, then the argument will be fallacious.

This sort of reasoning is fallacious when the person in question is not an expert. In such cases the reasoning is flawed because the fact that an unqualified person makes a claim does not provide any justification for the claim. The claim could be true, but the fact that an unqualified person made the claim does not provide any rational reason to accept the claim as true.

When a person falls prey to this fallacy, they are accepting a claim as true without there being adequate evidence to do so. More specifically, the person is accepting the claim because they erroneously believe that the person making the claim is a legitimate expert and hence that the claim is reasonable to accept. Since people have a tendency to believe authorities (and there are, in fact, good reasons to accept some claims made by authorities) this fallacy is a fairly common one.

Since this sort of reasoning is fallacious only when the person is not a legitimate authority in a particular context, it is necessary to provide some acceptable standards of assessment. The following standards are widely accepted:

1. The person has sufficient expertise in the subject matter in question.
Claims made by a person who lacks the needed degree of expertise to make a reliable claim will, obviously, not be well supported. In contrast, claims made by a person with the needed degree of expertise will be supported by the person's reliability in the area.

Determining whether or not a person has the needed degree of expertise can often be very difficult. In academic fields (such as philosophy, engineering, history, etc.), the person's formal education, academic performance, publications, membership in professional societies, papers presented, awards won and so forth can all be reliable indicators of expertise. Outside of academic fields, other standards will apply. For example, having sufficient expertise to make a reliable claim about how to tie a shoe lace only requires the ability to tie the shoe lace and impart that information to others. It should be noted that being an expert does not always require having a university degree. Many people have high degrees of expertise in sophisticated subjects without having ever attended a university. Further, it should not be simply assumed that a person with a degree is an expert.

Of course, what is required to be an expert is often a matter of great debate. For example, some people have (and do) claim expertise in certain (even all) areas because of a divine inspiration or a special gift. The followers of such people accept such credentials as establishing the person's expertise while others often see these self-proclaimed experts as deluded or even as charlatans. In other situations, people debate over what sort of education and experience is needed to be an expert. Thus, what one person may take to be a fallacious appeal another person might take to be a well supported line of reasoning. Fortunately, many cases do not involve such debate.

2. The claim being made by the person is within her area(s) of expertise.
If a person makes a claim about some subject outside of his area(s) of expertise, then the person is not an expert in that context. Hence, the claim in question is not backed by the required degree of expertise and is not reliable.

It is very important to remember that because of the vast scope of human knowledge and skill it is simply not possible for one person to be an expert on everything. Hence, experts will only be true experts in respect to certain subject areas. In most other areas they will have little or no expertise. Thus, it is important to determine what subject area a claim falls under. It is also very important to note that expertise in one area does not automatically confer expertise in another. For example, being an expert physicist does not automatically make a person an expert on morality or politics. Unfortunately, this is often overlooked or intentionally ignored. In fact, a great deal of advertising rests on a violation of this condition. As anyone who watches television knows, it is extremely common to get famous actors and sports heroes to endorse products that they are not qualified to assess. For example, a person may be a great actor, but that does not automatically make him an expert on cars or shaving or underwear or diets or politics.

3. There is an adequate degree of agreement among the other experts in the subject in question.
If there is a significant amount of legitimate dispute among the experts within a subject, then it will fallacious to make an Appeal to Authority using the disputing experts. This is because for almost any claim being made and "supported" by one expert there will be a counterclaim that is made and "supported" by another expert. In such cases an Appeal to Authority would tend to be futile. In such cases, the dispute has to be settled by consideration of the actual issues under dispute. Since either side in such a dispute can invoke experts, the dispute cannot be rationally settled by Appeals to Authority.

There are many fields in which there is a significant amount of legitimate dispute. Economics is a good example of such a disputed field. Anyone who is familiar with economics knows that there are many plausible theories that are incompatible with one another. Because of this, one expert economist could sincerely claim that the deficit is the key factor while another equally qualified individual could assert the exact opposite. Another area where dispute is very common (and well known) is in the area of psychology and psychiatry. As has been demonstrated in various trials, it is possible to find one expert that will assert that an individual is insane and not competent to stand trial and to find another equally qualified expert who will testify, under oath, that the same individual is both sane and competent to stand trial. Obviously, one cannot rely on an Appeal to Authority in such a situation without making a fallacious argument. Such an argument would be fallacious since the evidence would not warrant accepting the conclusion.

It is important to keep in mind that no field has complete agreement, so some degree of dispute is acceptable. How much is acceptable is, of course, a matter of serious debate. It is also important to keep in mind that even a field with a great deal of internal dispute might contain areas of significant agreement. In such cases, an Appeal to Authority could be legitimate.

4. The person in question is not significantly biased.
If an expert is significantly biased then the claims he makes within his are of bias will be less reliable. Since a biased expert will not be reliable, an Argument from Authority based on a biased expert will be fallacious. This is because the evidence will not justify accepting the claim.

Experts, being people, are vulnerable to biases and prejudices. If there is evidence that a person is biased in some manner that would affect the reliability of her claims, then an Argument from Authority based on that person is likely to be fallacious. Even if the claim is actually true, the fact that the expert is biased weakens the argument. This is because there would be reason to believe that the expert might not be making the claim because he has carefully considered it using his expertise. Rather, there would be reason to believe that the claim is being made because of the expert's bias or prejudice.

It is important to remember that no person is completely objective. At the very least, a person will be favorable towards her own views (otherwise she would probably not hold them). Because of this, some degree of bias must be accepted, provided that the bias is not significant. What counts as a significant degree of bias is open to dispute and can vary a great deal from case to case. For example, many people would probably suspect that doctors who were paid by tobacco companies to research the effects of smoking would be biased while other people might believe (or claim) that they would be able to remain objective.

5. The area of expertise is a legitimate area or discipline.
Certain areas in which a person may claim expertise may have no legitimacy or validity as areas of knowledge or study. Obviously, claims made in such areas will not be very reliable. What counts as a legitimate area of expertise is sometimes difficult to determine. However, there are cases which are fairly clear cut. For example, if a person claimed to be an expert at something he called "chromabullet therapy" and asserted that firing painted rifle bullets at a person would cure cancer it would not be very reasonable to accept his claim based on his "expertise." After all, his expertise is in an area which is devoid of legitimate content. The general idea is that to be a legitimate expert a person must have mastery over a real field or area of knowledge.

As noted above, determining the legitimacy of a field can often be difficult. In European history, various scientists had to struggle with the Church and established traditions to establish the validity of their disciplines. For example, experts on evolution faced an uphill battle in getting the legitimacy of their area accepted.

A modern example involves psychic phenomenon. Some people claim that they are certified "master psychics" and that they are actually experts in the field. Other people contend that their claims of being certified "master psychics" are simply absurd since there is no real content to such an area of expertise. If these people are right, then anyone who accepts the claims of these "master psychics" as true are victims of a fallacious appeal to authority.

6. The authority in question must be identified.
A common variation of the typical Appeal to Authority fallacy is an Appeal to an Unnamed Authority. This fallacy is Also Known as an Appeal to an Unidentified Authority. This fallacy is committed when a person asserts that a claim is true because an expert or authority makes the claim and the person does not actually identify the expert. Since the expert is not named or identified, there is no way to tell if the person is actually an expert. Unless the person is identified and has his expertise established, there is no reason to accept the claim.

This sort of reasoning is not unusual. Typically, the person making the argument will say things like "I have a book that says..." , or "they say...", or "the experts say...", or "scientists believe that...", or "I read in the paper.." or "I saw on TV..." or some similar statement. in such cases the person is often hoping that the listener(s) will simply accept the unidentified source as a legitimate authority and believe the claim being made. If a person accepts the claim simply because they accept the unidentified source as an expert (without good reason to do so), he has fallen prey to this fallacy.

Non‐Fallacious Appeals to Authority
As suggested above, not all Appeals to Authority are fallacious. This is fortunate since people have to rely on experts. This is because no one person can be an expert on everything and people do not have the time or ability to investigate every single claim themselves.

In many cases, Arguments from Authority will be good arguments. For example, when a person goes to a skilled doctor and the doctor tells him that he has a cold, then the patient has good reason to accept the doctor's conclusion. As another example, if a person's computer is acting odd and his friend, who is a computer expert, tells him it is probably his hard drive then he has good reason to believe her.

What distinguishes a fallacious Appeal to Authority from a good Appeal to Authority is that the argument meets the six conditions discussed above.

In a good Appeal to Authority, there is reason to believe the claim because the expert says the claim is true. This is because a person who is a legitimate expert is more likely to be right than wrong when making considered claims within her area of expertise. In a sense, the claim is being accepted because it is reasonable to believe that the expert has tested the claim and found it to be reliable. So, if the expert has found it to be reliable, then it is reasonable to accept it as being true. Thus, the listener is accepting a claim based on the testimony of the expert.

It should be noted that even a good Appeal to Authority is not an exceptionally strong argument. After all, in such cases a claim is being accepted as true simply because a person is asserting that it is true. The person may be an expert, but her expertise does not really bear on the truth of the claim. This is because the expertise of a person does not actually determine whether the claim is true or false. Hence, arguments that deal directly with evidence relating to the claim itself will tend to be stronger.

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.