Reasoning is a lot like chainsaw. It is a useful tool when handled properly, but when wielded badly (perhaps while impaired by fear) it can create a bloody mess. While this analogy can be applied broadly to the various methods of logic, the focus is on the inductive generalization and how it can be turned into a wayward chainsaw under the influence of fear.
Consisting of a premise and a conclusion, the inductive generalization is a simple argument:
Premise 1: P% of observed Xs are Ys.
Conclusion: P% of all Xs are Ys.
Briefly put, the quality of an inductive generalization depends on the quality of the first premise, which is usually referred to as being a sample. The larger and more representative the sample, the stronger the argument (the more likely it is that the conclusion will be true if the premise is true). There are thus two main ways an inductive generalization can be bad. The first occurs when the sample is too small to adequately support the conclusion. For example, a person might have a run-in with a single bad driver from Ohio and conclude that all Ohio drivers are terrible. This is known as a hasty generalization and is a standard fallacy.
The second occurs when the sample is biased so that it does not properly represent the population in question. For example, a person who concludes that most people are Christians because everyone at her Christian church is a Christian would commit this fallacy. This is also a standard fallacy and is known as a biased generalization.
While works on fallacies do discuss these two fallacies, it is worth considering them in the specific context of fear—what I am calling a fearful generalization. On the one hand, it is not a new fallacy: a fearful generalization is structurally a hasty generalization or, less often, a biased generalization. On the other hand, the hallmark of a fearful generalization (that it is fueled by fear) does seem to make it worth considering on its own. I think that the role of fear in this sort of bad reasoning is worth considering, especially since addressing the fueling fear seems to be key to disarming this sort of poor reasoning.
As noted above, a fearful generalization is not a new fallacy structurally. Its defining quality is that a fallacious generalization is committed because of the psychological impact of fear. In the case of a hasty fearful generalization, the error is to draw an inference from a sample that is too small, and the error is caused by fear. For example, a female college student who hears about incidents of sexual harassment and assault on campuses might, from fear, infer that all or most male students are likely to harass or assault her. As another example, a person who hears about an undocumented migrant/illegal alien who commits a murder might, from fear, infer that all or most undocumented migrants/illegal aliens are murderers. In such cases the inference is fueled by fear. Metaphorically, the fear fills out the sample, making it feel like the conclusion is true. However, this is obviously an error in reasoning.
The biased fearful generalization occurs when the inference is based on a sample that is not representative, but this fact is overlooked because of the emotion of fear. Metaphorically, the fear makes the sample feel diverse enough to support the conclusion. For example, a person might look at data about migrants arrested by the police for crimes other than being in a country illegally and infer from the conviction data that most migrants are guilty of crimes. The bias is, of course, that migrants arrested for other crimes will obviously not represent the migrant population. A good generalization about what percentage of migrants commits crimes needs to include the entire population, not a sample consisting solely of those arrested.
As another example, if someone who is terrified of guns looks at crime data about arrests of people who have guns and infers from the conviction data that most gun owners are criminals, they would commit a biased generalization. This is because those arrested for gun crimes will not represent the entire gun-owning population. A good generalization about what percentage of gun-owners commit crimes needs to include the entire population, not a sample consisting solely of those arrested for such crimes.
It must be noted that when considering any fallacy, there are three things to always keep in mind. First, not everything that looks like a fallacy is a fallacy. After all, a good generalization has the same argument form as a hasty or biased generalization. Second, to infer that a fallacy must have a false conclusion is itself a fallacy (the fallacy fallacy). So, a biased or hasty generalization could turn out to have a true conclusion. Third, having a true conclusion does not mean that a fallacy is thus not a fallacy. As just noted, a hasty generalization could have a true conclusion—the problem lies in the logic. For example, if I go to a forest and see one red squirrel and infer all the squirrels in the forest are red, then I have made a hasty generalization. Even if I am right that all the squirrels are red. To use an analogy, it is like a lucky guess on a math problem: getting the right answer does not mean that one did the math properly. But how does one neutralize the fearful generalization?
On the face of it a fearful generalization would seem to be easy to neutralize. One would simply present the argument and consider the size and representativeness of the sample in an objective manner. The problem is, of course, that a fearful generalization is motivated by fear and fear impedes rationality and objectivity. Even if a fearful person tries to consider the matter, they might persist in their error because of their fear. To use an analogy, I have an irrational fear of flying—I know that I am probably the safest I will ever be while in a plane, but this does not impact my fear (I still fly, since I learned long ago to lock away fear in its own special place). Likewise, someone who is afraid of migrants or men might be able to do the math yet persist in their fearful conclusion. As such, one way of dealing with fearful generalizations would be the best way to deal with fear in general—but this goes beyond the realm of critical thinking and into the realm of virtue.
One way to try to at least briefly defuse the impact of fear is to try the method of substitution. The idea is to replace the group one fears with a group that one belongs too, likes or at least does not fear. This works best when the first premise remains true when the swap is made, otherwise the person can obviously reject the swap. This might have some small impact on the emotional level that will help a person work through the fear—assuming they want to. I will illustrate the process using Chad, a hypothetical Christian white male gun owner who is fearful of undocumented migrants (or illegals, if you prefer).
Imagine that Chad reasons like this:
Premise 1: Some migrants have committed violent crimes in America.
“Premise” 2: I (Chad) am afraid of migrants.
Conclusion: Most or many migrants are violent criminals.
As “critical thinking therapy” Chad could try swapping in one of his groups and see if his logic still holds.
Premise 1: Some white men have committed violent crimes in America.
“Premise” 2: I (Chad) am a white man.
Conclusion: Most or many white men are violent criminals.
Chad would agree that each argument starts with a true first premise, but Chad would presumably reject the conclusion of the second argument. If pressed on why this is the case, Chad would presumably point out that the statistical data does not support the conclusion. At this point, a rational Chad would realize that the same applies to the first argument as well. If this does not work, one could keep swapping in groups that Chad belongs to or likes until Chad is able to see the bias caused by his fear or one gets exhausted by Chad.
This method is not guaranteed to work (it probably will not), but it does provide a useful method for those who want to check their fears. Self-application involves the same basic process: swapping in your groups or groups you like in place of what you fear to see if your reasoning is good or bad.