5.5.2 Fallacies of Weak Induction

The fallacies of weak induction are mistakes in reasoning in which a person’s evidence or reasons are too weak to firmly establish a conclusion. The reasoner uses relevant premises, but the evidence contained therein is weak or defective in some way. These errors are errors of induction. When we inductively reason, we gather evidence using our experience in the world and draw conclusions based on that experience. Earlier in the chapter I used a generalization about the return of the red-winged blackbirds in March. But what if I based my generalization on just two years of experience? Now my conclusion—that the blackbirds return every mid-March—seems much weaker. In such cases, the reasoner uses induction properly by using relevant evidence, but her evidence is simply too weak to support the generalization she makes. An inductive inference may also be weak because it too narrowly focuses on one type of evidence, or the inference may apply to a generalization in the wrong way.

Hasty Generalization

A hasty generalization is a fallacy of weak induction in which a person draws a conclusion using too little evidence to support the conclusion. A hasty generalization was made in the red-winged blackbird case above. Here is another example:

Don’t eat at the restaurant. It’s bad. I had lunch there once, and it was awful. Another time I had dinner, and the portions were too small.

This person draws the conclusion that the restaurant is bad from two instances of eating there. But two instances are not enough to support such a robust conclusion. Consider another example:

Sixty-five percent of a random poll of 50 registered voters in the state said they would vote for the amendment. We conclude that the state amendment will pass.

Fifty voters is not a large enough sample size to draw predictive conclusions about an election. So to say the amendment will pass based on such limited evidence is a hasty generalization. Just how much evidence we need to support a generalization depends upon the conclusion being made. If we already have good reason to believe that the class of entities that is the subject of our generalization are all very similar, then we will not need a very large sample size to make a reliable generalization. For instance, physics tells us that electrons are very similar, so a study drawn from observing just a few electrons may be reasonable. Humans (particularly their political beliefs and behaviors) are not the same, so a much larger sample size is needed to determine political behavior. The fallacy of hasty generalization highlights the empirical nature of induction—we need a basic understanding of the world to know exactly how much evidence is needed to support many of our claims.

Biased Sample

A biased sample has some things in common with a hasty generalization. Consider the following:

Don’t eat dinner at that restaurant. It’s bad. My book club has met there once a week for breakfast for the past year, and they overcook their eggs.

This seems much better than the restaurant example offered above. If the book club has gone to the restaurant once per week for a year, the arguer has more than 50 instances as data. However, notice that the arguer’s evidence concerns breakfast, not dinner, and focuses on the eggs. Suppose the restaurant has an entirely different, more extensive dinner menu; then we cannot draw reliable conclusions about the restaurant’s success at dinner. This is an example of a biased sample. With a hasty generalization, the problem is that not enough evidence is used. In a biased sample, the problem is that the evidence used is biased in some way.

Appeal to Ignorance

Appeal to ignorance is another type of fallacy of weak induction. Consider the following line of reasoning:

In my philosophy class, we reviewed all the traditional arguments for the existence of God. All of them have problems. Because no one can prove that God exists, we can only conclude that God doesn’t exist.

Notice that the arguer wants to conclude that because we do not have evidence or sufficient arguments for God’s existence, then God cannot exist. In an appeal to ignorance, the reasoner relies on the lack of knowledge or evidence for a thing (our ignorance of it) to draw a definite conclusion about that thing. But in many cases, this simply does not work. The same reasoning can be used to assert that God must exist:

In my philosophy class, we reviewed different arguments against the existence of God. All of them have problems. Because no one can prove that God doesn’t exist, we can only conclude that God exists.

Any form of reasoning that allows you to draw contradictory conclusions ought to be suspect. Appeals to ignorance ignore the idea that absence of evidence is not evidence of absence. The fact that we lack evidence for X should not always function as evidence that X is false or does not exist.

False Cause Attribution

The fallacy of false cause occurs when a causal relation is assumed to exist between two events or things when it is unlikely that such a causal relationship exists. People often make this mistake when the two events occur together. The phrase “correlation does not equal causation” captures a common critique of this form of false cause reasoning. For example, a person may think that swimsuits cause sunburns because people often get sunburned when wearing swimsuits. There is a correlation between sunburn and swimsuits, but the suits are not a cause of sunburns.

False cause fallacies also occur when a person believes that just because one event occurs after another, the first event is the cause of the second one. This poor form of reasoning, in tandem with confirmation bias, leads to many superstitious beliefs. Confirmation bias is the natural tendency to look for, interpret, or recall information that confirms already-established beliefs or values. For example, some sports fans may notice that their team won sometimes on days when they were wearing a specific item of clothing. They may come to believe that this clothing item is “lucky.” Furthermore, because of confirmation bias, they may remember only instances when the team won when they were wearing that item (and not remember when the team lost when they were also wearing the item). The resulting superstition amounts to believing that wearing a special team jersey somehow causes the team to win.

In short, as emphasized by Figure 5.7, just because two things are often correlated (connected in that they occur together in time or place) does not mean that a cause-and-effect relationship exists between them.