Observation: John came to class late this morning.
Observation: John's hair was uncombed.
Prior experience: John is very fussy about his hair.
Conclusion: John overslept.
The reasoning process here is directly opposite to that used in deductive syllogisms. Rather than beginning with a general principle (people who comb their hair wake up on time), the chain of evidence begins with an observation and then combines it with other observations and past experience to arrive at a conclusion.
There are three basic kinds of inductive reasoning: generalization, analogy, and statistical inference.
Generalization
This is the most basic kind of inductive reasoning. You generalize whenever you make a general statement (all salesmen are pushy) based on observations (the last three salesmen who came to my door were pushy). When you use specific observations as the basis of a general conclusion, you are said to be making an inductive leap.
Generally speaking, the amount of support needed to justify an inductive leap is based on two things: the plausibility of the generalization and the risk factor involved in rejecting a generalization.
Implausible inductive leaps require more evidence than plausible ones do. More evidence is required, for example, to support the notion that a strange light in the sky is an invasion force from the planet Xacron than to support the notion that it is a low-flying plane. Since induction requires us to combine what we observe with prior experience, and most of us have more prior experience with low-flying planes than with extraterrestrial invaders, it will take more evidence of an alien invasion force to overcome our prior experience of low-flying planes.
An inductive leap is more easily justified—that is, you can supply less support for it—when rejecting it carries a great risk. Consider the following two arguments:
I drank milk last night and got a minor stomachache. I can probably conclude that the milk was a little bit sour, and I should probably not drink that milk again.
I ate a mushroom out of my backyard last night, and I became violently ill. I had to be rushed to the hospital to have my stomach pumped. I can probably conclude that the mushroom was poisonous, and I should probably not eat mushrooms from my backyard again.
Technically, the evidence for these two arguments is the same. They both generalize from a single instance, and they both reach conclusions that could be accounted for by other factors. However, most people would take the second argument much more seriously, simply because the consequences for not doing so are much more serious.
There are two common errors in generalization: hasty generalization and exclusion.
Hasty generalization. Inductive fallacies tend to be judgment calls—different people have different opinions about the line between correct and incorrect induction. You commit a hasty generalization, the fallacy most often associated with generalization, when you make an inductive leap that is not based on sufficient information. Another term for this is "jumping to conclusions." Look at the following three statements and try to determine which generalizations are valid and which are hasty.
General Widgets is a sexist company. It has over five thousand employees, and not a single one of them is female.
General Widgets is a sexist company. My friend Jane, who has a degree in computer science, applied for a job there, and it went to a man who majored in history.
General Widgets is a sexist company. My friend Jane applied there, and she didn't get the job.
Because different people can be convinced by different levels of evidence, it can be surprisingly difficult to identify a hasty generalization.
Exclusion. A second fallacy that is often associated with generalization, exclusion occurs when you omit an important piece of evidence from the chain of reasoning that is used as the basis for the conclusion. If I generalize that my milk is bad based on a minor stomachache and fail to take into account the seven hamburgers I ate after drinking the milk, I have excluded the hamburgers from the chain of reasoning and am guilty of exclusion, which can lead to an invalid conclusion.
Analogy
To make an argument using an analogy is to draw a conclusion about one thing based on its similarities to another thing. Consider, for example, the following argument against a hypothetical military action in the Philippines.
In the 1960s, America was drawn into a war in an Asian country, with a terrain largely comprising jungles, against enemies that we could not recognize and accompanied by friends that we could not count on. That war began slowly, by sending a few "advisors" to help survey the situation and offer military advice, and it became the greatest military disgrace that our country has ever known. We all know what happened in Vietnam. Do we really want a repeat performance in the Philippines?
In other words, this argument is saying the following: A war in the Philippines would be disastrous. Our soldiers had a terrible time fighting in the jungles in Vietnam, and the terrain around Manila is even worse. An argument like this is an example of a valid analogy. It takes an observation (we had a hard time fighting in the jungles of Vietnam), makes a generalization (it is hard to fight modern warfare in a jungle terrain), and then applies it to another instance (we would have a hard time fighting in the jungles of the Philippines).
Analogies can be useful in illustrating key points (such as the inability of modern militaries to contain rebellions based in jungle terrains), but they do not prove their points simply by being analogies. The most common error found in arguments that use analogies is the false analogy. In a false analogy the characteristics considered are irrelevant, inaccurate, or insufficient.
If we decide to attack the Philippines, we should probably do it in January. In 1991, we attacked Iraq in January, and look how well that turned out.
Though it goes through the same process, this analogy is based on irrelevant information (the time of year we attacked Iraq).
Statistical inference
We employ this third variety of inductive reasoning whenever we assume that something is true of a population as a whole because it is true of a certain portion of the population. Politicians and corporations spend millions of dollars a year gathering opinions from relatively small groups of people to form bases for statistical inferences, upon which they base most of their major decisions. Inductions based on statistics have proven to be extremely accurate as long as the sample sizes are large enough to avoid large margins of error. Political exit polls, for example, often predict results extremely accurately based on small voter samples, and the Nielsen ratings report the television viewing habits of over a hundred million households based on sample sizes of about a thousand American families. However, using statistical inference carries the risk of using an unrepresentative sample.
Unrepresentative sample. This is a statistical group that does not adequately represent the larger group that it is considered a part of. Any sample of opinions in the United States must take into account the differences in race, age, gender, religion, and geographic location that exist in this country. Thus, a sample of one thousand people chosen to represent all of these factors would tell us a great deal about the opinions of the electorate. A sample of one thousand white, thirty- year-old, Lutheran women from Nebraska would tell us nothing at all about the opinions of the electorate as a whole. Because samples must be representative to be accurate, it is a fallacy to rely on straw polls, informal surveys, and self-selecting questionnaires to gather statistical evidence.
Logical Fallacies
Rhetoricians have identified hundreds of different ways that reasoning can be used incorrectly. Understanding the most common of these fallacies can help you recognize where reasoning—your own and that of other people—goes astray. In this way, you can make your own writing more persuasive, and you can avoid being deceived by someone whose arguments are not logically sound.