## Generalizing

We use deductive reasoning whenever we act on the basis of general knowledge--knowledge about classes of things and the properties they share. We acquire that knowledge in various ways, but primarily by generalizing from our experience--a form of inductive reasoning.

We cannot support a general proposition by merely appealing to other general propositions. At some point in our reasoning, we have to look at the actual instances of the general propositions.

However, there are dangers in generalizing from instances to a general proposition. We often generalize too quickly on the basis of insufficient evidence, committing the fallacy known as hasty generalization.

Hasty generalization is a fallacy because a single instance doesn't necessarily prove a general rule. Suppose we have a general proposition of the form "All S are P." Now consider the individual members of the class of Ss. If an individual S is P, it is called a positive instance, and it confirms the generalization. If an individual S is not P, it is a negative instance or counterexample, and it disconfirms the generalization.

There is a logical asymmetry here. A single negative instance decisively refutes a general statement. If I say that all athletes are dumb, and you point out that the varsity quarterback is getting excellent grades, you have proved me wrong.

A single positive instance, however, does not prove that a generalization is true. The fact that one athlete is a weak student doesn't prove that all of them are.

If S stands for a small, delimited class of things, we can solve this problem by examining each member of the class individually to see whether it is P. This is called the method of induction by complete enumeration.

However, most of the generalizations we employ in everyday reasoning do not involve classes that can be completely enumerated. They involve much larger classes that are open-ended in the sense that there is no limit on the number of members they may have.

So we have to rely on an incomplete survey of the class, a sample taken from the class as a whole. Our generalizations rest on the assumption that the sample is representative of the whole class.

A sample can provide evidence of a connection between S and P only if it is representative of the whole class of Ss, but how do we tell whether a sample is representative?

Three rules will help us decide. These rules are standards for assessing the strength of the inference from sample to generalization, and they are analogous to the rules for determining whether a syllogism is valid:

1. The sample should be sufficiently numerous and various.

Unlike a deductive argument, an inductive one is not self- contained. Its strength is affected by the context of other knowledge we possess. The truth of the premises does not guarantee the truth of the conclusion, and the degree of support the premises provide for the conclusion depends on factors not contained in the argument itself.

It is always possible to strengthen an inductive argument further by finding additional positive instances, especially if they increase the variety of the sample (Rule #1). However, the strength of the argument is dependent on our diligence in looking for disconfirming evidence as well (Rule #2). Its strength also depends on the initial plausibility of the generalization, which is determined by our theories and basic assumptions (Rule #3).

This is not a defect of induction. It means that inductive reasoning puts a special premium on integration, on looking beyond the argument itself to see how it fits with the rest of our knowledge.

Comprehension Questions

 1. Evaluate the following generalization inductively.The winters in the Northeast aren't so bad. I was in upstate New York in January once, and it was 55 degrees. a) The sample size used as a basis for generalizing is not sufficiently numerous and various. b) There is disconfirming evidence. c) The generalization is not plausible in the light of other knowledge we have. 2. In the following argument, what criticism is being raised about an inductive generalization?Researchers claimed to have produced the first self-sustaining cold fusion reaction. However, other researchers have not been able to reproduce their finds. a) The sample size used as a basis for generalizing is not sufficiently numerous and various. b) There is disconfirming evidence. c) The generalization is not plausible in the light of other knowledge we have. 3. In the following argument, what criticism is being raised about an inductive generalization? In a famous study on sexual activity, the research subjects were recruited by asking for volunteers and using prison inmates. It was found that 69 percent of men had been prostitutes. a) The sample size used as a basis for generalizing is not sufficiently numerous and various. b) There is disconfirming evidence. c) The generalization is not plausible in the light of other knowledge we have. 4. Evaluate the following generalization inductively.The hero of the movie singlehandedly saves the earth from a horde of alien invaders. So this is what this season's movies are about--violence, violence, and more violence. a) The sample size used as a basis for generalizing is not sufficiently numerous and various. b) There is disconfirming evidence. c) The generalization is not plausible in the light of other knowledge we have. 5. In the following argument, what criticism is being raised about an inductive generalization?The gesture of Etonia's new president should not be taken as a sign that Etonia wishes to mend its relationship with the United States. The United Nations has documented that Etonia is still the main sponsor of international terrorism against the United States. a) The sample size used as a basis for generalizing is not sufficiently numerous and various. b) There is disconfirming evidence. c) The generalization is not plausible in the light of other knowledge we have.

Causality