Chapter 8

Enumerative Induction As you may have noticed in Chapter 3, sometimes an inductive argument rea- sons from premises about a group, or class, of things to a conclusion about a single member of the group—that is, from the general to the particular, or the whole to the part. For example: Almost all of the students attending this college are pacifists. Wei-en attends this college. Therefore, Wei-en is probably a pacifist. Eighty-two percent of residents in this neighborhood have been victims of crimes is a resident of this neighborhood. Therefore, Samuel will probably be a victim of a crime.

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Most peace activists I know are kind-hearted. So probably all peace activists are kind-hearted. Every Gizmo computer I've bought in the last two years has had a faulty monitor. Therefore all Gizmo computers probably have faulty monitors. Forty percent of the pickles that you've pulled out of the barrel are exceptionally good. So 40 percent of all the pickles in the barrel are probably exceptionally good. More formally, enumerative induction has this form: X percent of the observed members of group A have property P. Therefore, X percent of all members of group A probably have property P. In this formal guise, our pickle argument looks like this: Forty percent of the observed pickles from the barrel are exceptionally good. Therefore, 40 percent of all the pickles in the barrel are probably exceptionally good.

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An inductive argument, on the other hand, is intended to supply only probable support for its conclusion, earning the label of "strong" if it succeeds in providing such support and "weak" if it fails. The conclusion of an inductively strong argument is simply more likely to be true than not.

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Arguments by analogy are easy to formulate—perhaps too easy. To use an analogy to support a particular conclusion, all you have to do is find two things with some similarities and then reason that the two things are similar in yet an- other way. You could easily reach some very loopy conclusions. You could argue this, for instance: Birds have two legs, two eyes, breathe air, and fly; and humans have two legs, two eyes, and breathe air; therefore, humans can also fly. So the question is, how do we sort out the worthy analogical inductions from the unworthy (or really wacky)? How do we judge which ones have conclusions worth accepting and which ones don't?

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Enumerative induction comes with some useful terminology. The group as a whole—the whole collection of individuals in question—is called the target population or target group. The observed members of the target group are called the sample members or sample. And the property we're interested in is called the relevant property or property in question. In the foregoing example, the target group is the pickles in the barrel. The sample is the observed pickles. And the property is the quality of being exceptionally good.

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If the argument's premises are true, it is said to be cogent. Unlike valid deductive arguments, an inductively strong argument cannot guarantee that the conclusion is true—but it can render the conclusion probably true, even highly likely to be true. Inductive arguments, then, cannot give us certainty, but they can give us high levels of probability—high enough at least to help us acquire knowledge in everything from physics to bird watching.

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Now, using this terminology we can study arguments by enumeration a little closer. Remember that an inductive argument can not only be strong or weak, but it can also vary in its strength—in the degree of support that the premises give to the conclusion. So argument strength depends on the premises as well as on how much is claimed in the conclusion. Let's look at some examples.

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Our main concern in this section, however, is a more common inductive argument that reasons from premises about individual members of a group to conclusions about the group as a whole (from particular to general, or the part to the whole). In such cases we begin with observations about some members of the group and end with a generalization about all of them. This argument pattern is called enumerative induction, and it's a way of reasoning that we all find both natural and useful:

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Recall that a deductive argument is intended to provide logically conclusive support for its conclusion, being valid or invalid, sound or unsound.

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Such an inductive argument has been known traditionally as a statistical syllogism. The word syllogism—which is usually reserved for deductive arguments—refers to the fact that this argument consists of three statements: two premises and a conclusion. Syllogism is used to indicate that the generalization expressed in one of the premises is less than universal. But the defining feature of this argument is that its line of reasoning goes from a statement about a group of things to a conclusion about a single member of that group.

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