Chapter 5 Chapter Summaries

CHAPTER 5 SUMMARY

Enumerative Induction

• There is a 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.

• 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.

• We’re guilty of hasty generalization whenever we draw a conclusion about a target group based on an inadequate sample size. In general, the larger the sample, the more likely it is to reliably reflect the nature of the larger group. A good rule of thumb is this: The more homogeneous a target group is in traits relevant to the property in question, the smaller the sample can be; the less homogeneous, the larger the sample should be
• In addition to being the proper size, a sample must be a representative sample—it must resemble the target group in all the ways that matter. If it does not properly represent the target group, it’s a biased sample. An enumerative inductive argument is strong only if the sample is representative of the whole

Opinion Polls

• Enumerative inductions reach a high level of sophistication in the form of opinion polls conducted by professional polling organizations. As inductive arguments, opinion polls should (1) be strong and (2) have true premises. More precisely, any opinion poll worth believing must (1) use a large enough sample that accurately represents the target population in all the relevant population features and (2) generate accurate data (the results must correctly reflect what they purport to be about). A poll can fail to meet this latter requirement through data-processing errors, botched polling interviews, poorly phrased questions, and the like.

• To ensure that a sample is truly representative of the target group, the sample must be selected randomly from the target group. In a simple random selection, every member of the target group has an equal chance of being selected for the sample. By chance, each attempt at sampling will yield slightly different results. Such differences are referred to as the margin of error for a particular sampling or poll. Competently executed opinion polls will state their results along with a margin of error. Connected to the concept of margin of error is the notion of confidence level. In statistical theory, the confidence level is the probability that the sample will accurately represent the target group within the margin of error.

Analogical Induction

• An analogy can be used to argue inductively for a conclusion. Such an argument is known as an analogical induction, or simply an argument by analogy. An analogical induction reasons this way: Because two or more things are similar in several respects, they are likely to be similar in some further respect.

There are criteria we can use to judge the strength of arguments by analogy: (1) relevant similarities, (2) relevant dissimilarities, (3) the number of instances compared, and (4) diversity among cases.