Concise Guide to Critical Thinking Chapter 5

Inductive reasoning gives us most of what we know about the empirical workings of the world, allowing us in science and in ordinary experience to soar reliably from what we know to what we don’t. It allows us to reason “beyond the evidence”—from bits of what is already known to conclusions about what those bits suggest is probably true. When we talk of probability, we enter the realm of statistics

Enumerative Induction: An inductive argument pattern in which we reason from premises about individual members of a group to conclusions about the group as a whole. 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.

Statistical Syllogism: An inductive argument pattern in which the inference goes from a statement about a group of things to a conclusion about a single member of that group. Almost all of the students attending this college are pacifists. Wei-en attends this college. Therefore, Wei-en is probably a pacifist.

Target group (or target population)—In enumerative induction, the whole collection of individuals under study. Sample (or sample member)—In enumerative induction, the observed members of the target group. Relevant property (or property in question)—In enumerative induction, a property, or characteristic, that is of interest in the target group.

Consider this enumerative induction: All the corporate executives Jacques has worked for have been crooks. Therefore, all corporate executives are probably crooks. Target group=corporate executives Sample=the corporate executives Jacques has worked for Relevant property=being a crook

All the corporate executives Jacques has worked for have been crooks. Therefore, all corporate executives are probably crooks. Verdict: This enumerative inductive falls short on at least one score: The sample is too small. We simply cannot draw reliable conclusions about all corporate executives based on a mere handful of them. The argument is weak.

Hasty generalization—The fallacy of drawing a conclusion about a target group based on an inadequate sample size. Biased sample—A sample that does not properly represent the target group. Representative sample—In enumerative induction, a sample that resembles the target group in all relevant ways.

Random sample—A sample that is selected randomly from a target group in such a way as to ensure that the sample is representative. In a simple random selection, every member of the target group has an equal chance of being selected for the sample. Confidence level—In statistical theory, the probability that the sample will accurately represent the target group within the margin of error. Margin of error—The variation between the values derived from a sample and the true values of the whole target group.

Self-Selecting Sample A type of sample that usually tells you very little about the target population. We would get a self-selecting sample if we publish a questionnaire in a magazine and ask readers to fill it out and mail it in, or if during a TV or radio news broadcast we ask people to cast their vote on a particular issue by clicking options on a website or emailing their responses.

Hasty Generalization—drawing a conclusion about a whole group based on an inadequate sample of the group. Example: The only male professor I’ve had this year was a chauvinist pig. All the male professors at this school must be chauvinist pigs. Faulty Analogy—an argument in which the things being compared are not sufficiently similar in relevant ways. Example: Dogs are warm-blooded, nurse their young, and give birth to puppies. Humans are warm-blooded and nurse their young. Therefore, humans give birth to puppies too.

Mean—the average of a set of numbers Mean—the average of a set of numbers. Median—the middle point of a series of values. Mode—the most common value.

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.

Argument by analogy: (also, analogical induction)—An argument making use of analogy, reasoning that because two or more things are similar in several respects, they must be similar in some further respect. Thing A has properties P1, P2, P3, plus the property P4. Thing B has properties P1, P2, and P3. Therefore, thing B probably has property P4.

Criteria for judging arguments by analogy: 1. The number of relevant similarities 2. The number of relevant dissimilarities 3. The number of instances compared 4. The diversity among cases