1. Material Theory

This is a book about induction and inductive inference. Since these terms may mean different things to different people, it is worth fixing at the outset what is meant by them here. Traditionally, induction has had a narrow meaning. At its narrowest, it refers to “induction by simple enumeration,” the inference from “Some As are B” to “All As are B.” This is an example of what is known as “ampliative inference,” for we have amplified the instances to which our knowledge applies. The premise applies just to the few cases of As at hand; the conclusion applies to all. I take this idea of amplification in its most general sense to be what induction is about. I shall use “induction” and “inductive inference” as the general term for any sort of ampliative inference; that is, any licit inferences that lead to conclusions logically stronger than the premises. Therefore the terms embrace what is sometimes called “abductive inference,” which is an inference to something that explains an otherwise puzzling phenomenon. A still broader form of induction commonly goes under the name of “confirmation theory.” It typically has no inferences with premises and conclusions. Rather it looks at degrees of support between propositions. The best-known and dominant form is probabilistic support.