5.1: Inductive Logics

Back in Chapter 1, we made a distinction between deductive and inductive arguments. While deductive arguments attempt to provide premises that guarantee their conclusions, inductive arguments are less ambitious. They merely aim to provide premises that make the conclusion more probable. Because of this difference, it is inappropriate to evaluate deductive and inductive arguments by the same standards. We do not use the terms ‘valid’ and ‘invalid’ when evaluating inductive arguments: technically, they’re all invalid because their premises don’t guarantee their conclusions; but that’s not a fair evaluation, since inductive arguments don’t even pretend to try to provide such a guarantee. Rather, we say of inductive arguments that they are strong or weak— the more probable the conclusion in light of the premises, the stronger the inductive argument; the less probable the conclusion, the weaker. These judgments can change in light of new information. Additional evidence may have the effect of making the conclusion more or less probable—of strengthening or weakening the argument.

The topic of this chapter and the next will be inductive logic: we will be learning about the various types of inductive arguments and how to evaluate them. Inductive arguments are a rather motley bunch. They come in a wide variety of forms that can vary according to subject matter; they resist the uniform treatment we were able to provide for their deductive cousins. We will have to examine a wide variety of approaches—different inductive logics. While all inductive arguments have in common that they attempt to give their conclusions more probable, it is not always possible for us to make precise judgments about exactly how probable their conclusions are in light of their premises. When that is the case, we will make relative judgments: this argument is stronger or weaker than that argument, though I can’t say how much stronger or weaker, precisely. Sometimes, however, it will be possible to render precise judgments about the probability of conclusions, so it will be necessary for us to acquire basic skills in calculating probabilities. With those in hand, we will be in a position to model an ideally rational approach to revising our judgments about the strength of inductive arguments in light of new evidence. In addition, since so many inductive arguments use statistics, it will be necessary for us to acquire a basic understanding of some fundamental statistical concepts. With these in hand, we will be in a position to recognize the most common types of statistical fallacies—mistakes and intentionally misleading arguments that use statistics to lead us astray.

Probability and statistics will be the subject of the next chapter. In this chapter, we will look at two very common types of inductive reasoning: arguments from analogy and inferences involving causation. The former are quite common in everyday life; the latter are the primary methods of scientific and medical research. Each type of reasoning exhibits certain patterns, and we will look at the general forms analogical and causal arguments; we want to develop the skill of recognizing how particular instances of reasoning fit these general patterns. We will also learn how these types of arguments are evaluated. For arguments from analogy, we will identify the criteria that we use to make relative judgments about strength and weakness. For causal reasoning, we will compare the various forms of inference to identify those most likely to produce reliable results, and we will examine some of the pitfalls peculiar to each that can lead to errors.