Deduction vs. Induction

The various systems of formal logic discussed in the preceding chapters—propositional logic, modal logic, and predicate logic—enable us to examine the logical structures and evaluate the validity of arguments within a broad category known as deductive inferences. In a valid deductive inference, as we have seen, the premises logically entail the conclusion: there is no logically possible way for the conclusion to be false while all the premises are true.

However, many of the inferences we employ in everyday reasoning involve premises that support a conclusion in a different way. For example, when you conclude on the basis of your past experiences that a bolt of lightning will be accompanied by a clap of thunder, the premises (that you just saw a lightning bolt, and that in your prior experience every such flash was accompanied by a subsequent thunderclap) do not logically entail the conclusion (that you will soon hear thunder). It is at least logically possible for the lightning to occur without you hearing the sound. So, the inference is deductively invalid. Nonetheless, given your prior experiences, the fact that you just saw lightning provides you with good evidence (i.e., a reason to believe) that you will soon hear thunder. In other words, the proposition that you saw lightning provides evidential support for your conclusion without logically entailing it.

The kind of reasoning illustrated in the preceding example is often called “induction.” However, the term induction is ambiguous. Some authors use the term in a broad sense to refer to any kind of non-deductive inference—that is, any form of inference in which the premises support the conclusion without logically entailing it. Understood in this broad way, induction just means non-deductive inference, and this category includes several different inference forms, as we will see. On the other hand, the term can also refer to a specific form of non-deductive inference called enumerative induction, which will be defined on the next page. To avoid confusion, I will use the term ‘induction’ only when referring specifically to enumerative induction, and I’ll use the term ‘non-deductive inference’ when referring to the broader category.

So, a non-deductive inference is an argument in which the premises are supposed to provide evidence for the conclusion, without logically entailing it. In other words, even if the premises of a non-deductive inference are true, the conclusion could still be false; but the argument is supposed to make the conclusion more plausible, or more likely to be true. In this chapter, we’ll examine four kinds of non-deductive inferences: enumerative induction, statistical syllogism, inference to the best explanation, and argument by analogy.

We’ll also consider how to evaluate the strength of a non-deductive argument—that is, the degree to which its premises support its conclusion. We can think of weaker and stronger arguments as lying on a spectrum that ranges from fallacies to deductively valid arguments. At the bottom of the spectrum are fallacies, which are just mistakes in reasoning. Even if the premises of a fallacious argument are true, they provide little or no support for the conclusion. At the top of the spectrum are deductively valid inferences. The premises of a deductively valid argument provide the strongest logical support for the conclusion: if the premises are true, the conclusion is guaranteed to be true as well. Non-deductive inferences lie somewhere in the middle of the spectrum. Some non-deductive inferences are quite strong—close to the “entailment” end of the spectrum—while others are so weak as to be nearly fallacious.

Evaluating the strength of a non-deductive inference is no easy task. In this chapter, we’ll consider some of the features that make non-deductive arguments stronger or weaker, but there is no straightforward way to test the logical strength of a non-deductive inference. There is no procedure comparable to the tests we used to determine the validity or invalidity of deductive arguments. In fact, there’s no such thing as a formal logic for non-deductive inferences. We can’t just analyze the form, or logical structure, of a non-deductive argument to determine whether the premises support the conclusion, as we did with deductive logic. (The reason why there can’t be any such thing as a formal logic for non-deductive inferences will become clear when we examine the so-called “problem of induction” near the end of this chapter.)

Fortunately, the situation isn’t hopeless. In later chapters, we’ll see that philosophers have developed strategies and even some formal tools that can aid us in evaluating non-deductive inferences. Although those tools won’t enable us to evaluate an argument based on its form (logical structure) alone, they can deliver useful verdicts when applied together with appropriate assumptions.