Deductive inferences can be evaluated using the methods of formal logic. By examining the form (logical structure) of a deductive argument, we can objectively determine whether the premises entail the conclusion. Can we use similar methods to determine whether the premises of a non-deductive argument support its conclusion? Unfortunately, the answer to this question is no. There is no such thing as a formal logic for induction, nor is there any purely formal method for evaluating any of the four kinds of non-deductive arguments listed on the previous page.
The reason is that the strength of a non-deductive argument—the degree to which its premises support its conclusion—does not depend solely on the argument’s logical form. In fact, a strong inductive argument and a fallacious one can have exactly the same grammatical and logical structure! (We’ll see an example when we encounter Nelson Goodman’s “new riddle of induction” later in this chapter.) The same can be said for the other kinds of non-deductive inferences listed above. Whether a non-deductive argument is strong or weak depends not only on its form but also on its content: the meanings of the premises and conclusion make a difference to its strength. Thus, we cannot evaluate the strength of a non-deductive argument by examining its form alone.
Nevertheless, philosophers have developed useful methods and strategies for evaluating the strength of a non-deductive inference. Some of the most powerful methods have been developed in a sub-discipline of philosophy called confirmation theory, which will be introduced in the next chapter. For now, let us consider what factors contribute to the strengths of each of the four kinds of non-deductive inferences we have encountered.
Since enumerative induction and statistical syllogism are closely related, we can consider them together. Both begin with the premise that a certain proportion of observed A’s are B’s, and conclude that the same proportion holds among unobserved A’s as well. Such inferences assume that the observed sample of things in category A is representative of A’s in general. (A sample may be representative with respect to one property but not with respect to another. In this case, the sample of A’s must be representative with respect to the property of being a B.) When that assumption is false, an inductive inference or statistical syllogism is likely to yield a false conclusion. Thus, the strength of these inferences depends on whether we have good reasons to believe that the observed sample is a representative sample.
Although we don’t know in advance whether an observed sample is representative or not, there are things we can do to improve our chances of getting a representative sample. For example, we can select a large number of A’s and use a randomized sampling method to avoid selection biases. Inductive and statistical inferences provide relatively strong support for their conclusions when the observed sample of A’s is a large, randomly-selected sample.
In many cases, a strong inductive or statistical inference can be founded on the principle of the uniformity of nature (PUN)—the assumption that all of nature exhibits the same general laws, regularities, or patterns. PUN can be characterized as the assumption that the patterns we observe in nature provide a representative sample of nature as a whole. Whether we are justified in making this assumption in general is a tricky question, to which we’ll turn later in this chapter when we consider the so-called “problem of induction.”
Another approach to evaluating inductive and statistical inferences has been proposed by Gilbert Harman. In his 1965 paper “The Inference to the Best Explanation,” Harman argues that we shouldn’t regard enumerative induction as a distinct form of inference in its own right, but rather as a special type of inference to the best explanation. According to Harman, an inference from all observed A’s are B’s to all A’s are B’s is justified if and only if the hypothesis that “all A’s are B’s” is the best explanation for the fact that all observed A’s have been B’s. Harman acknowledges, but does not attempt to answer, the difficult question of what makes one explanation better than another. We’ll turn to that issue next.