Types of Non-Deductive Inferences

In the next few pages, we’ll consider four common types of non-deductive inferences: enumerative induction, statistical syllogism, inference to the best explanation, and argument by analogy. Here’s a brief description of each:

Enumerative Induction

Enumerative induction, also called inductive generalization (or simply “induction” or “generalization”), is a form of inference that involves extrapolating observed patterns to unobserved cases. Enumerative induction begins with the premise that all observed things in one category are also members of another category (all observed A’s are B’s) and concludes that probably everything in the first category is in the second category (all A’s are B’s) or that the next thing we observe in category A will also be in category B (the next A is a B). For example, from the fact that all observed emeralds have been green, we can infer that probably, all emeralds are green. Similarly, from the fact that all the objects we have dropped have fallen to the ground, we infer that the next object we drop will probably fall to the ground. So, the structure of an inductive inference can be characterized in either of the following ways:

Enumerative induction, first form:

Premise: All observed A’s are B’s.
Conclusion: Probably, all (or nearly all) A’s are B’s.

Enumerative induction, second form:

Premise: All observed A’s are B’s.
Conclusion: Probably, the next A to be observed will be a B.

Statistical Syllogism

A closely related inference form is the statistical syllogism, which begins with the premise that a certain proportion (or percentage) of observed things in one category are also members of another category, and concludes that probably a similar proportion holds in general. The structure of a statistical syllogism can be characterized as follows:

Premise: N% of observed A’s are B’s.
Conclusion: Probably, approximately N% of all A’s are B’s.

We can think of statistical syllogism as a generalized form enumerative induction; or, conversely, we can think of enumerative induction as a special case of statistical syllogism: namely, the case where N is 100%.

Inference to the Best Explanation

Inference to the best explanation, sometimes called abduction or abductive inference, is an argument which concludes that the best available explanation of some phenomenon is probably the true explanation. (What makes an explanation “best” is a difficult question to which we’ll return later in this chapter.) The structure of an inference to the best explanation can be characterized as follows:

Premise: C1, C2, C3, … etc. are the only candidate explanations we have.
Premise: C1 is a better explanation than C2, C3, … etc.
Conclusion: Therefore, C1 is probably true.

Argument by Analogy

Argument by analogy, or analogical inference, is an argument that draws a conclusion about one thing based on that thing’s relevant similarities to something else. This type of reasoning is used, for example, when we infer that other people and animals have conscious experiences similar to our own. From the fact that my cat and I are similar in relevant ways, I infer that the cat and I have an additional similarity that I cannot observe: the cat has conscious experiences too. Argument by analogy has the following structure:

Premise: x is an A.
Premise: x and y have many similarities relevant to being an A.
Conclusion: Therefore, y is probably an A.