Chapter 8: Beliefs, Defaults, and Counterfactuals

Overview

You are so convinced that you believe only what you believe that you believe, that you remain utterly blind to what you really believe without believing you believe it.

—Orson Scott Card, Shadow of the Hegemon

Two types of reasoning that arise frequently in everyday life are default reasoning and counterfactual reasoning. Default reasoning involves leaping to conclusions. For example, if an agent sees a bird, she may conclude that it flies. Now flying is not a logical consequence of being a bird. Not all birds fly. Penguins and ostriches do not fly, nor do newborn birds, injured birds, dead birds, or birds made of clay. Nevertheless flying is a prototypical property of birds. Concluding that a bird flies seems reasonable, as long as the agent is willing to retract that conclusion in the face of extra information.

Counterfactual reasoning involves reaching conclusions with assumptions that may be counter to fact. In legal cases it is often important to assign blame. A lawyer might well want to argue as follows: "I admit that my client was drunk and it was raining. Nevertheless, if the car's brakes had functioned properly, the car would not have hit Mrs. McGraw's cow. The car's manufacturer is at fault at least as much as my client."

As the lawyer admits here, his client was drunk and it was raining. He is arguing though that even if the client hadn't been drunk and it weren't raining, the car would have hit the cow. This is a classic case of counterfactual reasoning: reasoning about what might have happened if things had been different from the way they actually were. (Note the use of the subjunctive clause starting with "even if"; this is the natural-language signal that a counterfactual is about to follow.)

Why am I discussing default reasoning and counterfactual reasoning at this point in the book? It should be clear that both involve reasoning about uncertainty. Moreover, it turns out that some of the representation of uncertainty that I have been considered—specifically, possibility measures, ranking functions, and plausibility measures—provide good frameworks for capturing both default reasoning and counterfactual reasoning. A closer look at these notions helps to explain why. In fact, it turns out that default reasoning and counterfactual reasoning are closely related, and are best understood in terms of belief. Thus, I start this chapter with a closer look at belief.