10 - Possible worlds, counterfactuals, and epistemic operators

Summary

In spite of its metaphysical appearance, the idea of possible worlds has found natural applications in the logical analysis of a variety of concrete experiences. In practical life, all of us are accustomed to comparing the actual world with a number of possible worlds that we consider more or less attractive. Our choices and actions seem to depend on such systematic comparisons. I will consider two examples that represent respectively a kind of successful and unsuccessful application of possible-worlds semantics: the theory of counterfactual conditionals and the semantics of epistemic logics. Both examples seem to play a relevant role in some game-theoretical problems.

COUNTERFACTUALS

As is well known, counterfactual arguments are not particularly appreciated in certain domains of knowledge. For instance, historians frequently repeat that “one cannot make history with ifs!” At the same time, in physics and in experimental sciences in general, counterfactual statements can hardly be avoided. Most physical laws have a counterfactual form, in the sense that they refer to boundary conditions that are generally not satisfied in our actual laboratories.

At first sight, counterfactual conditionals seem to behave in a silly way, because they violate some fundamental properties that we are accustomed to associate with our basic idea of implication. One of these properties is represented by transitivity, which notoriously constitutes the deep structure of the syllogistic argument. As a counterexample, let us consider the following odd inference.