On the Role of Counterfactuals in Inferring Causal Effects of Treatments

Causal inference in the empirical sciences is based on counterfactuals. This paper presents the counterfactual account of causation in terms of Lewis's possible-world semantics, and reformulates the statistical potential outcome framework and its underlying assumptions using counterfactual conditionals. I discuss varieties of causally meaningful counterfactuals for the case of a finite number of treatments, and illustrate these using a simple set-theoretical framework. The paper proceeds to examine proximity relations between possible worlds, and discusses implications for empirical practice