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 settheoretical framework. The paper proceeds to examine proximity relations between possible worlds, and discusses implications for empirical practice.
Causation counterfactuals possible worlds treatment effect