  Counterfactual statements, e.g., "my headache would be gone had I taken an
aspirin" are central to scientific discourse, and are formally interpreted as
statements derived from "alternative worlds". However, since they invoke
hypothetical states of affairs, often incompatible with what is actually known
or observed, testing counterfactuals is fraught with conceptual and practical
difficulties. In this paper, we provide a complete characterization of
"testable counterfactuals," namely, counterfactual statements whose
probabilities can be inferred from physical experiments. We provide complete
procedures for discerning whether a given counterfactual is testable and, if
so, expressing its probability in terms of experimental data.
