Counterfactual Conditionals

Counterfactual conditionals are statements of the form "If P had been the case, Q would have been the case," where P is known or assumed to be false. They are essential to causal reasoning (A caused B only if, had A not occurred, B would not have occurred), moral and legal responsibility (was the defendant's action the cause-in-fact of the harm?), and historical explanation (what would have happened if X had not occurred?). Their logical analysis is notoriously difficult because standard truth-functional logic makes every counterfactual with a false antecedent vacuously true — which is clearly wrong. David Lewis's possible-worlds semantics (1973) provides the standard analysis: "If P, then Q" is true if and only if the closest possible worlds in which P is true are also worlds in which Q is true. Closeness is measured by similarity to the actual world across relevant dimensions. The framework captures many intuitions but requires a primitive and contested notion of world-similarity. Nelson Goodman's earlier work identified the problem of distinguishing projectible from non-projectible predicates — not all regularities support counterfactuals in the same way. Causal graph approaches (Pearl) provide an alternative: a counterfactual is evaluated by intervening on the causal model, setting the antecedent's variable to the counterfactual value and propagating the change through the model while holding other exogenous variables fixed.