Counterfactual

Counterfactuals are conditional claims about what would be the case if circumstances in the past or in a system had been different. They typically take the form “If A had occurred, B would have followed,” where A describes an alternative to what actually happened. They aim to describe outcomes under hypothetically altered histories or conditions.

In philosophy and logic, counterfactuals are often analyzed using possible-world semantics. A statement is true if, in the nearest possible worlds where A holds, B also holds. This approach, associated with Stalnaker and Lewis, emphasizes similarity and relevance of the alternative world to the actual one. In formal logic, counterfactuals are distinguished from material implication because their truth depends on causal or normative connections rather than purely on truth-functional structure.

In causal inference, counterfactuals express outcomes under interventions. Structural causal models define counterfactuals by inferring the causes of observed data, replacing a variable with a specified value, and predicting the outcome under that intervention. Modern frameworks such as the do-calculus and potential-outcomes formalisms provide concrete methods for computing statements like “If X had been x, Y would have been y,” given a causal model.

Applications span philosophy, statistics, economics, medicine, law, history, and artificial intelligence. Examples include scientific explanations, moral and legal reasoning about responsibility, and policy evaluation. Limitations arise from reliance on causal assumptions, the choice of possible or intervenable alternatives, and questions about whether a given counterfactual is determinate in a given context. Overall, counterfactuals offer a formal way to discuss causation, responsibility, and hypothetical scenarios beyond actual events.