Philosophy
The Logic of Counterfactuals and Possible Worlds
Quick fact
David Lewis's semantics uses a 'closeness' ordering of possible worlds, where worlds that differ less from ours (e.g., in laws of physics) are considered more relevant when evaluating counterfactuals.
Why this is interesting
We say 'If I had left earlier, I would have caught the train.' But the past is fixed—so what makes that statement true or false? How can we judge a world that never happened?
Read the full explanation
Understanding The Logic of Counterfactuals and Possible Worlds
Imagine you're replaying a football match in your head. You think, 'If the striker had aimed better, we would have won.' This is a counterfactual—a statement about a world that differs from the actual one in some specific way. To evaluate it, we picture possible worlds: slightly different versions of reality. The world where the striker's shot is slightly more accurate is still very similar to ours—same teams, same rules, same laws of physics. But in that world, the ball goes in. That world is 'closer' than one where aliens abduct the goalie. So we say the counterfactual is true because in the closest possible world(s), the outcome differs as stated. This is the core idea: we compare our world to alternative possible worlds, and the 'closeness'—how minimally we have to change things—determines truth.
A deeper explanation
Formally, a counterfactual 'If A, then C' is evaluated using a model of possible worlds. For each world w, we consider the set of worlds where A is true that are most similar to w (the 'closest' A-worlds). The counterfactual is true at w if C is true in all those closest worlds. This was independently proposed by Robert Stalnaker (1968) and David Lewis (1973) with slightly different semantics. Lewis's approach uses a 'center' (our world) and spherical systems of spheres representing increasing dissimilarity. The theory handles nuances like vacuous truth: if there are no A-worlds at all (e.g., 'If 2+2=5, then I'm a billionaire'), the counterfactual is vacuously true. This logic has profound implications: it is used to analyze causation (C causes E if E is counterfactually dependent on C), to formalize thought experiments in science and ethics, and to model hypothetical reasoning in artificial intelligence and game theory. By making precise what we mean by 'what if', possible-worlds semantics turns our intuitive counterfactual reasoning into a rigorous logical system.