Philosophy
Counterfactuals and Possible Worlds Semantics
Quick fact
Classical logic's truth table says that 'If P, then Q' is true whenever P is false—so the claim 'If the moon is made of cheese, then 2+2=5' would be true. This paradox shows why counterfactuals need a richer semantic framework, one that compares actuality with nearby possible worlds.
Why this is interesting
If I had not dropped the glass, it would not have shattered. What makes that statement true? The glass did break, so how do we judge a claim about a scenario that never happened?
Read the full explanation
Understanding Counterfactuals and Possible Worlds Semantics
Think of possible worlds as branches that could have been taken. In our world, you did not study for the test. The counterfactual 'If I had studied, I would have passed' is about a nearby branch—one where you studied a little more. We evaluate whether in that nearby world you passed. If yes, the counterfactual is true. Sound familiar? It's like judging a 'what if' by looking at a similar scenario, not an arbitrary fantasy. The key idea is that we only consider worlds that are as similar to ours as possible, until we make the antecedent true. This avoids the bizarre consequences of material implication, which would treat such a statement as true merely because the antecedent is false.
A deeper explanation
The mechanism, as formalized by David Lewis and Robert Stalnaker, involves a similarity ordering over possible worlds. For a counterfactual 'If A were the case, C would be the case' to be true, we consider the set of worlds where A holds. Among those, we pick the world(s) most similar to the actual world. If C is true in all such 'closest' A-worlds (Lewis's variably strict conditional) or in the unique closest world (Stalnaker's semantics with the limit assumption), the counterfactual is true. This framework solves the paradoxes of material implication because the truth of a counterfactual depends on the content of the antecedent and consequent, not just their truth values. Crucially, this logic underpins analyses of causation: 'The glass breaking caused the shattering' can be understood as 'If the glass had not been dropped, it would not have shattered.' Thus, the logic of counterfactuals is not just an abstract exercise; it provides a tool for reasoning about causal dependency and for modeling hypothetical reasoning in artificial intelligence.