Counterfactual Conditionals and Similarity

Core Idea

Counterfactual conditionals are analyzed using possible worlds ordered by similarity to the actual world. A counterfactual is false when its consequent is false in the closest worlds where the antecedent is true, distinguishing them from material conditionals and strict conditionals.

Explainer

From your study of possible worlds semantics you know that modal claims — claims about what is possible, necessary, or contingent — are analyzed in terms of how things stand across different ways the world could be. A counterfactual conditional like "If the match had been struck, it would have lit" is a claim about what would have been true in a situation that did not actually occur. The antecedent ("the match was struck") is false in the actual world. The conditional is asking: in scenarios where that false antecedent was true instead, what else would have been true?

The problem with the material conditional analysis familiar from propositional logic is that a material conditional is simply false when its antecedent is false — which means all counterfactuals would be vacuously true (since their antecedents are false). But "If the match had been struck, it would have turned into a fish" is not true. We need an account that distinguishes good counterfactuals from bad ones. Robert Stalnaker and David Lewis independently developed the closest-worlds analysis: a counterfactual "If P had been the case, Q would have been the case" is true just in case Q holds in the closest possible worlds to the actual world where P is true. The match-would-light counterfactual is true because in the nearest worlds where the match is struck (dry conditions, oxygen present, not on Pluto) it lights. The match-would-become-a-fish counterfactual is false because even in nearby worlds where it is struck, fish don't appear.

The notion of world-similarity — what makes one possible world "closer" to actuality than another — does the main work and is the main source of debate. Lewis argued for a set of priorities: large-scale violations of actual laws of nature make a world less similar than small "miracles" confined to the antecedent event; then comes overall match of particular fact across history; then exact match of laws. This gives counterfactuals an asymmetry of time: "If Nixon had pressed the button, there would have been nuclear war" is evaluated by looking forward from the moment of pressing, not backward. The past remains as it was; the counterfactual consequence unfolds into the future. A backtracking reading — "If Nixon had pressed the button, something in his past must have been different to make him do so" — is non-standard, and Lewis's similarity ordering explains why.

Counterfactuals are not merely a semantic curiosity. They underpin the analysis of causation: on counterfactual theories, C caused E just in case if C had not occurred, E would not have occurred. They also figure centrally in scientific and practical reasoning: a law of nature supports counterfactuals in a way that an accidental regularity does not. "All copper conducts electricity" supports "If this penny were copper, it would conduct electricity"; "All coins in my pocket are copper" does not support the same form of reasoning about coins generally. The distinction between laws and accidents, between causal and non-causal regularities, and between robust and fragile generalizations all cash out, in part, in terms of which counterfactuals are supported.