Counterfactual Causation

Origin. David Hume raised the problem of causation; regularity theories proved insufficient. David Lewis (1973) developed the counterfactual analysis: "C causes E" means if C had not occurred, E would not have occurred. Builds on possible worlds semantics for counterfactual conditionals. Refined through debates with preemption, overdetermination, and late preemption cases.

Models. Causation as counterfactual dependence. What would have happened if things had been different? C causes E if E counterfactually depends on C — in the closest possible worlds where C doesn't occur, E doesn't occur either. Captures singular causation (this C caused this E) rather than general causal laws.

Formalism.

Counterfactual conditionals: φ □→ ψ (if φ were the case, ψ would be the case).

Semantics (Lewis): Possible worlds ordered by similarity to the actual world. φ □→ ψ is true at world w iff:

There are no φ-worlds (vacuously true), or
Some φ-world where ψ holds is closer to w than any φ-world where ψ doesn't hold

Similarity ordering: Lewis proposed criteria (most to least important):

Avoid big, widespread miracles
Maximize region of perfect match
Avoid small, localized miracles
Maximize approximate match

Causal dependence: E causally depends on C iff:

C □→ E (if C occurred, E would occur) — typically trivially true if both actually occurred
¬C □→ ¬E (if C had not occurred, E would not have occurred)

Causation: C causes E iff there is a chain of causal dependence from C to E. (This handles cases where intermediate events exist.)

Symbols.

Symbol	Unicode	Name	Meaning
□→	U+25A1 + U+2192	Counterfactual	If...were...would
◇→	U+25C7 + U+2192	Might-counterfactual	If...were...might
≤w	—	Closer-than	World similarity ordering
→	U+2192	Material conditional	Standard implication
¬	U+00AC	Negation	Not
C	—	Cause	Candidate cause event
E	—	Effect	Effect event

Metatheory. Counterfactual logic (Lewis's VC and VCS systems) is decidable. The similarity ordering is a partial preorder; Lewis axiomatized its properties. Stalnaker's simpler semantics assumes a unique closest world; Lewis allows ties. Counterfactual conditionals are non-monotonic: adding information to the antecedent can change the consequent's truth. Unlike material conditionals, counterfactuals don't satisfy strengthening of the antecedent.

Applies to. Philosophy of causation. Legal reasoning (causation in law). Historical counterfactuals. Explanation (explaining why by citing what would have been different). Moral responsibility (the agent's action made the difference).

Limitations. Preemption: C causes E, but D would have caused E if C hadn't. The counterfactual ¬C □→ ¬E is false, yet C caused E. Late preemption is particularly troublesome. Overdetermination: two causes each sufficient. The counterfactual test says neither caused E (since removing either leaves the other). Similarity ordering: which worlds count as "closest" requires judgment. Backtracking: should we allow counterfactuals that change the past? Different readings give different answers. Fine-graining events and fragility: how events are individuated affects the analysis. Lewis's theory captures token causation but doesn't directly handle type-level causal generalizations.