What makes one event cause another? When the cue ball strikes the eight ball and sends it rolling, something connects these events beyond mere succession. Yet specifying the nature of this connection has proven remarkably difficult.

Two dominant frameworks compete for our understanding. Regularity theories, following Hume, reduce causation to patterns of constant conjunction—causes are simply events regularly followed by their effects. Counterfactual theories, developed by David Lewis, analyze causation through dependence relations—causes are events without which their effects wouldn't have occurred.

The stakes extend far beyond metaphysical curiosity. How we understand causation shapes scientific methodology, legal attribution of responsibility, and everyday reasoning about intervention. A doctor choosing treatments, a jury assigning blame, a policymaker predicting consequences—each relies on some conception of what makes causes actually cause. Getting this right matters for how we navigate a world of causal connections.

Hume's empiricism demanded that legitimate concepts trace back to sensory impressions. When he searched for the impression corresponding to necessary connection between cause and effect, he found nothing. We observe the flame, then the heat—but we never observe the flame making the heat happen. The connection itself remains imperceptible.

From this epistemic observation, Hume drew a bold metaphysical conclusion. Causation just is constant conjunction: event type A causes event type B when events of type A are regularly followed by events of type B, with appropriate relations of contiguity and temporal priority. The mysterious necessary connection dissolves into something fully observable—patterns of succession.

This deflationary account carries significant theoretical virtues. It respects empiricist constraints by grounding causation in observable regularities. It avoids positing mysterious powers or hidden mechanisms. It provides clear truth conditions for causal claims: check whether events of the relevant types correlate appropriately. Scientific practice, with its emphasis on experimental regularities, seems to vindicate this approach.

Yet the regularity theory faces a fundamental objection: accidental generalizations. Suppose every coin in my pocket happens to be copper. 'All coins in my pocket are copper' states a true regularity, but being in my pocket doesn't cause coins to be copper. Similarly, night regularly follows day, but day doesn't cause night—both result from Earth's rotation. The theory struggles to distinguish genuinely causal regularities from merely accidental ones, threatening to conflate correlation with causation at the foundations of the analysis.

Takeaway

Regularity theories gain empiricist credentials by reducing causation to observable patterns, but they purchase this simplicity at the cost of distinguishing genuine causes from mere correlations.

David Lewis proposed a fundamentally different analysis. Rather than asking what patterns events fall into, we should ask: would the effect have occurred without the cause? Causation becomes counterfactual dependence—event C causes event E just when, if C hadn't occurred, E wouldn't have occurred either.

This analysis requires a semantics for counterfactual conditionals. Lewis provided one using possible worlds: 'If C hadn't occurred, E wouldn't have occurred' is true when the nearest possible worlds where C doesn't occur are worlds where E doesn't occur either. 'Nearness' involves overall similarity to the actual world, weighted toward match of laws and particular facts.

The counterfactual approach handles accidental generalizations elegantly. Being in my pocket doesn't cause coins to be copper because the nearest worlds where a particular coin isn't in my pocket are worlds where it remains copper—its material composition doesn't counterfactually depend on its location. The difference-making structure distinguishes genuine causes from mere correlates.

Lewis's account also connects causation to explanation and intervention in intuitive ways. When we explain an event by citing its cause, we identify what made the difference to its occurrence. When we intervene on causes to change effects, we exploit counterfactual dependencies. The theory vindicates the practical significance of causal knowledge: knowing causes means knowing how to make differences in the world.

Takeaway

Counterfactual theories capture causation as difference-making—causes are events whose absence would have meant the absence of their effects—grounding causal knowledge in our ability to reason about alternative possibilities.

Both theories face severe tests from cases involving backup causes. Consider preemption: assassin A shoots the victim, but assassin B stood ready to shoot if A hadn't. A's shot causes the death, but there's no counterfactual dependence—had A not shot, B would have, and the victim would have died anyway. The counterfactual analysis seems to deliver the wrong verdict.

Lewis responded with increasingly sophisticated machinery—chains of counterfactual dependence, fragility of events, influence rather than simple dependence. Each refinement handles some cases while generating new counterexamples. The dialectic suggests that simple counterfactual dependence captures something important about causation without exhausting its nature.

Regularity theories face analogous difficulties. In overdetermination cases—two bullets simultaneously striking a victim, each sufficient for death—both events instantiate regularities connecting them to death. Yet intuitively both are causes, which the theory accommodates. But distinguishing this from preemption cases, where only one bullet is the cause, strains the regularity framework. What pattern of succession separates actual from backup causes?

These problem cases reveal something deeper about causation's structure. Actual causal processes—the physical connections transmitting influence from cause to effect—seem to matter independently of both regularities and counterfactuals. Some philosophers conclude that causation is fundamentally pluralistic, involving multiple distinct relations that typically but not invariably coincide. Others seek unified analyses that incorporate processual elements alongside difference-making.

Takeaway

Problem cases involving backup causes and overdetermination reveal the limitations of both major frameworks, suggesting that a complete account of causation may need to incorporate actual causal processes alongside patterns of dependence.

The debate between regularity and counterfactual theories illuminates causation's complex nature. Hume's insight that we never perceive necessary connections remains powerful, yet his reduction to constant conjunction fails to capture what distinguishes causes from correlates.

Lewis's counterfactual analysis makes progress by grounding causation in difference-making—the structure that matters for explanation and intervention. But preemption cases show that actual causal processes cannot be fully analyzed away.

Perhaps causation is not a single relation but a family of related phenomena: regular succession, counterfactual dependence, and physical process transmission. Understanding each illuminates different aspects of how events connect in our causal world.