We constantly reason about what would have happened if things had been different. If I had left earlier, I would have caught the train. If the match hadn't been struck, the fire wouldn't have started. These counterfactual conditionals seem straightforward in everyday speech, yet they pose deep puzzles for logical analysis.

What makes a counterfactual true or false? The actual world contains no information about unstruck matches or missed trains. We need to look beyond actuality—to possible worlds where the antecedent holds—and determine what follows there. But which possible worlds? And how do we select among the infinitely many ways things might have been different?

The Stalnaker-Lewis semantics provides an elegant framework for answering these questions. By analyzing counterfactuals in terms of similarity between possible worlds, this approach gives precise truth conditions for statements about unrealized possibilities. Understanding this framework illuminates not just modal logic, but the foundations of causation, scientific explanation, and rational decision-making.

The core insight of the Stalnaker-Lewis approach is deceptively simple: a counterfactual If A had been the case, then C would have been the case is true when C holds at the possible worlds most similar to actuality where A holds. We evaluate counterfactuals by looking at the nearest A-worlds and checking whether C obtains there.

Robert Stalnaker proposed that there is a unique nearest antecedent-world for any counterfactual. David Lewis relaxed this to allow multiple equally-near worlds, requiring only that C hold at all the nearest A-worlds. This difference matters for cases where several worlds tie for closeness, but the fundamental machinery remains the same.

Consider If the match had been struck, it would have lit. We examine worlds minimally different from ours where the striking occurs. At these worlds, the match's composition, the presence of oxygen, and the laws of nature remain unchanged. The match lights. The counterfactual comes out true because lighting occurs at all the relevantly similar striking-worlds.

This framework handles nested counterfactuals and complex modal reasoning. It explains why If A, then C doesn't entail If A and B, then C—the nearest (A ∧ B)-worlds may be farther from actuality than the nearest A-worlds, crossing into regions where C fails. The semantics captures the non-monotonicity that distinguishes counterfactual from material conditionals.

Takeaway

Counterfactuals are true not by correspondence with the actual world, but by what holds at the nearest possible worlds where their antecedents obtain—truth conditions that reach beyond actuality into modal space.

The framework's power depends on specifying which worlds count as most similar. This proves surprisingly complex. Similarity is multi-dimensional—worlds can resemble actuality in some respects while differing dramatically in others. Which dimensions matter, and how should they be weighted?

Lewis proposed a system of weighted priorities. Avoiding large-scale violations of natural law ranks highest. Maximizing the spatiotemporal region of perfect match comes next. Then avoiding small, localized miracles. Finally, securing approximate similarity of particular facts. This ordering handles most ordinary counterfactuals while blocking problematic inferences.

Context crucially affects similarity judgments. If Nixon had pressed the nuclear button, there would have been nuclear war seems true because we hold fixed the causal connections between button-pressing and launching. But If Nixon had pressed the button, some wire would have malfunctioned highlights different similarity dimensions—worlds where the mechanism fails might be closer than worlds with nuclear devastation, depending on conversational purposes.

This context-sensitivity isn't a bug but a feature. Counterfactual reasoning serves different purposes—causal explanation, practical deliberation, assigning responsibility—and these purposes make different similarity respects salient. The framework's flexibility accommodates this while maintaining precise truth conditions relative to any given similarity ordering.

Takeaway

Similarity between possible worlds isn't fixed absolutely but varies with context, making counterfactual truth sensitive to which dimensions of resemblance we're implicitly prioritizing in a given reasoning situation.

A crucial distinction separates forward-tracking counterfactuals from backtrackers. Forward-trackers move from causes to effects: If the lightning hadn't struck, the fire wouldn't have occurred. Backtrackers move from effects to causes: If the fire hadn't occurred, the lightning wouldn't have struck. Only one of these sounds natural for most contexts.

Standard similarity orderings privilege forward-tracking readings. We hold fixed the past and the laws, introduce a small miracle to realize the antecedent, and trace forward. This gives If the lightning hadn't struck, no fire while blocking If no fire, no lightning—the latter requires changing the past, which our similarity metric penalizes heavily.

This asymmetry matters profoundly for counterfactual theories of causation. Lewis defined causation as chains of counterfactual dependence: C causes E when, roughly, if C hadn't occurred, E wouldn't have occurred. This analysis requires the standard non-backtracking interpretation. If backtrackers were freely available, effects would spuriously cause their causes.

The ban on backtracking isn't absolute. Special contexts license backtracking readings: If the barometer hadn't fallen, the storm wouldn't have been approaching. Here we reason from evidence to what it indicates. Distinguishing these contexts from causal contexts reveals something important about the structure of counterfactual reasoning—it tracks explanatory and inferential relationships, not just modal proximity.

Takeaway

The asymmetry between forward-tracking and backtracking counterfactuals isn't merely linguistic convention but reflects deep structural features of causal and explanatory reasoning.

Counterfactual semantics transforms vague intuitions about unrealized possibilities into precise logical machinery. The possible worlds framework shows exactly what we're doing when we reason about what would have been—selecting the nearest antecedent-worlds and checking what holds there.

This precision pays philosophical dividends. Counterfactual dependence provides the foundation for leading theories of causation, grounds analyses of dispositional properties, and clarifies the structure of scientific explanation. The framework reveals connections between modality, causation, and explanation.

Understanding counterfactuals illuminates everyday reasoning. Every time we consider alternatives, assign blame, or deliberate about choices, we navigate the space of nearby possible worlds. The logic of what would have been shapes how we understand what actually is.