Lewis vs Stalnaker on Counterfactuals
Closest possible worlds, uniquely or not
Venue: Stalnaker, "A Theory of Conditionals" (1968); Lewis, *Counterfactuals* (1973); subsequent debates in the philosophy of language.
A friendly, technical, and decades-long disagreement over how to evaluate "if A had been the case, B would have been."
Robert Stalnaker's 1968 paper "A Theory of Conditionals" proposed analysing counterfactuals via possible-worlds semantics: "if A were the case, then B would be" is true iff in the closest possible world to ours in which A is true, B is also true. Lewis's *Counterfactuals* (1973) developed a closely related but importantly different version: rather than a single closest world (Stalnaker), there may be ties or vagueness, so the counterfactual is true iff *all* the closest A-worlds are also B-worlds (or there are no A-worlds at all). The disagreement is technical but consequential: Stalnaker's system validates conditional excluded middle ("either if A then B, or if A then not-B"), Lewis's does not. Both authors held their positions across subsequent decades of refinement; the debate shapes the contemporary philosophy of conditionals, causation, and modality.
Historical Context
Lewis and Stalnaker were friends and respectful interlocutors; the dispute was conducted with technical care over many publications. Both made major contributions to modal metaphysics broadly: Lewis's genuine modal realism (all possible worlds are equally real) is the most controversial associated position; Stalnaker's ersatzism (possible worlds are abstract maximal consistent sets of propositions) is the more widely accepted alternative.
Parties
A counterfactual "if A were the case, B would be" is true iff B is true in the unique closest possible world in which A is true. The Limit Assumption (there always is a closest world) and the Uniqueness Assumption (there is exactly one) give clean semantics and validate conditional excluded middle.
Key arguments
- Conditional excluded middle: "either if A then B, or if A then not-B" — Stalnaker treats this as a genuine logical truth.
- Closest-world uniqueness avoids the messy ties Lewis has to admit.
- The semantics integrates cleanly with broader propositional / pragmatic theory of language.
- Counterexamples to uniqueness (e.g., "if the coin had been flipped, it would have come up heads") can be handled by appropriate context-sensitivity in the selection function.
Allied schools
A counterfactual is true iff all the closest A-worlds are B-worlds (or there are no A-worlds). Uniqueness is not justified — there can be genuine ties — and the loss of conditional excluded middle is a feature, not a bug.
Key arguments
- Ties: in cases of perfect symmetry, no single world is closest; Stalnaker has to legislate uniqueness Lewis treats as empirical.
- Conditional excluded middle fails in such cases ("if a fair coin had been flipped, it would have come up heads" and "would have come up tails" are both false).
- The Limit Assumption can also fail: there may be an infinite sequence of worlds with no closest, and the semantics should handle this.
- Genuine modal realism: possible worlds are concrete spatiotemporally-isolated worlds; the semantics is realistic in this strong sense.
Allied schools
Dimensions Engaged
Information
Information · Ontological Status: how should we analyse the semantic content of "if A were the case, B would be"?
Observer
Observer · Knowledge Extent: bears on what counts as a meaningful evaluation of a counterfactual claim.
Verdict in retrospect
No resolution. Both Stalnaker's and Lewis's systems have philosophical defenders. The Stalnaker semantics has practical advantages (it integrates with much linguistics); Lewis's avoids commitments his rivals find implausible. The debate continues to shape contemporary modal metaphysics, philosophy of language, causal modeling, and decision theory. Most working philosophers use whichever framework is most convenient for the problem at hand.
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Further reading
- Stalnaker, "A Theory of Conditionals" (1968)
- Lewis, *Counterfactuals* (1973)
- Williamson, "Counterfactuals, Causal Independence and Conceptual Circularity" (2007)