Possible worlds
from 1963 Kripke's semantics; the idea is Leibniz's
Turn questions about what must be and what could have been into questions about which ways the world could have gone, and then reason about those.
- Active
- from 1963
- Where
- Princeton
- Status
- In use
- Tradition
- Analytic tools
What it is
Possible-worlds analysis translates modal claims into claims about a space of complete alternatives. *Necessarily P* becomes *P holds in every world*; *possibly P* becomes *P holds in some world*; a counterfactual becomes a claim about the closest worlds where the antecedent holds.
That last one is the productive part. It converts *if this had happened, that would have followed* — a claim nothing observable can check — into a claim about similarity, which can at least be argued about.
How it works
State the modal claim. Identify the space of worlds it quantifies over — which alternatives are being treated as live. For a counterfactual, identify the closest worlds where the antecedent holds, holding fixed everything not required to change. Evaluate the consequent there. Read the verdict back.
The third step carries all the weight. What counts as closest is a judgement, and different answers give different verdicts from the same facts.
The moves, in order
- State the modal or counterfactual claim
- Fix the space of alternatives treated as live
- Locate the closest alternatives where the antecedent holds
- Evaluate the consequent in those alternatives
- Read the verdict back as a claim about the actual case
The procedure
Proposition The flood damage was not unavoidable.
- The policy excludes loss that could not reasonably have been avoided, which is a claim about alternatives, not about what happened.
- The live alternatives are those differing from the actual case only in what the insured could have done: everything about the weather, the catchment and the timing is held fixed.
- Among those, the closest in which the roller doors were closed is one where the shed took water to 200mm rather than 900mm, since the doors were the only path for the volume that entered.
- That alternative requires no change to the forecast, the warning time or the insured's knowledge — the warning was issued nine hours before the peak and was received.
- So there is a nearby alternative, differing only in an action available to the insured, in which most of the loss does not occur.
Therefore The loss was avoidable in the sense the policy means, because the closest alternative in which the available action is taken is one where it largely does not happen.
The whole dispute is about which alternatives count as close. The insurer wants worlds where the insured acts on the warning; the insured wants worlds where the warning was as unreliable as warnings usually are. Naming that as the disagreement is what the method contributes.
What it is good for
Counterfactuals of every kind — causation, liability, avoidability, historical what-ifs — and any question about necessity or essence. Legal causation is almost entirely this method under another name.
Where it fails
Closeness has no measure. Lewis gave an ordering of similarity and admitted it was rough, and two competent people can rank alternatives differently and reach opposite verdicts with no fact settling it. Every argument about legal causation is really an argument about this.
There is also the metaphysical embarrassment. Lewis held that possible worlds are real, concrete and as existent as this one, which almost nobody accepts and which he defended for thirty years on the grounds that the theory works and the alternatives do not.
Common misconceptions
That possible worlds are planets or parallel universes in the science-fiction sense. Most philosophers treat them as ways things could have been rather than places, and the disagreement about which is right does not affect the method's use.
Where it came from
Leibniz has the idea and the phrase. Kripke's semantics of the early 1960s made it rigorous, and Lewis's Counterfactuals of 1973 built the similarity ordering that made counterfactuals tractable.
What became of it
Standard equipment across metaphysics, philosophy of language, decision theory and the semantics of natural language.
Lasting influence
It made modality respectable again after the positivists had tried to eliminate it, and it underpins the modern treatment of causation, dispositions and laws of nature.
Why it still matters
High in philosophy, and present in every liability dispute that turns on what would have happened.
Put another way
Asking not what happened but what the nearest version of events looks like.
Texts
David Lewis, Counterfactuals
Short, clear and the source of the similarity account. The metaphysics is defended more fully in On the Plurality of Worlds.
Where to start
Read Lewis on counterfactuals, then read any judgment on causation. They are doing the same thing.
The surprising bit
The most useful tool in modern metaphysics rests on a similarity ordering its inventor admitted he could not make precise, and it has worked anyway for fifty years.
In their own words
If kangaroos had no tails, they would topple over
Who held it
Ruth Barcan Marcus
Connections
- Relies on
- Modal argument, Formalisation
- Parallel to
- The thought experiment
The verdict
A precise machine driven by a judgement nobody can formalise.