The Ambiguity of Similarity in Lewis's Counterfactuals — Epoche B2
Vagueness Is Not Indeterminacy: What Lewis's Similarity Ordering Actually Has to Do An objection aimed at the wrong theory A standard complaint against David Lewis's treatment of counterfactuals runs like this [1] . The truth of "if A were the case, C would be" is said to depend on what happens at the A-worlds most similar to ours. Similarity is vague. So there will be cases with no uniquely most similar world, and in those cases the counterfactual has no truth value. A semantics that leaves ordinary conditionals without truth values has failed. Every step of that complaint is a good objection to a real position, and the position is not Lewis's [2] . It is Robert Stalnaker's [3] . Lewis's truth condition in Counterfactuals (1973) is formulated precisely so that it needs no closest world and survives ties, and he says why at length. This review argues that the objection is misdirected, and that Lewis's account is vulnerable somewhere quite different: in the system of weights he introduced six years later, which is not semantics at all but a contingent claim about the physical asymmetry of our world. Two semantics, often merged Stalnaker's 'A Theory of Conditionals' (1968) is a semantics for conditionals, and it is worth saying that plainly, since the paper is sometimes cited as though it were a statement about the metaphysics of possible worlds. It is not; on that question it takes no side. Its machinery is a selection function that, given an antecedent and a world, returns the nearest world where the antecedent holds. The conditional is true when the consequent holds at that world. Uniqueness is built in, and it has a striking consequence. Either the consequent holds at the selected world or its negation does, so for any A and C, either "if A, C would" or "if A, not-C would" is true. This is conditional excluded middle, and Stalnaker accepts it. Lewis rejects both of the assumptions Stalnaker needs. There may be ties: nothing guarantees that one A-world beats all the others. And there may be no closest A-world at all. His own example is a line that is in fact under an inch: for any world where the line is longer than an inch, there is a world where it is longer by a smaller margin, and so closer to ours. The sequence has no last member. So Lewis states the truth condition differently. "If A were the case, C would be" is true at our world just in case either there are no A-worlds at all, or some A-world where C holds is closer to ours than any A-world where C fails. Read that carefully: it never mentions a closest world. It asks only whether the C-side of the A-worlds eventually wins out, and that question has an answer whether or not the ordering has a limit and whether or not there are ties. Conditional excluded middle fails on this semantics, which Lewis regards as a benefit rather than a cost. What vagueness does and does not imply Lewis does hold that comparative similarity is vague and that its resolution shifts with context. He is not conceding this under pressure; he says the vagueness of the relation is a feature, because counterfactuals in ordinary use are themselves vague and context-sensitive, and a semantics that made them sharp would be modelling something other than what we say. The inference from vagueness to truth-value gaps is in any case not valid. A vague term can determine a truth value when every admissible way of making it precise gives the same answer. "If I had let go of the glass, it would have fallen" comes out true on every reasonable resolution of the similarity relation, which is why nobody hesitates over it. Vagueness produces indeterminacy only in the cases near the boundary, which is exactly what one wants. Where the weights came from The famous ordering of priorities is not in the 1973 book. It appears in 'Counterfactual Dependence and Time's Arrow' (1979), and it was written to answer a specific objection that Kit Fine had raised [4] : that "if Nixon had pressed the button there would have been a nuclear war" seems true, while a world in which a tiny malfunction swallows the signal and history proceeds as it actually did looks far more similar to ours than a world reduced to ash. Lewis's reply is a system of weights on similarity, in this order of importance: Avoid big, widespread, diverse violations of law. Maximise the spatiotemporal region throughout which particular fact matches exactly. Avoid even small, localised, simple violations of law. Securing approximate similarity of particular fact matters little or not at all. The fourth item is a demotion, not a fourth positive criterion, and getting that wrong wrecks the analysis. Approximate resemblance in matters we care about — that the world after the button-press still contains cities and people — is deliberately given almost no weight. That is what allows the ash-strewn world to count as close: it matches ours exactly up to the moment of divergence, and item two rewards exact match while item four refuses to reward the rough resemblance the surviving world would offer afterwards. The real vulnerability The weights answer Fine, but they raise a question the indeterminacy complaint never reaches: what justifies them? Lewis's answer in the 1979 paper is not that they are stipulated. It is that they describe the similarity relation we actually employ, and that this relation delivers the right results because of a contingent feature of our world, the asymmetry of overdetermination. An event leaves an enormous number of traces afterwards and comparatively few before. A world can therefore diverge from ours by one small miracle, because nothing prior needs to be undone. It cannot reconverge by one small miracle, because reconverging would require erasing every trace of the divergence, which takes a large and widespread violation of law — penalised by item one. This is where the theory is exposed. The verdicts of the analysis depend on a physical claim about the direction in which traces accumulate. Were o