Online Papers - Brian Weatherson

David Lewis 59
and gave some natural language examples that suggest that it should be invalid. Lewis
also shows that contraposition, the implication of q � p by p � q, and conditional
syllogism, the implication of p � r by p � q and q � r, are invalid on his model,
and gives arguments that they should be considered invalid.
3.3 Similarity
In Counterfactuals, Lewis does not say a lot about similarity of worlds. He has some
short arguments that we can make sense of the notion of two worlds being similar.
And he notes that on different occasions we may wish to use different notions of similarity,
suggesting a kind of context dependency of counterfactuals. But the notion is
not spelled out in much more detail.
Some reactions to the book showed that Lewis needed to say more here. Kit Fine
(1975a) argued that given what Lewis had said to date, (3.5) would be false, when it
should be true.
(3.5) If Richard Nixon had pushed the button, there would have been a nuclear war.
(‘The button’ in question is the button designed to launch nuclear missiles.) The
reason it would be false is that a world in which the mechanisms of nuclear warfare
spontaneously failed but then life went on as usual, would be more similar, all things
considered, to actuality than a world in which the future consisted entirely of a postnuclear
apocalypse.
In “Counterfactual Dependence and Time’s Arrow” (1979b), Lewis responded by
saying more about the notion of similarity. In particular, he offered an algorithm for
determining similarity in standard contexts. He still held that the particular measure
of similarity in use on an occasion is context-sensitive, so there is no one true measure
of similarity. Nevertheless there is, he thought, a default measure that we use unless
there is a reason to avoid it. Here is how Lewis expressed this default measure.
1. It is of the first importance to avoid big, widespread, diverse violations of law.
2. It is of the second importance to maximize the spatio-temporal region throughout
which perfect match of particular fact prevails.
3. It is of the third importance to avoid even small, localized, simple violations of
law.
4. It is of little or no importance to secure approximate similarity of particular
fact, even in matters that concern us greatly. (1979b, 47-48)
Lewis argues that by this measure, worlds in which the mechanisms of nuclear warfare
spontaneously fail will be less similar to the actual world than the post-nuclear
apocalypse. That’s because the failure of those mechanisms will either lead to divergence
from the actual world (if they fail partially) or widespread, diverse violations
of law (if they fail completely). In the former case, there’s a violation of law that isn’t
made up for in an increase in how much spatio-temporal match we get. In the latter
case the gain we get in similarity is only an expansion of the spatio-temporal region
throughout which perfect match of particular fact prevails, but that doesn’t help in