Online Papers - Brian Weatherson

David Lewis 81
(1976). Given the negative definition of magical ersatzism, and given the fact that
primitivists do not think that possible worlds represent possibilities via any familiar
mechanism, it seems the primitivists should count as magical ersatzists, or, as Lewis
calls them, “magicians”. In any case, if magical ersatzism, in all its varieties, is objectionably
mysterious, that suggests ersatzism is in trouble, and hence if we want the
benefits of possible worlds, we have to pay for them by accepting concrete possible
worlds.
6.4 Counterparts or Double Lives?
The last chapter of Plurality changes tack somewhat. Instead of focussing on different
ways the world could be, Lewis’s focus becomes different ways things could be. The
chapter defends, and expands upon, Lewis’s counterpart theory.
Counterpart theory was first introduced by Lewis in “Counterpart Theory and
Quantified Modal Logic” (1968) as a way of making modal discourse extensional. Instead
of worrying just what a name inside the scope of a modal operator might mean,
we translate the language of quantified modal logic into a language without operators,
but with quantifiers over worlds and other non-actual individuals. So instead of
saying �Fa, we say ∀w∀x ((Ww ∧ Ixw ∧ Cxa) ⊃ Fx). That is, for all w and x, if w is
a world, and x is in w, and x is a counterpart of a, then Fx. Or, more intuitively, all
of a’s counterparts are F. The paper shows how we can extend this intuitive idea into
a complete translation from the language of quantfied modal logic to the language of
counterpart theory. In “Tensions” (1974b) Lewis retracts the claim that it is an advantage
of counterpart theory over quantified modal logic that it is extensional rather
than intensional, largely because he finds the distinction between these two notions
much more elusive than he had thought. But he still thought counterpart theory had
a lot of advantages, and these were pressed in chapter 4.
The intuitive idea behind counterpart theory was that individuals, at least ordinary
individuals of the kind we regularly talk about, are world-bound. That is, they
exist in only one world. But they do not have all of their properties essentially. We
can truly say of a non-contender, say Malloy, that he could have been a contender. In
the language of possible worlds, there is a possible world w such that, according to it,
Malloy is a contender. But what in turn does this mean? Does it mean that Malloy
himself is in w? Not really, according to counterpart theory. Rather, a counterpart
of Malloy’s is a contender in w. And Malloy himself has the modal property could
have been a contender in virtue of having a counterpart in w who is a contender. This
way of thinking about modal properties of individuals has, claims Lewis, a number
of advantages.
For one thing, it avoids an odd kind of inconsistency. Malloy might not only have
been a contender, he might have been 6 inches taller. If we think that is because there
is a world in which Malloy himself is 6 inches taller, then it seems like we’re saying
that Malloy can have two heights, his actual height and one 6 inches taller. And that
looks inconsistent. The obvious way out of this is to say that he bears one height in
relation to this world, and another to another world. But that turns height from an
intrinsic property into a relation, and that seems like a mistake. Lewis thinks this