David Lewis, “Counterparts and Double Lives” Modal Realism: “When I profess realism about possible worlds, I mean to be taken literally. Possible worlds are what they are, and not some other thing. If asked what sort of thing they are, I cannot give the kind of reply my questioner probably expects: that is, a proposal to reduce possible worlds to something else.I can only ask him to admit that he knows what sort of thing our actual world is, and then explain that possible worlds are more things of that sort, differing not in kind but only in what goes on at them.” (from Counterfactuals, p. 73)
Some fundamental theses of modal realism • Possible worlds exist. • Possible worlds are just like this one. • Possible worlds are irreducible. • ‘Actual’ is an indexical expression. • Possible worlds are unified by the spatiotemporal relations that its members have to each other. • Possible worlds are causally isolated from one another.
Ersatz Modal Realism Instead of an incredible plurality of concrete worlds, we can have one world only, and countless abstract entities representing ways that this world might have been. (PoW, 136) Possible worlds are sets of possible individuals. One world/one set is actual (or actualized by God). Linguistic ersatzism: constructs its ersatz worlds as maximal consistent sets of sentences (PoW, 142) Pictorial ersatzism: presents possible worlds as pictures of individuals. Magical ersatzism: worlds have no relevant inner structure; they are themselves simples (PoW, 174)
Good Questions and Bad • Is an F ever a G? • Is there ever identity between two worlds? I.e. do they overlap? • Is there ever anything that overlaps two different worlds? (Which is really a question about mereology: is there any reason to restrict mereology?) • Does it ever happen that anything exists according to two different worlds? But, • What is it for x to exist according to a world? This question demands different answers depending upon whether one is a genuine modal realist or an ersatzer.
Counterpart Theory Counterpart theory: the theory that allows us to talk about individuals in other possible worlds that stand in the place of the members of our world. Counterpart theorists and ersatzers are in agreement that there are other possible worlds in which Humphrey – he himself – really wins the election. Likewise, they are in agreement that Humphrey – he himself – is not part of those worlds. “For the counterpart theorist, the trick is to say that ‘Humphrey’ names not the Humphrey of our world, and not the Humphrey of another, but rather the trans-world individual who is the mereological sum of all these local Humphreys.” (157a)
Overlapping worlds and the problem of persistence The problem of the overlap of worlds parallels the problem of identity through time. Let us say (160a): • Something persists iff, somehow or other, is exists at various times. • Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time. • Something endures iff it persists by being wholly present at more than one time.
Lewis favors perdurance in the case of identity through time; and the parallel is to counterpart theory. That is, perdurance is analogous to the trans-world identity of a trans-world individual composed of distinct parts in non-overlapping worlds. The decisive objection to endurance is the problem of temporary intrinsics. The solution favored by Lewis is one in which there are distinct temporal parts of an individual that have different temporary intrinsic properties. (Presumably, we can talk about essentialism by saying that x is essentially F iff all temporal parts of x have F. Similarly, x is essentially F iff each of its counterparts is F.)
Unrestricted mereology Lewis believes in unrestricted mereological composition: “any old class of things has a mereological sum. Whenever there are some things, no matter how disparate and unrelated, there is something composed of just those things. Even a class of things out of different worlds has a mereological sum. That sum is a trans-world individual. It overlaps each world that contributes a part of it, and so is partly in each of many worlds.” (164b-65a)
If unrestricted composition is granted, Lewis can reformulate counterpart theory in terms of trans-world individuals. (166) Now, check it out, some definition-mongering: • A possible individual is an individual that is wholly part of one world. • If a possible individual X is part of a trans-world individual Y, and X is not a proper part of any other possible individual that is part of Y, let us call X a stage of Y. • Sometimes one stage of a trans-world individual will be a counterpart of another. • If all stages of a trans-world individual Y are counterparts of one another, let us call Y counterpart-interrelated. • If Y is counterpart-interrelated, and not a proper part of any other counterpart-interrelated trans-world individual (that is, if Y is maximal counterpart-interrelated), then let us call Y a *-possible individual.
Extend the star language to predicates and properties. Thus, A *-possible individual is a *-man at W iff it has a stage at W that is a man; it *-wins the presidency at W iff it has a stage at W that wins the presidency… It *-exists at world W iff it has a stage at W that exists… (166b) Two possible individuals are counterparts iff there is some *-possible individual of which they both are stages…. (167a) Now, let’s get rid of the stars. In this way, counterpart theory can account for everything that the fan of ‘trans-world identity’ wants.