David Lewis,

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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)

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Some fundamental theses of modal realism

1. Possible worlds exist.
2. Possible worlds are just like this one.
3. Possible worlds are irreducible.
4. Actual is an indexical expression.
5. Possible worlds are unified by the spatiotemporal
   relations that its members have to each other.
6. Possible worlds are causally isolated from one
   another.

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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)

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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.

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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)

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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.

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• 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.)

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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)

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• 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.

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• 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, lets get rid of the stars.
• In this way, counterpart theory can account for
  everything that the fan of trans-world identity
  wants.