Here are some of my (mostly unoriginal) thoughts on the topic of possible worlds. If I had more time I would organize these ideas better. But look, this is just a weblog, an online notebook! A natural-born scribbler, I bash these things out quickly. And you get what you pay for, muchachos. Double your money back if not completely satisfied.
0. The actual world is the total way things are. A merely possible world is a total way things might have been. Let that be our intuitive starting point.
1. The actual world is a possible world. This is because everything actual is possible. But of course the actual world is not merely possible. Mere possibility and actuality are mutually exclusive.
2. There is a plurality of possible worlds. This is because the possible outruns the actual: the set of actualia is a proper subset of the set of possibilia. So if there are possible worlds at all, there are many of them. If you say that there is only one possible world, the actual world, then that leads to the collapse of modal distinctions, or, to put it less dramatically, the extensional equivalence of the possible, the actual, and the necessary. Not good. But I will not here argue for the reality of modal distinctions. That is something we are now presupposing.
3. There is and can be only one actual world. This follows from the maximality property of worlds. Whatever one's exact conception of a world, worlds are all-inclusive totalities. (So much is built into the very word, 'world.') If a world is an abstract state of affairs, as A. Plantinga maintains, then it must be a maximal state of affairs: one that includes every state of affairs with which it is logically consistent. If a world is a (Fregean) proposition, then it must be a maximal proposition: one that entails every proposition with which it is logically consistent. If a world is a mereological sum of concreta, as D. Lewis holds, then it must be a maximal mereological sum of concreta. These maximal objects are so big that, to employ a chemical metaphor, they are 'saturated': adding another member to them would 'precipitate' a contradiction. So there cannot be two or more actual worlds.
4. There must be an actual world. It cannot be the case that every world is merely possible. If every world were merely possible, then that would be the case, actually the case, which implies that the total way things are would include its actually being the case, which implies that there is, after all, an actual world. So it cannot be the case that every world is merely possible. Think about it.
5. Possibilities come in world-sized packages: necessarily, if state of affairs S is possible, then there is a world W such that W includes S. This amounts to a denial of 'isolated' or 'worldless' possibilities. I am now blogging, but I might have been now sleeping, where 'now' picks out the very same time. Let S = BV's sleeping now. Had S been actual now, everything would have been different in a few major ways and in an infinity of miniscule ways. So if I had been sleeping now a world different from the world that is actual would have been actual.
6. Actuality is absolute, not world-relative. If by #2 there is a plurality of possible worlds, and by #3 there is only one actual world, then there is a distinction between merely possible worlds and that privileged possible world that is the actual world. Although every world is actual at itself, only one world is actual simpliciter, actual period. Compare: although every time is present at itself, only one time is present simpliciter. This comparison of course assumes (controversially) that the B-theory of time is false, the theory according to which time is exhausted by McTaggart's B-series, the series of events ordered by the relations earlier than, later than, and simultaneous with. I am assuming that in addition to the B-relations there are also the monadic A-properties of pastness, presentness, and futurity, and that these properties are instantiated. 'Now' of course is an indexical expression: it picks out the time of its tokening. Tokened at midnight, it picks out midnight, at noon, noon. But is 'actual' an indexical? Does its reference depend on the context of utterance so that, tokened in this world it refers to this world, tokened in another, to that other? That's what David Lewis maintains, but I say 'actual' is not an indexical. When I say that this world, our world, is actual, I mean to ascribe to it the monadic property of actuality, a property which only one world can have.
There are many possible worlds, but only one is actual. Furthermore, the one that is actual might not have been actual. So the one that is actual is contingently actual. If that were not the case, the merely possible worlds would not be possible. For whatever is possible, is possibly actual. The worlds that do not bear the privilege of actuality could have borne it.
7. X exists in/at world W =df were W actual, X would exist.
8. X is a contingent being =df X exists in some but not all possible worlds. It follows from this definition that something, Pegasus say, can be a contingent being even if it does not exist. If the word 'being' throws you, substitute 'item.'
9. X is a necessary being =df X exist in all possible worlds.
10. X is an impossible being =df X exists in no possible world.
11. X is actual =df X exists in the actual world, the one world that happens to be actual.
12. Puzzle: It looks as if, on the one hand, 'The actual world is not actual' is a contradiction. On the other hand, it is surely the case that the actual world might not have been actual. The puzzle is solved by distinguishing two uses of 'the actual world.' It can be used as a Kripkean rigid designator that picks out one particular world, this world, our world, and does so in every possible world. Used in this way, 'The actual world is not actual' is possibly true. But 'the actual world' can also be used as a definite description that applies to whichever world happens to be actual. Used in this second way, 'The actual world is not actual' is a contradiction.
13. But what exactly is a possible world? I take an abstractist line. Worlds are maximal (Fregean) propositions or maximal (abstract) states of affairs. They are not maximal mereological sums of concreta, pace David Lewis. If worlds are propositions, then actuality is truth. That is one interesting consequence. Another is that worlds are abstract objects which implies that the actual world must not be confused either with the physical universe (the space-time-matter system) or with that plus whatever nonphysical concreta (minds) that there might be. And if worlds are abstract objects then they are necessary beings. (See #9 above.) So every possible world exists in every possible world.
If actuality is truth, and individuals cannot be true (in the exact sense in which a proposition can be true), then perhaps there is a problem with #11 above.
Peter Lupu once maintained that possible worlds are "maximally consistent descriptions of the world." This is on the right track, except for a couple of problems. One is that descriptions are presumably linguistic entities. If so, they are contingent in which case they exist in only some possible worlds. I won't spell it out, but this seems to imply that possible worlds cannot be linguistic entities. They cannot be say maximally consistent sentences of English. The other problem is that 'world' occurs both in Peter's definiens and in his definiendum. Presumably, he doesn't mean to tell us that a possible world is a maximally consistent description of a maximally consistent description.