excerpted from Peter van Inwagen, Metaphysics, second edition
(Westview Press, 2002), pp. 97-98, (one footnote omitted)
This notion [the notion of a “possible world”] may be explained as follows. We have said the “the World” is the totality of everything there is. But it is obvious that the World might be different—indeed that it might always have been different—from the way it is. There might be fewer cats or more dogs. There might never have been any cats or dogs at all (if, say, evolution had taken a slightly different course). Napoleon might have lost the battle of Austerlitz or won the battle of Waterloo. As we saw in our discussion of the notion of a necessary being, the sun—perhaps even the physical universe—might never have existed. A list of the ways things might have been different (which is the same as a list of the ways the World might have been different) could go on and on without any discernible limit. By a possible world, we mean simply a complete specification of a way the world might have been, a specification so precise and definite that it settles every single detail, no matter how minor.1
If we assume that everything there is or could be is subject to the flow of time—almost certainly not a wise assumption—we could say that a possible world is a complete history-and-future that the World might have (or might have had), one whose completeness extends to every detail.
In order to make full use of the concept of a possible world, we need the idea of truth in a given possible world and we need the idea of existence in a given possible world. While various technical accounts of these ideas are available, we shall be content with an intuitive or impressionistic account of them. A few examples should suffice. If in a given world x there are no dogs—if that is how x specifies things: that there are no dogs—then in x dogs do not exist, and it is true in x that there are no dogs, and the proposition (assertion, statement, thesis) that there are no dogs is true in x. If in a given possible world y Napoleon won the battle of Waterloo, then it is true in y that Napoleon won the battle of Waterloo, and the proposition that Napoleon won the battle of Waterloo is true in y. And, of course, Napoleon must exist in y, for one cannot win a battle if one does not exist. But there are possible worlds in which Napoleon was never born (or even conceived) and in those possible worlds he does not exist.
Once we have the notion of a proposition’s being true in a possible world, we can say what it is for a proposition to be possibly true and for a proposition to be necessarily true. A proposition is possibly true if it is true in at least one possible world, and necessarily true if it is true in all possible worlds.
The possible world that specifies the way the World really is is called the actual world. A more formal definition is this: a possible world w is the actual world just in the case that something is true in w if and only if it is—without qualification—true. It is important not to confuse the actual world with the World. The actual world is a mere specification, a description of a way for things to be. It has only the kind of abstract reality that belongs to a story or a scenario or a computer program. The World, however, is not a description of a way for things to be: it is, so to speak, the things themselves. If it is an individual thing, it has you and me and every other individual thing as parts. If it is not an individual thing but a mere collection, it is at least the collection of all individual things. It is the features of the World that make one of the possible worlds the one that is actual, just as it is the geographical features of the earth that make some maps accurate or correct and other maps inaccurate or incorrect. It is the features of the World that confer on exactly one among all the ways things could be the status “the way things are.”
1. Or perhaps it would be better to say, “a complete specification of the way a World might have been, for it may be that ... if things had been sufficiently different [the] individual thing [that is the World] would not have existed at all, and some other individual thing ... would have been the referent of the description ‘the World’.