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By “a possible world” philosophers mean a total state of affairs in the conception of which no contradiction is involved. Our own world—the real world, the actual one—is just one of many possible worlds. Indeed, it is just one of infinitely many, since for any possible world containing, say, n atoms there is another logically possible world containing n + 1 atoms, and so on ad infinitum. All possible worlds other than the actual world we inhabit are nonactual.

A world the conception of which does involve a contradiction is said to be an impossible world. An impossible world, of course, is a nonactual one. There are many possible worlds in which you, the reader, exist; the actual world is one of them. And there are possible worlds in which you do not exist; any such world is nonactual. But there are none in which you both do and do not exist; any such world is an impossible one.

The Banality of Possible Worlds

Although the term possible worlds entered the philosophical lexicon only in the writings of Gottfried Leibniz (1646–1716), the fact is that we all think about them everyday, though not usually under that description. The idea of worlds different from the actual one is totally commonplace. One wonders what the world would have been like if one had done something different from what one in fact did: if one had chosen a different partner or profession, for instance. One wonders what history would have been like if Hitler had won the Second World War. Equally, one ponders whether one should do this or that, or something else, where each of the possibilities would make a difference in how the world, or one's little part of it, would then turn out. And one makes plans for the future hoping things will turn out one way though conscious of the fact that they may not.

The concept of possible worlds is implicit in all these ways of thinking. To imagine the past as having been different (even in the smallest respect) from the way it was, or the future (even in the smallest respect) as being different from what it will be, is to entertain the concept of different possible worlds branching out from the past (perhaps even from the beginning of the world), or from the present, or from the future.

Thus, there is nothing arcane about the notion of possible worlds, actual and nonactual alike. They feature in our dreams, our imaginings, our hopes and fears for the future, our regrets over past deeds and lost opportunities. We think about how the world might have been, and of how it might yet come to be.

They also feature in fiction, especially science-fiction novels and films in which we are invited in our imaginations to enter into worlds that often bear only the faintest resemblance to the real world that we in fact inhabit. Some are plausible. Some are not. And still others seem beyond the bounds of belief. Science-fiction stories involving time travel, in particular, often challenge our sense of what is possible and what is not. Are such stories internally consistent or is there a contradiction involved somewhere? Is time travel possible? Is it possible to change the past? Or the future, for that matter?

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