A philosophical concept first introduced by Leibnitz, the polymath philosopher, although it has precursors in almost every major thinker before him. A possible world in Leibnitz's sense is a way the entire world could have been; that this world, the actual world is the way it is is because God actualized it. (Due to his theological commitments, he thought that the actual world was the best of all possible worlds.)

In modern philosophy the concept has been made for the most part less metaphysical and more logical. Saul Kripke and Alvin Plantinga consider a possible world to be a maximal consistent set of propositions. On the other hand, a modal realist such as David K. Lewis keeps a metaphysical notion; a possible world to him is a world, though not necessarily the actual one. Lewis has argued at length for the metaphysical existence of possible worlds.

In philosophy it is common to use made up situations to test ideas and theories. These situations are said to take place in possible worlds.

You start with the actual world. That's the exact string of events that we are in.

The next biggest set is of the physically possible. This includes the actually possible, but also includes anything that could happen in our universe given our physical laws. Klingons may be physically possible, but it looks like warp drive is not.

Then comes logically possible. This contains both of the previous sets, but includes things that could not happen given our physical laws, while not contradicting themselves. These are things that could not happen in out universe, but could, logically, happen in some conceivable universe. Flatland was an attempted logically possible world.

You might or might not want to go on to logically impossible worlds. These are technically impossible worlds. They contain a logical contradiction. Nevertheless, they do pop up. A logically impossible universe is the only one that could contain both an unstoppable force and an unmovable object.

The clearest representation of all this that I have seen is drawing a set of concentric circles, the actual world being the smallest (a dot, even), and impossible worlds the largest.

Do possible worlds exist? We wont know until someone nodes
Modal Realism

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