A Little Modal Metaphysical Paradox for You!

Found this on Cheryl's website, it's awesome, check it out!

Which world is actual? Presumably, there is a proposition that states which world is actual. We take it that our world is actual, and all other worlds are merely possible. We'll call our world W. Now, the proposition stating this is simply, "W is the actual world." Is this true or false? Obviously, W is actual, since I've just named our world, the actual world, W. But now the question arises: is this proposition true in any other possible world? At first it would seem that it must be, since it is the actual world, it is true, so it should be true in other possible worlds, right? But if the proposition is indeed true in all possible worlds, then it is necessarily true. Uh-oh. It would turn out that actuality of the actual world is a necessary feature of it. But this would break down the whole notion of possibility in the first place, since the whole meaning of possibility is that some other world might have been actual. But if the proposition stating that, "W is the actual world", is true in all possible worlds, then none of the merely possible worlds could have been actual. But what does it mean to say that some possible world, say W₁, is possible and thus could have been actual? It is to say that the proposition, "W₁ is the actual world", is true in some possible world. Which world? Why, in W₁ of course! Each possible world is actual in itself. (Or in other words, the proposition stating that a given possible world is actual is true in that world, but not true in all the other worlds.) But now actuality turns into a world-relative feature. The actual world W is only contingently actual, thus the proposition stating such is not true in all possible worlds. But if it is not true in all possible worlds, and what is true in each possible world is the proposition stating that that world itself is actual, then each world is actual in that world (in itself), and actuality is world-relative. But if actuality is world-relative, each world to itself, then nothing metaphysically distinguishes our world from amongst the infinitely many, apparently merely possible worlds. If there is nothing metaphysically distinct about our world, and its actuality is merely relative from this particular world, then we must swallow the claim that all possible worlds exist, and actuality is merely indexical.

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