Counting Worlds

We might think that for all their similarity, LEGO worlds and real worlds at least differ in how many there are: there are many LEGO worlds, but only one real world. Not so, on Lewis’s view. He maintains that there are many, many more real worlds than LEGO worlds. Our world—the universe, the things whose size cosmologists are investigating—is just one among a multitude of worlds.2 In fact, he holds that there are infinitely many worlds. In this respect, the LEGO worlds as we know them are not a faithful model of his possible worlds: the number of actually created LEGO worlds is finite, and even the number of different LEGO worlds that could be made from all actual bricks is finite. (If Lewis is right though, and there are infinitely many possible worlds, there will likewise be infinitely many possible worlds which contain LEGO worlds as parts, just like our world.)

According to Lewis, there are worlds in which you were saved from entering the dark ages. There are worlds where you have a billion bricks at your disposal. But there are also worlds where LEGO has never been invented. More generally, everything that could have happened—everything that is possible—does happen in some such world. As mentioned before, Lewis thinks that the building blocks of the world—the fundamental properties instantiated at space-time points—are re-combinable. Accordingly, he accepts a principle of recombination for worlds: for every possible arrangement of such properties, there is a world where they are arranged in this way. So, in particular, every LEGO world that you may build will be an accurate model of a genuine world, spatio-temporally separated from all other worlds. There is a sense in which you are replicating rather than creating.

On Lewis’s view, other worlds are just as real as the actual world. They are concrete universes, typically very large ones. It is tempting to think of them as distant galaxies. But strictly speaking, worlds are not distant. For them to be so, they would need to belong to a common space, or space-time—a very large base plate. But there is no such thing. Things in different possible worlds do not stand in any spatial or spatiotemporal relations to each other.

If you find Lewis’s claim that there are infinitely many parallel universes incredible, you are not alone. When Lewis made it clear to other philosophers that he seriously believed this, he often met with an incredulous stare. On the face of it, asserting the existence of all these other worlds violates Ockham’s Razor.

But Lewis had a nice reply. He argued that if the principle is understood correctly, it favors theories that are parsimonious with respect to how many kinds of things they posit. A theory according to which the fundamental particles are protons, neutrons, and electrons is better, other things being equal, than a theory according to which the fundamental particles fall into thousands of different kinds. But a theory that says that there are five trillion protons is not better, on that account, than a rival that puts that number at ten trillion. Lewis argued that his theory just posits more things of a kind that everyone believes in—namely, universes—and that it is therefore quite compatible with Ockham’s Razor.

Be that as it may, Lewis’s plausible thesis of Humean superve- nience need not be combined with his extravagant claim that there is a real world for any possible arrangement of the fundamental building blocks. Whether it is so combined or not, there remains a difference between the number of real worlds and the number of actual LEGO worlds. The number of actual LEGO worlds is fairly large but finite. The number of real worlds is either one—as most philosophers think—or infinite—as Lewis and a handful of others think. Nobody holds that there 17, or 5,874,764 worlds—any finite number apart from one would look hopelessly arbitrary.

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