David Lewis, who spent most of his career at Princeton, was one of the most respected philosophers of the 20th century. Yet he is most famous for advocating a philosophical view that almost everyone else rejects.
In his 1986 book On the Plurality of Worlds, Lewis argued for a position he called “modal realism”. This is the idea that there are an infinite number of possible worlds (i.e. self-contained universes) different from our own, and that all of these possible worlds are as real as the world we live in. The only fact that sets our world apart from the rest of them is that it is ours.
Saying, therefore, that our world is the “actual” world is no different from saying that I am “here” and the time is “now”. There are people just like us and as real as you and me existing in other worlds who believe that their world is the only “actual” world. They are just as correct in their belief as we are in ours.
Most philosophers are comfortable with talking about possible worlds. They use this terminology to explain, for example, the nature of necessity and what it means to say that something could have happened but didn’t. A statement is necessarily true if it is true in every possible world. An event could have happened if it happened in some possible world, especially one similar to our own. Yet philosophers almost all deny that other possible worlds are as concretely real as this one.
Lewis knew, of course, that modal realism is very hard to accept. It clearly conflicts with common sense and ordinary language. He described the natural response to his position as the “incredulous stare” (as in “You can’t be serious, Professor Lewis!”). But he argued that there are excellent theoretical reasons for accepting modal realism. He thought that it best explains what it is to be a possible world.
It takes some education and intelligence to appreciate Lewis’s reasons for adopting modal realism and his arguments against competing views. Personally, I’m tempted to say that modal realism is self-contradictory. To claim that possible worlds exist in the same way that the actual world exists sounds like a contradiction in terms. (Which might explain why Lewis found modal realism to be such a useful view. Logic says that if you start with a contradiction, you can prove anything at all.)
On the other hand, many physicists believe that there are a multitude of universes, completely separate from each other, yet equally real. That might seem to be what Lewis had in mind, but it’s really not. For philosophers, there is a possible world for each possibility, every single one (although only one of them, contra Lewis, is real). For physicists, there might be many, many real worlds, just as real as ours, but they don’t reflect every single possibility. They are merely the result of whatever natural processes result in the creation of new universes.
In the philosophical sense, therefore, there is a possible world in which donkeys do calculus, since very bright donkeys could conceivably do that. Physicists don’t go that far, since there is no reason to believe that animals like donkeys (no offense, donkeys) would ever develop an interest in advanced mathematics.