What Is Modal Realism?

We often talk about possibilities or the way the world would have been. For example, I could be home sleeping in right now, or I could be a sailor in Hawaii. There are endless ways to talk about the way the world could have been, and these worlds actually exist. Under modal realism, any way the world could have been actually is. There are countless other worlds that are temporally-spatio isolated from us and from each other. They don’t overlap. They have no parts in common (except, maybe, universals). There is no causal connection. They exist truly and literally just as you are real and existing. There is no difference in the way they exist. They aren’t just real in our imagination, like in some abstract platonic heaven, but real and concrete. They exist simpliciter, or without qualification.

Modal realism is serviceable in that we can quantify modal claims. So if I were to claim, “It is possible that I was President of the United States” we would ask how we make sense of that claim. Instead of just relying on some gut feeling, we can quantify it as “Possibly, Yang is President of the United States iff, for some world W, Yang is President of the United States.” We can quantify necessities as well as contingencies. So we can say “Necessarily all cats are mammals iff, for any world W, all cats are mammals.” So modal claims, that is claims about possibility and necessity, are quantified by an accessibility relation.