Are there unicorns here?

Multiverse theories like David Lewis’s or Donald Turner’s populate reality with a multitude of universes containing strange things like unicorns and witches riding broomsticks. One might think that positing unicorns and witches makes a theory untenable, but the theorists try to do justice to common sense by saying that the unicorns and witches aren’t here. Each universe occupies its own spacetime, and the different spacetimes have no locations in common.

But why take the different universes to have no locations in common? Surely, just as a unicorn can have the same charge or color as I, it can have the same location as I. From the fact that a unicorn can have the same charge or color as I, we infer in a Lewisian setting that some unicorn does have the same charge or color as I (and likewise in Turner’s, with some plausible auxiliary assumptions about values). Well, by the same token, from the fact that a unicorn can have the same location as I, we should be able to infer that some unicorn does have the same location as I.

Not so, says Lewis. Counterpart theory holds for locations, but not for charges and colors. What makes it true that a unicorn can have the same charge as I now have is that some unicorn does have the same charge as I. But what makes it true that a unicorn can have the same location as I now have is that some unicorn has a counterpart of my location in a different spacetime.

But what justifies this asymmetry between the properties of charge and location? The asymmetry seems to require clauses in Lewis’s modal semantics that work differently for different properties. It seems there are properties—say, being green—whose possible possession is grounded in something’s having the property, and there are properties—say, being at this location—whose possible possession is grounded in something’s having a a counterpart of the property.

Specifying in a non-ad hoc way which properties are which rather complicates the system. Moreover, it leads to this oddity. Lewis thinks abstract objects exist in all worlds. So, he has to say that being at this location exists in all worlds. And yet the counterpart of being at this location in another world is a different property, even though this exact property does exist at that world.

There is a solution for Lewis. Lewis is committed to counterpart theory holding for objects. It is reasonable for him thus to take counterpart theory also to hold for properties defined de re in terms of particular non-abstract objects. Thus, what makes it true that a unicorn could have had the property of being a mount of Socrates is not that some unicorn in some universe has this property—for no unicorn in our universe has that property, and Socrates according to Lewis only exists in our world—but that some unicorn has a counterpart to this property, which counterpart property is the property of being a mount of S where S is a counterpart of Socrates.

If Lewis can maintain that location properties are defined de re by relation to non-abstract objects, then he has a way out of the objection. Two kinds of theories allow a Lewisian to do this. First, the Lewisian can be a substantivalist who thinks that points or regions of space are non-abstract. Then being here will consist in being locationally related to some point or region L, and Lewis can take counterpart theory to apply to points or regions L. Second, the Lewisian can be a relationalist and say that location is defined by relations to other physical objects, in such a way that if all the objects were numerically different from what they are, nothing could be in the same place it is, and counterpart theory is applied to physical objects by Lewis.

What Lewis cannot do, however, is take a view of location that either takes location to be a relation to abstract objects—say, sets of points in a mathematical manifold—or that takes location to simply be a non-relational determinable like charge or rest mass.

In particular, multiverse theorists like Lewis and Turner are committed to treating location as different from other properties. Anecdotally, most philosophers do treat location like that. But for those of us who are attracted to the idea that location is just another determinable, this is a real cost.