Time travel and sortal-relative predication
Here's an attractive picture. All there really is, at a fundamental level, are fields in spacetime (or something like that). The world as we know it, with its rocks and chairs and cats and people, somehow emerges from this basis: all truths about rocks and chairs etc. are made true by truths about fields in spacetime. But how? To explain this, it would help if we could locate the familiar objects – rocks and chairs etc. – in the physical description of reality. With the help of classical mereology, which is plausibly analytic, this seems possible: ordinary objects can be identified with aggregates of spacetime points. They are regions in spacetime. With this, we can explain how simple facts involving ordinary objects can emerge. For example, what makes it true that my chair has steel legs is that its region has a certain kind of subregion with high-amplitude excitations of quark and electron fields in a certain arrangement.
On this picture, objects are sortal-independent. If a lump of clay is created in the form of a statue and later destroyed in an explosion, the statue and the lump of clay are the same object. They are the same region in spacetime, with the same field values.
To be sure, we sometimes draw a distinction between the statue and the lump. The lump could survive smashing, the statue couldn't. But perhaps these modal predications require a special analysis. Counterpart theory provides the standard solution (as in Lewis 1986, 253–58). Fine 2003 claims that the statue and the lump also differ in non-modal properties: the statue is Romanesque (say), the lump isn't. I'm not sure I agree, but suppose it's true. I can certainly imagine that we learn to speak this way. What would this show?
Surely it wouldn't follow that there is more in fundamental reality than fields in spacetime. It would only follow that the simple analysis of ordinary predications doesn't work: we couldn't say that an ordinary "a is F" statement is true because "a" designates a certain physically specifiable object, "F" expresses a physically specifiable property, and the object in question has that property. Instead, we might say that ordinary singular terms are associated with a referent and a sort. The referent is a spacetime region; the sort isn't really an object, but an index that affects the interpretation of predicates: "a is F" is true because the region picked out by "a" has the physical property expressed by "F-qua-G", where G is the sort (compare Loets 2021). If even that fails, we might have to go for a syncategorematic analysis of the kind we probably need for statements like "The oil price is rising". ("The oil price" hardly picks out a region of spacetime.)
Anyway, we might hope that there is at least a wide range of ordinary "a is F" predications whose truth or falsity can be explained by assuming that "a" picks out a certain spacetime region and "F" a physical property of spacetime regions.
But now suppose we live in a universe in which time travel is possible. And suppose some ordinary object (a rock, a chair, a person, or even an electron) travels back in time, but only a short stretch, so that it arrives at a time at which it already existed. Concretely, let's say Tim travels back in time in order to warn his younger self of the perils of time travel. He then exists twice at the relevant time t, once in an older form, once in a younger form. What shall we say about Tim at t?
If young Tim weighs 70 kg at t and old Tim 80 kg, we don't want to say that Tim weighs 150 kg at t. But if "Tim" picks out the relevant spacetime region, why doesn't this region have a mass of 150 kg at t?
Compare Tim's bikini, which happens to be lying on the floor at t. (Don't ask.) The bikini consists of a top part and a bottom part. Its total mass is the sum of the masses of the two parts. So when we consider the bikini as a spacetime region R, and we ask about its mass at t, we have to add up all the mass in R at t. (Very loosely speaking.) Why isn't this true for Tim?
The problem obviously generalizes beyond mass. We could ask about Tim's shape, his volume, his velocity, his temperature, his electric charge. In each case, the intuitive answer doesn't aggregate the older and younger Tim. Not even if they stand very closely together.
It's not entirely clear what we want to say about Tim at t. I guess we want to say that he weighs both 70 kg and 80 kg. That's OK. We can give an explanation of these predications. Roughly: "Tim weighs 70 kg at t" is true because "Tim" picks out a spacetime region that divides into parts which stand in a certain relation – the "R-relation" of Lewis 1976 – to each other, and one of these parts is entirely located at t and has a mass of 70 kg. (See Wasserman 2018, sec. 9.2.)
But here's the problem. This analysis of "Tim weighs 70 kg at t" seems to crucially rely on the fact that we think of Tim as a person. If Tim is simply a region in spacetime, we should be able to think of him in other ways as well. Suppose we think of him as "the region with such-and-such boundaries", or as "the mereological fusion of Tim before the time-travel and Tim after the time-travel". If we ask about the shape or mass (etc.) of these objects, we get a different answer. We get the bikini-style answer on which the mass at t is 150 kg.
So even predications involving mass, shape, volume, temperature, and velocity are sortal-relative.