How many objects exist at t is not even partly grounded in facts about how things are at times later than t in worlds without backwards causation.
If standard four-dimensional unrestricted composition is true, then how many objects exists at t is partly grounded in fact about how things are at times other than t.
Standard four-dimensional unrestricted composition is false.
I think (1) is very plausible. What about (2)? Bracket God. Consider a world w2 without backwards causation whose timeline consists of two moments, t1 and t2, and where there is a simple a existining only at t1 aand a different simple b existing only at t2. On standard four-dimensional unrestricted composition, there are three objects in existence in w2: a, b and a + b. Of these, two objects, namely a and a + b, exist at t1. Now consider a world w1 just like w2 but without b, and hence without anything at t2. There is only one object, namely a, at t1 in w1.
What grounds the difference between the number of objects at t1 in the worlds is whether b exists at t2, contrary to (1).
The best escape from this argument is to suppose what I call five-dimensional unrestricted composition, where all modal profiles are filled. On that view, in both worlds there are infinitely many objects—probably beyond cardinality—at t1. But that has other plausibility problems.
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