According to the best A-theories (i.e., those that accept an Aristotelian view of propositions as changing in truth value), there is an objective and non-relational fact as to what time it is, a fact that won't obtain tomorrow. Assume this. Here is one way to think about this. Let w be the actual world. The actual world holds all the actually true facts, including presumably the fact that it is January 18, since it is indeed Tuesday. Moreover, there will be a world w* at which everything happens just as at w except that at w* it is some time t on January 19. World w* will be a world that we will inhabit at t, tomorrow.
On this view, at every time, we are in a different world. We will then have an earlier-than relation between worlds defined as follows: w is earlier than w* if and only if at w* it is true that w was actual. Assume the earlier-than relation is transitive. Say that two worlds are directly temporally related if and only if either they are identical or one is earlier than the other. We then get:
- The future is closed if and only if direct temporal relatedness is transitive.
We need one more thing in the formalism. We need a way to compare times between worlds that aren't directly temporally related. Thus, there is a simultaneity relation between worlds. Worlds w and w* are simultaneous provided that at both worlds it is the same time. This relation is also an equivalence relation, and we can let S(w) be the equivalence class of all worlds simultaneous with w.
Each world w is then a member of two orthogonal equivalence classes: T(w) which contains all the directly past and future worlds, and S(w) which contains all the simultaneous worlds. This provides resources for the formation of new modal operators, using one or the other of the equivalence relations as an accessibility relation.
Enough formalism. Maybe in a future post I will try to criticize the view.