What is the relationship between the series of truths in the world and the times in that world? That is, imagine that: !, @, #, $, % are maximally complete sets of truths (like an ersatz possible world for a world that lasts only an instant) and that time is discrete. How many different possible worlds can there be with this series of truths?:
!, @, #, $, %?
I think the most intuitive answer is one. Here is what makes that answer problematic. There can be two distinct times even though all and only the same things are true at those times. To see this, consider the following series of truths:
!, @, #, $, %, $, #, @, !
Then ask, how many instants are there in this world? I find it exceedingly implausible to say that there are only 5 instants of time in this world, one corresponding to each of the different maximally complete sets of truths. For then, which came first, the time that is corresponds to $ or the time that corresponds to %? This suggests that two non-identical times can realize a maximally complete set of truths.
But now the slippery slope kicks in. Why just two? What about this series of truths?:
!, @, #, @, !, #, !,
This suggests that any number of non-identical times could realize a maximally complete set of truths. But this is unattractive as well. It doesn't seem that we should have possible worlds that differ merely in the identities of the times in their world. [Suppose that t1 can realize # and t2 can realize #, but that t1 is distinct from t2. Now, there might be two different worlds that correspond to the following series of truths: #. One world is simply t1 and the other is simply t2. But that is weird.]