[By Jack]
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.]
Saturday, October 13, 2007
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Thanks for this, Jack. I definitely agree that we shouldn't have "possible worlds that differ merely in the identities of the times" (nor merely in the identities of the objects, for that matter! Though I take it you disagree with me there.) Still, I'm happy to slip down the slope, since it seems independently plausible that any particular time could hold any given instantaneous state of the world (e.g. #). (What's stopping it?)
ReplyDeleteTo avoid the weird conclusion, then, I think we should deny that there are any fundamental facts about the identities of times. Only qualities are fundamental: a difference between worlds requires a qualitative difference. This seems especially plausible for times. Consider the world sequence:
(w1) #,@,#
This sequence tells us all there is to know about the world. One state succeeds another, and then reverts to its earlier form. There is nothing more to say about the identities of the moments - no hidden haecceities that make them what they are. If we consider another world containing only the momentary state #, we should not wonder whether this is a world containing only the first moment from w1, or only the last, or some completely foreign moment displaying a similar form. That would be an empty question -- there is no further fact of which we remain ignorant. Our imagined world contains an isolated #-ish moment, and that's that.