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I have a two-part question about the definition of a possible world. I will make the assumption that time is tensed.

First of all, is a possible world a complete list of all propositions that are true now (at the time of the present temporal event), or a complete list of all temporal events and a complete list of all propositions that are true of each event? For example, if one gave a list of propositions that precisely described the position and motion of every fundamental particle at the present instant, and analogously described any additional mental or supernatural realities at the present instant, would this be a different possible world than a similar list describing an instant one year ago, or would these (along with all other instants) be part of the a single possible world?

EDIT: It seems I worded the first question a bit clumsily; I didn't mean to give such special weight to the "now" event. My point was to ask what the temporal scope of a possible world is. Is it a maximal description of reality during a single hypothetical (or actual) event, or a maximal description of a hypothetical (or actual) reality throughout its full duration?

Secondly, if the latter is correct, is the objective "now" part of the description of a possible world? If two descriptions of reality are identical, except that in one, 1990 is now, and in another, 2000 is now, do these constitute one or two distinct possible worlds?

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Your questions assumes a lot. The contemporary conception of possible worlds stem from the work of David Lewis. On his account, Modal Realism, worlds are defined as concrete maximal mereological sums, all of which parts are spatio-temporally related.

If you don't like Modal Realism (and no one really does), then, if you still want to employ possible worlds in your theory, one option is to think of them as sets of propositions. However, there is no reason to choose one of your two options. There is at least a third option available, namely, that a possible world is a set of propositions (probably closed under implication or so) that describe a possible scenario.

As to your first option (list of propositions true now): This would render possible worlds useless for most purposes. One application of possible worlds is to talk about possibilities. But if worlds only consist in sets of propositions that are true now, then there is no possible world in which things are different.

As to your second option (set of temporal events and propositions being true at each event), it is unclear what you need the events for. As I indicated in the second paragraph, worlds can just be sets of propositions. They describe how things could have been. Some propositions are about how things could have been in the past. Some propositions are about how things could have been in the future. Some propositions are about how right now things could have been different. For example, one propositions says that I am drinking tea in the kitchen. That proposition is false here, but it describes what could have been true.

Response to your edit: I didn't find a quote to back this, but I think a possible world as a set of propositions is assumed to be a maximal description of (actual or) possible realities thoughout its full duration. This in a sense includes the other option, because maximal descriptions of single events will be part of a possible world in the former sense.

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