Therefore, indiscernibility with respect to what propositions are asserted does not guarantee indiscernibility with respect to having asserted a true proposition when comparing across worlds

Sometimes there is an explanation of why weak supervenience holds despite the fact that strong supervenience does not. If, within a world, two individuals assert exactly the same propositions, then they are exactly alike vis-à-vis having asserted a true proposition: the one asserted at least one true proposition if and only if the other did. The reason is that a proposition will have a unique truth-value relative to a world. The following weak supervenience thesis thus holds: for any world w, an