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Distinguishability/Stalnaker: every thing possibly distinguishable. - Because possibly distinguishable things may be distinguished by their modal properties. - But distinguishable things are not necessarily distinguishable. - Distinctions may be missing in other possible worlds - For that we need an asymmetrical accessibility relation. - That means you cannot look back. - Information about the distinction is lost.
Solution: Timeliness Operator/Williamson/(s). in the actual world ... the information about each possible world accessible from the actual world is reflected in the actual world and therefore also in every other possible world in the model.
Distinguishability/Diversity/Stalnaker: in contrast, necessary diversity in the standard semantics is valid. - But not in the counterpart theory.
Ways a World may be Oxford New York 2003