The sentence "He must be Mr. White." can be interpreted as "In all the possible worlds, the proposition that he is Mr.White is true", right? But I'm just wondering all the possible worlds include the actual world right? In this way, how can we know the proposition that he is Mr.White is true in the actual world?
This question is confused about truth values of statements.
For an overview, we can assign different truthvalues to the phrase "He must be Mr. Wright".
For one, we are sure that it is truly a grammatically well formed sentence. But is the information also true?
We might say that it is equivalent in a many-world interpretation to the statement "In all the possible worlds, the proposition that he is Mr.White is true". But is the information also true?
The many-world interpretation is a much stronger claim. Logically, if there is no world in which "He" is not Mr. Wright, then the actual world either: a) doesn't exist and the many world interpretation is out of this world; or b) there is indeed a Mr. Wright that is "He".
This can be a useful construct if talking in general terms. For example, you may hold that certain adjectives are mutually exclusive so that, consequently, you may judge any sentence describing an object with both features be necessarily false, even if you have no other knowledge of the object.