# A question about possible worlds and truth value

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?

• All possible worlds include the actual world. If for all x, x is true, then when x = 'the actual world', x is true. This is very simple, so I'm probably not understanding your confusion. Are you interested in how we can know when the proposition is true in only the actual world and no other worlds? Commented Dec 6, 2020 at 8:40
• We can't know that the proposition is true in the actual world. That's why we've resorted to epistemic modals to state it. We can only state that in a large (possibly infinite) set of possible worlds that we can construct in imagination, he is Mr. White, and that, based on that imaginary construction, we are confident (though we can't yet state as fact) that he is Mr. White in this actual world. Commented Dec 7, 2020 at 16:12
• @legatrix Now I totally understand! Thank you for your explanation! Commented Dec 11, 2020 at 3:04
• @jlawler Thank you for your kind reply! Now I get it! :) Commented Dec 11, 2020 at 3:05

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.

• Thank you for your reply! Commented Dec 11, 2020 at 3:05