If the purpose of a statement, in language, is to denote something that can be accessed in the mind of the hearer/reader—not a “real thing,” as images or conception of the thing denoted will vary depending on the person (cf. Frege, Russell)—then this statement made by Bertrand Russell seems false:

The whole realm of non-entities, such as “the round square,” “the even prime other than 2,” “Apollo,” “Hamlet,” etc., can now be satisfactorily dealt with. All these are denoting phrases which do not denote anything… If “Apollo” has a primary occurrence, the proposition containing the occurrence is false; if the occurrence is secondary, the proposition must be true. So again “the round square is round” means “there is one and only one entity x which is round and square, and that entity is round,” which is a false proposition, not, as Meinong maintains, a true one.

Now, “Hamlet” and “Apollo,” as denoting phrases, could certainly conjure up something, some previous image or conception, in the minds of most speakers of English, and thus, “Hamlet” and “Apollo” could hardly be said to denote nothing. Most people might have more decided and concrete parameters for “Hamlet” than for something “real” like “the present Queen of England,” who, despite being an actual, living person, is so nebulous and inaccessible she only exists, for most people, within the confines of the supermarket tabloids and in related portions of their minds. If, however, primary occurrence and “reality” are the deciding factors to the truth or falsity of a statement, then the proposition “Hamlet originally recites the famous ‘to be or not to be’ monologue,” by Russell’s standard, is false.
The problem Russell would have with the truth or falsity of this proposition is not that it is illogical, but that the denotation refers to a fictional character. But certainly this in itself cannot make the statement false in any real sense. If denotation is based entirely upon what provably exists in the tangible world, then not only will nothing be denoted by “Hamlet,” but also nothing will be denoted by Russell’s very theory, which is also a hypothetical.