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How does Bertrand Russell’s theory of descriptions explain statements about things that do not exist?

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Austrian postage stamp featuring a portrait of philosopher Ludwig Wittgenstein, with German text above and below, and a denomination of 5 schillings. — Philosophy of language An Austrian stamp depicting Ludwig Wittgenstein.

Bertrand Russell’s theory of descriptions explains statements about non-existent entities by demonstrating that their surface grammatical form is misleading. Philosophers like Alexius Meinong previously argued that such statements required non-existent objects to have some form of "being" to be meaningful.12

Russell rejected this by showing that sentences containing definite descriptions—such as "The present king of France is bald"—are not simple subject-predicate statements. Instead, they are complex, existentially quantified assertions. When analyzed logically, the statement is revealed to be a conjunction of three claims:132
* There is at least one person who is the king of France.12
* There is at most one person who is the king of France.12
* Anyone who is the king of France is bald.12

Because this analysis treats the description as a quantifier rather than a singular term, the sentence can be meaningful and false without requiring a referent. Consequently, no "mysterious" non-existent entities are needed to account for the meaning of such statements, as they are simply shown to be false because the property described has no instance.21