How does Russell’s theory of definite descriptions handle phrases such as “the golden mountain”?

In analytic philosophy, Bertrand Russell’s theory of definite descriptions resolves the problem of phrases like "the golden mountain"—which appear to refer to non-existent objects—by demonstrating that they are not singular terms that must denote an entity to be meaningful.12

Instead of treating "the golden mountain" as a name, Russell analyzes sentences containing such phrases as complex, existentially quantified statements. For example, the statement "The golden mountain is high" is analyzed as a conjunction of three claims:13
1. There is at least one golden mountain.
2. There is at most one golden mountain.
3. Whatever is a golden mountain is high.12

Because this analysis reveals that the phrase "the golden mountain" is not a referring expression but part of a general logical structure, the sentence can be understood as false rather than nonsensical, even though no such mountain exists. By treating these descriptions as "logical fictions" rather than names, Russell avoids the need to posit mysterious forms of existence for objects that do not exist in the real world.32