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Russell argued that definite descriptions like 'the present King of France' are not names but complex logical constructions that can be eliminated through analysis. A sentence containing 'the F' should be analyzed as asserting existence, uniqueness, and a property—not as simply referring to an object. This solves puzzles about meaning and reference for non-denoting descriptions.
Analyze concrete descriptions like 'the King of France is bald' and 'the author of Waverley' to see how Russell's theory avoids the empty-referent problem that Frege faced.
Russell thought descriptions name objects—Russell explicitly denied this, arguing they have no referents, only truth-conditions. The theory only applies to 'the'—it applies to all definite quantifiers.
To appreciate what Russell was doing, recall the problem your prerequisite work on meaning and reference set up: expressions seem to get their meaning by referring to things. Names like "Aristotle" mean what they do because they latch onto a particular person. But what about expressions like "the present King of France" or "the golden mountain"? There is no such king, no such mountain. A theory that ties meaning entirely to reference seems to imply these expressions are meaningless — but the sentences containing them don't feel meaningless. "The present King of France is bald" seems false, not nonsense.
Russell's insight was that definite descriptions are not names. They look grammatically like names — "the F" occupies a noun position in a sentence — but their logical structure is completely different. A name contributes a referent; a definite description contributes a quantified claim. Specifically, Russell analyzed "the F is G" as asserting three things simultaneously: (1) something is F, (2) at most one thing is F (uniqueness), and (3) whatever is F is also G. This is a conjunction of existential and universal claims, not a referential act at all.
Run this analysis on "The present King of France is bald." You get: there exists at least one present King of France, there is at most one, and that individual is bald. Since France has no king, claim (1) fails — the whole conjunction is false. The sentence has a perfectly determinate truth value (false) without requiring any referent. The puzzle dissolves. This is why Russell called his theory a contribution to the "theory of incomplete symbols" — descriptions look like referring terms on the surface, but logical analysis reveals they contribute no object, only truth-conditions.
The contrast with Frege is instructive. Frege distinguished the *sense* of an expression (its mode of presentation) from its *reference* (the object it picks out), and proposed that non-denoting expressions have sense but no reference. Russell found this unsatisfying — why should sense be primitive? His analysis is more reductive: it eliminates descriptions entirely, replacing them with quantifiers and predicates in a language that contains only names (which must refer) and logical structure. There are no "incomplete symbols" at the fundamental level of analysis.
A key consequence: because descriptions are not names, they don't *rigidly* pick out an object across possible worlds the way names do. "The inventor of bifocals" refers to Franklin in the actual world, but in a counterfactual world where Jefferson invented bifocals first, it refers to Jefferson. This context-sensitivity is built right into Russell's analysis and has profound implications for modal reasoning — consequences that Kripke would later press against Russell's view, but that's the next chapter in the story.
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