When a name lacks a referent (like "Vulcan" or "the current king of France"), how do statements containing it have truth conditions? Frege proposed a truth-value gap; Russell proposed that descriptions are logically analyzable into quantified formulas that entail existence; direct reference theorists must explain what happens when reference fails. This problem reveals deep issues about semantic content and compositionality.
Compare solutions: Russell's analysis of "The current king of France is wise" shows it's false rather than truth-valueless by parsing it as "There exists a unique current king of France who is wise." Study how direct reference theorists handle empty names, and consider whether fictional names ("Sherlock Holmes") require special treatment. Examine whether presupposition failure is the right model.
From your work on Russell's theory of definite descriptions and Frege's sense/reference distinction, you're equipped to see why empty names create a genuine crisis for theories of meaning. Both Frege and Russell built their semantic theories around reference: expressions contribute their referents to the propositions they help express. But what happens when a name has no referent? The question is not merely abstract — it arises for names of myths ("Zeus"), fictional characters ("Sherlock Holmes"), failed scientific posits ("Vulcan," the planet once hypothesized to orbit inside Mercury), and ordinary speakers' mistaken beliefs.
Frege's response was the truth-value gap: a sentence like "Vulcan is larger than Mercury" is neither true nor false because "Vulcan" lacks a referent and thus the sentence fails to express a complete proposition. Frege softened this by distinguishing the literary and scientific contexts: in fiction, names have sense (a mode of presentation) without ordinary reference, referring instead to fictional objects or ideas. His theory can thus acknowledge that we understand and communicate successfully about fictional characters without committing to their literal existence. The cost is that compositionality becomes complicated — the semantic value of a complex expression depends on the semantic values of its parts, but what is the semantic value of a part with no referent?
Russell's strategy was more radical: deny that proper names (in the logical sense) can fail to refer. He distinguished between ordinary proper names ("Hamlet," "Vulcan"), which are disguised definite descriptions, and logically proper names, which are guaranteed to refer. "Vulcan" abbreviates something like "the planet between Mercury and the Sun." Russell's analysis of definite descriptions then handles the failure: "The planet between Mercury and the Sun is larger than Mercury" is analyzed as "There exists a unique planet between Mercury and the Sun that is larger than Mercury" — which is simply false, not truth-valueless, because the existential claim fails. This preserves bivalence (every proposition is either true or false) at the cost of denying that ordinary names are genuine referring expressions.
Direct reference theorists (Kripke, Kaplan) face the sharpest challenge. If a name's sole semantic contribution is its referent — no descriptive backing, no Fregean sense — then an empty name contributes nothing, and the sentence containing it fails to express a proposition at all. This makes it hard to explain how "Sherlock Holmes is a detective" seems to communicate something, how we can make true negative existential claims ("Vulcan does not exist"), and how fiction is intelligible. Responses include Meinongianism (names refer to non-existent objects that have properties), pretense theory (we are engaged in a game of make-believe), abstract artifact theories (fictional characters exist as abstract objects created by authors), and various hybrid theories. Each choice reflects deeper commitments about the metaphysics of existence, the semantics of reference, and the purpose of names in natural language.
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