Definite descriptions, like "the tallest building," are a key part of language. Russell's theory breaks them down into logical parts, helping us understand how they work in sentences and arguments.

This topic connects to the broader chapter by exploring how relations and identity play out in language. It shows how seemingly simple phrases can have complex logical structures, affecting meaning and truth.

Definite Descriptions and Russell's Theory

Definite Descriptions and Their Logical Form

• Definite descriptions refer to a unique individual that satisfies a certain description
  • Typically take the form "the F" where F is a predicate (the tallest building)
• Russell's theory of descriptions analyzes definite descriptions as quantified expressions rather than referring expressions
  • Breaks down "the F is G" into a conjunction of existence, uniqueness, and predication claims
    • There exists an x such that x is F
    • For any y, if y is F, then y is identical to x
    • x is G
• The denotation of a definite description is the unique individual that satisfies the description, if such an individual exists
  • If no such individual exists or if more than one individual satisfies the description, the definite description lacks a denotation
• The iota operator ($\iota$) is a formal device used to represent definite descriptions in logical notation
  • $\iota xFx$ represents "the unique x such that x is F"
  • Allows for a precise formulation of Russell's analysis (the tallest building is in Dubai: $\exists x(Tx \land \forall y(Ty \to y=x) \land Dx)$)

Contextual Definitions and Elimination

• Russell's theory provides a contextual definition of definite descriptions, eliminating them in favor of quantified expressions
  • Definite descriptions are not treated as primitives but are defined in terms of more basic logical notions
• The elimination of definite descriptions allows for a simpler ontology and avoids certain philosophical puzzles
  • Avoids postulating non-existent entities as referents of definite descriptions (the present King of France)
  • Resolves the problem of negative existential statements involving definite descriptions (the present King of France does not exist)
• Russell's analysis provides a systematic way to paraphrase sentences containing definite descriptions into first-order logic
  • Enables a clearer understanding of the logical structure and truth conditions of such sentences
  • Facilitates formal reasoning and inference involving definite descriptions

Scope, Existence, and Uniqueness

Scope Ambiguity and Interpretation

• Definite descriptions can interact with other logical operators, leading to scope ambiguities
  • The negation operator can take either wide or narrow scope relative to the definite description
    • Wide scope negation: It is not the case that the F is G ($\neg \exists x(Fx \land \forall y(Fy \to y=x) \land Gx)$)
    • Narrow scope negation: The F is not G ($\exists x(Fx \land \forall y(Fy \to y=x) \land \neg Gx)$)
• The interpretation of a sentence containing a definite description depends on the scope of the logical operators
  • Different scope assignments can yield different truth conditions and entailments
  • Disambiguating scope is crucial for accurately capturing the intended meaning of a sentence
• Similar scope interactions can occur with other operators such as modal operators and propositional attitude verbs
  • The scope of the definite description relative to these operators affects the interpretation and truth conditions of the sentence

Existence and Uniqueness Presuppositions

• Russell's analysis treats the existence and uniqueness claims as part of the asserted content of a sentence containing a definite description
  • The sentence is false if either the existence or uniqueness claim is not satisfied
• An alternative view, advocated by Strawson and others, treats existence and uniqueness as presuppositions rather than asserted content
  • If the presuppositions are not met, the sentence lacks a truth value rather than being false
• The referential use of a definite description assumes the existence and uniqueness of the referent
  • The speaker presupposes that the description has a unique denotation and uses it to refer to that individual
• The attributive use of a definite description does not assume existence or uniqueness
  • The speaker merely attributes certain properties to whatever individual, if any, satisfies the description
  • Attributive uses are more naturally captured by Russell's quantificational analysis

Objections to Russell's Theory

Strawson's Presupposition Failure Criticism

• Strawson argues that Russell's theory fails to account for the intuitive idea that sentences containing non-denoting definite descriptions lack a truth value
  • When the existence or uniqueness presuppositions of a definite description are not met, the sentence fails to express a proposition
  • Strawson distinguishes between a sentence (a linguistic expression) and a use of a sentence (an utterance in a particular context)
    • A use of a sentence may fail to express a proposition if the presuppositions are not satisfied in the context
• Strawson's view maintains that definite descriptions are primarily used referentially and that their successful use presupposes the existence and uniqueness of the referent
  • When these presuppositions are not met, the use of the sentence is infelicitous rather than false
• Strawson's criticism highlights the importance of pragmatic factors and contextual considerations in the analysis of definite descriptions
  • The appropriateness and interpretation of a definite description may depend on the speaker's intentions and the conversational context

Donnellan's Referential-Attributive Distinction

• Donnellan distinguishes between the referential and attributive uses of definite descriptions
  • The referential use involves the speaker intending to refer to a particular individual, even if that individual does not satisfy the descriptive content (the man drinking a martini, when the man is actually drinking water)
  • The attributive use involves the speaker attributing certain properties to whatever individual satisfies the description, without intending to refer to a particular individual
• Donnellan argues that Russell's theory fails to capture the referential use of definite descriptions
  • In the referential use, the speaker succeeds in referring to the intended individual even if the descriptive content is not satisfied
  • Russell's analysis would incorrectly predict that the speaker's utterance is false in such cases
• Donnellan's distinction challenges the adequacy of Russell's purely quantificational analysis of definite descriptions
  • It suggests that a complete account of definite descriptions should incorporate both semantic and pragmatic aspects
  • The referential use may require a separate mechanism for determining the intended referent based on the speaker's intentions and contextual factors
• The referential-attributive distinction has generated much debate in the philosophical literature
  • Some argue that it can be accommodated within a Russellian framework, while others see it as a fundamental challenge to Russell's theory