Glossary

11.3 Definite Descriptions and Russell's Theory

5 min read•august 7, 2024

Definite descriptions, like "the tallest building," are a key part of language. 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

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  • 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 analyzes definite descriptions as quantified expressions rather than referring expressions
    • Breaks down "the F is G" into a conjunction of existence, , 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 of a 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 (ι\iota) is a formal device used to represent definite descriptions in logical notation
    • ιxFx\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: ∃x(Tx∧∀y(Ty→y=x)∧Dx)\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
    • 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 (¬∃x(Fx∧∀y(Fy→y=x)∧Gx)\neg \exists x(Fx \land \forall y(Fy \to y=x) \land Gx))
      • Narrow scope negation: The F is not G (∃x(Fx∧∀y(Fy→y=x)∧¬Gx)\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 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 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

Key Terms to Review (24)

Attributive use: Attributive use refers to the manner in which a noun or description is employed to attribute a quality or property to an entity. In this context, it emphasizes the characteristics or attributes associated with a noun, rather than identifying or referring to a specific individual or object. This distinction is crucial when analyzing definite descriptions, as it influences how we interpret sentences and understand the meaning of terms in Russell's Theory.
Bertrand Russell: Bertrand Russell was a British philosopher, logician, and social critic known for his work in mathematical logic and philosophy of language. He made significant contributions to the development of modern logic, particularly through his theory of definite descriptions, which challenged traditional views on meaning and reference. His ideas laid the groundwork for later developments in predicate logic and influenced how quantified statements are understood in formal logic.
Critique of the Theory of Descriptions: The critique of the theory of descriptions refers to the philosophical examination and challenges posed to Bertrand Russell's approach to understanding definite descriptions, such as 'the current king of France.' This critique questions how definite descriptions relate to reference, meaning, and truth, leading to significant discussions on the implications for language, logic, and knowledge.
Definite description: A definite description is a phrase that refers to a specific individual or object, typically introduced by the word 'the' followed by a descriptive clause. This term highlights the distinction between descriptions that identify a particular entity and those that do not, emphasizing how language can imply uniqueness and specificity in communication. Definite descriptions play a crucial role in discussions of reference, meaning, and truth within philosophy and logic.
Denotation: Denotation refers to the explicit or literal meaning of a word or phrase, distinct from any associated emotions or connotations. It provides a straightforward definition that is universally recognized, which is essential when dealing with language and meaning in formal logic and philosophy. Understanding denotation is crucial for analyzing language accurately and helps avoid ambiguity when interpreting statements.
Donnellan's Referential-Attributive Distinction: Donnellan's referential-attributive distinction differentiates between two ways definite descriptions can function in language: as referential, where they point to a specific individual, and as attributive, where they describe a general property without necessarily referring to a specific person. This distinction is crucial for understanding how language conveys meaning and reference, particularly in the context of definite descriptions.
Existence presupposition: Existence presupposition refers to the assumption that certain entities or individuals exist when specific terms or phrases are used in language. This concept is particularly significant in understanding how definite descriptions function in logic and philosophy, as it reveals the implicit assumptions about existence that are made when asserting statements involving these descriptions.
Existential Quantification: Existential quantification is a logical construct used to express that there exists at least one element in a domain that satisfies a given property or condition. This concept plays a crucial role in formal logic, as it helps in formulating statements that indicate the presence of certain entities, often represented symbolically as '∃'. It allows us to differentiate between universal truths and specific instances that hold true in logic.
First-order logic: First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science that allows for the representation of statements about objects and their relationships through quantified variables. It extends propositional logic by introducing quantifiers, such as 'for all' ($$ orall$$) and 'there exists' ($$ orall$$), enabling more complex expressions about properties and relations of objects.
Frege: Gottlob Frege was a German philosopher, logician, and mathematician who is considered one of the founders of modern logic and analytic philosophy. His work focused on the philosophy of language and the foundations of mathematics, particularly in relation to meaning, reference, and truth. Frege's ideas about sense and reference provide crucial insights into understanding definite descriptions, which connect deeply with Russell's Theory.
Implicature: Implicature refers to the phenomenon where a speaker suggests or implies something beyond the literal meaning of their words, relying on context and shared understanding to convey additional meaning. It plays a crucial role in communication by allowing speakers to convey more nuanced thoughts without stating them directly, often influenced by conversational norms and expectations.
Iota operator: The iota operator is a symbol used in formal logic and philosophy to denote a unique individual or object that satisfies a given property. It captures the idea of definite descriptions, allowing for the representation of phrases like 'the current president' or 'the tallest building.' This operator plays a critical role in understanding Russell's theory of descriptions, particularly in distinguishing between existence and uniqueness in definite terms.
Ontological commitment: Ontological commitment refers to the assumption about what entities must exist in order for a particular theory or statement to be true. This concept is crucial in understanding how language and logic relate to reality, especially when dealing with definite descriptions, as it highlights the necessary existence of certain entities that such descriptions imply. The focus on ontological commitment also helps in distinguishing between different interpretations of statements and theories, especially in philosophical discussions about reference and meaning.
Predicate Logic: Predicate logic is a formal system in mathematical logic that extends propositional logic by incorporating quantifiers and predicates, which allow for the expression of statements involving variables and their relationships. It enables more complex statements about objects and their properties, facilitating deeper reasoning about arguments and relationships compared to simple propositional logic.
Referential opacity: Referential opacity occurs when a term or expression does not retain its reference in certain contexts, especially when substitution of co-referential terms changes the truth value of a statement. This phenomenon highlights the complexities of meaning and reference in language, particularly in relation to definite descriptions and how they interact with propositional attitudes.
Referential use: Referential use refers to the way in which a term or expression directly indicates or points to a specific entity or individual in the world. This contrasts with non-referential use, where a term may be used more generally or descriptively without pointing to a specific reference. Understanding this concept is crucial when analyzing definite descriptions, as it helps clarify how language functions in terms of reference and meaning.
Russell's Theory: Russell's Theory, proposed by philosopher Bertrand Russell, is a framework for understanding definite descriptions, which are phrases that uniquely identify an object. The theory argues that definite descriptions do not denote a specific object but instead express a proposition that can be either true or false, depending on the existence of the object in question. This approach significantly impacts how we analyze language and meaning, particularly in formal logic and philosophy.
Scope ambiguity: Scope ambiguity refers to the uncertainty that arises in sentences with quantifiers or definite descriptions due to multiple interpretations of their scope. This can lead to confusion about which parts of a sentence are affected by the quantifiers or descriptions, impacting the overall meaning. Understanding scope ambiguity is essential for analyzing logical structures and comprehending how different interpretations can emerge based on the placement of quantifiers or definite descriptions.
Sense and Reference: Sense and reference are two key components in the study of meaning in language. The 'sense' of an expression relates to its meaning or the mental concept it conveys, while 'reference' pertains to the actual entity or object in the world that the expression points to. Understanding this distinction is crucial for grasping how definite descriptions function within logical analysis, particularly in relation to how statements can refer to specific individuals or objects.
Strawson's Presupposition Failure Criticism: Strawson's presupposition failure criticism refers to the argument that certain statements or propositions presuppose the existence of specific entities or conditions, and if those presuppositions are not met, the statements become problematic or meaningless. This critique challenges Russell's theory of definite descriptions, which suggests that definite descriptions can be analyzed as existential claims, often neglecting the necessity of these presuppositions.
Theory of descriptions: The theory of descriptions is a philosophical concept introduced by Bertrand Russell, which aims to analyze the meaning of definite descriptions such as 'the current King of France.' It posits that such phrases do not refer to existing entities but rather assert specific conditions that must be met. This theory clarifies how language relates to reality, especially in cases where the described entities do not exist.
Truth-value: A truth-value is a property of a statement that indicates whether it is true or false. In formal logic, truth-values are essential for understanding the logical relationships between statements, especially when analyzing arguments or evaluating the validity of propositions. Each statement in logic can only have one of two truth-values, which helps in constructing logical proofs and determining the outcomes of logical operations.
Uniqueness: Uniqueness refers to the property of being the only one of its kind, particularly in the context of definite descriptions and how language is used to denote specific entities. This concept is crucial for understanding how certain phrases identify a single object or individual within a given context, highlighting the importance of clear reference in communication and logic.
Uniqueness presupposition: Uniqueness presupposition is the idea that certain expressions, particularly definite descriptions, imply the existence of a unique entity that satisfies the description. This notion plays a critical role in understanding how language conveys meaning and is deeply connected to the logic of reference, particularly in the context of statements about specific objects or individuals.
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