Definite descriptions like "the Queen of England" refer to unique individuals. But what happens when the described object doesn't exist? Russell's theory tackles this, stating that statements with non-referring descriptions are false, not meaningless.

Russell's approach eliminates the need for non-existent objects in our understanding of language. By analyzing statements as complex propositions, we can avoid logical puzzles and contradictions that arise from talking about things that don't exist.

Definite Descriptions and Existence

Definite descriptions and object existence

• Definite descriptions refer to a unique individual using phrases like "the X" ("the Queen of England")
• For a definite description to successfully refer, the described object must exist
• Non-referring definite descriptions fail to refer to anything due to the non-existence of the described object
• Russell's theory of descriptions addresses logical issues arising from non-referring definite descriptions
• According to Russell, statements with non-referring definite descriptions are false, not meaningless

Referential vs attributive descriptions

• Referential use: speaker has a particular individual in mind and uses the description to refer to them ("The person I met yesterday was kind")
• Attributive use: speaker does not have a particular individual in mind but uses the description to refer to whoever fits the description ("The fastest runner will win the race")

Truth values of non-referring descriptions

• According to Russell, statements with non-referring definite descriptions are false
• "The current King of France is bald" is false because there is no current King of France
• The statement can be analyzed as a conjunction of three propositions:
  1. There exists an x such that x is the current King of France
  2. For all y, if y is the current King of France, then y is identical to x
  3. x is bald
• If any of these propositions are false, the entire statement is false

Russell's theory for non-existent objects

• Russell's theory eliminates the need for non-existent objects in our ontology
• Statements with non-referring definite descriptions are analyzed as complex propositions that do not commit to the existence of the described object
• "The golden mountain is tall" can be analyzed as: $\exists x (Gx \land Mx \land \forall y ((Gy \land My) \rightarrow y = x) \land Tx)$
  • There exists an x such that:
    1. x is golden
    2. x is a mountain
    3. For all y, if y is golden and a mountain, then y is identical to x
    4. x is tall
• Analyzing statements this way avoids logical puzzles and contradictions arising from non-existent objects