3.4 Identity statements and opaque contexts

Identity statements and opaque contexts are crucial concepts in semantics. They explore how language refers to things and how meaning can change in certain contexts. These ideas challenge our understanding of how words relate to the world.

Opaque contexts, like belief reports and modal statements, show that swapping out words with the same meaning doesn't always work. This raises questions about how language conveys information and how we understand the relationship between words and reality.

Identity Statements and Opaque Contexts

Identity statements and opaque contexts

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• Identity statements assert two expressions refer to the same entity
  • "Mark Twain is Samuel Clemens" (author's real name and pen name)
  • "The morning star is the evening star" (both refer to Venus)
  • "Clark Kent is Superman" (superhero's alter ego and true identity)
• Opaque contexts are linguistic environments where substituting co-referential terms does not always preserve the sentence's truth value
  • Belief reports: "Lois Lane believes Superman can fly" vs. "Lois Lane believes Clark Kent can fly"
  • Modal contexts: "2 + 2 = 4 is necessarily true" vs. "The number of planets in the solar system = 4 is necessarily true"
  • Quotation contexts: "'Cicero' has six letters" vs. "'Tully' has six letters" (both refer to the same Roman orator)

Challenges in opaque contexts

• Substitutivity principle seems to fail in opaque contexts
  • Principle states co-referential terms should be interchangeable without affecting a sentence's truth value
• Frege's puzzle highlights identity statements can be informative, despite seeming trivially true
  • "Hesperus is Phosphorus" is informative, even though both names refer to Venus
• Co-referential terms may have different cognitive significance for a speaker
  • Leads to different truth values when substituted in opaque contexts

Solutions for identity puzzles

• Fregean sense theory distinguishes between an expression's reference (Bedeutung) and sense (Sinn)
  • Sense is the referent's mode of presentation
  • Accounts for cognitive significance and substitutivity failure in opaque contexts
• Russellian theory of descriptions analyzes definite descriptions as quantified expressions rather than referring expressions
  • Solves Frege's puzzle by denying identity statements are genuine identity statements
• Kripke's rigid designator theory argues proper names are rigid designators, referring to the same entity in all possible worlds
  • Explains substitutivity failure in modal contexts by distinguishing between necessity and aprioricity

Implications for meaning theories

• Opaque contexts challenge the compositionality principle
  • Principle states a complex expression's meaning is determined by its parts' meanings and their combination
  • In opaque contexts, the whole sentence's meaning is not always determined by its parts' meanings
• Direct reference theory, which views a term's meaning as simply its referent, faces difficulties accounting for cognitive significance and substitutivity failure in opaque contexts
• Two-dimensional semantics distinguishes between two aspects of meaning
  1. Primary intension (a priori, cognitive significance)
  2. Secondary intension (a posteriori, truth-conditional content)
• Aims to reconcile Fregean and Kripkean insights about meaning and reference in opaque contexts