Two-Dimensional Semantics

Origin. Kaplan (1977), Stalnaker, Chalmers. Context and circumstance. A priori vs necessary. Primary and secondary intensions. Foundation for epistemology of modality.

Models. Expressions evaluated at two indices. Context determines character. Circumstance determines content. Matrix semantics.

Formalism.

Two indices: c: context (world of utterance) w: circumstance (world of evaluation) ⟦φ⟧(c, w): value at context c, world w.

Character (primary intension): λc. ⟦φ⟧(c, c) Diagonal: evaluate at context. A priori necessity.

Content (secondary intension): λw. ⟦φ⟧(c*, w) Fix actual context c*. Metaphysical necessity.

Matrix representation: w₁ w₂ w₃ c₁ = w₁ T F F c₂ = w₂ F T F c₃ = w₃ F F T

A priori: Diagonal all true. True in every context at that context. e.g., "I am here now."

Necessary: Row (for actual context) all true. True at every world of evaluation. e.g., "Water is H₂O."

Contingent a priori: Diagonal true, some row false. "The meter stick is one meter."

Necessary a posteriori: Diagonal not all true, row true. "Water is H₂O" (if water existed). Discovered, not knowable a priori.

Indexicals: "I": speaker at context. "Now": time at context. Content varies with context.

Symbols.

Symbol	Unicode	Name	Meaning
c	—	Context	Utterance world
w	—	Circumstance	Evaluation world
λc	—	Character	Primary intension
λw	—	Content	Secondary intension

Metatheory. Separates epistemic and metaphysical modality. Handles indexicals. Explains Kripke cases.

Applies to. Philosophy of language. Epistemology. Consciousness (Chalmers). Indexicality.

Limitations. Which contexts possible? Epistemic interpretation. Multiple versions. Contested scope.