# 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.

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