Truthmaker Semantics

Origin. Fine (2010s). Exact verification. States as truthmakers. Hyperintensional. Foundation of exact semantics.

Models. States verify propositions. Exact vs inexact. State space. Fusion. Hyperintensional distinctions.

Formalism.

State space: ⟨S, ⊑, ⊔⟩ where: S: states. ⊑: parthood. ⊔: fusion. States are situations or facts.

Exact verification: s ⊩ A: s exactly verifies A. s is a truthmaker for A. s contains exactly what A requires. No excess.

Inexact verification: s ⊩⁺ A: s inexactly verifies A. s ⊑ s' and s' ⊩ A. Truthmaker somewhere in s.

Falsification: s ⊣ A: s exactly falsifies A. Dual to verification. Bilateral semantics.

Clauses: s ⊩ A ∧ B iff s = s₁ ⊔ s₂, s₁ ⊩ A, s₂ ⊩ B. s ⊩ A ∨ B iff s ⊩ A or s ⊩ B. s ⊩ ¬A iff s ⊣ A. Conjunction = fusion.

Hyperintensionality: A ∧ A ≠ A (different truthmakers). Impossible worlds not needed. Finer than possible worlds. Content, not just truth-conditions.

Subject matter: What a proposition is about. Truthmaker states. Relevance logic connection.

Symbols.

Symbol	Unicode	Meaning
⊩	U+22A9	exact verification
⊣	U+22A3	exact falsification
⊔	U+2294	state fusion
s	—	state/truthmaker

Metatheory. Exact semantics. Hyperintensionality. State spaces. Relevance.

Applies to. Relevance. Subject matter. Counterfactuals. Semantics of content.

Limitations. Nonstandard. State ontology. Compositionality debates. Technical complexity.