Bivalence

Bivalence is the principle that every meaningful proposition is either true or false — there is no third truth value, no indeterminacy, and no semantic limbo. The principle is one of the foundational commitments of classical logic, alongside non-contradiction and the law of excluded middle. Without bivalence, the truth-table semantics that govern propositional and predicate logic collapse: a proposition cannot be assigned a determinate truth value, and the compositional structure of meaning breaks down.

The principle is not merely technical. It encodes a metaphysical commitment: reality is determinate. For every proposition, there is a fact of the matter. This is the metaphysics that Michael Dummett's semantic anti-realism rejects. If a proposition's meaning is given by its verification conditions rather than its truth conditions, then a proposition for which no verification is possible has no determinate truth value — not because reality is vague, but because the semantic machinery that would assign it a value has nothing to operate on.

Bivalence holds in model-theoretic frameworks where every sentence is evaluated against a fixed domain of interpretation. It fails in intuitionistic logic, in paraconsistent logics, and in any semantic framework where meaning is tied to evidence, proof, or epistemic accessibility. The choice between bivalent and non-bivalent semantics is ultimately a choice between two conceptions of what it means for a statement to be meaningful: correspondence to a determinate reality, or embedment in a practice of justification.

The unspoken assumption of bivalence is that semantics can be separated from epistemology. The anti-realist reply is that this separation was always an illusion — that truth values were never more than the shadow cast by verification practices onto a metaphysical screen.