The principle of bivalence, concerning statements of the object-language, is easily statable in a theory of truth and it may or may not be a theorem of the theory.
As for the principle of bivalence, it does seem likely that it cannot be a theorem of a verificationist theory of meaning (if only because it cannot be expressed therein), but this needs argument and, besides, the principle of bivalence, while important, is not the same as realism.
This stage thus concludes: since there is no way for a speaker to manifest his assignment of this or that verification-transcendent truth-condition to a sentence, no sentence can possess such a truth-condition; hence we are never entitled in the interesting cases to accept the principle of bivalence, and realism must therefore be abandoned.
However, as Dummett is well aware, there is no obvious reason why such a reductionist scheme should not respect the principle of bivalence.
Sections XVII-XX concern the implications for the principle of bivalence
, the law of excluded middle, and the principle of noncontradiction.
Theorists of vagueness often reject the principle of bivalence
- every statement has one of two truth values - which they distinguish from the law of excluded middle - every disjunction of a statement with its negation is true.