Abstract

In 1909, Charles Sanders Peirce defined the first-operators for three-valued logic, thus rejecting the Principle of Bivalence. Commentators have consistently misunderstood Peirce's reasons for doing so. I argue that Peirce did not intend for the third value of his logic to be taken by: object-indeterminate propositions; indeterminate predications; modal propositions; or lawful generalizations or future-directed subjunctive conditionals. Further, I argue that Peirce intended for his third value to be taken by boundary-propositions, propositions which predicate of a continuity-breach one of the properties which is a boundary-property relative to that breach. I conclude by considering how Peirce's rejection of the Principle of Bivalence interacts with his pragmatic account of truth