Peirce was the first logician to define three-valued logical connectives. In 1909, he defined four one-place three-valued connectives and six two-place three-valued connectives, all of which were rediscovered by later logicians. Peirce’s motivation was to accommodate within formal logic a specific, narrow range of propositions he took to be neither true nor false, viz. propositions that predicate of a breach in mathematical or temporal continuity one of the properties that is a boundary-property relative to that breach.

Charles Peirce claimed that "anything is general in so far as the principle of excluded middle does not apply to it and is vague in so far as the principle of contradiction does not apply to it." This seems to imply that general propositions are neither true nor false and that vague propositions are both true and false. But this is not the case. I argue that Peirce's claim was intended to underscore relatively simple facts about quantification and negation, and (...) that it implies neither that general propositions are neither true nor false nor that vague propositions are both true and false. (shrink)