 The law of excluded middle (LEM) states that any proposition of the form \((\phi \vee \neg \phi)\) is logically valid. The semantic principle of bivalence states that every proposition is either true or false (and not both). Bivalence and LEM collapse in classical logic, but are distinguished for example in supervaluationism (van Fraassen 1966), which rejects the former, while retaining the latter. Since Aristotle, who was the first to state these principles, bivalence and LEM have been criticized on various grounds. This section first discusses intuitionistic logic, which invalidates LEM (and part of the De Morgan laws); and then presents some canonical arguments against bivalence and discuss how \(\vee\) is interpreted in a number of non-bivalent systems including many-valued logic, dynamic semantics, supervaluationism, as well as quantum logic, which besides bivalence also invalidates the classical distributive laws.