Knowra Principle of bivalence Principle of bivalence The principle that every declarative proposition is either true or false, with no third truth value. It is distinct from the law of excluded middle, which concerns a logical formula and its negation.
Proposition : A declarative statement capable of being assessed as true or false. Bivalence assigns exactly one of its two truth values to each proposition.
Many-valued logic : A logic that uses more than two truth values. It rejects the restriction to true and false by adding values such as indeterminate.
Boolean algebra : An algebraic system whose elements represent truth values and whose operations model logical connectives. Its two-element form models bivalent truth and underlies digital switching.
Aristotle : An ancient Greek philosopher whose writings shaped logic, metaphysics, and natural philosophy. His discussion of future contingents raised a lasting question about whether every statement is already true or false.
Truth value : A value representing whether a proposition is true, false, or another status in a logical system. Bivalence restricts propositions to the values true and false.
Intuitionistic logic : A logic that interprets truth through proof and does not generally accept excluded middle. Its rejection of unrestricted excluded middle separates it from classical reasoning, though it need not posit a third truth value.
Digital circuit : An electronic circuit that processes signals using components such as transistors and logic gates. Binary circuit states operationalize a true-or-false distinction, though physical voltages are not themselves propositions.
De Interpretatione : Aristotle's treatise on propositions, affirmation, negation, and logical opposition. Its chapter on the sea battle became central to debates about bivalence and future events.
Classical logic : A family of logical systems that includes classical propositional and predicate logic. Classical logic generally treats propositions as bivalent.
Fuzzy logic : A logic in which propositions can have degrees of truth, often represented by values between zero and one. Its graded truth values directly contrast with bivalence's two-valued assignment.
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