Definition
The principle of bivalence says that every statement is either true or false — there are exactly two truth values, and each statement takes one of them. It is one of the bedrock assumptions of classical logic, the framework most arguments are evaluated against.
Bivalence is easy to confuse with a related rule, the law of excluded middle, which says that for any statement the disjunction "it is true or it is false" itself holds. The two often travel together, but bivalence is the stronger metaphysical claim: not merely that the disjunction holds, but that one specific disjunct is settled.
Why it matters
How it works
In a bivalent system, every well-formed statement is assigned one of two values, and the connectives are functions on those values. This makes classical logic clean and decidable for simple cases, but it forces an answer even where reality seems not to provide one.
Priest highlights the awkward cases. A heap loses one grain at a time until it is no longer a heap, yet no single grain marks the switch — vagueness resists a sharp true/false line. Aristotle worried that a statement about a future contingent event has no truth value until the event occurs. Each pressure point suggests truth may come in gaps or degrees.