An element of the range of semantic evaluation assigned to a proposition or formula; in classical logic the canonical truth values are True and False (bivalence), while other systems may admit additional or partial values.

Principle

A truth value is what a valuation assigns to a well-formed formula under a given interpretation; logical operations and semantic clauses specify how complex formulas obtain truth values from those of their parts.

Demonstration

Under a standard valuation, the sentence 'Snow is white' receives the truth value True if in the relevant interpretation snow is white; in three-valued logic a sentence might receive an intermediate value such as 'undetermined'.

Misapplication

Confusing truth value with degree of belief or probability, treating it as a pragmatic property (assertability) rather than a semantic assignment, or reifying it as an ontological property of a sentence are common errors.

Consequence

Truth values provide the basis for semantic notions such as tautology, contradiction, satisfiability, and entailment; they enable mechanical model checking and rigorous semantic comparison of formulas.

Reversal

Rejecting bivalence yields truth-value gaps (neither true nor false) or truth-value gluts (both true and false) in nonclassical logics, which reverses many classical inference patterns and requires revised semantic rules.

Boundary

The term refers to semantic evaluation within a specified logic and interpretation; it does not by itself settle metaphysical questions about truth, nor is it equivalent to probability, justification, or pragmatic acceptability.

Semantic Tension

There is tension between the simplicity of two-valued truth evaluations and richer frameworks (many-valued, supervaluationist, paraconsistent) that aim to model vagueness, indeterminacy, or paradox; choosing a scheme affects which inferences hold.

Synthesis

A truth value is the semantic tag assigned to a formula by a valuation within a specified logical framework; as the primitive outcome of semantic evaluation it structures notions of validity and equivalence while varying across logical systems.