 Suszko’s Thesis is substantiated by a rigorous proof (the Suszko Reduction) showing that every structural Tarskian consequence relation and therefore also every structural Tarskian many-valued propositional logic is characterized by a bivalent semantics. (Note also that Richard Routley (1975) has shown that every logic based on a λ-categorical language has a sound and complete bivalent possible worlds semantics.) The dichotomy between designated values and values which are not designated and its use in the definition of entailment plays a crucial role in the Suszko Reduction. Nevertheless, while it seems quite natural to construe the set of designated values as a generalization of the classical truth value \(T\) in some of its significant roles, it would not always be adequate to interpret the set of non-designated values as a generalization of the classical truth value \(F\). The point is that in a many-valued logic, unlike in classical logic, “not true” does not always mean “false” (cf., e.g., the above interpretation of Kleene’s logic, where sentences can be neither true nor false).