A two-valued, ordered-pair semantics — generalized to n-tuple semantics for every n — that explains the extra truth values of many-valued logics such as Priest's Logic of Paradox (LP) and Kleene's strong three-valued logic (K3) using only classical truth and falsity plus an epistemic or semantic ingredient, following Haack's deflationary strategy. Students learn how Clemens' propositional ordered-pair semantics is extended to quantified languages and given a multi-agent epistemic reading, and how it applies to informative contradictions and to mixed consequence relations.
Many-valued logics add truth values beyond 'true' and 'false', raising the question of what those extra values mean. Following Susan Haack's strategy of explaining them away, this paper develops an o…