A Theory of Truth

The paradoxes about truth are the subject of extensive research. Developing an original approach, this book argues that we should diverge from classical logic and presents a number of formal theories of truth. Also included is a beginner-friendly introduction to semantic paradoxes, and a discussion of alternative non-classical theories.

How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly, and endorses principles like 'No sentence is both true and false' and 'No sentence is neither true nor false'. The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field's paracomplete approach, Ripley's nontransitive system and Zardini's contraction-free calculus.