This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth.

This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, andapplications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes

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Section I: Front Matter.- Chapter 1. Introduction Hitoshi Omori, Can Başkent, and Thomas Macaulay Ferguson.- Chapter 2. Scientific Autobiography Graham Priest.- Section II: Paradoxes, Consistency, and Dialetheism.- Chapter 3. Priest on Paradoxes of Truth and Sets Hartry Field.- Chapter 4. Denotation and Paradox Stephen Read.- Chapter 5. Why Are There Paradoxes?: Priest Inclosures, Lawvere Fixed Points, and the Inconsistency of the World Zach Weber.- Chapter 6. Comprehension, Fixed Points and Paradox Greg Restall.- Chapter 7. Inconsistency, Completeness, and Reflection Stewart Shapiro.- Chapter 8. Contradictory Information: Sometimes Better Than Nothing J. Michael Dunn.- Chapter 9. Into the Epistemological Suppositions of Dialetheism Diderik Batens.- Section III: Metaphysics, Ontology, and Noneism.- Chapter 10. On Unity and Oneness Aaron Cotnoir.- Chapter 11. Modal Meinongianism and the Logic of Intentionality Francesco Berto.- Chapter 12. On Non-Transitive « Identity » Heinrich Wansing.- Chapter 13. The Number of Logical Values Ross Brady.- Chapter 14. What Could Be a Falsity Maker for the Principle of Non-Contradiction ? Walter Carnielli and Abilio Rodrigues.- Chapter 15. Dialethic Modal Logic Patrick Girard.- Chapter 16. Propositional Surrogates and Quantifiers Marcelo Coniglio.- Section IV: Meaning, Language, and Logic.- Chapter 17. Consistency and Non-Triviality as Success-Words: Two Perspectives Patrick Allo.- Chapter 18. Assertion, Denial, and the Meaning of Connectives Francesco Paoli.- Chapter 19. Radical Foundations and Verbal Disputes Toby Meadows.- Chapter 20. Ambivalence and Contradiction Paul Egré.- Chapter 21. Hegel and Priest on Revising Logic Elena Ficara.- Chapter 22. Logic is Belief Revision Koji Tanaka.- Chapter 23. Priest on Negation Lloyd Humberstone.- Chapter 24. Deviating from Classical Logic Leon Horsten.- Chapter 25. Logics Need No Passport ! João Marcos.- Section V: Proof Theory, Model Theory, and Paraconsistency.- Chapter 26. On Core Logic Neil Tennant.- Chapter 27. Cut Elimination in Contraction Free Logics Maarten McKubre-Jordens and Erik Istre.- Chapter 28. Annotated Natural Deduction for Adaptive Reasoning Giuseppe Primiero.- Chapter 29. Plurivalence and Paraconsistency by Default Thomas Macaulay Ferguson.- Chapter 30. Implication in LP Barteld Kooi and Allard Tamminga.- Chapter 31. Game Semantics for LPs Can Başkent.- Chapter 32. Relevance and Dialetheism: Separating Truth and Consequences Edwin Mares.- Chapter 33. Relevant Entailment and Deductive Implication for Dialetheists Peter Verdée.- Section VI: Back Matter.- Chapter 34. Replies to Contributions Graham Priest.- Chapter 35. Bibliography of Graham Priest’s Work in Logic.