Paraconsistency: Logic and Applications

1. Front Matter

   Pages i-viii

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2. Paraconsistency: Introduction

   • Koji Tanaka, Francesco Berto, Edwin Mares, Francesco Paoli

   Pages 1-12

3. Logic

   1. Front Matter

      Pages 13-13

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   2. Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic

      • Koji Tanaka

      Pages 15-25

   3. On Discourses Addressed by Infidel Logicians

      • Walter Carnielli, Marcelo E. Coniglio

      Pages 27-41

   4. Information, Negation, and Paraconsistency

      • Edwin D. Mares

      Pages 43-55

   5. Noisy vs. Merely Equivocal Logics

      • Patrick Allo

      Pages 57-79

   6. Assertion, Denial and Non-classical Theories

      • Greg Restall

      Pages 81-99

   7. New Arguments for Adaptive Logics as Unifying Frame for the Defeasible Handling of Inconsistency

      • Diderik Batens

      Pages 101-122

   8. Consequence as Preservation: Some Refinements

      • Bryson Brown

      Pages 123-139

   9. On Modal Logics Defining Jaśkowski’s D2-Consequence

      • Marek Nasieniewski, Andrzej Pietruszczak

      Pages 141-161

   10. FDE: A Logic of Clutters

       • R. E. Jennings, Y. Chen

       Pages 163-172

   11. A Paraconsistent and Substructural Conditional Logic

       • Francesco Paoli

       Pages 173-198

4. Applications

   1. Front Matter

      Pages 199-199

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   2. An Approach to Human-Level Commonsense Reasoning

      • Michael L. Anderson, Walid Gomaa, John Grant, Don Perlis

      Pages 201-222

   3. Distribution in the Logic of Meaning Containment and in Quantum Mechanics

      • Ross T. Brady, Andrea Meinander

      Pages 223-255

   4. Wittgenstein on Incompleteness Makes Paraconsistent Sense

      • Francesco Berto

      Pages 257-276

   5. Pluralism and “Bad” Mathematical Theories: Challenging our Prejudices

      • Michèle Friend

      Pages 277-307

   6. Arithmetic Starred

      • Chris Mortensen

      Pages 309-314

   7. Notes on Inconsistent Set Theory

      • Zach Weber

      Pages 315-328

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

• Applications in logic
• Articular Logic
• D2 consequense
• Equivocal Logic
• Liar Paradox
• Logical Paradoxes
• Logical Systems
• Paraconsistency
• Paraconsistent logic
• Philosophical Logic
• Philosophy of Computation
• Pluralist Mathemathics
• Routley Functor
• Set Theory
• Sorites
• Vagueness

• , Department of Philosophy, University of Auckland, Auckland, New Zealand

  Koji Tanaka

• , Department of Philosophy, University of Aberdeen, Aberdeen, United Kingdom

  Francesco Berto

• , Department of Philosophy, Victoria University of Wellington, Wellington, New Zealand

  Edwin Mares

• , Department of Education, University of Cagliari, Cagliari, Italy

  Francesco Paoli

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