Outstanding Contributions to Logic 18 Can Başkent Thomas Macaulay Ferguson Editors Graham Priest on Dialetheism and Paraconsistency Outstanding Contributions to Logic Volume 18 Editor-in-Chief Sven Ove Hansson, Division of Philosophy, KTH Royal Institute of Technology, Stockholm, Sweden More information about this series at http://www.springer.com/series/10033 ş Can Ba kent Thomas Macaulay Ferguson (cid:129) Editors Graham Priest on Dialetheism and Paraconsistency 123 Editors CanBaşkent ThomasMacaulay Ferguson Department ofComputer Science Cycorp University of Bath Austin, TX,USA Bath, UK SaulKripke Center NewYork,NY, USA ISSN 2211-2758 ISSN 2211-2766 (electronic) Outstanding Contributions to Logic ISBN978-3-030-25364-6 ISBN978-3-030-25365-3 (eBook) https://doi.org/10.1007/978-3-030-25365-3 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Coverphotocredit:©StevePyke ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Contents 1 Introduction to Graham Priest on Dialetheism and Paraconsistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Thomas Macaulay Ferguson and Can Başkent 2 Modal Meinongianism: Conceiving the Impossible . . . . . . . . . . . . . 3 Franz Berto 3 The Number of Logical Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Ross T. Brady 4 Respects for Contradictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Paul Égré 5 Hegel and Priest on Revising Logic . . . . . . . . . . . . . . . . . . . . . . . . 59 Elena Ficara 6 Paraconsistent or Paracomplete? . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Hartry Field 7 Priest’s Anti-Exceptionalism, Candrakīrti and Paraconsistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Koji Tanaka 8 Looting Liars Masking Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Diderik Batens 9 Inferential Semantics, Paraconsistency, and Preservation of Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Walter Carnielli and Abilio Rodrigues 10 A Model-Theoretic Analysis of Fidel-Structures for mbC. . . . . . . . 189 Marcelo E. Coniglio and Aldo Figallo-Orellano 11 Unity, Identity, and Topology: How to Make Donuts and Cut Things in Half. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 A. J. Cotnoir v vi Contents 12 Contradictory Information: Better Than Nothing? The Paradox of the Two Firefighters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 J. Michael Dunn and Nicholas M. Kiefer 13 Variations on the Collapsing Lemma . . . . . . . . . . . . . . . . . . . . . . . 249 Thomas Macaulay Ferguson 14 Dialetheic Conditional Modal Logic . . . . . . . . . . . . . . . . . . . . . . . . 271 Patrick Girard 15 Priest on Negation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Lloyd Humberstone 16 From Iff to Is: Some New Thoughts on Identity in Relevant Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Edwin Mares 17 The Difficulties in Using Weak Relevant Logics for Naive Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Erik Istre and Maarten McKubre-Jordens 18 ST, LP and Tolerant Metainferences . . . . . . . . . . . . . . . . . . . . . . . 383 Bogdan Dicher and Francesco Paoli 19 Annotated Natural Deduction for Adaptive Reasoning . . . . . . . . . . 409 Patrick Allo and Giuseppe Primiero 20 Denotation, Paradox and Multiple Meanings . . . . . . . . . . . . . . . . . 439 Stephen Read 21 Two Negations Are More than One . . . . . . . . . . . . . . . . . . . . . . . . 455 Greg Restall 22 Inconsistency and Incompleteness, Revisited. . . . . . . . . . . . . . . . . . 469 Stewart Shapiro 23 GP’s LP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Neil Tennant 24 Expanding the Logic of Paradox with a Difference-Making Relevant Implication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 Peter Verdée 25 On Non-transitive “Identity” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Heinrich Wansing and Daniel Skurt 26 At the Limits of Thought . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Zach Weber 27 Some Comments and Replies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Graham Priest Contents vii 28 Crossing Boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Graham Priest Graham Priest: Publications.... ..... .... .... .... .... .... ..... .. 691 Editors and Contributors About the Editors Can Başkent received his Ph.D. from the City University of New York in 2012. He subsequently worked as a postdoctoral researcher at IHPST, Paris, and INRIA andtheUniversityofBath. Currently, heisapostdoctoralresearcherinEthicalAI at Oxford Brookes University. His research interests include modal and non-classical logics and foundations of game theory. Thomas Macaulay Ferguson works as an ontologist for the Cyc artificial intel- ligence project and is an affiliate research scholar at the Saul Kripke Center at the City University of New York. He is the author of Meaning and Proscription in Formal Logic (Springer 2017) and, with Graham Priest, is coauthor of the sup- plemental Dictionary of Logic (Oxford University Press 2016). His research includes work on philosophical logic, metaphysics, and the philosophy of mathe- matics. Contributors Patrick Allo Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Oxford Internet Institute, University of Oxford, Oxford, UK Can Başkent Department of Computer Science, University of Bath, Bath, UK Diderik Batens Centre for Logic and Philosophy of Science, Ghent University, Ghent, Belgium Franz Berto Department of Philosophy, University of St Andrews, St Andrews, UK; Institute for Logic, Language and Computation (ILLC), University of Amsterdam, Amsterdam, The Netherlands ix x EditorsandContributors Ross T. Brady La Trobe University, Melbourne, VIC, Australia Walter Carnielli State University of Campinas, Campinas, Brazil Marcelo E. Coniglio Institute of Philosophy and the Humanities (IFCH), Centre forLogic,EpistemologyandtheHistoryofScience(CLE),UniversityofCampinas (UNICAMP), Campinas, Brazil A. J. Cotnoir University of St Andrews, St Andrews, Scotland Bogdan Dicher Centre for Philosophy of the University of Lisbon, Lisbon, Portugal J. Michael Dunn Indiana University, Bloomington, USA Paul Égré CNRS, ENS, EHESS, PSL University, Paris, France Thomas Macaulay Ferguson City University of New York, New York City, USA; Saul Kripke Center, New York, NY, USA; Cycorp, Austin, TX, USA Elena Ficara University of Paderborn, Paderborn, Germany Hartry Field Philosophy Department, New York University, New York, NY, USA AldoFigallo-Orellano CentreforLogic,EpistemologyandtheHistoryofScience (CLE), University of Campinas (UNICAMP), Campinas, Brazil; Department of Mathematics, National University of the South (UNS), Bahía Blanca, Argentina Patrick Girard University of Auckland, Auckland, New Zealand Lloyd Humberstone Department of Philosophy and Bioethics, Monash University, Melbourne, VIC, Australia Erik Istre Queensbury, USA Nicholas M. Kiefer Cornell University, Ithaca, USA Edwin Mares Victoria University of Wellington, Wellington, New Zealand Maarten McKubre-Jordens Christchurch, New Zealand FrancescoPaoli DepartmentofPedagogy,Psychology,Philosophy,Universityof Cagliari, Cagliari, Italy Graham Priest Department of Philosophy, The Graduate Center, City University of New York, New York, USA; Department of Philosophy, The University of Melbourne, Melbourne, Australia Giuseppe Primiero Department of Philosophy, University of Milan, Milan, Italy