Volume 3 2006

The Age of Alternative Logics

Assessing Philosophy of Logic and Mathematics Today

ISBN: 978-1-4020-5011-4 (Print) 978-1-4020-5012-1 (Online)

Table of contents (21 chapters)

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  1. Proof, Knowledge and Computation

    1. Front Matter

      Pages 10-10

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      Pages 1-7

      Introduction: Alternative Logics and Classical Concerns

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      Pages 11-23

      Epistemic Models, Logical Monotony and Substructural Logics

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      Pages 25-36

      Semantics as Based on Inference

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      Pages 37-49

      Effectiveness

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      Pages 51-73

      Does Gödel's Incompleteness Theorem Prove that Truth Transcends Proof?

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      Pages 75-86

      Transpositions

  2. Truth Values Beyond Bivalence

    1. Front Matter

      Pages 88-88

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      Pages 89-101

      Many-Valued and Kripke Semantics

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      Pages 103-120

      The Logic of Complementarity

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      Pages 121-136

      Semantics for Naive Set Theory in Many-Valued Logics

  3. Category-Theoretic Structures

    1. Front Matter

      Pages 138-138

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      Pages 139-149

      Continuity and Logical Completeness: An Application of Sheaf Theory and Topoi

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      Pages 151-161

      What is Categorical Structuralism?

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      Pages 163-179

      Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism

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      Pages 181-192

      Categories, Sets and the Nature of Mathematical Entities

  4. Independence, Evaluation Games and Imperfect Information

    1. Front Matter

      Pages 194-194

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      Pages 195-219

      Truth, Negation and Other Basic Notions of Logic

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      Pages 221-241

      Signalling in IF Games: A Tricky Business

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      Pages 243-259

      Independence-Friendly Logic and Games of Incomplete Information

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      Pages 261-281

      IF and Epistemic Action Logic

  5. Dialogue and Pragmatics

    1. Front Matter

      Pages 284-284

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      Pages 285-297

      Naturalizing Dialogic Pragmatics

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      Pages 299-310

      Logic as a Tool of Science Versus Logic as a Scientific Subject

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      Pages 311-334

      Non-Normal Dialogics for a Wonderful World and More

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