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Paraconsistent Reasoning in Science and Mathematics: Introduction; 1 Holger Andreas and Peter Verdée: Adaptive Proofs for Networks of Partial Structures; 2 Franzesco Berto: Ceteris Paribus Imagination; 3 Bryson Brown: On the Preservation of Reliability; 4 Luis Estrada-González: Prospects for Triviality; 5 Andreas Kapsner: On Gluts in Mathematics and Science; 6 Carlos A. Oller: Contradictoriness, Paraconsistent Negation and Non-intended Models of Classical Logic; 7 Hitoshi Omori: From Paraconsistent Logic to Dialetheic Logic; 8 Martin Pleitz: Paradoxes of Expression
9 Corry Shores: Dialetheism in the Structure of Phenomenal Time10 Fenner S. Tanswell: Saving Proof from Paradox: Gödel's Paradox and the Inconsistency of Informal Mathematics; 11 Heinrich Wansing and Sergei Odintsov: On the Methodology of Paraconsistent Logic; 12 Zach Weber: Paraconsistent Computation and Dialetheic Machines; References; Adaptive Proofs for Networks of Partial Structures; 1 How to Reason with Inconsistent Theories?; 2 Networks of Partial Structures; 2.1 Partial Structures and Their Extensions; 2.2 Instances and Applications of Axioms; 2.3 Modular Semantics; 2.4 Local Worlds
2.5 Preferred Global Worlds2.6 The Inference Relation; 2.7 Prioritized Axiomatic Theories; 2.8 A Simple Example; 2.9 Modular Semantics Inference in Pure First Order Terms; 2.10 The Example Revisited: Now in First Order Terms; 3 Adaptive Proofs; 3.1 Adaptive Logics: An Introduction; 3.2 The Semantics of the Relevant Classes of Adaptive Logics; 3.3 Adaptive Logics for the Modular Semantics Inference Relations; 3.4 Adaptive Proofs: Definitions; 3.5 Adaptive Proofs: Example; 4 Conclusion; References; Inconsistency in Ceteris Paribus Imagination; 1 Intro: Imagination as a Modal
2 Impossible Worlds3 Imagination as Ceteris Paribus Activity; 4 A Semantics for Imagination; 5 Constraints; 6 Cotenability and Imaginative Modus Ponens; 7 Indicative or Subjunctive?; References; On the Preservation of Reliability; 1 Preservation of Reliability; 2 Other Examples:; 3 Preservation of Reliability, Scientific Revolutions and Scientific Realism; 4 Conclusion; References; Prospects for Triviality; 1 Introduction. The Anathema Against Triviality in Mathematics; 2 Dunn's Trivialization Result; 2.1 Terminological Preliminaries; 2.2 Sketch of Dunn's Proof
3 Degenerate Toposes and Dunn's Result3.1 Categorial Preliminaries; 3.2 Dunn's Result on the Light of Degenerate Toposes; 4 Summary and Conclusions; References; On Gluts in Mathematics and Science; 1 Introduction; 2 Epistemic Truth Values; 3 The Early Calculus; 4 Darwin and Kelvin on the Age of the Earth; 5 Conclusion; References; Contradictoriness, Paraconsistent Negation and Non-intended Models of Classical Logic; 1 Introduction; 2 ``Genuine'' and Paraconsistent Negations; 3 Classical Negation and Non-standard Models of Classical Logic
9 Corry Shores: Dialetheism in the Structure of Phenomenal Time10 Fenner S. Tanswell: Saving Proof from Paradox: Gödel's Paradox and the Inconsistency of Informal Mathematics; 11 Heinrich Wansing and Sergei Odintsov: On the Methodology of Paraconsistent Logic; 12 Zach Weber: Paraconsistent Computation and Dialetheic Machines; References; Adaptive Proofs for Networks of Partial Structures; 1 How to Reason with Inconsistent Theories?; 2 Networks of Partial Structures; 2.1 Partial Structures and Their Extensions; 2.2 Instances and Applications of Axioms; 2.3 Modular Semantics; 2.4 Local Worlds
2.5 Preferred Global Worlds2.6 The Inference Relation; 2.7 Prioritized Axiomatic Theories; 2.8 A Simple Example; 2.9 Modular Semantics Inference in Pure First Order Terms; 2.10 The Example Revisited: Now in First Order Terms; 3 Adaptive Proofs; 3.1 Adaptive Logics: An Introduction; 3.2 The Semantics of the Relevant Classes of Adaptive Logics; 3.3 Adaptive Logics for the Modular Semantics Inference Relations; 3.4 Adaptive Proofs: Definitions; 3.5 Adaptive Proofs: Example; 4 Conclusion; References; Inconsistency in Ceteris Paribus Imagination; 1 Intro: Imagination as a Modal
2 Impossible Worlds3 Imagination as Ceteris Paribus Activity; 4 A Semantics for Imagination; 5 Constraints; 6 Cotenability and Imaginative Modus Ponens; 7 Indicative or Subjunctive?; References; On the Preservation of Reliability; 1 Preservation of Reliability; 2 Other Examples:; 3 Preservation of Reliability, Scientific Revolutions and Scientific Realism; 4 Conclusion; References; Prospects for Triviality; 1 Introduction. The Anathema Against Triviality in Mathematics; 2 Dunn's Trivialization Result; 2.1 Terminological Preliminaries; 2.2 Sketch of Dunn's Proof
3 Degenerate Toposes and Dunn's Result3.1 Categorial Preliminaries; 3.2 Dunn's Result on the Light of Degenerate Toposes; 4 Summary and Conclusions; References; On Gluts in Mathematics and Science; 1 Introduction; 2 Epistemic Truth Values; 3 The Early Calculus; 4 Darwin and Kelvin on the Age of the Earth; 5 Conclusion; References; Contradictoriness, Paraconsistent Negation and Non-intended Models of Classical Logic; 1 Introduction; 2 ``Genuine'' and Paraconsistent Negations; 3 Classical Negation and Non-standard Models of Classical Logic