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Intro; Contents; Contradictions, from Consistency to Inconsistency; The Price of True Contradictions About the World; 1 Introduction; 2 Contradictions in Concrete Reality; 3 Problems with Real Contradictions; 3.1 The Most Common Objection: Negative Facts; 3.2 Dictating Science from the Armchair?; 3.3 Unequal Treatment of Observable and Unobservable Contradictory Objects; 3.4 The Solution of Aporias and Mutilation of Reason; 3.5 Contradictions and Theoretical Virtues; 4 Final Remarks: Where Can We Find True Contradictions?; References
The Possibility and Fruitfulness of a Debate on the Principle of Non-contradiction1 Introduction; 2 Aristotle's Principles of Non-contradiction; 3 Some Distinctions; 4 Aristotle on Demonstration, Refutation and the Possibility of a Fruitful Debate on PNC; 5 Aristotle's Refutation of Heracliteans; 6 The Consequences of Refutations for Demonstrators; 7 Methodologists and the Fruitfulness of the Debate; 8 Conclusions; References; Keeping Globally Inconsistent Scientific Theories Locally Consistent; 1 Introduction; 2 Trivialism and Modern Mathematics
3 Chunk and Permeate and General Remarks on Extending it4 Bundles: Local and Global Consistency; 5 Bundles and Chunk and Permeate; 6 Generalizing Further: Bundled Chunk and Permeate to Reconstruct Scientific Reasoning; 7 Some Preliminaries from Empirical Inconsistent Science; 7.1 Different Groups of Propositions; 7.2 Global and Local (In)Consistency; 8 A Scientific Example of Bundled Chunk and Permeate; 8.1 The Case Study; 8.2 Nuclear Physics and BC 9 Problems with Global Inconsistency in Science; 10 Philosophical Conclusions; References; What is a Paraconsistent Logic?; 1 Introduction
2 Different Inferential Ways of Being Paraconsistent2.1 Inferences and Meta-Inferences; 2.2 Explosion, Revisited; 3 Study Cases; 3.1 Matrix Logics; 3.2 q-Matrix Logics and p-Matrix Logics; 4 Philosophical Reflections; 4.1 Answers to Some Possible Objections; 5 Conclusion; References; Provided You're not Trivial: Adding Defaults and Paraconsistency to a Formal Model of Explanation; 1 Our Roadmap; 2 Example of Some Difficulties in Modeling Explanations; 3 Building Rules and Doxastic Systems on GMD; 4 Building a Default Theory on GMD; 5 Building a Paraconsistent Default Theory on GMD
6 Explanations in the GMD Formal Framework7 Concluding Remarks; References; Para-Disagreement Logics and Their Implementation Through Embedding in Coq and SMT; 1 Introduction; 2 Syntax; 3 Semantics; 4 Methods for Information Aggregation and Disagreement Resolution; 4.1 Consensus; 4.2 Dictatorship; 4.3 Expertise-Restricted Trust; 4.4 Voting; 5 Embedding of Para-Disagreement Logics in Coq; 6 Embedding of Para-Disagreement Logics in SMT; 7 Related Work; 8 Conclusion; References; Asymptotic Quasi-completeness and ZFC; 1 Introduction; 2 Modern History of the Singular Cardinals
The Possibility and Fruitfulness of a Debate on the Principle of Non-contradiction1 Introduction; 2 Aristotle's Principles of Non-contradiction; 3 Some Distinctions; 4 Aristotle on Demonstration, Refutation and the Possibility of a Fruitful Debate on PNC; 5 Aristotle's Refutation of Heracliteans; 6 The Consequences of Refutations for Demonstrators; 7 Methodologists and the Fruitfulness of the Debate; 8 Conclusions; References; Keeping Globally Inconsistent Scientific Theories Locally Consistent; 1 Introduction; 2 Trivialism and Modern Mathematics
3 Chunk and Permeate and General Remarks on Extending it4 Bundles: Local and Global Consistency; 5 Bundles and Chunk and Permeate; 6 Generalizing Further: Bundled Chunk and Permeate to Reconstruct Scientific Reasoning; 7 Some Preliminaries from Empirical Inconsistent Science; 7.1 Different Groups of Propositions; 7.2 Global and Local (In)Consistency; 8 A Scientific Example of Bundled Chunk and Permeate; 8.1 The Case Study; 8.2 Nuclear Physics and BC 9 Problems with Global Inconsistency in Science; 10 Philosophical Conclusions; References; What is a Paraconsistent Logic?; 1 Introduction
2 Different Inferential Ways of Being Paraconsistent2.1 Inferences and Meta-Inferences; 2.2 Explosion, Revisited; 3 Study Cases; 3.1 Matrix Logics; 3.2 q-Matrix Logics and p-Matrix Logics; 4 Philosophical Reflections; 4.1 Answers to Some Possible Objections; 5 Conclusion; References; Provided You're not Trivial: Adding Defaults and Paraconsistency to a Formal Model of Explanation; 1 Our Roadmap; 2 Example of Some Difficulties in Modeling Explanations; 3 Building Rules and Doxastic Systems on GMD; 4 Building a Default Theory on GMD; 5 Building a Paraconsistent Default Theory on GMD
6 Explanations in the GMD Formal Framework7 Concluding Remarks; References; Para-Disagreement Logics and Their Implementation Through Embedding in Coq and SMT; 1 Introduction; 2 Syntax; 3 Semantics; 4 Methods for Information Aggregation and Disagreement Resolution; 4.1 Consensus; 4.2 Dictatorship; 4.3 Expertise-Restricted Trust; 4.4 Voting; 5 Embedding of Para-Disagreement Logics in Coq; 6 Embedding of Para-Disagreement Logics in SMT; 7 Related Work; 8 Conclusion; References; Asymptotic Quasi-completeness and ZFC; 1 Introduction; 2 Modern History of the Singular Cardinals