This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions.
Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths.
Readers should understand the title of this book in a broad way, because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.
Cuprins
Chapter 1. Contradictions, from Consistency to Inconsistency (Walter Carnielli).- Chapter 2. The price of true contradictions about the world (Jonas R. Becker Arenhart).- Chapter 3. The possibility and fruitfulness of a debate on the Principle of Non-Contradiction (Luis Estrada-Gonzalez).- Chapter 4. Keeping Globally Inconsistent Scientific Theories Locally Consistent (Michele Friend).- Chapter 5. Title Not Available (Eduardo Barrio).- Chapter 6. Provided you’re not trivial: Adding defaults and paraconsistency to a formal model of explanation (David Gaytán).- Chapter 7. Para-Disagreement Logics and their Implementation through Embedding in Coq and SMT (Bruno Woltzenlogel Paleo).- Chapter 8. Asymptotic quasi-completeness and ZFC (Marco Panza).- Chapter 9. Interpretation and Truth in Set Theory (Rodrigo A. Freire).- Chapter 10. Coherence of the product law for independent continuous events (Daniele Mundici).- Chapter 11. A local-global principle for the real continuum (José Carlos Magossi).- Chapter 12. Quantitative Logic Reasoning (Marcelo Finger).- Chapter 13. Reconciling first-order logic to algebra (Walter Carnielli).- Chapter 14. Plug and play negations (Sergio Marcelino).
Despre autor
Walter Carnielli is professor of logic and philosophy at the Department of Philosophy, and a former Director of the Centre for Logic, Epistemology and the History of Science of the University of Campinas, Brazil. He received a Ph D in Mathematics from the University of Campinas and held research positions at the University of São Paulo, University of California Berkeley, University of Münster, University of Bonn, Superior Technical Institute Lisbon, and Université du Luxembourg. He has published several books and more than 100 scientific papers in combinatorics, proof theory, semantics for nonclassical logics, recursion theory and computability, set theory, modal logics, combinations of logics, and foundations of paraconsistent logics. His concerns involve the expansion of reasoning horizons by non-classical logics, including the connections between logic, probability and game theory, as well as the philosophical interpretation of non-classical logics. He is executive editor of the IGPL Journal (Oxford Journals), editor of The Non-classical Logics Corner of the Journal of Logic and Computation (together with Heinrich Wansing) and member of the editorial board of several other journals. Carnielli is a recipient of the Jabuti Prize, Brazil’s most prestigious literary prize.
Jacek Malinowski is professor of logic and philosophy at the Instituite of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland. He received a Master degree in Mathamatic from the University of Łódź, Poland, and Ph D and habilitation in Philosophy at Institute of Philosophy and Sociology, Polish Academy of Sciences. He held research positions at Free Univeristy of Brussels, Humboltd University in Berlin, University of Leipzig, the Netherland Institute of Advanced Study in Wasenaar. He publish papers in algebraic logics, quantuum logics, logical pragmatics. He is active as editor-in-chief of Studia Logica what he consider his main professional concern.
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