Contradictions, from Consistency to Inconsistency [electronic resource] /
Carnielli, Walter.editor.
Malinowski, Jacek.editor.
This volume investigates what is beyond the Principle of Non-Contradiction. It features 13 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.
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).
This volume investigates what is beyond the Principle of Non-Contradiction. It features 13 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.
Logic.
Ontology.
Mathematical logic.
Logic.
Ontology.
Mathematical Logic and Foundations.