Contradictions, from Consistency to Inconsistency

✍ Scribed by Walter Carnielli, Jacek Malinowski

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 323
• Series: Trends in Logic 47
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-vi
Contradictions, from Consistency to Inconsistency (Walter Carnielli, Jacek Malinowski)....Pages 1-9
The Price of True Contradictions About the World (Jonas R. Becker Arenhart)....Pages 11-31
The Possibility and Fruitfulness of a Debate on the Principle of Non-contradiction (Luis Estrada-González, María del Rosario Martínez-Ordaz)....Pages 33-51
Keeping Globally Inconsistent Scientific Theories Locally Consistent (Michèle Friend, María del Rosario Martínez-Ordaz)....Pages 53-88
What is a Paraconsistent Logic? (Eduardo Barrio, Federico Pailos, Damian Szmuc)....Pages 89-108
Provided You’re not Trivial: Adding Defaults and Paraconsistency to a Formal Model of Explanation (David Gaytán, Itala M. Loffredo D’Ottaviano, Raymundo Morado)....Pages 109-138
Para-Disagreement Logics and Their Implementation Through Embedding in Coq and SMT (Bruno Woltzenlogel Paleo)....Pages 139-158
Asymptotic Quasi-completeness and ZFC (Mirna Džamonja, Marco Panza)....Pages 159-182
Interpretation and Truth in Set Theory (Rodrigo A. Freire)....Pages 183-205
Coherence of the Product Law for Independent Continuous Events (Daniele Mundici)....Pages 207-212
A Local-Global Principle for the Real Continuum (Olivier Rioul, José Carlos Magossi)....Pages 213-240
Quantitative Logic Reasoning (Marcelo Finger)....Pages 241-271
Reconciling First-Order Logic to Algebra (Walter Carnielli, Hugo Luiz Mariano, Mariana Matulovic)....Pages 273-305
Plug and Play Negations (Sérgio Marcelino, Carlos Caleiro, Umberto Rivieccio)....Pages 307-322

✦ Subjects

Philosophy; Logic; Ontology; Mathematical Logic and Foundations