Contradictions, from Consistency to Inconsistency

1. Front Matter

   Pages i-vi

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2. Contradictions, from Consistency to Inconsistency

   • Walter Carnielli, Jacek Malinowski

   Pages 1-9

3. The Price of True Contradictions About the World

   • Jonas R. Becker Arenhart

   Pages 11-31

4. The Possibility and Fruitfulness of a Debate on the Principle of Non-contradiction

   • Luis Estrada-González, Maria del Rosario Martínez-Ordaz

   Pages 33-51

5. Keeping Globally Inconsistent Scientific Theories Locally Consistent

   • Michèle Friend, Maria del Rosario Martínez-Ordaz

   Pages 53-88

6. What is a Paraconsistent Logic?

   • Eduardo Barrio, Federico Pailos, Damian Szmuc

   Pages 89-108

7. 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

8. Para-Disagreement Logics and Their Implementation Through Embedding in Coq and SMT

   • Bruno Woltzenlogel Paleo

   Pages 139-158

9. Asymptotic Quasi-completeness and ZFC

   • Mirna Džamonja, Marco Panza

   Pages 159-182

10. Interpretation and Truth in Set Theory

    • Rodrigo A. Freire

    Pages 183-205

11. Coherence of the Product Law for Independent Continuous Events

    • Daniele Mundici

    Pages 207-212

12. A Local-Global Principle for the Real Continuum

    • Olivier Rioul, José Carlos Magossi

    Pages 213-240

13. Quantitative Logic Reasoning

    • Marcelo Finger

    Pages 241-271

14. Reconciling First-Order Logic to Algebra

    • Walter Carnielli, Hugo Luiz Mariano, Mariana Matulovic

    Pages 273-305

15. Plug and Play Negations

    • Sérgio Marcelino, Carlos Caleiro, Umberto Rivieccio

    Pages 307-322

16. Correction to: Contradictions, from Consistency to Inconsistency

    • Walter Carnielli, Jacek Malinowski

    Pages C1-C1

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.

• Principle of Explosion
• Paraconsistent Logics
• Logics of Formal Inconsistency
• Consistency
• Inconsistency
• Logic for Computer Science
• Logic and Philosophy of Science
• Negation
• Contradictions

“‘Contradictions, from Consistency to Inconsistency’ is a collection of interesting papers in the study of the notions of contradiction, inconsistency and triviality. … Carnielli and Malinowski have made it sure that a broad range of readers will benefit from the close study of many of its chapters. … The book provides us with papers for mathematically-oriented readers as well.” (Pedro Merlussi, Studia Logica, Vol. 107, 2019)

• Department of Philosophy, Centre for Logic, Epistemology and the History of Science, University of Campinas-Unicamp, Campinas, Brazil

  Walter Carnielli

• Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland

  Jacek Malinowski

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 PhD 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 PhD 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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