© 2018

Contradictions, from Consistency to Inconsistency

  • Walter Carnielli
  • Jacek Malinowski
  • Investigates what is beyond the Principle of Non-Contradiction

  • Details groundbreaking ideas on consistency and inconsistency

  • Explores the foundations of reasoning, including logical systems and philosophical considerations


Part of the Trends in Logic book series (TREN, volume 47)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Walter Carnielli, Jacek Malinowski
    Pages 1-9
  3. Jonas R. Becker Arenhart
    Pages 11-31
  4. Luis Estrada-González, Maria del Rosario Martínez-Ordaz
    Pages 33-51
  5. Michèle Friend, Maria del Rosario Martínez-Ordaz
    Pages 53-88
  6. Eduardo Barrio, Federico Pailos, Damian Szmuc
    Pages 89-108
  7. David Gaytán, Itala M. Loffredo D’Ottaviano, Raymundo Morado
    Pages 109-138
  8. Mirna Džamonja, Marco Panza
    Pages 159-182
  9. Rodrigo A. Freire
    Pages 183-205
  10. Olivier Rioul, José Carlos Magossi
    Pages 213-240
  11. Marcelo Finger
    Pages 241-271
  12. Walter Carnielli, Hugo Luiz Mariano, Mariana Matulovic
    Pages 273-305
  13. Sérgio Marcelino, Carlos Caleiro, Umberto Rivieccio
    Pages 307-322
  14. Walter Carnielli, Jacek Malinowski
    Pages C1-C1

About this book


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.


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

Editors and affiliations

  • Walter Carnielli
    • 1
  • Jacek Malinowski
    • 2
  1. 1.Department of Philosophy, Centre for Logic, Epistemology and the History of ScienceUniversity of Campinas-UnicampCampinasBrazil
  2. 2.Institute of Philosophy and SociologyPolish Academy of SciencesWarsawPoland

About the editors

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.

Bibliographic information

  • Book Title Contradictions, from Consistency to Inconsistency
  • Editors Walter Carnielli
    Jacek Malinowski
  • Series Title Trends in Logic
  • Series Abbreviated Title Trends in Logic
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-98796-5
  • Softcover ISBN 978-3-030-07534-7
  • eBook ISBN 978-3-319-98797-2
  • Series ISSN 1572-6126
  • Series E-ISSN 2212-7313
  • Edition Number 1
  • Number of Pages VI, 322
  • Number of Illustrations 22 b/w illustrations, 10 illustrations in colour
  • Topics Logic
    Mathematical Logic and Foundations
  • Buy this book on publisher's site


“‘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)