This book provides a comprehensive overview of different logics from a metainferential standpoint. It starts with a metainferential presentation of Classical Logic, and then moves onto other systems where one or more structural metainferences fail. These logics maybe considered non-classical in a robust sense, since they allow to build theories which are non-transitive, non-reflexive, non-monotonic and non-contractive. In some other sense, though, they also preserve many desirable features of classical logics, and thus may have an advantage over other non-classical alternatives. The authors show how these logics can be characterized both model and proof-theoretically. Besides some standard inferential properties, emphasis is placed on metainferential theorems, some of them quite standard, such as Cut-elimination, and other more idiosyncratic, such as metainferential Soundness and Completeness. It ends with a philosophical chapter which intends to illustrate some of these logics' applications, mainly regarding non-classical treatments of paradoxes. Each chapter comes with exercises which help fix the central concepts, learn to use some of the formal tools, and problematize the philosophical issues at stake. This book is aimed to anyone interested in the question of reasoning, argumentation and theory-building in the presence of contradictions, paradoxes and other puzzles.

The only book to provide a comprehensive introduction to the most popular logics The first book to systematically study the failures of classical metainferences in the S-valuationist framework Covers the formal properties and the main applications of nontransitive and nonreflexive logics

Autorentext

Paula Teijeiro is an Assistant Researcher at CONICET. She graduated from the University of Buenos Aires, from where she also subsequently obtained her PhD. Her main interests revolve around non-classical logics, both from a proof theory standpoint, as well as from a model theoretic one. In particular, she studies non-classical logics as they are used to deal with truth and vagueness-related paradoxes, both in formal theories and in natural language. Lately, her research focuses on theories in which some classically valid metainferences fail, such as substructural logics, and s-valuationism. She is a member of the BA Logic Group and a professor at UBA, where she teaches different logic courses. Some of her more recent publications include “Vague connectives” (2022), published in Philosophical Studies, “Metainferential paraconsistency” (2022), joint work with Bruno Da Re and Mariela  Rubin, published in in Logic and Logical Philosophy; and “Derivability and Metainferential validity” (2021), joint work with Bruno Da Re and Damián Szmuc, published in Journal of Philosophical logic.

Eduardo Alejandro Barrio is a Superior Researcher at CONICET. He graduated from the University of Buenos Aires, from where he also subsequently obtained his PhD. He is a full professor (tenure track) at University of Buenos Aires and a member of the Buenos Aires Logic Group (BA-LOGIC). He works in non-classical logics and philosophy of logic. He is mainly interested in substructural logics and metainferences. His most important papers have high international impact, mainly published by Journal of Philosophical Logic, Review of Symbolic Logic, Studia Logica, Analysis, Synthese, Journal of Applied Non-Classical Logics and Logical Journal of IGPL. He is Associate Editor in Analysis (OUP). He has published three books: La Verdad Desestructurada (Buenos Aires, EUDEBA, 1998), Paradojas, Paradojas y más Paradojas (Londres, College PU, 2014) and La Lógica de la Verdad (Buenos Aires, EUDEBA, 2014). He has also been a guest editor in Logical Journal of IGPL (in two times) and in Journal of Philosophical Logic.

Inhalt

1 Introduction (Paula Teijeiro & Eduardo Alejandro Barrio).- 2 Classical Logic (Bruno Da Ré, Damián Enrique Szmuc, & Paula Teijeiro).- 3 Non-Transitive Logics (Agustina Borzi & Camillo Fiore).- 4 Non-Reflexive Logics (Joaquín S. Toranzo Calderón & Martina Zirattu).- 5 Non-Contractive and Non-Monotonic Logics (Mariela Rubin, Miguel Álvarez Lisboa, & Yll Buzoku).- 6 Philosophical Applications (Edson Bezerra & Jonathan Erenfryd).