The Logical Legacy of Nikolai Vasiliev and Modern Logic (Synthese Library Book 387)

Annotation This volume offers a wide range of both reconstructions of Nikolai Vasiliev's original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev's Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev's contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights Front Matter ....Pages i-viii Nikolai A. Vasiliev, His Life and Imaginary Logic Legacy (Valentin A. Bazhanov)....Pages 1-8 N.A. Vasiliev in the Context of Philosophical and Methodological Disputes of the Early Twentieth Century (G. V. Sorina)....Pages 9-17 Is Modern Logic Non-Aristotelian? (Jean-Yves Beziau)....Pages 19-41 Vasiliev and the Foundations of Logic (Otávio Bueno)....Pages 43-58 Vasiliev’s Ideas for Non-Aristotelian Logics: Insight Towards Paraconsistency (Itala Maria Loffredo D’Ottaviano, Evandro Luís Gomes)....Pages 59-77 Epicurus, Vasiliev and Aristotle on the Law of the Excluded Third (José Veríssimo Teixeira da Mata)....Pages 79-82 Modern Reconstruction of Vasiliev’s Logical Systems (Vladimir Markin)....Pages 83-95 Nikolai Vasiliev’s Imaginary Logic and Stable Meaning (Ivan Mikirtumov)....Pages 97-125 Vasiliev and the Foundations of Logical Laws (Elena D. Smirnova)....Pages 127-133 The Impact of N.A. Vasiliev’s Imaginary Logic on Epistemic and Relevance Logic (Werner Stelzner)....Pages 135-157 Generalized Vasiliev-Style Propositions (Dmitry Zaitsev)....Pages 159-167 Plurivalent Logics (Graham Priest)....Pages 169-179 On Sublogics in Vasiliev Fragment of the Logic Definable with A. Arruda’s Calculus V1 (Vladimir M. Popov, Vasily O. Shangin)....Pages 181-188 Vasiliev’s Clue to Mourdoukhay-Boltovskoy’s Hypersyllogistic (Vladimir L. Vasyukov)....Pages 189-198 Experimenting with Consistency (Juliana Bueno-Soler, Walter Carnielli)....Pages 199-221 Vladimir Markin, Dmitry Zaitsev, Editors. International Workshop Nikolai Vasiliev's Logical Legacy And The Modern Logic (moscow, Russia, October 2013)--preface. Includes Bibliographical References.