Studies in Universal Logic Francine F. Abeles Mark E. Fuller Editors Modern Logic 1850 –1950, East and West Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council, Rio de Janeiro, Brazil) Editorial Board Members Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, USA) Razvan˘ Diaconescu (Romanian Academy, Bucharest, Romania) Josep Maria Font (University of Barcelona, Barcelona, Spain) Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France) Arnold Koslow (City University of New York, New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Łód´z, Łód´z, Poland) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University Tübingen, Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia) This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers. More information about this series at http://www.springer.com/series/7391 Francine F. Abeles • Mark E. Fuller Editors Modern Logic 1850-1950, East and West Editors Francine F. Abeles Mark E. Fuller Departments of Mathematics and Computer University of Wisconsin Science Janesville, WI Kean University USA Union, NJ USA ISSN 2297-0282 ISSN 2297-0290 (electronic) Studies in Universal Logic ISBN 978-3-319-24754-0 ISBN 978-3-319-24756-4 (eBook) DOI 10.1007/978-3-319-24756-4 Library of Congress Control Number: 2016939218 Mathematics Subject Classification (2010): 01A55, 01A60, 03A05, 03F03, 03G25 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com) Contents Introduction ............................................................................ 1 Francine F. Abeles and Mark E. Fuller Preface and Prospectus to a planned “History vs. Philosophy of Logic” Text........................................................................... 5 Irving H. Anellis The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen ................................................... 35 Irving H. Anellis and Francine F. Abeles Logic and Argumentation in Belgium: The Role of Leo Apostel ................. 99 Jean Paul Van Bendegem Tarski’s Recantation: Reading the Postscript to “Wahrheitsbegriff” ............ 119 Philippe de Rouilhan Paradox of Analyticity and Related Issues .......................................... 135 Jan Wolenski´ Naturalizing Natural Deduction ...................................................... 139 David DeVidi and Herbert Korté Category Theory and the Search for Universals: A Very Short Guide for Philosophers ........................................................................ 159 Alberto Peruzzi On the Way to Modern Logic: The Case of Polish Logic .......................... 183 Roman Murawski Russian Origins of Non-Classical Logics ............................................ 197 Valentin A. Bazhanov Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within ........................................................ 205 Vladik Kreinovich v vi Contents On Normalizing Disjunctive Intermediate Logics .................................. 237 Jonathan P. Seldin A Natural Axiom System for Boolean Algebras with Applications ............... 249 R.E. Hodel Contributors Francine F. Abeles is Professor Emerita at Kean University in Union, NJ, USA. For the ten years beforehand, she was Distinguished Professor of Mathematics and Computer Science and head of the graduate programs (master’s level) in mathematics, computing, statistics, and mathematics education. She has co-edited a proceedings of the Canadian Society for The History and Philosophy of Mathematics, and edited three volumes in the pamphlets of Lewis Carroll series for the University Press of Virginia. Dr. Abeles wrote a chapter on Charles L. Dodgson’s work in voting theory in Lewis Carroll Observed,a chapter on his mathematical work in yours very sincerely C. L. Dodgson (alias “Lewis Carroll”), a chapter on the popularizers of mathematics Martin Gardner, Richard Proctor, and Charles Dodgson in A Bouquet for The Gardner, and a chapter on Dodgson’s work in logic in volume 6 of Logica Universalis, “Toward a Visual Proof System: Lewis Carroll’s Method of Trees”. She is the author of nearly one hundred papers in journals on topics in geometry, number theory, voting theory, linear algebra, logic, and their history, most recently: “Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication” (History and Philosophy of Logic 35 (1), 2014, 24-37) and “Chiò’s and Dodgson’s Determinantal Identities” (Linear Algebra and Its Applications 454, 2014, 130-137). Dr. Abeles was a member of the editorial board and Reviews Editor of the international journal, Modern Logic and its successor, The Review of Modern Logic. Currently she is a member of the Publications Committee of The Lewis Carroll Society of North America and managing trustee of the Morton N. Cohen Publications Trust. A recipient of a grant from the American Philosophical Society and numerous faculty research grants from the State of New Jersey, she received an award from Kean University for distinguished research and a leadership award from Stevens Institute of Technology. Valentin A. Bazhanov is Chairperson in Philosophy at Ulyanovsk State University, a leading researcher at Tomsk State University, and member of the Russian Basic Research Foundation and the Russian Foundation for Humanities expertise committees. His major works include a biography of the logician, N.A.Vasiliev (1880–1940), Nauka, 1988, as well as the following: The Completeness of Quantum Theory, Kazan Univ. Press, 1983; Science as Self-Reflexive System, Kazan. Univ. Press, 1991; The Interrupted Flight. The History of University Philosophy and Logic in Russia (XIX - mid XX centuries),Moscow Univ. Press, 1995; Essays on the Social History of Logic in Russia, Mid Volga Research Center, 2002; British Philosophical and Social Sciences Ideas Reception in Russia vii viii Contributors (XIX - early XX centuries), Ulyanovsk Univ. Press, 2005; History of Logic in Russia and the USSR, Canon+, 2007; and Nicolai A. Vasiliev and his Imaginary Logic. The Revival of One Forgotten Idea, Canon+, 2009. In addition, Dr. Bazhanov has authored 480 published papers. Volumes which he has edited include: Mathematisation of Natural Sciences, Kazan Univ. Press, 1984; Vistas of Sciences, Kazan Univ. Press, 1989; The Scientists and Universities of Russia in the Transitional Period, Ulyanovsk, 1998; and Logic and Epistemology in Russian Philosophy of First Half of XX century, Rosspen, 2012. He also compiled A.V. Vasiliev’s book N.I. Lobachevsky (1792-1856), Nauka, 1992. Dr. Bazhanov is an Associate Editor of The Review of Modern Logic (formerly Modern Logic) since its founding in 1989, and an Associate Editor of Epistemology and Philosophy of Science; Reflexive Processes and Governing; News of Russia’s Universities.Volga Region (Humanities); Kant Studies; and Herald of Nizhny Novgorod University. He is the recipient of several research grants (British Academy, RBRF, RFH, Soros Foundation), including most recently a Lakatos Research Grant (2008). Philippe de Rouilhan is Directeur de Recherche émérite at the Centre National de la Recherche Scientifique (CNRS), and a member of the Institut d’histoire et de philosophie des sciences et des techniques (IHPST, of which he was the head for a long time). His works belong to logic lato sensu, or, more specifically, to formal ontology, formal semantics, philosophy of logic, philosophy