Synthese Library 386 Studies in Epistemology, Logic, Methodology, and Philosophy of Science Venanzio Raspa Thinking about Contradictions The Imaginary Logic of Nikolai Aleksandrovich Vasil’ev Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 386 Editor-in-Chief Otávio Bueno, University of Miami, Department of Philosophy, USA Editors Berit Brogaard, University of Miami, USA Anjan Chakravartty, University of Notre Dame, USA Steven French, University of Leeds, UK Catarina Dutilh Novaes, University of Groningen, The Netherlands More information about this series at http://www.springer.com/series/6607 Venanzio Raspa Thinking about Contradictions The Imaginary Logic of Nikolai Aleksandrovich Vasil’ev Venanzio Raspa Dipartimento di Studi Umanistici Università degli Studi di Urbino Carlo Bo Urbino, Italy Translated by Peter N. Dale Synthese Library ISBN 978-3-319-66085-1 ISBN 978-3-319-66086-8 (eBook) https://doi.org/10.1007/978-3-319-66086-8 Library of Congress Control Number: 2017949873 © Springer International Publishing AG 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland To Italo Cubeddu, with whom I began to study philosophy and the issue of contradiction To Silvio Bozzi, who taught me to love the study of logic and its history Preface This book is the result of a long, though not continuous, process. I first began to study Vasil’ev’s work for my PhD thesis (In-contraddizione. Il principio di contrad- dizione alle origini della nuova logica [In-contradiction. The Principle of Contradiction at the Origins of the New Logic]). I defended this dissertation in October 1996 and it was published in 1999. There I discussed, among other matters regarding the principle of contradiction, the works of a group of thinkers (Meinong, Łukasiewicz, Vasil’ev and Peirce) who made important contributions to the analysis of this principle and the problems related to it and played key roles in the birth of non-Aristotelian logics at the turn of the twentieth century. My initial interest in the topic of the principle of contradiction led me to a degree thesis, undertaken under the guidance of Italo Cubeddu, on Opposizione e contrad- dizione in Aristotele e in Kant [Opposition and Contradiction in Aristotle and Kant]. Professor Cubeddu also supervised my PhD dissertation. At the same time, I also had the good fortune to get to know Silvio Bozzi, whose guidance and stimulating input during many conversations and exchanges was fundamental for the direction and development of my research. Since then, I have continued to study Vasil’ev’s imaginary logic, and I have also had the opportunity to discuss it on several occasions: at the Congress of the Italian Society for Logic and the Philosophy of Science (SILFS), held in Cesena and Urbino on 15–19 February 1999; during a seminar on ‘Aristotle and the Birth of Non-Aristotelian Logics’, held at the then Institute of Philosophy of the University of Urbino on 7 May 2002; at the Congress ‘Knowledge as Network of Models’, which took place in Alghero on 20–23 September 2004; in a seminar on the imagi- nary logic of N. A. Vasil’ev, which I held at the Department of Philosophy and Human Sciences of the University of Macerata on 13 March 2009; during the lec- tures at the Department of Philosophy of the University of Ljubljana on 23 March 2009; and finally in the international workshop ‘On Contradictions’ which took place in Padova, on 12–13 December 2013. Some results of my researches on Vasil’ev and non-Aristotelian logics have been published in Logique et Analyse 40(159), 1997, 225–248; in the Journal of Philosophical Research 24, 1999, 57–112; in my monograph In-contraddizione. Il principio di contraddizione alle vii viii Preface origini della nuova logica (Trieste: Edizioni Parnaso, 1999); and in my contribu- tions to Prospettive della logica e della filosofia della scienza (Soveria Mannelli: Rubbettino, 2001, pp. 73–87) and L’impossibilità normativa (Milano: LED, 2015, pp. 127–148). In 2012, I published, together with Gabriella Di Raimo, the Italian translation of the logical texts by N. A. Vasil’ev (Logica immaginaria, Roma: Carocci). The present book is an expanded reworking of my introductory essay published in that work. I am very grateful to the publisher Carocci for the permis- sion to use it here. In completing the book, I have incurred many debts, not least to the Staatsbibliothek Preussischer Kulturbesitz Berlin, for enabling me to consult its extensive library holdings; to Giuseppe Ambrogi and Francesca Di Ludovico of the Biblioteca Centrale Umanistica of the University of Urbino, who have procured for me every book or article I have requested with promptness and diligence; to Peter Dale, who took charge of the translation of the manuscript and has always been willing to deal with my enquiries about language; and to Patricia Barzotti, Gabriella Di Raimo and Domenico Mancuso, who helped me in the final stage of editing the text. Urbino, Italy Venanzio Raspa 15 June 2017 Note to Readers Works are quoted with the publication date of the edition consulted (e.g. Venn 18942: 11–13). In the case of critical editions, the original date of publication is indicated (e.g. Peirce 1880: CP 3.192–193). For manuscripts, the completion date of the work is put into square brackets near the date of publication (e.g. Peirce [1898]/1992: 261); for new editions of works, the date of the first publication is also put before the date of the edition consulted (e.g. Łukasiewicz 1910a/1987). All translations, when the corresponding English one is not shown in square brackets and unless otherwise indicated, are mine. Collective works appear under the name of the editor. In some cases, abbreviations have been used: A = First edition of Kant’s Kritik der Reinen Vernunft (1781) Ak. = Kants Gesammelte Schriften (1910 ff.) B = Second edition of Kant’s Kritik der Reinen Vernunft (1787) CP = Collected Papers of Charles Sanders Peirce (1931–1935–1958) GA = Alexius Meinong Gesamtausgabe (1968–1978) W = Writings of Charles S. Peirce (1982 ff.) For Aristotle’s texts, the following abbreviations have been used: Cat. = Categoriae (Categories); transl. by J. L. Ackrill Int. = De Interpretatione (On Interpretation); transl. by J. L. Ackrill An. pr. = Analytica Priora (Prior Analytics); transl. by A. J. Jenkinson An. post. = Analytica Posteriora (Posterior Analytics); transl. by J. Barnes Top. = Topica (Topics); transl. by W. A. Pickard-Cambridge Metaph. = Metaphysica (Metaphysics); transl. by W. D. Ross ix Notes on Transliteration The transcription used for Cyrillic characters refers to English transliteration. Given the possibility of transliterating some of the characters in a different way, I will go on to specify what criteria are adopted in the following cases: • e is transliterated as e. • ë is transliterated as yo. • ж is transliterated as zh. • и is transliterated as i. • й is transliterated as i. • k is transliterated as k. • x is transliterated as kh. • ц is transliterated as ts. • ч is transliterated as ch. • ш is transliterated as sh. • щ is transliterated as shch. • ы is transliterated as y. • э is transliterated as e. • ю is transliterated as iu. • я is transliterated as ia. Such criteria have not however been observed in all cases as the transliteration of certain names has been established by convention for some time, and in particular in the case of well-known people, such transliterations also appear in the bibliogra- phies. A list follows of exceptions to the above: • The marked sign ъ is removed, whereas the weak sign ь is maintained in the majority of cases, with the exception of the word Казань which is always trans- literated as Kazan and several names of authors (e.g. Gogol, etc.; see Index of Names). • Certain names such as Дocmoeвcкuй, Πоccкuй, Πобачeвcкuй and similar, although ending in uй, are not transliterated according to the above-mentioned rules, but in accordance with English transliteration through which they have xi