Trends in Logic Volume 36
For further volumes: http://www.springer.com/series/6645
TRENDS IN LOGIC Studia Logica Library VOLUME 36 Managing Editor Ryszard Wójcicki, Polish Academy of Sciences, Warsaw, Poland Editors Daniele Mundici, Department of Mathematics ‘‘Ulisse Dini’’, University of Florence, Italy Ewa Orłowska, National Institute of Telecommunications, Warsaw, Poland Heinrich Wansing, Ruhr-University Bochum, Germany
SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica – that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time. Volume Editor Ryszard Wójcicki, Polish Academy of Sciences, Warsaw, Poland
Yaroslav Shramko Heinrich Wansing •
Truth and Falsehood An Inquiry into Generalized Logical Values
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Prof. Yaroslav Shramko Department of Philosophy State Pedagogical University 50086 Kryvyi Rih Ukraine e-mail:
[email protected]
ISBN 978-94-007-0906-5 DOI 10.1007/978-94-007-0907-2
Prof. Heinrich Wansing Department of Philosophy II Ruhr-University Bochum 44780 Bochum Germany e-mail:
[email protected]
e-ISBN 978-94-007-0907-2
Springer Dordrecht Heidelberg London New York Ó Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To our beloved spouses Natalia and Petra
Preface
This study is the result of a research enterprise that started in 2003 when Y.S. visited H.W. at Dresden University of Technology as a Friedrich Wilhelm Bessel awardee of the Alexander von Humboldt Foundation. Actually, Robert Meyer’s remark that taking semantical values such as both true and false and neither true nor false seriously leads to madness is what triggered our interest in moving from Nuel Belnap and Michael Dunn’s set of four truth values represented as the powerset of the set of classical truth values to its sixteen-element powerset 16. We soon realized that Bob’s provocative verdict, inspiring as it proved to be, should not inhibit a generalization of Belnap and Dunn’s approach. The outcome of our initial co-operation was published as [232, 233], and the central and fundamental structure of our investigations into generalized truth values became the trilattice SIXTEEN3 defined on 16. Since we had generated quite a few problems and ideas for additional research, we decided to apply for a research grant in order to further investigate The Logic of Generalized Truth Values. Eventually, the project was funded by the German Research Council (DFG) under grant WA 936/6-1. We are very grateful to the DFG for its generous support, including a sabbatical for H.W. in the summer term 2007. Moreover, we are grateful to Ed Zalta for giving us the opportunity to write a survey on the notion of truth values i