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Mereology and the Sciences SYNTHESE LIBRARY Mereology and the Sciences SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE Editor-in-Chief LUCIANO FLORIDI, University of Oxford, Oxford Internet Institute, United Kingdom Editors THEO A.F. KUIPERS, University of Groningen Fac. Philosophy, The Netherlands TEDDY SEIDENFELD, Carnegie Mellon University Dept. Philosophy, USA PATRICK SUPPES, Stanford University Ctr. Study of Language & Information, USA JAN WOLEÑSKI, Jagiellonian University of Kraków Institute of Philosophy, Poland DIRK VAN DALEN, Utrecht University Department of Philosophy, The Netherlands VOLUME 371 For further volumes: http://www.springer.com/series/6607 Claudio Calosi Pierluigi Graziani Editors Mereology and the Sciences Parts and Wholes in the Contemporary Scientific Context 123 Editors Claudio Calosi Pierluigi Graziani Department of Basic Sciences and Department of Basic Sciences and Foundations Foundations University of Urbino University of Urbino Urbino Urbino Italy Italy ISBN 978-3-319-05355-4 ISBN 978-3-319-05356-1 (eBook) DOI 10.1007/978-3-319-05356-1 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014939928 c Springer International Publishing Switzerland 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface and Acknowledgements The first idea behind this book came to us at the end of 2011 when we taught a seminar on Mereology and Set Theory at the University of Urbino. During several discussions it became clear that a comprehensive treatment of possible applications of mereology to contemporary sciences was missing. The present work is our modest attempt, as far as it is possible, to fill this gap. It grew from being a proposal for a special issue of a journal into a fully-fledged book. We want to thank all the contributors to the volume who accepted enthusiastically our invitation and had the patience to satisfy our requests. Each one of them has written a significant and important contribution. We are particularly grateful to Vincenzo Fano, Yuri Balashov and Achille Varzi for having supported this project right from the very start. A special mention goes to the referees for Springer who read the entire manuscript more than once. They provided invaluable suggestions and detailed criticisms on each and every part of the book: without them it would have been substantially worse. We would also like to thank Christie Lue at Springer. She was always kind and helpful. We have discussed many of the materials that are now in the book with both colleagues and friends. They know who they are so there is no need to mention them by name. We want to thank them all. v Contents Part I Physics 1 Building Enduring Objects Out of Spacetime .......................... 5 Cody Gilmore 2 Relativistic Parts and Places: A Note on Corner Slices and Shrinking Chairs ..................................................... 35 Yuri Balashov 3 Parthood and Composition in Quantum Mechanics................... 53 Claudio Calosi and Gino Tarozzi 4 Continuity of Motion in Whitehead’s Geometrical Space ............ 85 Vincenzo Fano and Pierluigi Graziani Part II Mathematics 5 Multi-valued Logic for a Point-Free Foundation of Geometry ....... 105 Cristina Coppola and Giangiacomo Gerla 6TheRelationsofSupremum and Mereological Sum in Partially Ordered Sets ................................................. 123 Rafał Gruszczynski´ and Andrzej Pietruszczak 7 Natural Mereology and Classical Mereology ........................... 141 Paul Hovda vii viii Contents Part III Natural Sciences 8 Crisp Islands in Vague Seas: Cases of Determinate Parthood Relations in Biological Objects ............................... 163 Ludger Jansen and Stefan Schulz 9 Developing the Mereology of Chemistry ................................ 189 Jean-Pierre Llored and Rom Harré Part IV Computer Sciences and Engineering 10 Mereology in Engineering and Computer Science ..................... 217 Lech Polkowski 11 Discrete Mereotopology ................................................... 293 Antony Galton 12 A Rôle for Mereology in Domain Science and Engineering: To Every Mereology There Corresponds a –Expression............. 323 Dines Bjørner Appendix: Formal Theories of Parthood ..................................... 359 Achille C. Varzi Selected Bibliography........................................................... 371 Claudio Calosi and Pierluigi Graziani Index .............................................................................. 375 Notes on Contributors Yuri Balashov is a Professor of Philosophy at the University of Georgia. He has published extensively in philosophy of science and metaphysics in leading philosophical journals. He is the author of Persistence and Spacetime and a co-editor of Einstein Studies in Russia and Philosophy of Science: Contemporary Readings. Dines Bjørner taught at Technical University of Denmark in Copenhagen before retiring in 2007. He was also a computer scientist working for IBM and responsible for establishing the United Nations University International Institute for Software Technology in Macau. He is an expert in domain engineering, requirements engineering and formal methods. He is the author of the influential three-volume monograph Software Engineering. Claudio Calosi is currently a post-doc at University of Urbino, Department of Basic Sciences and Foundations. He has been a Visiting Research Scholar at University of Pittsburgh, University of California at Irvine and New York University. His main research interests are philosophy of science and analytic metaphysics and he has published extensively on both in journals such as Synthese, Dialectica,and Foundations of Physics to mention a few. Cristina Coppola studied mathematics at University of Salento and University of Naples. She is currently a research fellow in mathematics at University of Salento. Her primary research interests are mathematics and education on the one hand and foundations of geometry on the other. She is the author of numerous scientific articles published in journals, books and conference proceedings. Vincenzo Fano is an Associate Professor of Logic and Philosophy of Science at University of Urbino. His works focuses particularly on the foundations of physics and philosophy of psychology. He is the author of five monographs and has authored more than a hundred papers in journals such as Foundations of Physics and Studia Liebniziana. Antony Galton is Reader in Knowledge Representation at the University of Exeter, where he is based in the College of Engineering, Mathematics and Physical ix x Notes on Contributors Sciences. He works in the area of logic, ontology, and knowledge representation, with a particular focus on space and time. His published books include The Logic of Aspect (1984) and Qualitative Spatial Change (2000). Giangiacomo Gerla is a Full Professor of Mathematics at University of Salento. His research focuses, in particular, on fuzzy logic, fuzzy set-theory, multi-valued logic and point-free geometry. He is the author of numerous scientific articles in mathematics and logic. He is also the author of numerous monographs including Fuzzy Logic. Mathematical Tools for Approximate Reasoning. Cody Gilmore is an Associate Professor of Philosophy at the University of California, Davis. He is interested in persistence, death, time travel, universals and propositions. He has published papers on these topics in Oxford Studies in Meta- physics, Philosophical Perspectives, Philosophical Studies, Australasian Journal of Philosophy, Philosophy Compass, The Stanford Encyclopedia of Philosophy, The Oxford Handbook of Philosophy of Death, and elsewhere. Pierluigi Graziani received his Ph.D. from University of Rome La Sapienza and is currently a post-doc and Assistant Professor of
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