564. Topology. 567. Totum Potentiale. 570. Transitivity. 572. Tropes. 581. Twardowski, Kazimierz. 587. Universal. 591. Whitehead, Alfred North. 595 ...
Handbook of Mereology
Analytica Investigations in Logic, Ontology and the Philosophy of Language Editors: Hans Burkhardt (Founding Editor †) Ignacio Angelelli, Joseph M. Bocheński (†) Christian Thiel Managing Editor: Stamatios Gerogiorgakis
_____ Handbook of Mereology Editorial Board Peter Forrest (Armidale, AU) Thomas Mormann (San Sebastian, E) Peter M. Simons (Dublin, IRL) Barry Smith (Buffalo, NY, US) Achille Varzi (Columbia, NY, US) Roberto Casati (Paris, F) Herbert Hochberg (Austin, Texas, US) Kevin Mulligan (Geneva, CH) Burkhard Schäfer (Edinburgh, UK)
Handbook of Mereology Editors Hans Burkhardt (Founding Editor †) Johanna Seibt Guido Imaguire Stamatios Gerogiorgakis
Philosophia
ISBN 978-3-88405-090-7 © 2017 by Philosophia Verlag GmbH München Printed in Germany 2017
Preface
The present volume is the first comprehensive reference work for research on partwhole relations – or better, and quite appropriately, a substantive part thereof. According to our guiding conception, developed by Burkhardt and Seibt more than a decade ago, the Handbook of Mereology was to offer a wide scope, inclusive presentation of contemporary research on part-whole relations that would draw out systematic, historical, and interdisciplinary trajectories, show the subject’s fertility, and inspire future explorations. In particular, we wanted to impress that mereology is much more than the study of axiomatised systems. The relationship between part and whole is a basic schema of cognitive organisation that operates not only at the level of language and propositional thought, but also at the level of sensory input processing, especially visual and auditory. In the natural, social, and human sciences, as well as in the Humanities, part-whole relations organize all three: data domains, methods, and theories. In short, part-whole relations play a fundamental role in how we perceive and interact with nature, how we speak and think about the world and ourselves, as societies and as individuals. For this reason the study of part-whole relations, both within and across domains, begins long before the metamathematically motivated inquiries of logicians at the beginning of the 20th century, and goes far beyond it. That this first edition of the Handbook of Mereology had to remain a part of the envisaged whole is to some extent a reflection of the current research landscape in mereology, the peculiarities of which led to an unusually protracted production process. The international research community in mereology is still so small that contributors and reviewers are not easily come by and often the only option was to wait rather than to replace. Moreover, since European scholars in the history of philosophy operate predominantly within their native language and abide by different national stylistic and expository conventions, extended review and revision periods were necessary, and translations and major editing tasks presented timeconsuming obstacles. But the delay of the production process also had quite contingent reasons. Due to illness, Hans Burkhardt soon had to decrease his involvement, and the second editor, with increasing support by the third editor, had to take over most of the handbook’s scientific and practical organisation. From 2012 onwards the second and third editor, who originally had committed themselves to short-term assignments, struggled with the unexpected task of having to accommo-
PREFACE
7
date over 3000 additional work hours within already busy work schedules. In 2013 Stamatios Gerogiorgakis joined the editorial team, lending additional research competences and linguistic editing support. When Hans Burkhardt died in May 2015, the three remaining editors decided to consolidate the results achieved so far and to present, in honor of his name and his sustained efforts for research on the history of mereology, a first edition of the Handbook that can qualify as a sufficiently substantive partial realisation of the project idea. We trust that the unique scope of the 131 contributions collected here will bring into view the fundamental significance of mereology in the wide sense of the term – not only for logic or ontology, but also for philosophy of biology, chemistry, and quantum physics; for a philosophy of nature that can accommodate chaos and emergence; for philosophy of art, for ethics; and for philosophy of cognition. The included domain-specific investigations of part-whole relations might even provide useful heuristics for researchers in various scientific disciplines (e.g., cognitive science, psychology, biology, or chemistry). There are of course a good many entries explaining and exploring the meta-mathematical interest of formal mereology and its use for the development of nominalist descriptions of the domain of mathematical science – the reader will find historically and systematically informative presentations of the relationship between mereology, Boolean algebra, and topology, as well as explorations in the intersection of metamathematics and metaphysics, such as on how to ground differential equations in a region-based ontology. But the Handbook also features several contributions that convey the richness and complexity of linguistic encodings of part-whole relations. Importantly, many entries suggest that and how our common sense reasoning departs from the classical formalisations of part-whole relationships that have influenced much of contemporary ontology. A considerable portion of the historical dimension of mereology could be documented, especially with respect to the medieval period and the phenomenological tradition. The Handbook’s entries are written by internationally renowned specialists but with an interdisciplinary readership in view. Most of the entries not only report the state of the art but present new original research published here for the first time. The protracted production process of this first edition has been unusually trying for all contributors, some of whom submitted their entries many years ago. We would like to thank all authors for their contributions, but we also want to express our particular gratitude to our authors for their sustained commitment and extraordinary patience. We gratefully acknowledge the support of many colleagues who served as external reviewers. Our special thanks go to Andrew Arlig, who took over several translations and language revisions. We also thank Ulrich Staudinger, the owner of the Philosophia Verlag, for staying with the project throughout the contingent difficulties we encountered. Perhaps it is quite fitting that this first edition of the Handbook of Mereology remains a part of the envisaged whole – it may serve as a useful reminder that some
8
PREFACE
ambitions can only be discharged piecemeal, with each new attempt garnering energies from the shortcomings of predecessors. We hope that this portion of a comprehensive reference work for research on part-whole relations will stimulate the preparation of a second edition to fill in what had to be omitted here. In other words, we hope that the mereological supplementation principle not only holds in theory but also in praxis. Johanna Seibt, Guido Imaguire, Stamatios Gerogiorgakis
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ENTRIES
Table of Entries
Abelard
22
Abstract
26
Act and Action
29
Activity
32
Albert of Saxony
40
Animal
42
Anselm
46
Aristotle’s Theory of Parts
50
Aristotle’s Theory of Wholes
57
Art
63
Artifact
69
Atomism in Ancient Greek Philosophy
71
Atomism, Logical
74
Atomism, Medieval
82
Atomism, Metaphysical Axiomatic Method
Comments on “The Calculus of Individuals and Its Uses”
129
Carnap, Rudolf
130
Category
133
Causation
135
Chaos
139
Chemistry
143
Coincidence
149
Collectives and Compounds
152
Common Sense Reasoning About Parts and Wholes 154 Conscious Experience
162
Continuants and Occurrents
170
Cosmology
173
86
Deontic modalities
181
90
Descartes
184
Dispositions
192
Dynamical Systems
195
Bergmann, Gustav
94
Biological Parts
97
Body
100
Elements
199
Boethius
104
Emergence
202
Bolzano, Bernard
107
Ethics
208
Boolean Algebras
115
Experience
211
Brentano, Franz
121
ENTRIES
Linguistic Structures
295
Locke
299
226
Mally, Ernst
309
229
Material Constitution
313
Medicine
317
Facts
215
Fiction
220
Fractals
225
Frege, Gottlob Fusion
Gestalt
233
God
237
Good Life, The
239
Goodman, Nelson
242
Grammar
244
Granularity
247
Grossmann, Reinhardt S.
251
Holes
255
Homeomerous and Automerous 257 Husserl, Edmund
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264
Medieval Discussions of Temporal Parts and Wholes 333 Medieval Mereology
340
Meinong, Alexius
347
Mereological Essentialism
351
Mereological Triangle
354
Mereotopology
356
Metamathematics of Mereology 363
Naïve Mereology
371
Natural Science
373
Nominalism
381
Ingarden, Roman
273
Non-literal Language Use and PartWhole Relations 384
Intentionality
276
Non-Wellfounded Mereology
385
Jurisprudence
279
Ontological Dependence
391
Order
395
Paradoxes
399
Parmenides
401
Language
289
Leśniewski, Stanisław and Polish Mereology 289
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ENTRIES
Perceptual Whole
403
Persistence
411
Philosophy of Mathematics
414
Phonology
426
Piece
430
Plato
434
Points
437
Possession and Partitives
440
Powers
444
Praedicabilia
446
Privation
449
Propositions
457
Quantum Mechanics
463
Quantum Mereology
478
Society, Individualism and Holism (Collectivism) in the Study of, 510 Stoics
512
Structure
514
Structure of Appearance, Goodman’s 521 Stumpf, Carl
524
Subject, Person, Self
527
Substance
531
Substrate
536
Sum
540
Syllogism
542
Syntax
546
Tarski, Alfred
551
Temporal Parts
553
Theoretical Mereology
556
Radulphus Brito
483
Thomas Aquinas
564
Raimundus Lullus and Lullism
484
Topology
567
Reduplication
489
Totum Potentiale
570
Reinach, Adolf
491
Transitivity
572
Rhetoric
494
Tropes
581
Russell, Bertrand
498
Twardowski, Kazimierz
587
Scherzer, Johann Adam
501
Universal
591
Segelberg, Ivar
504
Shadows
507
Whitehead, Alfred North
595
ENTRIES
Whitehead’s Metaphysics
600
World, Actual
604
Index
609
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CONTRIBUTORS
Contributors Albertazzi, Liliana Department of Humanities, University of Trento Perceptual Whole Andrae, Benjamin Munich School of Philosophy, Ludwig-Maximilians University Experience, Whitehead’s Metaphysics Arlig, Andrew Department of Philosophy, Brooklyn College, CUNY Abelard, Boethius, Medieval Mereology Bäck, Allan Department of Philosophy, Kutztown University Aristotle’s Theory of Parts, Reduplication, Syllogism Beck, Hans Institute for Physics, University of Neuchâtel Chaos Boucher, Pol Institut de l’Ouest: Droit et Europe, University of Rennes Jurisprudence Bränmark, Johan Department of Global Political Studies, Malmö University Ethics, The Good Life Bromand, Joachim Institute of Philosophy, University of Bonn/Institute of Philosophy, RWTH Aachen University Paradoxes Burkhardt, Hans Department of Philosophy, Ludwig-Maximilians University at Munich Albert of Saxony, Medicine, Mereological Triangle (with Stamatios Gerogiorgakis), Radulphus Brito, Raimundus Lullus and Lullism, Scherzer (with Stamatios Gerogiorgakis) Cameron, Ross P. Department of Philosophy, University of Virginia Mereological Essentialism
CONTRIBUTORS
Cohnitz, Daniel Department of Philosophy and Religious Studies, Utrecht University Goodman, Nelson (with Marcus Rossberg), Structure of Appearance, Goodman’s (with Marcus Rossberg) Correia, Fabrice Department of Philosophy, University of Geneva Ontological Dependence Cosans, Christopher Department of Philosophy, University of Marylands Animals Cotnoir, A. J. Department of Philosophy, University of St Andrews Non-Wellfounded Mereology Donelly, Maureen Department of Philosophy, University at Buffalo Granularity Eberle, Rolf Faculty of Philosophy, University of Rochester Order Enfield, Nicholas J. Max Planck Institute for Psycholinguistics, Nijmegen Body (with Asifa Majid) Forrest, Peter School of Humanities, University of New England in Armidale, NSW, Australia Theoretical Mereology Gerogiorgakis, Stamatios Philosophy Department, University of Erfurt Medieval Discussions of Temporal Parts and Wholes, Mereological Triangle (with Hans Burkhardt), Privation, Scherzer (with Hans Burkhardt), Individualism and Holism (Collectivism) in the Study of Society, Thomas Aquinas Hammond, Michael Department of Linguistics, University of Arizona Phonology
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CONTRIBUTORS
Harte, Verity Department of Philosophy, Yale University Plato Hawley, Katherine Department of Philosophy, University of St Andrews Fusion, Temporal Parts Hellman, Geoffrey Department of Philosophy, University of Minnesota Philosophy of Mathematics Herre, Heinrich Institute for Informatics, University of Leipzig Boolean Algebras Herstein, Gary Independent Scholar Cosmology Hochberg, Herbert Department of Philosophy, University of Texas at Austin Logical Atomism, Facts, Segelberg, Tropes Huebner, Johannes Department of Philosophy, Martin-Luther University at Halle-Wittenberg Act, Action Imaguire, Guido Department of Philosophy, Federal University of Rio de Janeiro Frege, Nominalism, Propositions, Russell Jacquette, Dale Philosophy Institute, University of Bern Fractals, Tarski Jansen, Ludger Institute of Philosophy, University of Rostock Collectives and Compounds, Dispositions, Substance, Substrate Johansson, Ingvar Department of Historical, Philosophical and Religious Studies, Umeå University Natural Science
CONTRIBUTORS
Kaiser, Marie I. Philosophy Department, University of Bielefeld Biological Parts Kanzian, Christian Department of Philosophy, Theological Faculty of the University Innsbruck Persistence Koons, Robert Department of Philosophy, University of Texas at Austin Causation Koptjevskaja-Tamm, Maria Department of Linguistics, Stockholm University Possession and Partitives Koslicki, Kathrin Department of Philosophy, University of Alberta Structure Krause, Décio Department of Philosophy, Federal University of Santa Catarina Quantum Mereology Krecz, Charles A. Department of Philosophy, University of Texas at Austin Piece Leonard, Henry S., Sr. Philosophy Department, Michigan State University Comments on “Calculus of Individuals and Its Uses” (prefaced by Henry S. Leonard, Jr.) Lowe, Jonathan E. Department of Philosophy, Durham University Coincidence Majid, Asifa Max Planck Institute for Psycholinguistics, Nijmegen Body (with Nicholas Enfield) McGivern, Patrick Department of Philosophy, University of Wollongong Dynamical Systems (with Alex Rueger)
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CONTRIBUTORS
McGregor, William B. Linguistics, Cognitive Science and Semiotics, School of Communication and Culture, Aarhus University Grammar Meixner, Uwe Institute of Philosophy, University of Augsburg Abstract, Axiomatic Method, Universal Michael, Emily Department of Philosophy, City University of New York Medieval Atomism Miller, Kristie Department of Philosophy, University of Sydney Holes, Actual World Mittmann, Rainer Independent Scholar Descartes Moravcsik, Edith Department of Linguistics, University of Wisconsin-Milwaukee Syntax Mormann, Thomas Department of Logic and Philosophy of Science, University of the Basque Country Carnap, Points, Topology Müller, Thomas Department of Philosophy, University of Konstanz Deontic modalities Mumford, Stephen Department of Philosophy, Durham University/School of Economics and Business, Norwegian University of Life Sciences Powers Needham, Paul Department of Philosophy, Stockholm University Chemistry, Elements
CONTRIBUTORS
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Oderberg, David S. Department of Philosophy, University of Reading Shadows Pietruszczak, Andrzej Department of Logic, Nicolaus Copernicus University Metamathematics of Mereology Poli, Roberto Department of Philosophy, University of Trento Aristotle’s Theory of Wholes Potter, Luke Department of Philosophy, University of Notre Dame Material constitution (with Michael Rea) Rea, Michael Department of Philosophy, University of Notre Dame Material constitution (with Luke Potter) Reicher, Maria E. Department of Philosophy, RWTH Aachen University Meinong Rijkhoff, Jan Department of Linguistics, Aarhus University Linguistic Structures, Non-literal Language Use and Part-Whole Relations Rosiak, Marek Department of Logic, University of Lodz Husserl, Ingarden, Twardowski Rossberg, Marcus Philosophy Department, University of Connecticut Goodman, Nelson (with Daniel Cohnitz), Structure of Appearance, Goodman’s (with Daniel Cohnitz) Rueger, Alex Faculty of Arts, University of Alberta Dynamical Systems (with Patrick McGivern) Salice, Alessandro Philosophy Department, University College Cork Brentano, Intentionality, Mally, Reinach, Stumpf
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CONTRIBUTORS
Sanford, David H. Department of Philosophy, Duke University Naïve Mereology, Sum Schaffer, Jonathan Department of Philosophy, Rutgers University Metaphysical Atomism Schalley, Andrea C. Department of Language, Literature and Intercultural Studies, Karlstad University Common Sense Reasoning About Parts and Wholes Schantz, Richard Department of Philosophy, University of Siegen Gestalt Scherb, Jürgen L. Department of Philosophy, Ludwig-Maximilians University at Munich Anselm Schnieder, Benjamin Department of Philosophy, University of Hamburg Bolzano Seibt, Johanna Department for Philosophy and the History of Ideas, University Aarhus Activity, Homeomerous and Automerous, Subject (with Bartłomiej Skowron), Transitivity Sedley, David Christ’s College, University of Cambridge Atomism in Ancient Greek Philosophy Silberstein, Michael Department of Philosophy, Elizabethtown College Conscious Experience, Quantum Mechanics Simons, Peter Department of Philosophy, Trinity College Dublin Artifact, Category, Whitehead
CONTRIBUTORS
Skowron, Bartłomiej International Center for Formal Ontology, Faculty of Administration and Social Sciences, Warsaw University of Technology Mereotopology, Subject (with Johanna Seibt) Stephan, Achim Institute of Cognitive Science, Osnabrück University Emergence Storm-Henningsen, Peter Lillebælt Academy, University of Applied Sciences Art Tegtmeier, Erwin Department of Philosophy, University of Mannheim Bergmann, Continuants and Occurrents, Grossman Thom, Paul Department of Philosophy, University of Sydney Parmenides, Stoics van Zantwijk, Temilo Institut of Philosophy, Friedrich-Schiller-University Jena Rhetoric von Wachter, Daniel International Academy of Philosophy in the Principality of Liechtentein God Woleński, Jan Department of Social Sciences, University of Information, Technology and Management at Rzeszow Leśniewski and Polish mereology Woods, John Department of Philosophy, University of British Columbia Fiction Wyllie, Guilherme Department of Philosophy, Fluminense Federal University Praedicabilia, Totum potentiale
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