Table Of ContentAXIOMATIC FORMAL ONTOLOGY
SYNTHESE LIBRARY
STUDIES IN EPISTEMOLOGY,
LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor:
JAAKKO HINTIKKA, Boston University
Editors:
DIRK VAN DALEN, University of Utrecht, The Netherlands
DONALD DAVIDSON, University of California, Berkeley
THEO A.F. KUIPERS, University ofGroningen, The Netherlands
PATRICK SUPPES, Stanford University, California
JAN WOLENSKI, Jagiellonian University, KrakOw, Poland
VOLUME264
UWEMEIXNER
University of Regensburg,
Regensburg, Germany
AXIOMATIC
FORMAL ONTOLOGY
SPRINGER-SCIENCE+BUSINESS l\1EDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress
ISBN 978-90-481-4898-1 ISBN 978-94-015-8867-6 (eBook)
DOI 10.1007/978-94-015-8867-6
Printed on acid-free paper
All Rights Reserved
© 1997 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1997
Softcover reprint of the hardcover 1st edition 1997
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
To my teacher
Franz von Kutschera
TABLE OF CONTENTS
PREFACE ix
INTRODUCTION
1: THE ONTOLOGY OF STATES OF AFFAIRS 23
1.1 The Central Axioms for the Part-Concept "P" 24
1.2 Concepts based on "P" and Elementary Theorems 29
1.3 The Concept of State of Affairs 34
1.4 Functional Terms Definable by "P" 42
1.5 The Conjunction Axiom 46
1.6 The Exhaustion Axiom 53
1.7 The Connection Axiom 56
1.8 Theorems for Negation, Conjunction and Disjunction 67
1.9 The Big Disjunction 69
1.10 Possible Worlds and Elementary States of Affairs 73
1.11 Possibility and Necessity 80
1.12 The World and the Truth 88
1.13 The Law of Non-Contradiction 93
1.14 The Law of Excluded Middle 97
1.15 Laws of Truth and Falsity I 03
1.16 Contingency I 09
1.17 A Further Examination of Axioms AP7 - AP9 114
1.18 The Hierarchies of States of Affairs 118
1.19 The Discreteness of "P*" 123
1.20 The Cardinality of the Universe of States of Affairs 126
II: ONTOLOGY OF PROPERTIES AND MEREOLOGY 131
11.1 Intensional Parthood between Properties 132
11.2 New Readings of Predicates and Functional Terms, and Inherence 137
11.3 Actual Existence for Accidents and Substances 145
11.4 Real Subsistence as a Property? 150
11.5 Laws of Actual Existence 154
11.6 Laws of Inherence, and Superessentialism 158
11.7 Leibniz's Principium 165
11.8 Once More: Real Subsistence as a Property? 169
11.9 The Philosophy of Leibniz and the Ontology of Properties 175
11.10 Meinongian Objects in the Ontology of Properties 181
11.11 Time-Free and Momentary Material Individuals 189
11.12 The Mereology of Gorups 206
Vlll TABLE OF CONTENTS
III: FULL ONTOLOGY LIMITED TO PROPERTIES OF INDIVIDUALS 219
111.1 Categorial Predicates, Language LPTI, System PTI 220
111.2 Saturation and Extraction 225
III.3 Parthood and Identity for Properties 231
III.4 Important Singular Terms for Properties 234
III.5 The Principle of Property-Quanta and the Exhaustion- and
Connection-Principle for Properties 239
111.6 Properties by Conjunction and Properties by Extraction 243
111.7 Essential and Accidental Properties 245
III.8 Maximally Consistent Properties and the Property Specific to an
Individual 251
111.9 <0>-Exemplification 253
111.10 The Relationship between Maximally Consistent Properties,
Individuals and Possible Worlds 255
III. II Individuals and Leibniz-lndividuals 259
111.12 Counterpart Theory 265
III.l3 Actual Existence for Individuals and Leibniz-Individuals 271
III.l4 The Modelling of Sets and Extensions 280
111.15 Predicates and Properties 285
111.16 Modalizers and Quantifiers 288
III.l7 Conceptions of Properties, and their Number 296
IV: UNIVERSAL INTENSIONAL ONTOLOGY 299
IV.l The System IOU: First Stage 300
IV.2 The System IOU: Second Stage 308
IV.3 The System IOU: Third Stage 312
IV.4 Actual Existence, Identity, and the Fundamental Status of
States of Affairs 320
EPILOGUE 323
APPENDIX: PRINCIPLES, PROOFS AND DEFINITIONS 325
System P 325
A Variant of System P 346
The Leibnizian System 351
The Mereology of Momentary Material Individuals 353
System PTl 354
System IOU 375
INDEX OF SUBJECTS 379
INDEX OF NAMES 388
LITERATURE 390
PREFACE
The contents of this book are set out in the introduction. Here a few words
remain to be said about the general intentions pursued by its author.
The book is intended as a fairly comprehensive systematic treatise on ontology
(metaphysica generalis). "Part" and "intension" are the core-concepts
around which the work is organized. Formal methods are used throughout; the
subject is treated axiomatically more geometrico on the basis of first-order
predicate logic. Philosophy more geometrico is an old ideal, to which many
philosophers have aspired - with dubious success, to say the least. I hope, I
have done better, sacrificing neither conceptual clarity nor logical stringency to
philosophical depth. Certainly these three values ought not to be a priori
inimical to each other.
I also hope that the use of formal methods has not overly impaired the
readability of the book. To aid readability I have presented the formulas in the
book in semi-formal fashion - they are composed out of abbreviated and
standardized elements of ordinary language. In addition, I have banished all the
proofs - with some exceptions - to the appendix, where a listing of axioms,
theorems and definitions can also be found.
The general philosophicai climate has changed considerably since the days of
Carnap; unfortunately, it has changed also with respect to the use of formal
methods. One can witness a diminishing patience with logical formulas in
philosophical writings, and the qualities of clarity and logical precision are
beginning to disappear from philosophical publications, even if they are written
from the point of view of analytic philosophy (strangely contrasted by speakers
of English with "continental philosophy," as if there were no analytic
philosophers on the Continent). To reassert the power and beauty of the use of
formal methods in philosophy (aside from formal logic) is thus one of the
additional aims of this book.
There has been more appreciation of such methods in philosophy in Poland
than anywhere else, and hence it is surely no accident that it was Jan Wole6ski
who first suggested to me that this book be published by Kluwer. I am greatly
indebted to him for making this opportunity of reaching a greater audience
available to me. I also would like to thank Barry Smith for his editorial help.
IX
INTRODUCTION
Every science has a field of reference and a point of view from which this field
is examined. The point of view determines a selection of facts from the totality
of facts pertaining to the corresponding field of reference; the point of view can
be identified with the set of scientific interests, by which the science is guided.
There are scientific interests which are shared by all sciences, others which are
restricted to specific sciences. Every science aims at cognizing facts (in its field
of reference) that lend themselves well to deductive systematization, that is, to
theory-construction. Such facts are, in particular, general facts; they are not
however arbitrary general facts, but only those which can be expressed by
employing certain selected terms. Every science aims at choosing such terms as
can be brought into a definitional system. But most of all its selection of terms
is determined by the scientific interests and the field of reference which are
specific for it.
The field of reference of the science of ontology consists of everything there
is. It comprehends everything that can be named, in other words: everything,
that which is only possible (if such there be), as much as that which actually
exists. Hence the field of reference of ontology is universal: we may call it ''the
totality of being.'' But not all facts with respect to this field form part of the
subject-matter of ontology. Ontology does not of course attempt to be a
universal science. Ontology examines being qua being, as Aristotle says. It aims
at cognizing those facts of all the facts there are about everything there is which
are the fundamental facts.
Every entirely precise delineation of what is a fundamental fact about the
totality of being is certainly bound to be to some degree arbitrary; but such a
delineation can nevertheless be made in a rough and ready manner which will
be sufficiently precise and natural for our purposes. The fundamental facts with
respect to the totality of being are those facts which concern the fundamental
distinctions and relations in that totality. We may expect that these are mirrored
in the core structures of (descriptive) language, the language we use to speak
about everything there is. This follows from the following consideration: ( 1)
language [* 1] is the main tool of cognition, and (2) a tool, if it is to be useful,
must fit what there is; but (3) language, in fact, is useful for the cognition of
what there is. [*2] Hence, if we ask what it is in the totality of being that
corresponds to this central linguistic distinction (for example, that between
sentence and predicate), or to this central linguistic relation (for instance,
predication), then we are led to the fundamental distinctions and relations in
that totality. These distinctions and relations are fundamental, since the core
structures of a language must precede every instance of concept- and theory-
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