Abstract Objects An Introduction to Axiomatic Metaphysics
In this book, I attempt to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a p
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SYNTHESE LIBRARY
STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor: JAAKKO HINTIKKA,
Florida State University, Tallahassee Editors:
DONALD DAVIDSON,
University of California
GABRIEL NUCHELMANS, WESLEY
University of Leyden
C. SALMON, University of Arizona
VOLUME 160
EDWARD N. ZALTA Department of Philosophy, Rice University, Houston, Texas
ABSTRACT OBJECTS
An Introduction to Axiomatic Metaphysics
D. REIDEL PUBLISHING COMPANY t...AII
A MEMBER OF THE KLUWER "
ACADEMIC PUBLISHERS GROUP
DORDRECHT/BOSTON/LANCASTER
Library of Congress Cataloging in Pnblication Data Zalta, Edward N., 1952Abstract objects. (Synthese library; v. 160) Bibliography~ p. Includes index. 1. Metaphysics. 2. Object (Philosophy) I. Title. BDll1.Z34 1983 111 82-20549 ISBN-13: 978-94-009-6982-7 e-ISBN-13: 978-94-009-6980-3 DOl: 10.1007/978-94-009-6980-3
Published by D. Reidel Publishing Company, P.O. Box 17, 3300 AA Dordrecht. Holland, Sold and distributed in the U.S.A. and Canada by Kluwer Boston Inc., 190 Old Derby Street, Hingham, MA 02043, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, AH Dordrecht, Holland.
All Rights Reserved Copyright to 1983 by D. Reidel Publishing Company, Dordrecht, Holland 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 informational storage and retrieval system, without written permission from the copyright owner
To my parents
"Sometimes, unexpected flashes of instruction were struck out by the fortuitous collision of happy incidents, or an involuntary concurrence of ideas, in which the philosopher to whom they happened had no other merit than that of knowing their value, and transmitting unclouded to posterity that light which had been kindled by causes out of his power." Samuel Johnson The Rambler Saturday, September 7, 1751
vii
T ABLE OF CONTENTS
Xl
PREFACE
INTRODUCTION
1. Theory, Data, and Explanation 2. The Origins of the Theory CHAPTER I. ELEMENTARY OBJECT THEORY
15 16 19
1. The Language
2. 3. 4. 5.
I I 6
The Semantics The Logic The Proper Axioms An Auxiliary Hypothesis
28
32 37
CHAPTER II. APPLICATIONS OF THE ELEMENTARY THEORY
40
1. Modelling Plato's Forms
41
2. Modelling the Round Square, etc. 3. The Problem of Existence Appendix
50 52
47
CHAPTER III. THE MODAL THEORY OF ABSTRACT OBJECTS
59 59
(WITH PROPOSITIONS)
1. 2. 3. 4.
The The The The
Language Semantics Logic Proper Axioms
61
68 73
1. Truth
77 77
2. 3. 4. 5.
84 91 99
CHAPTER IV. THE APPLICATIONS OF THE MODAL THEORY
Modelling Possible Wodds Modelling Leibniz's Monads Modelling Stories and Native Characters Modality and Descriptions ix
78
x
T ABLE OF CONTENTS
CHAPTER V. THE TYPED THEORY OF ABSTRACT OBJECTS
1. The Language
2. The Semantics 3. The Logic 4. The Proper Axioms CHAPTER VI. APPLICATIONS OF THE TYPED THEORY
1. Modelling Frege's Senses (I)
2. Modelling Freg
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