Table Of ContentLEIBNIZ'S METAPHYSICS OF NATURE
THE UNIVERSITY OF WESTERN ONTARIO
SERIES IN PHILOSOPHY OF SCIENCE
A SERIES OF BOOKS
IN PHILOSOPHY OF SCIENCE, METHODOLOGY,
EPISTEMOLOGY, LOGIC, HISTORY OF SCIENCE,
AND RELATED FIELDS
Managing Editor
ROBERT E. BUTTS
Dept. ofP hilosophy, University of Western Ontario, Canada
Editorial Board
JEFFREY BUB, University of Western Ontario
L. JONATHAN COHEN, Queen's College, Oxford
WILLIAM DEMOPOULOS, University of Western Ontario
WILLIAM HARPER, University of Western Ontario
JAAKKO HINTIKKA
CLIFFORD A. HOOKER, University ofN ewcastle
HENRY E. KYBURG, Jr., University ofR ochester
AUSONIO MARRAS, University of Western Ontario
JU'RGEN MITTELSTRASS, University ofK onstanz
JOHN M. NICHOLAS, University of Western Ontario
GLENN A. PEARCE, University of Western Ontario
BAS C. V AN FRAAS SEN , University of Toronto & University of
Southern California
VOLUME 18
Library of Congress Cataloging in Publication Data
Rescher, Nicholas.
Leibniz's metaphysics of nature.
(The University of Western Ontario series in philosophy of science; v. 18)
Includes bibliographical references and indexes.
1. Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716-Metaphysics.
2. Metaphysics. 3. Philosophy of nature. 4. Space and time. I. Title.
II. Series: University of Western Ontario series in philosophy of science; v. 18.
B2599.M7R47 110'.92'4 81-5944
ISBN·13: 978·90·277·1253·0 c·ISBN·13: 978·94-009·8445·5
001: 10.10071978·94-009·8445·5
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, 3300 AH Dordrecht, Holland.
D. Reidel Publishing Company is a member of the Kluwer Group.
All Rights Reserved
Copyright © 1981 by D. Reidel Publishing Company, Dordrecht, Holland
and copyright holders as specified on appropriate pages.
Softco\'el' reprint of the hal'dco\"C1' 1st edition 1981
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
NICHOLAS RESCHER
Department of Philosophy,
University ofP ittsburgh
LEIBNIZ'S
METAPHYSICS
OF NATURE
A Group of Essays
D. REIDEL PUBLISHING COMPANY
DORDRECHT: HOLLAND / BOSTON: U.S.A.
LONDON: ENGLAND
For Yvon Belaval
CONTENTS
PREFACE ri
INTRODUCTION xiii
I. LEIBNIZ ON CREATION AND THE EVALUATION
OF POSSIBLE WORLDS 1
1. S tagesetting 1
2. Mathematico-Physical Inspiration 8
3. Epistemological Implications 12
4. Leibniz as a Pioneer of the Coherence Theory of
Truth 15
II. THE EPISTEMOLOGY OF INDUCTIVE REASON-
ING IN LEIBNIZ 20
1. Introduction 20
2. The Extraction of General Truths from Experi-
ence 21
3. Concluding Observations 26
III. LEIBNIZ AND THE CONCEPT OF A SYSTEM 29
1. The Concept of a System 29
2. Leibniz as System Builder 32
3. Why System? 34
4. Cognitive vs. Ontological Systematicity 35
5. System and Infinite Complexity 37
vii
viii CONTENTS
IV. LEIBNIZ ON THE INFINITE ANALYSIS OF CON-
TINGENT TRUTHS 42
1. Introduction 42
2. Analysis 42
3. Calculus as the Inspiration of Infinite Analysis 48
4. A Metaphysical Calculus of Perfection-Optimiza-
tion 51
5. Conclusion 53
v. LEIBNIZ ON INTERMONADIC RELATIONS 56
1. Introduction 56
2. The Crucial Role of Relations in Incompossibility 56
3. The Reducibility of Relations 59
4. Relational Reducibility and Incompossibility 66
5. Reducibility Not a Logical But a Metaphysical
Thesis 68
6. The Reality of Intermonadic Relations 72
7. Abstract Relations 76
VI. LEIBNIZ AND THE PLURALITY OF SPACE-TIME
FRAMEWORKS 84
1. The Question of Distinct Frameworks 84
2. Spatiality: The Conception of Space as Every-
where the Same 85
3. One World, One Space 86
4. Distinct Worlds Must Have Distinct Spaces 87
5. How are Distinct Spaces Distinct? 88
6. Why Distinct Spaces? 91
7. A Superspace After All? 92
8. Cross-World Spatial Comparisons 93
9. Must the Spatial Structure of Other Worlds Be
Like that of Ours? 95
CONTENTS ~
10. The Important Fact That, for Leibniz, Time is
Coordinate With Space 96
11. Can a Possible Wodd Lack Spatiotemporal
Structure? 98
VII. THE CONTRIBUTIONS OF THE PARIS PERIOD
(1672-76) TO LEIBNIZ'S METAPHYSICS 101
I. Overview of Cardinal Theses of Leibniz's Meta-
physics 101
2. A Missing Piece 106
3. Conclusion 113
APPENDIX: RESCHER ON LEIBNIZ, WITH BIBLIOG
RAPHY 117
INDEX OF NAMES 123
SUBJECT INDEX 125
PREFACE
The essays included in this volume are a mixture of old and new.
Three of them make their first appearance in print on this occa
sion (Nos III, IV, and V). The remaining four are based upon
materials previously published in learned journals or anthologies.
(However, these previously published papers have been revised
and, generally, expanded for inclusion here.) Detailed acknowl
edgement of prior publications is made in the notes to the relevant
articles. I am grateful to the editors of these several publications
for their kind permission to use this material.
I am grateful to an anonymous reader for the Western Ontario
Series for some useful corrigenda. And I should like to thank John
Horty and Lily Knezevich for their help in seeing this material
through the press.
NICHOLAS RESCHER
Pittsburgh, Pennsylvania
May, 1980
xi
INTRODUCTION
The unifying theme of these essays is their concern with Leibniz's
metaphysics of nature. In particular, they revolve about his cos
mology of creation and his conception of the real world as one
among infinitely many equipossible alternatives.
The essays address themselves to the following issues: the theory
of creation as a selection among infinitely diversified alternatives,
the cognitive problems that confront man's finite intellect in scien
tific inquiry at a world of infinite complexity and diversity, the
central role of systematization in human cognition, the charac
teristic nature of contingent truth as a matter of infinitely ramified
comparisons, the infinite ramifications of the relations among the
substances comprising one self-contained world-system, the infinite
diversity of alternative space-time frameworks for different pos
sible worlds, and the contributions of Leibniz's work on the infini
tesimal calculus to his creation-metaphysics.
As is clear, even from this barebones summary, the idea of
infinity runs through Leibniz's philosophy of nature as an ever
recurrent theme. He was the true child of a Renaissance culture
for which the finitude of the classical world had burst asunder
once and for all. Nevertheless, he continued true to his Greek
heritage in insisting on the systemalizability of any and all rational
knowledge of the real. Philosophically it was not for nothing that
Leibniz was the inventor of the infintesimal calculus. For it was
this that provided him with the idea that one could systematize
with mathematical rigor thought regarding matters of infinite com
plexity and diversity. The calculus was Leibniz's model for con
tinuing the classical architectonic of antiquity with the infinitistic
xiii
