Leibniz: Representation, Continuity and the Spatiotemporal

204 Pages·1999·4.284 MB·English

by  Dionysios A. Anapolitanos (auth.)

LEIBNIZ: REPRESENTATION, CONTINUITYANDTHESPATIOTEMPORAL
Science and Philosophy
VOLUME?
SeriesEditor
NancyJ.Nersessian,Program inCognitiveScience, Georgia InstituteofTechnology, Atlanta
EditorialAdvisoryBoard
JosephAgassi,DepartmentofPhilosophy,York UniversityandTelAviv University
GeoffreyCantor,DepartmentofPhilosophy, University ofLeeds
NancyCartwright,DepartmentofPhilosophy,StanfordUniversity
JamesT.Cushing,DepartmentofPhysics, Notre Dame University
LindleyDarden,Committee ontheHistoryandPhilosophyofScience,
University ofMaryland
MaxDresden,Institutefor TheoreticalPhysics, SUNYStonyBrook
AllanFranklin,DepartmentofPhysics, University ofColorado,Boulder
MarjorieGrene,DepartmentofPhilosophy, University ofCalifornia,Davis
AdolfGriinbaum,DepartmentofPhilosophy,University ofPittsburgh
RichardLewontin,Museum ofComparativeZoology, Harvard University
ThomasNickles,DepartmentofPhilosophy, University ofNevada.Reno
DudleyShapere,DepartmentofPhilosophy,WakeForestUniversity
This series has been established as a forum for contemporary analysis of philosophical problems
which arise in connection with the construction of theories in the physical and the biological
sciences. Contributions will not place particular emphasis on anyone school of philosophical
thought. However, theywillreflectthebeliefthatthephilosophyofscience must befirmlyrooted
in an examination of actual scientific practice. Thus, the volumes.in this series will include or
dependsignificantlyuponananalysisofthehistoryofscience,recentorpast.TheEditorswelcome
contributionsfromscientistsaswellasfromphilosophersandhistoriansofscience.
DIONYSIOS A. ANAPOLITANOS
UniversityofAthens.Greece
LEIBNIZ:
REPRESENTATION,
. CONTINUITY AND
THE SPATIOTEMPORAL
Springer-Science+Business Media, B.Y:
AC.I.P.Cataloguerecordforthis book isavailablefrom theLibraryofCongress.
ISBN978-90-481-5138-7 ISBN978-94-015-9147-8(eBook)
DOI 10.1007/978-94-015-9147-8
Printedonacid-free paper
All RightsReserved
©1999 SpringerScience+BusinessMediaDordrecht
OriginallypublishedbyKluwerAcademicPublishersin 1999.
Softcoverreprintofthehardcoverlstedition 1999
No part ofthe materialprotectedbythis copyrightnoticemay bereproducedor
utilizedinanyform or byanymeans,electronicor mechanical,
includingphotocopying,recordingorbyanyinformationstorageand
retrievalsystem,withoutwrittenpermissionfrom thecopyrightowner
Dedicated to the memory of
Wilfrid Sellars
TABLE OF CONTENTS
PREFACE ix
ABBREVIATIONS xii
CHAPTERI ! REPRESENTATIONALISM 1
A.THEGENERALSETTING 1
B. REPRESENTATIONS ANDRELATIONS 12
C. INDIRECTREPRESENTATIONS 20
D. PERCEPTION 25
E. DISTINCT, CONFUSED, PETITE, ANDUNCONSCIOUSPERCEPTIONS 31
CHAPTERII ! CONTINUITy 50
A.THEPRINCIPLEOFCONTINUITYANDITSRELATIONTOOTHER
LEIBNIZIANPRINCiPLES 50
B. KINDSOFCONTINUITYANDAPPARENTCASESOFDISCONTINUiTy 63
C. DENSITYANDSEQUENTIALORCAUCHYCOMPLETENESS 69
D.THEROLEOFCONTINUITYINTHEFORMATION OFTHE
LEIBNIZIANSYSTEM 78
CHAPTERIII ! SPACE, TIME, THE SPATIO-TEMPORAL, AND
MONADIC REALITy 94
A. SPACE,THESPATIALLYEXTENDED,ANDITSMETAPHYSICAL
CORRELATE 94
B.THEPHENOMENALRELATION OF"SPATIALLY BETWEEN", ITS
METAPHYSICALBASIS,ANDDENSITYASAPROPERTYOFTHE
SPATIALLYEXTENDED 121
C. TIME, PHENOMENALCHANGE,ANDMONADICCHANGE.. 134
D. FORMALIZATIONOFTHETHIRDMODELASITREFERSTODENSITYOF
MONADICANDPHENOMENALCHANGE 153
E. ACTUALINFINITYANDTHELElBNIZIANSOLUTIONTOTHEPROBLEMOF
THECOMPOSITIONOFTHECONTINUUM 158
BIBLIOGRAPHY 175
INDEX 183
vii
PREFACE
The goal of this work is to articulate and defend a comprehensive new
interpretation of Leibniz's later views concerning representation, continuity,
and the spatio-temporal, Although the literature on Leibniz concerning these
issues is quite rich, no serious attempt has been made to give a unified
treatment ofthem. The interpretation proposed and defended is meant to fill
the existing gap.Representation isa key notion for the correct interpretation of
Leibniz. Strangely enough, despite its extensive use by Leibnizian scholars, an
important subspecies ofit, indirect representation, has been largely ignored. In
light ofWilfrid Sellars' work, I came to realize that indirect representation is
crucial for the understanding ofLeibniz's metaphysics ofthe continuous and
the spatio-ternporal.Along with the rest ofLeibniz's representational concepts
(such as, e.g., those ofdistinct, confused, unconscious, and petite perceptions)
indirect representation, appropriately used, yields an interesting interpretation
of Leibniz's later views on continuity, space, and time. Additionally, it
articulates and brings to the fore the appropriate interconnections between the
Leibnizian realms ofthe real, thephenomenal,and the ideal.
The first chapter is devoted to discussion of various aspects of Leibniz's
representational metaphysics. Among other things, the notion of indirect
representation is discussed in detail in its own right and the representational
framework ofthe continuous and the spatio-ternporal is established. The view
isadopted that Leibniz has a tri-level system, including the level ofthe real (or
metaphysical), ofthe phenomenal, and ofthe ideal. Special attention is paid to
the problem ofwhat sort of correspondence exists between the metaphysical
and the phenomenal level ingeneral.
In Section LA the distinction, common to the Cartesian tradition, between
formal and objective reality isbriefly discussed. More specifically, it is argued
that Leibniz tacitly employed this distinction, but modified it so that there was
no longer a second distinction between primary and secondary qualities. In
Section LB, I adopt, discuss, and expand the Sellarsian interpretation of
Leibniz's reduction of phenomenal relations to representational facts of the
world of monads as they represent one another. In Section LC the notion of
indirect representation, which, Iargue, has to be taken seriously ifone wants to
give a coherent interpretation of Leibniz's system, is defined and examined.
Leibniz holds that what really is in the world is monads, i.e., substantial
undivided units in their different representational states. So monads, by
representing the world, represent all the other monads as they represent. In
Section LD the view is presented and defended that monads (and therefore
ix
x PREFACE
"vulgar" individuals like human beings, animals, plants, chairs, etc.) are
continuously graded according to the distinctness or confusedness of their
representational structures. In Section I.E, I discuss in more detail distinct and
confused perceptions, and present a novel account of petite and unconscious
ones which ties up with my treatment of the continuity of what appears as
spatiallyextended.
The second chapter deals with various aspects of Leibniz's notion of
continuity. In Section ILA the most important architectonic principle of his
system, the principle ofcontinuity, is discussed. Iconsider two basic forms of
it: (a) nature never makes leaps, and (b) the correlations between cases in
nature-which can be considered as values of the same variable x-and their
consequences are described by continuous functions. I prove that these forms
are not equivalent, and propose a way out ofthis problem by an appropriate
modification of(b), which, Iargue,ispermissible inthe Leibnizian framework.
Appropriate reconstructions ofLeibniz's arguments for the derivation ofthis
principle from the principle of sufficient reason and the principle ofthe best
are also given. Additionally, it is argued that the principle of continuity is
independent of the principle of the identity of indiscernibles and is not
equivalent to the principle of plenitude. In Section ILB basic kinds of
continuity and apparent cases ofdiscontinuity are discussed as they appear in
the framework ofLeibniz's system. By using the distinct/confused dichotomy
together with the Leibnizian doctrine concerning the finitude of what can be
distinctly represented in the framework ofone and the same representation, I
establish that these apparent cases ofdiscontinuitydo not constitute a violation
of the principle ofcontinuity. In Section ILCthe position is developed that not
only density,but also traces ofwhat we would today call sequential or Cauchy
completeness can be found inLeibniz's writings. Finally, Section II.D contains
an account ofone ofthe basic frictions which, Ithink, led Leibnizto adopt his
non-spatial, monadic metaphysics.
Chapter III discusses space, time, the phenomenally spatio-temporal, and
monadic reality and change. In Section lILA an analysis ofLeibniz's tri-level
metaphysics as it refers to space (ideal), the spatially extended (phenomenal),
and to monadic momentary representational reality (metaphysical) is offered.
The property ofuninterruptedness is critically assessed, especially as it refers
to the continuity ofspace, considered as an ideal entity (and for that matter as
it refers to any Leibnizian ideal continuum.) Iargue that it is uninterruptedness
that led Leibniz to consider the ideal ones as the only genuine continua and
consequentlyto insist that he had solved the problem ofthe composition ofthe
continuum. Section III.B is devoted to the construction ofa model describing
PREFACE xi
the interconnection of the real with the phenomenal in the case of the
phenomenal relation "spatially between." In the course ofthe construction the
notion of indirect representation is used. In addition, a formalization is
proposed which leads to an exact account of spatial density in terms of its
metaphysical correlate,representational density. In Section III.C Idiscuss time,
phenomenal change, and monadic change. I present a model for phenomenal
simultaneity as based upon metaphysical simultaneity. I argue that one is
forced to admit monadic simultaneity as a feature of monadic change, if one
wishes to give a coherent interpretation of Leibniz's representational
metaphysics ofchange. This leads one to adopt the view that monadic change
relations are in one sense real (connecting together metaphysical past and
future) in a way in which metaphysical spatial relations are not. In the same
Section three models ofmonadic change are considered under the names the
Whiteheadian Model, the Discrete and Discontinuous Model, and the Discrete
and Continuous Model.Arguments for and against them are presented, and the
third is adopted. In Section III.D the Discrete and Continuous Model is used
for a formalization ofthe interconnection ofmonadic and phenomenal change
as it refers to temporal density. In Section III.E Leibniz's solution to the
problem of the composition of the continuum is critically assessed and
discussed. It is argued that Leibniz's solution was too easy a way out ofthe
labyrinthus continuiand, inasense,too heavily dependent upon his idea ofthe
uninterruptedness ofideal continua as the basic property ofgenuine continuity.
It is concluded, finally, that without substantial modifications, his metaphysics
could have allowed him to adopt a solution much closer to our modem
conception ofthe problem.
I was very fortunate to have had the opportunity to discuss many of the
ideas in this book with the late Wilfrid Sellars. I thank George Gale who read
through adraft ofthe book and provided me with extremely helpful comments.
I also have had many conversations with Nicholas Rescher, Hide Ishiguro,
James Edward McGuire, Joseph Camp and John Haugeland. I thank them all.
Finally my thanks go to Nancy Nerssesian for her continuous encouragement
while writing the book.
The responsibility for alltranslations ofthe quoted passages is mine, though
Ihave made use ofexisting translations along the way,sometimes modifying
them slightly. The following abbreviations are used throughoutthe text and
refer tothe corresponding items inthe bibliography.
ABBREVIAnONS
A [2] L [94]
AG [7] La [92]
BC [19] M [102]
Couto OF [24] NE [124]
F [45] R [128]
G [59] Th [43]
GM [58] W [152]
J [75]
xii