Kantian Questions, Leibnizian Responses - Matthew John Olsen

KANTIAN QUESTIONS, LEEBNIZIAN RESPONSES

BY

MATTHEW JOHN OLSEN

A.B., Albright College, 1996 A.M., University of Illinois at Urbana-Champaign, 2000

DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Philosophy

in the Graduate College of the University of Illinois at Urbana-Champaign, 2004

Urbana, Illinois

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C e r t i f i c a t e o f C o m m i t t e e A p p r o v a l

University of Illinois at Urbana-ChampaignGraduate College

April 6, 2004

We hereby recommend that the thesis by:

MATTHEW JOHN OLSEN

Entitled:KANTIAN QUESTIONS, LEIBNIZIAN RESPONSES

Be accepted in partial fulfillment of the requirements for the degree of:

Doctor of Philosophy

Signatures:

Director o f Research Head o f Department

Committee on Final Examination*

Chairperson

'ommittee Member

Committee Member

Committee Member

Committee A0mber Committee Member

* Required for doctoral degree but not for master’s degree


ABSTRACT

My dissertation is an examination of Immanuel Kant’s criticisms of G.W.

Leibniz’s metaphysics and possible Leibnizian responses to tliose objections. Kant’s

central criticism of Leibniz’s metaphysic is that it is based solely on intellectual, i.e.,

logical, principles and incorrectly dismisses the senses and sensible bodies as confusions.

While Kant grants that Leibniz’s system is internally coherent, he claims that Leibniz

seriously misunderstood human cognition and incorrectly reduced sensible bodies to the

monads that allegedly underlie them. My project is to show that although these are

powerful and original objections, Leibniz did not sacrifice the material world for the

monadic. I argue that Leibniz had an ontology that allowed for the real existence of

material bodies. Leibniz actually held that all monads have a material body and the

sensible world is aggregated out of these bodies. The senses, while limited, provide us

with useful, even essential, knowledge of the world. In addition to this broad ontological

claim, I also address specific Kantian criticisms of Leibniz’s views on space and time, the

identity of iiidiscernibies, and the pre-established harmony. In each case, I argue that

while Kant’s objections have merit and appropriately challenge Leibniz on the relation of

the monadic and the material, Leibniz often has the resources to deal with the objection,

and in a way that is much less fantastic than Kant thinks. Ultimately, I maintain that

while Leibniz did assume that the universe was rational and largely explainable through

intellectual means, he was also very concerned with accounting for our world of everyday

experience.

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TABLE OF CONTENTS

ABBREVIATIONS.......................................................................................... .vi

PREFACE .................................................................. viii

CHAPTER 1 KANT'S CRITICISMS OF LEIBNIZ ........... 1I. Concepts of Reflection........................ 1II. An Ontological Argument ...... 6III. Forms of Intuition........................................................ 12IV. The Concepts of Reflection Revisited................................................. ....20V. Summaries in WRP and OD............................................................. 26VI. Conclusion ............................................................................ 34

CHAPTER 2 THE ONTOLOGY OF BODIES........................................................... 36I. Kant’s Interpretation................................................................. 36II. The Motivation for Kant’s Interpretation......................................................... 39III. Kant’s Objections ....................................................... 41IV. The Need for Monads... ...... 42

IV. 1 Extension....................................... 44IV.2 Atoms....................... 45IV.3 Monads...................... 47

V. Kanf s First Criticism - Intellectual Intuition ..................... 50VI. Kant’s Second Criticism - Ontology of Sensible Objects ........................... 56

VI. 1 Sensing Monads............................. 57VI.2 The Ontology of Sensible Bodies.......................................................... 65VI.3 The Normative Status of Material Bodies............................ 76

VII. Conclusion............................................................. 77

CHAPTER 3 SPACE AND TIME IN LEIBNIZ’S METAPHYSICS ....... 80I. Points of Agreement and Disagreement....... ........... 80II. Background Considerations.. ........... 82III. The Standard Reading of Leibnizian Space and Time ....................... 84

111.1 Another View of Leibnizian Space and Time................................... 86111.2 Three Competing Views............................................. 88111.3 Problems with the Ideal Reading..................................... 89

IV. Kant’s Arguments .................................................. 91IV. 1 Kant’s Presupposition Argument ............ ........92IV.2 Leibniz’s Reply to the Presupposition Argument...... ...........................94IV.3 Kant’s Argument from Geometry.. ...... 99IV.4 Leibniz’s Reply to the Geometry Argument.............. 102IV.5 Kant’s Metaphysical Argument.......................... 105IV.6 Incongruent Counterparts... ..... 108IV.7 Leibniz’s Response to the Incongruent Counterparts Argument 111

V. Conclusion.................................................................. 114

IV


CHAPTER 4 THE IDENTITY OF INDISCERNIBLES.. ........ 116I. Statement of the Principle.............................. 116II. Kant’s Criticisms ................ 118III. Background for the Principle ........ 121IV. Source of the Principle at the Level of Body........................... 127

IV. 1 Freedom of Application...................... 130IV.2 The Principle of Sufficient Reason...................................... 133IV.3 Monad as Form of the Body......................................................................139IV.4 Empirical Reasons ...... 142

V. Conclusion........................................................................................................ 144

CHAPTER 5 PRE-ESTABLISHED HARMONY AND THE WORLD’S UNITY...... 149I. Kanf s Criticisms.............................................. 150II. Background to the Pre-Established Harmony .......... 161III. Responses to Kanf s Objections...................................... 169

111.1 Change in the Simple................................................................... 169111.2 Unity of the World........................................................ 176

IV. Conclusion ...................... 181

REFERENCES........ .................................................................... 183

VITA ...... 189


ABBREVIATIONS

CP Gottfried Wilhelm Leibniz. Confessio philosophi. Translated iiito Germanwith commentary by Otto Saame. Franlcfurt am Main: Vittorio Kiostemiann, 1967. The English translation from Saams’s German translation is my own.

CPR Immanuel Kant. Critique o f Pure Reason. Trans. Norman Kemp Smith.New York: St. Martin’s Press, 1929. Cited with pagination from the A and B editions of the work

DM Gottfried Wilhelm Leibniz. Discourse on Metaphysics, Correspondencewith Arnauld, Monadology. Trans. George Montgomery. La Salle: Open Court Publishing Company, 1902.

DS Immanuel Kant. “Concerning the Ultimate Ground of the Differentiationof Directions in Space.” In Immanuel Kant: Theoretical Philosophy 1755- 1770. Trans, and ed. by David Waldorf and Ralf Meerbote. Cambridge: Cambridge University Press, 1992: 361-372.

G Gottfried Wilhelm Leibniz. Die Philosophischen Schriften von GottfriedWilhelm Leibniz. Ed. C.I. Gerhardt. Berlin: Weidmannische Buchhandlung, 1890: Vol. 7. The translations from this volume are my own.

HCD Pierre Bayle. Historical and Critical Dictionary: Selections. Ed and trans.Richard H. Popkin. Indianapolis: Hackett Publishing Company, Inc., 1991.

ID Immanuel Kant. “On the form and principles of the sensible andintelligible world” {Inaugural Dissertation]. In Immanuel Kant: Theoretical Philosophy 1755-1770, trans. and ed. David Waldorf and Ralf Meerbote. Cambridge: Cambridge University Press, 1992: 373-416.

L Gottfried Wilhelm Leibniz. Philosophical Papers and Letters 2"* ed.Trans. Leroy E. Loemker. Dordrecht; D. Reidel Publishing Company, 1969.

LC The Leibniz-Clark Correspondence. Ed. H.G. Alexander. Manchester:Manchester University Press, 1965.

LNS Leibniz’s “New System ” and Associated Contemporary Texts. Trans, anded. R.S. Woolhouse and Richard Francks. Oxford: Clarendon Press, 1997.

Logic Immanuel Kant. Logic. Trans. Robert S. Hartman and Wolfgang Schwarz.New York: Dover Publications, Inc., 1988.

VI


NE Gottfried Wilhelm Leibniz. AGw Essays on Human Understanding. Trans.and ed. Peter Remnant and Jonathan Bennett. Cambridge: Cambridge University Press, 1996.

ND Immanuel Kant. “A New Elucidation of the First Principles ofMetaphysical Cognition.” In Immanuel Kant: Theoretical Philosophy 1755-1770. Trans, and ed. David Waldorf and Ralf Meerbote. Cambridge: Cambridge University Press, 1992: 1-45.

OD Immanuel Kant. On a Discovery According to which Any New Critique ofPure Reason Has Been Made Superfluous by an Earlier One. In The Kant- Eberhard Controversy. Henry E. Allison. Baltimore: The Johns Hopkins University Press, 1973.

P Immanuel Kant. Prolegomena to Any Future Metaphysics. Trans. LewisWhite Beck. Indianapolis: Bobbs-Merrill Educational Publishing, 1950.

PE Gottfried Wilhelm Leibniz. G. W. Leibniz: Philosophical Essays. Trans.Roger Ariew and Daniel Garber. Indianapolis: Hackett Publishing Company, 1989.

Theo Gottfried Wilhelm Leibniz. Theodicy. Ed. Austin Farrer. London:Routledge & Kegan Paul, 1952.

WRP Immanuel Kant. What Real Progress has Metaphysics Made in GermanySince the Time o f Leibniz and Wolff? Trans. Ted Humphrey. New York: Abaris Books, Inc., 1983.

YLC Gottfried Wilhelm Leibniz. The Labyrinth o f the Continuum: Writings onthe Continuum Problem, 1672-1686. Trans, and ed. Richard T.W. Arthur. New Haven: Yale University Press, 2001.

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PREFACE

This idea for this dissertation emerged when I began a close study of Leibniz’s

major metaphysical works and noticed similarities between Ms thought and Kant’s.

While all students of Kant, myself included, know that Hume awoke Kant from his

dogmatic slumber, before studying Leibniz I had done very little tMnkiiig about the

dogmatism from which he arose. In Leibniz I found a link to the tradition out of which

Kant emerged and gained some insight into how that background had shaped the

direction of Ms thought. When I looked back at Kant’s works I found that he addressed

Leibniz and his metaphysics head on in many of his writings. Kant’s criticisms tend to

focus on the connection between the world of monads and the material world in Leibniz’s

metaphysics and they accuse Leibniz of illegitimately prioritizing the intellect over the

senses. This line of criticism is unique and penetrates to the heart of Leibniz’s

philosophical project, which I attribute to a combination of Kant’s familiarity with

Leibniz and the backing of the Critical philosophy as a means of criticism.

Wriien I turned to the secondary literature I found that very little work had been

done on these criticisms and the work that had been done was either by a Leibnizian

criticizing Kant for misrepresenting Leibniz, or a Kantian claiming that Kant’s criticisms

were devastating to Leibniz. I felt that there was a need not only to get clear on Kant’s

criticisms, but also to consider Leibniz’s possible responses to them. As my own

thinking on Leibniz developed in light of Kant’s objections 1 found in Leibniz not a

desire to throw away the material world for an intellectual world of monads, but an

acknowledgement of the need for the sensible and the material in human knowledge and

experience.

Insofar as this dissertation is a work on Leibniz’s metaphysics, I see it as part of a

larger movement in Leibniz scholarship. Two of the most important works on Leibniz at

the turn of the last century by Louis Couturat and Bertrand Russell focused on the role of

logic in Leibniz’s metaphysical thought. These seminal writings set the tone for work on

Leibniz for much of the 20* Century. While they picked out what is surely an essential

part of Leibniz’s metaphysics, it is only part of the story. Such a rich thinker who

embraced the complexity in human thought and experience saw the world as more than

V lll


simply a proposition to be formalized or an equation to be solved. Recent work on

Leibniz has done a lot to correct this rather one-sided view of Leibniz and to show that

Leibniz’s metaphysical concerns encompass more than concepts and monads. It is my

hope that this work does its small part in contributing to a more complete view of

Leibniz’s rich thought.

I would also like to mention something about my methodology and approach in

writing this dissertation. First, one might ask, w'hy have you chosen to focus solely on

Leibniz and Kant? Where are all the Leibnizian contemporaries of Kant such as Wolff or

Eberhard? While I will admit that these thinkers may have influenced Kant’s

understanding on Leibniz, Kant in his writings tends to focus on Leibniz, not his

followers and for, what I take to be, obvious reasons. Why argue with the students when

you can disprove the master? I firmly believe that Kant felt that if he were to discredit

Leibniz himself—the dogmatism in its purest form— then its later incarnations would fall

also. Thus, in this work I have largely overlooked Kant’s Leibnizian contemporaries and

have focused on Leibniz directly.

There are also several questions about the anachronistic aspect of the debate that I

am creating between these two thinkers. Given that eight years separate Leibniz’s death

from Kanf s birth the possibility for any real dialog between the two is impossible. In

order to derive Kant’s criticisms of Leibniz I have drawn from a wide range of Kantian

texts from his first philosophical work “The New Elucidation” to some lesser known.

Critical works such as the What Real Progress? essay. A majority of my reading of

Kanf s criticisms is drawn from the important pre-Critical text the Inaugural Dissertation

and the first Critique itself.

There is another important question concerning the Leibnizian texts that were

available to Kant and that informed his reading of Leibniz. Leibniz was anything but a

systematic writer and other than the largely non-philosophical work the Theodicy,

Leibniz doesn’t have a major philosophical opus to which interpreters can look. Most of

his philosophical thought, and the most insightful of it, was relayed in letters and short

articles that have only become widely available in relatively recent times. Kant surely

did not have access to most of these writings. The Leibnizian works that Kant probably

had read include the Monadology, the Leibniz-Clarke correspondence, and the New

IX


Essays on Human Understanding. Yet, in this work I have availed Leibniz of a much

wider range of his writings in responding to Kant. Isn’t this an unfair advantage for

Leibniz? I don’t think that it is. While there are some details of Leibniz’s theory that

Kant simply wasn’t aware of and therefore omitted or unintentionally misrepresented, 1

feel that Kant presents a coherent and challenging interpretation of Leibniz’s

metaphysics. If there is any misrepresentation by Kant I feel that it is due more to Kant’s

reading of Leibniz through the Critical philosophy than it is due to an ignorance of

Leibniz’s writings. Thus, my concern in this dissertation is not as much v/ith whether

Kant got Leibniz right, although there is some of that, as it is with the philosophical

responses available to Leibniz to the criticisms that Kant does provide. Using a wide

range of Leibnizian texts seemed to me a more fruitful way of formulating possible

Leibnizian responses. It is a very daunting task to anticipate how such a brilliant thinker

might respond to philosophical challenges, especially one who was reluctant to publish

for fear that the “uninitiated” would misunderstand him, but in this dissertation I have

done my best to bring out some of what I take to be the true genius of G.W. Leibniz.


CHAPTER ONE

KANT'S CRITICISMS OF LEIBNIZ

My goal in this introductory chapter is to outline KanPs criticisms of Leibniz’s

metaphysics. More specifically, I v/ill show that Kant’s criticisms center around the

requirement that human cognition involve a sensible intuition with its forms of space and

time. I will also show that Kant’s disagreement with Leibniz is as much ontological as it

is epistemological. In other words, Kant is taking issue with what there is as well as what

we can know. In order to demonstrate these points I will be looking at Kantian criticisms

of Leibniz from a number of sources including the Critique o f Pure Reason and the

Inaugural Dissertation. In most of the works that I will discuss Kant also picks out

specific elements of Leibniz’s philosophy for criticism and I will be examining these as

well in order to support my general interpretation and to lay the groundwork for the

debate in later chapters.

I. Concepts of Reflection

The best place to start if one w'-ants to examine Kant’s criticisms of Leibniz is the

Critique o f Pure Reason. In a work that fails to mention almost any philosophers by

name, Kant devotes an entire section of the first Critique to Leibniz. This section is an

appendix to the “Transcendental Analytic” entitled “The Amphiboly of the Concepts of

Reflection,” in which Kant makes the famous claim that Leibniz committed a major

philosophical mistake when due to a “transcendental amphiboly” he subsequently

“intellectualized appearances.” What Kant is claiming is that Leibniz arrived at the

central principles of his philosophy by using the intellect alone, and in so doing he

illegitimately discounted the senses and failed to realize that our knowledge is limited to

the sensible objects that we can intuit. While this criticism in outline is easy to

understand, grasping its details requires figuring out what a “concept of reflection” is,

what a “transcendental amphiboly” is, and how from a general criticism Kant thinks that

he can explain how Leibniz developed the central principles of his philosophy while

simultaneously explaining the problems with those principles.


As the title of the section indicates, Kant’s focus is on the “concepts of

reflection.” These are concepts according to which representations can be related to one

another. Unlike the concepts that constitute the categories, which determine or at least

order the material that the intuition provides, the concepts of reflection simply deal with

representations as they are given. According to Kant, before an objective judgment can

be made it is necessary that one compare concepts in certain ways in order to carry out

the judgment successfully. In other words, the act of reflection involves the comparison

of representations prior to the determination of an object. The representations that are the

material for reflection are simply assumed or given rather than synthesized as they are in

cognition enabled by the categories {CPR A79/B104). In the Prolegomena Kant

describes the concepts of reflection as “concepts of a mere comparison of concepts

already given” while the pure concepts of the understanding are “concepts of connection,

and thereby of the objects themselves” {P §39 73). The concepts according to which we

make the comparison are grouped into four relational pairs: identity and difference,

agreement and opposition, the inner and the outer, and the determinable and the

determination (matter and form) {CPR A261/B317). Kant derives these pairs of concepts

from the table of judgments.

It might be helpful at this point to consider an example to see better what Kant is

talking about. If we take the first pair of concepts, identity and difference, Kant is

claiming that we begin the process of reflection by asking if a concept that we possess is

identical to or different from another concept. At this point, we are not actually

determining the content of the concepts, but we are simply considering if one is the same

or different from the other. We make this comparison in order that we may go on and

make an objective judgment. If our comparison determines that the concepts are identical

then we will be able to make a universal judgment. If we find a difference then we may

be able to make a particular judgment (ibid.). The process is intended to be the same for

the other concepts; each concept of reflection is tied to a particular judgment and in a

sense anticipates the corresponding judgment. The concepts of reflection are prior to the

objective judgment.

According to Kant, if we wish to use our findings objectively, that is if we wish

our comparison to be useful in the determination of the nature of objects, we must


consider the subjective faculty to which these representations belong. This is what makes

the reflection transcendental. Kant defines the process of transcendental reflection as;

“that state of mind in which we first set ourselves to discover the subjective conditions

under which [alone] w'c are able to anive at concepts” (CPR A260/B316).

Transcendental reflection is a subjective act whereby we determine what kind of objects

we are dealing with without determining the objects themselves; it is “the consciousness

of the relation of given representations to our different sources of knowledge” (ibid.).

Kant presents us with two possible sources of knowledge for transcendental reflection,

the sensibility and the understanding. According to Kant each faculty has its own

standards that determine how the comparison will be executed. Thus, in the example

above, our comparison of similarity and difference will vary depending on whether we

are comparing sensible representations or representations of the understanding (CPR

A261/B317). After determining the kind of concepts that we are comparing we can then

make the comparison and determine if the concepts are identical or different, which will

inform our subsequent judgment.

This is an outline of the process that Kant is concerned with in this section and

immediately several important elements come into view. First, it is important to see that

there are actually two processes in the course of transcendental reflection. While it is true

that the concepts of reflection are concepts of comparison, as we have seen, finding out

the type of representations that we are dealing with is an essential element in making the

comparison correctly. Prior to the comparison we must determine if the representations

that we are dealing with are sensible or intellectual. This is the actual act of reflection

(reflexio) and is what Kant describes as the assignment of a “transcendental location” to a

given concept (CPR A268/B324). “[T]he interrelations of given representations can be

determined only through transcendental reflection, that is, through [consciousness of]

their relation to one or the other of different kinds of knowledge” (CPR A262/B318).

The act of comparison (compamtio) follows the determination of transcendental location

that is achieved through the reflection (ibid.). The comparison of the concepts according

to the concepts of the reflection is certainly what initiates the reflection, but it is

subsequent to the determination of the transcendental location. Thus, transcendental


reflection requires two steps: the determination of the “location” of the concepts and then

their comparison.

Second, Kant simply assumes the two “kinds of knowledge,” as well as the

unique criteria that each brings to the comparison, as our choices in the reflective act.

Quite clearly Kant is leaning heavily on findings made at earlier points in the Critique.

In fact, the process of transcendental reflection relies on Kant’s entire theory of

cognition. For Kant, cognition requires two distinct faculties that must be in a certain

kind of relation; roughly, the sensible intuition provides the material for cognition, while

the imderstanding orders the manifold of intuition according to its pure concepts, i.e., the

categories. “In every cognition there is to be distinguished matter, i.e., the object [which

is intuited], and form, i.e., the manner how we cognize the object” {Logic 37). The

synthesis of the intuition and the understanding results in an objective judgment. The

synthesis also generates experience, i.e., “knowledge by means of connected perceptions”

(CPi?B161).

Kant’s claim is that transcendental reflection is prior to the synthesis of cognition,

but cannot be made in ignorance of it. One must consider if these representations are

going to be employed in cognition, i.e., if we are going to apply to them to objects.

Certainly we cannot determine the content of these representations, this is the role of

cognition itself, but we must consider if they are to be employed in experience. In this

sense, the reflection is transcendental. ‘‘'Transcendental reflection ... since it bears on the

objects themselves, contains the ground of the possibility of the objective comparison of

representations with each other” {CPR A262/B319). Kant is claiming that reflection is a

process of thought that is prior to cognition but is essential if one is to go on and cognize

properly. Before we can make a judgment of, say, identity, we must first ask if the

concepts that we are considering are identical to each other and to make that comparison

correctly we must ask what kind of concepts we are dealing with. Since this comparison

is logically prior to our experience of the objects whose concepts we are determining, the

identity or non-identity of the comparison is, in Kanf s terms, “a priori.'" “[Tjhis

transcendental consideration is a duty from which nobody who wishes to make an a

priori judgment of things can claim exemption” {CPR A263/B319).


It is legitimate to forgo transcendental reflection if one does not wish to “advance

to the objects with these concepts” and instead undertake “logical reflection” (CPR

A269/B325). In logical reflection one is merely making the comparison of concepts

within the understanding and is concerned only with the form of the concepts and does

not address their source or how the concepts arose {Logic 99). Therefore, one does not

have to be concerned with determining the faculty that the object of the representation

belongs to. Logical reflection has a more limited scope of application since its findings

cannot be employed in experience. We, for example, may make determinations as to

what constitutes identity as far as concepts alone are concerned but we cannot apply these

logical findings to objects. Objects have their own standard that must be informed by our

manner of apprehending them, i.e., the sensible intuition. This comparison of form

without consideration of content must subsequently have application only with regard to

logic and not to the objects themselves.

Kant uses the distinction between transcendental and logical reflection to explain

the difference between his Critical philosophy and earlier metaphysical views. Without

the proper understanding of Kantian transcendental reflection, metaphysicians prior to

Kant attempted to make objects in the world conform to conceptual truths. These

“dogmatic” metaphysicians undertook logical reflection and subsequently took truths that

they derived relating to concepts alone and applied them to the world of experience.

Kant calls the failure to reflect transcendentally a “transcendental amphiboly,” i.e., “the

confounding of an object of pure understanding with appearance” {CPR A270/B326).

Leibniz committed this fallacy. Just as an amphiboly in natural language involves a

sentence that can be taken in two ways and a speaker or writer only acknowledges one of

them, Leibniz only recognized one aspect of the comparison of concepts, namely the

comparison of the concepts according to the dictates of the understanding or, we might

say, the comparison of concepts alone. He subsequently made objective judgments on

the basis of these comparisons and made claims about the nature of the world. Leibniz

did not, for example, acknowledge that we differentiate concepts and sensible objects in

different ways (through their content and their location respectively); he simply

determined how we differentiate concepts and then claimed that sensible objects must be

individuated in the same way.


Kant claims that in any cases where Leibniz discovered a discrepancy between his

purely intellectuai findings and the conditions that obtain in the sensible world, he

claimed that the disparity arose because the world that we experience is only a poor

approximation of the world that is clearly known through the intellect. In other words, he

made the senses subservient to the understanding. Of course, he did not deny that we

apprehend sensibly or have sensible representations, he merely claimed that what we

sensibly experience is only a confused manner of apprehending what we know to be true.

Kant describes Leibniz’s process of subordinating the sensible to the intellectual as

“inteilectualiziiig appearances.”

He [Leibniz] compared all things with each other by means of concepts alone, and naturally found no other differences save those through which the understanding distinguishes its pure concepts from one another. The conditions of sensible intuition, which carry with them their own differences, he did not regard as original, sensibility being for him only a confused mode of representation, and not a separate source of representations. (CPR A270/B326)

While Kant’s principle target with the transcendental amphiboly is Leibniz, he

also uses it to point out the problem with empiricism as well. According to Kant, the

empiricists, of whom he focuses on Locke as the paradigm, did the opposite of the

dogmatists and subordinated the intellect to the senses. Locke also committed the

amphiboly by compromising the concepts of the understanding and making them

determined by appearance. Kant claims that Locke, “sensualized all concepts of the

understanding” (CPR A271/B327). While Leibniz stated that all things, internal and

external, were intelligible and subject to the determination of the understanding, Locke

did the reverse and claimed that everything, both inward and outward was empirical and

determined through our empirical interaction with the world. In both cases, an incorrect

understanding of cognition led these thinkers to a wrong view of reflection and ultimately

to the wrong view of the world.

II. An Ontological Argument

Although I have tried to be as clear as possible so far in presenting the mechanics

of Kant’s argument in the “Amphiboly,” my discussion has still been quite thick with

Kantian terms. Thus, I want to spend the next few sections trying to figure out just what


Kant’s criticisms amount to. Not surprisingly, commentators who try to understand this

section have tended to focus on Kant’s own summary of his claims that I mentioned

above that “[i]n a word, Leibniz intellectualised appearances” {CPR A271/B327). For

example, G.H.R. Paridnson takes issue with this claim explicitly in his article “Kant as a

Critic of Leibniz.”* According to Parkinson, Kant’s claim amounts to a criticism of

“Leibniz’s account of sensation.” According to Parkinson, Kant is charging Leibniz

with a failure to recognize two distinct faculties of representation, namely the sensibility

(what Kant called the intuition) and the understanding, both of which must be used

together in cognition. Leibniz instead prioritizes the understanding and makes the

difference between it and the sensibility a matter of degree. For Leibniz, sensation is

simply a confused form of thinking and not a distinct form of representation.

Leibniz did not see in the understanding and the sensibility two different sources of our representations, which must act together if they are to supply objectively valid Judgments about things. Instead, he saw sensibility as a confused form of thinking.^

Parkinson considers Kant’s interpretation fundamentally incorrect, even if Leibniz

does at times speak as though this were the case. For Leibniz sensation is not confused

thought in the way that Kant describes. Parkinson has two potential responses that

Leibniz could employ to counter Kant’s objection. The first relies on the role of

perception in Leibniz’s epistemology. For Leibniz, monads, including ourselves qua

monad, constantly perceive an infinity of things. Of course, we are not aware of all of

these perceptions, only the ones of which we take notice of, i.e., that we apperceive, at a

given moment qualify as sensations. Sensations are confused perceptions because they

are a way of apperceiving the infinity through our limited faculties. For a more powerful

being, notably God, there is no need for this limited form of apperception, i.e., sensation,

since God’s infinite power allows Him to think what we must sense. Both God and more

limited beings such as ourselves perceive an infinity, what separates the two is the power

of the faculty of apperception. Thus, sensation is not a kind of thought, confused or

otherwise, but is a kind of perception, as thinking is also. As Parkinson puts it, “a

* See also Parkinson, “The 'Intellectualisatlon of Appearances': Aspects o f Leibniz’s Theory of Sensation and Thought.” Parkinson, “Kant as a Critic of Leibniz,” 304.

^Ibid.


sensation is not a species of the genus thought; rather both sensations and abstract

thoughts involve perceptions.”' ’ One cannot say that sensations are confused thought

since both are kinds of perceptions.^

Parkinson’s second line of argnmentation deals with Leibniz’s division of

knowledge as presented in, for example, Ms 1864 paper “Meditationes de Cognitione,

Veritate, et Ideis.” On Leibniz’s epistemological hierarchy, clear Imowledge, i.e.,

knowledge that allows us to distinguish objects or concepts, is divided into confused and

distinct. For example, our knowledge of color qualifies as clear but confused knowledge

because although we can distinguish one color from another we cannot specify the marks

that allow us to make the distinction. For distinct knowledge, on the other hand, we can

distinguish the marks, that is we can explain or give the causes for the differentiation

between two things. On this view the difference between confused and distinct is the

ability to analyze the relevant concept, not the distinction between the kinds of

perception. While one may need thought to move beyond the confused concepts that

sensation provides, this does not mean that sensation is confused thought, “it merely

implies that if we rely on sensation exclusively, our knowledge and our concepts can only

be confused.”*’

Parkinson finishes his treatment of this topic by suggesting that not only is Kant

wrong that the senses are an epistemologically inferior version of tMnking, but also the

senses have a much more important role for Leibniz than the “despicable” one that Kant

imagines. Parkinson cites statements from the New Essays on Human Understanding in

which Leibniz emphasize the need for the senses and sense experience in knowing

contingent truths.’ In Parkinson’s defense, there are also a number of other places in this

work where Leibniz makes it clear that the senses are essential for beings like ourselves.

For example, Leibniz claims that, “[tjhe senses provide us with materials for reflections;

we could not think even about thought if we didn’t think about something else, i.e., about

“ Ibid., 306. A problem with Parkinson’s response is that it seems to exchange one continuum for another. While

sensation may not be confused thought, perception seems to remain a common element. He seems to be saying that sometimes we apperceive clearly, have thoughts, and sometimes confusedly, have sensations, but they are all perceptions. It is not clear that this solution obtains the separation of thought and sensation that Parkinson, and Kant, is seeking. Parkinson, “Kant as a Critic o f Leibniz,” 308.

’ Ibid.


the particular fact which the senses provide” (NE 212). In fact, Leibniz says that any

finite spirit, even angels, must have bodies and the sensory capacities that a body

provides, which seems to reinforce the importance of the senses (NE 58).

In the end I think that Parkinson is essentially correct that Kant has

mischaxacterized Leibniz’s epistemology. Quite clearly the senses are not despicable for

Leibniz, but are an essential, unique, albeit limited, way of apprehending the world. I do

have reservations concerning Parkinson’s construal of perception as solving the problem,

as mentioned above, but maldng sense of this crucial Leibnizian notion is a notorious

point of controversy. However, the real shortcoming that I see in Parkinson’s analysis is

that it only addresses one aspect of Kanf s argument.

In construing Kanf s criticism as solely epistemological, Parkinson has missed an

essentia! ontological component of Kanf s critique. When Kant makes the claim that

Leibniz “intellectualized appearances” he is not only making the epistemological claim

that Parkinson identified, but he is also making an important ontological claim about the

kind of thing that is being perceived. Kant wants to draw a sharp distinction between

appearances and intellectual objects as kinds o f things. Kant is saying that for Leibniz the

objects that we sense are contused representations of objects as they really are, i.e., the

monads that underlie them. When appearances are “intellectualized” they are

ontologically subordinated to objects that are known fully through the intellect. For

Kant, appearances and things in themselves, i.e., phenomena and noumena, are radically

different things and cannot be equated merely on the basis of one being more confusedly

represented than the other. Appearances are sensibly intuited and thereby subject to the

forms of space and time, which makes them different kinds of things than those that

could be known through the understanding. Kanf s use of “appearance” as both a kind of

representation and a kind of object is ubiquitous in the Critique and there are several

reasons to suppose that this dual use is also in effect in this context.

First, we must remember exactly what transcendental reflection is. It is the

process that must be undertaken if we are to “advance to the objects with these concepts

[that we are comparing]” (CPR A269/B326). Surely the comparison that we make after

the reflection is a comparison of concepts, but the process of reflection determines what

kinds of objects those concepts pertain to and it is this determination that is crucial to


making the proper comparison. We must determine “for which cognitive faculty they

[the concepts] are to be objects, whether for pure understanding or for sensibility” {CPR

A269/B326). This is more than to say how the objects are going to be apprehended, but

it is a commitment to the kinds of objects tliat one is going to be dealing with. Thus,

when Kant describes Leibniz’s amphiboly he does not couch his description in terms of

confusing methods of representation, but in terms of confusing the kinds of objects that

we are apprehending. The transcendental amphiboly is a “confounding of an object of

pure understanding with appearance” {CPR A270/B326, emphasis mine).

Secondly, throughout the “Amphiboly” noumena or things in themselves play a

prominent role. Leibniz, in committing the transcendental amphiboly, assumed that we

could have knowledge of the real things that underlie sensible objects. Sensible objects

were made subservient to intellectual objects that accounted for their character. In Kant’s

words: “Appearance was, on his [Leibniz’s] view, the representation of the thing in itself'

(ibid.). Kant’s discussion of things in themselves is intended to show not only that we

could not have knowledge of such an object, but also that for us there cannot be such an

object. “If by merely intelligible objects we mean those things that are thought through

pure categories, without any scheme of sensibility, such objects are impossible” {CPR

A286/B342). This is certainly not an epistemological claim about our access or lack of

access to such objects, but whether such object exist for us at all.

Thirdly, if we look closely at what Kant takes to be the two findings of the

“Amphiboly” we see again his concern for both the manner of apprehension and the thing

apprehended.

What makes this critique of conclusions based merely on acts of reflection so exceedingly useful is that it renders manifest the nullity o f all conclusions about objects which are compared with each other solely in the understanding, and at the same time confirms our principal contention, namely, that although appearances are not included as things-in-themselves among the objects of pure understanding, they are yet the only objects in regard to which our knowledge can possess objective reality, that is, in respect of which there is an intuition corresponding to the concepts. {CPR A278-9/B334-5)

First we see Kant making an epistemological claim that the understanding alone cannot

provide us with knowledge of objects. Second we see him making the ontological claim

10


that sensible objects (appearances) are the only kinds of objects that we can have

knowledge about.

A potential problem with Kant’s use of “appearance” in both an epistemological

and an ontological sense is that it appears circular. Kant is using the term to talk about

both the kind of representation and the thing that is represented and it seems that he is

justifying each use with the other. How do we know that we must use the conditions of

sensible intuition when making the transcendental reflection? Because the objects that

the concepts are referring to are sensible objects. And how do we know that they must be

sensible objects? Because it is only by using the sensible intuition that one can

apprehend these objects. In other words, the mode of our apprehension is being

determined by the type of object that we are apprehending, but the type of object that we

are apprehending is determined by the mode of apprehension that we must employ.

I am not sure how to deal with this circularity other than to say that it is a problem

that runs throughout the Critique. For example, Henry Allison points out the problems

with this equivocal use of “appearance” in Kant’s arguments on the uniformity of

experience found in the “Transcendental Deduction” in his article “Transcendental

Affinity - Kant’s Answer to Hume.” One way to understand this argument against

Hume’s skepticism concerning the regularity of experience is to see Kant claiming that

appearances, i.e., sensible objects, must have a necessary association because without the

regularity of appearances, i.e., objects sensibly intuited, we would not have the proper

unity of consciousness, i.e., the representations would mean nothing to us.* In other

words, the necessary unity of consciousness requires that objects be necessarily

associated also. Allison rejects the argument as a petitio principii, and he also claims that

it relies on findings of the “Transcendental Aesthetic,” which he labels as one of the

“most dubious sections of the Critique” and one that can also be subjected to a “similar

dialectic,” i.e., the kind of circular argument that is used in the “Deduction.”® Allison

subsequently identifies two strands of idealism in Kant, one which he labels genuinely

critical and transcendental and the other subjective and dogmat ic .To use the

“Aesthetic” and the affinity of appearance as both subjective state and kind of object falls

Allison, “Transcendental Affinity - Kant’s Answer to Hume,” 122. ® Ibid., 124.

11


into the second camp for Allison. Allison instead favors making the transcendental unity

of apperception bear the weight of the argument and switching the talk from

“appearance” to “possible experience.”’’ In this way Kant’s idealism becomes genuinely

critical and transcendental.

I don’t want to get caught up in the details of Allison’s argument and I want to

abstain from commenting on the strength or accuracy of the argument, I simply want to

point out that equivocal use of “appearance” that Allison is chastising here is the same

that is at work in the “Amphiboly.” If Allison has discovered a dual use of the term

“appearance” at other points in the Critique, this supports my reading of Kant as making

both an ontological and epistemological claim. Allison’s claim that Kant’s equivocation

of “appearance” is a result of him leaning too heavily on the “Aesthetic” is also

important, for, as we shall see shortly, this section of the Critique is actually the crucial

element in his critique of Leibniz.

III. Form s of Intuition

To this point I have argued that in the “Amphiboly” Kant’s central criticism that

Leibniz “intellectualized appearances” amounts not only to an epistemological claim

about the senses being a confusion, but also to the ontological claim that Leibniz has

blurred the distinction between appearances and things in themselves. So far I have just

tried to prove that this is the claim that Kant is making. In order to provide support for

the claim itself, Kant must explain why sensible objects have a unique ontological status.

He also needs to explain how things in themselves are epistemologically and

ontologically isolated from us. The component of Kant’s philosophy that substantiates

these claims is the sensible intuition and its forms of space and time. After briefly

explaining how the sensible intuition accomplishes these tasks, I will begin to show that

Kant’s views of space and time are really the driving force in his criticisms of Leibniz.

On Kant’s mature view, space and time are a priori forms of intuition. Kant

explains in the “Transcendental Aesthetic” section of the Critique that an intuition is the

way that we are immediately related to objects {CPR A19/B33). In other words, to intuit

Ibid., 127. " Ibid., 124.

12


an object is to bring the object before us in some sense. Human beings relate to objects

sensibly, thus we have a sensible intuition. According to Kant, while the senses

providing the material for cognition, our sensible intuition also has a priori forms which

are prior to any particular thing that is sensibly intuited; these forms are space and time.

As forms of intuition, time and space are the conditions of our sensibility and accompany

every sensible intuition that we have. The forms of intuition also make a priori synthetic

propositions possible {CPR A39/B56).

In the “Transcendental Aesthetic” Kant provides his arguments that space and

time must be a priori forms of intuition and cannot be real entities or systems of

relations. For example, Kant claims that our experience of things presupposes space and

time, thus space and time are not derived from our outer experience {CPR A23/B38). He

also claims that while it is possible for us to think of space as empty of objects, “we can

never represent to ourselves the absence of space” {CPR A24/B39). Whether or not

these, and the other arguments that Kant provides, are successful, it is clear that it is

because Kant claims that space and time accompany all of our sensible intuitions as their

form that the material of our sensation, i.e., the objects that we sense, must be situated in

space and time. According to Kant, because space and time are forms of our intuition

and because any object that we intuit is spatially and temporally situated, the objects

themselves are “appearances,” which “cannot exist in themselves, but only in us” {CPR

A42/B59). Kant is claiming the “appearances” have an ontology as spatial and temporal

objects that is directly dependent on our kind of intuition. Not only does this mean that

every object that we intuit is located in space and time, but also that we cannot speak

about what objects are like independent of our intuition, which in Kant’s terminology is

referred to as “in themselves.”

On Kant’s view of cognition in the Critique, the sensible intuition works with the

understanding and its categories to provide us with the cognition of an object. The

categories are applied to our sensible intuitions in order to provide for a judgment.

Human cognition must involve both the understanding and the sensible intuition, and

cognition is only possible when they are used in conjunction. One cannot bypass the

intuition and apply these categories directly to objects. For Kant, it is also impossible to

employ our understanding in conjunction with another type of intuition. The nature of

13


our understanding is such that it only functions with our sensible intuition. The only

objects for human beings are those that are known through the sensible intuition and are

cognized through the categories of our understanding.

Kant’s claim that Leibniz “inteliectualized appearances” means that Leibniz

ignored the conditions of human cognition and the nature of our intuition and tried to

discover things about the world using Ms intellect alone. Kant takes Leibniz’s

monadology to be an attempt to move beyond the sensible intuition and say something

about what things are really like in themselves. Kant summarizes Leibniz’s futile attempt

to say things about intellectual objects in the following passage from the “Amphiboly.”

If by merely intelligible objects we mean those things which are thought through pure categories, without any schema of sensibility, such objects are impossible. For the condition of the objective employment of all our concepts of understanding is merely the mode of our sensible intuition, by which objects are given us; if we abstract from these objects, the concepts have no relation to any object. Even if we were willing to assume a kind of intuition other than this our sensible kind, the functions of our thought would still be without meaning in respect to it. {CPR A286/B342)

We can see Kant drawing heavily on the view of cognition that I outlined above as he is

saying that there is no way for us to know objects through the intellect alone and that

even if we had another kind of intuition to come into contact with these entities, we

would not be able to form a judgment about them because our understanding and its

categories work only with our sensible intuition. We can only speak about intellectual

objects, or noumena, in a strictly negative sense as those things that lie outside of our

possible cognition but may, perhaps, play some unspecified role in appearances.

On this view of cognition that requires both an intuition that brings that material

to cognition and the understanding that orders that material, Kant claims that for someone

to have knowledge of objects that aren’t spatially situated one must have an “intellectual

intuition,” i.e., a means of coming into contact with non-sensible entities. On Kant’s

view, in order for Leibniz to make positive claims about the nature of the non-sensible

monads he needs some way to contact these entities. “For what is demanded is that we

should be able to know things, and therefore to intuit them, without senses, and therefore

that we should have a faculty of knowledge altogether different from the human, and this

not only in degree but as regards intuition likewise in kind” {CPR A277-8/B333-4). In

14


effect, Kant is claiming that Leibniz is attributing humans, perhaps without realizing it,

with an intellectual intuition.

The notion of an intellectual intuition is certainly not unique to the “Amphiboly;”

Kant discusses and argues against it at various points in the Critique. For example in the

B edition of the “Transcendental Aesthetic” he makes the following claim. “Intellectual

intuition seems to belong solely to the primordial being, and can never be ascribed to a

dependent being” {CPR B72). The primordial being is, of course, God, for whom the

processes of thought and interaction wdth an object are synonymous. An intellectual

intuition is “original;” it does not require the mediation of thought, it immediately intuits

them, i.e., is in immediate contact with them (ibid.). The idea seems to be that for a being

such as God, thinking of an object and the existence of the object are the same thing, thus

the forms of our sensibility, space and time, are not applicable to such a being. For

limited, dependent beings such as ourselves there is a need for a sensible intuition to

apprehend objects. For Leibniz to say that we can have direct knowledge of intellectual

objects is to claim that we can experience objects through the intellect alone and to grant

us with a capacity we just do not have. Moreover, our understanding only works with our

form of intuition, which provides another block to our experiencing objects solely

through the intellect.

As I have tried to demonstrate, it is not really the act of reflection that

substantiates Kant’s criticism that Leibniz inteliectualized appearances, but an underlying

view of human intuition and cognition. Thus, it is strange that Parkinson chastises Kant

for bringing “doctrines of the Transcendental Aesthetic” into his discussion of Leibnizian

principles in the “Amphiboly.”* It only makes sense that Kant would appeal to this

section in the “Amphiboly” because it is those findings that allow Kant to diagnose

Leibniz with his amphiboly in the first place. Space and time as necessary, a priori forms

of intuition allow Kant to criticize Leibniz’s subordination of the sensible to the

intelligible and play the principle role in his attack on Leibniz’s ontology. Appearances

are the only objects for us because of the necessary, a priori forms of intuition. The very

division of human faculties into the intuition and the understanding that are fundamental

to the amphiboly itself are products of other arguments in the Critique.

Parkinson, “Kant as a Critic of Leibniz,” 313.

15


While Kant’s entire view of cognition is brought to bear on Leibniz in the

“Amphiboly,” I now want to push the point that it is really the sensible intuition that is

doing the majority of the work. I want to do this by first looking at Kant’s 1770

Inaugural Dissertation, which is one of his most important pre-Critica! wiitings. In this

work Kant has not yet developed Ms view of space and time as forms of intuition.

Instead he refers to them as products of sensation that are the “formal principles of the

phenomenal universe” and that are “absolutely primary and universal” {ID §13 392). In

this work, Kant also has not yet developed his complete view of cognition and allows for

the independent activity of the intellect and a subsequent ability to have knowledge of

noumena {ID §5 385). Thus, Kant continues to grant access to “the concepts themselves,

whether of things or relations” (ibid.).

Despite the fact that Kant allows for a use of the understanding by itself and has

not developed his view of cognition or the concepts of reflection, we still find him

making the same kind of criticisms that he makes in the “Amphiboly.” For example,

Kant criticizes Leibniz’s distinction between the sensible and the intellectual on the basis

of a confusion. In this work Kant claims that confusion is merely a logical distinction

that does not touch “the things given, which underlie every logical comparison” {ID §7

387). In other words Leibniz’s manner of characterizing the difference between the two

is only a conceptual distinction that ignores the character of the objects themselves. Kant

points out that objects of the sense can be very distinct, while representations of the

intellect can be very confused. His example of a clear, sensible representation is “that

paradigm of sensitive cognition, geometry, ” while metaphysics is his example of

confused intellectual representation (ibid.). According to Kant, by viewing the difference

between the sensible and intellectual as a matter of confusion, Leibniz is threatening to

undermine geometry.

Kanf s argument that Leibniz’s view would turn geometry into a confusion seems

to work the following way. On Leibniz’s view that sensible objects are confused

representation of intelligible objects, sensible properties would also have to be a product

of confusion. Colors and tastes would obviously drop out in a purely conceptual

understanding of the world, but other properties would be eliminated too. Things like

spatial position and relation are seen by Leibniz as dependent on simple substances that

16


lack these properties within their concepts. According to Kant, this would entail that the

sciences that employ descriptions of these properties would also be the product of

confusion. This means that geometry, which Kant considered the science of the sensible,

would lose its necessity. What we hold to be necessarily true geometrically would

become essentially empirical, as it is only our confiised representation of substances that

cause the relations and space that geometry describes.Fundamental principles of

Euclidean geometry such as the three dimensionality of space, would become the product

of our limited experience of the world. There w'ould be no reason why space would have

to have any certain properties; further investigation might reveal that this principle, which

geometers regarded as necessarily true, was in fact only contingently true. "* Kant

threatens that Leibniz’s view of space is in “headlong conflict with the phenomena

themselves” and would undermine “the most faithful interpreter of all phenomena,

geometry” {ID §15.D 397).

In addition to the critical components of his argument, Kant also provides a

positive account of why space and time should be seen as “the schemata and conditions

of everything sensitive in human cognition” {ID §13 391). 1 will not rehearse these

arguments other than to say that they are intended to show that space and time are

necessary conditions of all sensible apprehension that precede all sensible cognition and

have their source within the subject. However, 1 would like to point out a few key

moments in Kant’s argument. First, Kant’s view of space, and of time, is that it is

presupposed in all of our sensations. We would not be able to cognize objects as outside

one another if we did not first locate them in space {ID §15. A 395). In other words,

individuation of sensible objects requires space; we can only talk about objects that are

outside of us if we represent them as situated in space. Second, space is a pure intuition,

which accounts for the necessary properties that geometry attributes to it, e.g., three

dimensionality and continuity {ID §15.C 396). What Kant means is that there is nothing

that follows from the concept of space that requires that it have the properties that

geometry attributes to it. The fundamental principles that geometry describes can only be

It is important to mention that Leibniz did not think that this was the case, as we shall see in chapter three, but at this point I am simply trying to outline Kant’s objections without commenting on their merit or accuracy.

17


“apprehended concretely ... in space itself’ (ibid.). In geometry this entails that one does

not arrive at demonstrations, according to Kant, by thinking about objects “through a

■universal concept” instead one places them “before the eyes by means of a singular

intuition” {ID § 15.C 397). Although Kant often talks about the “concept of space” it is

clear that this understanding is not “conceptual” in the normal sense. His claim is that

one cannot account for space through concepts; we can only have a conception of space

and understand it as having its known properties necessarily if we see space as a form of

intuition. Indeed a clearer understanding shows that this is how geometry has always

operated.

In addition to providing a characterization of space and time themselves, Kanf s

view also provides an understanding of those sensible objects that are situated in space

and time, i.e., phenomena. In other words, Kanf s findings also have ontological import

just as they did in the “Amphiboly.” As we saw above, we can only talk about objects

that are external to us if we first presuppose an intuition of space. This means that space

is not a predicate that can be applied to objects, but it is what sensible objects essentially

are, i.e., they are and can only be spatial and temporal. In any sensible representation we

are presented with the matter, which is the sensation itself, and a certain form that is

contributed by the subject and is a certain law that is “inherent in the mind” {ID §4 384).

This form is present in every sensory cognition and it is what makes cognition possible.

This means that ail sensory objects are essentially spatial and situated in time. What

Leibniz saw as a mere product of the relations between things becomes irreducible for

Kant. As he claims in the “Amphiboly,” spatially and temporally situated objects consist

“wholly of relations” and cannot be understood independently of them {CPR

A285/B341).

Because space and time are not predicates, there is no way for one to remove

them and still talk about the objects. Kant points out explicitly in the Dissertation that

objects of the understanding, which, again, Kant still allows access to in the Dissertation,

should not be understood as abstracted from phenomena; they “contain no form of

sensitive cognition and they have been abstracted from no use of the senses” {ID §6 386).

Of course, with the emergence of non-Euclidean geometry it turns out that space doesn’t necessarily have the properties that Euclidean geometers attributed to it, but that is beyond the scope o f this debate.

18


Certainly one can abstract from some sensible properties to generate more general

concepts of sensible objects, but this does not mean that one can abstract to an object of

the understanding. What Kant is attempting to do is cut off any possible connection

bebA een objects of the understanding of those of sense. Kant’s view of space and time

ensure not only that phenomena are a certain way, but also that they must he a certain

way, which further prevents seeing objects of sense as confused objects of understanding.

Kant’s view of space and time, even in its early stages of development as found in

the Inaugural Dissertation, has provided him with the crucial elements of his criticism of

Leibniz. Assuming that his arguments are successful, Kant has provided an account of

the difference between objects of the sense and the understanding and for the necessity

for these objects and their conditions (space and time). Kant has provided a certain

legitimacy to sensory representation that ensures that we don’t have to see the senses as

confusing intelligible objects. They provide a unique kind of object in their own right.

Kant’s mature, 1788 work What Real Progress has Metaphysics Made in

Germany Since the Time o f Leibniz and Wolff? provides additional support that his view

of intuition is essential in his criticisms of Leibniz. In this work Kant is even more

explicit that Leibniz’s discounting of the sensible intuition as a confusion in favor of a

purely conceptual understanding is his major philosophical mistake.

[T]he lack o f any a priori intuition, which was not recognized as a principle, and which Leibniz instead inteliectualized, i.e., transformed into nothing more than confused concepts, was the reason that he regarded what could not be represented by means o f mere rational concepts as impossible, and set up fundamental principles that cannot stand scrutiny and do violence to common sense. {WRP 99)

At this point my goal is simply to explain Kant’s criticisms of Leibniz while

highlighting the importance of the sensible intuition in these criticisms. Later on in this

work I want to argue that the sensible intuition not only provides Kant with his principle

means of criticizing Leibniz, it also is the most important point that differentiates the two

thinkers. In order to substantiate this claim I will need to provide more background on

Kant’s philosophical development and the specific differences between Leibniz and Kant.

For right now I simply want to point out that we really need look no further than the

“Amphiboly” itself to see Kant claiming that it is the sensible intuition that separates his

own view from Leibniz. At several points in the “Amphiboly” Kant claims that Leibniz

19


would be correct were it not for the sensible intuition and its necessary role in our

cognition.

These contentions [the monadology] would be entirely justified, if beyond the concept of a thing in general there were no further conditions under which alone objects of outer intuition can be given us— those from which the pure concept has [as a matter of fact] made abstraction. ... Through mere concepts I cannot, indeed, think what is outer without thinking something that is inner; and this for the sufficient reason that concepts of relation presuppose things w'hich are absolutely [i.e. independently] given, and without these are impossible. But something is contained in intuition which is not to be met with in the mere concept of a thing; and this yields the substratum, which could never be known through mere concepts, namely, a space which with all that it contains consists solely of relations, formal or, it may be, also real.{CPR A284/B340)

In this passage I take Kant to be making the claims that I have been discussing

throughout. He is saying that Leibniz has arrived at his monadology by considering

objects through their concepts alone. For humans, however, the only objects that we can

encounter, i.e., that can exist outside of us, are those objects that are sensibly intuited and

as such are subject to space and time as the conditions of the sensible intuition. Space is

something that is unique to our intuition alone and cannot be known through the intellect,

i.e., it is not a concept. Because all objects are necessarily spatial, and temporal, we

cannot know them through the intellect alone. All that we can be aware of through our

intellects alone are concepts, not objects. If we could intuit through the intellect alone,

i.e., had an intellectual intuition, Kant is claiming that Leibniz would be correct, but his

failure to acknowledge the essential role of the sensible intuition led him to the

monadology.

IV. The Concepts of Reflection Revisited

As the quote from the What Real Progress paper above indicates, Kant thinks that

by focusing on the sensible intuition he not only can identify the principal problem with

Leibniz’s metaphysics, but he can also explain why Leibniz arrived at his specific

principles. In the “Amphiboly” Kant claims that the concepts of reflection can explain

Leibniz’s “chief ground of this peculiar way of thinking,” while also having the

“unexpected advantage of putting before our eyes the distinctive features of his system in

all its parts” {CPR A270/B326). In other words, the concepts of reflection not only

20


provide a method of criticizing Leibniz, but also an explanation of why he was led to his

(incorrect) principles. In the “Amphiboly” Kant picks out the identity of indiscernibles,

the lack of real opposition in Leibniz’s system, the monadology, the pre-established

harmony, and his view of space and time as the central tenets in Leibniz’s system. At

times it takes Kant a little shoehorning to fit Leibniz’s central tenets into his schema, but

the fact that he identifies essentially the same principles in the What Real Progress paper

indicates a consistency in his description of Leibniz, even if it took some work to stay

true to that description in the “Amphiboly.” In What Real Progress, Kant more

succinctly picks out the identity of indiscernibles, the principle of sufficient reason, the

pre-established harmony, and the monadology, while his view of space and time lurk in

the background of all of Kant’s criticisms. These principles also correspond to many of

the central points that Leibniz raises in the Monadology, which is a major published work

that Kant would have had access to. I would like to begin by looking briefly at each of

the principles as presented in the “Amphiboly” not only to support my reading of the

importance of the sensible intuition to Kant’s criticism, but also to provide material for

my discussion in subsequent chapters.

The first Leibnizian principle that Kant addresses is the identity of indiscernibles,

which arises, according to Kant, through the concepts of identity and difference. This

principle is a common target for Kant and he discusses it not only in the “Amphiboly,”

but also at great length in What Real Progress. This principle states that “there are never

two things in nature which are perfectly alike and in which it is impossible to find a

difference that is internal or founded on an intrinsic denomination” {Monadology §9 L

643). Essentially this principle states that it is impossible to have two things that are

internally identical and that vary only in a relational aspect, e.g., spatial position. Kant

claims that Leibniz arrived at this principle due to his attempt to understand objects

strictly through their concepts, since conceptually objects cannot be distinguished based

on relational, i.e., external, differences. Kant’s response is that this distinction does not

hold for sensible objects where differences of location, i.e., relational differences, can

individuate objects, as is evidenced by the identical objects that we observe in the world.

Of course, Leibniz could still reply that although phenomenal objects may appear

identical, these differences are still a manifestation of internal differences; just because

21


two things are sensibly indistinguishable does not mean that there aren’t imperceptible,

internal differences that account for their difference in spatial location.

Kant’s forms of intuition are necessary in order to close off this line of argument

to Leibniz. For example, take Kant’s own case of two identical water droplets in

different spatial locations. The two water droplets are sensible objects, and as such they

are subject to the conditions of space and time that are the forms of the sensible intuition.

You cannot “get around” those forms and say something about what the objects are really

like because we cannot know what objects are really like; we can’t even talk about

objects that are not sensibly apprehended in space and time. And, because they are

sensible objects and spatiality is an essential attribute of them it is perfectly legitimate to

individuate them based on their spatial position. Objects are apprehended in space and

time and can only be individuated, identified, and discussed as such. If you try to ignore

those sensible conditions and talk about things in themselves, things as they really are,

i.e., noumena, you are either confused or trying to make things conform to logic, which

doesn’t work, as we have seen. Kant even goes so far as to say that it is on this

misunderstanding of the relationship of individuals and concepts that “the whole

intellectual system of Leibniz is based: and with this principle it therefore falls” {CPR

A281/B337).

Kant’s second set of relational concepts are agreement and opposition. Kant

maintains that Leibniz’s misunderstanding of these concepts caused him to hold that there

is no opposition between substances and that all substance carry their ‘opposition’ within

themselves. Conceptually considered there is, “no relation of such a kind that, when

combined in the same subject, they cancel each other's consequences and take a form like

3 -3 = 0” {CPR A264/B320). Kant appears to be attacking both Leibniz’s view of evil as

discussed in the Theodicy, wherein he claims that evil is merely a limitation in a created

thing, and the fact that for Leibniz there is no real opposition anywhere in the physical

world (KCL310).

According to Kant there is real opposition in the world. “[T]he real in appearance

{realitas phaenomenon) may certainly allow of opposition” {CPR A265/B320). An

example would be the counterbalancing of pleasure and pain within the individual or, in

the physical world, the opposition of two opposing forces moving on the same line {CPR

22


A265/B321). Kant’s evidence for this is simply all the “hindering and counteracting

processes in nature,” which are “before our eyes incessantly” and depend on real forces

{CPR A273/B329). Kant’s criticism of Leibniz is here again based on the relational

nature of the phenomenal world. Appearances allows for the real contact and opposition

between and within individuals that we observe around us; this conflict can be

represented to ourselves “only in terms of conditions presented to us in sensibility” {CPR

A274/B330). The idea that evil may only be a limitation, is, for Kant, “offensive to

common sense as well as morals”' {WRP 101).

The third pair of relational concepts are the inner and the outer. According to

Kant, if we begin with concepts we are forced to see the relation of the inner and outer as

a dependence of the latter on the former. Conceptually it is possible to abstract away

from all outer determinations, including all relations, and consider the concept of a thing

that is determined only internally and is free from all composition or relation. This

conceptual object would not have place, shape, contact, or motion, since all of these

determinations are dependent on outer determinations {CPR A274/B330). This “simple”

cannot be free from all determinations, otherwise all simple substances would be

identical. The only entirely internal determinations that we are familiar with are the

representations that occur within us, thus an “analogy with our own inner sense” forced

Leibniz to grant the same abilities to the simple substances {CPR A283/B339). Based on

this rationale, Leibniz posited the monad, a simple entity endowed with the power of

perception, whose internal states provide the foundation for the relational characteristics

of the phenomenal world. All of the relational characteristics of our experience, place,

movement, even space and time themselves, are dependent on these simple entities that

lack any of these characteristics.

Although the monads are “the basic material of the whole universe” their efficacy

is confined “strictly speaking, to themselves,” and there is no real interaction between

them {CPR A274/B330). In order to account for their community and the subsequent

interaction and relation that is perceived in the phenomenal world Leibniz posited a pre-

The idea that Leibniz’s principles are somehow offensive to common sense is a criticism that Kant raises in several places, especially in What Real Progress. It is clear that Kant thought that his system had the additional quality o f providing a more plausible and perhaps even commonsensical alternative to Leibniz’s fantastic metaphysical picture.

23


established harmony between the monads. He avoided the constant intervention of God

that the occasionalists described by instead appealing to a “universal law” to explain the

correspondence of the monads (CPR A275/B331). According to the pre-established

harmony God’s “universal law” ensures in one decree that each monad’s internal states

will correspond with all others in such a way that each monad reflects all the other

monads and their actions.

Kant’s analysis of the inner and the outer has given him two of the most important

principles in Leibniz’s philosophy, and Kant maintains that in order for him to arrive at

these principles he had to regard “substances as noumena,” i.e., as things in themselves,

rather than objects of intuition (CPR A266/B321). Kant concedes that if one assumes

that sensible objects are actually substantiae noumena, then this picture of the relation of

the inner and the outer, the monadology, and the pre-established harmony would all

obtain. We would be left with nothing but the “inner in general and its interrelations,

through which alone the external is possible” (CPR A284/B341).

However, this view overlooks the conditions of the intuition under which objects

must be represented to us. A substantia phaenomenon must be positioned in space and

its inner determinations are “nothing but relations, and it itself is entirely made up of

mere relations” (CPR A265/B321). Objects that we encounter in experience are

essentially relational and in order to understand this possibility one must acknowledge the

sensible intuition as providing something like a substrate in which real relations can

subsist in the forms of space and time. “[Intuition] yields the substratum, which could

never be known through mere concepts, namely a space which with all that it contains

consists solely of relations, formal, or, it may be, also real” (CPR A284/B340). Leibniz,

by denying the integrity of the intuition and its special role in the constitution of sensible

objects, was forced into both the monadology and the pre-established harmony. Both of

these elements are counter to our experience of objects whose very constitution relies on

the relation that they have with other sensible objects.

The final pair of relational concepts is matter and form. Kant clearly considered

this pair of concepts the most critical as he claims that they “underlie all other reflection,

so inseparably are they bound up with all employment of the understanding” (CPR

A266/B322). According to the understanding it is necessary that one begin with

24


something and then attribute the predicates to it. In a judgment, the concept can be

considered the matter of the judgment, while the relation of the concepts, or their

attributes can be considered the form (ibid.). According to Kant, this is also the view of

traditional metaphysicians who begin with prime matter and then attribute a form to it. It

is little surprise then that Leibniz, in seeking to address traditional conceptions of

substance, begins with matter, i.e., the monad, and then determines the monads through

predications. “Leibniz first assumed things (monads), and within them the power of

representation, in order afterwards to found on this their outer relation and the community

of their states (i.e., of the representations)” {CPR A267/B323).

The outer relations of the monads gives rise to our perceptions of space and time,

which are the product of the relation of all the monads at a given moment and their

successive states respectively. Kant’s principle focus in dealing with this relational pair

is clearly space and time because in most of his discussion of this pair he simply forgoes

any discussion of matter and form and discusses space and time exclusively. Leibniz’s

own view is that space is the “certain order in the community of substances, and time is

the dynamical sequence of their states” (CPR A275/B331). The upshot of this view, of

course, is that space and time become completely dependent on the underlying monads

and any qualities that they seem to possess in themselves are in fact dependent on the

monads, and are, what Kant calls, “a confusion of their concepts” (CPR A276/B332).

Kant characterizes this rather uncharitably as leaving “to the senses nothing but the

despicable task of confusing and distorting the representations of the [intuition]” (ibid.).

As with the other concepts of reflection, Kant admits that this view of the

relational concepts would be the case if our “pure understanding could be directed

immediately to objects, and if space and time were determinations of things-in-

themselves” (CPR A267/B323). Of course, the understanding alone cannot be directed

towards objects on its own and Leibniz has again tried to apply logical determinations to

objects in the world. If one has the proper understanding of the limits of the

understanding and the role of intuition in our apprehension of appearances, then one

develops a much different view of the relation of matter to form. Our a priori forms of

intuition ensure that the forms of space and time are prior to our cognition of objects. A

proper understanding of transcendental reflection actually reveals that the form precedes

25


matter, since the forms of space and time are antecedent to the sensible things, i.e., the

matter, that we perceive.

But since sensible intuition is a quite specific subjective condition, which lies a priori at the foundation of all perception, as its original form, it follows that the form is given by itself, and that so far is the matter (or the things themselves which appear) from serving as the foundation (as we should have to judge if we followed mere coEcepts) that on the contrary its own possibility presupposes a formal intuition (time and space) as antecedently given. {CPR A268/B324)

It is important to see, however, that simply asserting the necessity of a sensible intuition

in the apprehension of objects is not enough to switch the roles of matter and form in the

relation. An empiricist would equally maintain the need for the sensible in our

knowledge of objects, but the matter would still proceed the form since, for the

empiricist, we apprehend the objects before we know what they are, i.e., order them or

provide a form. What Kant needs is his specific kind of intuition in which space and time

are its a priori forms. Thus, this pair of concepts, which Kant himself calls the most

important, clearly illustrate the central role of the Kantian intuition in his criticisms of

Leibniz. Kant has rejected Leibniz’s theory of space and time by claiming that it is a

product of overextending logic. A theory that provides for the reality of space and time is

one that recognizes the need for an a priori intuition in our interaction with the world.

V. Summaries in WRP and OD

As I mentioned earlier, Kant essentially focuses on the same principles in his

What Real Progress essay as he does in the “Amphiboly,” and I would like to look at that

essay now to deepen our understanding of Kant’s criticisms and to provide further

support of my claim that the sensible intuition is the essential element in Kant’s criticisms

of Leibniz. The What Real Progress essay was Kant’s response to a prize question

announced by the Royal Academy of Sciences at Berlin in 1788. Kant’s essay was not

completed by the deadline for the prize and in fact was never fully completed. The work

that we have today by this name is actually a collection of three incomplete manuscripts

compiled in 1800 or 1802 by Kant’s friend Frederich Theodor Rink and published by

Rink in April, 1804 two months after Kant’s death (WRP 13). Although the text lacks the

polish of a work fully prepared for publication by the author, it is nonetheless an

26


important work for Kant scholarship. It presents a detailed account of the history of

metaphysics, as the question demands, and also indicates Kant’s view of his own place in

that history {WRP 11). This work is also one of the most extensive critiques of

Leibnizian philosophy and illuminates what Kant held to be both its central tenets and its

principle difficulties. It is especially with the last point in mind that I want to examine

this work.

In this essay Kant claims that metaphysics has progressed through three distinct

phases. It began with dogmatism, which was driven by individuals who were impressed

with the ability of mathematics to make progress in a priori knowledge and who assumed

that the same could be done in metaphysics {WRP 57). Such great names as Plato,

Aristotle, Leibniz, and Wolff all imagined success by following the model of

mathematics. They ignored, however, the relation of the super-sensible concepts to

experience and engaged in conceptual investigation and in the process made sure only

that their concepts did not contradict each other (ibid.).

The second stage of metaphysics is fueled by the apparent failures of the

dogmatists to make progress in their investigations. Without any way to ground the

principles that they were developing, the anemic principle that one merely avoid

contradiction allowed for many different metaphysical systems, all of which seemed

equally well supported {WRP 59). Thus, the skeptic began to question the a priori

principles that are advanced by the dogmatist, and eventually extended this doubt to

principles of sensible cognition and even experience itself (ibid.). Hume is the paradigm

of a skeptical metaphysician for Kant.

The third step, initiated by Kant, is a “critique of pure reason’s general ability to

extend a priori human knowledge” (ibid.). Kant claims that he was the first to recognize

the need for the investigation of reason and its abilities. The central question for the

Critical philosopher is: “How is it possible to gain a priori cognition from synthetic

judgments?” {WRP 65).

Immediately prior to Kant in Germany metaphysics had been dominated by the

Leibnizian-Wolffian philosophy, which Kant claims made two additions to philosophy in

its prior Aristotelian incarnation. These two thinkers contributed the principle of

sufficient reason and tried to explain the difference between conceptual and intuitive

27


knowledge as the distinction between the distinct and the obscure representations (JVHF

87). Both of these advances, however, are really only logical determinations and

contribute nothing to metaphysics, thereby showing that neither of these famous

philosophers had hit upon the analytic-synthetic distinction that began Kant’s own

progress in metaphysics (ibid.).

In the second section of this work Kant makes his most detailed analysis of the

different stages of metaphysical progress beginning with the dogmatists. Although Kant

admits the dogmatic philosophers made great advances in clarifying concepts their work

remained incomplete (fFJlF 97). These philosophers lacked a notion of a priori intuition

and instead inteliectualized intuition as confused concepts. According to Leibniz, what

could not be represented by rational concepts was deemed impossible {WRP 99). With

this misguided agenda Leibniz developed four main principles that “do violence to

common sense”; the identity of indiscernibles, the principle of sufficient reason, the

system of pre-established harmony, and the monadology.'®

According to Kant, the principle of the identity of indiscernibles holds that if we

form a concept of two different things that are qualitatively identical and call them two

different things, then we have in fact made a mistake and are actually positing the same

thing twice, since from a conceptual standpoint internally identical things are the same

thing (ibid.). Kant claims that Leibniz developed this principle because he prioritized the

conceptual and did not acknowledge the possibility of purely external relations

individuating objects. Leibniz’s view that space and time are the coexistence and

succession of things as they are in themselves denies the possibility of space and time

individuating entities, but Kant’s own view that space an time are a priori forms intuition

makes perfect sense of the possibility of two internally identical objects being

differentiated based on their location alone (ibid.). Just as in the “Amphiboly,” it is

Leibniz’s inability to treat space and time in an acceptable way that continues to be

Kant’s main gripe with the identity of indiscernibles. In this work Kant looks at space

itself to discredit Leibniz’s view. Kant points out that we can differentiate spaces despite

the fact that all spaces are qualitatively identical (ibid.). Kant concludes by reiterating his

Again, we see Kant’s claim that Leibniz’s principles “do violence to common sense” or “grossly offend reason.”

28


point that to deny the possibility of tv/o identical objects, e.g., two identical water

droplets, in two separate places “offend[s] common sense” (ibid.).

Next, Kant turns to the principle of sufficient reason. This discussion

approximates the one in the “Amphiboly” under the concepts of agreement and

opposition. If this principle is metaphysically considered, and is taken to hold of all

things, then all things would be composed of both reality and negation or being and non-

being (ibid.). On this view, the “only reason for a negation is that there is no ground for

something to be postulated, that is, no reality exists” (ibid.). On a purely conceptual view

there can be no real opposition because concepts cannot oppose each other. There can

only be a lack of a reason within the concept that accounts for the lack. Thus, evil must

be seen not as an active force, but simply as a 0 or as a limitation and not another reality

{WRP 101). The same would hold for bodies. Rather than allowing for an opposition of

bodies, Leibniz’s formulation of the principle of sufficient reason would entail that a

body’s lack of motion would be the result of an internal limitation (ibid.). All of this

follows, according to Kant, from Leibniz formulating the principle of sufficient reason

merely in terms of concepts. For Kant, in order to bring forces or tendencies into true

opposition one must posit an intuition, since true opposition cannot be captured strictly

conceptually. The inability of this view to account for a satisfactory notion of conflict

either in physics or in morals, is for Kant, “offensive to common sense as well as to

morals” (ibid.). Ultimately, Leibniz’s principle of sufficient reason remains an analytic

principle that did not help him to proceed beyond the principle of contradiction (ibid.).

Third, Kant addresses the principle of the pre-established harmony. As Kant

points out, this principle was originally intended to explain the interaction of the mind

and the body but eventually came to explain the interaction between all substances,

especially in virtue of which they constitute a whole (ibid.). If one represents substances

only insofar as they are known conceptually then they must be seen as completely

isolated since it is impossible for accidents of one substance to be transmitted to another

(ibid.). True substances must be unities and thus cannot depend on another thing to

provide their qualities. Substances also do not depend on one another even though all

substances are ultimately dependent on a final substance, i.e., God (ibid.). Thus, the

community of substances can only be a virtual community; real or physical influence

29


must be ruled out (WliF 103). In order to maintain this virtual community the creator

must be seen as either setting the initial conditions to provide for this community, i.e.,

arranging the isolated substances so that they harmonize with each other even insofar as

they mimic the relation of cause and effect, or on the occasion of action the creator

harmonizes the relation between the substances (ibid.). Since the former system is more

easily explainable on the basis of a single principle Leibniz chose this alternative and

posited the pre-established harmony, what Kant calls, “the most whimsical figment that

philosophy has ever contrived” (ibid.).

Again, Kant draws on his views of space and time to discredit Leibniz’s principle.

If one assumes that space is a pure intuition this provides us with a means to posit a

single space in which all bodies are placed and in which there can be real interaction

(ibid.). All of these interacting bodies and the space that they occupy becomes a single

whole and a unified world rather than the multitude of worlds extrinsic to one another as

Leibniz’s view forces one to hold.

Finally, Kant examines Leibniz’s most famous principle, the monadology. Kant

claims that if one is considering things conceptually then all things must either be simple

or composed of simples, since composition is only a relation and all relations must be

founded on entities that are truly simple, i.e., substances (ibid.). Thus all bodies, if

considered conceptually as collections of substances, must be seen as reducible to the

simple. These substances must have some inner determinations if they are to be

something more than empty simples (WMF 103,105). The only inner determinations that

we know of that can be attributed to simple objects are those determinations that are

internal to us, namely representations and what depends on representations (WRP 103).

Leibniz called these simple substances with the power of representations monads (WRP

105). The monads make up the bodies that we sensibly apprehend and can themselves be

seen as mirrors of the universe since they are endowed with the powers of representation

(ibid.). The monads that constitute the universe differ only from us in that they lack

consciousness, although we cannot be sure whether they will wake from this “sleeping

state” or not (WRP 105). Once again, Kant claims that Leibniz posited this “enchanted

world” because he took sensible representations as representations of things as they are in

30


themselves and not as appearances which are known intuitively, i.e., in a way that is

completely distinct from conceptual knowledge.

A final Kantian work in the debate between Leibniz and Kant that I want to look

at is the essay On a Discovery According to which Any New Critique o f Pure Reason has

been made Superfluous by an Earlier One. This work is a polemic response to Johann

August Eberhard, a Leibnizian and a contemporary of Kant’s, who claimed that the

Critique o f Pure Reason provided no real advancement over the Leibnizian metaphysics

and that any divergence from Leibniz simply finds Kant incorrect. In On a Discovery,

Kant works to undermine the legitimacy of Eberhard’s claims by showing that he has

misunderstood or misinterpreted the Critical philosophy on several key points. This work

differs from the others that I have looked at in the sense that it is not a direct comparison

of the Critical and Leibnizian philosophy but a discussion of Leibniz via Eberhard. The

work can be divided into roughly four parts. Kant begins by talking about the distinction

between the logical and the transcendental use of principles. He then turns to the correct

understanding of intuition, which Kant claims Eberhard has misrepresented as images of

space and time {OD 222). Next, he addresses the possibility of synthetic judgments,

which is basically a discussion of the analytic/synthetic distinction. Kant concludes with

a series of what appears to be only half-serious claims that the Critical philosophy is the

true apology for Leibnizian philosophy. Although the entire discussion is interesting and

exhibits Kant in a rather rare polemic form, here I want to focus on the final section of

the work.

Kant concludes On a Discovery by turning the tables on Eberhard and claiming

that he is the true heir of Leibnizian philosophy, not Eberhard. It is difficult to tell how

serious Kant is in this claim since his “interpretation” seems contrived to say the least.

Kant picks out three elements that he claims are the “defining characteristics” of

Leibnizian philosophy: the principle of sufficient reason, the monadology', and the

doctrine of pre-established harmony {OD 247). Kant claims that on the basis of these

three principles Leibniz has been both attacked and supported, with neither group fully

understanding him. Kant, however, does not provide any reasons why these three

principles are the ones that he focuses on. There is no mention of the concepts of

reflection, nor an explanation of the lack of the identity of indiscernibles and the

31


prominent role that the principle of sufficient reason plays, a principle that is hardly

mentioned in his discussion in the Critique. Allison, in his commentary of the work,

speculates that Kant was simply following Eberhard’s choice of topics and that the

omission of the identity of indiscernibles is simply due to its absence in Eberhard’s

criticisms {OD 102). It is also worth noting, as Allison also points out, that Kant’s

interpretation of these principles misconstrues central Leibnizian doctrines while at the

same time contradicting Kant’s own claims about Leibniz in other places (ibid.). Kant is

clearly trying to provide a creative interpretation of Leibniz in light of the findings of the

Critical philosophy and subsequently embarrass Eberhard, without being particularly

concerned with accuracy.

The first principle that Kant addresses is the principle of sufficient reason. Kant’s

claim is that this principle cannot be seen as a objective principle, or what Kant calls a

“natural law” since it is “so manifestly clear that not even the weakest mind could believe

itself to have made thereupon a new discovery” {OD 247). Instead this principle should

be seen as a subjective requirement that points the way towards the critique of reason

(ibid.). Leibniz’s formulation of the principle of sufficient reason is in effect saying that

in addition to the principle of contradiction something more is needed if one wishes to

say something about an object that extends beyond its concept {OD 248). Thus, it is a

primitive formulation of the difference between analytic and synthetic judgments. It is

quite clear that Kant did not think that Leibniz actually hit upon this important distinction

because to Eberhard’s charge that Kant’s philosophy is, in the end, not all that original,

Kant responds that no one before him has asked that all important question of how

synthetic judgments are possible a priori {OD 154). If anyone had asked this question he

would have been forced to undertake the critique of reason that Kant did, and because

Kanf s critique is the first of its kind this demonstrates that no one before him had

discovered the explicit formulation that drove the investigation of the first Critique.

Thus, to construe the principle of sufficient reason in this way is to be generous to

Leibniz in a way that is clearly not completely genuine.

Next, Kant turns to the monadology. Kant claims that the great mathematician

Leibniz could not have plausibly maintained that physical bodies were really composed

of simple parts, i.e., monads. Instead, he was talking about the intelligible world that

32


underlies the physical world (OD 248). It is an “idea of reason,” Kant claims, that

objects we think as composite must be composed of simple substances (ibid.). What is

especially interesting is that Kant claims that for Leibniz to posit such an intellectual

world he must be attributing to humans an “original, although now only obscure,

intellectual intuition of these super-sensible beings [monads]” (ibid.). The problem is

that we do not have an intellectual intuition, the intellectual world is unknown to us, and

the only world that we can know is the world of appearance, which requires a sensible

intuition (OD 249). This discussion of the monadology is reminiscent of claims that Kant

makes in the Critique. Not only is Kant once again saying a sensible intuition is required

for us to have objective knowledge, but also he attributes an “obscure” intellectual

intuition to Leibniz. Just as in the “Amphiboly,” Kant is claiming that Leibniz is using an

impossible faculty to grant knowledge of the monads, thus his entire metaphysics is

brought into question.

Finally, Kant turns to perhaps his most creative re-interpretation of Leibniz and

discusses the principle of the pre-established harmony. According to Kant, if we

understand Leibniz in the common way as asserting a harmony between soul and body,

then he would be proclaiming idealism (ibid.). If everything that occurs in the soul is a

result of its own power, then there is no reason to posit bodies in the first place, if all the

same things would happen without them (ibid.). Kant claims that what Leibniz was

really groping for was a way to establish a harmony between the faculties of the

understanding and the intuition. These two faculties are very distinct and it is impossible

to explain why they have the natures that they do. Yet, despite their complete

heterogeneity, their inexplicable harmony is what allows for experience (OD 250). To

say that these two things are harmonized does not commit one to idealism in the way

Leibniz’s view does since this is an internal harmony of our faculties that allows for our

knowledge of the world, not a harmony of externally existing things. Kant further asserts

that Leibniz’s harmony between the realms of nature and grace should also be seen as

essentially an internal harmony between “two completely different faculties in us;” one

that accounts for our freedom and the other for our natural existence, a harmony which is

required for morality (ibid.).

33


VI. Conclusion

At this point it would perhaps be helpful to review what I have done in this

chapter, while pointing towards work that I will do in subsequent chapters. I began by

looking at the central Kantian criticism of Leibniz that he “inteliectualized appearances.”

In order to make sense of this claim I looked at transcendental reflection and its role in

Kant’s view of cognition. I then assessed what this claim amounted to and in so doing

brought out that there is both an ontological as well as an epistemological facet of this

claim. I went on to argue that the ontological component of the claim is substantiated by

Kant’s sensible intuition, which accounts for the ontological difference between

appearances and things in themselves. I provided further evidenee that the sensible

intuition is the driving foree in the argument against Leibniz by looking at the Inaugural

Dissertation. I then went on to look at the different individual principles discussed in the

“Amphiboly” to support the centrality of the sensible intuition in Kant’s criticisms while

also pointing out some of the specific elements that Kant foeused on in Leibniz’s

philosophy. Additionally, I looked at two other works to reinforce the eentral tenets that

Kant is foeusing on and to introduce these works for later discussion.

If one were to summarize Kant’s criticism of Leibniz in the “Amphiboly” I think

that the following quote would function as well as any.

The conditions of sensible intuition, which carry with them their own differences, he [Leibniz] did not regard as original, sensibility being for him only a confused mode of representation, and not a separate source of representations. {CPR A270/B326)

All one needs to do is establish the character of this “separate source of representations”

and its role in cognition and one has arrived at Kanf s position vis-a-vis Leibniz. Kant

could not attack Leibniz for being internally inconsistent, but he could attribute to him a

fantastie metaphysics that failed to latch on to reality. The way that he accomplished this

was by essentially cutting off his contact with the intelligible world and explaining

phenomena through the forms of the intuition. The only things that we can have

knowledge of are those objects (appearances) that are subject to the forms of space and

time. Through an understanding of these a priori forms of intuition we are not only able

to give a more satisfactory account of space and time, we are also able to account for our

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knowledge of the objects that are situated in space and time. Thus, what Allison called

one of the “most dubious sections of the Critique''’ becomes central in defining the debate

between Leibniz and Kant. Eventually I want to argue that the sensible intuition is not

only important in motivating Kant’s criticisms of Leibniz, but also that it is essential in

differentiating Mm from Leibniz. The several times in the “Amphiboly” that Kant claims

that Leibniz would have been right if not for the sensible intuition alludes to the

importance of the sensible intuition in differentiating these two thinkers, but it will be

necessary to look at these issues in more depth to substantiate these claims.

In the chapters that follow I will be looking at Kant’s criticisms in greater depth

and considering what means Leibniz has at his disposal to respond to the charges. I will

begin by addressing Kant’s central ontological claim and will consider if Leibniz really

committed the amphiboly that Kant describes. Then I will go on to look at space and

time directly as these are so central in the debate between the two. Finally I will look at

two important Leibnizian principles, the identity of indiscernibles and the pre-established

harmony not only to shed further light on the debate between the two, but also to

reinforce my central interpretation that space and time are the crucial topic between these

two thinkers.

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CHAPTER TWO

THE ONTOLOGY OF BODIES

As I discussed in the previous chapter, Kant’s project in the “Amphiboly” is to

give an account of Leibniz’s metaphysical methodology and explain how the details of

his system follow from this methodology. I also argued that Kant’s criticism of Leibniz’s

methodology has an ontological component in addition to the epistemological element

that is usually identified. Leibniz’s general ontological view is that the universe is

composed of simple substances (monads) with the power of perception and that sensible

bodies are somehow based upon this simple foundation. Kant argues that Leibniz does

not or cannot admit an ontological difference between sensible objects and the monads

that underlie them and thereby reduces the former to the latter. In this chapter I will

evaluate the accuracy of this claim. I will begin by looking at Kant’s reconstruction of

Leibniz’s arguments for this position and the difficulties that he perceives in them. As

with my first chapter, I will be focusing on Kant’s arguments in the “Amphiboly” section

of the first Critique. Kant’s presentation in the “Amphiboly” is quite repetitive and he

restates Leibniz’s position and his criticisms several times, with a slightly different

emphasis in each formulation. I will thus do my best to reproduce what I take to be

Kant’s common interpretation among these variations.

I. Kant’s Interpretation

Kant’s starting point in every case is the claim that Leibniz’s approach to

metaphysical investigation is through concepts alone. By this Kant means that Leibniz

began his metaphysical investigation by asking what must be true of objects generally,

i.e., in the concept of an object qua object. According to Kant, pure conceptual

consideration requires a certain methodology, namely that we begin with a concept of

something, of which we can subsequently predicate qualities. The mental faculty that

Kant posits Leibniz using in this investigation is the understanding, which is the “facult)

of knowledge through concepts” {OD 132 fn.). When the understanding employs

concepts by itself the matter precedes the form, or we posit a thing that is subsequently

determined to have certain properties {CPR A270/B326).

36


If a conceptual knowiedge of the world via the understanding was Leibniz’s

methodology, then the material of Ms investigation was substance. According to Kant,

Leibniz’s strictly inteilectualist approach to the question of substance profoundly

influenced Ms view. When Leibniz was considering the fundamental constituents of the

universe he could not choose any relational concepts, because all relations presuppose

some thing that is being related. This holds not only for relations such as spatial

relations, but also for relations such as place, shape, contact, and motion {CPR

A274/B330). Material bodies are inlierently relational, not only because of the external

relations that I listed above, but also because of internal relations of their parts, and are

thus not suitable candidates for the ultimate metaphysical constituents of the world. In

fact, any type of externality would constitute a relation and would have to be stripped

away in order to arrive at the concept of a true substance.

Kant describes a process of abstraction as the means by which all relational

predicates are left behind and one can arrive at the concept of a pure substance.

Abstraction from every relational property reveals that a true substance must be perfectly

simple, i.e., lacking any parts or other relations {CPR A283/B339).’ These substances

do, however, have internal determinations. Although Kant is never explicit on why these

simple entities must have internal determinations, the steps in the reasoning are simple to

fill in. In order to arrive at simple things, i.e., a plurality of things, it is necessary that

there is some way to distinguish the things (remember that spatial position, shape, etc.

cannot play that role since they are all relations), otherwise we would end up with one

simple thing, i.e., Spinozism. One of Leibniz’s goals, stated or otherwise, was to avoid

the heretical views of Spinoza, and his discussion of monads indicates that the simples

that he posited must be plural and therefore somehow liable to individuation.

Providing a criterion for determining, i.e., differentiating, truly simple things is

seemingly no simple task given the fact that we cannot rely on any of the properties that

we use to differentiate the objects that populate our world of experience, e.g., place, size,

' Parkinson in “Kant as a Critic of Leibniz” expresses dissatisfaction with Kant’s move from freedom of outer relations to a freedom from composition. Parkinson claims that a composite substance lacks outer relations but still has inner relations among the parts of the “substance,” thus Kant’s analysis doesn’t get us to the simples that Leibniz desires (312). Parkinson seems to be placing too much emphasis on the ‘outer’ and not enough on the ‘relation,’ which is what Kant really envisions Leibniz as abstracting from. A “composite substance” still has parts that make it up and thus those parts are in relation to one another. Thus, it would seem that Kant’s formulation of Leibniz’s argument could get us to simple substances.

37


shape, etc. We can, however, by considering the only simple substance that we are

clearly acquainted with, i.e., ourselves or our soul, argue by analogy that these simple

substances must also possess varied representations, i.e., internal perceptual states, by

which they may be differentiated (CPR A283/B339). Thus, Leibniz, through his maimer

of considering an object strictly through its concepts arrived at a world composed of

simple substances that are differentiated based on their representations.

After establishing monads as the ultimate constituents, i.e., substances, of the

universe, it was necessary to explain the relationship between the simple monads and the

phenomenal world of experience. To our senses the world appears populated with

composite things that are situated in space and time and that exhibit various kinds of

relations among themselves. In our experience of the world we do not see, touch, or

otherwise sense monads or anything like them. In fact, given the nature of monads as

simple entities without extension, mass, or shape, it seems impossible to sense them in

any way. The question is how something with the nature of the monads can be

ontologically responsible for sensible things, which have a completely different nature.

According to Kant, Leibniz’s means of resolving this dilemma was to employ

confusion as the distinction between the sensible and the intellectual (CPR A271/B327).

Leibniz had to acknowledge the difference between objects as they appear (material

bodies) and as they really are (monads) and a way to honor this difference was to

maintain that sensible representations are confused representation of simple things. In

other words, the senses distort our view of things (monads) and only the understanding

by itself is able to clear away this distortion and arrive at a view of things as they really

are. The result is that the world of sensible objects is a kind of blurred or smeared

presentation of what is in reality perfectly simple.

Leibniz’s alleged insistence that the sensible is simply a confused form of the

intellectual is the amphiboly that Kant is describing in this section and that I discussed at

length in the last chapter. This interpretation not only completely demeans the role of the

senses in Leibniz’s philosophy, but as I argued earlier, it demeans the ontological status

of sensible objects as well. If sensible things are nothing more than a constellation of

monads that are smeared together in our senses then it is hard to see how sensible objects

can be anything more than the monads that constitute them. Sensible bodies may be

38


taken to be things that have an independent ontological status, but in actuality they are

completely ontoiogicaily reducible to the monads that constitute them. Trees and

buildings do not really exist, ail that there really are are a collection of monads that we

are perceiving directly yet confusedly. Simple entities may make outer determination

possible, but these outer determinations are nothing more than the simple things that

underlie them {CPR A283/B339). This means that any predicates that we can apply to

sensible objects such as shape, location, and mass, etc. would be reduced to a confusion

as well. They are merely the product of our limited sense faculties and ways of talking

about our confused representations, not anything real.

II. The Motivation for K an t’s In terpretation

I think that Kant has several reasons for interpreting Leibniz and the role of

confusion in this way. First, it provides a nice contrast with Kant’s own view. Put very

loosely, Kant is trying in the Critique to establish the intellect and the senses as two

independent faculties that must be used in conjunction to provide objective knowledge.

Describing Leibniz’s methodology as a reliance on the intellect alone, at the expense of

the sensible, shows a clear difference between the two views. It also allows Kant to

pigeonhole Leibniz into an intellectualist camp, and allows him simultaneously to point

out problems with the empiricists as well, e.g., Locke, who emphasized the senses at the

expense of the intellectual.

Secondly, this interpretation allows Kant to show his view as a direct

improvement on Leibniz’s own view. According to Kant, confusion is a “logical”

distinction that does not apply to objects. Kant contrasts this with his own

“transcendental method,” which provides a better understanding of the sensibility and the

understanding; Kant’s method deals with the “origin and content” of representations and

while denying us knowledge of things in themselves, provides us with clear and

necessary knowledge of sensible objects {OD 134). While Leibniz’s findings may be

correct as far as logic is concerned, his findings cannot be applied to objects in the way

that Kant’s transcendental method can. This way Kant is able to acknowledge the virtues

in Leibniz’s philosophy while at the same time point out its shortcomings

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Thirdly, I think that Kant may have chosen an interpretation that focused on the

role of confusion as distinguishing between the sensible and the intellectual because, in

Kant’s mind, it provided a more coherent and perhaps more charitable way of

understanding Leibniz’s philosophy. This becomes especially evident in his later debate

with Eberhard. As I explained in the last chapter, Kant’s “On a Discovery” is his

polemical response to Eberhard’s claim that Kant’s philosophy represents no real

advancement over the Leibnizian one. In order to make his point Eberhard makes some

important concessions to Kant in the course of the disagreement. In this context one of

the most important is that Eberhard grants that sensibility is not merely a confused

representation of the intellectual, but a means of representation in its own right and thus

sensible objects are real. At the same time, one of Eberhard’s projects is to prove that

sensible things can be known to be grounded on simple objects. The problem with

granting a unique ontological status to sensible objects is that if Eberhard continues to

maintain that sensible objects are composed of simples, which are essentially non-

sensible, he is getting himself into what looks like a contradiction. If a whole is sensible,

it would seem that all of its parts would have to be sensible too, but Eberhard is denying

that the simples are sensible.^ As Kant points out, “it is obvious that if no simple part of

a sensible object is sensible, then neither can the whole of it be so, and conversely, if

something is an object of the senses and sensation, all of its simple parts must be so, even

though they may lack clarity of representation” (OD 121-2). In other words, differences

in the power of perception cannot be responsible for differences in ontology {OD 125).

I believe that Kant saw a major difficulty in explaining how monads can provide

the ontological foundation of sensible things, i.e., be their constituents, while remaining

themselves non-sensible. By focusing on confusion this problem essentially goes away

because sensible things simply are intellectual things, i.e., monads, on this view. Kant

points out quite clearly in On a Discovery the problem with the view that Eberhard

developed and the impossibility of interpreting Leibniz as holding that view.

In this context when I am talking about something being ‘sensible,’ I mean not that it can be sensed with the naked eye or even with existing or possible technology, but that it is possible to be sensed at all. Monads, which lack any properties by which they could be even potentially sensibly observed, most be thoroughly non-sensible.

40


It is, however, an obvious contradiction to assert that—if these objective grounds (the simple elements) lie as parts in the appearances themselves, and merely because of their confusedness cannot be perceived as such, but can only be known to be there by demonstration—they should thus be called sensible, and yet not merely sensible, but also, because of this latter reason, intellectual intuitions. Leibniz’s conception of sensibility and appearance can not be interpreted in this manner, and either Mr. Eberhard has given an entirely erroneous interpretation of this opinion, or it must be rejected without hesitation. {OD 133)

III. Kant’s Objections

So far, I have outlined Kant’s interpretation of the development of Leibniz’s

ontological view and have considered possible reasons why Kant adopted this

interpretation. Now, I would like to look at Kant’s specific objections to the view. First,

Kant thinks that even if Leibniz is correct he is so in concept only. That is, a logical

analysis of the concept of substance may get us to the simple things that Leibniz is

positing. The problem is that there is no way to verify that this is actually the case, i.e.,

that these monads really exist. Kanf s position is that for us to have knowledge of an

object there must be some way to come in contact with the thing in order to ensure its

existence; this is the role of the intuition. For Leibniz to move beyond a mere conceptual

analysis and demonstrate that monads really are the ontological constituents of the

universe one must be able to contact, i.e., intuit, these entities. A thing that has no

sensible properties is obviously not a candidate for sensible apprehension, thus Leibniz

would require something like an intellectual intuition to come in contact with them. As I

discussed previously, Kant denies the possibility of a human intellectual intuition and

therefore any positive knowledge of the existence or nature of monads. In the Critique

Kant is only willing to allow noumena in the “negative” sense, i.e., as things that we can

know nothing about. Kant is therefore skeptical that Leibniz can prove that monads exist

or can say anything positively about them at all.

Kant is also unhappy with using confusion as the means of understanding the

difference between monads and the sensible things that they compose.^ Confusion is

what Kant calls a “logical distinction” that does not honor the real differences between

Kant also dislikes using confusion to distinguish the sensible because o f its implications for mathematics, primarily geometry, and the empirical sciences, which I discussed in chapter one. I address these important criticisms in detail in chapter three.

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the sensible and the intelligible. If Kanf s interpretation is correct and sensible things can

be reduced without remainder to the monads that underlie them, then the ontological

status of sensible objects and our knowledge of them is seriously called into question.

Sensible objects v/ould only be real to the extent that our limited senses blur the monads

together. Ail of the things that we take for real, all of the things that populate our world

of experience would become mere illusions, and would be real only to the extent that our

perceptions of them were confused.

This last point becomes even more complicated in light of the concession that I

made to Parkinson in the last chapter; it seems that Leibniz does want to separate the

senses and the understanding, at least epistemologically. If sensing is not confused

thinking, then are sensible objects not completely reducible to the intellectual objects

(monads) that underlie them? If that is the case then what is the relationship between

these two things? Do we really sense monads? These questions take us into the heart of

the Leibnizian metaphysics, with a particular focus on confusion as the differentiating

factor between the sensible and the real that is rather unique. I will address this central

issue after first examining some of Leibniz’s own arguments for monads and our

knowledge of them.

IV. The Need for Monads

Kant is undoubtedly correct that one of Leibniz’s principle metaphysical concerns

is to give a satisfactory account of substance. In almost all of his papers and letters

dealing with metaphysical matters, a desire to explain substance and the relation among

substances, as well as the relation of substance to matter emerges as a central concern.

An emphasis on substance is certainly not surprising given that many of Leibniz’s

contemporaries, e.g., Spinoza, Locke, etc. were also interested in the topic. Leibniz’s

development out of an Aristotelian and Scholastic tradition are also partially responsible

for his focus on substance. The particular direction that Leibniz’s view took was also

influenced by these sources, sometimes as a response to what he viewed as shortcomings,

at other times as an adoption of what he held as truths in the view. Leibniz’s mature view

is basically the one that Kant describes; the universe is composed of perfectly simple

substances that are each a locus of an activity that is a kind of perception. These monads

42


are independent of each other yet in mutual harmony of their perceptions. They are also

dense throughout the universe; there is no void or empty spaces, the universe is filled

with monads. Of course, Leibniz has many arguments for each of these attributes, but I

would like to focus for right now on those characteristics that Kant had picked out,

namely monads as simple, immaterial beings, capable of perception, and ontoiogicaily

responsible for phenomena! bodies.

Leibniz’s position that true substances must be simple unities runs deep in his

philosophy and can be traced back at least to his “Discourse on Metaphysics” and his

subsequent correspondence with Antoine Amauld. For example, in his April 30, 1687

letter to Arnauld, Leibniz makes his famous claim that being, in order to qualify as true

being, must be one. “I consider as an axiom this identical proposition, namely, that what

is not truly a being is not truly a being"' (DM 191). Leibniz’s thinking on this point is at

least partially informed by the scholastic principle that ens et unum convertuntur, or that

being is essentially a unity

Leibniz’s arguments for this position tend to revolve around the claim that

without truly simple entities composite substances would not have any reality. For

example, in his 1695 “A New System of Nature and the Communication of Substances,

as well as the Union between the Soul and the Body,” the first published account of his

mature system, he claims that: “a multitude can derive its reality only from the true

unities” (L 454). If one denies that there are true substantial unities, “there would be

nothing substantial or real in the collection” (L 456). According to Leibniz, collections

require something unified out of which they are composed because otherwise we would

be left with an infinitely divisible aggregate; in other words, something whose reality

would only be illusory.

This line of argumentation is interesting because it seems to directly contradict

Kant’s position that Leibniz is unconcerned with sensible objects, which is a point that I

will touch on in greater detail later. As an argument for simple substance in the way that

Leibniz wants to understand them, however, it looks quite inadequate. On the surface it

does seem to hold that when considering an aggregate it must be made out of something,

otherwise it is hard to see it as an aggregate in the first place. This argument does not,

* Rescher, Leibniz: An Introduction to his Philosophy, 13.

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however, tell us very much about what the nature of these unities must be. In order to

flesh this argument out it is necessary to place it within the context of competing analyses

of substance.

IV. 1 Extension

One of the most powerful views of substance at Leibniz’s time was the Cartesian

view that substance should be understood as extension. As Descartes makes explicit in

his Principles o f Philosophy, it is extension for him, rather than any other property, that

constitutes matter’s nature and can subsequently qualify as substance. “In this way we

shall perceive that the nature of matter, or body in its universal aspect, does not consist in

its being hard, or heavy, or colored, or affecting our senses in some other way, but solely

in its being something extended in length, breadth, and depth.” The Cartesian view

focuses on essential attributes of matter and states that of the properties that can be

attributed to a thing, every other attribute of an object other than extension can be

removed and the thing that we are talking about still remain. This shows that extension

must be the nature of bodies or substance. This view was popular at the time and Leibniz

was concerned to show its inadequacy and the superiority of his own view.

Leibniz argues against substance as extension by holding the necessity of

substance being simple and pointing out the inadequacy of extension on this score. The

Cartesian would have to admit that extension is divisible and that it is subsequently made

up of parts. In this sense, it is an aggregate and subject to the same kind of argument that

we have seen previously. Any aggregate must be composed out of unities if it is to be

real. Leibniz states in his 1692 work “Thoughts on the General Part of the Principles of

Descartes” that, “there is required in extension, the notion of which is relative, a

something which is extended or continued as whiteness is in milk, and that very thing in a

body which constitutes its essence; the repetition of this, whatever it may be, is

extension” (L 390). Essentially Leibniz is depicting extension as a kind of attribute that

is used to describe when a number of homogenous things are brought together in a certain

relationship.

Descartes, “Philosophical Essays and Correspondence,” Part II, §4, 254.

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This ties into a second line of axgumentation against extension as substance that

Leibniz empioys that relies on an analysis of the concept of extension. Leibniz contends

that the concept of extension is actually a composite of three different notions. First,

extension is a plurality, there are things that go into the extension, secondly, the things

that enter into the extension must coexist, and thirdly extension is continuous. Leibniz

describes the analyzability of extension in his June 23,1699 letter to De Voider, a

contemporary of Leibniz and a Cartesian. “Nor should I think that the concept of

extension is primitive, or one from which nothing can be withdrawn, since it may be

analyzed into plurality, which it has in common with number; into continuity, which it

has in common with time; and into coexistence in common even with things that are not

extended” (L 519). In this passage Leibniz is in part trying to disprove De Voider’s

claim that extension does represent a “single, unified something” and therefore qualifies

as substance (ibid.). As Leibniz has pointed out the concept of extension does not

represent a single thing, but a plurality of things that are coextensive and continuous.

If we consider these arguments in light of Kant’s analysis we find that Kant is

correct that concepts play an important role in Leibniz’s emphasis on substance and the

subsequent development of his view. However, he is incorrect that Leibniz arrives at his

view by abstraction; in fact, Leibniz seems to be denouncing abstraction as a

methodology for arriving at substance.

Leibniz instead is relying on a certain conception of logic and the nature of

propositions. For Leibniz every proposition is composed of a subject and predicate and

ail truths can be put into this form. When we are talking about substances we find that

substances are those things that can act as subjects but are never predicates of

propositions. Extension does not fit this bill because extension is essentially an attribute.

Matter is extended. “Extension is an attribute; the extended, or matter, is not substance

but substances” (ibid.). Since things when put together properly are extended, extension

is essentially a predicate and cannot qualify as a true substance.

IV.2 Atoms

Of course, after writing off extension as a candidate for substance one does not

immediately arrive at Leibniz’s monads. One could hold that extension does not

45


constitute substance and agree that some things must be brought together to form an

extended whole, yet maintain that these constituents are atoms or some other part of

matter. When Leibniz describes his own intellectual progression in his “New System of

Nature” he states that he briefly held an atomist view, but found it ultimately

unsatisfactory.

At first, after freeing m yself from bondage to Aristotle, I accepted the void and the atoms, for it is these that best satisfy the imagination. But, in turning back to them after much thought, I perceived that it is im possible to find the principles o f a true unity in m atter alone or what is m erely passive, since everything in it is but a collection o f parts or aggregation o f parts to infinity.(L 454)

Again, we find Leibniz looking for principles of “true unity” and finding material

atoms unable to fulfill this essential requirement. The problem with atoms that he is

indicating here is that even if we suppose the atoms to be little pieces of infinitely hard,

indivisible matter, they would still be composed of parts, since matter by definition is

spatial and extended. Thus, atoms would be potentially divisible, no matter how small

they were, and liable to the argument that Leibniz has already leveled against aggregates

as substances. Leibniz also suggests that atoms of matter that are infinitely hard and

composed of parts that cannot be separated from each other is itself “contrary to reason”

(L 456). This indicates that nothing material could qualify for the true unity that Leibniz

is seeking for substance.

Leibniz has a number of other interesting arguments that are intended to show the

problems with making atoms the substantial constituents of the universe. According to

Leibniz a world in which bodies were composed entirely of matter would be one that

would “consist of a flux and ... have nothing substantial” (L 502). Without true unities

to ground bodies, we would be left with infinitely divisible matter that was “evanescent”

and “flowing” without any true ground to stand upon (ibid.). At other times, Leibniz

argues that a world comprised entirely of matter would actually be completely static. If

we assume that all of the parts of matter would be completely identical, as atoms are

supposed to be, then there would be no internal principle of determination between

things, and one would have to resort to external differences such as motion. However,

the displacement of one piece of matter with an identical one would not provide a way to

distinguish between the two pieces. This confusion would hold for all of matter, if

46


completely identical parts were in flux so that no one, “not even an omniscient one, will

see even the smallest indication of a change” (L 505).

Leibniz also has a very interesting argument that appears in Ms correspondence

with Des Bosses and starts out with the premise that the world cannot be known in its

entirety. If we assume that the world is composed of a finite number of atoms, then it

could be known, theoretically by a finite mind (L 599). This “finite mind of sufficient

excellence,” as Leibniz calls it, would be able to grasp a folly material world, which is an

epistemologica! position that must be reserved for God alone. Leibniz also maintains that

the same can be said for any piece of matter, which an atomist would have to hold could

be known if all of its parts were known. Since “no part of matter can be known perfectly

by a created being” (ibid.), this entails that things cannot be composed entirely of atoms.

Overall these arguments are intended to show that neither material atoms nor

extension can qualify as true substance. In order to meet the criterion of true unity that

Leibniz is advocating an immaterial substance is needed. Leibniz therefore posits “atoms

of substance” or what he called in his “New System” “metaphysical points” as the

universe’s true ontological constituents (L 456). Only these immaterial unities, later to

be called monads, can provide the true simplicity that is necessary for substance to be

truly real.^

IV.3 Monads

If at this point Leibniz has established that monads must be simple and

immaterial, he has not given us any insight into their nature. One of Leibniz’s arguments

against atomism serves to support perception as the internal activity of monads and the

way in which they can be individuated. Leibniz begins with the obvious claim that there

is perception in the world, e.g., in us, and then seeks a way to explain this perception.

Leibniz often talks about perception as the paradigm mental activity, which he

understands as “the representations of the compound, or of that which is without, in the

® Loemker explains that it is generally accepted that Leibniz’s first use of the term was in September 1696 in a letter to Fardella (L 508, note 11). In earlier writings Leibniz employed the Greek monas or monades (ibid.).

47


simple” (L 636)7 Leibniz’s claim is that passive matter cannot provide the active

capacity of perception. Perception also cannot be the result of material parts working

together to provide for mental activity. “Materia! particles, however small they might be,

could not be combined or modified so as to produce perception” (NE 440). Leibniz’s

claim is that no material machine could have a structure that provides for mental activity.

Leibniz holds that this is obvious if we imagine a mechanism, e.g., the brain, expanded to

the size of a mill so that one could walk through it and observe the movements of the

mechanisms. In this now famous example, Leibniz contends that nowhere within this

mill could one find perception, just as one cannot find perception within the mechanisms

of the brain. What is needed is a simple substance, since no composite substance could

provide for perception (Monadology §17 L 644). In addition to the capacity for

perception, monads are also capable of having a series of perceptions, that is, moving

from one perception to the other. These appetitions, as Leibniz calls them, are the

tendency of a monad to change from one perception to the other (L 636).

This particular argument, if successful, may show that matter is not capable of

perception and that we are perceiving monads, but it does nothing to show that all

monads are capable of perception. At this point I think that Kant is correct that Leibniz

must rely heavily on an argument from analogy to attribute to all monads the power of

perception. If the entire world is composed of monads and our monad has the power of

perception, then we must assume that all the other simple substances in the universe have

roughly the same properties as our souls. Thus, Leibniz posits a universe populated with

souls or soul like things: “we must think of them [all monads] in terms similar to the

concept we have of souls” (L 454). Of course, not all monads are souls, in fact most are

not, since most monads are not as sophisticated and capable of reason as our souls.

Therefore, most monads in the universe are what Leibniz sometimes calls simple monads,

which lack the sophistication and light of reason that our souls enjoy.* “And even if

Trying to pin down exactly what Leibniz means be “perception” is a notoriously difficult task since he is trying to encompass a much larger spectrum of mental activity with this term than is normally understood. For the moment 1 would like to overlook these difficulties and simply consider perception as a kind of mental activity without being more specific than that.® In the Monadology Leibniz establishes a three level hierarchy of monads. At the bottom are the “naked monads” that are constantly in a “state o f stupor” and are not aware o f any o f their perceptions {Monadology §24 L 645). Ostensibly the majority o f monads would be o f this type. Next, are the “souls,”

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dominaBt souls, and hence intelligent souls such as there are in men, cannot be

everywhere, this is no objection to the view that there should everywhere be souls, or at

least things analogous to souls” (L 504).

In order to make his analogical argument work Leibniz assumes a principle of

regularity in nature. “For the nature of things is uniform, and our nature cannot differ

infinitely from the other simple substances of which the whole universe consists” (L

537). Leibniz also appeals to theological reasons and maintains that his view provides a

better understanding of God’s creation of the universe, since it would better match an all-

powerfiil creator to imbue all of nature with souls or soul-like things rather than

providing them only to a select group of beings. A world populated with minds that are

perceiving with varying degrees of clarity also allows us to talk coherently about animals

and other beings having souls and subsequently avoids the Cartesian position that denied

souls to animals and saw them merely as biological machines. “[The] Cartesians think

that only spirits are monads and that there is no soul in beasts” (L 637).

Leibniz also has another line of argumentation for the internal activity of monads

that focuses not on perception per se, but the activity of monads more generally. Leibniz

often refers to monads as entelechies, or sources of internal action {Monadology §18 L

644).^ Attributing monads with internal principles of activity provides an account of the

physical principle of force and the inertia that we observe in material bodies, an account

that Leibniz feels that inert matter cannot provide. The same can be said for extension,

which lacks the ability to generate activity in the physical world. Often Leibniz goes so

far as to describe monads entirely through their force. We see this especially in his

correspondence with De Voider where he states that, “I believe that our thinking is

completed and ended in the concept of force rather than that of extension” (L 516).

Providing an account of force is a place where Leibniz’s metaphysics and his

physics cross. Leibniz did not feel that activity could be explained purely though

material principles. Neither the resistance of matter nor its activity could arise from

something that was completely inert. He was also dissatisfied with Newton’s and others’

which have the capacity for memory {Monadology §26 L 645). Animals have these type of monads.Finally, there are the “spirits” or “rational souls” that are found in humans {Monadology §29 L 545).* The term “entelechy” is from Aristotle, who uses it in De anima to describe the capacity of the soul for activity. This term underwent some development in Leibniz’s use o f it, but by the time of the Monadology “entelechy” is used synonymously with “monad” (cf. NE Ixi-lxii).

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account of force, which left properties such a gravity as an “occult quality” rather than

giving a sufficient explanation. Leibniz maintained that within the physical world it was

impossible to give a sufficient explanation of activity and change, thus he looked outside

the physical world to the metaphysical principle of monadic activity. It is only through

recourse to a metaphysical substance that is a force that one can give a full account of the

activity and inertia of matter, as well as other natural forces such as gravity. Leibniz did

not consider this foundational metaphysical principle as a necessary element in particular

physical calculations, it is only when one is trying to give an account of the general

principles. “Once this [the general principle of monadic force] is established, we need

not admit entelechies any more than we admit superfluous faculties or inexplicable

sympathies, as long as we are dealing only with the immediate and particular efficient

causes of natural things” (L 441).

I don’t think that one should see the description of monads as possessing

perception and appetition and another description as possessing force as descriptions of

two different qualities of monads, but rather two different aspects of monads as

entelechies. When talking about monads strictly as simple substances and the sole, true

constituents of the universe, describing them as simple entities with the power of

perception is the correct terminology. “Indeed, considering the matter carefully, it may

be said that there is nothing in the world except simple substances and, in them,

perception and appetite” (L 537). It is when Leibniz is talking about the monads in

relation to matter or the bodies of the material world that he cashes out the monad’s

activity as force. Thus, perception and force are not two separate abilities that monads

possess, simply two aspects of the same thing.

V. Kant’s First Criticism - Intellectual Intuition

Now that we have established the general character of Leibniz’s simple

substances, as well as some of his arguments for them, it is time to return to Kant’s

criticisms of this view. The first criticism that I would like to consider is the Kantian

claim that monads are intellectual objects and subsequently inaccessible to us. I think

that Leibniz would actually be in complete agreement with Kant that monads are

intellectual objects insofar as they are only accessible through the intellect. Leibniz says

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as much in a number of sources, many of which were probably not available to Kant.

However, Leibniz has something special in mind when he claims that monads are

intellectual objects. In order to understand this special sense it is important to look at

Leibniz’s epistemologicai views and their relation to concepts and objects.

In his 1702 paper “On what is Independent of Sense and Matter” Leibniz explains

the role of the senses and the intellect in terms of a hierarchy of concepts. This is the

same hierarchy that I explained briefly in the last chapter with relation to Parkinson’s

understanding of Kant’s epistemologicai claim. In this paper, Leibniz first discusses

concepts of a single sense. These include things such as sounds, colors, and heat.

Although these sensations are the product of a single sense, Leibniz does not consider the

sensations themselves to be simple. For example the color green is a combination of blue

and yellow or a single tone is a result of multiple oscillations of the air (L 547). While

people often take sensory concepts as simple, they only appear so “because they are

confused and thus do not provide the mind with any way of making discriminations with

what they contain” (NE 120). It is impossible to provide a definition for a sensory

concept or to provide any kind of description other than to point out the sensory quality

that we are trying to explain. The difficulty is something like trying to explain the color

“aqua” to a blind person. The only way to definitively identify aqua is to point it out to

someone. For this reason Leibniz refers to sensory concepts as conceptually “clear,”

since we can discriminate on the basis of them, e.g., pick out different colors, but they are

not “distinct” but “confused” because we cannot “develop the content included in them”

(L 548). Sometimes Leibniz even goes so far as to refer to sensible qualities as “occult

qualities,” since we cannot give an account of what makes up the particular concept (L

547).

The next kind of concept, concepts of the common sense, are not only “clear”

because we can isolate these concepts from others, but they are also “distinct” because

we can pick out the elements that combine to form the concepts (L 548). When Leibniz

talks about the common sense he does not have in mind concepts that arise from senses

used in conjunction, but rather the commonalities among the senses that are discovered

by the understanding. For example, the common sense allows us to identify the figure

that is common to a particular object when it is sensed by both sight and touch (ibid.).

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Both concepts of the senses and those of the common sense are what Leibniz calls

imaginable, and he discusses the role of the imagination in bringing these concepts

together, e.g., those from the individual senses and those of the common sense.

For Leibniz there is a third level of concepts that rise above those of the

imagination. These are the concepts of the understanding. The clearest way to arrive at a

concept of the understanding is to think of ourselves. Leibniz claims that there is

evidence of ourselves in every thought that we might have; we can, for example,

distinguish our thought of a particular color from the thought that I am thinking the

thought (L 891). This apperception provides us with evidence of ourselves, which is

something that carmot be sensed or otherwise imagined. This conception of the T’ also

gives us our general conception of substance, according to Leibniz, and “other concepts

in metaphysics, such as those of cause, effect, action, similarity, etc.” (ibid.). What

Leibniz means by this is that these central metaphysical concepts cannot be found in the

senses or the common sense, i.e., they are not imaginable, but are found within the

understanding. These intellectual truths are discovered within ourselves and do not come

from outside. According to Leibniz as rational souls we have a “natural light” that allows

us to arrive at these purely intellectual truths, e.g., the status of the soul as a simple being

that is capable of perception.

In an interesting take on the famous Cartesian argument, Leibniz claims that our

capacity for purely intellectual knowledge is what makes us certain that a mind or soul

exists before we can be sure that there are sensible things (L 549). “[T]he existence of

intelligible things, particularly of the 1 who think [sic] and am called a mind or soul, is

incomparably more certain than the existence of materia! things” (ibid.). In fact, Leibniz

goes as far as to state that “speaking with metaphysical rigor” we can never be sure that

there are sensible things external to us, but certain truths such as in mathematics we can

be sure of since they are demonstrative truths that are not dependent on particular sensory

information; they could even be arrived at in a dream or other hallucination (ibid.).

In our ability to discover intellectual truths Leibniz states that we mimic God to

our own, small degree. We “resemble God in miniature not only through our knowledge

of order but also through the order which we can ourselves impart to the things within our

grasp” (L 552). Sometimes Leibniz talks not only about the intellect being able to reveal

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certain truths that are accessible only to it, i.e., metaphysical principles, but also that

these findings belong to an intelligible world. “This intelligible world of which the

ancients speak so much is in God and in some way also in us” (L 585). Because these

things are accessible only through the intellect and not through the senses, to try to

imagine these objects or otherwise sensibly represent them is impossible. As Leibniz

points out in an especially vivid passage, many of the problems that people have with his

views, especially his view of substance, result from people are trying to imagine what can

really only be understood. “The residual problem exists only for those who want to

imagine something that can only be thought, like wanting to see sounds or hear colours”

(AE381).

Anyone who would try to imagine what a monad would look like is committing a

category mistake and using essentially the wrong faculty of knowledge to get at monads.

This is why Leibniz’s analogy with seeing sounds is especially illuminating. We cannot

see a sound because sounds are essentially heard. Although we may try to approximate

the experience of hearing, for example, a loud sound with a bright red flash, this certainly

is not the same thing as the sound. When it comes to monads, certain things can be

known to be true of them through the understanding alone, but our imaginative faculties,

i.e., the five senses and the common sense, are limited in such a way that they simply

cannot grant us access to monads. Thus, as Leibniz explains in a letter to Des Bosses,

although we may fancifully imagine the world full of monads crowded together to form

objects and the world, this is to use “certain fictions of our mind when we seek to

visualize freely what can only be understood” (L 604).

Is Leibniz attributing an intellectual intuition to us in order to gain knowledge of

monads, as Kant has maintained? If we understand the intellectual intuition as a way to

know purely intellectual truths, then it does seem as though Leibniz is granting us this

ability. Leibniz’s “natural light” is something that we share with God and is an ability

that allows us to have knowledge of things that transcends the senses. However, Leibniz

is not claiming that humans can directly intuit other intellectual objects. The only

intellectual object that we can intuit, i.e., have immediate contact with, is ourselves. All

other intellectual objects, i.e., monads, are impossible to know directly. As I mentioned

earlier, Leibniz’s means of establishing the nature of other monads is by using an analogy

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from our own nature to theirs. The direct apprehension of monads is reserved for God,

thus, although we resemble God it is only to a very limited degree. Our “natural light” is

much dimmer than God’s, but it can operate on its own and independently of the senses,

which is certainly contrary to Kant’s view that only things that we can sensibility intuit

are those things that we can have knowledge of.

One real virtue of Kant’s emphasis on the intellectualist component of monads

and our knowledge of them, is that it forces us to understand monads as intellectual

objects. There is, as Leibniz acknowledged, the naive tendency to try to visualize small,

impenetrable little balls as making up the universe on his view; this would actually be the

view of the atomists, which Leibniz is trying hard to distance himself from. Rather, we

should take seriously Leibniz’s claims that monads are a “power of action” that are not

“derivable from sensory images” (L 501). Monads are a “certain action or entelechy ...

midway between the faculty of acting and the action itself’ (L 433).

Leibniz sometimes characterizes monads as the law of a series, which is also

helpful in discerning their nature.M onads, as we have seen, are loci of activity that is

internally generated. The perfect simplicity of monads also means that they are devoid of

parts and thus do not interact in any way with other monads. This means that monads are

“windowless” and must be internal principles of activity; they are responsible for all their

changes of states as well. When talking in terms of perceptions, this entails that monads

generate their own series of perceptions, even those that represent monads that lie outside

of themselves.’* Leibniz’s pre-established harmony is his way of ensuring that the

progression of monads stays in step and that external perceptions match those of other

monads. Within any given monad this pre-ordered, by God, series of states can be

understood as a lawful progression of a series. Leibniz explains this situation in a letter

late in his correspondence to Amauld. “Each of these substances contains in its own

While I am presenting the “law of a series” view of monads as simply an alternate depiction of the monad for Leibniz, there is the possibility that it represents a change in emphasis for Leibniz away from the complete concept view as found in the “Discourse” and towards a view that better understands the role of monads as principles o f activity and not static concepts. Donald Rutherford advances this interpretation in his Leibniz and the Rational Order o f Nature, 151.

To talk about monads as outside of each other is for Leibniz a misnomer and simply a way of trying to imagine, in Leibniz’s technical sense, what we can simply know to be the truth. Although we want to represent to ourselves monads as crowded together or dispersed throughout space, this is simply not the case. The relation o f monads to space will become especially important in the next chapter.

54


nature a law of the continuation of the series of its own operations and everything that has

happened and will happen to it” (L 360). In a later letter to De Voider Leibniz goes as far

as to claim that ail monads really are is the series that dictates their changing states. “For

me nothing is permanent in things except the law itself which involves a continuous

succession and which corresponds, in individual things, to that law which determines the

whole world” (L 534). These two characterizations, monads as the law of the series of

perceptions and as the series of activity, should not be seen as two competing

characterizations, but simply alternate formulations of what Leibniz wants to take as the

same thing. This is analogous to the way he alternates between characterizations of

monads as loci of force and as perceiving, mind-like entities.

The upshot is that while monads are to be understood as simple substances they

cannot be seen as things in any sense of the word. Their nature and our way of

apprehending them precludes any possibility of ever sensibly representing them and their

lack of any of the qualities that sensible things have means that they are much different in

nature than the material bodies, the things, that populate our world of imaginable

experience. Monads are active principles or laws of a series.

Kant therefore seems essentially on the mark when he describes monads as

intellectual objects. Monads are known only through the intellect and have properties

that are not possible for material things. Our knowledge of monads comes through

ourselves and our own monad, i.e., soul, provides the only direct evidence of monads that

we have. The existence of other monads and the status of the universe as composed of

monads is “proved” based on certain premises, as Leibniz has attempted to show with his

various proofs for the ontology of substance. Kant’s claim that Leibniz is dealing merely

with the manipulation of concepts and not touching on things is one that Leibniz would

roundly deny. We can see evidence of this in a draft of a letter to De Voider in which he

resists De Voider’s push to develop a more logical notion of substance.

You [De Voider] assert that the notion of substance is formed out o f concepts and not out of things. But are not concepts themselves formed from things?You say that the notion of substance is a concept of the mind, or a rational entity, as they say. But the same can be said o f any concept, if I am not mistaken, and, furthermore, it is not about concepts, but about the objects of concepts that we say entities are either real or rational. But substance, I believe, is a real entity - indeed, the most real. (L 518)

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Leibniz clearly holds himself to be making claims about reality, not merely about the

relation of concepts.

VI. Kant’s Second Criticism - Ontology of Sensible Objects

As I explained above, Kant is essentially correct in his estimation of monads as

intellectual objects and of Leibniz’s contention that we can have knowledge through the

intellect alone, although that knowledge is not of other monads directly. According to

Kant, after Leibniz arrived at Ms view of monads as the ultimate constituents of reality,

he then went on to describe the senses and sensible objects as a confusion of that reality.

On Kant’s reading of Leibniz, our sensible experience is simply a blurred way of

experiencing the world of monads. “The conditions of sensible intuition, which carry

with them their own differences, he [Leibniz] did not regard as original, sensibility being

for him only a confused mode of representation, and not a separate source of

representations” (CPR A271/B327). This is the second strain of Kantian criticism that I

identified above.

There are actually three important components in this ontological criticism, each

of which needs to be explicated and addressed. First, Kanf s interpretation that sensing is

simply confused thought requires that we sense monads directly. If sensibility is simply a

confused form of knowing, then my perception of a chair, for example, is not a

perception of a thing, but of things, i.e., monads. The second component of the criticism

is that sensible things have no ontology independent of the monads that underlie them.

Because sense perception is confused perception of monads, sensible things must also be

confused approximations of their underlying monads and thus nothing in themselves.

Confusion, Kant claims, is merely a logical distinction and cannot be used to ground

ontology (ID §7 387); sensible bodies must be completely reducible to the monads that

underlie them. A third, related aspect, is that the sensible bodies themselves must be

mere illusions, or more accurately, mere confusions. This is a normative statement

concerning the epistemologicai and ontological worth of sensible bodies. On Kant’s

reading of Leibniz not only is empirical knowledge inferior to intellectual knowledge, but

also sensible objects are inferior to intellectual objects. As far as objects go, Leibniz has

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allegedly prioritized the intellectual at the expense of the sensible or material. I will

attempt to address each of these Kantian claims in turn.

VI, 1 Sensing Monads

The first thing that one needs to keep in mind in assessing Kant’s criticisms is that

for Leibniz “confusion” is a technical notion. Although Kant uses confusion as a

pejorative term, for Leibniz confusion is not necessarily a bad thing. As I outlined above,

in Leibniz’s epistemology confused perceptions are not distinct, but they can be clear.

An indistinct perception is simply one in which we cannot discern the parts that go into

the perception. A clear perception is one that allows us to distinguish the object of the

perception, e.g., discern between the colors red and green. Leibniz also claims that sense

impressions can be “vivid,” in fact the confused perceptions of the senses are often more

vivid then the distinct ones of the intellect (NE 187). It is exactly because sensory

information is more vivid to us that we tend to prioritize it over intellectual knowledge

that is distinct and more accurate. Kant is certainly correct that confusion represents a

kind of limitation, but in itself confusion is not a bad thing, it is just a condition endemic

to the senses.

Leibniz provides very specific conditions under which we are liable to confusion,

namely when impressions are either “too minute, and too numerous, or else too

unvarying, so that they are not sufficiently distinctive on their own” (NE 53). In other

words, perceptions can become confused when their components are too small, there are

too many of them, or we have become accustomed to them, e.g., the way that one no

longer hears noisy neighbors because one has “gotten used to them.”

If we look at Leibniz’s fundamental metaphysical level of the monadic, we find

that confusion is a way for Leibniz to account for the differences among monads. As we

have already seen, if one speaks with strict metaphysical rigor we can only accept the

existence of monads. These are the real constituents of the universe and what all else

must be ontoiogicaily grounded upon. However, the absolute simplicity of substances

entails that they cannot interact. Unlike composite substances that have parts that can

come and go, monads don’t have any “windows” through which “anything could enter or

depart” (Monadology §7 L 643). Monads must be “windowless” because any addition or

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loss of parts would violate their absolute simplicity. Leibniz’s view on accidents, namely

that they cannot exist independently of any substance and are therefore non-transferable,

further ensures the perfect independence of monads from each other. This view of simple

substances requires that evejy state of the monad must be internally generated. What

ensures that the monads move in step with each other, i.e., appear to causally interact in a

community, is Leibniz’s pre-established harmony. In principle there is nothing to prevent

Leibniz’s God from creating a universe of disharmonious monads, i.e., a universe filled

with monads acing independently of each other. In actuality, God’s reason for choosing

this universe is based on the principle of perfection, i.e., that God’s goodness provides the

motivation for his choice. Leibniz asserts that perfection, in this context, is a function of

variety and order {Monadology §58 L 648). A most perfect universe is one that

maximizes both of these variables. According to Leibniz, a universe dense with

substances, each of which represents and thus is in step with every other, ensures a

maximum degree of order and variety.

I am going to skip over the details of this relationship between perfection and

God’s creation of the universe as I will discuss it in more depth in my final chapter, but

for now what is important is that the end result is a universe ruled by the pre-established

harmony, which causes “each simple substance to have relations which express all others

and consequently to be a perpetual living mirror of the universe” {Monadology §56 L

648). Every monad’s internal state reflects or expresses every other’s but only God is

distinctly aware of the state of every monad. “Each soul knows the infinite, knows

everything, but confusedly. ... Only God has a distinct knowledge of everything, for he is

the source of everything” (L 640). Confusion enters in at this fundamental ontological

level because no created monad is able to achieve the perceptive powers of God.

Confusion becomes a way to express the limitations of monads as well as differentiate

them. Monads are more or less confused in their perceptions proportional to how perfect

they are. Each monad has “perfection in proportion to the distinctness of its perceptions”

(ibid.). Thus, Leibniz finds an interesting way to combine moral goodness with

perceptual acuity. The more distinctly a monad is able to perceive the others the more

perfect it is; since God is able to perceive all monads distinctly He is all perfect.

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In addition to providing a connection between moral perfection and confusion,

Leibniz also uses confusion to explain the existence of the body or at least the relation of

the soul to the body. Leibniz’s view is that a monad’s confused representations simply

are those representations of the body. For example, Leibniz says the following in a reply

to Pierre Bayle. “Hence the common usage is not wrong in speaking of a conflict

between body and spirit, since our confused thoughts represent the body or the flesh and

constitute our imperfection” (L 581). This tie between imperfection and the body is a

crucial one and it is one of the reasons that Leibniz holds that all created monads have

some type of body, even the higher beings such as angels. “I agree with most of the

ancients that every Spirit, every soul, every created simple substance is always united

with a body and that no soul is ever entirely without one” (NE 58).

Of course, as we have seen, because of the monads’ absolute simplicity, strictly

speaking we cannot say that they ever perceive another monad or anything external to

themselves; monads are windowless and every perceptual state is internally generated.

“[I]t is impossible for the soul or any other true substance to receive something from

without, except by divine omnipotence” (L 457). Thus our perception of a body, i.e.,

something external to us, is a mistaken perception that Leibniz calls a confusion.

As for the very existence of the body, I think that Leibniz was never really in

doubt. Unlike many of his contemporaries, Leibniz was relatively unconcerned with

skeptical arguments. At one point he claims that even if the entire world is a dream, its

agreement and coherence would provide us with “something equally as valuable in all the

practice of life as would be real phenomena” (L 364). I suspect also that he assumed the

existence of the body for largely non-philosophical, viz. religious reasons, since the

relation of body and soul is a central issue in Christian theology. Leibniz was also

actively involved in the contemporary debates that revolved around the mind-body

problem. He commonly remarks that his view provides a distinct advantage over the

Cartesian and occasionalist positions. I also think that Kant is essentially correct that

Leibniz first developed his pre-established harmony as a way to explain the mind-body

interaction and subsequently expanded its application to cover the relation of all monads.

Leibniz’s description of his own intellectual development in “A New System of Nature”

bears this out as Leibniz talks about the relationship of the soul and the body as a

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problem that he had to solve before he realized its application to the relationship between

monads (L 457).

According to Leibniz, in a living being the body is a group of monads that are

dominated over by one principle monad. In humans this is our soul. The composite of

body and soul, what Leibniz calls an “organic corporeal substance” is created out of a

dominant monad and the secondary matter “or the organic machine in which innumerable

subordinate monads occur” (L 531).^ The entire being is “the animal or corporeal

substance which the dominating monad makes into one machine” (ibid.). Domination in

organic entities is a matter of the clarity of perceptions. Each of the monads that

constitutes the body perceive the other constituent monads more clearly than any others

outside of the body, but the dominant monad is the one that perceives the other monads

of its body more clearly than any of the others. Thus, there is a structural relation

between a dominant monad and its body that relies on clarity of perceptions. According

to Leibniz every monad, even those that are considered “sleeping” monads and constitute

inanimate matter are connected to a body. “Together with a particular body, each monad

makes a living substance. Thus not only is there life everywhere, joined to members and

organs, but there are infinite degrees of it in the monads, some of which dominate more

or less over the others” (L 637). The monads that constitute the body may change over

time—there is no one particular set of monads that the dominant monad is tied to—but

there is always a body for the dominant monad and this body is what the dominant monad

perceives most clearly. “The perceptions of the soul always correspond naturally to the

state of the body” (NE 117).

Some dominant monads are sophisticated enough and associated with bodies that

are structured in such a way that they have sense organs. The senses are a more powerful

way for the body to perceive things that are external to it and deliver those perceptions to

the dominant monad.

But when the m onad has organs so adjusted that by m eans of them the impressions which are received, and consequently also the perceptions which represent the impressions, are heightened and distinguished (as, for example,

This view is actually more complicated than I have presented it here. In the letter to De Voider that this is taken from, Leihniz also discusses the dominant monad itself as being a composite o f “the primitive entelechy or soul” and “primary matter or primitive passive power” (L 530). I will discuss these components in more depth in section VI.2 below.

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when rays o f light are concentrated by means o f the shape o f the humors of the eye and act with greater force), then this may amount to sensation, that is to say, to a perception accompanied by m em ory... (L 637)*^

The body, thus, acts as a conduit by which the soul is able to have knowledge of things

that are outside of it. Leibniz explains in his “Reply to the Thoughts on the System” that

the soul is not only aware of what takes place in its body, but “by means of it [the body],

that which happens outside of if ’ (L 580).

Sensations arise because our sense organs are affected by various things in the

environment and subsequently pass that information on to the dominant monad. The

number of things that impinge on our senses is so great however, that we are not able to

sort out each distinct part within our sense perception; in this way the sense perception is

necessarily confused. “'[Sjensory ideas' depend on detail in the shapes and motions,

which they precisely express, though the mechanical processes which act on our senses

are too small and too great in number for us to sort out this detail within the confusion”

(NE 403)}^

Why any given sense perception has the particular nature that it does is something

that Leibniz holds is ultimately unknowable. While we may eventually be able to explain

the cause of the color red, e.g., in terms of certain light waves hitting the retina, we will

never be able to explain why red has the particular nature that it does. However, Leibniz

disagrees with Locke that our sensory perceptions are arbitrary or completely

unconnected to the multitude of perceptions that cause them. Leibniz holds that there is a

certain structural relationship between our confused, seemingly simple sense perceptions

and their complex causes that has to do with an orderly expression of the one in the other.

“I would say ... that there is a resemblance [between colors and their cause] of a kind -

not a perfect one which holds all the way through, but a resemblance in which one thing

” Memory is crucial to sensation because we need to do more than simply have a perception, we also need to consider that perception, that is maintain it in a way before the mind. “Memory is need for attention: when we are not alerted, so to speak, to pay heed to certain o f our present perceptions, we allow them to slip by unconsidered and even unnoticed” {NE 54). Animals also have the faculty of memory as is evidenced by dogs being scared o f sticks that they were once hit by, etc.

This is a view that is in stark contrast to someone like Locke who held that sense perceptions are simple. On Locke’s view, red is a simple perception that cannot be broken up into any parts. For Leibniz, a red perception is caused by a number of other, smaller perceptions, which are blended together, i.e., confused, into what appears to us to be one perception. “It can be maintained, I believe, that these sensible ideas appear simple because they are confused and thus do not provide the mind with any way of making discriminations within what they contain” {NE 120).

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expresses another through some orderly relationship between them” (NE 131). The

orderly relation is one that is maintained by God, or at least originally established by

Him, and therefore cannot be arbitraiyc If there were no “relation or natural connection”

then God would have no reason to associate sense perceptions with their causes, which is

in direct violation of the principle of sufficient reason. According to Leibniz, God never

acts in such an “unruly and unreasoned fashion” (ibid.).

Leibniz describes sensory perception as a form of symbolic knowledge. Symbolic

knowledge is knowledge that expresses complex concepts in a way that does not discern

their parts, but is nonetheless an accurate expression. Humans tend to rely on symbolic

knowledge because our faculties are too limited to keep all the parts of a complex

concept within our mind (L 292). For example, when one talks about a chiliogon one

does not think of the thousand equal sides, but one simply uses the word “chiliogon” in

place of that complex concept and this approximation serves our purposes (ibid.).

Leibniz claim is that sensory knowledge also serves as a way for limited beings to

express a reality that is too complex for them to understand intuitively in all of its part.

For this reason, Leibniz claims in the New Essays that all limited beings, i.e., all beings

other than God employ some kind of sensation in order to symbolically represent the

world. “I am convinced that created minds and souls never lack organs and never lack

sensations, as they cannot reason without symbols” (NE 212).

This brings us to the central question of this section: What then do the senses

actually perceive? Are they confused perceptions of monads as Kant maintains? If we

put together Leibniz’s views on the body and on the senses, I think that we see that

Leibniz held that the senses operate completely on the level of the body and provide us

with perceptions of other bodies and not monads directly. First, all of the examples that

Leibniz uses to explain the relation of the confused senses to their complex causes refer

to “mechanical process” that operate on our senses, or “motion” striking our sense

organs, all of which indicates that he is discussing processes that occur at the level of the

material (NE 403, 54). For example, in his 1702 essay “On What is Independent of Sense

and Matter” Leibniz talks about specific senses qualities, such as color or heat and

describes the possible cause of color as small globes and heat as the “eddy of very fine

dust” (L 547). Although the science here is rather primitive, it is important to note the

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lack of any mention of monads’ movements or properties as the cause of sensible

qualities. Leibniz discussion occurs strictly at the level of the physical or the level of

bodies and not the monadic.

Leibniz certainly allowed that scientific investigation may reveal deeper causes of

sensory impressions that are themselves sensory and require an even further

investigation. These kinds of degrees of complexity are fully in line with Leibniz’s own

thinking. Seventeenth century scientific advances having to do with microscopy and

other scientific apparatus probably played an active role in Leibniz’s development of this

position (cf. NE 220). This is not to say however, that further scientific advances will

grant us empirical access to monads. According to Leibniz it is the very nature of

sensible perception “to be confused and remain so” {NE 403).

A further reason why we do not directly sense monads has to do with the nature of

the body and our relation to other bodies. As we have already seen, on Leibniz’s view

every created monad is endowed with a body and although a dominant monad and its

body are completely isolated, their perceptions most clearly reflect each other. Leibniz’s

understanding of body goes even further to assert that not only does a dominant monad

perceive its own body more clearly than other things but also it is through its own body

that a monad perceives all other things. Leibniz states in a letter to De Voider that;

“every soul or entelechy whatever expresses its own body and through it all other things”

(L 531). Leibniz use of “things” here as the objects of perception is admittedly a little

vague. Is he referring to monads or is he referring to bodies? Given what he says

elsewhere 1 think that it is through the body that a dominant monad is perceiving the

bodies of other monads. He says exactly this in the New Essays. “Every finite spirit is

always joined to an organic body, and represents other bodies to itself by their relation to

its own body” {NE 155). In the Monadology he asserts that the body perceives matter,

but this seems to amount to the same thing, i.e., we sense other bodies and not monads.

“And, as this body expresses the whole universe by the connection between all matter in

the plenum, the soul also represents the whole universe in representing the body which

belongs to it in a particular way” {Monadology §62 L 649).

The situation that Leibniz is describing here seems to be the following, at least for

animals and humans. There is a dominant monad that controls the body and that serves

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as the soul for the body. The soul is aware of what is going on in the body. The way that

the body, and by association the soul, is aware of things that are outside of it is through

sense perception. For example, I am aware that there is a dog in front of me by looking

at the dog, petting the dog, smelling the dog, etc. This is also the means by which I

become aware of the state of the dog’s dominant monad. I observe the manifestations of

the dog’s dominant monad through its body, i.e., I observe the dog in action. I can, for

example, tell the dog is thirsty by watching it drink. With humans there is also the

possibility for language, another symbolic form of communication, to become more

directly aware of the inner state of another person, but this interaction also involves

sensory perception and mediation through our bodies, e.g., the communication from their

vocal chords and mouth to my ears. There is no way that I can contact their soul directly.

This relationship becomes admittedly less comprehensible when we are talking

about the dominant monad of a tree perceiving me through its body, which also seems to

follow from Leibniz’s view. But, for animals with sensory perception, which is our

focus, the relationship is relatively clear. There is no monadic interaction involved either

actually or virtually. What we are sensing is other bodies, whether they are bodies that

are immediately controlled by a dominant monad as is the case with animals, or whether

they are non-living things that are aggregates of other bodies.

I think that a final sense in which it is correct to say that monads do not sense

other monads is because strictly speaking monads never perceive other monads, and to

say that monads do sense other monads directly violates that principle. The complete

isolation of monads is a fundamental metaphysical truth for Leibniz and as soon as we

begin to talk about any kind of external relation we are talking about something that can

only be a phenomenon and cannot be fully real. As we saw earlier, the body is a

manifestation that arises when we imagine that we are dealing with something that is

external. In his 1695 “New System of Nature,” Leibniz claims that, “the body ... has

also been adapted to the soul to fit those situations in which the soul is thought of as

acting externally” (L 458). Sense perception, which is necessarily an external relation is

something that is phenomenal and cannot have something real, i.e., monads, as its object.

I think that ultimately sensation should be thought of as a symbolic means of expressing

truths that God has endowed us with so that we may know things despite our limitations.

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Sensation is a way that we can discover truths that are actually contained within us by

appearing to come from without, i.e., from other bodies through our own body.

For these reasons I think that Kant is wrong to assert that we are confusedly

sensing monads. The senses are necessarily confused and are intimately tied up with the

body, which ensures that their object is bodies and not other monads. But what about

those bodies themselves? If monads are the only things that are truly real, doesn’t this

mean that bodies must be composed of monads in order to be themselves real? This leads

us into questions of the ontological status of bodies and the second Kantian question: are

bodies completely reducible to the monads that underlie them?

VI.2 The Ontology of Sensible Bodies

In the “Amphiboly” Kant understands Leibniz’s position to be that bodies actually

are monads. “Appearance was, on his [Leibniz’s] view, the representation of the thing in

itself' (CPR A270/B326). Although Kant in this passage makes it sound like there is a

one to one correspondence between sensible objects and monads, at other points he

makes it clear that sensible bodies are collections of monads. In What Real Progress he

states:

[Ijntuition is distinguished from concepts o f things only in virtue o f the degree o f consciousness, not specifically, so that, for example, if one were completely conscious o f all the representations contained in the intuition o f a body, that would [Leibnizians contend] provide a concept o f it as an aggregate of monads. {WRP 89)

On Kant’s view of Leibniz, material bodies simply are the monads that comprise them.

Only the limits of our faculties prevent us from perceiving the monads that make up

material bodies. Any properties that we may wish to attribute to bodies qua bodies are

simply the result of our confused perception. This is more than simply to say that

material bodies are composed of smaller parts, as an atomist might do. Kant is claiming

that for Leibniz any properties that bodies exhibit that cannot be attributed to the monads

that comprise them are a product of our own misperception. In other words, material

bodies are completely ontologically reducible to monads.

The first question that Leibniz must address is: what exactly are material bodies in

his philosophy? Leibniz actually provides two answers to this question, the first of which

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follows from what I have called Ms “strict metaphysical view” and a second that provides

for a richer ontology. As we have seen previously in his proofs for monads, Leibniz’s

commitment to the perfect simplicity of substance ensures that the only things that can be

really said to exist are completely independent monads and the only properties that these

monads have are their perceptions. Strictly speaking then, all that Leibniz can allow into

his ontology are individual, isolated monads. Because these monads are completely

“windowless” any relation that they have must be virtual, i.e., an internal product of their

own perceptions. On this strict view, material bodies can only be a product of

perceptions, either of the constituent monads or of the monad that is perceiving the body.

This extreme form of phenomenalism entails that at best material bodies are the

collective perceptions of all monads, but do not have any reality beyond those

perceptions.'^

In addition to what I have been calling his strict metaphysical view, Leibniz also

talks about material bodies as more than simply the perceptions of individual monads, but

as real things that are collections or aggregates of monads. “Compound substance is a

collection of simple substances, or monads” (L 636). In this context Leibniz’s emphasis

is usually on living beings and their composition out of monads. In a letter to De Voider

Leibniz distinguishes between the “primitive entelechy or soul,” “primary matter or

primitive passive power,” and “the complete monad formed by these two” (L 530).

This position is often called Leibniz’s “phenomenalism,” but I think that one must be careful labeling his position in this way. If one views phenomenalism as the reduction o f statements about objects to statements about sensory perceptions, then the position that Leibniz has established cannot be called phenomenalism. Leibniz is attempting to reduce talk about material bodies to perceptions of monads, in his rather obtuse sense o f perception. On Leibniz’s view of monads, even the “sleeping monads” have perceptions of the entire universe, although they are not distinctly aware o f those perceptions. We have also seen in our discussion o f body that it is wrong to attribute even more advanced monads with sensory perceptions. It is the role o f the body to sensibly perceive and the most that monads can do is perceive through that body. Individual monads cannot really be said to sense.

Leibniz’s position is also very different from someone like Berkeley whose project was to reduce physical objects to sensory perceptions. A large part of Berkeley’s project was to defend common sense in the face o f scientific criticisms that the nature of the world is actually much different than it appears to our senses. By reducing material objects to sensory perceptions Berkeley ensured that the world is as it appears to the everyday observer. This is not Leibniz’s project. As I pointed out earlier, the senses provide symbolic knowledge that while useful for us to make our way through the world does not reveal the true nature o f the universe. Even within sensory knowledge further investigation can reveal things to be much different than they appear, such as the difference between everyday observation and atomic theory as related to material objects. See Margaret Wilson’s paper “The Phenomenalisms o f Leibniz and Berkeley” in her Ideas and Mechanism: Essays on Early Modem Philosophy, Chapter 21 for a nice discussion of the differences between Berkeley and Leibniz’s phenomenalisms.

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Together with “mass or secondary matter,” each of these monads makes an entire living

being, “which the dominating monad makes into one machine” (L 531). “Together with

a particular body, each monad makes a living substance” (L 637). According to Leibniz

every monad has this constitution, thus every monad has a body that is itself composed of

an infinity of other monads. “And each outstanding simple substance or monad which

forms the center of a compound substance (such as an animal, for example), and is the

principle of its uniqueness, is surrounded by a mass composed of an infinity of other

monads which constitute the body belonging to this central monad.. (ibid.).

On the macro level of a living being, for example a dog, the dominant monad is

called the soul and is responsible for unifying the entire composite into one being.

Inanimate objects, such as a book or rock, lack a dominating monad, but are still

collections of matter, and thereby contain monads and their bodies in their parts. Because

Leibniz considers these monads and their bodies to be living things, he often says that all

of nature is full of life.

It is true according to my system that there is no part whatever of matter which does not contain an infinity of organic and animated bodies, among which I include not only animals and plants but perhaps also other kinds which are entirely unknown to us. (L 586)

This view differs significantly from the strictly perceptual picture that I outlined

above. Here Leibniz seems to be indicating that material things literally are collections

of monads and their bodies and not merely the perceptions of monads. On the surface it

is very difficult to see how these two views can be reconciled. How can material bodies

be the perceptions of monads and aggregates of them at the same time? How can the

isolated monads form an aggregate at all? Catherine Wilson describes this tension nicely

in her book Leibniz’s Metaphysics: “Leibniz not only seems confused as to whether

bodies are the foundation of perception or perceptions the foundation of bodies; he seems

to think that both can be the case.”**" Wilson contends that these two views cannot be

reconciled and that Leibniz simply doesn’t have a “single theory of monadic

perception.” ’ According to Wilson, Leibniz was tom between a strictly phenomenalist

position and a more robust position that employed corporeal substances as part of his

Wilson, Leibniz’s metaphysics: A historical and comparative study, 195.Ibid.

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ontology. In the end, Wilson contends that Leibniz opted for “strict phenomenalism” and

was willing to sacrifice the reality of bodies along the way.*®

I agree with Wilson that in an important sense all that Leibniz could maintain

were monads and their perceptions, which relegates corporeal bodies to the realm of

phenomena. At several points in his writing Leibniz asserts that all he can be sure of is

that there are independent, perceiving monads. For example, in his essay “On the

Method of Distinguishing Real from Imaginary Phenomena,” Leibniz states that bodies

can be taken to be real only with “moral certainty” but not with “metaphysical certainty”

(L 364). What Leibniz means is that while the reality of bodies have the highest degree

of probability, their non-existence does not imply a contradiction and thus their existence

is not necessary. “Thus by no argument can it be demonstrated absolutely that bodies

exist, nor is there anything to prevent certain well-ordered dreams from being the objects

of our mind” (ibid.).

Leibniz seems to maintain this line in his later correspondence with Des Bosses.

This correspondence is rather notorious because in it Leibniz seems to make claims that

contradict some central elements of this philosophy that he has established in almost all

of his other writings. However, this correspondence is also very important in this context

because it represents one of his most extensive discussions on the reality of body. In the

course of the correspondence Leibniz introduces the notion of a substantiale vinculum, or

“substantial bond.” This bond between monads, which would have to be introduced by

God, would unify the constituent monads in a body in such as way that they would

become a real substance (L 600). Leibniz’s context for introducing this concept in his

correspondence with the Jesuit teacher Des Bosses was primarily for religious reasons,

namely to account for the reality of the Eucharist (ibid.). If Leibniz really held such a

substantial bond then it would provide for a reality of body beyond mere perceptions.

The problem with Leibniz introducing the substantial bond is that it would

contradict his basic metaphysical position that only simple entities can be considered

substances. Commentators have struggled with how to deal with this seeming

inconsistency, and many have chosen to simply discount this position as Leibniz

Ibid., 193.

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exploring a pMlosopMcal possibility with a trusted correspondent/® The generally very

candid tone of the coixespondence seems to support this reading. Leibniz had an

extensive correspondence with Des Bosses and Ms letters have the tone of man exploring

philosophical possibilities.

A close examination of the correspondence also shows Leibniz asserting that

while the substantial bond is a hypothetical possibility it is not a definite reality; it is

more that Leibniz is saying what must be true 2/bodies are to be substances. “[I]f a body

is a substance, it is the actualization of phenomena proceeding beyond their mere

congruence” (L 600). At several places Leibniz also asserts that while the substantial

bond may be a possibility all he can be sure of is that there are individual monads. “I

consider the explanation of all phenomena solely through the perceptions of monads

functioning in harmony with each other, with corporeal substances rejected, to be useful

for a fundamental investigation of things” (L 604). Essentially Leibniz seems to be

saying that constructing a substantial bond is a possibility for God and that it would

account for the reality of corporeal bodies, but in fact all that we can know to be true are

that monads exist and that bodies are phenomena. “I should prefer to say that there are

no substances over and above monads, but only appearances, but these are not illusory,

like a dream, but that they are true phenomena” (L 614).

Although the existence of material bodies lacks metaphysical necessity and

Leibniz may reject their existence when under pressure or when trying to speak with

“metaphysical strictness,” Leibniz does say that it is of the highest probability that there

are material bodies. As I pointed out in my earlier discussion of body, I believe that

Leibniz really held that there were bodies and he often talks as though they really exist.

As I also mentioned above, at least part of Leibniz motivation for positing material

bodies was for non-philosophical, i.e., religious, reasons. Leibniz provides for the “moral

certainty” of material bodies via the regularity and vividness of experience. In doing so

he draws a distinction between mere phenomena and what he calls real or “well-founded”

phenomena. The method for distinguishing between mere phenomena, i.e., things that

exist only in the mind, and well-founded phenomena has to do with certain qualities of

R.M Adams’ book Leibniz: Determinist, Theisl, Idealist has a nice and very clear representation o f this position (303-307).

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our perceptions as well as relations between them. “Real phenomena” are those that axe

“vivid, complex, and internally coherent” (L 363). Perceptions that do not match these

criteria can be dismissed as dreams or illusions, i.e., mere phenomena. Mere phenomena

are things like mirages and daydreams and have no reality outside of the mind. They axe

simply products of our minds or imagination and do not have an independent existence.

Perceptions that axe sufficiently vivid and complex are deemed real or well-founded.

“Well-founded” phenomena are things that while held together by the mind have a basis

in something else. Leibniz claims that matter is an example of such a phenomenon.

“[MJatter itself is nothing but a phenomenon—though well-founded—which results from

the monads” (L 659).

A “well-founded phenomenon” is a semi-mental entity that is a product of the

mind and something external to the mind working together. It is important to see here

that Leibniz is using “phenomena” in a different sense than he did in his strict

metaphysical view. As Donald Rutherford points out, phenomena in the sense that

Leibniz is using it here is intended as an ontological category and not as a psychological

one.^ Although there is a mental component to phenomena, i.e., to accoimt for their

unity, their existence is not solely in the mind. They are real phenomena because of the

monads that make them up, and not merely because of the monad that is perceiving them.

Rutherford goes as far as to call this understanding of phenomena a “central feature of

Leibniz’s position.

An example of a real phenomenon that Leibniz often provides is a herd. A herd

of cows only comes about when we identify a collection of individual cows as being a

herd, yet without the cows, i.e., the real things, the herd would also not exist. According

to Leibniz, any aggregate has this status.^ Only those aggregates that are made up of real

Rutherford, “Leibniz and the Problem of Monadic Aggregation,” 70. Glenn Hartz draws a similar distinction in his paper “Leibniz’s Phenomenalisms.” Hartz’s position is that Leibniz talks about phenomena in two distinct senses, phenomena as mental phenomena and as derivative phenomena. In this context, the notion of derivative phenomena is apropos. Hartz states that x is a derivative phenomenon, if “x is an aggregate of corporeal substances or monads whose reality is completely derived from that of its constituents” (516). This is opposed to what Hartz calls mental phenomena, in which case “x is the appearance of an aggregate of corporeal substances or monads whose unity is only apparent, since it is manufactured by the mind” (513).

Rutherford, “Leibniz and the Problem of Monadic Aggregation,” 70.^ This view follows principally from Leibniz’s view o f relations. Because relations cannot exist in two things at the same time, although the basis o f the relation may be in both things, it is the mind that

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things, i.e., monads, can be deemed “weli-founded.” “[A] body is not a true unity; it is

only an aggregate, which the Scholastics call a being per accidens, a collection like a

herd. Its unity comes from our perception. It is a being of reason or, rather of

imagination, a phenomenon” (L 623). Leibniz’s use of phenomenon here clearly differs

from the phenomenalism of his strict metaphysical view. Well-founded phenomena are

more real than those things that are simply products of the mind. Thus, Leibniz says

things like the following to De Voider. “For there can be nothing real in nature except

for simple substances and the aggregates resulting from them” (L 539).

The well founding of a herd of cows is relatively easy to understand. We simply

need a group of cows that are collected together, usually on the basis of their spatial

proximity, and someone to identify them as a herd. For a collection of monads, however,

it is not as clear how they can “well found” a material body. How can completely

independent, immaterial things well found matter, which has a completely different

nature than the monads? If the monads are the parts or constituents of material bodies in

the way that cows are the parts of a herd it would seem that Leibniz would be liable to the

same kind of criticisms that Kant leveled against Eberhard; immaterial things would be

the parts of something material.

Leibniz does not, however, claim that monads are the parts of material bodies.

Rather, he claims that they are the requisites of material bodies. A body is not literally an

aggregate of monads, rather it results from an aggregate of monads (L 578). Leibniz

states this explicitly in a letter to Des Bosses. “[TJhey [monads] are not really ingredients

but merely requisites of matter” (L 604). Clearly he does not have in mind that monads

somehow coalesce to form a body, rather they are ontologically responsible for the

existence of material bodies.

maintains the relation and is responsible for the existence o f the aggregate as a single thing. In this sense any thing that derives its reality from parts being put together in the mind is deemed a phenomenon. “Relations and orderings are to some extent ‘beings o f reason’, although they have their foundation in things” {NE 227). As we have already seen, for Leibniz only truly simple things can qualify as substances. Because properties o f simple things must adhere within those simple things— as Leibniz says, accidents never move between substances— and a relation spans the gap between the two things, relations must be less real than the things that are related. “My judgment about relations is that paternity in David is one thing, sonship in Solomon another, but that the relation common to both is a merely mental thing whose basis is the modification o f the individuals” (L 609). Whether we see bodies as composed o f monads or of matter, bodies are an aggregates whose existence is dependent on the parts o f the aggregate being related to each other to form a whole. Because these relations are not real, the reality o f the body as a whole must be phenomenal as well.

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Also, while aggregates are formed in the physical world on the basis of their

spatial proximity, e.g., a herd is formed by putting a number of cows in proximity to each

other or a rubber band ball is formed by putting a number of rubber bands together,

Leibniz claims that this is not the case with monads, because monads are themselves

soul-like and non-spatial.^^ Leibniz also makes it quite clear that we cannot think about

these non-spatial monads as being proximally related to each other to form bodies. “For

we cannot say that monads are parts of bodies which touch each other, any more than we

can say this of points or souls” (L 600). Thus, it is clear at least that we are dealing with

a much different type of aggregation that the one that we are accustomed to in the

physical world.

In order to explain the relationship between monads and the material bodies

Leibniz often resorts to analogies. For example, he talks about the relation of monad to

body being like raindrops to a rainbow or the spokes of a rapidly spinning wheel to the

blurred disk that results from the movement (NE 403). The following lengthy quote from

the New Essays is representative of Leibniz’s thinking on this topic, and also brings

together the notion of “phenomenal entity” with “being by aggregation.”

The unity of the idea of an aggregate is a very genuine one; but fundamentally we have to admit that this unity that collections have is merely a respect or relation, whose foundation lies in what is the case with each o f the individual substances taken alone. So the only perfect unity that the ‘entities by aggregation’ have is a mental one, and consequently their very being is also in a way mental, or phenomenal, like that of a rainbow. (NE 146)

1 think that the advantage of these analogies is that they are helpful in illuminating

how things of a much different nature (raindrops) can be responsible for something else

(the rainbow) itself. These examples also show how we can know the cause of

something, the rainbow by the raindrops, yet never be able to see, i.e., imagine in

Leibniz’s technical sense, the parts in the perception itself. We could never see raindrops

in a rainbow because they are simply two different things. The same holds for the disk

The relation of monads to spatial relations is a complicated one, as I will discuss in chapter three. For right now I will simply claim that monads are non-spatial and, thus, will be in agreement with someone like Donald Rutherford who, in his “Leibniz and the Problem of Monadic Aggregation,” claims that, “[i]n Leibniz’s view, the spatial summation of monads is literally inconceivable; monads are not spatial parts of bodies, nor are they located in space” (66).

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that results from the rotating spoked wheel. Each of the spokes is necessary for the

perception of a solid disk, yet the disk itself is not the teeth, it merely results from them. '

The shortcoming of these analogies is that they describe a causal relation between

two material things that is readily explainable. The relation between monads and the

material things that result from them is much less clear and camot be causal in the same

way. It is hard to see how something that is non-material can be causally responsible for

somethiing that is material. Donald Rutherford in his paper “Leibniz and the Problem of

Monadic Aggregation” takes a line that Kant would probably appreciate and says that the

well founding relation between monads and material bodies is a “logical relation.”^ By

this Rutherford means that it is not a physical or causal relation, but one that holds

between the concepts of the things. According to Rutherford, Leibniz has two criteria

that are essential for results. “[A] result is any entity which can immediately be

understood to exist on the condition (a) that certain things have been posited to exist; and

(b) that there are conceivable relations among those things which would determine the

existence of the entity in question.R utherford stresses the hypothetical nature of this

first criterion; the idea is that if one entity is posited to exist then the other must exist.

This interpretation seems to match up with the statements that Leibniz made above in his

proofs of monads. If aggregates, i.e., material things are to be real, then they must have a

real basis. That is, they must result from monads. It is clear that Leibniz wants to avoid

the Eberhardian problem of having immaterial parts making up a material objects.

Rutherford’s second criterion asks what must be true of the constituent monads

for the material aggregate that results from them to be real. This is essentially a question

concerning a principle for monadic aggregation and is a question that has been pursued to

great length in the literature. As I pointed out above, Leibniz cannot rely on any of the

principles that are responsible for aggregation in the physical world, i.e., spatial

■“* This understanding also supports my reading o f the senses for Leibniz. Within the context of the analogy, we would not want to say that one is sensing the raindrops, but rather the rainbow that is caused by the raindrops. On my view, the same holds, more or less, for monads.

Rutherford, “Leibniz and the Problem of Monadic Aggregation,” 73. Hide Ishiguro expresses a similar view in the paper “Unity Without Simplicity: Leibniz on Organisms,” 548. Here Ishiguro states that although Leibniz describes the situation of A well founding B to be that B “results” from A and that this seems to suggest a causal relation, it is, in fact, a “logical relations” that Leibniz is describing through the relation of well-founding (ibid.).^ Rutherford, “Leibniz and the Problem o f Monadic Aggregation,” 73.

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proximity or physical connection, when explaining why monads aggregate to form a

materia! body. What is needed is an explanation of the condition of each monad that

constitutes an aggregate. Presumably this condition will also explain why an aggregate

appears the way that it does, i.e., as a particular material body.

Glenn Hartz argues in Ms article “Leibniz’s Phenomenalisms” that there is no

“metaphysical principle [that] binds the parts of an aggregate to g e th er.H artz ’s

position is that there is nothing outside of the perceiving monad that accounts for the

aggregate, i.e., the perceiving monad alone accounts for the unity of the aggregate.^^

“The substances exist and can be grouped in various ways by minds into collections, but

the substances themselves are not grouped.”^ Hartz is committed to the fact that no

principle internal to the constituent monads can account for their aggregation, especially

spatial relations, which would be to bring “spatial matters to bear on Leibniz’s purely

qualitative realm of subs tances .The role of the aggregate is to provide the reality, not

the unity to bodies. WMle I agree that spatial position cannot the grounds for the

aggregation, a problem with this view is that if there is nothing within the aggregated

monads that accounts for their unity, it seems possible that a world could exist with all

the same substances, i.e., the same monads, with no aggregates at all. Hartz responds to

this objection with the reply that “thw world is the one described: it contains exactly the

substances it has, and no extra-mental aggregates.”^

While I agree with Hartz that the primary role of the constituent monads is to

provide for the ontological reality of the material bodies, Hartz’s response to the

objection above strikes me as very un-Leibnizian. Leibniz never states that certain

conditions obtain in this world simply because it is this world; everything happens for a

reason, even if that reason is unknown to us. It seems to be more than simply a

contingent fact that all of the monads perceive the aggregates that they do. It is also

Hartz, “Leibniz’s Phenomenalisms,” 538.Hartz’s position can be contrasted with someone like R.M. Adams’ position in his paper

“Phenomenalism and Corporeal Substance in Leibniz,” wherein Adams’ maintains that spatial position does in fact account for the unity of aggregates. The spatial position, however, is not that of monads, which Adams asserts are not spatial, but of the bodies of monads; the bodies appear to be spatially related in such a way that they form an aggregate. “[T]he aggregation o f monads as belonging to a single corporeal mass depends entirely on their bodies appearing to occupy contiguous or overlapping spaces” (241).

Hartz, “Leibniz’s Phenomenalisms,” 542.“ ibid.

Ibid.

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difficuit to see how the monads could provide the reality to aggregates if there wasn’t

something true of the constituent monads. On this point I want to follow Rescher and his

claim that it is the perceptions of the constituent monads that accounts for aggregates.^^

This is precisely the difference between mere aggregates, i.e., bodies that are united or

fabricated solely within the mind, and well-founded aggregates that result from an

infinity of other monads. I think that the perceptions of the monads that constitute the

body must agree with the monad that is perceiving the collection in order to have a “well-

founded” body. Ultimately I think that the principle that governs all these perceptions

must be the pre-established harmony. As I stated earlier the pre-established harmony is

something that was initially set up to explain the relation of body and mind, thus it is

logically extended to cover those monads that constitute the body and the relation among

those monads as Leibniz theory develops.

Overall, dealing with the relation between monads and material bodies is

incredibly sticky in Leibniz. Kant’s criticisms of Leibniz on this point certainly provide a

unique interpretation that correctly identifies monads as intellectual entities. Kant also

forces the Leibnizian to provide an account of material bodies within the framework of a

metaphysics that employs monads as its fundamental constituents. As I indicated earlier,

I think that Kant saw no way that Leibniz could reconcile monads and material bodies,

thus he interpreted Leibniz as reducing material bodies completely to monads.

Despite the difficulties in explaining the relation of bodies and monads, it is clear

that Leibniz wanted to maintain the existence of bodies and that he wanted to

ontologically ground bodies on monads. Leibniz also wanted to use monads to account

for some real features of material bodies. This is especially evident in his discussions of

monadic force that I outlined above. Leibniz resorts to monadic explanations not only for

the activity of material bodies, but also the inertia that material bodies are able to provide,

neither of which can result from completely passive matter. “The forces which arise

from mass and velocity are derivative and belong to aggregates or phenomena” (L 530).

Leibniz is clearly trying to provide for real features of the material world and wants to do

so not simply by ontologically demoting material things to confused representation of

monads.

Rescher, Leibniz: An Introduction to his Philosophy, 78.

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In the end I maintain that all Leibniz can be sure of is perceiving monads. His

principles of well founding and monadic aggregation provide a plausible model for how

material things could exist on his view of monads. However, Leibniz himself admitted

that he was not able to provide all the details of the relationship between a given monad

and its body. He admits as much in a 1709 letter to Des Bosses.

I do not deny some real metaphysical union between the soul and the organic body, according to which it can be said that the soul is truly in the body; ...But because such a thing cannot be explained by the phenomena and changes nothing in them, I cannot explain any more distinctly o f what this union formally consists. (L 598)

I thinlc that Leibniz uses analogies to explain the relationship between monads and

body because he was not able to fully explain how this relationship functioned. I think

that what Leibniz is trying to provide is a possible model for how monads could be

responsible for material bodies. When pressured, however, Leibniz was forced to admit

that he couldn’t be sure that there really were bodies or anything external to the mind.

However, even if it turned out that there only were monads and their perceptions and

there were no real phenomena Leibniz did not really find that terribly problematic. The

regularity of experience remains usefiil to us and “provides us with something equally as

valuable in all the practice of life as would be real phenomena” (L 364).

VI.3 The Normative Status of M aterial Bodies

The final aspect of Kant’s criticism, i.e., that Leibniz’s view discounts the

material for the monadic, has essentially been addressed by what I have discussed in the

past two sections. On Leibniz’s metaphysical view, monads are the fundamental

constituents of the universe. These are the substances whose existence Leibniz can be

sure of, so he claims, and with which he was most interested. Nonetheless, Leibniz does

very much want to provide ontologically for material bodies. Not only are material

bodies what we sense, but also they are connected with monads in the sense that every

limited monad possesses a body which is a well-founded phenomenon resulting from the

underlying monads. If this is truly Leibniz’s view, then there is no need or possibility to

do away with material bodies. Science may certainly change our understanding of the

material world and cause us to modify our conceptions of what material things are or how

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they are put together, but we will never be in a situation to move beyond bodies and to

the monads themselves. We lack the capacity to make this leap as limited beings whose

ability to represent things outside of ourselves is restricted to the use of the body and its

accompanying senses. Thus, just as the senses are a forai of representation that Leibniz

does not think that we can move totally beyond — according to Leibniz every

representation that we have contains some traces of the sensible — at the same time the

bodies that are the objects of the senses are an essential part of our ontology as well.

VII. Conclusion

I have covered a lot of ground in this chapter, so it may be helpful to outline what

I have said before drawing any conclusions. I began this chapter by considering Kant’s

interpretation of how Leibniz arrived at his ontology and the reasons why Kant may have

chosen this interpretation. As I explained in the previous chapter, Kant casts Leibniz as

someone who used the intellect to discover things about the world and was willing to

sacrifice the sensible along the way. Kanf s view of the intuition replies to this view by

making the sensible an essential element of human cognition.

Next, I considered how Leibniz arrived at his view of substance. This process

involved eliminating other possible candidates, such as extension and atoms, and positing

simple, mind-like entities as the substances of his metaphysics. After talking at some

length about the nature of the monads, I returned to Kant’s criticisms and responded to

them in turn. First, I explained that monads are intellectual entities for Leibniz and

explained what this entails. Secondly, I addressed Kant’s criticisms having to do with the

epistemological and ontological connection between material bodies and the monads. I

argued that Leibniz does not think that we sense other monads directly, rather the body is

a means by which we sense other bodies and sensation is a process that takes place

entirely at the material level. I also argued that for Leibniz material bodies are not made

up of monads, but result from the monads in the way that a rainbow results from a

collection of water droplets. Lastly, I pointed out that what I had discussed in the first

two responses makes it clear that Leibniz does not want to eliminate material bodies and

instead holds that they are an integral part of our connection to the world.

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If it hasn’t become evident from what I have said so far, let me make it explicit

now that one of the underlying themes of this chapter has been that Kant’s criticisms

challenge Leibniz at a crucial point in his ontology. The connection between the monads

whose existence Leibniz is sure of and the material bodies that he also wanted to preserve

is a difficult one for Leibniz to explain and a difficult one for us to understand. Kanf s

solution, which in a way foreshadows Wilson’s conclusion that I mentioned earlier, is

essentially to eliminate the material for Leibniz. With that general point made, there are

a few other concluding points that I would like to make.

First, for Leibniz, bodies are a way for us to know what is outside of us. This is

somewhat confusing because strictly speaking all monads’ representations are generated

internally, thus it is really impossible for us to contact what is other than us. The problem

for limited beings, such as ourselves, is that we do not have clear access to the multitude

of perceptions that are contained within us. To make up for this limitation, God has

given us bodies and the senses which allow us to represent things that are other than us in

a symbolic way. Through the senses we can have perceptions of other material bodies

that express the monads that underlie them without knowing the monads themselves. Our

bodies and our senses are a way for us as limited beings to know things other than

ourselves. This means that bodies, both our own and the bodies of ail other monads, are

crucial as they are the way that beings with limited minds are able to know and

experience things about the world.

If bodies and monads are both important parts of Leibniz’s epistemology and

ontology, the questions remains how monads can provide ontologically for bodies. As I

discussed, Leibniz does provide us with the notion of well founding and gives us very

pregnant analogies, but ail of the examples and analogies have major flaws as well. We

know that monads aren’t parts of material bodies and we know that they are intellectual

entities, but how can they well-found bodies? How can bodies “result” from them?

Rainbows may result from raindrops while being less real than the parts that are

responsible for them in the same way that bodies rely on and are less real than monads,

but in the rainbow example we can also readily explain the causality of the situation and

the role that light plays through refraction in creating the rainbow. But what is the analog

in the monad/body situation? What is the sunlight that causes monads to result in bodies

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for us? Ultimately I think that this relationship is somewhat mysterious for Leibniz.

Leibniz is coming from the monads in one direction and the bodies from the other and

explaining how the two things meet is very difficuit. I think that something like

Rutherford’s explanation is really the best we can do. Leibniz thought that both bodies

and the underlying monads are important ontological constituents of our world, with the

later being more fundamental than the former. We know that bodies result from monads,

but how this process actually occurs is, perhaps, impossible to explain.

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CHAPTER THREE

SPACE AND TIME IN LEIBNIZ’S METAPHYSICS

In this chapter I will be looking at Leibniz’s view of space and time and then

considering Kant’s criticism of the view. Throughout this discussion my emphasis will

be primarily on Leibniz’s view of space, although I will be talking about Ms view of time,

which is very similar, as well. Initially I will lay out three possible readings of Leibniz’s

view: the Kantian interpretation that space and time are a confusion, the view that space

and time are well-founded entities as several important commentators have understood

them, and a third reading of space and time as ideal. I will side with the ideal reading and

point out the advantages that it has over the others while modifying it slightly. Then, I

will go on to look at Kant’s criticisms of Leibniz’s views, of which I will identify four.

Examining these criticisms will help to clarify the reading of Leibnizian space and time

that I will be advocating, while also bringing out some important elements in Leibniz’s

larger metaphysics such as his understanding of the role of geometry and the importance

of substances.

L Points of Agreement and Disagreement

One of the most interesting things that emerges from the juxtaposition of Leibniz

and Kant’s views on space and time is how much in common they share. Kant and

Leibniz actually agree on many of the important features of space and time. For

example, both thinkers identify continuity as one of he essential features of space and

time. Their understanding of continuity is also very similar. For both, continuity implies

freedom from composition. Moments and points are the limits of time and space, and not

the parts out of which they are composed. In continuous quantities the whole is prior to

the parts. Finally, the lack of composition also implies that continuous quantities are

infinitely divisible.^

As an example, consider the following statement by Kant from the Critique of

Pure Reason: “Space and time are quanta continua, because no part of them can be given

* Kant demonstrates the infinite divisibility o f space via the division o f a line in his early (1756) treatise Physical Monadology, Proposition III, 54-55.

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save as enclosed between limits (points or instants), and therefore only in such fashion

that this part is itself again a space or a time. Space therefore consists solely of spaces,

times solely of times” (CPR A169/B211). We find Leibniz saying strikingly similar

things in Ms work “The Metaphysical Foundations of Mathematics.” “For in a straight

line as in time, a part is similar to the whole and can therefore itself be cut in the same

ration as the whole” (L 669). In a 1705 letter to Princess Sophie Leibniz states that;

“space or perfect continuity, which is ideal, represents only an indeterminate possibility

of division as one wishes” (G 562). Although Leibniz cashes out continuity in terms of

possible division and contrasts this with the actual division of real things, both thinkers

have a view of space and time as continuous, infmitely divisible quantities.

Despite their agreement on many of the features of space and time, Kant and

Leibniz fundamentally disagree as to what space and time are. Leibniz claims that space

and time are the relations of substances and their states. For Kant they are a priori forms

of intuition. As I discussed in chapter one, Kant maintained that Leibniz’s

misunderstanding of space and time was responsible for other major errors in his

philosophy. At the heart of Kant’s interpretation is the claim that Leibniz tried to

“intellectualize” space and time. According to Kant, Leibniz’s general approach was to

try to solve metaphysical problems through intellectual means. By this Kant means that

Leibniz considered what reason (essentially logic) holds must be true and posited this as

the true nature of the world. His purely intellectual inquiry focused on substance and

eventually led him to posit that the universe was dense with monads, each of wMch is

independent of the other but which are synchronized through the pre-established

harmony. On Leibniz’s view monads and their states are the foundation of the universe.

According to Kant, Leibniz’s entire methodology is a product of a profound

misunderstanding of human cognition. On Kant’s view the intellect and the sensibility

are not only two different human faculties, but they also must be used in conjunction to

provide knowledge. Furthermore, the sensible intuition has space and time as its forms,

which precede the objects of experience. Viewing space and time as a confusion is only

a “logical distinction” that does not address the real differences between the sensible and

the intellectual worlds.

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As I explained in the first chapter, the amphiboly in the “The Amphiboly of

Concepts of Reflection” section that Kant is describing is Leibniz’s failure to realize that

the sensible representation is subject to the forms of intuition, i.e., space and time, while

intellectual representation is not. Leibniz’s failure to understand these two separate

sources of representation and their necessary connection in human cognition also led Mm

to draw incorrect conclusions about the nature of the objects. For Kant, because space

and time are a priori forms of intuition all of our sensible representations are necessarily

situated in space and time and the objects that we sensibly perceive are appearances, i.e.,

objects that are fundamentally spatial and temporal. Things in themselves or noumena

are not subject to these forms and are subsequently different things (if we can call them

things at all). It is important to see that Kant is making more than an epistemological

claim in this context; he is referring to a radically different ontology between himself and

Leibniz. The forms of intuition not only ensure that all objects are appearances, but also

that we cannot have a positive conception of noumena, i.e., things in themselves, which

are non-spatial and a-temporal. Because noumena are “nothing” for us—we can only

have a negative conception of them—Leibniz’s metaphysics based around the

monadology is completely jeopardized. According to Kant, Leibniz simply dismissed the

fundamental distinction between appearances and things in themselves as a confusion.

As I argued in chapter two, I think that Kant is wrong in this charge and that

Leibniz did not use confusion to mask ontological distinctions and that ultimately he is

not subject to the amphiboly that Kant is describing. Nonetheless, Kant’s disagreement

over the nature of space and time remains and this disagreement has important

consequences for other aspects of Leibniz’s metaphysics.

II. Background Considerations

Before looking at the details of Leibniz’s position, I would like briefly to identify

two important background considerations that inform Leibniz’s views on space and time.

The first relevant consideration is that Leibniz held what I have been calling a

metaphysics of substance. Leibniz held a particular notion of substance that focused on

perfect unity as a necessary criterion. As I explained in the previous chapter, Leibniz

eventually came to hold the view that fundamentally simple, non-material substances and

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their properties form the ontological basis for the entire universe. The other central

Leibnizian principles such as the idea that the universe is dense with monads, each of

which are windowless, i.e., completely isolated from every other one, and that they move

in step with each other and express each other’s states via the pre-established harmony

are all predicated on this basic view of substance.

Leibniz’s development of his view of space and time is also subsequent to his

view of substance and the former is profoundly influenced by the latter. Given the

priority of substances, it follows that anything that is not a monad or a property of a

monad must somehow result from monads. All of the objects of the material world are

thus ontologically reducible to monads. The properties of the material world, including

space and time, must also be dependent on a monadic foundation. The nature of the

dependency is that of relation. Leibniz held space and time to be relations of things, and

because relations are neither substances nor accidents—if they are anything at ail they are

accidents that are simultaneously in two things at the same time—Leibniz held that

relations could not be real things. The following statement by Leibniz from his fifth

letter to the Newtonian Clarke helps to explain his metaphysical commitments with

regard to relations.

The ratio or proportion between two lines L and M, may be conceived three several ways; as a ratio of the greater L, to the lesser M; as the ratio o f the lesser M, to the greater L; and lastly, as something abstracted from both, that is, as the ratio between L and M, without considering which is the antecedent, or which the consequent . . . i t cannot be said that both o f them, L and M together, are the subject of such an accident; for if so, we should have an accident in two subjects, with one leg in one, and the other in the other, which is contrary to the notion of accidents. Therefore we must say, that this relation, in this third way o f considering it, is indeed out of the subjects; but being neither a substance nor an accident, it must be a mere ideal thing, the consideration of which is nevertheless useful. {LC 71)

Leibniz’s description of three ways of understanding the relations of two lines is intended

to be analogous to the relation of the things that are related in space and time. Just as we

can consider the relation of two lines in itself, we can also think about space and time in

themselves. However, like the ratio of the two lines, space and time as a system of

relations must be mind dependent or “ideal” things (ibid.). I will explain what Leibniz

means by an “ideal” entity in the sections below.

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The second major influence on Leibniz’s development of his views on space and

time was a philosophical problem he called the “labyrinth of the continuum.” According

to Leibniz there were two major problems that human thinking must overcome. One is

the problem of evil and the other is a satisfactory explanation of continuity. In the

introduction of the Theodicy, Leibniz lays out these two problems as the major

“labyrinths” in which human thinking becomes entangled.

There axe two famous labyrinths where our reason very often goes astray: one concerns the great questions o f the Free and the Necessary, above all in the production and origin o f Evil; the other consists in the discussion o f continuity and o f the indivisibles which appear to be the elements thereof, and where the consideration o f the infinite m ust enter in. The first perplexes almost all the human race, the other exercises philosophers only. (Theo 53)

In short, the labyrinth of the continuum is the following. In order for there to be real

substance in the universe it is necessary that there be simple entities, i.e., monads.

Leibniz’s oft repeated claim is that in order for any aggregate to be real it is necessary

that it be composed of completely indivisible entities, otherwise we would be left with

things that were divisible to infinity, in other words all things would be merely illusions

{Monadology §3 L 643). This is another route to Leibniz’s monads, because true

indivisibility can come only from a perfectly simple, immaterial entity, i.e., a monad. On

the other hand, mathematics deals with continuous objects, i.e., lines and spaces. It also

appears that material entities, insofar as they are extended objects, are continuous. The

dilemma or labyrinth out of which human thought must emerge is how to account for the

possibility of continuity while at the same time acknowledging that real substances must

be discreet.

What I have been calling the metaphysics of substance and the problem of the

labyrinth of the continuum form the background for Leibniz’s view of space and time and

any account of them must take them into consideration.

III. The Standard Reading of Leibnizian Space and Time

Leibniz’s view of space and time is most completely articulated in his 1715 and

1716 correspondence with Samuel Clarke. In the correspondence Leibniz defends his

relational view of space and time against Clarke’s Newtonian view of space as an entity

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in its own right. The following statement from Leibniz’s third letter is representative of

the position that he is trying to defend. “I hold space to be something merely relative, as

time is; ... I hold it to be an order of coexistences, as time is the order of successions”

{LC 25-6). As Leibniz tells Clarke, space is the order or relation of all things that exist at

the same time, while time is the relation of successive states of things.

The most widely accepted reading of Leibniz’s view of space and time is

probably that they are “well-founded entities.” This is Nicholas Rescher’s interpretation

in Ms book Leibniz: An Introduction to his Philosophy, a view that Benson Mates

endorses in his own book on Leibniz as “far and away the best available account of this

entire subject.” According to Rescher, space and time are based on the relations of

substances and are “well founded phenomena, and as such their existence is secondary,

since it is derivative from the substances (and their properties) wMch they 'contain.'”^

The interpretation of space that Rescher is advocating is the following. Leibniz’s

metaphysical view is that the universe is composed of an infinite number of perceiving

monads each of which is situated in such a way that it perceives the state of every other

monad with varying degrees of clarity. The perspective of a given monad is called its

point of view. Of course, Leibniz’s view is also that each monad is completely isolated,

thus all of its states are internally generated; monads never directly perceive other

monads, they only express other monad’s states through their own states. On Rescher’s

reading space is a relation that is based on the points of view of the monads. It is a

phenomenon because it exists only in the monads’ perception of the relation. It is well-

founded because the relation is based upon the situation, i.e., point of view, of the

independent monads.

The situation is very similar for time, except rather than being a product of the

simultaneous states of monads, time is the result of the successive states of monads. Just

as Leibniz held that all the monads express each other’s states as a result of the pre-

established harmony, he held that successive states of the monads move in step with each

other due to the same principle. This succession of states Leibniz saw as the foundation

of time. Just as monads are non-spatial, Leibniz also held that they are a-temporal; they

Mates, The Philosophy o f Leibniz: Metaphysics and Language, 230. Rescher, Leibniz: An Introduction to his Philosophy, 84.

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contain all of their states at their creation. Leibniz often talks about the “unfolding” of

monadic states as the foundation of time, which is formulated to suggest that a given

monad contains all of its states internally and that it passes from one state to another in

the ordering.

Because Rescher sees the states of the individual monads as the foundation of

space and time, he posits two different kinds of space and time in Leibniz’s philosophy, a

metaphysical space and time and a phenomenal space and time.

Taking the ‘th ings’ at issue here [which are related] as monads, we arrive at metaphysical space; taking them as aggregates [of monads], as phenomena we arrive at the perceived space with which one deals in ordinary life and in the sciences. Both, o f course, are ultim ately phenom enal - space is never a substance, a thing in its own right.'*

As Rescher points out, in both cases space and time are not real things; they are the

product of relations, and although well-founded on those things, remain phenomenal.

TTT.1 Another View of Leibnizian Space and Time

As I indicated above, Rescher’s view is quite prominent in the literature and is

picked up in large part by Mates in his book on Leibniz as well. The general

metaphysical picture that emerges on this reading is a ‘two-level metaphysic,’ according

to which there are real things, i.e., monads and their states, and the things that are well-

founded on them, e.g., material bodies, many of their attributes, and space and time. A

very interesting challenge to this accepted view emerges in an article by Glenn Hartz and

J.A. Cover entitled “Space and Time in the Leibnizian Metaphysic.” In this paper, Hartz

and Cover attribute to Leibniz not a two level but a three level metaphysical view on

which space and time are not well-founded phenomenal entities, but ideal entities.^

What is different about this view? According to Hartz and Cover, ideal and

phenomenal things have different properties. Phenomenal entities are more closely

“ Ibid. 87. Rescher certainly noticed that Leibniz in the Clarke correspondence referred to space and time as ideal

entities, however, it seems that he did not acknowledge this as grounds for a metaphysical difference. In the following quote from Leibniz: An Introduction to his Philosophy we can see Rescher equating ideal and well founded. “Space and time are ideal, or rather are phenomena, space because it is nothing but the order or relation of (simultaneous) existents, and time since it is relational, and involves the labyrinth of the continuum. However, space and time are not chimera but well founded phenomena, phenomena bene fundata” (90).

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linked to the real things that underlie or well-founded them. They are semi-mental

entities that involve the real things and a mental component. On their reading, material

bodies would qualify as phenomenal. Ideal things, on the other hand, are completely

abstracted from any real foundation and exist only in the mind; they are fully mental

entities. Unlike phenomenal entities that are an aggregate of real parts, ideal entities are

composed of possible parts. This means that ideal things are continuous. Ideal entities

also have their whole prior to the parts while phenomenal things are discrete and have

their parts prior to the whole; in other words they are really composed of parts, while

ideal things are not. Space and time, as well as motion, would qualify as ideal for Hartz

and Cover.^

The principle defense of their interpretation comes via a “patient look at what

Leibniz in fact says,” especially in his later writings.^ For the most part I will not

rehearse those arguments here other than to say that textual evidence provides at least

prima facie support for their interpretation. For example in his fifth letter to Clarke

Leibniz claims that “[space] can only be an ideal thing; containing a certain order,

wherein the mind conceives the application of relations” {LC 70). Leibniz also seems to

make similar claims at other points in his writings, as for example in his 1702 reply to

Bayle in which he states that “I acknowledge that time, extension, motion, and the

continuum in general, as we understand them in mathematics, are only ideal things—that

is, they express possibilities, just as do numbers” (L 583). Even in more obscure places,

such as a 1705 letter to Princess Sophie that Hartz and Cover identify, he claims that

unlike matter which is composed of real substances, “it is not the same with mathematical

bodies or with space, which is something ideal, and which is not composed of points” (G

561).

In addition to being a better account of what Leibniz actually says, the advantage

of this view is that it places “less weight” on the well founding relation.® Rather than

basing space and time on the monads themselves, as the well-founded view does, this

view posits a third metaphysical level above the well-founded. According to Hartz and

Cover, space and time as ideal entities are arrived at by means of abstraction from

® Hartz and Cover, “Space and Time in the Leibnizian Metaphysic,” 503-7. ’’ Ibid., 495.® Hartz and Cover, 517.

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material bodies and not from the monads themselves. “We perceive such bodies and, due

to our ability to abstract various features from the concrete things which have them, we

conceptualize the empty continua of space and time.”® In this way the ideal entities of

space and time are a step further removed from the monads that provide the ultimate

reality of the universe. According to Hartz and Cover, space and time are a

“continuously arbitrary-divisible conceptual ‘event-space’ which, though usefully applied

to bodies, [are] clearly not on ontological par with them.” ®

IIL2 Three Competing Views

What has now emerged are three competing notions of Leibnizian space and time.

Kant’s reading that Leibnizian space and time are confused concepts, Rescher’s

understanding that they are well-founded phenomena, and the Hartz/Cover reading that

they are ideal entities. I think that the view that Hartz and Cover are advocating has a lot

going for it. First, it provides what we might call a much cleaner understanding of

Leibniz’s metaphysics. It avoids the dual view of space and time that Rescher’s reading

entails. Viewing space and time as the result of bodies and not monads means that we do

not have to discuss both metaphysical and phenomenal space. This reading also avoids

lumping material bodies and space and time together as “well-founded entities” that are

on ontological par. Given what Leibniz says about bodies and his general focus on

substance any reading that grants a greater reality to bodies than to space and time and

any related mathematical entities appears to be more Leibnizian in tenor.

A second advantage is that this view works nicely with Leibniz attempt to deal

with the labyrinth of the continuum. If space and time are mental entities that deal with

possibilities and not the real determinations that are present in material bodies, then it is

easier to see how mathematical objects, which are also ideal, can have properties that

cannot be instantiated in real things. Ideal entities deal with possibilities and are

subsequently continuous while material bodies are real things that are subject to

determinate divisions and are made up of discreet parts. “But we confuse ideal with real

Hbid., 512.Ibid., 499. This is basically the position o f I.E. McGuire in his article “'Labyrinthus Continui': Leibniz

on Substance, Activity, and Matter,” in which he advocates a similar, ideal reading o f space and time. In this article McGuire states that the notions o f space and time, with motion conceived as a mathematical function of these, form a conceptual grid that the mind imposes upon fundamental change” (308).


substances when we seek for actual parts in the order of possibilities, and indeterminate

parts in the aggregate of actual things, and so entangle ourselves in the labyrinth of the

continuum and in contradictions that cannot be explained” (L 539). Because

mathematical entities are continuous and subsequently composed out of possible entities,

it is difficult to see how they can be well-founded. A reading of them as idea! therefore

seems more coherent.

A further advantage of the idea! reading is that it emphasizes that space and time

are abstract entities rather than confused concepts, as Kant would have it.” For example

in the New Essays Leibniz asserts that space and time, like other mathematical bodies, are

abstract entities. “Things which are uniform, containing no variety, are always mere

abstractions; for instance, time, space, and the other entities of pure mathematics” {NE

110). Contra Kant, space and time in themselves are not the product of confusion, but are

an abstraction from the things that are related. Leibniz compares space and time to

numbers, which can also be applied to any number of possible things. “But space and

time taken together constitute the order of possibilities of the one entire universe, so that

these orders—space and time, that is—relate not only to what actually is but also to

anything that could be put in its place, just as numbers are indifferent to the things which

can be enumerated” (L 583).

III3 Problems with the Ideal Reading

While I think that the Hartz and Cover’s position on space and time as ideal

entities is helpful in giving an account of independent or mathematical space and time,

i.e., the empty void of space, this view runs into problems in dealing with the application

of space and time to material bodies. This problem stems from their view of a

“metaphysical apartheid between ideal things and well-founded phenomena.”’ Their

strict separation of the phenomenal and the ideal forces them to make the counter

intuitive assertion that “strictly speaking bodies are neither in space nor endure through

'* Hartz and Cover, “Space and Time in the Leibnizian Metaphysic,” 512.Hartz and Cover, 512. The inspiration for this line of criticism comes from R.M. Adams book Leibniz:

Determinist, Theist, Idealist, 254. Although Adams has a different context for his criticism, he too sees a continuum between the real and the ideal and not the strict separation of metaphysical levels that Hartz and Cover envision.

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time, and are ... only apparently spatio-temporally continuous.”^ Here Hartz and Cover

identify the confusion of our senses as the reason that we attribute continuity and

spatiality, to material bodies.

The question at issue is whether material bodies are truly spatial or not. The

tension is that material things as well-founded phenomena are an aggregate of discrete

things and are actually divided in a determinate although infinite way. Space is the order

of possibly coexisting things and thus is continuous. Because extended objects are

composed of actual coexisting things, that entails, according to Hartz and Cover that they

are not continuous and subsequently not spatial (or temporal). The only reason that we

take extended things to be spatial is due to the confusion of the senses. I would respond

to Hartz and Cover’s position with the reminder that we only take an extended thing to be

a thing insofar as our senses are confused. An extended thing is actually a collection of

things. Extended bodies are really no more spatial than they are extended. This does not

prevent us from considering them as extended, and should not prevent us from calling

them spatially situated.

I think that we should deny the apartheid that Hartz and Cover are advocating and

instead posit a spectrum between the ideal and the well-founded. At one end of the

spectrum we have the purely ideal, i.e., space and time in themselves or empty space. It

is not surprising that Leibniz continually states that space and time are ideal in his

correspondence with Clarke since he is trying to give an account of the ontology of space

and time. Leibniz says the following in his fifth letter to Clarke: “space is ... an order of

situations; or (an order) according to which, situations are disposed; and ... abstract space

is that order of situations, when they are conceived as being possible” {LC 89). Here

Leibniz is clearly distinguishing between space as it is when applied to things and when it

is considered in itself. When he follows up this statement by saying that “space is

therefore something [merely] ideal,” we should read this as space in itself is something

that is merely ideal (ibid.). However, Leibniz also allows that bodies may be situated in

Hartz and Cover, “Space and Time in the Leibnizian Metaphysic,” 508.Ibid. 502.What I am getting at is intended to be analogous to the distinction that Leibniz draws between the ratio of

the two lines as dependent on the lines and the relation considered by itself (cf. p83 above). The relation as it is considered independent of the two lines would be like space in itself while the ratios of the lines would be like space as it is applied to the objects. The latter depends on truths on truths about the bodies, just as the relation “greater than” is dependent on truths about the lines.

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space and time. “The parts of time or place, considered in themselves, are ideal things ...

but it is not so with two concrete ones, or with two real times, or two spaces filled up, that

is, truly actual” {LC 63). The spaces “filled up” that he mentions surely refer to bodies

that are actually located in space. Here Leibniz seems to be stating quite clearly that

objects should be understood as spatially and temporally located. What Leibniz is

denying is that space is the same as extension. In other words he is denying Clarke’s

position that space, and time, are real properties of objects.

On the other end of the spectrum we have bodies as the aggregates of monads. In

this respect they are well-founded phenomena. Leibniz misleadingly refers to this

property of bodies as their “extension” in his eorrespondence with Clark. For example,

he states that “finite space, is not the extension of bodies; as time is not their duration.

Things keep their extension; but they do not always keep the same space. Everything has

its own extension, its own duration” {LC 69). This is a rather special use of the term

extension, since Leibniz at other places indicates that continuity is one of the qualities of

extension (cf. L 519). What Leibniz is talking about here, I believe, is the property of a

body being an aggregate. Leibniz is saying that things remain, more or less, the same

aggregate, but can be located in different spatial locations. I agree with Hartz and Cover,

and with Kant, that on Leibniz’s view we attribute continuity to bodies because of a

confusion. Bodies are or result from an aggregate of monads and thus cannot be truly

continuous; our senses blend the discreet parts together to give the appearance of a

continuous body. Between continuity and the very existence of a body lie a number of

properties, such as color, texture, shape, and motion, and the spatial properties of a body.

Some of these properties will be more closely tied to the monads that underlie them and

some will depend on our perception for their existence, but I see no reason why Leibniz

has to draw a sharp division between them in the way that Cover and Hartz envision.

IV. Kant’s Arguments

I would now like to examine specific arguments that Kant levels against Leibniz’s

view of space and time. The first is the claim that objects actually presuppose space and

time rather than grounding them as a system of relations as Leibniz posits. The second is

Kant’s claim that Leibniz’s view of space and time as a confusion endangers the science

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of space—geometry—and those sciences that rely on geometry, for example physics.

The third argument is one that Paul Guyer identifies in his book Kant and the Claims of

Knowledge. This argument appears in the first Critique and involves the difficulty of

basing space and time on the relations of things that are themselves non-relational, i.e.,

monads. Finally, I will look at Kanf s most famous argument against Leibniz’s theory of

space and time, namely his “incongraent counterparts” argument.

IV. 1 Kant’s Presupposition Argument

What I will call Kant’s “presupposition argument” appears in both the Inaugural

Dissertation and in the “Aesthetic” section of the Critique and is applicable both to

Leibniz’s view of space and his view of time. In both places the argument proceeds from

the claim that objects outside of us and the succession of their states actually presuppose

space and time rather than grounding them. According to Kant, space and time are

actually prior to objects; we cannot derive these notions from the representations of

things.

In the case of time, Kant claims that it is “only through the idea of time that it is

possible for the things which come before the senses to be represented as simultaneous or

successive” (ID §14 391-2). The idea is that we cannot talk about things that happen one

after the other, or even things happening at the same time, unless we already have the

notion of time. “For those things come after one another which exist at different times,

just as those things are simultaneous which exist at the same time'" (ID §14 392). Kant is

claiming that the concepts of simultaneity and succession presuppose a prior conception

of time. Time is the necessary condition for successive representation.

This argument cuts against Leibniz’s view that time is grounded on the successive

states of objects, the earlier of which we call the cause and the later the effect. Kant’s

claim is that in order for us to make sense of the changing states of objects we must first

have a notion of succession, or a notion of time, thus we cannot derive time from

conditions that presuppose it. The same is the case with simultaneity. “Simultaneous

things are joined together at the same moment of time, just as successive things are joined

together at different moments” (ID §14 394 note). This aspect of the argument also

works against Leibniz’s view of space, which Leibniz defined as the relation of the

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simultaneous states of objects. Kant, however, has specific arguments against the

relational view of space, although they are quite similar to those he uses against Leibniz’s

view of time.

In the case of space, Kant claims that in order for us to represent a thing as

external to us or things outside of one another we first need to have a conception of

space. “For I may only conceive of something as placed outside of me by representing it

as in a place which is different from the place in which I am myself; and I may only

conceive of things outside one another by locating them in different places in space” {ID

§15 395). The claim is that we can only represent an object as other or a plurality of

objects if we already have a notion of “outside” or “externality,” and these notions are

essentially spatial. Any view that attempts to derive the notion of space from things that

are externally related to each other or that have a certain place in relation to each other

has in fact presupposed what it is trying to prove.

In the “Amphiboly,” Kant expresses this disagreement more abstractly as a

difference in the two thinkers’ understanding of matter and form. According to Kant, an

intellectualist philosopher like Leibniz begins with something and subsequently attaches

a form to it, i.e., gives it attributes and relations. The problem with this view is that it

fails to understand that in human intuition the forms of intuition of space and time come

before anything that is situated in space and time, and, in fact, makes these things

possible for us. Kant expresses this position rather clearly in the following quote from

the “Amphiboly.”

[I]n the concept of the pure understanding matter is prior to form; and for this reason Leibniz first assumed things (monads), and within them a power of representation, in order afterwards to found on this their outer relation and the community o f their states (i.e. o f the representations). ... But if they [space and time] are only sensible intuitions, in which we determine all objects merely as appearances, then the form of intuition (as a subjective property of sensibility) is prior to all matter (sensations); space and time come before all appearances and before all data o f experience, and are indeed what make the latter at all possible, {CPR A267/B323)

Of course, what exactly Kant means when he claims that space and time are

“forms” of intuition is a point of notorious debate; thankfully we can sidestep much of

this, since in this context it is necessary only to focus on the critical aspect of these

arguments, i.e., as disproving the relational view of space. Kant is depicting Leibniz’s

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adoption of the traditional metaphysical focus on substance and the shortcomings of this

view through this discussion of matter and form.

IV.2 Leibniz’s Reply to the Presupposition Argument

The first, very general statement that I would like to make is that Kant is certainly

correct that Leibniz began with substance and then attributed a form to it. Leibniz’s

metaphysics is clearly a metaphysics of substance and in part his view of space and time

is required simply by these very general metaphysical considerations. On this point I am

in agreement with Kant.

Insofar as the presupposition argument is an argument against Leibniz’s relational

view of space, there are really two levels at which this issue can be addressed, the

monadic and the phenomenal (the same is true for time as well). In the former case, I

think that Leibniz has quite a strong response, in the latter his position is weaker. I do not

think that Kant’s argument is effective at the monadic level because, unlike Rescher, et

ah, I maintain that Leibniz does not have a notion of monadic space. As I indicated in

my discussion above, Leibniz’s monadology entails that there are strictly speaking only

monads and their states. These monads are completely independent of each other (in

order to provide for their complete simplicity) yet are synchronized through the pre-

established harmony. While the pre-established harmony ensures that every monad

reflects or expresses the states of every other monad, the monads don’t directly perceive

each other, but merely have internal states that are in perfect harmony, i.e., are as though

the monads perceived each other. Thus, at the monadic level the relation of monads is

not direct but only virtual. Leibniz does sometimes say that each monad “represents the

universe according to its point of view,” which is a function of the clarity of the monad’s

perceptions (L 637, cf. Monadology §57 L 648). Rescher and others have the view that

there is a kind of monadic space according to which monads are related at the

fundamental metaphysical level. However, on the view that I am advocating, I take this

to be more a way of speaking than anything else. While it is certainly helpful for us to

imagine that monads are spatially related or to talk this way, these are merely ways of us

representing the relation of monads to our limited minds. The monads are ordered in a

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certain way, but this is not a spatial ordering. We are better served to think of the

universe of monads as a list of things and their states rather than a spatial arrangement.

Leibniz’s own writings support this reading. For example, in a 1703 letter to De

Voider Leibniz asserts that “although monads are not extended, they nevertheless have a

certain kind of situation [situs] in extension, that is, they have a certain ordered relation

of coexistence with others, namely, through the machine which they control” (L 531).

Although this statement could provide evidence for some kind of spatiality of monads,

the emphasis should be on the fact that monads have a kind of situation in extension.

Any situation that we can attribute to monads is derivate of their relation to the material

bodies that they underlie. Given Leibniz’s view that the senses were a symbolic form of

knowledge that God provided in order to approximate of the fundamental reality, it is not

surprising that our sensible perceptions should indicate the ordering of monads via our

perceptions of space, but they are not that ordering.

As further evidence of my reading, consider that Leibniz prefaces these

statements by asserting that while time “enters in all things, spiritual as well as corporeal,

.. .extension [space] enters only into corporal things” (ibid.). Here Leibniz is directly

asserting that space is only a relation of material bodies and not present at the level of the

monads. As he says in a letter to Des Bosses: “[TJhere is no spatial or absolute nearness

or distance between monads” (L 604).

The upshot is that space does not even enter at the fundamental level of Leibniz’s

metaphysics. Leibniz’s assertion of the non-spatiality of monads means that the

presupposition argument is neither an argument against Leibniz’s view of space nor his

fundamental ontology.

At the level of phenomenal bodies it seems that Kant’s argument against

relational space carries more weight. In his fifth letter to Clarke, Leibniz lays out his own

view on the process whereby people arrive at a “notion of space” {LC 69). According to

Leibniz, a person observes a number of coexisting things and notices that there is a

certain order among them. Leibniz calls this their situation or distance. When one thing

changes its order with relation to the others we call this motion and the thing that comes

to stand in roughly the same order as the thing that has moved we say occupies the same

place. The totality of places is called space (ibid.). This account is intended to show how

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space is dependent on the things that we say occupy it and also how space is not

something more than the relations of things (ibid.). It is important to note that on

Leibniz’s metaphysics two different things cannot occupy the exact same place because

this would entail that the same accident, in this case the relation, would be in two separate

things. This is contrary to his view of subjects and accidents {LC 70). This shows how

space is an ideal relation, i.e., something that we impose of subjects, but is not internal to

them.

Given this view on the development of our concept of space, it seems that Leibniz

has two potential responses to Kant’s accusation that objects presuppose space rather than

ground it. The first would be to deny that situation implies spatial location. Leibniz

could say that we derive our notion of location from the situation of phenomenal objects,

but the objects themselves do not presuppose space. The problem with this solution is

that it does not seem particularly effective. Even if Leibniz could somehow demonstrate

that objects have a situation that is prior to their spatial location, which itself seems

problematic, the objects themselves are presumably extended, which again presupposes

some kind of spatiality.

A second possibility would be to take a quasi Kantian position and claim that

indeed space is prior to our individual perceptions of objects, but it is simply a feature of

our sensory experience in the way that color or taste is. When Hartz and Cover talk about

space and time as a “continuous arbitrarily-divisible conceptual ‘event-space’” they seem

to suggest that space is a feature of our perception that is perhaps prior to perception of

individual objects.

Although this response looks vaguely Kantian, it is important to see that this

would not be an admission that space and time are a priori forms of intuition. On this

reading things would admittedly look spatial or otherwise appear spatial, but this would

not say anything ontologically about the objects situated in space and time. It would just

be another statement about the way things appear to us. We would see or experience

things as extended and spatially located, and based on these spatially located things we

would derive a geometrical notion of space, which encompasses not only real things, but

possible things also.

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Although this reading does seem to respond to Kant’s criticisms I would be

reluctant to attribute it to Leibniz. If spatiality is simply a product of the sense, then its

nature as a relation is lost. This is clearly a problem since a relational foundation is

central to Leibniz’s notion of space. Leibniz asserts that space is the relation of either

real things or possible things, but is a relation in either case. Consider the following

quote from the New Essays in which Leibniz seems to assert that although space and time

are helpful for us to distinguish objects, these objects do not presuppose space.

“ [A ]lthough tim e and place (i.e., the relations to w hat lies outside) do distinguish for us things which we could not easily tell apart by reference to them selves alone, things are nevertheless distinguishable in themselves. So time and place do not constitute the core o f identity and diversity, despite the fact that diversity in time and place brings with it differences in the states that are im pressed upon a thing, and thus go hand in hand with the diversity of things. To which it can be added that it is by means o f things that we must distinguish one time or place from another, rather than vice verse; for times and places are in them selves perfectly alike, and in any case they are not substances or complete realities.” {NE 230)

I think that in an important sense Leibniz simply assumed that there were things outside

of us and this was a carry over from his independent arguments that the universe is

composed of an infinite number of monads.

If Leibniz were to respond to Kant’s own view, I think that he would claim that

the notion of space as a “form of intuition” is basically incoherent and makes too much of

the senses in their determination of the nature of objects. Seeing space as a form of

intuition does not provide for a sufficient explanation of the concept of space.

Time poses a much stronger challenge to Leibniz. Leibniz’s view of time is

intended to be relational and therefore analogous to his view of space. However, unlike

space, Leibniz held that time was also applicable at the monadic level, as I indicated in

his letter to De Voider above. His view is the following. God created a universe that is

maximally full of monads. The means of achieving this was to make as many monads as

were compossible with each other, i.e., whose attributes do not conflict with each other.

However, the monads are not static entities, but dynamic loci of force that change their

states under their own power. Of course, the monads maintain their compossibility.

In fact, Leibniz seemed to believe that many of the principles that he proved at the monadic level are also applicable among material bodies. An important subtext in many of Kant’s arguments, which I will focus more on in chapter five, is the illegitimacy that he perceives in this transition.

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which means that they move in step with each other; this is the pre-established harmony

as it applies to changing states of monads. Leibniz called the movement from one state to

another the unfolding of the monad, and he envisioned each state of the monad leading to

the other in a relation of cause and effect. However, Leibniz also held that the monad has

ail of its states within it at its creation; the unfolding is an internal process. Also, just as

we can have a notion of abstract or geometrical space when we abstract from the real

relations and posit possible relations, Leibniz maintained that we can arrive at an abstract

notion of time in the same way. This gives us the illusion that time is continuous.

“Time is the order of existence of those things which are not simultaneous. Thus time is

the universal order of changes when we do not take into consideration the particular kinds

of changes” (L 666).

The changing states of the monads are intended to ground a notion of time.

“[T]ime is the order of existence which is not simultaneous” (L 656). Thus, although he

often defines space in terms of time and time as “successive” states, which itself seems to

be a temporal notion, this must only be a manner of speaking. “For space is nothing but

the order of existence of things possible at the same time, while time is the order of

existence of things possible successively” (L 536). At other places he refers to time as

the inconsistent states of monads. “[T]ime is the order of possibilities that are

inconsistent but nevertheless have a connection” (L 583, cf. L 531).’®

However, it is hard to see how time can be posterior to things and grounded on

their relation. Whether he is talking about the “unfolding” of monads or the cause of one

state by the prior, or especially the “succession” of states, all of these make appeal to the

notion of temporality. I think that Leibniz may be able to give an account of simultaneity

that does not make direct appeal to the notion of time by employing the notion of

compossible states of monads, but the problem is that every monad contains all its states

and thus all the states of all the monads are compossible. Either Leibniz must assert that

the states of monads are a-temporal, in which case there is no possibility for giving an

account of time at all, i.e., there is no notion of time passing or a “now.” Or, Leibniz

This point is complicated because Leibniz also maintained that nature never proceeds by leaps. Thus, he has to have a notion o f density that is applicable to the monads and simultaneity which applies to abstract entities.

Donald Rutherford makes Leibniz’s point nicely when he claims in his Leibniz and the Rational Order of Nature that change is “merely an aggregate or ‘result’ of two contradictory states o f a monad” (162).

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could allow that the states of monads somehow succeed each other, in which case it

seems that he must make an appeal to temporality.'® Even within a given monad it seems

that some reference to time must be made, given the fact that every monad will contain

many inconsistent predicates, just as an individual will have hair at one point in time and

be bald at a later time. '' To account for these disparate states it seems that Leibniz must

allow for some time index ascribed to the states of monads, in which case time has again

reappeared. And in any case this still does not give any account of the “now” of time.

Perhaps tliis is asking too much of Leibniz though. Maybe his view is not that

monadic states are somehow prior to time but that time is somehow ontologically

dependent on the monadic states or, even weaker, that time is determined by the monadic

states. Since Leibniz allowed for time at the monadic level, which he didn’t do for space,

he clearly holds that time is somehow more important or more fundamental to his

metaphysics than space. Perhaps Leibniz would even grant to Kant that we cannot

understand the passage of monadic states without a conception of time since our own

monads experience time internally. I am not sure whether this reading of Leibniz is

coherent or not, but I am simply trying to highlight that for Leibniz what is ultimately

important is that the monadic states are ontologically prior to time in itself, which is

continuous and therefore ideal.

IV.3 Kant’s Argument from Geometry

The second Kantian argument that I want to look at, which I will call the

“argument from geometry,” is Kant’s most frequent argument against Leibniz’s relational

view of space. According to Kant, one of the most serious problems with Leibniz’s view

of space is that it deprives geometry of its necessity. For Kant, geometry “contemplates

relations o f space” and in doing so is the science of space {ID §15 396). The importance

A third possibility is that monads are sempiternal entities, in which case they exist at all moments of time. McGuire suggests this possibility in his “'Labyrinthus Continui': Leibniz on Substance, Activity, and Matter,” p317. This possibility still makes appeal to the notion o f time, however.

Kant makes an interesting connection between time and the principle of contradiction in the Inaugural Dissertation by claiming that the principle o f contradiction itself “presupposes the concept o f time and bases itself on it as a condition” {ID §24 394). In other words, A and non-A are impossible at the same time, but are possible at different times. In the Critique o f Pure Reason Kant identifies the principle of contradiction as an analytic or logical principle that cannot be used as a “determining ground o f the truth of our cognition,” because its application to human cognition involves a reference to time {CPR AI52/B191). In either case the ubiquity o f temporality in human cognition is evident.

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of geometry extended beyond itself and to the other sciences as well because Kant held

geometry as the “paradigm and the means of all evidence in the other sciences” (ibid.).

As Kemp Smith states in his commentary on the Critique: “Geometry is for Kant the

fundamental and chief mathematical science.” *

Leibniz’s relational view of space results, according to Kant, in a complete

devaluing of geometry and also those sciences that are based on geometry, e.g., physics.

Kant has two variations of the geometry argument, one has to do with the empirical

nature of geometry on the relational view of space, the other has to do with the result of

seeing space as a confusion. I will deal with them in turn.

Kant’s argument that the relational view of space makes geometry an empirical

science is most completely articulated in the Inaugural Dissertation. Kant’s own

formulation of the argument is relatively clear, thus I will quote it in full.

For if all the properties o f space are merely borrowed by experience from outer relations, then there would only be a comparative universality to be found in the axioms of geometry, a universality that such as is obtained by induction, that is to say, such as extends no further than observation. Nor would the axioms of geometry possess any necessity apart from that which is in accordance with the established laws o f nature, nor any precision apart from what was arbitrarily constructed. {ID §15 397-8)

Kant argument is basically a modus tollens. If the relational view of space is correct,

Kant is claiming, then we derive our notion of space based on our experience of objects

standing in a certain relation to each other and any properties that we attribute to space

are only based on these experiences. New experiences of relations could change our

notions of what is true about space; we might find that space is endowed with “different

fimdamental properties” {ID §15 398).^ Kant’s second premise is that geometry as the

science of space is not an empirical science and must be necessary. Thus, Kant

concludes, the relational view of space must be incorrect.^^ This argument clearly turns

Kemp Smith, A Commentary to Kant’s ‘Critique o f Pure Reason,' 96.^ Kant often cites examples of particular properties that are threatened by this view. For example, in the Inaugural Dissertation he picks out that a figure might be bounded by two sides {ID §15 398). In On a Discovery, Kant returns to these arguments when he asks Eberhard how he can account for space having three dimensions or that a point is the absolute limit o f space {CD 220).^ This same kind of argument could presumably be leveled against the Newtonian, absolute theory of space, although Kant does not do so in the Inaugural Dissertation. If space were an entity, given that we have only experienced a small corner o f it, it would seem that we might find spaces that are endowed with different properties.

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on the assumption that geometry is a necessary and universal science whose axioms are

not arrived at by induction.

Another version of this geometry argument draws on Kant’s view of Leibnizian

space as a confusion. Here Kant focuses on the nature of space on Leibniz’s view, rather

than our means of arriving at a conception of space. This argument also appears in the

Inaugural Dissertation. Kant begins this argument by identifying the distinction between

the sensible and the intellectual for Leibniz as between confused and distinct cognition.

This is the same distinction that Kant attributes to Leibniz in the “Amphiboly” that I

discussed above. Kant’s claim is that confusion is only a logical distinction that does not

“touch at all the things given” {ID §7 387). Sensitive cognition can in fact be very clear,

while intellectual cognition is often quite confused. If space is seen as a confused

concept then geometry as the science of space would also be liable to confusion. Because

Kant takes geometry as the “paradigm of sensitive cognition,” Leibniz’s understanding of

space is obviously incorrect (ibid.).

These two criticisms were clearly linked in Kant’s mind; we see him explicitly

connecting them in What Real Progress. The “metaphysician of the good old kind can

grant the validity of space only as a merely empirical and confused representation of the

juxtaposition of the [elements of the] manifold outside one another” {WRP 89). In both

variations of the argument the status of geometry as a necessary science of space is

crucial in Kant pointing out the deficiency in Leibniz’s relational view of space. Kanf s

own view is that space is an a priori intuition and thus endowed with a necessity that the

other theories of space are not able to provide. This view also ensures the necessity of

geometrical principles. “The apodictic certainty of all geometrical propositions, and the

possibility of their a priori construction, is grounded in this a priori necessity of space”

{CPR A24). According to Kant, the geometer operates not through deduction or

induction but through construction, thereby necessarily involving the a priori intuition.

“[Gjeometrical propositions, that, for instance, in a triangle two sides together are greater

than the third, can never be derived from the general concepts of line and triangle, but

only from intuition, and this indeed a priori, with apodictic certainty” {CPR A25/B39).

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IV.4 Leibniz’s Reply to the Geometry Argument

First, I will respond to the claim that Leibniz’s view of space as confused

endangers geometry. On the reading that I am advocating, Leibniz held space to be an

abstraction. Confusion arises when we try to apply spatial properties to material bodies.

According to Leibniz, the principle of sufficient reason ensures that no two things in

nature can be exactly the same. “There is ... no substance which does not have

something which distinguished it from every other” (NE 110). Mathematical entities,

such as space, can be completely uniform and identical to each other. Take two lines, for

example. Not only can each of the lines be perfectly identical to each other, but each line

is continuous and therefore infinitely divisible. According to Leibniz, this is because the

lines are composed of possible parts and not actual parts. Because they are composed of

possible parts they can be divided in any number of ways and thus are truly continuous.

Real entities are not only unique, but are composed of actual parts, thus their division is

not possible but determinate. This radical difference in the nature of mathematical

entities and real entities ensures that mathematical entities are abstract and cannot be

found in nature (NE 109). This also means that mathematical entities can be perfectly

clear.

At this point it seems that Kant could object that even if mathematical entities are

abstract and not confused, it is not clear why these abstract entities should match up with

the world. In other words, couldn’t geometry simply be a coherent fiction without any

application to the natural world? This is one of the real virtues of Kant’s objection, I

think. Namely it brings to light an assumption that Leibniz must make concerning the

application of mathematics to the natural world. Leibniz explains in his second reply to

Bayle that there is a correspondence with the continuity we find in mathematical entities

and the discrete real.

It is true that perfectly uniform change, such as the mathematical idea of motion, is never found in nature any more than are actual figures which possess in full force the properties which we leam in geometry ... yet the actual phenomena of nature are arranged, and must be, in such a way that nothing ever happens which violates the law of continuity. (L 583)

In the end, I think that this connection between the mathematical and the real must be

traced back to God. “This [the agreement of the ideal and the real] is because everything

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is governed by reason; otherwise there could be no science and no rale, and this would

not at all conform with the nature of the sovereign principle” (L 544). In other words,

Leibniz must assume a principle of rationality in the universe in order to connect the

abstract and the real.

Leibniz does maintain, however, that the discrepancy between the mathematical

and the real is only the concern of the metaphysician. The conformity of the

mathematical and the real ensures that mathematicians need not be bothered by the fact

that their findings do not match up exactly to the real world. “[M]athematicians do not

need all these metaphysical discussions, nor need they embarrass themselves about the

real existence of points, indivisibles, infinitesimals, and infinites in any rigorous sense”

(L 583). The findings of the mathematician approximate closely enough the real, thus

there is no reason to worry that the entities that they deal with do not really exist or that

nature does not match their findings exactly. I would speculate that Leibniz’s thinking on

this topic was informed by his findings with the calculus and the approximations that it

deals with.

As for the Kantian claim that Leibniz’s relational view of space makes geometry

empirical, I think that Leibniz would have the following things to say. Leibniz admits

that while the senses may be essential in prompting us to begin thinking about

geometrical principles, he denies that they are derived from the senses in any way.

Leibniz has several reasons for holding this view. One is that it seems that a person who

lacks, for example, sight must have the same geometry as a sighted person or someone

who lacks the sense of touch. “These two geometries, the blind man’s and the

paralytic’s, must come together, and agree, and indeed ultimately rest on the same ideas,

even though they have no images in common” (NE 137). Leibniz’s view of the senses is

also that they can only provide us with particular instances and thus do not provide

suitable evidence for use in mathematics.

Although the senses are necessary for all of our actual knowledge, they are not sufficient to provide it all, since they never give us anything but instances, that is particular or singular truths. ... From this [the contingency of observation] it appears that necessary truths, such as we find in pure mathematics and particularly in arithmetic and geometry, must have principles whose proof does not depend on instances nor, consequently, on the testimony of the senses, even through without the senses it would never occur to us to think of them. (NE 49-50)

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Leibniz does grant that the senses begin our thinking and provide us the material

for thought, but it is necessary to demonstrate by reason “things that experience and

sense-images make very evident” {NE 50). Because the senses are limited and our

imagination is also a limited faculty, just because we can or cannot imagine something

says nothing about its ultimate possibility. For example, Leibniz cites that fact that two

straight lines can only meet once as proved by Euclid. Leibniz claims that although our

imagination cannot represent two straight lines meeting more than once, this is not strong

enough to prove it as a geometrical principle. “Imagination, drawing on sense-

experience, does not allow us to depict two straight lines meeting more than once, but

this is not the right foundation for a science” {NE 451). " Leibniz’s claim is that we need

to demonstrate these truths, not imagine them.

Leibniz also makes clear the necessity of geometrical principles within the

Theodicy and a discussion of the three-dimensionality of space. In this passage Leibniz

wants to refute Bayle’s objection that the number of dimensions of matter depends on

God’s choice. Leibniz asserts that “the ternary number [of dimensions] is determined for

it not by the reason of the best, but by a geometrical necessity” {Theo §351 335). As

evidence Leibniz cites that geometricians have proven that only three perpendicular lines

can be demonstrated to intersect in the same point (ibid.). According to Leibniz, this

shows that this geometrical principle is not a matter of moral necessity or a choice of the

best on God’s part, but a “geometrical and blind necessity” {Theo §351 336).

While the argument for the three-dimensionality of space in the Theodicy may not

be the most convincing—it looks completely circular—it does seem to reveal that Leibniz

ultimately considered geometry to be an analytic science. Leibniz also held the view that

mathematical principles, like all truths of reason, were innate and “contained within us in

an implicit way” {NE 77). We bring this knowledge to light either through experience or

through the prompting of other people. Leibniz refers to Plato’s dialogue the Meno to

reinforce his understanding of all mathematical knowledge as innate (ibid.).

^ Interestingly Leibniz continues on in this passage to claim that our imagination with regard to geometrical principles are “confused ideas” (NE 541). Given that Kant had probably read the New Essays, statements such as these could have led him to claim that Leibniz’s view o f geometry was based on confusion.

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Leibniz’s assertion of the rationalit} of the universe and the innateness of

mathematical knowledge indicates that he must look outside of his relational view of

space to other aspects of his philosophy to defend his position. It is in this respect that I

find Kant’s objections most interesting. Kant’s criticisms bring to light the relation of the

sciences and the world on Leibniz’s philosophy. For Leibniz mathematical and scientific

knowledge is a way for us to come to have knowledge of the world that approximates its

actual infinite complexity. Kant has no need for this kind of grand metaphysical picture

as his a priori intuition is intended to provide for the necessity of geometrical principles

within his understanding of human cognition. I think that Leibniz would ultimately

dismiss Kant’s own view as itself empirical and unnecessarily tying geometry to our

particular constitution. In this regard I think that the debate over geometry is intractable

between these two thinkers. Nonetheless, by juxtaposing these two view we see larger

philosophical commitments that the two thinkers are making.

IV.5 Kant’s Metaphysical Argument

In his book Kant and the Claims o f Knowledge, Paul Guyer picks out what he

takes to be Kant’s only metaphysical argument for his view of space and time. This

argument is found in the “Transcendental Aesthetic” section of the second edition of the

Critique. The argument is actually quite brief and consists of only two premises. The

first premise asserts the non-relational nature of things in themselves. “Now a thing in

itself cannot be known through mere relations” {CPR B67). The second premise asserts

the relational nature of objects that are cognized. “[Ojuter sense gives us nothing but

mere relations” (ibid.). From these two conditions, Kant concludes that outer sense must

therefore “contain in its representation only the relation of an object to a subject, and not

the inner properties of the object in itself’ (ibid.). In other words, because space is not a

property of the things in themselves, and it is an element in our cognition of objects,

space must be a product of the subject itself, i.e., a form of intuition. Kant claims that the

same is the case with the inner intuition, i.e., time (ibid.).

Guyer dismisses this argument because of two assumptions that Kant makes in the

course of the argument. The first is the assumption that relations are not real, which he

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takes to be the basic claim of the first premise?^ According to Guyer, Kant’s claim arises

because he equivocates considering a thing absolutely as considering a thing in its

“ultimate reality” with considering a thing in isolation.^^ Guyer further claims that in a

post-Fregeian age it is impossible to claim the unreality of relations. The second

illegitimate assumption that Guyer claims Kant is guilty of is the assertion that space and

time are a system of relations. If this fact has been proven it must have been done in

another place, according to Guyer, namely within the “metaphysical exposition.” If Kant

could successfully lay claim to these assumptions, then he would have a “sound

metaphysical argument for transcendental idealism” according to Guyer.^^

In this context it is not necessary to evaluate the success of this argument in

proving transcendental idealism. What is interesting to consider is how Leibnizian

Kant’s argument is in its assumptions. If we understand Kant’s claim that a “thing in

itself cannot be known through mere relations” as the claim that things in themselves are

non-relational then this seems to match up with Leibniz’s claim that monads are non-

spatial and a-temporal.In both cases, the non-reality of relations is asserted. Kant’s

claim that space and time are thoroughly relational also seems to align very closely with

Leibniz’s position that space and time are a system of relations.

Insofar as this argument represents a challenge to the Leibnizian view, it seems

that it could be understood in the following way. Kant is claiming that things in

themselves are non-relational and subsequently cannot ground the inner or outer relations

that we do perceive. Since there must be some ground to these relations, we must be the

ones that contribute them. In other words, Kant is asking how can non-relational things

provide the ground for relations.

Guyer, Kant and the Claims o f Knowledge, 352. “ Ibid.

Ibid.There does seem to be a problem with the fact that Kant holds this position, however. Namely how can

he positively assert that things in themselves are non-relational when he states that we can only have a negative conception o f things in themselves? Couldn’t things in themselves be relational in themselves, even if they are relational in a different way for us?^ In the “Amphiboly” Kant also discusses the thoroughly relational nature o f the objects of cognition and in that context he makes it clear that this property entails that we do not cognize things in themselves, but rather appearances. “It is certainly startling to hear that a thing is to be taken as consisting wholly of relations. Such a thing is, however, mere appearance, and cannot be thought through pure categories” {CPR A285/B34I).

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A lot of what I have said in addressing the presupposition argument speaks to this

question. As far as space is concerned, I think that Leibniz has a rather strong response.

Namely monads themselves do not provide the grounds for the relations of space, rather

it is the material bodies that the monads well found. Time, v/hich is revealed through the

inner sense, represents a more serious challenge, however. According to Kant, the “time

in which we set these representations [of external objects] ... is itself antecedent to the

consciousness of them in experience, ... and underlies them as a formal condition of the

mode in which we posit them in the mind” {CPR B67). In other words, our cognition of

the objects of representation as successive or simultaneous presupposes that we already

have the “form” of time in our intuition. Kant’s claim is that because this representation

of temporality arises in the mind, this shows that it is a product of the mind; it is “nothing

but a mode in which the mind is affected through its own activity” {CPR B67-8).

This is a variation of the same problem that arose in my discussion of the

presupposition argument above. Namely, if a monad contains all of its states internally at

its conception, how can we make sense of the succession of states? In this case we are

focusing on our own monad and our internal representations of temporal succession. No

matter how Leibniz describes the succession of states of the monad or its unfolding, if he

maintains that monads somehow move from state to state or that one state succeeds the

other, he seems to appealing to some notion of time. The other possibility seems to be to

somehow index the order of states of a given monad, perhaps by numbering the

individual states. However, this possibility seems to do away with any conception of a

“now” or a real succession of states.

Overall, I think that this argument, in conjunction with what I have said about the

presupposition argument, shows that Leibniz’s relational view is much more plausible in

the case of space than it is time. Developing a theory that successfully accounts for both

things, i.e., space and time, is a challenge, but one that must be undertaken given the

interrelated nature of these two things. Leibniz’s view of relational space seems much

more successful on this count and perhaps not surprisingly given Leibniz’s concern with

the “labyrinth of the continuum.” However, this does not free him from the difficulties of

his view.

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IV.6 Incongruent Counterparts

The last argument that I want to consider is perhaps Kant’s most famous

argument against Leibniz’s relational view of space. This is the argument dealing with

“incongruent counterparts.” This argument first appears and is presented in its greatest

detail in the 1768 essay “Concerning the Ultimate Ground of the Differentiation of

Directions in Space.” In this paper Kant focuses on the distinction between the concepts

of “position” (die Lage) and “direction” (die Gegend).^° Kant defines position as “the

reference of one thing in space to another” and that which can be determined by

“reference to the thing itself,” independently of the larger space that it occupies (DS 365).

Kant is directly referring to Leibniz’s understanding that it is the relation of the position

of bodies that is the foundation of space. Direction is the orientation of the parts and

“refers to the space outside of the thing” (ibid.). The idea is that direction is a property of

a body that cannot be accounted for by internal principles, i.e., position, but can only be

understood in relation to the space that it occupies. According to Kant, the position of

parts in space presupposes direction (ibid.).

In order to clarify the distinction between position and direction, Kant introduces

the concept of an “incongruent counterpart.” He defines this type of entity as “a body

which is exactly equal and similar to another, but which cannot be enclosed in the same

limits as that other” (DS 370). His most famous example of an incongruent counterpart,

which is also employed in this essay, is a human hand. Kant encourages us to think about

the difference between a left and right human hand, or a hand as it appears when it is held

before a mirror (ibid.). He claims that in either case the two hands are examples of

spaces that are “perfectly similar and equal and yet incongruent” (ibid.). In other words,

the two hands are completely identical in all of their features, yet they are not the same,

i.e., they cannot be placed in the same space. For example, for both hands the thumb and

the pinky finger may be 10 cm apart, the fingers may each be 5 cm long, and the palm

may be 7 cm across. The two hands can be differentiated by saying that for one hand the

thumb is 10 cm to the left of the pinky finger or the index finger is to the right of the

^ “Die Gegend” is commonly translated as “region;” in this context, however, Walford and Meerbote provide rather convincing evidence in this translation that “Gegend” is better translated as direction, cf. DS, note 1, 365.

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thumb, in which case one is clearly referring to direction to differentiate them. Kant’s

claim is that the only way to distinguish the two hands is with reference to direction. On

purely relational terms, i.e., position alone, the hands are identical.

To further prove his point, Kant asks us to “imagine that the first created thing

was a human hand” (DS 371). According to Kant, this one hand would have to be either

a left hand or a right hand, as the “creative cause” required to make one rather than the

other would be different (ibid.).^ However, the reiationist would be unable to account

for the handedness of the single hand. The reasons are the following. First, because the

reiationist denies the existence of space external to the bodies that occupy space, all of

space would be comprised by this single hand. Thus, there would be no things external to

the hand that could be used as a reference, e.g., comparing the hand to our own hands to

determine its handedness. Secondly, the position of the parts would be identical whether

the hand were a left or right hand, thus the reiationist could not account for the

handedness of the object based on internal relations without presupposing direction.

Thus, even though the hand would clearly, Kant claims, belong either to the right or the

left, the reiationist could not account for this fact.

In this paper Kant takes the inability of the relational view to account for the

necessary handedness of the single hand and direction more generally to show that

objects must be related to ‘‘''absolute and original space"' (DS 371).^ This “absolute and

original space” makes “the relation of physical things to each other possible” and makes

possible “all such outer sensations” (ibid.). This ensures the concept of space as it is used

in geometry and in the “system of natural science” (DS 372). Again, we see Kant

motivation is to defend a view of space which he thinks better accounts for the necessity

of geometry, and in this case he is doing so by the reiationist’s inability to account for

direction. At the end of the paper Kant claims that he has provided for the concept of

Kant’s use of “creative cause” is another reference to Leibniz and his principle o f sufficient reason. Kant is claiming that direction is one of the factors that truly differentiates objects, and, in Leibnizian thinking, plays a role in God’s creation o f them. As we will see, Kant later uses this fact to show that the hands are fundamentally spatial and subsequently “appearances” and not things in themselves.

Since Kant is defending an absolutist, i.e., Newtonian, view of space in this paper this makes it clearly a pre-Critical work. It is amazing that only two years separate this paper from the Inaugural Dissertation, in which Kant has developed an entirely new view on space and time that is clearly the precursor to his Critical view.

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space as it is used by geometers, rather than dismissing it as a “figment of the

imagination” as relationists do (ibid.).

In the Inaugural Dissertation Kant gives up the absolutist’s view of space for his

Critical view that space is a form of intuition. Yet, he maintains the incongruent

counterparts argument as a way to argue against the reiationist by now claiming that we

must intuit direction. Kant uses essentially the same argument to show that the

incongruity of two hands can “only be apprehended by a certain pure intuition” and

cannot be Imown conceptually, in the same way that space is not a “universal concept”

{ID §15 396). Kant also continues to use this argument to support a reading of space that

ensures that geometry and geometrical principles are necessarily true. As Kant points

out, this view of space also ensures that geometry uses principles that are “indubitable

and discursive” precisely because geometry operates by the intuition and not by means of

concepts (ID §15 396-7).

By the time of the Prolegomena Kant has the full resources of his Critical view,

including the distinction and role of the understanding and intuition in cognition, and he

uses the same argument not only to support the Critical view of space, but also to lay an

ontological claim against Leibniz. Kant maintains that the difference in the incongruent

counterparts can only be accounted for by the senses and this difference “immediately

refers to intuition” (P §13 34). He also goes on to claim that this argument shows the

hands themselves to be appearances or “sensuous intuitions” and not “things as they are

in themselves” {P §13 33).

These objects [incongruent counterparts] are not representations o f things as they are in themselves and as some mere understanding would know them, but sensuous intuitions, that is, appearances whose possibility rests upon the relation o f certain things unknown in themselves or something else, namely, to our sensibility. (P §13 33-4)

Because the hands have a direction that is inherent to them and can only be

known through the senses, this shows that they are essentially objects, i.e.,

“appearances.” This is essentially the same ontological claim that we saw in the

“Amphiboly” that objects are appearances and not confused representations of things in

themselves. The difference here is that rather than arguing from the faculties themselves,

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Kant is arguing from a specific kind of object, which is, for him, telling both as to the

nature of objects and the nature of space itself.

Kant is also clearer in the Prolegomena on the implications of incongruent

counterparts for geometry. Because incongruent counterparts show that space must be a

form of intuition and the objects themselves are appearances, i.e., subject to the form of

intuition, geometrical principles must apply to all of space and all spatial objects. On his

view, there is no doubt as to the objective application of geometry to nature itself, as, he

claims, earlier philosophers had been subject (P §13 34).

IV.7 Leibniz’s Response to the Incongruent Counterparts Argum ent

A great deal has been written on Kant’s incongruent counterparts arguments and

his success in using this argument to defend either an absolutist view of space and/or the

Critical view of space. I will limit myself to considering these arguments as a criticism

of Leibniz’s relational view of space and ignore their ability to provide a positive

account. Since the changes in the subsequent versions of this argument are most

important for the positive elements of the view, i.e., what view of space is being

defended, I will focus on Kant’s claim in the “Directions in Space” paper that Leibniz

would not be able to account for the handedness of a single hand.

Again, Kant’s claim is that given a universe composed of a single hand, Leibniz’s

relational view of space would not be able to determine whether the hand was a left or

right hand. The hand, according to Kant, must be either right or left, thus Leibniz’s view

of space is incorrect. I think that Leibniz has two possible answers to this form of the

argument, one offensive and one defensive. Offensively, Leibniz can claim that this

question is either nonsensical or contains an illicit assumption. If the universe really was

composed of a single hand, it is not clear that it would be possible to tell if it were right or

left handed. And, if Kant is so sure that the direction must be determinable, then perhaps

he is assuming that there is something other than the hand in the universe to make that

determination. Especially in the Critical formulation of the objection it seems that Kant

is assuming that there is someone there to intuit the hand and make the determination as

to its handedness. If this is the case, then Leibniz could also assume that there was

something else to compare the hand to, such as another hand.

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Leibniz could also take a more defensive route and account for the handedness of

the hand by resorting to possible objects. If Leibniz employs possible objects to which

the hand can be related then it is possible to determine if it is a left or right hand.^ The

composition of space out of both possible and actual objects is clearly in keeping with

both the reiationist’s view of space and Leibniz’s particular brand of it and would be

sufficient to respond to Kant.

However, as Jill Buroker Vance points out in her book Space and Incongruence:

The Origin o f Kant’s Idealism, perhaps the question that Kant is really asking is if the

hand is an “enantiomorph” or not.^”* The property of something being an enantiomorph

depends on the space in which the object occupies. Consider two congruent shapes taken

on a Euclidean plane. These figures can be made to coincide if one of the figures is

rotated outside of the plane in three-dimensional sp ace .T h e same would be true for

three-dimensional incongruent counterparts; if it were possible to rotate one of the hands

through a fourth dimension, it could be made to coincide with the other hand.^ Thus, the

direction of an object refers directly to the overall structure of the space and the situation

of the object in the spa ce .T h e incongruence of two hands is dependent on them being

three-dimensional objects.

It is certainly possible for the reiationist to account for the dimensionality of space

based on the relation of actual and possible objects. However, we must keep in mind that

Kant is attacking Leibniz’s version of relational space. For Leibniz, non-spatial relations

form the foundation of space, this is the concept of position insofar as Kant understands

it. The handedness of the hand is something that can only be understood in three-

dimensional space and requires that space have a particular nature. On the enantiomorph

argument, Kant is claiming that Leibniz lacks the means to provide for this feature and

must simply assume that space is three-dimensional if he is to account for the direction of

the hand. This clearly makes the argument related to his argument from geometry in

Sklar, “Incongruous Counterparts, Intrinsic Features and the Substantivality o f Space,” 281-2.^ Buroker, Space and Incongruence: The Origin o f Kant’s Idealism, 59. An enantiomorph is the “mirror image” of an object and cannot be brought into congruence with its incongruent counterpart through a continuous rigid motion, i.e., rotation (Sklar, 279).

Buroker, 55.Ibid., 56. There is a further question about the “orientability’ of the space (cf. Sklar, 279), but I will

focus only on the dimensionality for the sake o f simplicity.Sklar, 280.

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which he criticized Leibniz’s abii% to account for the necessity of certain geometrical

principles, including the three-dimensionality of space. Kant’s thinking is that the

absolutist view and later the Critical view had three-dimensionality built into them thus it

was easy to account for the directions of the hands. In the direction arguments, Kant has

picked out a specific feature of space that requires three dimensions and questioned

Leibniz’s ability to account for the necessity of this feature. If this is Kant’s argument,

then Leibniz’s reply would have to be the same that he used in response to the geometry

argument, namely the defense of three dimensionality in the Theodicy.

While the enantiomorph reading of the argument certainly seems plausible, I think

that there is even another way that the argument can be understood. I think that we can

understand Kant as saying more than that Leibniz cannot account for the necessity of

direction, which, as we have seen, is dependent on the three-dimensionality of space; he

is claiming that Leibniz cannot account for direction at all. Kant is saying that for

Leibniz, space is based on the relation of position, which itself must be non-spatial

because it grounds space and could only be spatial on pains of being circular. Leibniz

cannot claim that the parts are situated to the left of one another or that one is above the

other without already assuming the space that he is trying to provide for. Incongruents,

e.g., a left and a right hand, are objects whose parts are identically related, but which are

clearly different. This difference can only be accounted for when one considers the

spatial relation of the parts, i.e., the direction. Thus, Leibniz is unable to account for

direction. In the Prolegomena, Kant also makes the further, ontological claim, that the

hands are essentially directional and thus essentially spatially situated objects, i.e.,

appearances.

Viewing the incongruent counterparts argument as questioning the very

possibility of direction for Leibniz can also be viewed as a special form of an objection

that we have already seen, namely Kant’s question of how Leibniz can derive spatial

relations from non-spatial entities. In fact, I think that this aspect Kant’s incongruent

counterparts argument does little to move beyond the kind of argument that we have

already seen in the presupposition argument. The incongraent counterparts argument

simply provides us with a very salient example.

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V. Conclusion

In this chapter I have argued that Leibnizian space and time are ideal entities.

This ideal reading not only matches up to Leibniz’s late writings, but also allows Leibniz

a solution to the problem of the labyrinth of the continuum. At the level of body, space is

a function of the relation of material bodies and is derived from them. I argued that

bodies really are in space, and time, and that there is no reason to draw a sharp division

between the ideality of space and time in themselves and the weli-foundedness of bodies.

While bodies are ontologically tied to the monads that ground them, they are also

phenomena, so there is no reason to dismiss space and time completely from this level of

Leibniz’s metaphysics.

Kant’s criticisms of Leibniz’s view are helpful in showing that Leibniz’s view of

time is open to some real criticisms involving the seemingly circular nature of trying to

base temporal progression on a succession of states. I also pointed out that while

Leibniz’s monadic level is immune from this challenge as far as space is concerned, at

the level of the material Kant’s criticisms do gain some purchase as it is hard to see how

the bodies can be prior to spatial relations as their existence as other seems to presuppose

space. I also pointed out that Kant’s incongruent counterparts can also be seen as an

argument in a similar vein.

Kant’s criticisms also bring to light the importance of geometry in Kant’s

understanding of space; at the same time they show Leibniz’s much different

understanding of geometry and the mathematical sciences overall. For Leibniz, geometry

is science that deals with ideal entities and does not match up exactly with the world. For

example, material bodies are discreet and not mathematically continuous, yet we use

geometry to describe the world because it approximates geometry to a high degree. At

the same time that Kant’s view of geometry is perhaps better able to account for the

necessity of geometrical principles, his view is also wedded to a view of space as

necessarily Euclidean. Leibniz is not tied to one description of space and thus his view

would be able to accept developments such as non-Euclidean geometries much more

comfortably than Kant’s view of space as a form of intuition.

In the largest sense, this discussion of Leibnizian space and time has further

emphasized the role of substances and their states as fundamental to Leibniz’s ontology.

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Leibniz’s solution to the labyrinth of the continuum is essentially to divorce space and

time from the underlying bodies. While this ideal reading of space and time does in a

sense bring Leibniz’s view closer to Kant’s own, as I pointed out earlier, to say that space

and time are ideal entities that are abstracted from the underlying bodies is not to say that

they are forms of intuition.

In the chapters that follow I will turn to two particular aspects of Leibniz’s

metaphysics, the identity of indiscernibles and the pre-established harmony, in order to

demonstrate Kant’s criticisms of these particular aspects while at the same time revealing

the importance of Kant’s view of space and time in driving those criticisms.

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CHAPTER FOUR

THE IDENTITY OF INDISCFRNIBLFS

The identity of indiscernibies is one of the cornerstone principles in Leibniz’s

mature philosophy. He mentions this principle throughout his mature writings, including

his most important works such as the correspondence with Clarke, the New Essays, and

the Monadology. In Ms correspondence with Clarke, Leibniz claims that the identity of

indiscernibles, along with the principle of sufficient reason, are “those great principles”

that “change the state of metaphysics” {LC 37). According to Leibniz, the identity of

indiscernibles not only makes an important contribution to metaphysical debates on

identity, but also it determines other metaphysical questions and proves the impossibility

of certain entities such as atoms, absolute space, or a vacuum {LC 36). I would like to

begin by briefly investigating what exactly the identity of indiscernibles entails before

looking at Kant’s criticisms of it.

I. Statem ent of the Principle

In his fifth paper to Clarke, Leibniz explains that “the vulgar philosophers were

mistaken, when they believed that there are things different solo numero, or because they

are two; and from this error have arisen their perplexities about what they called the

principle o f individuation” (LC 62-3). In the Monadology, Leibniz claims that: “It is

even necessary for each monad to be different from every other. For there are never two

things in nature which are perfectly alike and in which it is impossible to find a difference

that is internal or founded on an intrinsic denomination”' {Monadology §9 L 643). These

two statements lay out the important elements of the identity of indiscernibles, yet they

require a degree of explanation to illuminate the principle and to make Leibniz’s

assumptions clear.

’ Leibniz’s use of the term “denomination” takes its precedent from medieval scholars such as Aquinas and Suarez. A denomination (denominatio) should be understood along the lines of a determination or specification and not as a synonym for “relation.” Leibniz’s denial of purely extrinsic denominations amounts to the claim that all determinations of a subject lie within that subject. Thus, “no one becomes a widower in India by the death of his wife in Europe unless a real change takes place in him” (L 606). For an insightful discussion of the etymology and philosophical usage of this term see its Glossary entry in Suarez on Individuation: Metaphysical Disputation V: Individual Unity and Its Principle, trans. Jorge J.E. Gracia, 202-4.

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First, at the heart of the identity of indiscernibles is the denial that two things can

differ solo numero. A solo numero difference, or difference only by number, arises when

two things that are in all respects identical are differentiated simply because they are two.

The easiest way to think about a solo numero difference is by imagining two identical

objects that are separated spatially, for example, two cars that are identically constructed,

yet are differentiated because one is this car and the other is that car, i.e., one car is

located here and the other there. The identity of indiscernibles denies that two objects

can be identical but located in different places or otherwise considered the same but

different.

The denial of solo numero differences leads to the principle itself. In his fourth

paper to Clarke, Leibniz explains that: “to suppose two things indiscernible, is to suppose

the same thing under two names” {LC 37). More formally, Leibniz’s claim is that if A

and B share all of the same properties, then A is B. This is why it is an identity of

indiscernibles. Two things that share the same properties are really identical, just

differently considered in some way.

An important component of the identity of indiscernibles is the assertion that only

internal properties are pertinent to the identity of an individual. This is what Leibniz is

getting at when he claims that all differences are based on internal denominations. Any

external determination, what Leibniz calls an extrinsic denomination, is based on an

internal denomination. This means that all relational differences are based on internal

differences.^ For example, we perceive the two cars as different or in different relations

because of differences that are internal to them. To say that A is spatially distinct from

B, is to make a claim that is dependent on internal aspects of A and B, according to

Leibniz, and not simply to assert the relation (cf. LC 69-71). In other words, the

difference that we experience in spatial position is a product of differences internal to the

Benson Mates in his The Philosophy o f Leibniz: Metaphysics and Language claims that Leibniz intends extrinsic denominations to be excluded from the concept of an individual. His reasoning is the following.If we imagine car A as being distinct from car B, then car A would have the property “distinct from B” while B would lack this property. The problem, according to Mates, is that this would be trivially true for any two objects, thus external denominations must be excluded from the concept of the individual (135). I don’t think that this is quite right. It isn’t that the extrinsic denominations don’t count, but that they are dependent on internal denominations. For Leibniz cars A and B stand in the relation that they do, i.e., have the extrinsic denominations that they do, because of things that are true of them internally. Real differences within the individual manifest or express themselves through the external denominations.

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bodies and, by extension, in the underlying monads. It should also be obvious that this

view of individuals is consistent with the Leibnizian, relational view of space that I

explored in the last chapter. Things and their properties are prior to their external

denominations, i.e., relations, in the same way that objects are prior to the spatial

relations that they establish.

From the identity of indiscernibles it follows that each individual must be unique.^

At the monadic level the identity of indiscernibles entails that each monad is a unique

entity. Unlike atoms or extension, which is uniform, each monad is an individual

because of the perceptions that it contains. However, Leibniz not only applies the

identity of indiscernibles to monads, but also to material bodies. Thus, when he claims

that “there are never two things in nature which are perfectly alike” he intends this claim

to cover all things in nature {Monadology §9 L 643). Leibniz’s favorite example of the

uniqueness of each material object involves Princess Sophie and an incident in which she

asked Carl August von Alvensleben, an official at the Hanoverian court, to find two

identical leaves in her garden {NE xciv). As Leibniz explains to Sophie in an October 31,

1705 letter, von Alvensleben’s inability to find two identical leaves shows that “no two

pieces of matter entirely resemble each other, in the large as in the small” (G 563).'*

Thus, according to this principle it is impossible that any two material things can be

internally identical and solely differentiated through their spatial location. Even if two

things appear to be identical, closer inspection, either with the naked eye or with

scientific instruments, will reveal a difference. “Two drops of water, or milk, viewed

with a microscope will appear distinguishable from each other” {LC 36).

II. Kant’s Criticisms

Given that Leibniz mentions the identity of indiscernibles in several well-known

works, in addition to the general fame of this principle, it is no surprise that Kant

The reasoning here is the following. According to the identity of indiscernibles any two things with all the same properties are actually the same thing differently considered. Since all properties, according to Leibniz, are internal properties, there is no way for two objects to be two different objects unless they have some internal difference. Thus, every individual is unique for Leibniz.

Leibniz also relates this story in the New Essays and the correspondence with Clarke (NE 231, LC 36). In every case, Leibniz uses this story to support the identity of indiscernibles and the impossibility of two identical material bodies.

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addresses it in his criticisms of Leibniz. In the “Amphiboly” section of the Critique,

Kant deals with the identity of indiscernibles under the concepts of identity and

difference. As with the other concepts of reflection, Kant’s aim is to shovvf that Leibniz’s

principle results from an illegitimate application of a conceptual truth to the material

world.^ Kant grants that insofar as we consider objects conceptually or concepts

themselves, it is their inner determinations, what he calls their qualitas et quaniitas, that

determines their identity (CPR A263/B319). If one considers two concepts that are

identical then they are not really two separate concepts, but the same concept. According

to Kant, Leibniz applied this logical principle to sensible objects because he saw no

difference between the concept of an object and the object itself. For Leibniz, the only

difference between an object of the understanding, i.e., the concept of an object, and an

object of experience is the confusion in the concept that the senses introduce (CPR

A264/B320). Thus, Leibniz applied the identity of indiscernibles to objects of experience

and claimed that every object is unique and is individuated through internal differences.

In this case, as with the other concepts of reflection, Kant attributes Leibniz’s

mistake to a failure to realize the necessary role of the intuition in our cognition of

objects and the objects status as sensible objects or “appearances.” According to Kant,

Leibniz abstracted from the conditions of the intuition and dealt only with the concept of

an object, which is not really an object at all (CPR A281/B337). Because appearances

are subject to the forms of the intuition they are essentially spatial (and temporal). Thus,

spatial location can be used to differentiate objects and the principle of the identity of

indiscernibles cannot be applied to sensible objects. What Leibniz took to be an

important fact about material objects is not really a “law of nature” but is only an

“analytic rule or comparison of things through mere concepts” (CPR A273/B329).

The example that Kant very often uses to support his criticism is two water

droplets.*’ “Thus in the case of two drops of water ... the mere fact that they have been

intuited simultaneously in different spatial positions is sufficient justification for holding

As I discussed in chapter one, each of Kant’s criticisms of Leibniz in the “Amphiboly” is a variation on this claim that Leibniz confused objects and their concepts. While Kant’s discussion of each of Leibniz’s principles in the “Amphiboly” follows this general pattern, his treatment of the identity of indiscernibles is perhaps the clearest example of this form of criticism.® Kant’s use of water droplets as an example is probably not a coincidence, but a direct reference to Leibniz’s correspondence with Clarke wherein he uses the same example (cf. LC 62).

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them to be numerically different” (CPR A264/B320). Kant is asserting that simply

intuiting two separate objects, regardless of their internal properties, is sufficient to

differentiate them. This means that objects could be internally identical yet differentiated

tlirough their spatial location. In What Real Progress, Kant claims that it is so obvious

that location can differentiate objects that Leibniz “offended common sense” when he did

not allow that there could be two identical objects in different spatial locations (WRP

99)?

Kant even goes so far as the claim that relations are not only sufficient to

differentiate objects, but also that they are essential to the identity of the objects

themselves. Because objects are “appearances” the forms of intuition and the spatial and

temporal relations that they enable are constitutive of the objects. “All that we know in

matter is merely relations (what we call the inner determinations of it are inward only in a

comparative sense), but among these relations some are self-subsistent and permanent,

and through those we are given a determinate object” (CPR A285/B341).

This last point is important to note and is in keeping with the ontologically

oriented reading that I have been giving of Kant’s criticisms. When talking about

individuation, one can differentiate between the “problem of individuation” and the

“problem of discemibility,” where the former is seen as a metaphysical or ontological

problem and the latter as an epistemological problem.® From what I have said it should

be clear that Kant is not only claiming that we can use relations, e.g., spatial locations, to

discern objects, but also that the objects are individuated based on relations. This is a

truth about the objects themselves insofar as they are appearances and not merely an

epistemological truth about our identification of them.

Kant also discusses space itself as further evidence that Leibniz’s principle does

not apply to the sensible world. According to Kant, different parts of empty space share

all of the same properties, yet it is quite possible for one space to be outside another or

for two spaces to be added to each other “in order to constitute a larger space” (CPR

’’ The idea that location is sufficient to differentiate objects can be found much earlier in Kant’s career, well before his development of the Critical view of space and time. In his 1755 New Elucidation paper, Kant asks rhetorically: “Is there anyone who has excluded place from this complete determination [of the identity of a thing] ?” {ND 35). He concludes that, “no matter how great the agreement of things in respect of their internal characteristic marks, things which are distinguished at least in virtue of place are not one and the same thing at all” (ibid.).® Jorge J.E. Gracia, “Christian Wolff on Individuation,” p219.

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A264/B320). This demonstrates that numerical difference can be given by space itself as

the “condition of outer appearance” (ibid.). If this were not the case and all spaces were

identical then ail of space could be compressed into a “cubic inch or even less” {WBJ^

99). In other words, given the homogeneity of spaces, the identity of indiscernibies

would preclude the possibility of discussing parts of space or larger and smaller spaces as

there would be no way to differentiate them. Space itself would essentially disappear if

Leibniz’s theory was correct.

In each of Kant’s criticisms of the identity of indiscernibles the intuition plays an

important role whether it is in establishing objects as “appearances” or defining the

nature of space. ® Because of the centrality of the intuition in Kanf s arguments, I think

that it is best to see Kant focusing on Leibniz’s application of the identity of

indiscernibles to material bodies and abstaining from comment on the individuation of

the monads, which, if they exist, are not subject to our intuition. When it comes to

material bodies, Kant and Leibniz are squarely in opposition. Leibniz claims that things

in nature cannot be distinguished based on location alone and Kant claims that spatial,

and other relational, differences are essential to the identity of objects. Before trying to

adjudicate this dispute it is important to look more closely at why Leibniz held the

identity of indiscernibles and why he thought it was an important metaphysical principle.

In order to gain a clearer understanding of this background, I would like to examine one

of the most important and clearest formulations of his reasoning as found in his 1686

work Discourse on Metaphysics.

III. Background for the Principle

Leibniz’s arguments on the individuality of substance (monads) begins in section

8 of the Discourse. He begins by considering a substance in Aristotelian terms as that

which can be assigned predicates, but can never be a predicate of another {DM §8 13).

® In the pre-Critical New Elucidation paper Kant agreed that in organic bodies or “other bodies of extreme complexity” there would be an internal “discernible difference” {ND 36). Thus, the identity of indiscernibles would apply to many material bodies. However, he rejected the “metaphysical universality” of the principle and cites the possibility of crystalline formations, which out of their infinite diversity allows the possibility of one or two being identical (ibid.). The difference between this more modest criticism and his later, broader criticism is quite clearly enabled by Kant’s development of space and time as forms of intuition and the subsequent status of all material bodies as appearances.

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Leibniz dismisses this as a suitable definition of substance because it is “merely nominal”

(ibid.). Instead, he claims that the mark of substances “in reality” is that every true

predication is contained in the subject, is in-esse, whether expressly or virtually (ibid.).^°

This entails that if one imows the complete concept of the individual, then one will know

all of the possible predicates for the individual (ibid.). Leibniz uses Alexander the Great

as his example. From the property of king we cannot determine anything, or at least very

little, else about Alexander. However, from the complete concept of Alexander one can

derive all of his properties, e.g., student of Aristotle, conqueror of Darius, etc. Within the

individual concept of Alexander or his “haecceity”^ there are marks of all that has

happened to him and traces of all that will happen to him, although the infinite

complexity of the complete concept ensures that only “God alone could recognize them

all” (DM §8 14).

From the fact that every substance has a complete concept, Leibniz claims that a

number of things follow. These include: no two substances can be exactly alike and

differ only in number {solo numero), each substance is a unity, every substance mirrors

the entire universe from its situation, and every substance is, to a limited degree,

omniscient and omnipotent because each expresses the entire universe and is expressed

by the entire universe, although confusedly (DM §9 14-15).

Virtual predicate containment results when a given proposition does not on its surface ascribe a predicate to the subject, but can be reduced to such an ascription. An express predication would be something like “the car is red,” while a virtual predication would be something like “John is in love with Jane.” In the latter, relational statement, something is being said of both John and Jane, namely that each is in love with the other. Whether Leibniz can successfully reduce all “virtual” predication to “express” predication, indeed if there is anything such as “virtual” predication at all is a matter of great controversy. See for example J.A. Cover’s “Relations and Reduction in Leibniz” and Mark Kulstad’s “A Closer Look at Leibniz's Alleged Reduction of Relations.”

Leibniz’s use of this Scotist term is curious because he denied the concept of haecceity (thisness) and the “formal” distinction on which it was based. I take Leibniz’s use of the term here as a reference to the idea of a thisness and to provide a familiar reference point to his reader, but he is clearly using the complete concept to achieve the individuation and not Scotus’ haecceity. J.A. Cover and John O’Leary-Hawthorne in chapter four of their work Substance and Individuation in Leibniz argue that Leibniz actually adhered to a kind of haecceity that they refer to as “weak haecceitism” because he allowed for claims about transworld individuals, among other reasons.

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This argument still leaves a number of questions unanswered, principle among

them the question of why substances must have a complete concept in the first place.

This is the question that Arnauld focused on in his first reply to Leibniz after receiving

the Discourse. Arnauld asked Leibniz how on his viev/ one can make clairns about other

possible individuals, (other possible Adams is the example that is used), or how an

individual in this world can possibly do one thing as opposed to the other if its concept is

truly complete at its creation (DM94). Arnauld instead advocates a view on which some

predicates are essential to the individual while others are accidental. An “incomplete”

concept view would allow for the possibility that Amauld, the same Arnauld, could have

married and had a family, rather than be celibate (ibid.).

Leibniz’s reply draws on a distinction that we have already seen in chapter three,

namely the difference between abstract entities and determinate individuals. According

to Leibniz, when we talk about possible Adams or things that Adam could have done, we

are considering a vague or incomplete concept of Adam that only encompasses some of

his most important predicates, e.g., the first man, put in Eden, Eve taken from his rib, etc.

(DM 110-1). True individuals, on the other hand, are “complete and determined,”

according to Leibniz (DM 111).^^

The requirement that individuals’ concepts be complete stems directly from his

logical views. According to Leibniz all contingently true propositions are analytic, thus

for a true proposition the predicate is contained within the individual either literally or

virtually.Leibniz claims that “the predicate is contained in the subject [for every

affirmative proposition] or else I don’t know what truth is” (DM 132). From the concept

containment theory of truth Leibniz derives the need for a substance’s complete concept.

“[Wjhen I say that the concept of Adam involves ail that will ever happen to him I mean

nothing else than what the philosophers understand when they say that the predicate is

contained in the subject of true propositions” (DM 113). He also claims that a complete

Leibniz often refers to Aquinas’ individuation of angels to provide a similar account of individuation. According to Aquinas, because angels lack the matter that individuates material beings within a species, each angel must be its own species and the species, i.e., individuals, are individuated based on their “diverse degrees of intellectual nature” {Summa Theologica, i, question 50, article 4). Leibniz expands Aquinas’ view and asserts that every individual substance is unique and thus its own species. Leibniz’s assertion that clarity of perception individuates monads would also seem to roughly correspond to Aquinas’ position that intellectual nature individuates angels,

cf. note #10, pl22.

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concept allows us to account for sustained individuality over time. He asks us to consider

Ms existence from a period of time A to B when he was in Paris and a subsequent period

of time, B to C, when he was in Germany. In order to provide for the continued existence

of the same person, a fact that Leibniz claims we normally acknowledge a posteriori

tlirough experience, it is necessary that the predicates at the earlier time and the

predicates at a later time are both predicates of the same subject (ibid.).

Leibniz also claims that the completeness of the individual’s concept does not

stop at all the predicates that are true of it past, present, and future. For the concept to be

truly complete it must not only contain the truths that pertain to the given substance, but

also truths about the entire universe, i.e., all other existent substances. In his

correspondence with Amauld, Leibniz is less than explicit why a substance’s complete

concept must involve the whole universe. Although he discusses the “interconnection

between things” and asserts that “every individual substance expresses the whole

universe according to its way and under certain aspects, or, so to speak, according to the

point of view from which it is regarded,” he never really explains how this follows from

his complete concept view {DM 110, 133).

In his slightly earlier paper “First Truths” we can find his clarification of this

point. Leibniz begins his argument with the claim that there is nothing in the universe

that cannot be related or compared to something else in the universe (L 269). His second

premise is that there are no purely extrinsic denominations (ibid.). The idea is that there

are no truths that are purely relational or involve comparison alone. All relational truths

can be reduced to tmths intemal to each of the substances that are being related. TMs

follows from Leibniz’s predicate in subject conception of truth discussed above. From

the potential relation of all substances in the universe and his denial of purely extrinsic

denominations we arrive at the conclusion that the whole universe must be contained in

the complete concept of a substance. In this way every substance “expresses” every other

substance in the universe (rather than being in direct contact with it). '* TMs is the

support for the Leibnizian claim that I mentioned earlier that each substance is to a

limited degree omniscient and omnipotent. It is omniscient because it contains truths

In his correspondence with Arnaud, Leibniz clarifies that the interconnection of substances isn’t the cause of the concept being complete, but instead the interconnection follows from the complete concept (DM 112). I will discuss the nature of this interconnection and its relation to harmony in the next chapter.

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about each other substance in the universe and it is omnipotent because every other

substance contains truths about it. However, each substance is limited in its power and

knowledge because of the confusion of the perceptions that are contained within it.

From the complete concept view of substance, Leibniz claims that it follows that

each substance is unique. Two identical, but different substances would be different

without being different, which is impossible. Given that the substances’ concepts are

complete there must be some reason within their concepts that accounts for any

difference between them and this means that the two substances really would be different

(L 269). It is important to see that the denial of purely extrinsic denominations that

follows from the complete concept is central in supporting the identity of indiscernibles.

As I mentioned above, one of the easiest ways to conceive of a solo numero difference

between two things is to think about two objects that are internally alike and yet in two

different spatial locations. For Leibniz a spatial, external relation, must be reducible to a

truth contained within the related substances, thus a perceived spatial difference is the

result or is true because of a truth intemal to each of the substances. Leibniz makes this

quite clear in his fourth paper to Clarke, where he claims that external differences, in this

case for parts of space, must be dependent on intemal differences. “[A]ny external

reason to discern between them, can only be grounded upon some intemal one” {LC 39).

In addition to using the complete concept view of substance to argue for the

identity of indiscernibles, Leibniz also employs the principle of sufficient reason,

especially in his later wri t ings .In the “First Truths” paper Leibniz begins with the

predicate in subject view of trath and argues to the principle of sufficient reason, without

mentioning it by name, and then goes on to say that no two things in nature differ only

numerically (L 268). In this argument, Leibniz begins by making the now familiar

logical claim that for every affirmative trath the predicate is either contained explicitly in

the subject or it is implied and can be arrived at through the analysis of the concepts (L

267). From this logical truth, Leibniz claims that one can arrive at the “accepted axiom”

Russell in his The Philosophy of Leibniz claims that the complete concept view does not appear explicitly in Leibniz’s later writings because of the force with which Amauld picked on it in their correspondence. In keeping with his entire reading of Leibniz, Russell claims that this change was more for political reasons, i.e., the fear that others might single it out for criticism, than because of philosophical soundness (cf. 44). As I mentioned in chapter two, Donald Rutherford, in his Leibniz and the Rational Order of Nature, attributes this change to an evolving understanding of the monad and not due to political reasons (148-154).

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that “there is nothing without a reason, or no effect without a cause” (L 268). Leibniz’s

reasoning is the following. To say that there is something without a reason is to assert

that a certain predicate that is true of a substance does not follow from the concept of the

substance, i.e., is not an identity. TMs, however, is contrary to the nature of trath and

subsequently impossible. From the principle of sufficient reason it follows that no two

individuals can be alike because it must be possible to provide a reason why they are

different and this difference must come from within the individuals (ibid.). Another way

of saying the same thing is to assert that if two things are indiscernible then there is no

reason for their difference, thus they are actually the same thing considered differently.

In either case, it should be obvious that for the principle of sufficient reason to

accomplish Leibniz’s task here and support the identity of indiscernibles, all extrinsic

denominations must be dependent on intemal denominations, otherwise relational

properties or purely extrinsic denominations, such as location, could provide the reason

for the difference.

In his correspondence with Clarke, Leibniz begins with the principle of sufficient

reason and argues from it exclusively. Leibniz defines the principle of sufficient reason

in the “Principles of Nature and Grace” as: “nothing occurs for which it would be

impossible for someone who has enough knowledge of things to give a reason adequate

to determine why the thing is as it is and not otherwise” (L 639). Of course, because the

complete concept of a substance is infinitely complex, for contingent truths the analysis

to reasons is infinite and thus God is usually implicated in Leibniz’s discussion of this

principle. The manner in which God is brought into the discussion by Leibniz is not

necessarily as an omniscient but an omnipotent being. Thus, the focus is usually on

God’s choice to create substances and not his knowledge of them per se. For example,

Leibniz tells Clarke in his fifth letter that:

I infer from that principle [the principle of sufficient reason], among other consequences, that there are not in nature two real, absolute beings, indiscernible from each other; because if there were God and nature would act without reason in ordering the one otherwise than the other; and that therefore God does not produce two pieces of matter perfectly equal and alike. {LC 61)

For Leibniz, God has two separate capacities, will and reason, and they both act

together when He creates. WMle it is within God’s power to will the creation of two

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identical things, this would be a “will without a motive” and subsequently contrary to

divine reason {LC 79). Two indiscernible things would be completely identical and God

would have no reason to choose to create one rather than the other. Leibniz also points

out that it is wrong to conceive of God as creating substances and then placing them in

the world. Rather God considers all of the means and all the circumstances when he

chooses to create things {LC 78). In other words, God considers all the substances and

their interrelation prior to their creation.

This is a rough sketch of the identity of indiscernibles at the level of substance,

i.e., at the monadic level. However, as I pointed out above, Kant’s real problem is with

the application of this principle to material bodies. In order for Leibniz to respond to this

criticism it is necessary to figure out why he extended the identity of indiscernibles

beyond the simple monads to the bodies that they well found. I would like to consider

several possible candidates for this explanation before looking at Leibniz’s possible

responses to Kant.

IV. Source of the Principle at the Level of Body

In Leibniz’s metaphysics there are certain parallels between the monadic and the

material levels. As we have seen, Leibniz’s complete concept view of substances entails

that each substance is completely determined. The completeness of a monad is achieved

through its infinite perceptions. The analog in material bodies is their composition out of

determinate, but infinite parts. “But in real things, that is, bodies, the parts are not

** I will discuss the use of the principle of sufficient reason to support the identity of indiscernibles, especially the “divine choice” version of the argument, in more detail in section Iil.2 below.

Perhaps the easiest reply to Kant would be to claim that in fact the identity of indiscernibles does not necessarily apply to material bodies at all. Nicholas Rescher in his Leibniz: An Introduction to his Philosophy claims that the identity of indiscernibles does not necessarily apply to material bodies. Rescher views the identity of indiscernibles as deriving directly from Leibniz’s logical view of “one concept—one substance” (50). He claims that the identity of indiscernibles is not necessarily applicable to phenomena, i.e., bodies, because phenomena might not be distinguishable to humans with their limited observational powers. However, things are distinguishable by God who alone knows “the complete individual notions of the substances at issue” (52). I am very skeptical of Rescher’s claims here for a number of reasons. First, Rescher seems to be ignoring the distinction that I drew above between discemibility and identity. Second, Rescher moves from bodies to the monads that well found them too quickly. While this may be in keeping with his larger position on Leibniz, I want to grant more ontological status to material bodies. Lastly, there is the simple fact that Leibniz constantly uses examples of material bodies to support the identity of indiscernibles. While I agree with Rescher that the identity of indiscernibles may derive from the monadic level, I disagree that it isn’t a ubiquitous principle for him.

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indefinite ... but actually specified in a fixed way according to the divisions and

subdivisions which nature actually introduces through the varieties of motion” (L 536).

The perceptions of the monads also allows them to express all the other monads. Just as

with monads, each material body influences and is influenced by every other body in the

universe, although the influence in the material world is one of physical interaction.

“Every body acts on every other body, and is acted upon by it” {YLC 249). Also, like

monads, each material body is unique, which entails that no two bodies are identical.

“Hence it cannot happen in nature that two bodies are at once perfectly similar and equal”

(L 529). This entails, I thinlc, that Leibniz intended the identity of indiscernibles to apply

to material bodies. As I mentioned above, the anecdote involving Princess Sophie and

von Alvensleben looking for identical leaves in her garden is Leibniz’s favorite empirical

example of the identity of indiscernibles at work.

Kant is in agreement with Leibniz on the infinite divisibility of material bodies

and their interrelation, yet he denies the claim that no two bodies in nature are alike. For

Kant, material bodies are appearances and essentially spatial and temporal, thus they can

be individuated based on spatial and temporal properties. It is just common sense, Kant

claims, that two identical objects can exist in different locations. The reason for their

differentiation is simply that object A is in location Li and object B is in location Li,

regardless of their intemal properties. Leibniz denied common sense because he

illegitimately applied logical principles to material bodies. According to Kant, Leibniz

thought he could make this extension because he took material bodies to be intellectual

entities confusedly perceived. I have already argued against this “confusion” reading of

Leibniz in chapter two. There I advocated an ontological distinction between monads

and the bodies that result from them. Even if that reading is correct, it remains to be

explained how Leibniz can apply the identity of indiscernibles to material bodies. For

example, Leibniz allows that collision and impact can occur in material bodies, but not in

monads. If this physical influence occurs at the material level, why can’t material bodies

be identical even if the underlying monads are not? In other words, why can’t there be

two identical drops of water in two different locations on Leibniz’s view?

There are two things that I would like to note before I tackle this question. First,

Leibniz does not deny that we can imagine two identical objects that differ only in

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number, but he claims that in doing so we are working either with incomplete or abstract

concepts (L 268). Geometry, for example, deals with identical lines or shapes. We can

imagine things “diverse without diversity” such as “two equal parts of a straight line”

because the line is “incomplete and abstract” (L 529). The incompleteness of abstract

entities allows them to be identical to each other in a way that real, determinate things are

not. “But in nature every straight line is distinguishable by its content from every other”

(ibid.). It may also happen that through our senses we perceive certain bodies as being

identical or homogeneous, but this is only because of the limitation of the senses and is

not true in an “exact sense” (L 268).

Leibniz does seem to indicate that we can imagine determinate things that are

identical to each other when he makes the following claim in his fifth letter to Clarke:

W hen I deny that there are tw o drops o f water perfectly alike, or any two other bodies indiscernible from each other; I d on ’t say, ‘tis absolutely impossible to suppose them; but that ‘tis contrary to the divine wisdom, and which consequently does not exist. {LC 62)

Leibniz is saying that while it is not a contradiction to posit two identical objects, it is

contrary to God’s wisdom. As I mentioned above, God not only wills when He creates,

but also uses His reason. Thus, while God has the power to create two identical objects,

His reason would prevent Him from creating two identical objects that even He could not

tell apart.

Second, Leibniz does allow that we can use differences in location for purposes of

discemibility, even though it is not a part of the identity of objects. “Thus, although time

and place (i.e., the relations to what lies outside) do distinguish for us things which we

could not easily tell apart by reference to themselves alone, things are nevertheless

distinguishable in themselves” (NE 230). In fact, spatial location is often the only way

that we can account for the identity of individuals, given that each body is infinitely

complex. “You see, paradoxical as it may seem, it is impossible for us to know

individuals or to find any way of precisely determining the individuality of any thing

except by keeping hold of the thing itself’ (NE 289). Leibniz states that due to our

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epistemic limitations, the only way that we can account for the individual is by direct

contact with the thing, which I take to be a function of the object’s spatial location.'*

With those caveats in mind, I would like to consider four possible reasons why

Leibniz applied the identity of indiscernibles to material bodies: 1. Leibniz simply

assumed similarities between concepts, monads, and material bodies 2. The principle of

sufficient reason 3. Monads are forms of bodies and thus the individuation is an extension

of monadic individuation 4. Leibniz held the impossibility of indiscernible identicals for

empirical reasons.

IV. 1 Freedom of Application

Throughout his writings, and especially in the early works of his mature period,

i.e., 1686 and beyond, Leibniz has a tendency to move freely between propositions,

concepts, and things, often using these terms and their extensions interchangeably.

Benson Mates, in his The Philosophy o f Leibniz, focuses on Leibniz’s tendency to be

careless of the distinction between propositions and sentences as well as his tendency not

to distinguish between “concepts and the individuals falling under them.”' We have

already seen an indication of this in Leibniz’s discussion of the complete concept in the

Discourse. There Leibniz uses the claim that a complete understanding of a concept will

entail that one will know what predicates “appertain” to it (DM §8 13). From this he

transitions, in the next sentence, to a discussion of the nature of an “individual substance”

or “a complete being,” and in the following sentence goes on to use Alexander the Great

as an example (ibid.). In the course of one paragraph it seems that Leibniz has moved

from a logical finding about complete concepts, to a truth about substances, and then on

There is evidence that early in Leibniz’s career space and time were the determining factors in distinguishing objects. In his 1673 work Confessio philosophi, Leibniz claimed that two eggs could be so similar that “even an Angel (on the assumption of [the eggs] perfectly similarity) cannot discern a difference” {CP 125). Leibniz goes on to claim that “it is possible neither for an Angel nor, dare I say, for God to establish another differentiation between the eggs ... other than that at the present moment this [egg] is in place A and that [egg] is in place B” {CP 127). In other words, Leibniz is claiming that two objects can be so similar that even God can only tell them apart by their spatial and temporal location. That Leibniz is using a different standard of individuation is clear when he identifies the “Principle of Individuation” as “the differentiation of things, which are to be differentiated solely by their number [solo numero]" {CP 125). As for the discrepancies between Leibniz’s writings in the Confessio and his later works, I simply chalk these changes up to his philosophical development.

Mates, The Philosophy o f Leibniz: Metaphysics and Language, 50.

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to a truth about a material thing, Alexander, which may or may not qualify as a

substance.

With regard to the identity of indiscernibles, I think that there are two kinds of

assumptions that are especially important. The first is Leibniz’s move from the predicate

in subject view of truth to the property in substance view of substances as a way to

exclude purely extrinsic denominations. The second is the move from substances to

material bodies.

I have already discussed Leibniz’s view of truth as essentially that of identity. On

this view, a true proposition ascribes a predicate that is contained within the subject.

Thus, one can say that the predicate is contained within the concept. However, for

essentially the same reason, Leibniz describes all properties as being “within” the

substance. For example, Leibniz claims the following as his fundamental principle in a

letter to Amauld: “there must always be some foundation for the connection of the terms

of a proposition and this is found in their concepts” {DM 132). From this Leibniz

concludes that all denominations of the substance are contained within it and “every

individual substance or complete being is ... a world apart” {DM 133). In this particular

argument Leibniz is clearly moving from every predicate being contained in the subject

in a logical sense to the claim that every property is in the substance in a physical sense.

How is Leibniz able to move from the concept of the substance to the substance itself?

That this is an illegitimate move is essentially Kant’s criticism of Leibniz.

Remember that Kant claims that Leibniz confused objects and their concepts. While

Kant was not aware of, or ignored, the specific Leibnizian terminology of denominations

and complete concepts, the criticism is the same. According to Kant, there is no reason

why substances must be individuated in the same way that their concepts are. Kant’s

claim is that the intuition adds information to the individual that is not contained in the

concept alone, although it is a truth that is predicated of it. This means that objects can

be individuated based on information provided by the intuition, even if the concepts are

the same. The necessity of the intuition in our sensible interaction with the world also

ensures that this information is necessarily attributed to the objects. We cannot know the

objects through their concepts alone. Thus, Kant’s criticism cuts against Leibniz’s denial

of purely extrinsic denominations and the identity of indiscernibies.

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Now, if at this point we are strictly talking about the move that Leibniz makes

from concepts to substances, then perhaps Leibniz has some room to maneuver away

from Kant’s criticism. If we ignore the more basic Kantian criticism that because we

cannot sensibly intuit monads we cannot know anything about them, then perhaps he

would grant that monads as strictly inteilectuai entities are more closely aligned to their

concepts. Leibniz also has independent arguments for the simplicity and isolation of

monads, e.g., his claim to Arnauld that a being must be a being. However, these kinds of

arguments do not apply to material bodies, which are a collection and physically

connected to other bodies. This brings up Leibniz’s second move from substances

(monads) to bodies.

There are many instances of Leibniz moving seamlessly from talk of substances

to bodies. For example, in a letter to De Voider, Leibniz claims that “two individual

substances must be distinguished more than modally” (L 528). In this denial of a

Cartesian possibility for distinguishing extension, e.g., through its shape or motion,

Leibniz is presumably referring to monads when he mentions substances. However, he

next asks De Voider to assume two bodies that are similar and asks if it is possible for

them to be internally identical. A little later he refers to the possibility of two things

being diverse, which completely blurs any distinction between substances and bodies.

The same kind of blurring occurs in the Monadology, where Leibniz claims that “it is

even necessary for each monad to be different from every other” {Monadology §9 L 643).

He goes on to claim that there are never “two things in nature which are perfectly alike”

(ibid.). Are “things in nature” monads, bodies, or both?

In Leibniz’s defense, he does sometimes acknowledge the difference between

substances and bodies. In the Monadology, in his discussion of the relation of all monads

to each other, he maintains that the same is true for material bodies and states that a

“symbolic agreement” exists between the compound and the simple {Monadology §61 L

649). But what does it really mean to say that there is a “symbolic” agreement? Leibniz

seems to be simply asserting that they are similar in this regard without really providing a

reason why this is the case.

There are two things that I would like to say about this move from substances to

bodies on the topic of the identity of indiscernibles. First, I want to look at more

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evidence on the application of the identity of indiscernibles to material bodies before

giving any final comments on this move. Presumably Leibniz is doing more than simply

assuming the similarity between the two. Second, there is no doubt that on the whole

Leibniz is less than careful in some of his discussions of these topics and the relation

between logic, language, ideas, and things; however, I think that Leibniz did maintain a

symmetry between all of these things but that he thought his principles provided him

license to do this. Thus, I think that it is better not to see Leibniz’s asserted symmetry

between concepts, substances, and things as a slip of the pen or mere carelessness on his

part, but a belief that in certain respects one can move freely between these things

because there is a connection between things and their concepts. For example, when De

Voider claimed that they were really debating about the concept of substance and not the

nature of substances themselves, Leibniz asks, “are not concepts themselves formed from

things?” (L 518). He continues on to claim that “it is not about concepts but about the

objects of concepts that we say entities are either real or rational” (ibid.). Thus we can

see that Leibniz is at least taking himself as talking about more than concepts, but about

the things themselves.

IV.2 The Principle of Sufficient Reason

A second possible account of the application of the identity of indiscernibles to

material bodies relies on the principle of sufficient reason. Again, according to this

principle nothing happens without an adequate reason or there must be a reason why a

thing is as it is and not otherwise (L 639). This principle requires that there must be a

reason why substance A is in state Si at time T, rather than in state Si. This principle also

entails that there must be some reason why substance A is different from substance B.

I have already briefly described the principle of sufficient reason’s application at

the monadic level, but why should this “great principle” of reasoning apply at the

material level as well? If, as I mentioned above, Leibniz allows for the possibility of

collision and impact between material bodies and there are other properties of the

material world, e.g., size, shape, and sensible qualities such as color and texture, etc., that

are not found at the monadic level, why can’t indiscernible identicals also exist at the

material level? What is to prevent two different constellations of monads from

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generating two identical material individuals, e.g., two identical drops of water? Leibniz

himself claims in the New Essays in a discussion of our process for distinguishing species

that it could happen that “two different constitutions result in the same appearance” {NE

309). Thus, the same color blue can occur in the rainbow as occurs in a turquoise (ibid.).

Why and how would the principle of sufficient reason prevent indiscernible identicals?

Also, it seems that even if one accepts its application at the materia! level, spatial location

could serve as the reason for the difference. This solution would preserve the principle of

sufficient reason yet deny the identity of indiscernibles.^®

To begin to reply to these questions, I think it is relatively clear that Leibniz does

intend the principle of sufficient reason to apply to the world in all respects or at all

levels. This is because he understands the principle of sufficient reason as a principle

applying to all contingent truths. Truths that are necessary are covered under the

principle of contradiction and are called truths of reason {Monadology §33 L 646).

Truths that are contingent, or truths of fact, are those truths for which its opposite is

possible (ibid.). Truths of fact are covered under the principle of sufficient reason. For

example, in the Monadology, Leibniz claims that by virtue of this principle, “there can be

found no fact that is true or existent, or any true proposition, without there being a

sufficient reason for its being so and not otherwise” {Monadology §32 L 646). Leibniz

hints at the ubiquity of the principle of sufficient reason in the New Essays when he

claims that “nothing happens without a reason” {NE 179).

The principle of sufficient reason manifests itself in two ways in the material

world. First, it is a principle of causality, thus every state of a being follows from a

preceding one and every motion arises from a preceding motion (L 486, 639). This

“physical necessity” ensures that later things are determined by earlier ones (L 486). The

second manner in which the principle of sufficient reason manifests itself is through final

causes. These are God’s reasons for choosing to create the world based on the criterion

of the best. As I pointed out in chapter two, God’s principal plan when creating the

universe was to maximize variety and order (L 639). Accordingly, God has created the

most ordered universe with the greatest variety of things, in other words the best of all

“ Kant often claims that even if the principle of sufficient reason applied at the material level, which he thought that it did not as it is merely a logical principle, difference in location could be the reason for the differentiation, e.g., WRP 99.

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possible worlds. This order also extends to things that we would call miracles and seem

to fall outside of the natural order of things because these things are still within God’s

more general plan for the universe (DM §7 11).

The upshot is that for any materia! event, E, or particular state of a being, S, there

will be two available explanations. The first is E or S’s causation by physical means and

the second is God’s choice of E or S as the best possible event or being. Leibniz

maintains that any complete dynamics or physics will have to take into account both

kinds of reasons. For example, God chose the laws of motion not for purely physical

reasons, but for “abstract or metaphysical reasons” as well (L 639). Thus, one must have

“recourse to final causes,” i.e., God’s choice of the best, in addition to “efficient causes or

matter alone” in order to fully explain the laws of motion (ibid.).

While the principle of sufficient reason may apply to the material and monadic

levels for our world, could God have created a world that wasn’t orderly and in which the

principle of sufficient reason did not apply? I think not, principally because of the way

that Leibniz conceives God. As I pointed out above, for Leibniz, God’s act of creation is

a function of both His will and His intellect. For God to create a world randomly or

without order would be for His will to act without His intellect, i.e., without reason.

“And God’s perfection requires, that all his actions should be agreeable to wisdom; and it

may not be said of him, that he has acted without reason” {LC 60, cf. 79). Leibniz also

points out in the Discourse that God couldn’t operate in an unorderly way. He uses the

analogy of points jotted randomly on a piece of paper. No matter how seemingly random

the arrangement of dots, a geometrical line could be found whose “concept shall be

uniform and constant, that is, in accordance with a certain formula” and which passes

through all of the points in the order that they were put down {DM §6 10). “Thus we may

say that in whatever manner God might have created the world, it would always have

been regular and in a certain order” {DM §6 11), even if that order might appear arbitrary

and random to us. Thus, it seems that the principle of sufficient reason applies not only

to all aspects of this world, but also to any other possible world that God could have

created as well.

Leibniz has two different kinds of arguments employing the principle of sufficient

reason in support of the identity of indiscernibles. The first is perhaps better known and

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appears extensively in the correspondence with Clarke. It appeals directly to God and Ms

choices in creating material entities.

In his reply of Leibniz’s fourth letter, Clarke asks why God couldn’t have a

reason to create two identical objects and then subsequently use Ms reason to place them

in a certain location {LC 49-50). Leibniz’s response is that this is an inadequate way of

understanding God. Although humans may operate in this “abstract and imperfect” way

when they create objects, God considers the ends, manner, and circumstances all at once

{LC 78). In fact, God’s resolution to create takes in the “whole universe” (ibid.). This

means that God could not create two identical objects and then place them, rather he

considers their location as part of their creation. “God will not choose to create a cube,

without choosing its place at the same time” (ibid.).

This argument is not convincing as it stands, however. All Leibniz has shown is

that God considers the object’s location when He creates it; this does not rule out the

possibility that two identical things can occur at different locations and the location itself

could be the reason for their difference. Leibniz needs the additional claim that the parts

of space are identical. This is a point on which both he and Clarks agree. In his fourth

letter, Leibniz claims that, “space being uniform, there can be neither any external nor

intemal reason, by wMch to distinguish its parts, and to make any choice among them”

{LC 39). Clarke agrees on the “uniformity of all parts of space,” but claims that space’s

homogeneity is no argument “against God’s acting in any part, after what manner he

pleases” {LC 49). Leibniz’s response is that Clarke is misunderstanding the nature of

God and how He operates. If the parts of space really are all the same, then “there is no

way to find any reason for assigning them [two identical cubes] different places” because

“there would be a will without a motive” {LC 79). If God placed identical objects in a

certain location (all of which are identical). He would be doing so without a real reason.

This violates the principle of sufficient reason and is contrary to God’s nature, which

employs both will and reason (ibid.). This means that objects must be intemally different

to provide God a reason to create and place them.^^

I can think of at least two examples that are helpful in fleshing out Leibniz’s ’ point here. If we imagine God creating a universe composed of only two identical things, then according to Leibniz God would have no reason to place one in one location as opposed to another. We can also imagine a world such as ours, i.e., fully populated with objects, that contained two intemally identical objects. In this case God would

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This form of the argument is conciliatory to Ciarke, because Leibniz is basing Ms

argument on the homogeneity of space. However, as I explained in chapter three,

Leibniz holds a relational view of space and time. He also holds that in themselves space

and time are not real things, as Clarke and Newton hold, but ideal things. According to

Leibniz to see space as differentiating objects is impossible because the objects are prior

to space. “The parts of space are not determined and distinguished, but by the things

which are in it: and the diversity of things in space, determines God to act differently

upon different parts of space” (ibid.). Leibniz’s relational view of space entails that space

arises only as the relation of the objects, or possible objects, thus to derive truths about

the objects from what is actually posterior to them is impossible. “[Tjhings which differ

in position must express their position, that is, their surroundings, and are hence not to be

distinguished merely by their location or by a solely extrinsic denomination” (L 529).

“[I]t is by means of things that we must distinguish one place or time from another, rather

than vice versa” (NE 230). The claim is that we can only call a place this place or that

place because of the objects that differentiate them.

In itself this argument is not really based directly on the principle of sufficient

reason. Leibniz is simply appealing to his relational view of space to dismiss the

possibility of location differentiating object. However, one of the reasons why Leibniz

sees space as ideal or an abstraction and subsequently holds Ms relational view is because

of the principle of sufficient reason. Because each part of space is identical to each other,

there is no way to differentiate spaces, thus they cannot be real. “But space without

things, has nothing whereby it may be distinguished; and indeed not anytMng actual” (LC79)22

Leibniz also raises the possibility of interpenetration to illustrate that space cannot

be used to differentiate objects and that the individuation must come from within the

individual. In the New Essays Leibmz has his character Theophilus make the following

claim to Philalethes, who represents Locke.

have no reason to place A in location Lj and B in location L, rather than the other way around. In other words, the locations of the two objects could be switched without any real change. This, according to Leibniz, violates God’s reason.“■ It is interesting to note that Leibniz and Kant work with essentially the same premise that parts of space are indifferent to the objects that occupy them, yet arrive at very different conclusions about what this says about the objects that occupy those spaces. “[Pjhysical locations are ... quite indifferent to the inner determinations of things” {CPR A272/B328).

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The method that you seem to be offering here [differentiations based on time and space] as the only one for distinguishing between things o f the same kind, is founded on the assumption that interpenetration is contrary to nature. This is a reasonable assumption; but experience itself shows that we are not bound to it when it comes to distinguishing things. For instance, we find that two shadows or twm rays o f light interpenetrate, and we could devise an imaginary w orld where bodies did the same. Yet, we can still distinguish one ray from the other ju st by the direction o f their paths, even when they intersect. {NE 230)

The idea here seems to be that we could imagine two material bodies that

interpenetrate, i.e., lack any form of spatial differentiation, but can still be differentiated.

Leibniz takes this to mean that differentiation must arise from within the individual or

from properties that are internal to the object rather than from spatial, or temporal,

relations.

The second kind of argument that appeals to the principle of sufficient reason to

support the identity of indiscernibles relies on the determinate nature of material bodies.

I have already provided a quote to support Leibniz assertion of the determinate nature of

real entities from his correspondence with De Voider. “But in real things, that is, bodies,

the parts are not indefinite ... but actually specified in a fixed way according to the

divisions and subdivisions which nature actually introduces through the varieties of

motion” (L 536). Real things are to be contrasted with abstract entities whose parts are

not determinate and whose concept is vague. Abstract entities also cannot be resolved

into determinate parts in the same way that real entities can. For example, a line (as an

abstract, mathematical object) is not composed of parts and is infinitely divisible. Real

things are also infinitely divisible, but these divisions are “all the result of fixed primary

constituents or real unities, though infinite in number” (ibid.). The infinite division of

material bodies also means that there is “no precise and fixed shape in bodies,” thus we

cannot find a perfectly straight line nor a perfect circle in nature {YLC 297, 315). Each

object will have some infinite variation that will prevent them from matching up with

perfectly uniform geometrical shapes. For example, we will never find in nature a circle

that is perfectly circular. Due to the determinate nature of material bodies, Leibniz not

only holds that real entities will not perfectly match ideal entities, but also each body will

differ from every other body. Leibniz points out in the introduction to the New Essays

that variation in the individuals will lead to their individuation. “I have also pointed out

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that in consequence of imperceptible variations no two individual things could be

perfectly alike, and they must always differ more than numerically” (NE 57).

I have included the determinate nature of bodies under the principle of sufficient

reason because I believe that Leibniz’s principle reason for positing material bodies as

completely determinate entities is because of the principle of sufficient reason.

Indeterminacy in a body simply indicates that there is no reason why it has the nature that

it has or that there are many possible ways to divide the object without any reason for the

division.^^ For Leibniz, the complete determination of material bodies is achieved

through the infinite divisibility along definite lines, which is so because they result from

an infinite number of monads.

I have identified two different types of argument that employ the principle of

sufficient reason in support of the identity of indiscemibles, one follows from God’s

choices and the other from the nature of space and the things in space. In each of these

cases we find that Leibniz’s project is to look within the individual for its principles of

distinctness and reject external denominations as relevant in the individuation of

individuals. These kinds of arguments are clearly central to his endorsement of the

identity of indiscemibles since the most obvious objection to this principle is that

location, in either space or time, should qualify as a criterion for distinguishing objects.

IV.3 Monad as Form of the Body

A third possibility for applying the identity of indiscemibles at the material level

involves using the monad as the “form” of the body. This view represents a kind of

inversion of the traditional Aristotelian view. Rather than seeing matter as what

individuates within a species, the monad (form) that dominates a particular body

individuates that body and provides for its continued identity over time.

^ One might ask why there must be divisibility at ail. For example, an atomist might claim that there is some degree of division in material bodies, but that it terminates in atoms at some point. Leibniz has specific arguments against this possibility, some of which rely on the principle of sufficient reason. In the postscript to his fourth letter to Clarke, Leibniz asks why God would choose to create the vacuum that must accompany atoms and how he would choose the ratio of void to atoms (LC 44). Leibniz also asks, “what reason can one assign for confining nature in the progression of subdivision?” (ibid.). Leibniz is asking what reason could be given why God would limit the division of matter as atoms require.

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Leibniz employs the temiinology of the monad as the form of the body

throughout his mature writings. This idea is especially prevalent in his correspondence

with Des Bosses and his contemplation of the possibility of a “substantial form” that

would allow composite bodies to be real substances. In chapter two I dismissed the

substantial form as a real possibility for Leibniz and described this correspondence as

Leibniz exploring possibilities with a trusted friend rather than actively asserting the

existence of such a form. In other places Leibniz simply talks about the soul as the form

of the body. For example, in his “First Truths” paper Leibniz claims that, “there is

something in corporeal substances analogous to the soul, which is commonly called

form” (L 269). In the “Principles of Nature and Grace” Leibniz claims that each body

has an “outstanding simple substance or monad which forms the center” and “is the

principle of its uniqueness” (L 637). Also, in the New Essays he discusses the

importance of such a form to provide for the identity of bodies over time. “[0]ne can

rightly say that they [those substances which have a real unity] remain perfectly ‘the

same individual’ in virtue of this soul or spirit which makes the I in substances which

think” {NE 232).

What Leibniz is getting at here seems pretty clear for things like human beings. A

human being is composed of a dominant monad, the soul, and a body which is also

composed or results from an infinity of other monads. The relationship of domination

and subordination is a function of the clarity of the perceptions of the participating

monads, just as is the case for activity and passivity among monads (Monadology §52 L

648). '* Bodies are not static for Leibniz; the body of a human being is constantly

changing, i.e., getting and giving off parts, but the dominant monad remains the same

throughout. The dominant monad is also unique, as all monads are, and it extends that

uniqueness to the body as the body’s “form.” Thus, Leibniz claims in his “New System”

paper that the “by means of the soul or form there is a true unity corresponding to what is

called T in us” (L 456). The situation is basically the same for animals and other

^ For Leibniz the connection between the clarity of perceptions and action is that substances are active when their perceptions are approaching a state of greater clarity and are passive when their perceptions are becoming more confused (NE 210). Thus, action is an “endeavor towards perfection” while passion is the opposite (ibid.).

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organic beings, where the dominant monad would provide for a principle of “vital” unity

over time {NE 232).

The application of this view to inorgariic things is much more problematic,

however. It is very difficult to see how an inorganic thing, e.g., a rock, can have a

dominant monad that can provide for its uniqueness.Moreover, if we hold Leibniz to

his claim that bodies are in a constant state of flux and only “equivalent” from moment to

moment, then the rock would not only lack a principle of uniqueness, but would be

constantly changing over time. The result is a very chaotic view of the world. Not only

would each individual be unique from every other, i.e., be its own species, but also from

moment to moment each material thing would be different in itself. Leibniz seems to

accept this result.

Two physical individuals will never be perfectly the same species in this manner [as geometrical shapes can be in the same species], because they will never be perfectly alike; and furthermore, a single individual will move from species to species, for it is never entirely similar to itself for more than a moment. {NE 308)

Those things that we consider as all belonging to one species or as being identical

individuals, do possess a similarity in nature and it is one the basis of this similarity that

we draw our distinctions. However, those things that we take to be individuals of the

same species are in fact unique, even if that uniqueness is not available to us. “It can be

said ... that whatever we truthfully distinguish or compare is also distinguished or made

alike by nature, although nature has distinctions and comparisons which are unknown to

us and which may be better than ours” {NE 309).

The limitation of the form of the body to organic beings means that it is at most a

partial answer to the application of the identity of indiscemibles to material bodies.

Because inorganic things lack a dominant monad, Leibniz must provide another account

of why these things, e.g., two rocks, are different from each other.

One might ask, but what of the monads out of which the rock is composed, can’t they provide for the identity of the individual? It is true that Leibniz maintains that every monad is associated with some body, but these are the monads out of which the rock is aggregated and not the rock itself. Leibniz explicitly denies a substantial form in inorganic bodies in his 1705 paper “Consideration on Vital Principles and Plastic Natures.” “I say 'No' to anyone who takes the term [substantial form] in the sense of those who imagine that there is a substantial form in a piece of stone or in any other inorganic body” (L 586).

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IV,4 Empirical Reasons

In addition to Ms “metaphysical” reasons for applying the identity of

indiscemibles at the material level, Leibniz also provides empirical support. Leibniz tells

us that von Aivensleben’s inability to find two identical leaves convinced Mm “by his

own eyes that a difference [between materia! bodies] could always be found” (NE 231).

Experience in the material world reveals that every object is intemally distinct from every

other object. Leibniz tells Sophie in a letter of October 31, 1705: “There is true diversity

everywhere and never a perfect uniformity; no two pieces of matter entirely resemble

each other; in the large as in the small” (G 563). Even if two objects appear superficially

identical, closer inspection, such as through a microscope, can reveal a difference (LC

36). Thus, “there are never two pure drops of water where one cannot observe some

difference through closer consideration” (G 563). “It is our own imperfection and the

deficiency of our senses, which makes us conceive physical things as Mathematical

Beings, in which there is indeterminacy” (ibid.). By this Leibniz means that two lines or

two circles can be exactly identical, but this is only because they are abstractions. Two

real lines or two real circles, e.g., those that a geometer might draw on a piece of paper or

otherwise construct, may look identical, but they actually have some degree of difference.

Although Leibniz commonly refers to the leaves example, there is little doubt that

he didn’t think that empirical support could really prove the identity of indiscemibles at

the material level. Leibniz explicitly tells Sophie that the determinacy of material objects

is taught to the soul by the “divine perfection” and it is “what experience confirms by our

senses” (ibid.). In other words, experience just supports what is known through the

intellect.

One may ask why Leibniz is even coneemed with this kind of empirical support at

all. ® If material individuals are infinitely complex and known only to God in full, why

even bother with empirical examples? Even if we found two material entities that were

similar to the point that no scientific instrument could detect a difference, Leibniz would

continue to maintain that there must be a difference that could be discovered by finer

instruments or by God Himself. One could also cite Leibniz’s seeming disparagement of

“ Benson Mates asks this question in his The Philosophy o f Leibniz: Metaphysics and Language, 134.

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the empirical for providing proof for metaphysical principles. For example, in the New

Essays he claims that experience is like a “little wheeled device vAich keeps toddlers

from falling down” {NE 371). If experience is like training wheels and metaphysical

discoveries are made beyond the confines of the sensible, then why does Leibniz even

bother to provide examples of different leaves or eggs to support the identity of

indiscemibles?

I think that there are at least two answers to this question. The first draws on the

relationship between the sensible and the intellectual for Leibniz. According to Leibniz,

experience is limited in that it provides us with knowledge of individual cases but it can

point the way to general truths {NE 416). By itself experience can provide us with a

certain kind of physical certainty. “For it seems to me that, in the case of propositions

which we have learned from experience alone and not by the analysis and connection of

ideas, we rightly attain to certainty (moral or physical, that is) but not to necessity

(metaphysical certainty)” {NE 406).^ The identity of indiscemibles is a necessary

principle thus it must be proved through intellectual means, but this does not mean that

the sensible and the intellectual are at odds with each other. The sensible can be used to

support intellectual/metaphysical findings. “And the linking of phenomena which

warrants truths o f fact about sensible things outside of us is itself verified by means of

truths o f reason, just as optical appearances are explained by geometry” {NE 375). Thus,

I think that when Leibniz employs empirical examples such as the uniqueness of every

leaf in the garden, he is lending support to his principle, even if he is not proving his

principle metaphysically. The second that we must remember is that Leibniz was

someone who was very aware of his audience and was very concemed with convincing

his readers and critics through his writings. Therefore, examples of everyday things that

abide by his principle would lend further support to his principle and perhaps make it

easier to understand.

^ This statement is a bit confusing because Leibniz seems to be indicating two different kinds of certainty, which in itself is not entirely clear. What I think Leibniz is getting at here is that experience can provide us with a degree of certainty (he doesn’t want to invalidate scientific discoveries), but for true metaphysical certainty we must look to ideas and intellectual knowledge.

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V. Conclusion

I have looked at four possible explanations for Leibniz’s application of the

identity of indiscemibles to material bodies; 1. the extension of a logical truth about

concepts 2. the principle of sufficient reason 3. the dominant monad extends its

uniqueness to the material body 4. empirical reasons. As my comments above have

pointed out, I don’t take reasons three or four as plausible candidates. Viewing the

uniqueness of material bodies as an extension of the dominant monad’s uniqueness may

work for organic bodies, and especially human beings, but it does not work for inorganic

bodies and thus will not provide for the necessity of the identity of indiscemibles. I think

that the monad as form of the body is more an explanation of the identity of some bodies

over time, e.g., Leibniz as the same individual human being at time Ti and T2, and not a

real explanation of the application of the identity of indiscemibles to that material world.

Leibniz indicates the importance of a monadic form in providing for the sustained

identity of an organic individual in the New Essays. “But for substances [i.e., things, not

monads] which possess in themselves a genuine, real, substantial unity ... one can rightly

say that they remain perfectly ‘the same individual’ in virtue of the soul or spirit which

makes the / in substances which think” {NE 231-2). It is the dominant monad, which

forms the soul of the body in human beings that maintains the same “I” over time.

Shortly after this passage Leibniz questions whether plants and “bmtes” have souls. If

they do have souls then their identity is “strictly genuine” and if not “their identity is only

apparent,” but in either case their “organic bodies do not retain such an identity” {NE

232). This statement makes it clear that while the dominant monad may provide identity

to the “I” over time, the body of the individual is constantly changing and is not identical

from moment to moment. Thus, even in bodies that do have a dominant monad, i.e., a

soul, the identity and the uniqueness of the body is not provided for by the dominant

monad. We may identify dominant monads through the body and the dominant monad

may provide for a functional unity, but it does not directly support the application of the

identity of indiscemibles to bodies.

I also do not think that the empirical evidence that Leibniz provides proves the

application of the identity of indiscemibles to material bodies. As I pointed out above,

Leibniz’s use of empirical examples is intended to support the application of the identity

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of indiscemibles to material bodies and is intended to make the principle clearer but it

does not prove the principle. In his largely epistemological paper “What is Independent

of Sense and Matter,” Leibniz reminds us that while the senses may “help us after a

fashion to know what is , ... they cannot help us to know what must be or what cannot be

otherwise” (L 550). That Leibniz did fee! that empirical evidence was helpful in

supporting his principle can be seen in his correspondence with Clarke wherein he claims

that “'tis a great objection against indiscemibles, that no instance of them can be found,”

but it is not the reason for the truth of the identity of indiscemibles {LC 62).

This leaves the logical reason and those associated with the principle of sufficient

reason to support the identity of indiscemibles. As I described above, Leibniz attributes

each monad with a complete concept, which contains every predicate that could possibly

be attributed to it. Due to the infinite number of predicates, the complete concept is

known fully only to God. Because each monad has a complete concept, each substance is

completely determined. Leibniz also claims that from the complete concept it follows

that there are “no two individual things in nature which differ only numerically” and

“there are no purely extrinsic denominations” (L 268). I pointed out above that Leibniz

seems to be moving seamlessly from predicate in subject to property in substance.

The matter seems more complicated for material bodies. Although Leibniz often

uses material examples, e.g., the two leaves or drops of water, to support the role of the

predicate in subject view of truth in proving the identity of indiscemibles, I don’t think

that material substances have a complete concept as monads do. Remember that material

bodies are constantly changing for Leibniz and constantly giving off and receiving parts,

no matter how stable they may appear to us. This should be starkly contrasted with

monads which are simple, generate all of their states intemally, and perfectly retain their

identity over time. Even if material bodies lack complete concepts, Leibniz still

maintains that material bodies are completely determinate, and this is achieved through

their infmite divisibility. The determinate nature of bodies is intended to be analogous, I

think, to the monad’s complete concept. If this view of material substances is correct,

then this means that Kant’s criticism of Leibniz confusing concepts and things, or logic

and physics, as found in the “Amphiboly” applies only to monads and not to material

bodies.

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There still remain a couple of problems though. First, does making material

bodies infinitely divisible along determinate lines really support the application of the

identity of indiscemibles to material bodies? CouldnT two bodies be determinate in the

same way? Certainly the divisibility of bodies does enable the identity of indiscemibles,

that is it allows them to be intemally different, but it doesn’t seem to lead to its necessity.

The infinite divisibility of material bodies along determinate lines does seem to be

effective as a way to argue against two popular forms of indiscemibles, namely atoms

and extension, the first of which is not infinitely divisible and the second of which is

homogenous. According to Leibniz material bodies exhibit neither of these properties

and thus ai'e not indiscernible in those ways.

The second problem is Leibniz’s denial of purely extrinsic denominations. As I

pointed out earlier, one of Leibniz’s reasons for denying the possibility of purely extrinsic

denominations at the monadic level is because all the properties are contained within the

substance. Insofar as each monad has a complete concept and is a mind-like entity

without any physical presence, the close connection between logic and metaphysics is

more understandable, even if it still has difficulties. However, Leibniz denies purely

extrinsic denominations at any metaphysical level. For example, in a letter to De Voider,

Leibniz claims that the fact that there is no denomination “so extrinsic that it does not

have a intrinsic denomination as its basis” is “one of my most important doctrines” (L

526-7). In the New Essays, Leibniz claims that distinguishing objects based on extrinsic

denominations alone is “contrary to the greatest principles of reason” {NE 231). Leibniz

is not explicit what “principles of reason” he has in mind here, but if he is referring to the

predicate in subject view as grounds for denying purely extrinsic denominations, then this

is especially problematic in its application to material bodies that have a physical

location, exhibit relational properties, and lack a complete concept.

Leibniz does have other, more metaphysical arguments for denying purely

extrinsic denominations. These are Aristotelian arguments that deny that accidents can

move from one subject to another. For example, in the New Essays Leibniz declares that

the possibility of an “accident’s passing from one subject to another” is “inconceivable”

{NE 224). In a letter to Des Bosses, Leibniz denies the possibility of a relation as a

purely extrinsic denomination when he says, “1 do not believe that you will admit an

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accident that is in two subjects at the same time” (L 609). According to Leibniz,

“paternity in David is one thing, sonship in Solomon another” and the relation between

the two is a “merely mental thing” (ibid.).

The upshot is that it seems that Leibniz’s strongest arguments for the application

of the identity of indiscemibles to material bodies rely on the principle of sufficient

reason. It is on the basis of the principle of sufficient reason that Leibniz is able to

discount perhaps the most important extrinsic denomination, namely space itself. As I

pointed out, Leibniz has a few different arguments to discount spatial location alone in

distinguishing material bodies and these arguments are especially pertinent in his

potential responses to Kant’s objections.

If we took specifically at Kant’s claim that it is simply common sense that two

identicals can be in different places, I think that Leibniz has two possible responses.

First, Leibniz could claim that two identical looking things could be in different places.

Closer inspection would have to reveal that what first appears identical does in fact have

subtle difference. Although Leibniz is willing to use empirical examples to support the

identity of indiscemibles, its metaphysical roots ensure that it cannot be disproved

through empirical means. Leibniz’s second possible reply is to claim that Kant is

conceiving two abstract objects, on the order of two identical circles or triangles. Leibniz

would allow that these abstract objects could be identical, but they are also not real and

could not be found in nature. If common sense allows for indiscemibles, then this just

shows common sense’s tendency to operate with vague or incomplete concepts. Every

real thing is determinate and although common sense can imagine two identical things, it

could not discover them in nature.

Finally, Kant claims that Leibniz’s view would eliminate space because all spaces

are homogeneous. I actually think that Leibniz’s response would be to agree with Kant.

Yes, he would claim, my view does do away with space. It shows that space is not a real

thing, and does not exist except as an idealization of the relations of material bodies.

Leibniz would also claim that we can add spaces to each other or imagine spaces outside

of each other, but these are mental activities and do not represent any reality outside of

the mind. In a way Leibniz would agree with Kant that in a sense we are responsible for

the existence of empty space because such a thing cannot exist in nature, but he would

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strongly disagree with the view that space is prior to the objects that are in space and he

would also disagree with the role of the senses/intuition in geometry.

In the end I think that there are two conclusions to draw from this discussion of

the identity of indiscemibles. The first is that Leibniz does have arguments to support the

application of this principle to material bodies, even if they are not always convincing.

Also, these arguments do not just move directly from conclusions about logical

principles, i.e., truths about concepts, to things in the way that Kant describes. In fact, as

I pointed out above, this version of Kant’s objection may actually be more effective at the

monadic level than the material, i.e., the move from complete concepts to monads.

The second thing to consider is that we again find Kant using his view that space

and time are forms of intuition as a way to argue against a Leibnizian principle, in this

case by claiming that spatial properties are integral to the identity of objects. While this

aspect of the debate may be irresolvable between the two, or at least reduces down to

their debate over the nature of space and time, Kant is able to provide an altemative to

Leibniz’s view that is quite strong. Whether Kant’s view of space and time as forms of

intuition is ultimately tenable or not, Kant has in any case provided us with a very rich

altemative to Leibniz’s view, which I think that someone like Clarke was unable to do.

Clarke ultimately seems to claim that God simply could create identical objects and that

space and time simply are things that are prior to the objects that are in them without

providing Kant’s rich theoretical foundation for the existence of indiscernible identicals.

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CHAPTER FIVE

PRE-ESTABLISHED HARMONY AND THE WORLD’S UNITY

For my final chapter I will examine Kant’s criticisms of Leibniz’s pre-established

harmony and possible Leibnizian replies to those objections. The pre-established

harmony is a well-known and central Leibnizian principle that is intended to explain the

interaction of the mind and the body. The pre-established harmony sprang from

Leibniz’s desire, which he shared with many of his contemporaries, to explain how the

radically different substances of mind and body could interact. He was dissatisfied with

other popular theories including Descartes’ view and Malebranche’s occasionalism,

which he took to involve the constant miracle of God’s intervention in the material world.

Leibniz’s solution was to deny any interaction between the mind and the body at all.

What we take to be the interaction between the two, for example the pain one feels when

a finger is pricked, is actually the result of a perfect harmony between the two. God pre-

established at my creation that at the moment my finger is pricked a corresponding .

perception of pain occurs in my mind, but without any real interaction between the mind

and body. This correspondence is so perfect that for every case of physical activity there

is an associated activity within the mind and for every act of the mind to will the body

there is a perfect correspondence in the body as well. It is important to see that this

correspondence is set up as an initial condition at the creation of the universe and is not

initiated by God at the moment that the event occurs, that would be a form of

occasionalism.

Leibniz uses the term “pre-established harmony” principally to explain the virtual

interaction of the mind and body. There is, however, another important harmony in

Leibniz’s metaphysics. This is the pre-established harmony between each of the monads.

As we have seen previously, each monad is a simple, independent entity that is

completely isolated from the other monads. This entails that the states of each monad are

intemally generated. At the same time, each monad reflects the entire universe and its

succession of states is coordinated with ail the other monads. Leibniz maintains that the

coordination of monadic states is enabled through a harmony of their perceptions that is

pre-established by God at their creation.

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Kant’s criticisms cover both roles of the pre-established h a rm o n y , but he tends to

focus on the latter role of the principle, namely its explanation of the virtual interaction of

the monads. Kant identifies two shortcomings of the view. First, Kant questions the

possibility of the completely simple, isolated substances that underlie the harmony.

Second, Kant objects that Leibniz’s view does not provide the basis for a single, unified

world, but instead establishes a plurality of worlds, each of which is external to the other.

The second criticism is unique to Kant and represents his long-standing dissatisfaction

with Leibniz’s ability to account for a unified world of interacting substances. In what

follows I will point out how developments in Kant’s philosophy allow his criticisms to

evolve and increasingly provide him the means to address the perceived shortcomings in

Leibniz’s view. I will also examine why Leibniz held the pre-established harmony and

how it relates to other aspects of his philosophy. Finally, I will look at Leibniz’s ability

to address Kant’s criticisms and I will explore the dialectic between the two on this topic.

Ultimately I will show that the disagreement provides further evidence for the central role

of the sensible intuition in distinguishing the two that I have been describing all along.

I. Kant’s Criticisms

Kant’s disagreement with Leibniz over the pre-established harmony can be traced

to very early in his philosophical career and to a time when he still maintained an

essentially dogmatic, i.e., Leibnizian and Wolffian, approach to philosophy. In his first

purely philosophical work A New Elucidation o f the First Principles o f Metaphysical

Cognition, which he wrote in 1755, twenty-six years prior to the publication of the first

Critique, we can already find Kant making serious objection to Leibniz’s position. The

work is comprised of thirteen propositions that are intended to “throw some light . . .on

the first principles of our cognition” {ND 5). The first three propositions deal with Kant’s

rejection of the principle of contradiction as the ultimate principle of truth in favor of a

law of identity. Propositions four through eleven deal with the “principle of the

determining ground” or the principle of sufficient reason. Propositions twelve and

thirteen, which are our concern, deal with two principles that derive from the principle of

the determining ground. In proposition twelve, Kant proves that “no change can happen

to substances except in so far as they are connected with other substances” and

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proposition thirteen proves that finite substances are connected in a state of harmony by

the divine understanding {ND 37, 40).

In proposition twelve, Kant provides three separate demonstrations of the need for

connection between substances if they are to experience change. In the first

demonstration, Kant asks us to begin by supposing simple substances that are completely

isolated from one other {ND 37). Each substance is in a particular state due to a certain

reason within the substance. Kant calls the state the “determination” and the reason the

“ground.” According to Kant, the presence of a particular ground in a substance means

that its opposite is excluded. In order for an isolated substance to change to another state,

there must be a ground within the object that causes the change. However, the opposite

of that ground is already in the substance and because there is no communication between

the substances it is “patently obvious that the new determination cannot be introduced

into the being” (ibid.).

An example should help to make Kant’s point clearer. Imagine a substance that is

blue. The blue color is a determination for which there must be some ground. Having

the ground for blue entails that the ground for red is excluded, otherwise the substance

would be blue and red, which is impossible. In order for the substance to become red

there must be a red ground, i.e., a reason for it to be red, but as we have seen that ground

is presently excluded from the substance, thus it cannot be generated intemally. Because

there is no interaction between the substances it is impossible for the red ground to come

from outside the substance. Consequently, without interaction there is no way for the

substance to change its states from blue to red.

Kant’s other two formulations of the argument are similar. In the second

demonstration, which he labels “the same differently,” Kant emphasizes the temporal

relation between a determination and its ground. His claim is that the determining

ground and its effect are simultaneous {ND 38). In other words, when there is a cause for

something, its effect is immediate or when the cause is present its effect is present also.

If the grounds for all of the determinations of a substance were really generated

intemally, then all of the different effects would have to be present in the substance

simultaneously, which is clearly impossible. Thus, the ground for the determination

cannot come from within the individual, but must arise from an “extemal connection”

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(ibid.). In Ms third variation of the argument, Kant points out that for a substance without

any external contact, because no new grounds are introduced into the substance, it must

be the same ground that both determines a substance one way and determines it in the

opposite way as well, which is “absurd” (ibid.).

One of the applications of this proof is that it “utterly overthrows the Leibnizian

pre-established harmony” {ND 39). If the human mind or sou! was completely isolated in

the way that the pre-established harmony understands, then according to this argument it

would be impossible to account for the changes that the mind experiences. Without the

connection of the mind and body, which Kant claims this proof requires, the soul would

have to be static; it could not intemally generate the grounds necessary to effect any

changes.

Kant emphasizes that this type of objection is different from those that are usually

leveled against the pre-established harmony. Instead of arguing against the principle by

means of “final causes,” this criticism emerges from the “intemal impossibility of the

thing itself,” i.e., the impossibility of isolated but changing substances (ibid.).'

After establishing the need for related substances, in the next proposition of the

New Elucidation Kant seeks to explain the nature of the relation. Kant claims that

substances in themselves have a separate existence {ND 40). In other words, there is

nothing within the substances that is the cause of their interrelation and the interrelation

cannot be derived from their existence alone. Yet, Kant claims, “all things in the

universe are found to be reciprocally connected with each other” {ND 41). The ground

for this relation arises through God. God has conceived, in addition to the existence of

objects, their interrelation; thus, “the universal interaction of all things is to be ascribed to

the concept alone of this divine idea” (ibid.). The nature of the interrelation is a

“universal harmony” of things that is enabled by God. Kant is quite adamant that this is

not the pre-established harmony, which is more “specific” and is only an “agreement

between substances, not their reciprocal dependency on each other” {ND 44). The

* Kant’s reference to the “final causes” that critics o f the pre-established harmony commonly focus on probably refers to the determinism that seems to follow if each state of the substance is preordained by God. He could also be referring to the seeming role that God would play in evil since He is choosing each of the actions every individual will take in their lifetime, including our evil ones. Leibniz has a reply to the second objection: he claims that God chooses the person that will sin and is not causing the sin Himself, but the first problem, i.e., that loss o f freedom that his view seems to entail, is something that Leibniz struggled with throughout his career.

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universal harmony is not occasionalism either, as on Kant’s view the universal inter

dependence of substances is established at their creation and not constantly maintained by

God as it is in occasionalism (ibid.). The interaction that Kant is positing is also better

than the “popular system” of physical influence, which tries to derive the interaction of

substances from their nature (ibid.). Kant’s proof is intended to show that something

more must be added to the concept of the substances to explain their interaction.

By the time of the Inaugural Dissertation thirteen years later, Kant has dropped

the argument against isolated substances, but continues to deal with the question of

interaction. At this point in his philosophical career Kant had begun to develop his

Critical views of space and time and had already rejected both the relational view and the

Newtonian absolutist view.^ However, Kant still had not established time and space as

forms of intuition and instead refers to them as “sensible laws.” He also had not limited

human cognition to the sensible and continued to be concemed with questions that are

purely intellectual and deal with the nature of substances in themselves. In other words,

Kant still allowed that the understanding alone is capable of making metaphysical

discoveries.

In section 4 of the Inaugural Dissertation Kant makes a rather speculative

investigation into the “form of the intelligible world.” The question that Kant asks is:

“what is the principle upon which this relation of substances itself rests, and which, when

seen intuitively, is called space?” or to put the question more generally “how it is possible

that a plurality of substances should be in mutual interaction with each other, and in this

way belong to the same whole, which is called a world” {ID §16 401). Kant also points

out that he is not concemed with explaining, “the natures of the substances of which it

[the world] consists,” but more generally how “a connection between a plurality of

substances comes to be” (ibid.).

As in the New Elucidation, Kant rejects direct physical influence as the correct

explanation of the relation of substances. The “itpcoxov of the physical

influence theory is that it maintains that from the existence of substances alone one can

posit their interaction {ID §17 402). As in his earlier work, Kant argues that something

In the New Elucidation Kant continued to maintain a Leibnizian, relational view o f space and time, and with Leibniz maintained that the substances themselves are prior to place, position, and space (ND 42).

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must be added to the concept of substance to explain their interaction; the interrelation

doesn’t follow from their existence alone. Kant goes on to explain that the world is

composed of contingent beings all of which derive their existence from one necessary

being, which provides the unity of the conjunction of substances {ID §20 403). While it

is metaphysically possible for there to be multiple worlds, the one necessary cause of the

world prohibits the possibility of multiple worlds existing outside of each other {ID §21

403). The common cause, i.e., God, that is responsible for the world also provides for a

“common principle” that sustains the interaction of all created substances {ID §22 404).

The result is a “generally established harmony,” which provides for real, physical

interaction between all substances (ibid.). This is different from an “individually

established harmony” that correlates individual states of the substances and allows for

only “ideal and sympathetic” interaction between substances (ibid.). In this work Kant

lumps the pre-established harmony and occasionalism together as both instances of an

individually established harmony. The only difference between the two is whether the

interaction is established at the creation of each substance (pre-established harmony) or

on the occasion of some change (occasionalism). On Kant’s view of universal harmony,

physical influence between substances is provided for and the world becomes a real

whole (ibid.). Because Kant takes interaction as the crucial element in establishing the

unity of the world, on either the pre-established harmony or occasionalism where the

interaction is only “sympathetic,” the world can only be an “ideal whole” (ibid.).

The universal harmony that Kant is positing here is clearly the same as, or at least

very similar to, the one that he posited in the New Elucidation. Although Kant has

provided a proof in both cases to establish the principle, I am not sure how secure he is in

his findings. Kant states his insecurity in the Inaugural Dissertation when he claims that

although his own view has not been demonstrated it has been rendered “fully acceptable

for other reasons” (ibid.).^ It is not clear how much Kanf s dissatisfaction on this

particular point motivated his philosophical development, but by the time of the first

Critique Kant is able to provide a very robust, but admittedly much different, account of

the interaction of substances.

■’ These “other reasons” are presumably the degree and kind of interaction that the view enables.

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Ib the Critique, Kant establishes space and time as forms of intuition and

integrates them as essential elements into human cognition, thereby eliminating his

ability to ask the Inaugural Dissertation question concerning the form of the world as a

whole. Human cognition is now limited to appearances, i.e., objects situated in space and

time, the totality of which Kant refers to as “nature” or “experience.” The role of the

Critique is, in part, to provide an account of the conditions of the possibility of our

experience and it is within the framework of human experience that questions concerning

the unity of the world and the interaction of substances must be asked.

The nature of the forms of intuition play an important role in establishing the

unity of the world. The singularity of the forms of intuition ensure that all objects are

located within a single space and time. One of the findings of the “Aesthetic” section of

the Critique is that “space is essentially one” {CPR A25/B39). When we talk about parts

of space or separate spaces, these must be part of one total space that encompasses them.

There is also only one dimension of time and different times are “not simultaneous but

successive (just as different spaces are not successive but simultaneous)” {CPR

A31/B47).

In addition to accounting for the singularity of the world, Kant is still concerned

in the Critique to explain the interaction between substances. Again, given the restriction

of human cognition to the sensible, Kant no longer has to provide an account of how

substances in general interact, but he must now explain the community of appearances.

This is Kant’s project in the “Third Analogy of Experience.” In this section Kant uses

the notion of “simultaneity” to demonstrate the necessity of the interaction of substances.

Very briefly, the argument runs as follows. Things that are simultaneous exist at the

same time and can be perceived reciprocally {CPR A211/B257). In other words, if A and

B are simultaneous with each other then it is possible to observe A and then B or B and

then A. Kant’s principle claim is that if objects were completely isolated from each

other, then it would be impossible to perceive them simultaneously because given the

separation of the objects it would be impossible to determine if a perception of A and

then B entailed that B succeeded A or was simultaneous with it {CPR A212/B259).

Because we experience simultaneity, it is necessary that there be a real or “dynamical”

community among all objects {CPR A213/B260).

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In the course of this argument, Kant distinguishes between a communio and a

commercium (ibid.). While both are kinds of communities, the latter refers to a

“dynamical community” or one in which there is interrelation among the parts (ibid.).

The former is simply a collection of parts forming a whole but without the interaction.

Although Kant doesn’t mention it by name, it seems that Leibniz’s world of reflecting but

independent substances would qualify as a communio but not a commercium. Kant is

ver} clear that he is after the second kind of relation. “But this is a reciprocal influence,

i.e., a real community {commercium) of substances, without which the empirical

simultaneity could not obtain in experience” {CPR A214/B261). Kant describes the

nature of the reciprocal influence as each object determining the other.

Thus each substance ... must simultaneously contain the causality of certain determinations in the other and the effects of the causality o f the other, i.e., they must stand in dynamical community . . . i f their simultaneity is to be cognized in any possible experience. {CPR A212/B259)

Kant is describing each object serving as a determination of the ground of the others and

thus simultaneity in experience can be realized.

I consider this argument as the heir of the one against simple substances in the

New Elucidation. There Kant established the need for a determination extemal to the

object if it is to experience change, yet at that point he still did not have a satisfactory

account of how that interaction could be realized. With the advent of the Critical

philosophy Kant develops a way to account for the interaction, i.e., within experience,

while changing the argument to provide for an aspect of experience: simultaneity."^

At the end of the “Analogies,” Kant, in a rather dense passage, argues that it is the

real relation or community of all objects that is responsible for the world being a real

whole.

'' Kant makes important changes to the B edition of the “Third Analogy” that give a more prominent role to the intuition o f space in providing for the interaction o f substances. For example, he changes the statement of intent of the section to “all substances, in so far as they can be perceived to coexist in space, are in thoroughgoing reciprocity” {CPR B256). Kant also adds an additional paragraph in which he emphasizes that the “coexistence o f substances in space” is enabled by their mutual interaction. As Kemp Smith points out in his commentary on the Critique, although Kant redirected the emphasis o f this section away from the form of time to the form of space, he does not “remodel his proof in a sufficiently thoroughgoing fashion” (385). Whether Kant’s proof is ultimately successfiil or not, this change is at least consistent with Kant’s later criticism in What Real Progress, where he also emphasizes the importance of the form o f space in providing for a unified world.

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The unity o f the world-whole, in which all appearances have to be connected, is evidently a m ere consequence o f the tacitly assum ed principle o f the com m unity o f all substances that are coexistent. For if they were isolated, they would not as parts constitute a whole. And if their connection (the reciprocal action o f the manifold) were not already necessary because o f their coexistence, we would not argue from this latter, which is a merely ideal relation, to the former, which is a real relation. We have, however, in the proper context, shown that community is really the ground o f the possibility o f an em pirical knowledge o f coexistence, and that the inference rightly regarded, is sim ply from this em pirical know ledge to com m unity as its condition. {CPR A218/B265)

I take Kant to be making the following claims here. He is saying that our

experience of coexistence requires a community with real interaction. This interacting

community of appearances or commercium is also the necessary condition of a unified

world, which Kant calls the “unity of the world-whole.” Earlier Kant claims that the

“Analogies” cannot be proven by concepts alone, which presumably Leibniz, Wolff, and

the other dogmatists tried to do. In the process they just ended up assuming the unity of

the world. According to Kant, he has brought these assumptions to light and provided a

real proof for the world’s unity.

It is not surprising then, that we find Kant’s principle argument in the Critique

against the pre-established harmony focusing on the conceptual approach that Leibniz

took to this problem. This criticism appears in the “Amphiboly” section under the

concepts of the “irmer and the outer.” According to Kant, Leibniz approached this pair of

concepts in the same manner as the other concepts of reflection, namely through the

understanding alone. Substances, considered in their concept or through the

understanding alone, must have an inner that is free of all outer relations, e.g., place,

shape, contact, or motion {CPR A274/B330). The only inner state that these simple

substances can possess is representations, as is the case with our own souls; our souls are

simple entities that are intemally complex due to the variety of perceptions within them.

The representing simple substances are the monads, which Leibniz considered the “basic

material of the whole universe” (ibid.). Because of the isolation of these simple

substances and the subsequent lack of any effective connection between them, the only

way to establish a community was through a pre-established harmony set up by “some

third cause” {CPR A275/B331). This correspondence is not an occasional influence, but

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is effected by “universal laws” responsible for their “existence and permanence, and

consequently also their reciprocal correspondence” (ibid.).

Kanf s criticism is that while Leibniz’s view may hold for things in themselves,

which we can only speculate about, it is not the case for matter, which is inherently

relational. The “absolutely inward [nature] of matter, as it would have to be conceived

by pure understanding, is nothing but a phantom” {CPR A277/B333). Only by

abstracting from the conditions of the intuition was Leibniz able to arrive at his false

metaphysics of simple substances that subsequently required the pre-established

harmony. Thus, Kant appeals to his findings earlier in the Critique, e.g., that all objects

are appearances and his findings in the Third Analogy, to discredit the pre-established

harmony.

Kant also uses the Critical philosophy and its principles to address the mind/body

relation, which the pre-established harmony is also intended to explain. Kant tackles this

relation in the “Paralogisms” section.^ Interestingly, Kant begins his discussion by

agreeing with Leibniz that there are really only three possible systems of explaining the

interaction of the body and soul; physical influence, pre-established harmony, and

occasionalism {CPR A390). As in his earlier writings, Kant dismisses physical influence

as a viable candidate and again refers to a “jrpcorov of physical influence,

although in this context he points out the inadequacy of the “dualistic presupposition”

that grounds the view {CPR A391). Kant’s transcendental idealism is a rejection of a

dualist metaphysics that sees matter as a separate thing standing in opposition to the

mind. For the transcendental idealist, matter is “appearance” and cannot be understood

without the mind; thus the ontology that grounds the physical influence view is corrupt

and the view is discredited (ibid.). The illegitimacy of the physical influence view also

works to undermine the pre-established harmony and occasionalism as Kant claims that

these two views are really only objections to the possibility of physical influence {CPR

It is worth noting that a discussion that takes up several pages in the A edition is all but missing in the B edition of the “Paralogisms,” wherein Kant dismisses the question as “lying outside the field of all human knowledge” {CPR B428). Kemp Smith speculates that this change is due to Kant’s loss of interest in this question and subsequent focus on the immortality o f the soul rather than the soul/body interaction (Kemp Smith, A Commentary to Kant’s ‘Critique o f Pure Reason,’’ 471). In any case, Kant’s continued interest in the interaction o f substances and his downplaying of the mind/body relation is consistent with my reading of him as more concemed with that aspect o f the pre-established harmony.

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A390). Because there is no matter that stands outside and independent of the mind, there

is no reason for an occasionalist view or for the pre-established harmony.

For the transcendental idealist, the connection between mind and body becomes a

question of the possibility of outer intuition. In other words, the question for the Critical

philosophy is: “how in a thinking subject outer intuition, namely, that of space, with its

filling in of shape and motion, is possible” (CPR A393). To this question, Kant claims,

there can really be no answer. It is impossible to speculate how outer intuition is possible

for human beings because there is no way to cognize outside of it or to find its cause. We

cannot even speculate how the soul might otherwise intuit or will possibly intuit after the

death of the body (CPR A394). Kant claims that we can only reason as far as experience

reaches, and because the grounds and nature of outer intuition lie outside of that domain,

we cannot know anything about it (CPR A395).

Within the Critical philosophy, Kant has thus established the unity of the world

within the confines of experience, i.e., for objects as appearances, and subsequently

redefined the interaction of the mind and the body. On the one hand, there is no question

as to the relation of mind and body as the world is mind dependent. On the other hand,

why the intuition is sensible and how it relates to things in themselves is deemed

unknowable. The upshot is that the problem of connecting the mind and the body

essentially goes away.

Kant continues his criticism of the pre-established harmony in What Real

Progress in a way that is rerniniscent of his earlier arguments. Kant begins by pointing

out that although Leibniz intended to use the pre-established harmony to explain the

interaction of mind and body, he also employed it antecedently to explain the interaction

of all substances (WRP 101). Kant claims that if one considers substances purely in their

concept, then one will need to see them as completely isolated, because every accident

must adhere within the substance to accoimt for its sustained existence (ibid.). Even if

there are a plurality of substances, they in no way depend on each other, but they are all

dependent on a third being, “the original being” (ibid.). Thus, the community between

the substances is only ideal. There are two ways to view this ideal community, either the

creator constantly maintains it, i.e., occasionally, or He arranges it initially so that all of

the substances’ states corresponded. According to Kant, Leibniz took the second route

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because it is more easily explained through a single principle. The result was the pre-

established harmony, “the most whimsical figment philosophy has ever contrived,” which

follows directly from the attempt to explain the world through concepts alone {WRP 103).

Kant claims that if one instead understands space as a pure intuition then it is ,

possible to account for a single space that enables the relation of substances such that

physical influence is possible and they can “constitute a whole” (ibid.). The result, Kant

claims, is that all things in space constitute a “single world” and not “several worlds

which are extrinsic to one another,” as Leibniz presumably describes (ibid.). Kanf s

general point is that the “world’s unity” cannot be accounted for through concepts alone,

i.e., in Leibniz’s manner, but requires a pure intuition (ibid.).

There are two things to note about this argument. The first is the prominent role

that the intuition of space plays. This is consistent with the changes that Kant made to

the B edition of the “Third Analogy,” which also highlights the role of the form of space.

The second is the lack of any real argument. Kant simply asserts that physical influence

is necessary for the unity of the world and that his view is able to provide for it in a way

that Leibniz’s conceptual approach cannot. I think that Kanf s claims here point to

arguments that he has made in other places, as well as the perceived self-evidence of the

need for interaction to explain unity.

From this sample of Kantian writings we can see a general pattern of criticism

emerge. Kant’s first and earliest criticism is that the isolated substances that the pre-

established harmony relates are metaphysically impossible. The simple yet changing

substances that Leibniz posits cannot exist. Kant’s second criticism is that the lack of

interaction in the pre-established harmony results in a world that is not sufficiently

unified. In his earlier works interaction was achieved through God’s universal harmony

and in the Critical works by the intuition and the nature of objects as appearances. While

the second objection is persistent in Kanf s writings the first objection aimed at the

substances themselves drops out or, perhaps better said, is absorbed into the second

objection.^ In the later writings the problem of providing for unity, interaction, and an

® This is only a conjecture on my part, but it would seem that Kant’s increasing reluctance to talk about substances in themselves as well as an increased tendency to criticize Leibniz through his misunderstanding of the nature o f cognition, as is the case in the “Amphiboly,” are at least partially responsible for the disappearance of the argument against simple substances.

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account of bodies that allows for the interaction ail become intertwined. It is only when

Kant fully establishes the nature of bodies as appearances that he is able to succeed in

that task. In all of Kant’s writings the direct connection is between unity and interaction.

For Kant, only a world composed of substances in mutual interaction can be a true whole.

I want to see how well Leibniz can respond to both lines of criticism. However, before I

do that I would first like to look at Leibniz’s reasons for positing the pre-established

harmony.

II. Background to tie Pre-Established Harmony

Harmony is an important and ubiquitous concepts in Leibniz’s metaphysics. In

his mature writings Leibniz refers to a number of different kinds of harmonies: a

harmony between the mind and the body, between final and efficient causes, between the

realms of nature and grace, and between each of the monads. In order to understand

these different kinds of harmonies it is important to take a step back and look at the role

of harmony more generally in Leibniz’s philosophy.

In his essay “On Wisdom,” Leibniz defines harmony as nothing but “unity in a

plurality” (L 426). Unfortunately, this definition really doesn’t tell us too much, other

than that harmony involves a variety of elements working together or somehow unifying.

A better way to understand harmony is by viewing its relation to other central Leibnizian

concepts. In a letter to Christian Wolff dated May 18, 1715, Leibniz describes the degree

of perfection in a thing as the extent to which there is “more agreement in a greater

variety” {PE 233). This clearly shows a connection between harmony and perfection as

Leibniz understands both involving an agreement or unity among a variety of elements.’

Indeed in both of these writings Leibniz explicitly connects harmony and perfection, and

other concepts as well such as happiness, pleasure, and love by claiming their mutual

coexistence (L 426, PE 233-4). The higher the degree of harmony, the greater perfection,

happiness, pleasure, etc.

The connection between perfection and harmony, as well as these other concepts,

becomes especially important when we consider Leibniz’s view of God. For Leibniz,

The difference between the two seems to be that more perfection implies greater variety, while harmony is only a function o f the agreement or unity among the parts. I will say more about the difference below.

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God is not only the most perfect being, but also the most regular being and a being that

always acts according to rules (PE 231, 233). Leibniz also connects regularity and

harmony when he claims that the divine intellect produces the “most regular” system and

that this is the system that is as “hannonious as possible” (PE 233). Therefore, God, who

is the most perfect, operates according to that which is most regular, i.e., most easily

explainable by general rules, and that is the most harmonious. Leibniz also intends to

connect all of these concepts with a notion of moral goodness, or the “best.” For

example, in his letter to Wolff, Leibniz claims that God’s intellect is “unlimited in its

kind with respect to the best, since it produces infinite harmonies” (ibid.).

The harmony and regularity of the divine perfection becomes especially important

when we consider God’s role in the creation of the universe. God, the supreme

perfection, has chosen, according to Leibniz, to create the universe that is most perfect,

and because of the connection of perfection and harmony, the most perfect world is the

most harmonious. Leibniz claims as much in a 1715 letter to Nicolas Redmond: “it is

impossible that the universe as a whole should not be well regulated [i.e., harmonious],

since the superiority of its perfections is the reason for the existence of this system of

things in preference to any other possible system” (L 659). Leibniz is claiming that

God’s choice to create the most perfect world entails that it must be the most harmonious.

Leibniz makes similar claims at earlier points in his writings. For example, in a

1671 letter to Magnus Wedderkopf, he claims that “God wills the things which he

understands to be best and most harmonious and selects them ... from an infinite number

of possibilities (L 146). Here Leibniz is again connecting divine perfection and harmony

with the moral notion of the best. Another early example of Leibniz connecting

perfection and harmony occurs in his Paris notes from 1676, in which he claims that “that

has most harmony which is most perfect to the most perfect of minds” (L 159).

When considering God’s choice to create the most harmonious universe it is

important not to confuse the role of harmony with the important but independent

Leibnizian notion of compossibility. Compossible substances are those that can exist

simultaneously without contradicting each other. A possible universe for Leibniz is any

collection of compossible substances. There are a number of possible universes each of

which is composed of a certain set of compossibles. Leibniz clarifies the relation of

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possibility and compossibility in a 1714 letter to Louis Bourget. Bourget claims that

because the universe is a collection, then it must collect ail possible entities and there is

subsequently only one possible universe. Leibniz responds that:

This would be true if the universe was a collection o f all possibles, but it is not, since all possibles are not compossible. Thus the universe is a collection o f a certain order o f compossibles only, and the actual universe is a collection o f all possibles, which exist, that is to say, those w hich form the richest composite. And since there are different combinations o f possibilities, some o f them better than others, there are many possible universes, each collection o f compossibles making up one o f them. (L 662)

Leibniz’s mention of the “richness” of the universe brings up another important

point conceming God’s creation of the most perfect universe. Given what we have

discovered about harmony thus far, namely that it involves unity or agreement among a

set of things according to rules, it would appear that a universe which satisfied the

requirement of being maximally harmonious could ostensibly be one which was very

simple or composed of very few elements. For example, a universe composed of two

uniform balls that remain stationary with respect to each other would be a very

harmonious universe. However, as I discussed in chapter two and as Leibniz indicates in

the passage above, God’s choice to create the most perfect universe is not only a function

of harmony, but also variety. Leibniz indicates in the Monadology that it is through the

“greatest possible order” and the “greatest variety possible” that God attains “as much

perfection as possible” in His created universe (Monadology §58 L 648). Maximal

variety in the universe is attained not only through the sheer number of monads, but also

through their nature as well. Each monad is a perceiving substance that is a “mirror of

the universe in its own way” and the monads “vary and represent” the universe “in an

infinite number of ways, all different and all true” (L 559). The idea is that each

substance is a point of “refraction” for the entire universe thereby expanding its

complexity. Leibniz explains to Bayle that the monads are nothing but “different

concentrations of the universe represented according to their different points of view by

which they are distinguished” (L 493). His persistent analogy is that of a city viewed

from different sides which is “multiplied in perspectives” (Monadology §57 L 648).

Leibniz’s thinking is that for the city example, the multitude of perspectives on the city

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add to the variety of the situation; the same is intended to hold for the universe as a

whole.

There are, however, a few points of disanalogy between a city observed from

different locations and the perspectives of the monads. First, as I established in chapter

three, monads are not actually situated in space, thus they caimot occupy a point of view

in any real, spatial sense. Thus, when Leibniz talks about the monadic point of view he

must be referring to something metaphorical Presumably he is referring to the clarity

with w%ich the monads are perceiving each other. A monad that is perceived more

clearly is one that is “closer” than one that it not as distinctly perceived. However, any

degree of real proximity based on clarity must also be metaphorical; indeed this must be

the case for any reference to space or spatiality.

Second, unlike a traveler who approaches a city from a certain perspective, for the

monads there is nothing like the city to observe. There are only other monads and their

perceptions. This raises a well-documented objection that what Leibniz is positing is a

universe of monads wherein each monad is only perceiving the perceptions of other

monads, which leaves no unique content within the monads. If we take just two of those

monads, A and B, A is perceiving the perceptions of B while B is perceiving the

perceptions of A, but the perceptions of A just are the perceptions of B. The result is that

the monads perceive the perceptions of other monads without any real content in the

system. In other words, this objection claims that Leibniz’s position entails an infinite

regress of monadic perceptions.^

Bertrand Russell in a 1903 article and later Benson Mates in greater detail provide

a mathematical model of monadic states that allows for monadic expression and

subsequently avoids this problem.® Briefly, the idea is that expression for Leibniz entails

a 1:1 correspondence between monadic states. Such an expression could be achieved

through a set of mathematical series such as 1 - 1/n, 2 -1/n, 3 -1/n, etc., where each

series would be unique, but where from each series the other series in the set could be

* For a good, brief discussion o f these kinds o f objections see Benson Mates, The Philosophy o f Leibniz: Metaphysics and Language, 78-80.* Russell, “Recent Work on the Philosophy of Leibniz,” 397 and Mates, 80-83.

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“read off.” This would satisfy Leibniz’s need for universal expression while at the same

time making each monad unique.*®

I find Russell and Mates’ arguments convincing and I think that their use of

mathematical models is certainly in the Leibnizian spirit. I would add two things. First,

although as the above objection points out, it is true that each monad expresses every

other monad and thus contains its perceptions within its own, I see nothing in Leibniz’s

view that disallows the possibility of unique content within each of the monads. For

example, when I look at a book I am confusedly perceiving the states of the monads that

comprise the book, just as they are perceiving me in relation to them. However, there is

also my own state or perspective on the book, which is unique to me. Thus, there does

seem to be some unique content within each of the monads in addition to their expression

of the other monads’ states. While Russell and Mates’ models may capture this

possibility mathematically, it seems that we can understand this possibility in a more

straightforward way. Second, I would also add that as I will discuss below, the notion of

perception is somewhat mysterious in Leibniz, thus the monad’s ability to reflect without

becoming mere reflection may be something that Leibniz felt he did not have to describe

in any great detail.

By this point it should be quite clear the importance of harmony for Leibniz, not

only for understanding God, but also for understanding the universe as well. Our

universe is the one out of an infinite number of possibilities that God has chosen to

create. It must be the most varied and the most harmonious, which entails that it is also

the best. With the degree of harmony serving as a central criterion for God’s choice of

the universe, it should thus be no surprise to find that harmony appears in various ways

and at various levels in Leibniz’s philosophy. The most harmonious universe should

exhibit its harmony in many ways. One of the most important harmonies occurs between

the monads, which are the metaphysical foundation of the universe.

Leibniz’s Discourse on Metaphysics and the subsequent correspondence with

Amauld provide a good place to explore one of Leibniz’s earlier discussions of monadic

“ Russell, “Recent Work on the Philosophy o f Leibniz,” 397.

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harmony within his mature thought.* As we saw in the previous chapter, Leibniz lays

out his view of the complete concept and the total independence of substances in the

Discourse (DM §8 12-14). Leibniz’s view is that in order for a substance to be a trae

being it must be a true unity; as Leibniz famously explained to Amauld, “what is not

truly a being is not truly a being’' (DM 191). We have also seen that each monad is a

perceiving, mind-like entity, which reflects the other monads (DM §9 15). Because of

their complete independence the mutual expression by each of the monads must emerge

from the monad itself, i.e., from its complete concept. As Leibniz explains, “every

person or substance is like a little world which expresses the great world” (DM §16 27).

Because the states of each monad are self-generated the progression of the states of a

monad would remain the same even if no other monads existed. Leibniz puts it the

following way using our own monad as the example. He states that the perceptions of

my monad would continue unabated “even if all that which is outside of me were

destroyed, save only that God and myself were left” (DM §14 25).

From this view it follows that if there is to be harmony among the monads, i.e., if

their perceptions are to truly express the states of the other monads, the connection must

be ideal. In his correspondence with Amauld, Leibniz refers to the virtual relation among

substances as the theory of “concomitance.” Leibniz is quite explicit in his discussion

with Amauld that the concomitance among the monadic states is a direct result of their

nature as isolated substances.

The hypothesis of concomitance or o f the agreement of substances among themselves, follows from what I have said regarding each individual substance; that it involves, forever, all the accidents that will happen to it and it expresses the whole universe in its manner. (DM 152)

In the Discourse and correspondence Leibniz also uses “concomitance” to explain

another kind of harmony, namely a harmony between mind and body. The mind or soul

is also a monad for Leibniz and is the only monad that we can have direct contact with.

Our soul, as with any other monad, cannot directly influence or contact anything else in

** For a nice discussion o f the historical development o f the pre-established harmony see Christia Mercer’s Leibniz's Metaphysics, especially chapters 8 and 9. In these chapters Mercer argues that Leibniz first developed the pre-established harmony in 1671, before traveling to Paris and much earlier than commonly thought. Mercer contends that Leibniz’s development was mainly pushed along by his adherence to what she calls a “Complete-itufio Theory of Substance” and a move towards phenomenalism.

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the universe, including our own body. Our perception of our body and any assumed

interaction betw'een the mind and body must be only virtual, in the same way that

interaction between monads is virtual. The result is a certain “parallelism” between the

soul and the body {DM §33 56). In a letter late in Ms correspondence with Amauld,

Leibniz explains that, “the union of the sou! with the body and even the action of one

substance on another consists only in the perfect mutual accord, expressly established by

the ordinance of the first creation” (DM 244). Here Leibmz points out clearly that the

harmony between mind and body is established as an initial condition at the creation of

the universe.

Leibniz contends that his view of concomitance is superior to the two competing

notions of the relation of the mind and body, the possibility of physical influence and

occasionalism {DM 118-9). Leibniz’s criticisms of the view of physical influence is

usually directed to Descartes and his view that while the soul may not be able to cause

the motion of material bodies, it can determine their direction and subsequently influence

the body. In the correspondence with Amauld, Leibniz not only questions how the

directions of bodies would be related to thought, but also, and more importantly, direction

has been shown to be conserved in nature and thus the possibility for the mental to

influence the physical in tMs way is eliminated (DM 186). In a letter to Nicolas

Redmond, Leibniz goes so far as to claim that if Descartes has realized that direction was

also conserved by nature then he would have immediately been led to Leibniz’s view (L

655).'^

Leibniz also thought that concomitance surpassed the occasionalist view of mind

and body interaction. Occasionalism and concomitance do exhibit some similarities in

that both require God to establish and maintain the relationship between the body and the

soul. Leibniz often illuminates the difference between the two theories using the analogy

of two clocks.'^ Leibniz likens occasionalism to two poorly designed clocks that are

constantly being adjusted in order to keep them synchronized. Conversely, concomitance

would be like two clocks that were made with such “skill and accuracy” that they are

At other points in his writings, for example in the “New System” essay, Leibniz indicates that Descartes really just gave up on the problem of explaining how the mind and body influence each other. “So far as we can know from his writings, Descartes gave up the struggle over this problem” (L 457).

For an interesting discussion o f Leibniz’s clocks examples and their inadequacy see David Scott’s “Leibniz and the Two Clocks.”

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constantly in agreement (L 460). The problem with occasionalism is that it makes God

too involved in the world. He becomes a “deus ex machina” and general busybody,

which is unworthy of God’s goodness and perfection (ibid.). However, Amauld objects

to this reading and argues that for the occasionalist God does not act on each occasion of

my willing, but He has established by a “single act of the eternal will” all that He will

have to do in the future (DM 173). In other words, God is not the busybody that Leibniz

describes, but acts by general principles. This would seem to bring Leibniz’s view closer

to occasionalism and eliminate his objection.

Leibniz’s response to Amauld is that occasionalism holds that God must intervene

to relate mind and body, whether by general principles or at each specific point. This

means that occasionalism involves a constant miracle, where a miracle is understood as

that which “surpasses the power which He has given to created things” {DM 185). In

other words, occasionalism involves a miracle because the changes in the body do not

follow from the body itself, but must be effected by God, whether on the occasion of the

action or initially, as Amauld suggests. On the occasionalist view, it is necessary for

“God to be the executor of his own laws” (L 580). The theory of concomitance, on the

other hand, claims that each state of mind and body follows from the preceding state and

is fully contained within its nature (DM 181). According to concomitance the soul, and

the body, is executor of its own laws. Moreover, Leibniz maintains that his view better

“betokens the wonderful wisdom of the Creator” as He has established and ordered a

world of infinite complexity at its inception {DM 187). In later writing Leibniz goes so

far as to claim that his theory proves God {NE 443, LC 83).’'

Leibniz continued to refer to his theory as the theory of concomitance until

relatively late in his philosophical development when in 1696 in his “Third Explanation

of the New System” he refers to his theory as ‘"‘'the way o f pre-established harmony'’' {LNS

63).’ In his mature writings Leibniz tends to apply the term “pre-established harmony”

The argument seems to be that given the existence o f the universal harmony that the pre-established harmony establishes, only a being as powerful and as good as God would be able to create such a system. Therefore, God must exist.

Although the “Third Explanation,” which was a published postscript to a letter to Henri Basnage de Beauval from January 3, 1696, is Leibniz’s first published use of the term, the first recorded use of the term is in a letter to Marquis de I’Hopital from September 30, 1695. To further complicate matters Leibniz’s first conscious use o f the term is in the “First Explanation” when he mentions a “'pre-established harmony'

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specifically to the mind/body relationship while emphasizing that this relation mirrors the

harmony that exists between final and efficient causes (L 637, Monadology §79 L 651).

This refers to the fact that minds operate according to the final causes of good or evil,

while material bodies operate according to the laws of efficient causality or motion (L

637).

III. Responses to K ant’s Objections

Now that we have a better idea of the role of harmony in Leibniz’s metaphysics

and of the pre-established harmony more specifically it is time to return to Kant’s

criticisms. We should recall that Kant’s first criticism of the pre-established harmony

questions the view of substance that underlies it. According to Kant, if substances are

truly simple in the fashion that Leibniz posits, then it would be impossible for them to

undergo any change. Without any type of contact it would be impossible for new

grounds to be introduced into the monads and subsequently there would be no new

determinations. Kant’s claim is that truly isolated monads must be static. Kant’s second

criticism deals with Leibniz’s ability to account for a unified world. According to Kant,

Leibniz’s pre-established harmony really provides an account of worlds and not one

world. In the following sections I will consider Leibniz’s possible replies to these

objections in turn.

IILl Change in the Simple

In order to explore Leibniz’s possible response to Kant’s first objection, we can

look at his debate with Bayle concerning the pre-established harmony, during which a

similar kind of objection is raised. Bayle’s Dictionnaire historique et critque provided

the spark for a debate on the topic when in the article “Rorarius” Bayle criticized

Leibniz’s “New System” paper and the pre-established harmony more specifically. In the

“New System” Leibniz asserts the self-generation of monadic states in passages like the

following: “This is what we must say that God has originally created the soul, and every

other real unity [monad], in such a way that everything in it must arise from its own

(if I may use the expression)” {LNS 51). This work was published in April 1696 but written in September 1695. For an interesting discussion on the use of this term see LNS 137, note 20.

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nature by a perfect spontaneity with regard to itself, yet by a perfect conformity to things

without” (L 457). Bayle’s objection to this position bears a strong resemblance to Kant’s

objection, albeit in a simpler form. Leibniz directly references Bayle’s first edition of the

Dictionnaire in Ms “Clarification of the Difficulties which Mr. Bayle has Found in the

New System of the Union of Soul and Body” and I will relay Bayle’s arguments from

Leibniz’s presentation. Bayle writes:

Finally, since he [Leibniz] assumes with good reason that all souls are simple and indivisible, we cannot understand how they can be com pared to a clock.... We conceive clearly that a simple being will always act uniformly if no external cause interferes with it. I f it were composed o f m any pieces, like a m achine, it would act diversely because the particular activity o f each piece could at any m om ent change the course o f the others. B ut in a single substance, where can you find the cause o f a change in operation? (L 495)

The similarity to Kant’s argument should be clear. Bayle is asking how a simple

substance that is devoid of any parts or of any external contact is capable of change.

Leibniz’s response in the “Clarification” essay is that in a sense the monads are

uniform in that they “follow perpetually the same law of order or of succession” (ibid.).

The “law of order” that Leibniz is referring to is the law of the series that is dictated by

the complete concept of a monad. Each monad follows a set path that is determined by

the law of its series and each state of the monad is a result of the preceding state. Leibniz

makes this point earlier in his reply to Bayle by claiming that “the present state of each

substance is a natural result of its preceding state” (ibid.).

However, Leibniz claims, the uniformity of the unfolding of monadic states does

not entail that the monads act similarly, i.e., without any change. Using a mathematical

analogy, Leibniz compares the actual progression of the monad to a parabola and Bayle’s

proposed movement to a straight line. While a parabola does follow a set path, the “parts

of the parabolic curve are not similar to each other as are the parts of straight line” (ibid.).

So far Leibniz has simply asserted that monadic states do change without

explaining from where this difference emerges. In the “Clarification” essay, Leibniz does

provide an explanation and in a way that is not entirely surprising. Leibniz reminds us

that while the soul is simple, i.e., is not composed of parts, it is composed of many

perceptions at once (L 496). In fact, each monad is composed of an infinite number of

perceptions, which Leibniz here calls a “veritable infinite multitude of little

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indistinguishable feelings” and it is out of this multitude that a changing series is

developed (ibid.). Of course, this multitude of perceptions is not immediately available

to the monad; the perceptions are “small” and “indistinguishable” and can only be

developed over time. Thus, although the monads are simple entities the variety of

perceptions contained within them provide the possibility for change. Leibniz asserts that

this multitude of perceptions “serves our purpose as well as if it [the monad] were

composed of parts like a machine” (ibid.).

In 1702 Bayle published a second edition of the Dictionnaire in which he

continued his debate with Leibniz on this topic. Again in the article “Rorarius” Bayle

pushes roughly the same line of criticism forward while at the same time responding to

Leibniz’s comments in the “Clarification.” Bayle’s new criticisms take two directions,

one is his continued questioning of how change is possible within the soul or monad and

the other concerns several problems with the nature of the proposed change. For the first

criticism, Bayle begins by comparing the soul to Epicurus’ atom. Both of these entities

are supposed to have a “natural power of self-movement” and both exist in complete

isolation from either “spirit or body” {HCD 249). Bayle contends that when a simple

entity is caused to be in a certain state it must remain in that state. Any change in the

soul or atom must simply be a continuation of the same state. Bayle claims in a statement

very reminiscent of Kant’s criticism that “when the total cause of an effect remains the

same, the effect cannot change” {HCD 251). For an atom in the void this translates into

the atom traveling in a completely straight line. For the soul this would mean that it

would be impossible for it to change its states as there would be no cause for the change

in the soul (ibid.).

Bayle continues on that even if we choose not to limit the soul so “narrowly,”

there are still problems for Leibniz’s view (ibid.). Bayle contends that a “metamorphosis

of thoughts” requires that the transition from one thought to another must involve some

“reason of affinity” (ibid.). Bayle’s example is of Caesar observing a flowering tree.

From this observation one could conceive Caesar imagining a tree with only leaves or

with only flowers. This ability would arise because of the similarity between the

observed image and the imagined image. Bayle also observes that there are often

“strange changes from black to white and from yes to no, or those tumultuous leaps from

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earth to heaven, which are common in man’s thoughts” (ibid.). Bayle’s contention is that

on Leibniz’s view these abrupt changes within our souls must be the result of an internal

principle. The problem is that this would deny the principle of affinity that Bayle has

established. In other words, in order to account for those moments in our experience

when we abruptly change our thoughts, Leibmz would have to say that these changes are

internally generated, but there is no reason why we should change states in this way or

any explanation of how this sudden change would be possible. Bayle sees this as

evidence for the falsity of Leibniz’s view and proof that God must place these states

within us.

Bayle does say that one could solve this problem by asserting that the soul is

actually a “legion of spirits” (HCD 252). The problem, of course, is that this would make

the soul into a being by aggregation and subsequently deny the singularity of the soul,

which both Leibniz and Bayle maintain.

Bayle has another criticism on the nature of change that involves our relation to

our future states. Bayle compares Leibniz’s view of the soul to an animal that God has

created to sing incessantly (HCD 253). In order to get this being to sing properly it is

necessary that it follow the correct musical score. In order to follow this score it seems

necessary that the being “know the series of notes and actually think about them” (ibid.).

Of course, in our soul we do not have an awareness of our future thoughts, which Bayle

takes as evidence that these states are not contained intemally. Again, Bayle contends

that Leibniz could solve this problem by positing a soul composed of “a series of

particular instruments,” however, this would also violate the unity that is essential to the

soul. In the end Bayle claims that it is “not possible that the human soul executes this

[divine] law” that Leibniz is positing (ibid.). Bayle does acknowledge that the confusion

within the soul that Leibniz posits is intended to combat this difficulty, but he also points

out that all the difficulties of this view have not been worked out (HCD 254). The upshot

of Bayle’s criticism is that he is contending that the human soul on its own, if conceived

as Leibniz intends, i.e., as an isolated, simple substance, cannot provide for the changes

that we observe within it.

As with the first criticism, Leibniz responds direetly to Bayle in an artiele also

from 1702 entitled “Reply to the Thought on the System of Pre-Established Harmony

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Contained in the Second Edition of Mr. Bayle’s Critical Dictionary, Article Rorarius.”

Leibniz basically works through Bayle’s criticisms in order, beginning with the

impossibility of an isolated soul undergoing change. Leibniz begins by admitting that on

Ms view the soul or monad is an “atom of substance” (L 579). The difference between

Epicurus’ atoms and the monad is that while the parts of the atom do not change their

relation to one another, the monad contains a “composite tendency,” that is a “multitude

of present thoughts” which tend to change by virtue of an “essential relationship to all

other tMngs in the world” (ibid.).'^ Monads are, on Leibniz’s view, “worlds in abridged

form, fruitful simplicities, substantia! unities, but virtually infinite by the multitude of

their modifications” (ibid.). The variety of little thoughts or perceptions within the

monad allow them to change their relation to each other and produce a series of changes.

The variety contained within the monad also provides the resources to answer

Bayle’s second objection, which dealt with our ability to abruptly change from one

mental state to another. Leibniz contends that thoughts that appear to be simple are in

fact infinitely complex. For example, the thought of pleasure “involves everything that

surrounds us and therefore everything which surrounds our environment” (ibid.). TMs

view helps to solve Bayle’s problem because we can now see that, for example, the

feeling of pain is not a simple thought, but contains a variety within it. Leibniz agrees in

principle that there must be a connection between subsequent mental states and his claim

is that the complexity of a thought or emotion that he is positing allows for this

possibility (ibid.). As he points out, “it is often but a step from pleasure to pain” (ibid.).

What he means by tMs is that the perception of pleasure is composed of many parts, some

of which may be painful and thus provide the connection to a later mental state.

As for Bayle’s final objection involving our lack of knowledge about our future

states, Leibniz has the following to say. Leibniz’s basic line of argument is that these

future states are contained within the soul, just in a confused state. Leibniz claims that

there are lots of examples of mental content that is witMn our soul but not readily

available to us. This is the case for things that we forget and later remember (L 580). It

is then just a matter of degree from these everyday cases of hidden content to the infinite

This statement is somewhat misleading in that it makes it sound like Leibniz is positing a relationship between the monads. This cannot be the case, however. He must be referring to the expression o f the universe that is present in each monad, but the monad’s states must be generated internally.

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degree that he requires. Leibniz also points out that if the soul were to have all the future

states available to it then it would be God, because it would be “distinctly conscious of

the whole infinite which it includes” (ibid.).

In both of these responses Leibniz is simply assuming the presence of these

complex internal states, not proving their existence. The first response explains how they

are present and we are not aware of them, while the second explains why we can’t be

aware of them, but both cases simply assume their presence. I think that Leibniz is

simply drawing on work that he has done to prove the internality of monadic states

elsewhere, e.g., in the Discourse, thus all he really has to do here is provide for their

possibility, and the role of confusion in our mental lives seems to accomplish this task.

Leibniz also points out that our experience and common opinion allow for a great variety

in the soul and just because someone has a hard time imagining how this system works,

its consistency with reason proves that it must be the case (L 581).

If we now return to Kant’s criticism directly we see that Leibniz’s response to

Bayle provides him with ample material for a reply. Kant’s first variation of the

argument against Leibniz’s view of substance is that there is no possibility of introducing

a new ground for a different determination because the opposite of that determ in ation is

already present in the substance. Leibniz’s response would surely be that although the

cause of a certain effect appears to be simple it is actually complex. This allows for the

possibility of the elements rearranging themselves to provide for a different

determination. As Leibniz points out to Bayle; “We must also take into consideration

that the soul [monad], however simple it may be, always has a feeling [sentiment]

composed of many perceptions at once” (L 496).

This response also helps with Kant’s second variation of the argument, which

stresses the simultaneity of the cause and effect. Kant asks how it is possible that all of

the determinations can be in the monad while the effects are delayed. Again, the

complexity of the monadic perception allows for their rearrangement such that different

results can obtain at different times. This process of rearrangement is dictated by the law

of the substance and each subsequent state is a result of the one proceeding it. In addition

to the different relationships that the perceptions have to each other, it would seem that it

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is also a function of the clarity of those perceptions as to how they will determine the

state of the monad.

It would seem that Kant could press this objection and ask how one determines

which state the monad currently occupies if all of the states are contained within the

monad. Leibniz could respond that one need only look to the rest of the universe since

the monads reflect each other and the states of all the monads must correspond. This

reply simply expands the scope of the question, however, as Kant could continue to ask

how the determination is made as to what state all the monads currently occupy. This is

really a variation of the objection that I addressed in chapter three with regard to

Leibniz’s view of time. There I indicated that Leibmz has a real difficulty determining a

“now” either for individual monads or for the universe as a whole. This objection is

another variation of the same argument and as I indicated earlier, this presents a real

problem for Leibniz.

The final variation of Kant’s criticism is that for Leibniz’s simple substances the

ground would have to determine the substance in different ways over time as the

introduction of different grounds into a simple substance is an impossibility. Again,

Leibniz’s position that the states of monads are “virtually infinite” means that different

grounds could be generated over time, which could provide the cause for different effects

(L 579).

Although it does seem that Leibniz has a response to Kant’s objections on the

simplicity of substance, one might argue that Leibniz’s solution comes though less than

perspicuous means. More specifically Leibniz employs a view of monadic perception

that does provide for complexity in the simple, but only though an obscure understanding

of perception. For example, Leibniz’s famous definition of perception in the

Monadology as “the passing state which enfolds and represents a multitude in unity or in

the simple substance” does not really give us a very clear understanding of what

perception is or how it can be infinitely complex (Monadology §14 L 644). While this

may be the case, I think that Leibniz would argue that there is indeed something

mysterious about perception and that the mystery is simply endemic to its nature and

provides further support of the need for monadic, soul-like entities replete in nature.

Leibniz states in his letter “On What is Independent of Sense and Matter” that:

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“perception ... cannot be explained by any mechanism, whatever it may be” (L 552). His

famous “mill” example in the Monadology is also intended to lend support to the idea

that no mechanism or collection of parts is capable of providing for perception

{Monadology §17 L 644).

I also think that Leibniz simply assumed that the sou! was a simple entity and

introspection reveals that the soul perceives and that it can move from one state to

another on its own. Leibniz points out in his second response to Bayle that even Father

Malebranche agrees that the soul has “internal voluntary actions” (L 580). One only

needs to extend the limited powers of the soul to all its activities, including those that we

would today call subconscious. The real novelty in Leibniz’s theory is the extension of

the properties of the soul, which again I think that Leibniz took as self-evident, to all

substances in the universe in the form of the mind-like monads.

III.2 Unity of the World

As I pointed out earlier, Kant’s criticism of Leibniz’s simple substances only

appears explicitly in the New Elucidation. In later writings, Kant focuses on Leibniz’s

inability to account for a unified universe. For Kant, a true unity can only be achieved

through a community of interacting substances. As I also pointed out, Kant struggled to

develop a theory that could account for this necessary interaction. In his pre-Critical

writings he posited a “universal harmony” that allowed for a God-given, real interaction

among substances. This solution was, even by Kant’s own lights, obscure and somewhat

ad hoc. In the Critique Kant was able to provide for a unified universe with true

interaction through the forms of intuition and the nature of bodies as appearances. The

intuitions of space and time provide for one universe and the objects, i.e., appearances,

populating it are by nature interrelated.

Kant views the pre-established harmony as Leibniz’s answer to the need for a

principle of the unity of the universe. Kant sees this principle, insofar as it is intended to

explain the relation of monads among themselves, as a consequence of his prior view of

substances as isolated unities. According to Kant, what the pre-established harmony

really provides for is a plurality of worlds and not the one, interacting universe that is

required. Now I will examine Leibniz’s ability to account for the world’s unity.

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To begin, I think that Kant is undoubtedly correct in his estimation of the view of

substance driving the need for the pre-established harmony. My analysis of the

Discourse and Leibniz’s subsequent correspondence with Amauld bears this out. Leibniz

was convinced that true substance requires true unity and that the complexity of

substances issues not from their material parts - they are completely simple and

immaterial - but the complex perceptions of each mind-like entity. Although each of the

monads reflects all of the others in its perceptions, each monad is a completely

independent entity. The combination of their complete isolation and their expression of

the entire universe prompts Leibniz to tell Amauld that each substance is a “world by

itself, independent of everything excepting God” {DM 188). Leibniz also tells Bayle in

his second reply that the monads are “worlds in abridged form” (L 579). Famously in his

“New System” paper Leibmz claims that “each mind is a world apart and sufficient unto

itself, independent of every other created being” and that each monad operates as if

“there existed nothing but God and itself’ (L 458, 457).

If each monad is a world apart and it is as i f only God and it existed why for

Leibniz is this possibility not actual? How can Leibniz be sure that there are other

monads? Leibniz himself admits in a letter to Des Bosses that it is not necessary that

there are other monads, just as it is not necessary that the “earth should stand still”

because most humans once believed it to (L 611). Yet he also claims that it is

“impossible” for there to be the soul without the body. “In this system [pre-established

harmony] bodies act as if there were no souls (to assume an impossibility), and souls act

as if there are no bodies, and act as if each influenced each other” {Monadology §81 L

651).^ In order to understand Leibniz’s position we must keep in mind his difference

between logical necessity and real, or what he sometimes call “moral,” necessity. It is

logically possible for there to be a world with just God and me; there is a possible world

Benson Mates points out that for Leibniz to even consider bodies without minds is ridiculous because bodies are really phenomena and cannot exist without minds (Mates, The Philosophy o f Leibniz: Metaphysics and Language, 207). One might also point out that because minds are monads, and bodies are composed of monads, Leibniz seems to be imagining a world both with and without monads, which is clearly absurd. Perhaps Leibniz is appealing to the difference between the simple monads that compose the body and the developed monad, i.e., mind, that controls the body. Certainly these simple monads could exist without the mind, thus there would be something like a body without a mind.

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like this for Leibniz.^* However, this cannot be the actual world for two reasons. First,

God’s perfection, which as we have seen, dictates that He create the most perfect world

possible, which means the world with the greatest harmony in the greatest variety (L

613). A universe with only one being in it would clearly not have the most variety. The

second reason appeals to the principle of sufficient reason. Leibniz claims, in what might

be a half joking way, to Des Bosses that there is no reason why “we alone should be

preferred over all other possible beings” (ibid.). Beneath this rather glib response does

seem to lie a more serious answer that there is really no reason why there should be only

one being when the collection of beings that Leibniz describes seems to be a better

explanation of both God’s role in the world and the underlying nature of our phenomena.

Leibniz, thus, somewhat misrepresents his case when he claims it is a “probable

judgment” that there are things outside of us (L 611). While the existence of other

substances may not be logically necessary, it is morally necessary given Leibniz’s

understanding of God’s nature and the principle of sufficient reason.

If we grant Leibniz the isolated nature of substances and that there are many of

them then they cannot influence each other directly. The connection that the monads

have to each other must be a virtual and it must be achieved through the harmony of their

states. Leibniz asserts the harmony of states to Amauld when he claims that “all

substances must have a harmony and union among themselves, and all must express in

themselves the same universe and the universal cause [God]” (DM216). In his paper

“On Distinguishing Real from Imaginary Phenomena” Leibniz makes it clear that the

union of the substances arises from their shared perceptions, and that the harmony of

perceptions results from God’s action. “But the cause which leads all minds to have

intercourse with each other or to express the same universe ...is that cause which

perfectly expresses the universe, namely, God” (L 365). Notice that Leibniz simply

equates the intercourse of substances with their shared perceptions. In his “On Nature

Itself’ paper Leibniz reaffirms this position when he claims that “the intercourse of

substances or of monads ... arises not from influence but from a consensus originating in

their preformation by God” (L 503).

** There is an important caveat here. Because Leibniz denied the possibility o f transworld individuals, e.g., there is really only one Adam, I can only exist in this universe. The me in the universe that contained only God and me would be a me like me, but not actually me.

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Thus the harmony of monadic states ensures that the monads represent the same

universe and ensures the harmony and unity of the. world. The harmony of monadic

states is also responsible for the “union of soul and body” (ibid.). Leibniz explains to

Bayle that if the monadic perceptions weren’t harmonized then there wouldn’t be one

world but many worlds.

God could give to each substance its own phenomena independent of those of others, but in this way he would have made as many worlds without connection, so to speak, as there are substances, almost as we say that, when we dream., we are in a world apart and that we enter into a common world when we wake up. (L 493)

Although each monad’s states are completely in harmony with the others, every monad is

unique. The identity of the monad comes from the monad’s point of view according to

Leibniz. This is explained by city analogy that I talked about above.

It is the harmony of the monads and their independent states that ensures that

there is a single world for Leibniz. Not only does he not feel the need to provide for

interaction among substances, but also he claims that any interaction among substances is

impossible. Leibniz tells Amauld quite clearly that any interaction among substances is

“absolutely inexplicable” (DM 150).'^ Leibniz tells Bayle that the “perfect accord

between all these substances” produces the same effect as if they “communicated with

each other by a transmission of species or of qualities, as the common run of philosophers

imagine” (L 457-8).

Given the emphasis that Kant places on mutual interaction as a necessary

condition for the unity of the world it is becoming clear that the debate between Leibniz

and Kant on this topic is in some sense intractable. Leibniz claims that substantial

interaction is impossible and Kant that interaction among substances is essential and the

only way to account for unity.

If we imagine the two extending their dialog further, then we could imagine

Leibniz chastising Kant for unnecessarily limiting his investigation to the phenomenal

level. Certainly, he might claim, interaction takes place at the material level or among

In this passage Leibniz is talking specifically about the action o f other substances on the soul, but given that the soul is just another monad, this statement holds for the connection among monads. Leibniz makes the similarity between the soul and other monads explicit at other points in his writings. For example in this first reply to Bayle Leibniz claims that for the “soul or any other true substance” it is impossible to “receive something from without, except by the divine omnipotence” (L 457).

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material bodies, but this says nothing about the essential substantial level. Not only does

Ms view provide the only possible explanation of substantial interaction, but also its

ability to provide a simultaneous explanation of mind/body interaction lends further

support to its correctness. Leibniz might also claim that Ms view of compossibiiity does

provide for one universe because the universe is the collection of all compossible

substances. This is the best that one can do since reason shows that there is no way for

substances to interact.

For his part, Kant might accuse Leibniz of actually assuming some of the findings

of the Critique in his own explanation. For example, Kant might point to Leibniz’s

discussion of the monadic “point of view” to illustrate that Leibniz is really assuming a

kind of monadic space that underlies the community of monads. He might also point to

passages like the following to Bayle, where Leibniz seems to assume that space and time

are actually fundamental to the world’s unity. “But space and time taken together

constitute the order of possibilities of the one entire universe ...” (L 583).^^

Kant might also point out the dangerous consequences of Leibniz’s view. If his

arguments against skepticism are unconvincing, then the monadic view quite easily

devolves into solipsism with my monad generating a world intemally and no assurance

that there is anything external to it. In other words, it really could be the case that there

was only me and God. At the end of On a Discovery when Kant steals Eberhard’s

thunder by claiming that he, in fact, is the tme heir of Leibniz, Kant points out that the

pre-established harmony cannot be understood as a way to “adapt” beings that by their

nature are complete isolated. If this were what Leibniz intended, then it would be to

“proclaim idealism; for why should one accept bodies in general, if it is possible that

everything which occurs in the soul can be viewed as an effect of its own power, which

would occur in this way if it were in complete isolation?” (OD 158-9). Interestingly,

Kant goes on to claim that there is a pre-established harmony between our two sources of

knowledge; the understanding and the intuition. The harmony is not between two things,

but between two faculties within us.

^ Donald Rutherford argues that this is Leibniz’s position and that for Leibniz every world contains a spatial and temporal ordering. Rutherford claims that Leibniz identifies a world as the “totality o f things that exist in the limits o f space and time” (Rutherford, Leibniz and the Rational Order o f Nature, 189).

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IV. Conclusion

Given Leibniz’s insistence that interaction between substances is impossible and

his general lack of concern with skepticism and given Kant’s view that interaction is the

only way to account for a unified world, perhaps there really is no way to resolve the

debate between the two on this point. However, exploring where and how the debate

occurs has revealed important, and by now familiar, insights. The where of the debate is,

in Kantian terminology, over the role of the understanding and the intuition in

determining the character of the world. The how of the debate is that Leibmz prioritizes

the understanding and the nature of substances as they must be as determined by the

intellect. Given the need for completely isolated substances and the importance of the

concept of harmony, the pre-established harmony is not too much of a leap.

On the other hand, Kant sides with the intuition and the nature of substances as

appearances. As I have tried to illustrate above, Kant’s accusation that Leibniz’s view

does not provide for a unified world is really an assertion that Leibniz cannot provide for

the necessary interaction. As we have found previously, Kant’s method for solving this

problem lies in the forms of intuition, especially space. It is because there is one space,

and one time, that substances can interact and that there is subsequently one world.

There is an important point of similarity between the two, however. While

Leibniz’s pre-established harmony appeals to God quite directly - He not only establishes

the harmony, but also maintains it and the existence of the monads - there is the harmony

of Kantian faculties that I mentioned above. This harmony is also divinely established

and allows the principles of the understanding to work with the intuition to provide us

with knowledge and experience.^^

In the end, their disagreement over the pre-established harmony once again has

Leibniz occupying the role of philosopher of substance while Kant is the philosopher of

experience. While Kant tends to cash this difference out in terms of faculties, i.e.,

This particular aspect of Kant’s philosophy was criticized by Kant’s contemporaries after the publication of the Critique. For example, Maimon asked the skeptical question o f why the intuition and the understanding should be in harmony and proclaimed an unbridgeable gap between the two. Ironically, Maimon’s solution was to revert to a roughly Leibnizian line and assert the primacy o f the understanding and its central and creative role in our knowledge. For an insightful discussion o f these criticisms as well as a discussion of Maimon’s own view see Frederick Beiser’s The Fate o f Reason: German Philosophy from Kant to Fichte, chapter 10.

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understanding versus combined intuition and understanding, in keeping with my

metaphysical emphasis, we can see this difference in terms of the kinds of objects that

they are dealing with. Leibniz is concerned with the substances themselves, while Kant

subsequently restrict us to appearances. It is out of these different things that each

philosopher does, or does not, build an entire world.

182


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VITA

Matthew John Olsen was bom in Bangor, Maine on January 10, 1974. He graduated

from Albright College in Reading, PA in 1996 with a degree in philosophy and German.

After a year working in Maine, Olsen moved to Champaign, Illinois to pursue graduate

study in philosophy. He received a Masters of Philosophy in 2000 and completed work

on his Ph.D. in 2004. During his time at the University, Olsen taught classes in

introduction to philosophy and introduction to logic.

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