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Title: Leibniz's New Essays Concerning the Human Understanding - A Critical Exposition
Author: Dewey, John, 1859-1952
Language: English
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  [ Transcriber's Notes:

    Every effort has been made to replicate this text as faithfully
    as possible, including inconsistencies in spelling and hyphenation.
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  Copyright, 1888,
  By S. C. Griggs and Company.


The purpose of the series of which the present volume is one, is not,
as will be seen by reference to the statement in the initial volume,
to sum up _in toto_ the system of any philosopher, but to give a
"critical exposition" of some one masterpiece. In treating the
"Nouveaux Essais" of Leibniz, I have found myself obliged, at times,
to violate the letter of this expressed intention, in order to fulfil
its spirit. The "Nouveaux Essais," in spite of its being one of the
two most extended philosophical writings of Leibniz, is a compendium
of comments, rather than a connected argument or exposition. It has
all the suggestiveness and richness of a note-book, but with much also
of its fragmentariness. I have therefore been obliged to supplement my
account of it by constant references to the other writings of Leibniz,
and occasionally to take considerable liberty with the order of the
treatment of topics. Upon the whole, this book will be found, I hope,
to be a faithful reflex not only of Leibniz's thought, but also of his
discussions in the "Nouveaux Essais."

In the main, the course of philosophic thought since the time of
Leibniz has been such as to render almost self-evident his limitations,
and to suggest needed corrections and amplifications. Indeed, it is
much easier for those whose thoughts follow the turn that Kant has
given modern thinking to appreciate the defects of Leibniz than to
realize his greatness. I have endeavored, therefore, in the body
of the work, to identify my thought with that of Leibniz as much
as possible, to assume his standpoint and method, and, for the most
part, to confine express criticism upon his limitations to the final
chapter. In particular, I have attempted to bring out the relations
of philosophy to the growing science of his times, to state the
doctrine of pre-established harmony as he himself meant it, and to give
something like consistency and coherency to his doctrine of material
existence and of nature. This last task seemed especially to require
doing. I have also endeavored to keep in mind, throughout, Leibniz's
relations to Locke, and to show the "Nouveaux Essais" as typical of the
distinction between characteristic British and German thought.


_May_, 1888.



  The Man.


  His Parents                                                          1

  His Early Education                                                  2

  His University Training at Leipsic                                   4

  At Jena                                                              8

  At the University of Altdorf                                        10

  His Removal to Frankfurt                                            10

  His Mission to Paris                                                11

  Discovery of the Calculus                                           12

  Librarian at Hanover                                                13

  His Activities                                                      14

  His Philosophic Writings                                            15

  His Ecclesiastic and Academic Projects                              17

  His Later Years and Death                                           18


  Sources of his Philosophy.

  Character of the Epoch into which Leibniz was born                  20

  The Thought of the Unity of the World                               23

  The two Agencies which formed Leibniz's Philosophy                  24

  The Cartesian Influences                                            26

  Rationalistic Method                                                28

  Mechanical Explanation of Nature                                    30

  Application of Mathematics                                          32

  Idea of Evolution                                                   33

  Interpretation of these Ideas                                       35

  Idea of Activity or Entelechy                                       39

  Idea of Rationality                                                 40

  Idea of Organism                                                    42


  The Problem and its Solution.

  Unity of Leibniz's Thought                                          43

  Relation of Universal and Individual                                44

  Descartes' Treatment of this Question                               46

  Spinoza's Treatment of it                                           48

  Leibniz's Solution                                                  50

  All Unity is Spiritual                                              53

  And Active                                                          54

  Is a Representative Individual                                      56

  Contrast of Monad and Atom                                          58

  Pre-established Harmony reconciles Universal and Individual         59

  Meaning of this Doctrine                                            62


  Locke and Leibniz.--Innate Ideas.

  Necessity of Preliminary Account of Leibniz's Philosophy            66

  Locke's Empiricism                                                  67

  Leibniz's Comments upon Locke                                       69

  The Controversies of Leibniz                                        72

  The Essay on the Human Understanding                                73

  Locke's Denial of Innate Ideas                                      75

  Depending upon

    (1) His Mechanical Conception of Innate Ideas                     77

  Leibniz undermines this by substituting an Organic Conception       80

  And upon

    (2) His Mechanical Conception of Consciousness                    84

  Leibniz refutes this by his Theory of Unconscious Intelligence      85


  Sensation and Experience.

  Importance of Doctrine regarding Sensation                          87

  The Two Elements of Locke's Notion of Sensation                     89

  Its Relation to the Object producing it: Primary and Secondary
  Qualities                                                           91

  Locke criticized as to his Account

    (1) Of the Production of Sensation                                92

    (2) Of its Function in Knowledge                                  95

  The Meaning of Physical Causation                                   97

  Bearing of this Doctrine upon Relation of Soul and Body             98

  Criticism of Locke's Dualism                                        98

  Leibniz's Monism                                                   101

  Summary of Discussion                                              103

  Leibniz on the Relation of Sensations to Objects
  occasioning them                                                   105

  Nature of Experience                                               106

  Distinction of Empirical from Rational Knowledge                   107


  The Impulses and the Will.

  The Doctrine of Will depends upon that of Intelligence             109

  The Character of Impulse                                           111

  Of Desire                                                          112

  Half-Pains and Pleasures                                           113

  The Outcome of Desire                                              115

  Nature of Moral Action                                             117

  Of Freedom                                                         118

    (1) Freedom as Contingency                                       119

        Limitation of this Principle                                 121

    (2) Freedom as Spontaneity                                       123

        This Principle is too Broad to be a Moral Principle          125

    (3) True Freedom is Rational Action                              125

  Our Lack of Freedom is due to our Sensuous Nature                  128

  Innate Practical Principles                                        129

  Moral Science is Demonstrative                                     130


  Matter and its Relation to Spirit.

  Locke's Account of Matter and Allied Ideas the Foundation of the
  Philosophy of Nature Characteristic of British Empiricism          132

  Space and Matter wholly Distinct Ideas                             134

  Leibniz gives Matter a Metaphysical Basis                          137

  Ordinary Misunderstanding of Leibniz's Ideas of Matter             138

  Matter is not composed of Monads                                   139

  Matter is the Passive or Conditioned Side of Monads                140

  Passivity equals "Confused Representations," _i. e._ Incomplete
  Development of Reason                                              144

  Matter is logically Necessary from Leibniz's Principles            145

  Bearing of Discussion upon Doctrine of Pre-established Harmony     146

  Summary                                                            147


  Material Phenomena and their Reality.

  What is the Connection between Matter as Metaphysical and as
  Physical?                                                          151

  The Latter is the "Image" of the Former                            151

  Leibniz's Reaction from Cartesian Theory                           152

  His Objections are (1) Physical and (2) Logical                    153

  (1) Motion is Source of Physical Qualities of Bodies               155

  Hence there are no Atoms                                           158

  Secondary Qualities as well as Primary depend upon Motion          160

  (2) What is the Subject to which the Quality of Extension
  belongs?                                                           161

  It is the Monad _as Passive_                                       162

  Space and Time connect the Spiritual and the Sensible              164

  Distinction between Space and Time, and Extension and Duration     166

  Space and Time are Relations                                       167

  Leibniz's Controversy with Clarke                                  168

  Leibniz denies that Space and Time are Absolute                    170

  What is the Reality of Sensible Phenomena?                         173

  It consists

    (1) In their Regularity                                          174

    (2) In their Dependence upon Intelligence and Will               175

  Leibniz and Berkeley                                               177


  Some Fundamental Conceptions.

  Locke's Account of Substance as Static                             179

  The Distinction between Reality and Phenomena                      180

  Leibniz's Conception of Substance as Dynamic                       181

  His Specific Criticisms upon Locke                                 182

  The Categories of Identity and Difference Locke also explains in
  a Mechanical Way                                                   183

  Leibniz regards them as Internal and as Organic to each other      184

  Locke gives a Quantitative Notion of Infinity                      188

  And hence makes our Idea of it purely Negative                     189

  Leibniz denies that the True Notion of Infinity is Quantitative    189

  He also denies Locke's Account of the Origin of the Indefinite     192

  In General, Locke has a Mechanical Idea, Leibniz a Spiritual, of
  these Categories                                                   193


  The Nature and Extent of Knowledge.

  Locke's Definition and Classification of Knowledge                 196

  Leibniz's Criticism                                                197

  Leibniz, Berkeley, and Kant regarding Knowledge of Objects         198

  The Degrees of Knowledge,--Intuitive, Demonstrative, and
  Sensitive                                                          199

  Locke's Contradictory Theories regarding the Origin of Knowledge   202

  Locke starts both with the Individual as given to Consciousness
  and with the Unrelated Sensation                                   204

  Either Theory makes Relations or "Universals" Unreal               205

  As to the Extent of Knowledge, that of Identity is Wide, but
  Trifling                                                           205

  That of Real Being includes God, Soul, and Matter, but only as to
  their Existence                                                    206

  And even this at the Expense of contradicting his Definition of
  Knowledge                                                          206

  Knowledge of Co-existence is either Trifling or Impossible         207

  Leibniz rests upon Distinction of Contingent and Rational Truth    209

  The Former may become the Latter, and is then Demonstrative        210

  The Means of this Transformation are Mathematics and
  Classification                                                     215

  There are Two Principles,--One of Contradiction                    217

  The Other of Sufficient Reason                                     218

  The Latter leads us to God as the Supreme Intelligence and the
  Final Condition of Contingent Fact                                 219

  The Four Stages of Knowledge                                       222


  The Theology of Leibniz.

  Leibniz's Three Arguments for the Existence of God                 224

  The Value of the Ontological                                       225

  The Cosmological                                                   226

  The Teleological                                                   226

  The Attributes of God                                              227

  The Relation of God to the World, his Creating Activity            228

  Creation involves Wisdom and Goodness as well as Power             229

  The Relation of God to Intelligent Spirits: they form a Moral
  Community                                                          230

  Leibniz as the Founder of Modern German Ethical Systems            231

  The End of Morality is Happiness as Self-realization               232

  The Three Stages of Natural Right                                  234

  The Basis of Both Leibniz's Ethics and Political Philosophy is
  Man's Relation to God                                              236

  His Æsthetics have the Same Basis                                  237

  Man's Spirit as Architectonic                                      238


  Criticism and Conclusion.

  Leibniz's Fundamental Contradiction is between his Method and his
  Subject Matter                                                     240

  The Use which Leibniz makes of the Principle of Sufficient Reason
  reveals this Contradiction                                         242

  The Contradiction is between the Ideas of Formal and of Concrete
  Unity                                                              243

  From this Contradiction flow

    (1) The Contradiction in the Notion of Individuality             246

        Which becomes purely Negative                                247

        The Negative he interprets as merely Privative               249

    (2) The Contradiction in his Conception of God has the Same
    Source                                                           250

        He really has Three Definitions of God                       250

        One results in Atomism, another in Pantheism                 251

        The Third in a Conception of the Organic Harmony of the
        Infinite and Finite                                          252

    (3) The Contradiction between the Real and the Ideal in the
    Monads has the Same Source                                       253

    (4) As have also the Contradictions in the Treatment of the
    Relations of Matter and Spirit                                   254

    (5) And finally, his Original Contradiction leads to a
    Contradictory Treatment of Knowledge                             257

  Summary as to the Positive Value of Leibniz                        259

  The Influence of Leibniz's Philosophy                              261

  Especially upon Kant                                               262

  Kant claims to be the True Apologist for Leibniz                   263

    (1) As to the Doctrine of Sufficient Reason and Contradiction    263

        Which finds its Kantian Analogue in the Distinction between
        Analytic and Synthetic Judgment                              266

    (2) As to the Relation of Monads and Matter                      268

        Which finds its Kantian Analogue in the Relation of the
        Sensuous and Supersensuous                                   268

    (3) And finally, as to the Doctrine of Pre-established Harmony   269

        Which Kant transforms into Harmony between Understanding
        and Sense                                                    269

        And between the Categories of the Understanding and the
        Ideas of Reason                                              270

  Conclusion                                                         272




"He who knows me only by my writings does not know me," said
Leibniz. These words--true, indeed, of every writer, but true of
Leibniz in a way which gives a peculiar interest and charm to his
life--must be our excuse for prefacing what is to be said of his "New
Essays concerning the Human Understanding" with a brief biographical

Gottfried Wilhelm Leibniz was born in Leipzig June 21, 1646. His
father, who died when Leibniz was only six years old, was a professor
in the university and a notary of considerable practice. From him the
future philosopher seems to have derived his extraordinary industry
and love of detail. Such accounts as we have of him show no traces of
the wonderful intellectual genius of his son, but only a diligent,
plodding, faithful, and religious man, a thoroughly conscientious
husband, jurist, and professor. Nor in the lines of physical heredity
can we account for the unique career of Leibniz by his mother's
endowments. The fact, however, that she was patient in all trial,
living in peace with her neighbors, anxious for unity and concord with
all people, even with those not well disposed to her, throws great
light upon the fundamental trait of Leibniz's ethical nature. As in so
many cases, it is the inherited moral characteristics which form the
basis of the intellectual nature. The love of unity which was a moral
trait in Leibniz's mother became in him the hunger for a harmonious and
unified mental world; the father's devotion to detail showed itself
as the desire for knowledge as minute and comprehensive as it was

Left without his father, he was by the advice of a discerning friend
allowed free access to the library. Leibniz never ceased to count this
one of the greatest fortunes of his life. Writing in after years to a
friend, he says:--

"When I lost my father, and was left without any direction in my
studies, I had the luck to get at books in all languages, of all
religions, upon all sciences, and to read them without any regular
order, just as my own impulse led me. From this I obtained the great
advantage that I was freed from ordinary prejudices, and introduced to
many things of which I should otherwise never have thought."

In a philosophical essay, in which he describes himself under the name
of Gulielmus Pacidius, he says:--

"Wilhelm Friedlieb, a German by birth, who lost his father in his early
years, was led to study through the innate tendency of his spirit; and
the freedom with which he moved about in the sciences was equal to this
innate impulse. He buried himself, a boy eight years old, in a library,
staying there sometimes whole days, and, hardly stammering Latin, he
took up every book which pleased his eyes. Opening and shutting them
without any choice, he sipped now here, now there, lost himself in one,
skipped over another, as the clearness of expression or of content
attracted him. He seemed to be directed by the _Tolle et lege_ of a
higher voice. As good fortune would have it, he gave himself up to the
ancients, in whom he at first understood nothing, by degrees a little,
finally all that was really necessary, until he assumed not only a
certain coloring of their expression, but also of their thought,--just
as those who go about in the sun, even while they are occupied with
other things, get sun-browned."

And he goes on to tell us that their influence always remained
with him. Their human, their important, their comprehensive ideas,
grasping the whole of life in one image, together with their clear,
natural, and transparent mode of expression, adapted precisely to
their thoughts, seemed to him to be in the greatest contrast with the
writings of moderns, without definiteness or order in expression, and
without vitality or purpose in thought,--"written as if for another
world." Thus Leibniz learned two of the great lessons of his life,--to
seek always for clearness of diction and for pertinence and purpose
of ideas.

Historians and poets first occupied him; but when in his school-life,
a lad of twelve or thirteen years, he came to the study of logic,
he was greatly struck, he says, by the "ordering and analysis
of thoughts which he found there." He gave himself up to making
tables of categories and predicaments, analyzing each book that he
read into suitable topics, and arranging these into classes and
sub-classes. We can imagine the astonishment of his playmates as
he burst upon them with a demand to classify this or that idea, to
find its appropriate predicament. Thus he was led naturally to the
philosophic books in his father's library,--to Plato and to Aristotle,
to the Scholastics. Suarez, in particular, among the latter, he read;
and traces of his influences are to be found in the formulation of his
own philosophic system. At about this same time he took great delight
in the theological works with which his father's library abounded,
reading with equal ease and pleasure the writings of the Lutherans
and of the Reformed Church, of the Jesuits and the Jansenists, of the
Thomists and the Arminians. The result was, he tells us, that he was
strengthened in the Lutheran faith of his family, but, as we may easily
imagine from his after life, made tolerant of all forms of faith.

In 1661 the boy Leibniz, fifteen years old, entered the University of
Leipzig. If we glance back upon his attainments, we find him thoroughly
at home in Latin, having made good progress in Greek, acquainted with
the historians and poets of antiquity, acquainted with the contemporary
range of science, except in mathematics and physics, deeply read and
interested in ancient and scholastic philosophy and in the current
theological discussions. Of himself he says:--

"Two things were of extraordinary aid to me: in the first place, I was
self-taught; and in the second, as soon as I entered upon any science
I sought for something new, even though I did not as yet thoroughly
understand the old. I thus gained two things: I did not fill my mind
with things empty and to be unlearned afterwards,--things resting
upon the assertion of the teacher, and not upon reason; and secondly,
I never rested till I got down to the very roots of the science and
reached its principles."

While there is always a temptation to force the facts which we know
of a man's early life, so as to make them seem to account for what
appears in mature years, and to find symbolisms and analogies which do
not exist, we are not going astray, I think, if we see foreshadowed in
this early education of Leibniz the two leading traits of his later
thought,--universality and individuality. The range of Leibniz's
investigations already marks him as one who will be content with
no fundamental principle which does not mirror the universe. The
freedom with which he carried them on is testimony to the fact
that even at this age the idea of self-development, of individual
growth from within, was working upon him. In the fact, also, that he
was self-taught we find doubtless the reason that he alone of the
thinkers of this period did not have to retrace his steps, to take
a hostile attitude towards the ideas into which he was educated, and
to start anew upon a foundation then first built. The development of
the thought of Leibniz is so gradual, continuous, and constant that it
may serve as a model of the law by which the "monad" acts. Is not his
early acquaintance with ancient literature and mediæval philosophy
the reason that he could afterwards write that his philosophical
system "connects Plato with Democritus, Aristotle with Descartes, the
Scholastics with the moderns, theology and morals with reason"? And
who can fail to see in the impartiality, the comprehensiveness, of
his self-education the prophecy of the time when he can write of his
ideas that "there are united in them, as in a centre of perspective,
the ideas of the Sceptics in attributing to sensible things only
a slight degree of reality; of the Pythagoreans and Platonists,
who reduce all to harmonies, numbers, and ideas; of Parmenides and
Plotinus, with their One and All; of the Stoics, with their notion of
necessity, compatible with the spontaneity of other schools; of the
vital philosophy of the Cabalists, who find feeling everywhere; of the
forms and entelechies of Aristotle and the Schoolmen, united with the
mechanical explanation of phenomena according to Democritus and the

But we must hurry along over the succeeding years of his life. In
the university the study of law was his principal occupation, as he
had decided to follow in the footsteps of his father. It cannot be
said that the character of the instruction or of the instructors at
Leipzig was such as to give much nutriment or stimulus to a mind like
that of Leibniz. He became acquainted there, however, with the Italian
philosophy of the sixteenth century,--a philosophy which, as formulated
by Cardanus and Campanella, formed the transition from Scholastic
philosophy to the "mechanical" mode of viewing the universe. He had
here also his first introduction to Descartes. The consequences of the
new vision opened to Leibniz must be told in his own words: "I was but
a child when I came to know Aristotle; even the Scholastics did not
frighten me; and I in no way regret this now. Plato and Plotinus gave
me much delight, not to speak of other philosophers of antiquity. Then
I fell in with the writings of modern philosophy, and I recall the
time when, a boy of fifteen years, I went walking in a little wood
near Leipzig, the Rosenthal, in order to consider whether I should
hold to the doctrine of substantial forms. Finally the mechanical
theory conquered, and thus I was led to the study of the mathematical

To the study of the mathematical sciences! Surely words of no mean
import for either the future of Leibniz or of mathematics. But his
Leipzig studies did not take him very far in this new direction. Only
the elements of Euclid were taught there, and these by a lecturer
of such confused style that Leibniz seems alone to have understood
them. In Jena, however, where he went for a semester, things were
somewhat better. Weigel, a mathematician of some fame, an astronomer,
a jurist, and a philosopher, taught there, and introduced Leibniz
into the lower forms of analysis. But the Thirty Years' War had not
left Germany in a state of high culture, and in after years Leibniz
lamented the limitations of his early mathematical training, remarking
that if he had spent his youth in Paris, he would have enriched science
earlier. By 1666 Leibniz had finished his university career, having
in previous years attained the degrees of bachelor of philosophy and
master of philosophy. It is significant that for the first he wrote
a thesis upon the principle of individuation,--the principle which
in later years became the basis of his philosophy. This early essay,
however, is rather an exhibition of learning and of dexterity in
handling logical methods than a real anticipation of his afterthought.

For his second degree, he wrote a thesis upon the application
of philosophic ideas to juridic procedure,--considerations which
never ceased to occupy him. At about the same time appeared his
earliest independent work, "De Arte Combinatoria." From his study of
mathematics, and especially of algebraic methods, Leibniz had become
convinced that the source of all science is,--first, analysis; second,
symbolic representation of the fundamental concepts, the symbolism
avoiding the ambiguities and vagueness of language; and thirdly,
the synthesis and interpretation of the symbols. It seemed to Leibniz
that it ought to be possible to find the simplest notions in all the
sciences, to discover general rules for calculating all their varieties
of combination, and thus to attain the same certainty and generality
of result that characterize mathematics. Leibniz never gave up this
thought. Indeed, in spirit his philosophy is but its application,
with the omission of symbols, on the side of the general notions
fundamental to all science. It was also the idea of his age,--the
idea that inspired Spinoza and the _Aufklärung_, the idea that
inspired philosophical thinking until Kant gave it its death-blow by
demonstrating the distinction between the methods of philosophy and of
mathematical and physical science.

In 1666 Leibniz should have received his double doctorate of philosophy
and of law; but petty jealousies and personal fears prevented his
presenting himself for the examination. Disgusted with his treatment,
feeling that the ties that bound him to Leipzig were severed by the
recent death of his mother, anxious to study mathematics further,
and, as he confesses, desiring, with the natural eagerness of youth,
to see more of the world, he left Leipzig forever, and entered upon
his _Wanderjahre_. He was prepared to be no mean citizen of the
world. In his education he had gone from the historians to the poets,
from the poets to the philosophers and the Scholastics, from them
to the theologians and Church Fathers; then to the jurists, to the
mathematicians, and then again to philosophy and to law.

He first directed his steps to the University of Altdorf; here he
obtained his doctorate in law, and was offered a professorship,
which he declined,--apparently because he felt that his time was
not yet come, and that when it should come, it would not be in
the narrow limits of a country village. From Altdorf he went to
Nürnberg; here all that need concern us is the fact that he joined a
society of alchemists (_fraternitas roseæcrucis_), and was made their
secretary. Hereby he gained three things,--a knowledge of chemistry; an
acquaintance with a number of scientific men of different countries,
with whom, as secretary, he carried on correspondence; and the
friendship of Boineburg, a diplomat of the court of the Elector and
Archbishop of Mainz. This friendship was the means of his removing
to Frankfurt. Here, under the direction of the Elector, he engaged
in remodelling Roman law so as to adapt it for German use, in writing
diplomatic tracts, letters, and essays upon theological matters, and
in editing an edition of Nizolius,--a now forgotten philosophical
writer. One of the most noteworthy facts in connection with this
edition is that Leibniz pointed out the fitness of the German language
for philosophical uses, and urged its employment,--a memorable fact
in connection with the later development of German thought. Another
important tract which he wrote was one urging the alliance of
all German States for the purpose of advancing their internal
and common interests. Here, as so often, Leibniz was almost two
centuries in advance of his times. But the chief thing in connection
with the stay of Leibniz at Mainz was the cause for which he left
it. Louis XIV. had broken up the Triple Alliance, and showed signs of
attacking Holland and the German Empire. It was then proposed to him
that it would be of greater glory to himself and of greater advantage
to France that he should move against Turkey and Egypt. The mission of
presenting these ideas to the great king was intrusted to Leibniz, and
in 1672 he went to Paris.

The plan failed completely,--so completely that we need say no
more about it. But the journey to Paris was none the less the
turning-point in the career of Leibniz. It brought him to the
centre of intellectual civilization,--to a centre compared with
which the highest attainments of disrupted and disheartened Germany
were comparative barbarism. Molière was still alive, and Racine was
at the summit of his glory. Leibniz became acquainted with Arnaud,
a disciple of Descartes, who initiated him into the motive and spirit
of his master. Cartesianism as a system, with its scientific basis and
its speculative consequences, thus first became to him an intellectual
reality. And, perhaps most important of all, he met Huygens, who became
his teacher and inspirer both in the higher forms of mathematics
and in their application to the interpretation and expression of
physical phenomena. His diplomatic mission took him also to London,
where the growing world of mathematical science was opened yet wider to
him. The name of Sir Isaac Newton need only be given to show what this
meant. From this time one of the greatest glories of Leibniz's life
dates,--a glory, however, which during his lifetime was embittered by
envy and unappreciation, and obscured by detraction and malice,--the
invention of the infinitesimal calculus. It would be interesting, were
this the place, to trace the history of its discovery,--the gradual
steps which led to it, the physical facts as well as mathematical
theories which made it a necessity; but it must suffice to mention that
these were such that the discovery of some general mode of expressing
and interpreting the newly discovered facts of Nature was absolutely
required for the further advance of science, and that steps towards
the introduction of the fundamental ideas of the calculus had already
been taken,--notably by Keppler, by Cavalieri, and by Wallis. It
would be interesting to follow also the course of the controversy
with Newton,--a controversy which in its method of conduct reflects no
credit upon the names of either. But this can be summed up by saying
that it is now generally admitted that absolute priority belongs to
Newton, but that entire independence and originality characterize
none the less the work of Leibniz, and that the method of approach and
statement of the latter are the more philosophical and general, and,
to use the words of the judicious summary of Merz, "Newton cared more
for the results than the principle, while Leibniz was in search of
fundamental principles, and anxious to arrive at simplifications and

The death of Boineburg removed the especial reasons for the return of
Leibniz to Frankfurt, and in 1676 he accepted the position of librarian
and private councillor at the court of Hanover. It arouses our interest
and our questionings to know that on his journey back he stopped at the
Hague, and there met face to face the other future great philosopher
of the time, Spinoza. But our questionings meet no answer. At Hanover,
the industries of Leibniz were varied. An extract from one of his own
letters, though written at a somewhat later date, will give the best
outline of his activities.

"It is incredible how scattered and divided are my occupations. I
burrow through archives, investigate old writings, and collect
unprinted manuscripts, with a view to throwing light on the
history of Brunswick. I also receive and write a countless number of
letters. I have so much that is new in mathematics, so many thoughts
in philosophy, so many literary observations which I cannot get into
shape, that in the midst of my tasks I do not know where to begin,
and with Ovid am inclined to cry out: 'My riches make me poor.' I
should like to give a description of my calculating-machine; but time
fails. Above all else I desire to complete my Dynamics, as I think
that I have finally discovered the true laws of material Nature, by
whose means problems about bodies which are out of reach of rules now
known may be solved. Friends are urging me to publish my Science of
the Infinite, containing the basis of my new analysis. I have also on
hand a new Characteristic, and many general considerations about the
art of discovery. But all these works, the historical excepted, have
to be done at odd moments. Then at the court all sorts of things are
expected. I have to answer questions on points in international law;
on points concerning the rights of the various princes in the Empire:
so far I have managed to keep out of questions of private law. With all
this I have had to carry on negotiations with the bishops of Neustadt
and of Meaux [Bossuet], and with Pelisson and others upon religious

It is interesting to note how the philosophic spirit, the instinct
for unity and generality, showed itself even in the least of Leibniz's
tasks. The Duke of Brunswick imposed upon Leibniz the task of drawing
up a genealogical table of his House. Under Leibniz's hands this
expanded into a history of the House, and this in turn was the centre
of an important study of the German Empire. It was impossible that
the philosopher, according to whom every real being reflected the
whole of the universe from its point of view, should have been able to
treat even a slight phase of local history without regarding it in its
relations to the history of the world. Similarly some mining operations
in the Harz Mountains called the attention of Leibniz to geological
matters. The result was a treatise called "Protogäa," in which Leibniz
gave a history of the development of the earth. Not content with seeing
in a Brunswick mountain an epitome of the world's physical formation,
it was his intention to make this an introduction to his political
history as a sort of geographical background and foundation. It is
interesting to note that the historical studies of Leibniz took him on
a three years' journey, from 1687 to 1690, through the various courts
of Europe,--a fact which not only had considerable influence upon
Leibniz himself, but which enabled him to give stimulus to scientific
development in more ways and places than one.

His philosophical career as an author begins for the most part with
his return to Hanover in 1690. This lies outside of the scope of the
present chapter, but here is a convenient place to call attention to
the fact that for Leibniz the multitude of his other duties was so
great that his philosophical work was the work "of odd moments." There
is no systematic exposition; there are a vast number of letters, of
essays, of abstracts and memoranda published in various scientific
journals. His philosophy bears not only in form, but in substance,
traces of its haphazard and desultory origin. Another point of
interest in this connection is the degree to which, in form, at least,
his philosophical writings bear the impress of his cosmopolitan
life. Leibniz had seen too much of the world, too much of courts,
for his thoughts to take the rigid and unbending form of geometrical
exposition suited to the lonely student of the Hague. Nor was the
regular progression and elucidation of ideas adapted to the later
Germans, almost without exception university professors, suited to
the man of affairs. There is everywhere in Leibniz the attempt to
adapt his modes of statement, not only to the terminology, but even
to the ideas, of the one to whom they are addressed. There is the
desire to magnify points of agreement, to minimize disagreements,
characteristic of the courtier and the diplomat. His comprehensiveness
is not only a comprehensiveness of thought, but of ways of exposition,
due very largely, we must think, to his cosmopolitan education. The
result has been to the great detriment of Leibniz's influence as a
systematic thinker, although it may be argued that it has aided his
indirect and suggestive influence, the absorption of his ideas by men
of literature, by Goethe, above all by Lessing, and his stimulating
effect upon science and philosophy. It is certain that the attempt to
systematize his thoughts, as was done by Wolff, had for its result the
disappearance of all that was profound and thought-exciting.

If his philosophy thus reflects the manner of his daily life,
the occupations of the latter were informed by the spirit of
his philosophy. Two of the dearest interests of Leibniz remain
to be mentioned,--one, the founding of academies; the other, the
reconciling of religious organizations. The former testifies to his
desire for comprehensiveness, unity, and organization of knowledge;
the latter to his desire for practical unity, his dislike of all
that is opposed and isolated. His efforts in the religions direction
were twofold. The first was to end the theological and political
controversies of the time by the reunion of the Protestant and Roman
Catholic Churches. It was a plan which did the greatest honor to the
pacific spirit of Leibniz, but it was predestined to failure. Both
sides made concessions,--more concessions than we of to-day should
believe possible. But the one thing the Roman Catholic Church would not
concede was the one thing which the Protestant Church demanded,--the
notion of authority and hierarchy. Indeed, it may be questioned whether
the terms on which Leibniz conceived of their reunion do not point to
the greatest weakness in his philosophy,--the tendency to overlook
oppositions and to resolve all contradiction into differences of
degree. Hardly had this plan fallen through when Leibniz turned to
the project of a union of the Lutheran and Reformed branches of the
Protestant Church. This scheme was more hopeful, and while unrealized
during the life of our philosopher, was afterwards accomplished.

It is noteworthy that even before Leibniz went to Paris and to
London he had conceived the idea of a society of learned men for the
investigation, the systematization, and the publication of scientific
truth in all its varied forms,--a society which should in breadth
include the whole sphere of sciences, but should not treat them as so
many isolated disciplines, but as members of one system. This idea
was quickened when Leibniz saw the degree in which it had already
been realized in the two great world-capitals. He never ceased to
try to introduce similar academies wherever he had influence. In
1700 his labors bore their fruit in one instance. The Academy at
Berlin was founded, and Leibniz was its first, and indeed life-long,
president. But disappointment met him at Vienna, Dresden, and
St. Petersburg, where he proposed similar societies.

Any sketch of Leibniz's life, however brief, would be imperfect which
did not mention the names at least of two remarkable women,--remarkable
in themselves, and remarkable in their friendship with Leibniz. These
were Sophia, grand-daughter of James I. of England (and thus
the link by which the House of Brunswick finally came to rule over
Great Britain) and wife of the Duke of Brunswick, and her daughter
Sophia Charlotte, wife of the first king of Prussia. The latter,
in particular, gave Leibniz every encouragement. She was personally
deeply interested in all theological and philosophical questions. Upon
her death-bed, in 1705, she is said to have told those about her that
they were not to mourn for her, as she should now be able to satisfy
her desire to learn about things which Leibniz had never sufficiently

Her death marks the beginning of a period in Leibniz's life which it is
not pleasant to dwell upon. New rulers arose that knew not Leibniz. It
cannot be said that from this time till his death in Hanover in 1716
Leibniz had much joy or satisfaction. His best friends were dead; his
political ambitions were disappointed; he was suspected of coldness
and unfriendliness by the courts both of Berlin and Hanover; Paris and
Vienna were closed to him, so far as any wide influence was concerned,
by his religious faith; the controversy with the friends of Newton
still followed him. He was a man of the most remarkable intellectual
gifts, of an energy which could be satisfied only with wide fields
of action; and he found himself shut in by narrow intrigue to a petty
round of courtly officialism. It is little wonder that the following
words fell from his lips: "Germany is the only country in the world
that does not know how to recognize the fame of its children and to
make that fame immortal. It forgets itself; it forgets its own, unless
foreigners make it mindful of its own treasures." A Scotch friend of
Leibniz, who happened to be in Hanover when he died, wrote that Leibniz
"was buried more like a robber than what he really was,--the ornament
of his country." Such was the mortal end of the greatest intellectual
genius since Aristotle. But genius is not a matter to be bounded in
life or in death by provincial courts. Leibniz remains a foremost
citizen in that "Kingdom of Spirits" in whose formation he found the
meaning of the world.



What is true of all men is true of philosophers, and of Leibniz
among them. Speaking generally, what they are unconsciously and
fundamentally, they are through absorption of their antecedents
and surroundings. What they are consciously and reflectively,
they are through their reaction upon the influence of heredity
and environment. But there is a spiritual line of descent and a
spiritual atmosphere; and in speaking of a philosopher, it is with this
intellectual heredity and environment, rather than with the physical,
that we are concerned. Leibniz was born into a period of intellectual
activity the most teeming with ideas, the most fruitful in results,
of any, perhaps, since the age of Pericles. We pride ourselves justly
upon the activity of our own century, and in diffusion of intellectual
action and wide-spread application of ideas the age of Leibniz
could not compare with it. But ours _is_ the age of diffusion and
application, while his was one of fermentation and birth.

Such a period in its earlier days is apt to be turbid and
unsettled. There is more heat of friction than calm light. And such had
been the case in the hundred years before Leibniz. But when he arrived
at intellectual maturity much of the crudity had disappeared. The
troubling of the waters of thought had ceased; they were becoming
clarified. Bacon, Hobbes, Descartes, each had crystallized something
out of that seething and chaotic mass of new ideas which had forced
itself into European consciousness. Men had been introduced into a
new world, and the natural result had been feelings of strangeness,
and the vagaries of intellectual wanderings. But by the day of Leibniz
the intellectual bearings had been made out anew, the new mental
orientation had been secured.

The marks of this "new spiritual picture of the universe" are
everywhere to be seen in Leibniz. His philosophy is the dawning
consciousness of the modern world. In it we see the very conception and
birth of the modern interpretation of the world. The history of thought
is one continuous testimony to the ease with which we become hardened
to ideas through custom. Ideas are constantly precipitating themselves
out of the realm of ideas into that of ways of thinking and of viewing
the universe. The problem of one century is the axiom of another. What
one generation stakes its activity upon investigating is quietly taken
for granted by the next. And so the highest reach of intellectual
inspiration in the sixteenth century is to-day the ordinary food of
thought, accepted without an inquiry as to its source, and almost
without a suspicion that it has a recent historic origin. We have to
go to Bacon or to Leibniz to see the genesis and growth of those ideas
which to-day have become materialized into axiomatic points of view
and into hard-and-fast categories of thought. In reading Leibniz the
idea comes over us in all its freshness that there was a time when
it was a discovery that the world is a universe, made after one plan
and of one stuff. The ideas of inter-relation, of the harmony of law,
of mutual dependence and correspondence, were not always the assumed
starting-points of thought; they were once the crowning discoveries
of a philosophy aglow and almost intoxicated with the splendor of its
far-reaching generalizations. I take these examples of the unity of
the world, the continuity and interdependence of all within it, because
these are the ideas which come to their conscious and delighted birth
in the philosophy of Leibniz. We do not put ourselves into the right
attitude for understanding his thought until we remember that these
ideas--the commonest tools of our thinking--were once new and fresh,
and in their novelty and transforming strangeness were the products
of a philosophic interpretation of experience. Except in that later
contemporary of Leibniz, the young and enthusiastic Irish idealist,
Berkeley, I know of no historic thinker in whom the birth-throes
(joyous, however) of a new conception of the world are so evident as
in Leibniz. But while in Berkeley what we see is the young man carried
away and astounded by the grandeur and simplicity of a "new way of
ideas" which he has discovered, what we see in Leibniz is the mature
man penetrated throughout his being with an idea which in its unity
answers to the unity of the world, and which in its complexity answers,
tone to tone, to the complex harmony of the world.

The familiarity of the ideas which we use hides their grandeur from
us. The unity of the world is a matter of course with us; the dependent
order of all within it a mere starting-point upon which to base
our investigations. But if we will put ourselves in the position of
Leibniz, and behold, not the new planet, but the new universe, so one,
so linked together, swimming into our ken, we shall feel something of
the same exultant thrill that Leibniz felt,--an exultation not indeed
personal in its nature, but which arises from the expansion of the
human mind face to face with an expanding world. The spirit which
is at the heart of the philosophy of Leibniz is the spirit which
speaks in the following words: "Quin imo qui unam partem materiæ
comprehenderet, idem comprehenderet totum universum ob eandem
περιχώρησιν quam dixi. Mea principia talia sunt, ut vix a se invicem
develli possint. Qui unum bene novit, omnia novit." It is a spirit
which feels that the secret of the universe has been rendered up to
it, and which breathes a buoyant optimism. And if we of the nineteenth
century have chosen to bewail the complexity of the problem of life,
and to run hither and thither multiplying "insights" and points of
view till this enthusiastic confidence in reason seems to us the
rashness of an ignorance which does not comprehend the problem, and
the unity in which Leibniz rested appears cold and abstract beside
the manifold richness of the world, we should not forget that after
all we have incorporated into our very mental structure the fundamental
thoughts of Leibniz,--the thoughts of the rationality of the universe
and of the "reign of law."

What was the origin of these ideas in the mind of Leibniz? What
influences in the philosophic succession of thinkers led him in this
direction? What agencies acting in the intellectual world about him
shaped his ideal reproduction of reality? Two causes above all others
stand out with prominence,--one, the discoveries and principles of
modern physical science; the other, that interpretation of experience
which centuries before had been formulated by Aristotle. Leibniz has a
double interest for those of to-day who reverence science and who hold
to the historical method. His philosophy was an attempt to set in order
the methods and principles of that growing science of nature which
even then was transforming the emotional and mental life of Europe;
and the attempt was guided everywhere by a profound and wide-reaching
knowledge of the history of philosophy. On the first point Leibniz
was certainly not alone. Bacon, Hobbes, Descartes, Spinoza, each felt
in his own way the fructifying touch of the new-springing science,
and had attempted under its guidance to interpret the facts of nature
and of man. But Leibniz stood alone in his interest in the history of
thought. He stands alone indeed till he is greeted by his compeers
of the nineteenth century. To Bacon previous philosophy--the Greek,
the scholastic--was an "eidol of the theatre." The human mind must be
freed from its benumbing influence. To Descartes it was useless rubbish
to be cleared away, that we might get a _tabula rasa_ upon which to
make a fresh start. And shall Locke and the empirical English school,
or Reid and the Scotch school, or even Kant, be the first to throw a
stone at Bacon and Descartes? It was reserved to Leibniz, with a genius
almost two centuries in advance of his times, to penetrate the meaning
of the previous development of reflective thought. It would be going
beyond our brief to claim that Leibniz was interested in this _as_ a
historical movement, or that he specially concerned himself with the
genetic lines which connected the various schools of thought. But we
should come short of our duty to Leibniz if we did not recognize his
conscious and largely successful attempt to apprehend the core of truth
in all systems, however alien to his own, and to incorporate it into
his own thinking.

Nothing could be more characteristic of Leibniz than his saying,
"I find that most systems are right in a good share of that which
they advance, but not so much in what they deny;" or than this other
statement of his, "We must not hastily believe that which the mass
of men, or even of authorities, advance, but each must demand for
himself the proofs of the thesis sustained. Yet long research generally
convinces that the old and received opinions are good, provided they
be interpreted justly." It is in the profound union in Leibniz of
the principles which these quotations image that his abiding worth
lies. Leibniz was interested in affirmations, not in denials. He was
interested in securing the union of the modern _method_, the spirit
of original research and independent judgment, with the conserved
_results_ of previous thought. Leibniz was a man of his times; that is
to say, he was a scientific man,--the contemporary, for example, of men
as different as Bernouilli, Swammerdam, Huygens, and Newton, and was
himself actively engaged in the prosecution of mathematics, mechanics,
geology, comparative philology, and jurisprudence. But he was also a
man of Aristotle's times,--that is to say, a philosopher, not satisfied
until the facts, principles, and methods of science had received an
interpretation which should explain and unify them.

Leibniz's acquaintance with the higher forms of mathematics was
due, as we have seen, to his acquaintance with Huygens. As he made
the acquaintance of the latter at the same time that he made the
acquaintance of the followers of Descartes, it is likely that he
received his introduction to the higher developments of the scientific
interpretation of nature and of the philosophic interpretation of
science at about the same time. For a while, then, Leibniz was a
Cartesian; and he never ceased to call the doctrine of Descartes
the antechamber of truth. What were the ideas which he received from
Descartes? Fundamentally they were two,--one about the method of truth,
the other about the substance of truth. He received the idea that the
method of philosophy consists in the analysis of any complex group of
ideas down to simple ideas which shall be perfectly clear and distinct;
that all such clear and distinct ideas are true, and may then be used
for the synthetic reconstruction of any body of truth. Concerning
the substance of philosophic truth, he learned that nature is to be
interpreted mechanically, and that the instrument of this mechanical
interpretation is mathematics. I have used the term "received" in
speaking of the relation of Leibniz to these ideas. Yet long before
this time we might see him giving himself up to dreams about a vast
art of combination which should reduce all the ideas concerned in
any science to their simplest elements, and then combine them to any
degree of complexity. We have already seen him giving us a picture
of a boy of fifteen gravely disputing with himself whether he shall
accept the doctrine of forms and final causes, or of physical causes,
and as gravely deciding that he shall side with the "moderns;" and
that boy was himself. In these facts we have renewed confirmation of
the truth that one mind never receives from another anything excepting
the stimulus, the reflex, the development of ideas which have already
possessed it. But when Leibniz, with his isolated and somewhat
ill-digested thoughts, came in contact with that systematized and
connected body of doctrines which the Cartesians presented to him in
Paris, his ideas were quickened, and he felt the necessity--that final
mark of the philosophic mind--of putting them in order.

About the method of Descartes, which Leibniz adopted from him, or
rather formulated for himself under the influence of Descartes,
not much need be said. It was the method of Continental thought
till the time of Kant. It was the mother of the philosophic systems
of Descartes, Leibniz, and Spinoza. It was equally the mother of
the German _Aufklärung_ and the French _éclaircissement_. Its
fundamental idea is the thought upon which Rationalism everywhere bases
itself. It says: Reduce everything to simple notions. Get clearness;
get distinctness. Analyze the complex. Shun the obscure. Discover
axioms; employ these axioms in connection with the simple notions,
and build up from them. Whatever can be treated in this way is capable
of proof, and only this. Leibniz, I repeat, possessed this method in
common with Descartes and Spinoza. The certainty and demonstrativeness
of mathematics stood out in the clearest contrast to the uncertainty,
the obscurity, of all other knowledge. And to them, as to all before
the days of Kant, it seemed beyond doubt that the method of mathematics
consists in the analysis of notions, and in their synthesis through the
medium of axioms, which are true because identical statements; while
the notions are true because clear and distinct.

And yet the method led Leibniz in a very different direction. One of
the fundamental doctrines, for example, of Leibniz is the existence
everywhere of minute and obscure perceptions,--which are of the
greatest importance, but of which we, at least, can never have
distinct consciousness. How is this factor of his thought, which
almost approaches mysticism, to be reconciled with the statements just
made? It is found in the different application which is made of the
method. The object of Descartes is the _erection of a new structure
of truth_ upon a _tabula rasa_ of all former doctrines. The object of
Leibniz is the _interpretation of an old body of truth_ by a method
which shall reveal it in its clearest light. Descartes and Spinoza
are "rationalists" both in their method and results. Leibniz is a
"rationalist" in his method; but his application of the method is
everywhere controlled by historic considerations. It is, I think,
impossible to over-emphasize this fact. Descartes was profoundly
convinced that past thought had gone wrong, and that its results were
worthless. Leibniz was as profoundly convinced that its instincts had
been right, and that the general idea of the world which it gave was
correct. Leibniz would have given the heartiest assent to Goethe's
saying, "Das Wahre war schon längst gefunden." It was out of the
question, then, that he should use the new method in any other than an
interpreting way to bring out in a connected system and unity the true
meaning of the subject-matter.

So much of generality for the method of Leibniz. The positive substance
of doctrine which he developed under scientific influence affords
matter for more discussion. Of the three influences which meet us here,
two are still Cartesian; the third is from the new science of biology,
although not yet answering to that name. These three influences are, in
order: the idea that nature is to be explained mechanically; that this
is to be brought about through the application of mathematics; and,
from biology, the idea that all change is of the nature of continuous
growth or unfolding. Let us consider each in this order.

What is meant by the mechanical explanation of nature? To answer a
question thus baldly put, we must recall the kind of explanations which
had satisfied the scholastic men of science. They had been explanations
which, however true, Leibniz says, as general principles, do not touch
the details of the matter. The explanations of natural facts had been
found in general principles, in substantial forces, in occult essences,
in native faculties. Now, the first contention of the founders of the
modern scientific movement was that such general considerations are
not verifiable, and that if they are, they are entirely aside from the
point,--they fail to explain any given fact. Explanation must always
consist in discovering an immediate connection between some fact and
some co-existing or preceding fact. Explanation does not consist in
referring a fact to a general power, it consists in referring it to an
antecedent whose existence is its necessary condition. It was not left
till the times of Mr. Huxley to poke fun at those who would explain
some concrete phenomenon by reference to an abstract principle ending
in --ity. Leibniz has his word to say about those who would account for
the movements of a watch by reference to a principle of horologity, and
of mill-stones by a fractive principle.

Mechanical explanation consists, accordingly, in making out an actual
connection between two existing facts. But this does not say very
much. A connection of what kind? In the first place, a connection of
the same order as the facts observed. If we are explaining corporeal
phenomena, we must find a corporeal link; if we are explaining
phenomena of motion, we must find a connection of motion. In one of his
first philosophical works Leibniz, in taking the mechanical position,
states what he means by it. In the "Confession of Nature against the
Atheists" he says that it must be confessed to those who have revived
the corpuscular theory of Democritus and Epicurus, to Galileo, Bacon,
Gassendi, Hobbes, and Descartes, that in explaining material phenomena
recourse is to be had neither to God nor to any other incorporeal
thing, form, or quality, but that all things are to be explained
from the nature of matter and its qualities, especially from their
magnitude, figure, and motion. The physics of Descartes, to which was
especially due the spread of mechanical notions, virtually postulated
the problem: given a homogeneous quantity of matter, endowed only with
extension and mobility, to account for all material phenomena. Leibniz
accepts this mechanical view without reserve.

What has been said suggests the bearing of mathematics in this
connection. Extension and mobility may be treated by mathematics. It is
indeed the business of the geometer to give us an analysis of figured
space, to set before us all possible combinations which can arise,
assuming extension only. The higher analysis sets before us the results
which inevitably follow if we suppose a moving point or any system of
movements. Mathematics is thus the essential tool for treating physical
phenomena as just defined. But it is more. The mechanical explanation
of Nature not only requires such a development of mathematics as will
make it applicable to the interpretation of physical facts, but the
employment of mathematics is necessary for the very discovery of these
facts. Exact observation was the necessity of the growing physical
science; and exact observation means such as will answer the question,
_How much?_ Knowledge of nature depends upon our ability to _measure_
her processes,--that is, to reduce distinctions of quality to those of
quantity. The only assurance that we can finally have that two facts
are connected in such a way as to fulfil the requirements of scientific
research, is that there is a complete quantitative connection between
them, so that one can be regarded as the other transformed. The advance
of physical science from the days of Copernicus to the present has
consisted, therefore, on one hand, in a development of mathematics
which has made it possible to apply it in greater and greater measure
to the discussion and formulation of the results of experiment, and to
deduce laws which, when interpreted physically, will give new knowledge
of fact; and, on the other, to multiply, sharpen, and make precise all
sorts of devices by which the processes of nature may be measured. The
explanation of nature by natural processes; the complete application
of mathematics to nature,--these are the two thoughts which, so far,
we have seen to be fundamental to the development of the philosophy
of Leibniz.

The third factor, and that which brings Leibniz nearer, perhaps, our
own day than either of the others, is the growth of physiological
science. Swammerdam, Malpighi, Leewenhoek,--these are names which
occur and recur in the pages of Leibniz. Indeed, he appears to be the
first of that now long line of modern philosophers to be profoundly
influenced by the conception of life and the categories of organic
growth. Descartes concerned himself indeed with physiological problems,
but it was only with a view to applying mechanical principles. The
idea of the vital unity of all organs of the body might seem to
be attractive to one filled with the notion of the unity of all in
God, and yet Spinoza shows no traces of the influence of the organic
conception. Not until Kant's famous definition of organism do we see
another philosopher moved by an attempt to comprehend the categories of
living structure.

But it is the idea of organism, of life, which is radical to the
thought of Leibniz. I do not think, however, that it can truly be said
that he was led to the idea simply from the state of physiological
investigation at that time. Rather, he had already learned to think of
the world as organic through and through, and found in the results of
biology confirmations, apt illustrations of a truth of which he was
already thoroughly convinced. His writings show that there were two
aspects of biological science which especially interested him. One
was the simple fact of organism itself,--the fact of the various
activities of different organs occurring in complete harmony for one
end. This presented three notions very dear to the mind of Leibniz,
or rather three moments of the same idea,--the factors of activity,
of unity brought about by co-ordinated action, and of an end which
reveals the meaning of the activity and is the ideal expression of
the unity. The physiologists of that day were also occupied with the
problem of growth. The generalization that all is developed _ab ovo_
was just receiving universal attention. The question which thrust
itself upon science for solution was the mode by which ova, apparently
homogeneous in structure, developed into the various forms of the
organic kingdom. The answer given was "evolution." But evolution had
not the meaning which the term has to-day. By evolution was meant
that the whole complex structure of man, for example, was virtually
contained in the germ, and that the apparent phenomenon of growth was
not the addition of anything from without, but simply the unfolding
and magnifying of that already existing. It was the doctrine which
afterwards gave way to the epigenesis theory of Wolff, according to
which growth is not mere unfolding or unwrapping, but progressive
differentiation. The "evolution" theory was the scientific theory of
the times, however, and was warmly espoused by Leibniz. To him, as we
shall see hereafter, it seemed to give a key which would unlock one of
the problems of the universe.

Such, then, were the three chief generalizations which Leibniz found
current, and which most deeply affected him. But what use did he make
of them? He did not become a philosopher by letting them lie dormant in
his mind, nor by surrendering himself passively to them till he could
mechanically apply them everywhere. He was a philosopher only in virtue
of the active attitude which his mind took towards them. He could not
simply accept them at their face-value; he must ask after the source of
their value, the royal stamp of meaning which made them a circulatory
medium. That is to say, he had to interpret these ideas, to see what
they mean, and what is the basis of their validity.

Not many men have been so conscious of just the bearings of their
own ideas and of their source as was he. He often allows us a direct
glimpse into the method of his thinking, and nowhere more than when
he says: "Those who give themselves up to the details of science
usually despise abstract and general researches. Those who go into
universal principles rarely care for particular facts. But I equally
esteem both." Leibniz, in other words, was equally interested in the
application of scientific principles to the explanation of the details
of natural phenomena, and in the bearing and meaning of the principles
themselves,--a rare combination, indeed, but one, which existing,
stamps the genuine philosopher. Leibniz substantially repeats this
idea when he says: "Particular effects must be explained mechanically;
but the general principles of physics and mathematics depend upon
metaphysics." And again: "All occurs mechanically; but the mechanical
principle is not to be explained from material and mathematical
considerations, but it flows from a higher and a metaphysical source."

As a man of science, Leibniz might have stopped short with the
ideas of mechanical law, of the application of mathematics, and of
the continuity of development. As a philosopher he could not. There
are some scientific men to whom it always seems a perversion of their
principles to attempt to carry them any beyond their application to the
details of the subject. They look on in a bewildered and protesting
attitude when there is suggested the necessity of any further
inquiry. Or perhaps they dogmatically deny the possibility of any such
investigation, and as dogmatically assume the sufficiency of their
principles for the decision of all possible problems. But bewildered
fear and dogmatic assertion are equally impotent to fix arbitrary
limits to human thought. Wherever there is a subject that has meaning,
there is a field which appeals to mind, and the mind will not cease
its endeavors till it has made out what that meaning is, and has made
it out in its entirety. So the three principles already spoken of were
but the starting-points, the stepping-stones of Leibniz's philosophic
thought. While to physical science they are solutions, to philosophy
they are problems; and as such Leibniz recognized them. What solution
did he give?

So far as the principle of mechanical explanation is concerned,
the clew is given by considering the factor upon which he laid
most emphasis, namely, motion. Descartes had said that the essence
of the physical world is extension. "Not so," replied Leibniz;
"It is motion." These answers mark two typical ways of regarding
nature. According to one, nature is something essentially rigid
and static; whatever change in it occurs, is a change of form,
of arrangement, an external modification. According to the other,
nature is something essentially dynamic and active. Change according
to law is its very essence. Form, arrangement are only the results
of this internal principle. And so to Leibniz, extension and the
spatial aspects of physical existence were only secondary, they were
phenomenal. The primary, the real fact was motion.

The considerations which led him to this conclusion are simple
enough. It is the fact already mentioned, that explanation always
consists in reducing phenomena to a law of motion which connects
them. Descartes himself had not succeeded in writing his physics
without everywhere using the conception of motion. But motion cannot
be got out of the idea of extension. Geometry will not give us
activity. What is this, except virtually to admit the insufficiency
of purely statical conceptions? Leibniz found himself confirmed in
this position by the fact that the more logical of the followers
of Descartes had recognized that motion is a superfluous intruder,
if extension be indeed the essence of matter, and therefore had been
obliged to have recourse to the immediate activity of God as the cause
of all changes. But this, as Leibniz said, was simply to give up the
very idea of mechanical explanation, and to fall back into the purely
general explanations of scholasticism.

This is not the place for a detailed exposition of the ideas of Leibniz
regarding matter, motion, and extension. We need here only recognize
that he saw in motion the final reality of the physical universe. But
what about motion? To many, perhaps the majority, of minds to-day it
seems useless or absurd, or both, to ask any question about motion. It
is simply an ultimate _fact_, to which all other facts are to be
reduced. We are so familiar with it as a solution of all physical
problems that we are confused, and fail to recognize it when it appears
in the guise of a problem. But, I repeat, philosophy cannot stop with
facts, however ultimate. It must also know something about the meaning,
the significance, in short the ideal bearing, of facts. From the point
of view of philosophy, motion has a certain function in the economy of
the universe; it is, as Aristotle saw, something ideal.

The name of Aristotle suggests the principles which guided Leibniz
in his interpretation of the fact of motion. The thought of Aristotle
moves about the two poles of potentiality and actuality. Potentiality
is not _mere_ capacity; it is being in an undeveloped, imperfect
stage. Actuality is, as the word suggests, activity. Anything is
potential in so far as it does not manifest itself in action; it is
actual so far as it does thus show forth its being. Now, movement, or
change in its most general sense, is that by which the potential comes
to the realization of its nature, and functions as an activity. Motion,
then, is not an ultimate fact, but is subordinate. It exists for an
end. It is that by which existence realizes its idea; that is, its
proper type of action.

Now Leibniz does not formally build upon these distinctions; and
yet he is not very far removed from Aristotle. Motion, he is never
weary of repeating, means force, means energy, means activity. To
say that the essence of nature is motion, is to say that the natural
world finally introduces us to the supremacy of action. Reality is
activity. _Substance c'est l'action._ That is the key-note and the
battle-cry of the Leibnizian philosophy. Motion is that by which being
expresses its nature, fulfils its purpose, reveals its idea. In short,
the specific scientific conception of motion is by Leibniz transformed
into the philosophic conception of force, of activity. In motion he
sees evidence of the fact that the universe is radically dynamic.

In the applicability of mathematics to the interpretation of nature
Leibniz finds witness to the continuity and order of the world. We
have become so accustomed to the fact that mathematics may be directly
employed for the discussion and formulation of physical investigations
that we forget what is implied in it. It involves the huge assumption
that the world answers to reason; so that whatever the mind finds to be
ideally true may be taken for granted to be physically true also. But
in those days, when the correlation of the laws of the world and the
laws of mathematical reasoning was a fresh discovery, this aspect of
the case could not be easily lost sight of.

In fact it was this correlation which filled the _Zeitgeist_ of
the sixteenth century with the idea that it had a new organ for the
penetration of nature, a new sense for learning its meaning. Descartes
gives the following as the origin of his philosophy: "The long chains
of simple and easy reasons which geometers employ, even in their
most complex demonstrations, made me fancy that all things which are
the objects of human knowledge are _similarly interdependent_." To
Leibniz also mathematics seemed to give a clew to the order, the
interdependence, the harmonious relations, of the world.

In this respect the feeling of Plato that God geometrizes found
an echoing response in Leibniz. But the latter would hardly have
expressed it in the same way. He would have preferred to say that God
everywhere uses the infinitesimal calculus. In the applicability of the
calculus to the discussion of physical facts, Leibniz saw two truths
reflected,--that everything that occurs has its reason, its dependent
connection upon something else, and that all is continuous and without
breaks. While the formal principles of his logic are those of identity
and contradiction, his real principles are those of sufficient reason
and of continuity. Nature never makes leaps; everything in nature has
a sufficient reason why it is as it is: these are the philosophic
generalizations which Leibniz finds hidden in the applicability
of mathematics to physical science. Reason finds itself everywhere
expressed in nature; and the law of reason is unity in diversity,

Let us say, in a word, that the correlation between the laws of
mathematics and of physics is the evidence of the rational character
of nature. Nature may be reduced to motions; and motions can be
understood only as force, activity. But the laws which connect motions
are fundamentally mathematical laws,--laws of reason. Hence force,
activity, can be understood only as rational, as spiritual. Nature
is thus seen to mean Activity, and Activity is seen to mean
Intelligence. Furthermore, as the fundamental law of intelligence is
the production of difference in unity, the primary law of physical
change must be the manifestation of this unity in difference,--or,
as Leibniz interpreted it, continuity. In nature there are no breaks,
neither of quantity nor of quality nor of relationship. The full force
of this law we shall see later.

Such an idea can hardly be distinguished from the idea of growth or
development; one passes naturally into the other. Thus it is equally
proper to say that the third scientific influence, the conception of
organism and growth, is dominant in the Leibnizian thought, or that
this is swallowed up and absorbed in the grand idea of continuity. The
law of animal and vegetable life and the law of the universe are
identified. The substance of the universe is activity; the law of
the universe is interdependence. What is this but to say that the
universe is an organic whole? Its activity is the manifestation of
life,--nay, it is life. The laws of its activity reveal that continuity
of development, that harmony of inter-relation, which are everywhere
the marks of life. The final and fundamental notion, therefore, by
which Leibniz interprets the laws of physics and mathematics is that of
Life. This is his regnant category. It is "that higher and metaphysical
source" from which the very existence and principles of mechanism
flow. The perpetual and ubiquitous presence of motion reveals the
pulsations of Life; the correlation, the rationality, of these motions
indicate the guiding presence of Life. This idea is the alpha and omega
of his philosophy.



Leibniz, like every great man, absorbed into himself the various
thoughts of his time, and in absorbing transformed them. He brought
into a focus of brilliancy the diffused lights of truth shining here
and there. He summed up in a pregnant and comprehensive category
the scattered principles of his age. Yet we are not to suppose that
Leibniz considered these various ideas one by one, and then patched
them into an artificial unity of thought. Philosophies are not
manufactured piecemeal out of isolated and fragmentary thoughts; they
grow from a single root, absorbing from their environment whatever
of sustenance offers itself, and maturing in one splendid fruit of
spiritual truth. It is convenient, indeed, to isolate various phases
of truth, and consider them as distinct forces working to shape one
final product, and as a convenient artifice it is legitimate. But it
answers to no process actually occurring. Leibniz never surrendered
his personal unity, and out of some one root-conception grew all his
ideas. The principles of his times were not separate forces acting upon
him, they were the foods of which he selected and assimilated such as
were fitted to nourish his one great conception.

But it is more than a personal unity which holds together the thinking
of a philosopher. There is the unity of the problem, which the
philosopher has always before him, and in which all particular ideas
find their unity. All else issues from this and merges into it. The
various influences which we have seen affecting Leibniz, therefore,
got their effectiveness from the relation which he saw them bear to the
final problem of all thought. This is the inquiry after the unity of
experience, if we look at it from the side of the subject; the unity
of reality, if we put it from the objective side. Yet each age states
this problem in its own way, because it sees it in the light of some
difficulty which has recently arisen in consciousness. At one time,
the question is as to the relation of the one to the many; at another,
of the relation of the sensible to the intelligible world; at another,
of the relation of the individual to the universal. And this last
seems to have been the way in which it specifically presented itself
to Leibniz. This way of stating it was developed, though apparently
without adequate realization of its meaning, by the philosophy
of scholasticism. It stated the problem as primarily a logical
question,--the relation of genera, of species, of individuals to each
other. And the school-boy, made after the stamp of literary tradition,
knows that there were two parties among the Schoolmen,--the Realists,
and the Nominalists; one asserting, the other denying, the objective
reality of universals. To regard this discussion as useless, is to
utter the condemnation of philosophy, and to relegate the foundation
of science to the realm of things not to be inquired into. To say that
it is an easy matter to decide, is to assume the decision with equal
ease of all the problems that have vexed the thought of humanity. To
us it seems easy because we have bodily incorporated into our thinking
the results of both the realistic and the nominalistic doctrines,
without attempting to reconcile them, or even being conscious of
the necessity of reconciliation. We assert in one breath that the
individual is alone real, and in the next assert that only those forms
of consciousness which represent something in the universe are to be
termed knowledge. At one moment we say that universals are creations of
the individual mind, and at the next pass on to talk of laws of nature,
or even of a reign of law. In other words, we have learned to regard
both the individual and the universal as real, and thus ignoring the
problem, think we have solved it.

But to Leibniz the problem presented itself neither as a logical
question, nor yet as one whose solution might be taken for granted. On
the contrary, it was just this question: How shall we conceive the
individual to be related to the universe? which seemed to him to be the
nerve of the philosophic problem, the question whose right answer would
solve the problems of religion, of morals, of the basis of science,
as well as of the nature of reality. The importance of just this way
of putting the question had been rendered evident by the predecessors
and contemporaries of Leibniz, especially by Descartes, Spinoza, and
Locke. His more specific relations to the last-named will occupy us
hereafter; at present we must notice how the question stood at the
hands of Descartes and Spinoza.

Descartes had separated the individual from the universal. His
philosophy began and ended with a dualism. I have just said that the
problem of philosophy is the unity of experience. Yet we find that
there have been thinkers, and those of the first rank, who have left
the matter without discovering any ultimate unity, or rather who have
made it the burden of their contention that we cannot explain the world
without at least two disparate principles. But if we continue to look
at the matter in this historical way, we shall see that this dualism
has always been treated by the successors of such a philosopher, not
as a solution, but as a deeper statement of the problem. It is the
function of dualistic philosophies to re-state the question in a new
and more significant way. There are times when the accepted unity of
thought is seen to be inadequate and superficial. Men are thrashing old
straw, and paying themselves with ideas which have lost their freshness
and their timeliness. There then arises a philosopher who goes deep,
beyond the superficial unity, and who discovers the untouched
problem. His it is to assert the true meaning of the question,
which has been unseen or evaded. The attitude of dualism is thus
always necessary, but never final. Its value is not in any solution,
but in the generality and depth of the problem which it proposes, and
which incites thought to the discovery of a unity of equal depth and

Except for Descartes, then, we should not be conscious of the gulf
that yawns between the individual mind and the universe in front of
it. He presented the opposition as between mind and matter. The essence
of the former is thought; of the latter, extension. The conceptions
are disparate and opposed. No interaction is possible. His disciples,
more consistent than their master, called in a _deus ex machina_,--the
miraculous intervention of God,--in order to account for the appearance
of reciprocal action between the universe of matter and the thinking
individual. Thus they in substance admitted the relation between
them to be scientifically inexplicable, and had recourse to the
supernatural. The individual does not act upon the universe to produce,
destroy, or alter the arrangement of anything. But upon the _occasion_
of his volition God produces a corresponding material change. The world
does not act upon the soul of the individual to produce thoughts or
sensations. God, upon _occasion_ of the external affection, brings
them into being. With such thoroughness Descartes performed his task
of separation. Yet the introduction of the _deus ex machina_ only
complicated the problem; it introduced a third factor where two were
already too many. What is the relation of God to Mind and to Matter? Is
it simply a third somewhat, equally distinct from both, or does it
contain both within itself?

Spinoza attempted to solve the problem in the latter sense. He
conceived God to be the one substance of the universe, possessing the
two known attributes of thought and matter. These attributes are one
in God; indeed, he is their unity. This is the sole legitimate outcome
of the Cartesian problem stated as Descartes would have it stated. It
overcomes the absoluteness of the dualism by discovering a common and
fundamental unity, and at the same time takes the subject out of the
realm of the miraculous. For the solution works both ways. It affects
the nature of God, as well as of extension and thought. It presents
him to us, not as a supernatural being, but as the unity of thought and
extension. In knowing these as they are, we know God as he is. Spinoza,
in other words, uses the conception of God in a different way from
the Cartesians. The latter had treated him as the God of theology,--a
being supernatural; Spinoza uses the conception as a scientific one,
and speaks of _Deus sive Natura_.

Leibniz recognized the unphilosophic character of the recourse to a
_deus ex machina_ as clearly as Spinoza, and yet did not accept his
solution. To find out why he did not is the problem of the historian
of thought. The one cause which stands out above all others is that in
the unity of Spinoza all difference, all distinction, is lost. All
particular existences, whether things or persons, are _modes_
of extension and thought. Their _apparent_ existence is due to the
imagination, which is the source of belief in particular things. When
considered as they really are,--that is, by the understanding,--they
vanish. The one substance, with its two unchanging attributes of
thought and extension, alone remains. If it is a philosophic error
to give a solution which permits of no unity, is it not equally a
philosophic error to give one which denies difference? So it seemed
to Leibniz. The problem is to reconcile difference in unity, not to
swallow up difference in a blank oneness,--to reconcile the individual
with the universe, not to absorb him.

The unsatisfactoriness of the solution appears if we look at it from
another side. Difference implies change, while a unity in which all
variety is lost implies quiescence. Change is as much an illusion of
imagination to Spinoza as is variety. The One Reality is permanent. How
repugnant the conception of a static universe was to Leibniz we have
already learned. Spinoza fails to satisfy Leibniz, therefore, because
he does not allow the conceptions of individuality and of activity. He
presents a unity in which all distinction of individuals is lost,
and in which there is no room for change. But Spinoza certainly
presented the problem more clearly to Leibniz, and revealed more
definitely the conditions of its solution. The search is henceforth
for a unity which shall avoid the irresolvable dualism of Descartes,
and yet shall allow free play to the principles of individuality and of
activity. There must be, in short, a universe to which the individual
bears a real yet independent relation. What is this unity? The answer,
in the phraseology of Leibniz, is the _monad_. Spinoza would be right,
said Leibniz, were it not for the existence of monads. I know there are
some who have done Leibniz the honor of supposing that this is his way
of saying, "Spinoza is wrong because I am right;" but I cannot help
thinking that the saying has a somewhat deeper meaning. What, then,
is the nature of the monad? The answer to this question takes us back
to the point where the discussion of the question was left at the end
of chapter second. The nature of the monad is life. The monad is the
spiritual activity which lives in absolute harmony with an infinite
number of other monads.

Let us first consider the reasons of Leibniz for conceiving the
principle of unity as spiritual. Primarily it is because it is
impossible to conceive of a unity which is material. In the sensible
world there is no unity. There are, indeed, aggregations, collections,
which seem like unities; but the very fact that these are aggregations
shows that the unity is factitious. It is the very nature of matter to
be infinitely divisible: to say this is to deny the existence of any
true principle of unity. The world of nature is the world of space
and time; and where in space or time shall we find a unity where we
may rest? Every point in space, every moment in time, points beyond
itself. It refers to a totality of which it is but a part, or, rather,
a limitation. If we add resistance, we are not better situated. We
have to think of something which resists; and to this something we must
attribute extension,--that is to say, difference, plurality. Nor can we
find any resistance which is absolute and final. There may be a body
which is undivided, and which resists all energy now acting upon it;
but we cannot frame an intelligible idea of a body which is absolutely
indivisible. To do so is to think of a body out of all relation to
existing forces, something absolutely isolated; while the forces of
nature are always relative to one another. That which resists does so
in comparison with some opposing energy. The absolutely indivisible,
on the other hand, would be that which could not be brought into
comparison with other forces; it would not have any of the attributes
of force as we know it. In a word, whatever exists in nature is
relative in space, in time, and in qualities to all else. It is made
what it is by virtue of the totality of its relations to the universe;
it has no ultimate principle of self-subsistent unity in it.

Nor do we fare better if we attempt to find unity in the world of
nature as a whole. Nature has its existence as a whole in space and
time. Indeed, it is only a way of expressing the totality of phenomena
of space and time. It is a mere aggregate, a collection. Its very
essence is plurality, difference. It is divisible without limit,
and each of its divisions has as good a right to be called one as
the whole from which it is broken off. We shall consider hereafter
Leibniz's idea of infinity; but it is easy to see that he must deny
any true infinity to nature. An ultimate whole made up of parts is a
contradictory conception; and the idea of a quantitative infinite is
equally so. Quantity means number, measure, limitation. We may not
be able to assign number to the totality of occurrences in nature,
nor to measure her every event. This shows that nature is indefinitely
greater than any _assignable_ quantity; but it does not remove her from
the category of quantity. As long as the world is conceived as that
existing in space and time, it is conceived as that which has to be
measured. As we saw in the last chapter, the heart of the mechanical
theory of the world is in the application of mathematics to it. Since
quantity and mathematics are correlative terms, the natural world
cannot be conceived as infinite or as an ultimate unity.

In short, Leibniz urges and suggests in one form and another those
objections to the mechanical theory of reality which later German
philosophers have made us so familiar with. The objections are indeed
varied in statement, but they all come to the impossibility of finding
any unity, any wholeness, anything except plurality and partiality in
that which is externally conditioned,--as everything is in nature.

But the reasons as thus stated are rather negative than positive. They
show why the ultimate unity cannot be conceived as material, rather
than why it must be conceived as spiritual. The immediate evidence
of its spiritual nature Leibniz finds in the perception of the one
unity directly known to us,--the "me," the conscious principle within,
which reveals itself as an active force, and as truly one, since not a
spatial or temporal existence. And this evidence he finds confirmed by
the fact that whatever unity material phenomena appear to have comes to
them through their perception by the soul. Whatever the mind grasps in
one act, is manifested as one.

But it is not in any immediate certainty of fact that Leibniz finds
the best or completest demonstration of the spiritual nature of the
ultimate unity. This is found in the use which can be made of the
hypothesis. The truest witness to the spiritual character of reality
is found in the capacity of this principle to comprehend and explain
the facts of experience. With this conception the reason of things
can be ascertained, and light introduced into what were otherwise a
confused obscurity. And, indeed, this is the only sufficient proof of
any doctrine. It is not what comes before the formulation of a theory
which proves it; it is not the facts which suggest it, or the processes
which lead up to it: it is what comes after the formation of the
theory,--the uses that it can be put to; the facts which it will render
significant. The whole philosophy of Leibniz in its simplicity, width,
and depth, is the real evidence of the truth of his philosophical

The monad, then, is a spiritual unity; it is individualized
life. Unity, activity, individuality are synonymous terms in the
vocabulary of Leibniz. Every unity is a true substance, containing
within itself the source and law of its own activity. It is that
which is internally determined to action. It is to be conceived
after the analogy of the soul. It is an indivisible unity, like
"that particular something in us which thinks, apperceives and
wills, and distinguishes us in a way of its own from whatever else
thinks and wills." Against Descartes, therefore, Leibniz stands for
the principle of unity; against Spinoza, he upholds the doctrine
of individuality, of diversity, of multiplicity. And the latter
principle is as important in his thought as the former. Indeed, they
are inseparable. The individual is the true unity. There is an infinite
number of these individuals, each distinct from every other. The law
of specification, of distinction, runs through the universe. Two beings
cannot be alike. They are not individualized merely by their different
positions in space or time; duration and extension, on the contrary,
are, as we have seen, principles of relativity, of connection. Monads
are specified by an internal principle. Their distinct individuality is
constituted by their distinct law of activity. Leibniz will not have
a philosophy of abstract unity, representing the universe as simple
only, he will have a philosophy equal to the diversity, the manifold
wealth of variety, in the universe. This is only to say that he will be
faithful to his fundamental notion,--that of Life. Life does not mean
a simple unity like a mathematical one, it means a unity which is the
harmony of the interplay of diverse organs, each following its own law
and having its own function. When Leibniz says, God willed to have more
monads rather than fewer, the expression is indeed one of _naïveté_,
but the thought is one of unexplored depth. It is the thought that
Leibniz repeats when he says, "Those who would reduce all things to
modifications of one universal substance do not have sufficient regard
to the _order_, the _harmony_ of reality." Leibniz applies here, as
everywhere, the principle of continuity, which is unity in and through
diversity, not the principle of bare oneness. There is a kingdom of
monads, a realm truly infinite, composed of individual unities or
activities in an absolute continuity. Leibniz was one of the first,
if not the first, to use just the expression "uniformity of nature;"
but even here he explains that it means "uniform in variety, one in
principle, but varied in manifestation." The world is to be as rich as
possible. This is simply to say that distinct individuality as well as
ultimate unity is a law of reality.

But has not Leibniz fallen into a perilous position? In avoiding the
monotone of unity which characterizes the thought of Spinoza, has
he not fallen into a lawless variety of multiplicity, infinitely
less philosophic than even the dualism of Descartes, since it has
an infinity of ultimate principles instead of only two? If Spinoza
sacrificed the individual to the universe, has not Leibniz,
in his desire to emphasize the individual, gone to the other
extreme? Apparently we are introduced to a universe that is a mere
aggregate of an infinite multiplicity of realities, each independent
of every other. Such a universe would not be a universe. It would
be a chaos of disorder and conflict. We come, therefore, to a
consideration of the relation between these individual monads and
the universe. We have to discover what lifts the monads out of their
isolation and bestows upon them that stamp of universality which makes
it possible for them to enter into the coherent structure of reality:
in a word, what is the universal content which the monad in its formal
individuality bears and manifests?

The way in which the question has just been stated suggests the
Leibnizian answer. The monad, indeed, in its form is thoroughly
individual, having its own unique mode of activity; but its content,
that which this activity manifests, is not peculiar to it as an
individual, but is the substance or law of the universe. It is the
very nature of the monad to be representative. Its activity consists
in picturing or reproducing those relations which make up the world of
reality. In a conscious soul, the ability thus to represent the world
is called "perception," and thus Leibniz attributes perception to all
the monads. This is not to be understood as a conscious representation
of reality to itself (for this the term "apperception" is reserved),
but it signifies that the very essence of the monad is to produce
states which are not its own peculiar possessions, but which reflect
the facts and relations of the universe. Leibniz never wearies in
finding new ways to express this purely representative character of the
monad. The monads are little souls; they are mirrors of the world; they
are concentrations of the universe, each expressing it in its own way;
borrowing a term from scholasticism, they are "substantial forms." They
are substantial, for they are independent unities; they are forms,
because the term "form" expresses, in Aristotelian phraseology, the
type or law of some class of phenomena. The monad is an individual,
but its whole content, its objectivity or reality, is the summation of
the universe which it represents. It is individual, but whatever marks
it as actual is some reproduction of the world. His reconciliation
of the principles of individuality and universality is contained
in the following words: "Each monad contains within itself an order
corresponding to that of the universe,--indeed, the monads represent
the universe in an infinity of ways, all different, and all true, thus
multiplying the universe as many times as is possible, approaching
the divine as near as may be, and giving the world all the perfection
of which it is capable." The monad is individual, for it represents
reality in its own way, from its own point of view. It is universal,
for its whole content is the order of the universe.

New light is thus thrown upon the former statement that reality
is activity, that the measure of a being is the action which it
puts forth. That statement is purely formal. It leaves the kind
of activity and its law wholly undetermined. But this relation of
"representativeness" which we have discovered gives definiteness. It
is the law of the monad's action to mirror, to reflect, the universe;
its changes follow each other so as to bring about this reflection in
the completest degree possible. The monad is literally the many in the
one; it is the answer to the inquiry of Greek philosophy. The many
are not present by way of participation in some underlying essence,
not yet as statically possessed by the one, as attributes are sometimes
supposed to inhere in a substratum. The "many" is the manifestation of
the activity of the "one." The one and the many are related as form
and content in an organic unity, which is activity. The essence of a
substance, says Leibniz, consists in that regular tendency of action
by which its phenomena follow one another in a certain order; and that
order, as he repeatedly states, is the order in which the universe
itself is arranged.

The activity of a monad may be advantageously compared to that of a
supposed atom, granting, for the sake of the illustration, that there
is such a thing. Each is in a state of change: the atom changes its
place, the monad its representation, and each in the simplest and
most uniform way that its conditions permit. How, then, is there such
a similarity, such a monotony, in the change of an atom, and such
variety and complexity in the change of a monad? It is because the
atom has merely parts, or external variety, while the monad has an
internal variety. Multiplicity is organically wrought into its very
being. It has an _essential_ relation to all things in the universe;
and to say that this relation is essential, is to say that it is one
which constitutes its very content, its being. Hence the cause of the
changes of the monad, of their variety and complexity, is one with the
cause of the richness, the profusion, the regulated variety of change
in the universe itself. While we have employed a comparison with atoms,
this very comparison may serve to show us the impossibility of atoms as
they are generally defined by the physicist turned philosopher. Atoms
have no internal and essential relation to the world; they have no
internal connection with any one thing in the world: and what is this
but to say that they do not enter anywhere into the structure of the
world? By their very conception they are forever aliens, banished from
any share or lot in the realm of reality. The idea which Leibniz never
lets go, the idea which he always accentuates, is, then, the idea of an
individual activity which in its continual change manifests as its own
internal content and reality that reality and those laws of connection
which make up the world itself.

We are thus introduced naturally to the conception which plays so
large a part in the Leibnizian philosophy, that of pre-established
harmony. This term simply names the fact, which we see to be
fundamental with Leibniz,--the fact that, while the form of every
monad is individuality, a unique principle of action, its content
is universal, the very being and laws of the world. For we must
now notice more explicitly what has been wrapped up in the idea all
along. There is no direct influence of monads upon each other. One
cannot affect another causally. There is no actual interaction of one
upon another. Expressed in that figurative language which was ever
natural to Leibniz, the monads have no windows by which anything can
get in or out. This follows, of course, from the mutual independence
and individuality of the monads. They are a true democracy, in
which each citizen has sovereignty. To admit external influences
acting upon them is to surrender their independence, to deny their
sovereignty. But we must remember the other half. This democracy is not
after the Platonic conception of democracy, in which each does as it
pleases, and in which there is neither order nor law, but the extremest
assertion of individuality. What each sovereign citizen of the realm
of reality expresses is precisely law. Each is an embodiment in its own
way of the harmony, the order, of the whole kingdom. Each is sovereign
because it is dynamic law,--law which is no longer abstract, but has
realized itself in life. Thus another way of stating the doctrine of
pre-established harmony is the unity of freedom and necessity. Each
monad is free because it is individual, because it follows the
law of its own activity unhindered, unretarded, by others; it is
self-determined. But it is self-determined to show forth the order, the
harmony, of the universe. There is nothing of caprice, of peculiarity,
in the content of the monad. It shows forth order; it is organized
by law; it reveals the necessary connections which constitute the
universe. The pre-established harmony is the unity of the individual
and the universe; it is the organic oneness of freedom and necessity.

We see still further what it means when we learn that it is by this
conception that Leibniz reconciles the conceptions of physical and
final causation. There is no principle closer to the thought of Leibniz
than that of the equal presence and efficiency everywhere of both
physical and final causes. Every fact which occurs is susceptible
of a mechanical and of a rational explanation. It is necessarily
connected with preceding states, and it has a necessary end which
it is fulfilling. The complete meaning of this principle will meet
us hereafter; at present we must notice that it is one form of the
doctrine of pre-established harmony. All things have an end because
they form parts of one system; everything that occurs looks forward
to something else and prepares the way for it, and yet it is itself
mechanically conditioned by its antecedents. This is only another way
of saying that there is complete harmony between all beings in the
universe; so that each monad in fulfilling the law of its own existence
contributes to the immanent significance of the universe. The monads
are co-ordinated in such a way that they express a common idea. There
is a plan common to all, in which each has its own place. All are
making towards one goal, expressing one purpose. The universe is
an organism; and Leibniz would have applied to it the words which
Milne-Edwards applied to the human organism, as I find them quoted
by Lewes: "In the organism everything seems to be calculated with one
determined result in view; and the harmony of the parts does not result
from the influence which they exert upon one another, but from their
co-ordination under the rule of a common force, a preconceived plan,
a pre-existent force." That is to say, the universe is teleological,
both as a whole and in its parts; for there is a common idea animating
it and expressed by it; it is mechanical, for this idea is realized and
manifested by the outworking of forces.

It ought to be evident even from this imperfect sketch that the
Leibnizian theory of pre-established harmony is not that utterly
artificial and grotesque doctrine which it is sometimes represented
to be. The phrase "pre-established harmony" is, strictly speaking,
tautologous. The term "pre-established" is superfluous. It means
"existent." There is no real harmony which is not existent or
pre-established. An accidental harmony is a contradiction in terms. It
means a chaotic cosmos, an unordered order, a lawless law, or whatever
else is nonsensical.

Harmony, in short, means relation, means connection, means
subordination and co-ordination, means adjustment, means a variety,
which yet is one. The Leibnizian doctrine is not a factitious product
of his imagination, nor is it a mechanical scheme for reconciling a
problem which has no existence outside of the bewildered brains of
philosophers. It is an expression of the fact that the universe is
one of order, of continuity, of unity; it is the accentuating of this
doctrine so that the very essence of reality is found in this ordered
combination; it is the special application of this principle to the
solution of many of the problems which "the mind of man is apt to
run into,"--the questions of the relation of the individual and the
universal, of freedom and necessity, of the physical and material,
of the teleological and mechanical. We may not be contented with the
doctrine as he presents it, we may think it to be rather a summary
and highly concentrated statement of the problem than its solution,
or we may object to details in the carrying out of the doctrine. But
we cannot deny that it is a genuine attempt to meet a genuine problem,
and that it contains some, if not all, of the factors required for
its adequate solution. To Leibniz must remain the glory of being the
thinker to seize upon the perfect unity and order of the universe as
its essential characteristic, and of arranging his thoughts with a view
to discovering and expressing it.

We have but to notice one point more, and our task is done so far as
it serves to make plain the standpoint from which Leibniz criticised
Locke. There is, we have seen, the greatest possible continuity and
complexity in the realm of monads. There is no break, quantitative nor
qualitative. It follows that the human soul has no gulf set between it
and what we call nature. It is only the highest, that is to say the
most active and the most representative, of all monads. It stands,
indeed, at the head of the scale, but not outside it. From the monad
which reveals its presence in that stone which with blinded eyes we
call dead, through that which acts in the plant, in the animal, up
to that of man, there is no chasm, no interruption. Nay, man himself
is but one link in the chain of spiritual beings which ends only in
God. All monads are souls; the soul of man is a monad which represents
the universe more distinctly and adequately. The law which is enfolded
in the lower monads is developed in it and forms a part of its
conscious activity. The universe, which is confusedly mirrored by the
perception of the lower monad, is clearly brought out in the conscious
apperception of man. The stone is representative of the whole world. An
all-knowing intelligence might read in it relations to every other
fact the world, might see exemplified the past history of the world,
and prefigured the events to come. For the stone is not an isolated
existence, it is an inter-organic member of a system. Change the
slightest fact in the world, and in some way it is affected. The law
of the universe is one of completed reciprocity, and this law must be
mirrored in every existence of the universe. Increase the activity, the
representative power, until it becomes turned back, as it were, upon
itself, until the monad not only is a mirror, but knows itself as one,
and you have man. The soul of man is the world come to consciousness
of itself. The realm of monads in what we call the inorganic world
and the lower organic realm shows us the monad let and hindered in
its development. These realms attempt to speak forth the law of their
being, and reveal the immanent presence of the universe; but they do
not hear their own voice, their utterance is only for others. In man
the universe is manifested, and is manifested to man himself.



The reader, impatient of what may have seemed an over-long
introduction, has perhaps been asking when he was to be brought to the
subject under consideration,--the relations of Leibniz to Locke. But
it has been impossible to come to this question until we had formed for
ourselves an outline of the philosophical position of Leibniz. Nowhere
in the "Nouveaux Essais" does Leibniz give a connected and detailed
exposition of his philosophy, either as to his standpoint, his
fundamental principles, or his method.

Some preliminary view of his position is therefore a necessity. The
demand for this preliminary exposition becomes more urgent as we
recognize that Leibniz's remarks upon Locke are not a critique of Locke
from the standpoint of the latter, but are the application of his own
philosophical conclusions. Criticism from within, an examination of
a system of thought with relation to the consistency and coherency
of its results, the connection between these results and the method
professedly employed, investigation which depends not at all upon the
position of the critic, but occupies itself with the internal relations
of the system under discussion,--such criticism is a product of the
present century. What we find in the "Nouveaux Essais" is a comparison
of the ideas of Locke with those of Leibniz himself, a testing of the
former by the latter as a standard, their acceptance when they conform,
their rejection when they are opposed, their completion when they are
in partial harmony.

The value of this sort of criticism is likely to be small and
evanescent. If the system used as a standard is meagre and narrow,
if it is without comprehensiveness and flexibility, it does not repay
after-examination. The fact that the "Nouveaux Essais" of Leibniz
have escaped the oblivion of the philosophical criticism of his day is
proof, if proof still be needed, of the reasoned basis, the width of
grasp, the fertility of suggestion which characterize the thought of
Leibniz. But the fact that the criticism is, after all, external and
not internal has made necessary the foregoing extended account of his
method and general results.

On the other hand, what of Locke? How about him who is the recipient
of the criticism? I assume that no extended account of his ideas
is here necessary, and conceive myself to be justified in this
assumption by the fact that we are already better acquainted with
Locke. This acquaintance, indeed, is not confined to those who have
expressly studied Locke. His thought is an inheritance into which
every English-speaking person at least is born. Only he who does not
think escapes this inheritance. Locke did the work which he had to do
so thoroughly that every Englishman who will philosophize must either
build upon Locke's foundations, or, with conscious purpose, clear the
ground before building for himself. And it would be difficult to say
that the acceptance of Locke's views would influence one's thought
more than their rejection. This must not, of course, be taken too
literally. It may be that one who is a lineal descendant of Locke in
the spiritual generations of thought would not state a single important
truth as Locke stated it, or that those who seek their method and
results elsewhere have not repudiated the thought of Locke as expressly
belonging to him.

But the fundamental principles of empiricism: its conception of
intelligence as an individual possession; its idea of reality as
something over against and distinct from mind; its explanation of
knowledge as a process of action and reaction between these separate
things; its account of our inability to know things as they really
are,--these principles are congenital with our thinking. They are so
natural that we either accept them as axiomatic, and accuse those who
reject them of metaphysical subtlety, or, staggered perchance by some
of their results, give them up with an effort. But it is an effort, and
a severe one; and there is none of us who can tell when some remnant
of the conception of intelligence as purely particular and finite
will catch him tripping. On the other hand, we realize much better
than those who have behind them a Leibniz and a Kant, rather than a
Locke and a Hume, the meaning and the thorough-going necessity of the
universality of intelligence. Idealism must be in some ways arbitrary
and superficial to him who has not had a pretty complete course of

Leibniz seems to have been impressed with the Essay on the Human
Understanding at its first appearance. As early as 1696 we find
him writing a few pages of comment upon the book. Compared with his
later critique, these early "reflections" seem colorless, and give the
impression that Leibniz desired to minimize his differences from Locke
rather than to set them forth in relief. Comparatively slight as were
his expressions of dissent, they appear to have stung Locke when they
reached him. Meantime Locke's book was translated into French, and made
its way to a wider circle of readers. This seems to have suggested to
Leibniz the advisability of pursuing his comments somewhat further;
and in the summer of 1703 he produced the work which now occupies us. A
letter which Leibniz wrote at about this time is worth quoting at large
for the light which it throws upon the man, as well as for suggesting
the chief points in which he differed from Locke. Leibniz writes:--

"I have forgotten to tell you that my comments upon the work of Locke
are nearly done. As he has spoken in a chapter of his second book about
freedom, he has given me an opportunity to discuss that; and I hope
that I may have done it in such a way as will please you. Above all,
I have laid it upon myself to save the immateriality of the soul, which
Locke leaves doubtful. I justify also the existence of innate ideas,
and show that the soul produces their perception out of itself. Axioms,
too, I approve, while Locke has a low opinion of them. In contradiction
to him, I show that the individuality of man, through which he
preserves his identity, consists in the duration of the simple or
immaterial substance which animates him; that the soul is never without
representations; that there is neither a vacuum nor atoms; that matter,
or the passive principle, cannot be conscious, excepting as God unites
with it a conscious substance. We disagree, indeed, in numerous other
points, for I find that he rates too low the noble philosophy of the
Platonic school (as Descartes did in part), and substitutes opinions
which degrade us, and which may become hurtful to morals, though I am
persuaded that Locke's intention was thoroughly good. I have made these
comments in leisure hours, when I have been journeying or visiting, and
could not occupy myself with investigations requiring great pains. The
work has continued to grow under my hands, for in almost every chapter,
and to a greater extent than I had thought possible, I have found
matter for remark. You will be astonished when I tell you that I have
worked upon this as upon something which requires no great pains. But
the fact is, that I long ago established the general principles of
philosophic subjects in my mind in a demonstrative way, or pretty
nearly so, and that they do not require much new consideration from

Leibniz goes on to add that he has put these reflections in the form of
a dialogue that they may be more attractive; has written them in the
popular language, rather than in Latin, that they may reach as wide a
circle as the work of Locke; and that he hopes to publish them soon,
as Locke is already an old man, and he wishes to get them before the
public while Locke may still reply.

But unfortunately this last hope was destined to remain
unrealized. Before the work of revision was accomplished, Locke
died. Leibniz, in a letter written in 1714, alludes to his controversy
with Locke as follows: "I do not like the thought of publishing
refutations of authors who are dead. These should appear during their
life, and be communicated to them." Then, referring to his earlier
comments, he says: "A few remarks escaped me, I hardly know how, and
were taken to England. Mr. Locke, having seen them, spoke of them
slightingly in a letter to Molineux. I am not astonished at it. We
were somewhat too far apart in principle, and that which I suggested
seemed paradoxical to him." Leibniz, according to his conviction here
expressed, never published his "Nouveaux Essais sur l'Entendement
Humain." Schaarschmidt remarks that another reason may have restrained
him, in that he did not wish to carry on too many controversies at once
with the English people. He had two on his hands then,--one with the
Newtonians regarding the infinitesimal calculus; the other with Bishop
Clarke regarding the nature of God, of time and space, of freedom, and
cognate subjects. However, in 1765, almost fifty years after the death
of Leibniz, his critique upon Locke finally appeared.

It is somewhat significant that one whose tendency was conciliatory,
who was eminently what the Germans delight to call him, a "mediator,"
attempting to unite the varied truths which he found scattered in
opposed systems, should have had so much of his work called forth
by controversy. Aside from the cases just mentioned, his other
chief work, the Theodicy, is, in form, a reply to Bayle. Many of
his minor pieces are replies to criticism or are developments of
his own thought with critical reference to Descartes, Malebranche,
and others. But Leibniz has a somewhat different attitude towards
his British and towards his Continental opponents. With the latter
he was always in sympathy, while they in turn gave whatever he
uttered a respectful hearing. Their mutual critiques begin and end
in compliments. But the Englishmen found the thought of Leibniz
"paradoxical" and forced. It seemed to them wildly speculative,
and indeed arbitrary guess-work, without any special reason for its
production, and wholly unverifiable in its results. Such has been the
fate of much of the best German thought since that time in the land of
the descendants of Newton and Locke. But Leibniz, on the other hand,
felt as if he were dealing, in philosophical matters at least, with
foemen hardly worthy of his steel. Locke, he says, had subtlety and
address, and a sort of _superficial_ metaphysics; but he was ignorant
of the method of mathematics,--that is to say, from the standpoint of
Leibniz, of the method of all science. We have already seen that he
thought the examination of a work which had been the result of the
continued labor of Locke was a matter for the leisure hours of his
courtly visits. Indeed, he would undoubtedly have felt about it what
he actually expressed regarding his controversy with Clarke,--that he
engaged in it

    "Ludus et jocus, quia in philosophia
    Omnia percepi atque animo mecum ante peregi."

He regarded the English as superficial and without grasp of principles,
as they thought him over-deep and over-theoretical.

From this knowledge of the external circumstances of the work of
Leibniz and its relation to Locke, it is necessary that we turn to
its internal content, to the thought of Leibniz as related to the
ideas of Locke. The Essay on the Human Understanding is, as the name
implies, an account of the nature of knowledge. Locke tells us that
it originated in the fact that often, when he had been engaged in
discussions with his friends, they found themselves landed in insoluble
difficulties. This occurred so frequently that it seemed probable that
they had been going at matters from the wrong side, and that before
they attempted to come to conclusions about questions they ought to
examine the capacity of intelligence, and see whether it is fitted to
deal with such questions. Locke, in a word, is another evidence of that
truth which lies at the basis of all forms of philosophical thought,
however opposed they may be to one another,--the truth that knowledge
and reality are so organic to each other that to come to any conclusion
about one, we must know something about the other. Reality equals
objects known or knowable, and knowledge equals reality dissolved in
ideas,--reality which has become translucent through its meaning.

Locke's Essay is, then, an account of the origin, nature, extent, and
limitations of human knowledge. Such is its subject-matter. What is
its method? Locke himself tells us that he uses the "plain historical
method." We do not have to resort to the forcing of language to learn
that this word "historical" contains the key to his work. Every page
of the Essay is testimony to the fact that Locke always proceeds
by inquiring into the way and circumstances by which knowledge of
the subject under consideration came into existence and into the
conditions by which it was developed. Origin means with Locke, not
logical dependence, but temporal production; development means temporal
succession. In the language of our day, Locke's Essay is an attempt to
settle ontological questions by a psychological method. And as we have
before noticed, Leibniz meets him, not by inquiry into the pertinence
of the method or into the validity of results so reached, but by the
more direct way of impugning his psychology, by substituting another
theory of the nature of mind and of the way in which it works.

The questions with which the discussion begins are as to the existence
of innate ideas, and as to whether the soul always thinks,--questions
which upon their face will lead the experienced reader of to-day to
heave a sigh in memory of hours wasted in barren dispute, and which
will create a desire to turn elsewhere for matter more solid and
more nutritive. But in this case, under the form which the discussion
takes at the hands of Leibniz, the question which awaits answer under
the meagre and worn-out formula of "innate ideas" is the function of
intelligence in experience.

Locke denies, and denies with great vigor, the existence of innate
ideas. His motives in so doing are practical and theoretical. He
sees almost every old idea, every hereditary prejudice, every vested
interest of thought, defended on the ground that it is an innate
idea. Innate ideas were sacred, and everything which could find no
defence before reason was an innate idea. Under such circumstances
he takes as much interest in demolishing them as Bacon took in
the destruction of the "eidols." But this is but a small portion
of the object of Locke. He is a thorough-going empiricist; and the
doctrine of innate ideas appears to offer the greatest obstacle to the
acceptance of the truth that all the furnishing of the intellect comes
from experience. Locke's metaphors for the mind are that it is a blank
tablet, an empty closet, an unwritten book. The "innate idea" is only a
sentence written by experience, but which, deified by a certain school
of philosophers, has come to be regarded as eternally imprinted upon
the soul.

Such, indeed, is Locke's understanding of the nature of innate
ideas. He conceives of them as "characters _stamped_, as it were,
upon the mind of man, which the soul has received in its first being
and brings into the world with it;" or they are "constant _impressions_
which the souls of men receive in their first beings." They are "truths
_imprinted_ upon the soul." Having this conception of what is meant by
"innate ideas," Locke sets himself with great vigor, and, it must be
confessed, with equal success, to their annihilation.

His argument is somewhat diffuse and scattered, but in substance it
is as follows: Whatever is in the mind, the mind must be conscious
of. "To be in the mind and not to be perceived, is all one as to say
that anything is and is not in the mind." If there be anything in the
mind which is innate, it must be present to the consciousness of all,
and, it would seem, of all at all times, savages, infants, and idiots
included. And as it requires little philosophical penetration to
see that savages do not ponder upon the principle that whatever is,
is; that infants do not dwell in their cradle upon the thought of
contradiction, or idiots ruminate upon that of excluded middle,--it
ought to be evident that such truths cannot be innate. Indeed, we must
admit, with Locke, that probably few men ever come to the explicit
consciousness of such ideas, and that these few are such as direct
their minds to the matter with some pains. Locke's argument may be
summed up in his words: If these are not notions naturally imprinted,
how can they be innate? And if they are notions naturally imprinted,
how can they be unknown?

But since it may be said that these truths are in the mind, but in such
a way that it is only when they are proposed that men assent to them,
Locke goes on to clinch his argument. If this be true, it shows that
the ideas are not innate; for the same thing is true of a large number
of scientific truths, those of mathematics and morals, as well as of
purely sensible facts, as that red is not blue, sweet is not sour,
etc.,--truths and facts which no one calls innate. Or if it be said
that they are in the mind implicitly or potentially, Locke points
out that this means either nothing at all, or else that the mind is
_capable_ of knowing them. If this is what is meant by innate ideas,
then all ideas are innate; for certainly it cannot be denied that the
mind is capable of knowing all that it ever does know, or, as Locke
ingenuously remarks, "nobody ever denied that the mind was capable of
knowing several truths."

It is evident that the force of Locke's contention against innate
ideas rests upon a certain theory regarding the nature of innate ideas
and of the relations of consciousness to intelligence. Besides this,
there runs through his whole polemic the assertion that, after all,
innate ideas are useless, as experience, in the sense of impressions
received from without, and the formal action of intelligence upon
them, is adequate to doing all they are supposed to do. It is hardly
too much to say that the nerve of Locke's argument is rather in this
positive assertion than in the negations which he brings against
this existence. Leibniz takes issue with him on each of these three
points. He has another conception of the very nature of innate ideas;
he denies Locke's opinions about consciousness; he brings forward
an opposed theory upon the relation of experience to reason. This
last point we shall take up in a chapter by itself, as its importance
extends far beyond the mere question as to the existence of ideas which
may properly be called innate. The other two questions, as to the real
character of innate ideas and the relation of an idea to consciousness,
afford material to occupy us for the present.

The metaphor which Locke constantly uses is the clew to his conception
of innate ideas. They are characters stamped or imprinted upon the
mind, they exist _in_ the mind. The mind would be just what it is,
even if they had no existence. It would not have quite so much "in"
it, but its own nature would not be changed. Innate ideas he conceives
as bearing a purely external relation to mind. They are not organic
to it, nor necessary instruments through which it expresses itself;
they are mechanically impressed upon it. But what the "intellectual"
school had meant by innate ideas was precisely that the relation of
ideas to intelligence is _not_ that of passive holding or containing
on the side of mind, and of impressions or stamps on the side of the
ideas. Locke reads the fundamental category of empiricism--mechanical
relation, or external action--into the nature of innate ideas, and
hence easily infers their absurdity. But the object of the upholders
of innate ideas had been precisely to deny that this category was
applicable to the whole of intelligence. By an innate idea they meant
an assertion of the dynamic relation of intelligence and some of its
ideas. They meant to assert that intelligence has a structure, which
necessarily functions in certain ways. While Locke's highest conception
of an innate idea was that it must be something ready made, dwelling
in the mind prior to experience, Leibniz everywhere asserts that it
is a connection and relation which forms the logical prius and the
psychological basis of experience. He finds no difficulty in admitting
all there is of positive truth in Locke's doctrine; namely, that we are
not conscious of these innate ideas until a period later than that in
which we are conscious of sensible facts, or, in many cases, are not
conscious of them at all. This priority in time of sensible experience
to rational knowledge, however, can become a reason for denying the
"innate" character of the latter only when we suppose that they are two
entirely different orders of fact, one knowledge due to experience,
the other knowledge already formed and existing in the mind prior to

Leibniz's conception of the matter is brought out when he says that it
is indeed true that we begin with particular experiences rather than
with general principles, but that the order of nature is the reverse,
for the ground, the basis of the particular truths is in the general;
the former being in reality only instances of the latter. General
principles, he says, enter into _all_ our thoughts, and form their
soul and interconnection. They are as necessary for thought as muscles
and tendons are for walking, although we may not be conscious of their
existence. This side of the teaching of Leibniz consists, accordingly,
in the assertion that "innate" knowledge and knowledge derived from
experience are not two kinds of knowledge, but rather two ways of
considering it. If we consider it as it comes to us, piecemeal and
fragmentary, a succession of particular instances, to be gathered up at
a future time into general principles, and stated in a rational form,
it is seen as empirical. But, after all, this is only a superficial
and external way of looking at it. If we examine into it we shall see
that there are contained in these transitory and particular experiences
certain truths more general and fundamental, which condition them, and
at the same time constitute their meaning.

If we inquire into the propriety of calling these truths "innate,"
we find it is because they are native to intelligence, and are not
acquisitions which it makes. Indeed, it may be said that they _are_
intelligence, so close and organic is their relation, just as the
muscles, the tendons, the skeleton, are the body. Thus it is that
Leibniz accepts the statement, _Nihil est in intellectu quod non
fuerit in sensu_, with the addition of the statement _nisi ipse
intellectus_. The doctrine of the existence of innate ideas is thus
shown to mean that intelligence exists with a real content which counts
for something in the realm of experience. If we take intelligence
and examine into its structure and ascertain its modes of expression,
we find organically inherent in its activity certain conceptions like
unity, power, substance, identity, etc., and these we call "innate." An
idea, in short, is no longer conceived as something existing in the
mind or in consciousness; it is an activity of intelligence. An innate
idea is a necessary activity of intelligence; that is, such an activity
as enters into the framework of all experience.

Leibniz thus succeeds in avoiding two errors into which philosophers
whose general aims are much like his have fallen. One is dividing _a
priori_ and _a posteriori_ truths from each other by a hard and fixed
line, so that we are conceived to have some knowledge which comes
wholly from experience, while there is another which comes wholly
from reason. According to Leibniz, there is no thought so abstract
that it does not have its connection with a sensible experience,
or rather its embodiment in it. And, on the other hand, there is no
experience so thoroughly sensuous that it does not bear in itself
traces of its origin in reason. "_All_ our thoughts come from the
depths of the soul," says Leibniz; there are none that "come" to us
from without. The other error is the interpretation of the existence
of innate ideas or "intuitions" (as this school generally calls them)
in a purely formal sense. They are thus considered as truths contained
in and somehow expressed by intelligence, but yet not so connected with
it that in knowing them we necessarily know intelligence itself. They
are considered rather as arbitrary determinations of truths by a power
whose own nature is conceivably foreign to truth, than as so many
special developments of an activity which may indifferently be called
"intelligence" or "truth." Leibniz, however, never fails to state that
an innate truth is, after all, but one form or aspect of the activity
of the mind in knowing.

In this way, by bringing to light a deeper and richer conception of
what in reality constitutes an innate idea, Leibniz answers Locke. His
reply is indirect; it consists rather in throwing a flood of new
light upon the matter discussed, than in a ponderous response and
counter-attack. But when Leibniz touches upon the conception of a
_tabula rasa_, of a mind which in itself is a mere blank, but has
the capacity for knowing, he assumes the offensive. The idea of a
bare capacity, a formal faculty, of power which does not already
involve some actual content within itself, he repudiates as a relic
of scholasticism. What is the soul, which has nothing until it gets
it from without? The doctrine of a vacuum, an emptiness which is real,
is always absurd; and it is doubly so when to this vacuum is ascribed
powers of feeling and thinking, as Locke does. Accepting for the
moment the metaphor of a _tabula rasa_, Leibniz asks where we shall
find a tablet which yet does not have some quality, and which is not
a co-operating cause, at least, in whatever effects are produced upon
it? The notion of a soul without thought, an empty tablet of the soul,
he says, is one of a thousand fictions of philosophers. He compares
it with the idea of "space empty of matter, absolute uniformity
or homogeneity, perfect spheres of the second element produced by
primordial perfect cubes, abstractions pure and simple, to which our
ignorance and inattention give birth, but of which reality does not
admit." If Locke admits then (as he does) certain capacities inherent
in the soul, he cannot mean the scholastic fiction of bare capacity
or mere possibility; he must mean "real possibilities,"--that is,
capacities accompanied with some actual tendency, an inclination, a
disposition, an aptitude, a preformation which determines our soul in a
certain direction, and which makes it necessary that the possibility
becomes actual. And this tendency, this actual inclination of
intelligence in one way rather than another, so that it is not a matter
of indifference to intelligence what it produces, is precisely what
constitutes an innate idea. So Leibniz feels certain that at bottom
Locke must agree with him in this matter if the latter is really in
earnest in rejecting the "faculties" of the scholastics and in wishing
for a real explanation of knowledge.

But the argument of Locke rests upon yet another basis. He founds
his denial of innate ideas not only upon a static conception of their
ready made existence "in" the soul, but also upon an equally mechanical
conception of consciousness. "Nothing can be in the mind which is not
in consciousness." This statement appears axiomatic to Locke, and by
it he would settle the whole discussion. Regarding it, Leibniz remarks
that if Locke has such a prejudice as this, it is not surprising that
he rejects innate ideas. But consciousness and mental activity are not
thus identical. To go no farther, the mere empirical fact of memory is
sufficient to show the falsity of such an idea. Memory reveals that
we have an indefinite amount of knowledge of which we are not always
conscious. Rather than that knowledge and consciousness are one, it
is true that actual consciousness only lays hold of an infinitesimal
fraction of knowledge. But Leibniz does not rely upon the fact of
memory alone. We must constantly keep in mind that to Leibniz the
soul is not a form of being wholly separate from nature, but is the
culmination of the system of reality. The reality is everywhere
the monad, and the soul is the monad with the power of feeling,
remembering, and connecting its ideas. The activities of the monad,
those representative changes which sum up and symbolize the universe,
do not cease when we reach the soul. They are continued. If the soul
has the power of attention, they are potentially conscious. Such as
the soul actually attends to, thus giving them relief and making them
distinct, are actually conscious. But all of them exist.

Thus it is that Leibniz not only denies the equivalence of soul and
consciousness, but asserts that the fundamental error of the psychology
of the Cartesians (and here, at least, Locke is a Cartesian) is in
identifying them. He asserts that "unconscious ideas" are of as great
importance in psychology as molecules are in physics. They are the link
between unconscious nature and the conscious soul. Nothing happens all
at once; nature never makes jumps; these facts stated in the law of
continuity necessitate the existence of activities, which may be called
ideas, since they belong to the soul and yet are not in consciousness.

When, therefore, Locke asks how an innate idea can exist and the soul
not be conscious of it, the answer is at hand. The "innate idea"
exists as an activity of the soul by which it represents--that is,
expresses--some relation of the universe, although we have not yet
become conscious of what is contained or enveloped in this activity. To
become conscious of the innate idea is to lift it from the sphere of
nature to the conscious life of spirit. And thus it is, again, that
Leibniz can assert that all ideas whatever proceed from the depths of
the soul. It is because it is the very being of the soul as a monad
to reflect "from its point of view" the world. In this way Leibniz
brings the discussion regarding innate ideas out of the plane of
examination into a matter of psychological fact into a consideration
of the essential nature of spirit. An innate idea is now seen to be
one of the relations by which the soul reproduces some relation which
constitutes the universe of reality, and at the same time realizes its
own individual nature. It is one reflection from that spiritual mirror,
the soul. With this enlarged and transformed conception of an idea apt
to be so meagre we may well leave the discussion. There has been one
mind at least to which the phrase "innate ideas" meant something worth
contending for, because it meant something real.



A careful study of the various theories which have been held
concerning sensation would be of as much interest and importance as
an investigation of any one point in the range of philosophy. In the
theory of a philosopher about sensation we have the reflex of his
fundamental category and the clew to his further doctrine. Sensation
stands on the border-line between the world of nature and the realm of
soul; and every advance in science, every development of philosophy,
leaves its impress in a change in the theory of sensation. Apparently
one of the simplest and most superficial of questions, in reality
it is one of the most difficult and far-reaching. At first sight it
seems as if it were a sufficient account of sensation to say that
an object affects the organ of sense, and thus impresses upon the
mind the quality which it possesses. But this simple statement
arouses a throng of further questions: How is it possible that
one substance,--matter,--should affect another,--mind? How can a
causal relation exist between them? Is the mind passive or active
in this impression? How can an object convey unchanged to the mind
a quality which it possesses? Or is the sensational _quale_ itself
a product of the mind's activity? If so, what is the nature of the
object which excites the sensation? As known, it is only a collection
of sensuous qualities; if these are purely mental, what becomes of
the object? And if there is no object really there, what is it that
excites the sensation? Such questionings might be continued almost
indefinitely; but those given are enough to show that an examination
of the nature and origin of sensation introduces us to the problems
of the relation of intelligence and the world; to the problem of
the ultimate constitution of an object which is set over against a
subject and which affects it; and to the problem of the nature of mind,
which as thus affected from without must be limited in its nature,
but which as bearer of the whole known universe must be in some sense
infinite. If we consider, not the mode of production of sensation,
but its relation to knowledge, we find philosophical schools divided
into two,--Sensationalists, and Rationalists. If we inquire into its
functions, we find that the empiricist sees in it convincing evidence
of the fact that all knowledge originates from a source _extra mentem_;
that the intellectual idealist finds in it evidence of the gradual
transition of nature into spirit; that the ethical idealist, like Kant
and Fichte, sees in it the material of the phenomenal world, which is
necessary in its opposition to the rational sphere in order that there
may occur that conflict of pure law and sensuous impulse which alone
makes morality possible. We thus realize that as we look at the various
aspects of sensation, we are taken into the discussion of ontology, of
the theory of knowledge and of ethics.

Locke virtually recognizes the extreme importance of the doctrine of
sensation, and his second book might almost be entitled "Concerning the
Nature and Products of Sensation." On the other hand, one of the most
characteristic and valuable portions of the reply of Leibniz is in his
development of a theory of sensation which is thoroughly new, except as
we seek for its germs in its thoughts of Plato and Aristotle. According
to Locke, knowledge originates from two sources,--sensation and
reflection. Sensations are "the impressions made on our senses by
outward objects that are extrinsic to the mind." When the mind "comes
to reflect on its own operations about the ideas got by sensation,
and thereby stores itself with a new set of ideas," it gets ideas of

If we leave out of account for the present the ideas of reflection,
we find that the ideas which come through sensation have two main
characteristics. First, in having sensations, the mind is passive;
its part is purely receptive. The objects impress themselves upon
the mind, they obtrude into consciousness, whether the mind will or
not. There is a purely external relation existing between sensation
and the understanding. The ideas are offered to the mind, and the
understanding cannot refuse to have them, cannot change them, blot
them out, nor create them, any more than a mirror can refuse, alter,
or obliterate the images which objects produce in it. Sensation,
in short, is a purely passive having of ideas. Secondly, every
sensation is simple. Locke would say of sensations what Hume said of
all ideas,--every distinct sensation is a separate existence. Every
sensation is "uncompounded, containing nothing but one uniform
appearance, not being distinguishable into different ideas." Knowledge
is henceforth a process of compounding, of repeating, comparing, and
uniting sensation. Man's understanding "reaches no further than to
compound and divide the materials that are made to his hand."

It hardly need be said that Locke has great difficulty in keeping up
this thoroughly atomic theory of mind. It is a theory which makes all
relations external; they are, as Locke afterwards says, "superinduced"
upon the facts. It makes it impossible to account for any appearance
of unity and connection among ideas, and Locke quietly, and without
any consciousness of the contradiction involved, introduces certain
inherent relations into the structure of the ideas when he comes to his
constructive work. "Existence and unity are two ideas," he says, "that
are suggested to the understanding by every object without, and every
idea within."

At other places he introduces the idea of quality of a substance,
effect of a cause, continued permanence or identity into a sensation,
as necessary constituents of it; thus making a sensation a unity of
complex elements instead of an isolated bare notion. How far he could
have got on in his account of knowledge without this surreptitious
qualifying of a professedly simple existence, may be seen by asking
what would be the nature of a sensation which did not possess existence
and unity, and which was not conceived as the quality of a thing or as
the effect of an external reality.

This digression has been introduced at this point because the next
character of a sensation which Locke discusses is its objective
character,--its relation to the object which produces it. To
discourse of our ideas intelligibly, he says, it will be convenient
to distinguish them as they are ideas in our minds and as they are
modifications of matter in the bodies that cause them. In other
words, he gives up all thought of considering ideas as simply mental
modifications, and finds it necessary to take them in their relations
to objects.

Taking them in this way, he finds that they are to be divided into
two classes, of which one contains those ideas that are copies and
resemblances of qualities in the objects, ideas "which are really in
the object, whether we take notice of them or no,"--in which case we
have an idea of the thing as it is in itself; while the other class
contains those which are in no way resemblances of the objects which
produce them, "having no more similitude than the idea of pain and of a
sword." The former are primary qualities, and are solidity, extension,
figure, motion or rest, and number; while the secondary qualities
are colors, smells, and tastes. The former ideas are produced by
impulse of the bodies themselves, which simply effect a transference
of their qualities over into the mind; while the secondary qualities
are arbitrarily annexed by the power of God to the objects which excite

It will be noticed that there are two elements which make the sensation
of Locke what it is. With reference to its _production_, it is the
effect which one substance, matter, has upon another substance,
mind, which is unlike it in nature, and between which whatever
relations exist, are thoroughly incomprehensible, so that, indeed,
their connections with each other can be understood only by recourse
to a _tertium quid_, an omnipotent power which can arbitrarily produce
such collocations as please it. With reference to its _function_, it
is the isolated and "simple" (that is, non-relational) element out
of which all actual forms of knowledge are made by composition and

Leibniz, without entering into explicit criticism of just these two
points, develops his own theory with reference to them. To Leibniz,
reality constitutes a system; that is, it is of such a nature that
its various portions have an essential and not merely external
relation to one another. Sensation is of course no exception. It is
not a mere accident, nor yet a supernatural yoking of things naturally
opposed. It has a meaning in that connection of things which constitute
the universe. It contributes to the significance of the world. It
is one way in which those activities which make the real express
themselves. It has its place or reason in the totality of things, and
this whether we consider its origin or its position with regard to
knowledge. In a word, while the characteristic of Locke's theory is
that he conceives sensation as in external relation both to reality,
as mechanically produced by it, and to knowledge, as being merely
one of the atomic elements which may enter into a compound, Leibniz
regards reality as organic to sensation, and this in turn as organic
to knowledge. We have here simply an illustration of the statement
with which we set out; namely, that the treatment of sensation always
reflects the fundamental philosophical category of the philosopher.

All reality exists in the form of monads; monads are simple substances
whose nature is action; this action consists in representing, according
to a certain law of succession, the universe. Various monads have
various degrees of activity; that is, of the power of reflecting
the world. So much of Leibniz's general philosophical attitude it is
necessary to recall, to understand what he means by "sensation." The
generic name which is applied to this mirroring activity of the monads
is "perception," which, as Leibniz often says, is to be carefully
distinguished from apperception, which is the representation become
conscious. Perception may be defined, therefore, as the inclusion of
the many or multiform (the world of objects) in a unity (the simple
substance). It was the great defect of previous philosophy that it
"considered only spirits or self-conscious beings as souls," and
had consequently recognized only conscious perceptions. It had been
obliged, therefore, to make an impassable gulf between mind and matter,
and sensations were thus rendered inexplicable. But Leibniz finds his
function as a philosopher in showing that these problems, which seem
insoluble, arise when we insist upon erecting into actual separations
or differences of kind what really are only stages of development
or differences of degree. A sensation is not an effect which one
substance impresses upon another because God pleased that it should, or
because of an incomprehensible incident in the original constitution of
things. It is a higher development of that representative power which
belongs to every real being.

Certain monads reach a state of development, or manifestation of
activity, which is characterized by the possession of distinct
organs. Such monads may be called, in a pre-eminent sense, "souls,"
and include all the higher animals as well as man. This possession of
differentiated organs finds its analogue in the internal condition of
the monad. What appears externally as an organ of sense appears ideally
as a conscious representative state which we call "sensation." "When,"
Leibniz says, "the monad has its organs so developed that there
is relief and differentiation in the impressions received, and
consequently in the perceptions which represent them, we have feeling
or sensation; that is, a perception accompanied by memory," to which
at other times he adds "attention." Life, he says, "is a perceptive
principle; the soul is sensitive life; mind is rational soul." And
again he says in substance that when the soul begins to have interests,
and to regard one representation as of more value than others, it
introduces relief into its perceptions, and those which stand out are
called "sensations."

This origin of sensations as higher developments of the representative
activities of a monad conditions their relation to further processes
of knowledge. The sensations are confused knowledge; they are ideas
in their primitive and most undifferentiated form. They constitute,
as Leibniz somewhere says, the vertigo of the conscious life. In every
sentient organism multitudes of sensations are constantly thronging in
and overpowering its distinct consciousness. The soul is so flooded
with ideas of everything in the world which has any relation to
its body that it has distinct ideas of nothing. Higher knowledge,
then, does not consist in compounding these sensations; that would
literally make confusion worse confounded. It consists in introducing
distinctness into the previously confused sensations,--in finding out
what they mean; that is, in finding out their bearings, what they point
to, and how they are related. Knowledge is not an external process
performed upon the sensations, it is the development of their internal

It follows, therefore, that sensation is organic to all forms of
knowledge whatever. The monad, which is pure activity, that which
culminates the scale of reality, has no confused ideas, and to it
all knowledge is eternally rational, having no sensible traces about
it. But every other monad, having its activity limited, has ideas
which come to it at first in a confused way, and which its activity
afterwards differentiates. Thus it is that Leibniz can agree so
heartily with the motto of the Sensationalist school,--that there is
nothing in the intellect which was not first in the sensory. But
Leibniz uses this phrase as Aristotle would have done, having
in mind the distinction between potentiality and actuality. _In
posse_, sensation is all knowledge; but only _in posse_. And he, like
Aristotle, interprets the relation between potentiality and actuality
as one of a difference of activity. The potential is that which
becomes real through a dynamic process. The actual is capacity plus
action. Sensation, in short, is spiritual activity in an undeveloped
and hence partial and limited condition. It is not, as Locke would have
it, the real factor in all knowledge.

The marks of sensation which Locke lays down,--their passivity, their
simplicity, their position as the real element in knowledge,--Leibniz
either denies, therefore, or accepts in a sense different from that of
Locke. Strictly speaking, sensation is an activity of the mind. There
are no windows through which the soul receives impressions. Pure
passivity of any kind is a myth, a scholastic fiction. Sensation is
developed from the soul within; it is the activity of reality made
manifest to itself. It is a higher kind of action than anything we find
in minerals or in plants. If we look at sensation ideally, however,
that is, according to the position which it holds in the system
of knowledge, it is properly regarded as passive. It represents the
limitation, the unrealized (that is, the non-active) side of spiritual

"Efficient causality" is a term which has its rightful and legitimate
use in physical science. Simply from the scientific point of view
we are correct in speaking of objects as affecting the body, and the
body, through its nervous system, as affecting the soul and producing
sensations. But philosophy does not merely use categories, it explains
them. And Leibniz contends that to explain the category of causality
in a mechanical sense, to understand by it physical influence actually
transferred from one thing to another, is to make the idea inexplicable
and irrational. The true meaning of causality is ideal. It signifies
the relative positions which the objects concerned have in the
harmonious system of reality. The body that is higher in the scale
impresses the other; that is to say, it dominates it or gives its
law. There is no energy or quality which passes physically from one
to the other. But one monad, as higher in the stage of development
than another, makes an ideal demand upon that one. It places before
the other its own more real condition. The less-developed monad, since
its whole activity consists in representing the universe of reality,
answers to this demand by developing the corresponding quality in
itself. The category of harmonious or co-operative action is thus
substituted for that of external and mechanical influence. Physical
causality when given a philosophic interpretation means organic
development. The reality of a higher stage is the more active: the
more active has a greater content in that it mirrors the universe more
fully; it manifests accordingly more of the law of the universe, and
hence has an ideal domination over that which is lower in the scale. It
is actually (that is, in activity) what the other is potentially. But
as the entire existence of the latter is in representing or setting
forth the relations which make the world, its activity is aroused to a
corresponding production. Hence the former is called "cause," and the
latter "effect."

This introduces us to the relation of soul and body, or, more generally
stated, to the relation of mind and matter. It is the theory of
co-operation, of harmonious activity, which Leibniz substitutes for
the theory which Descartes had formulated, according to which there
are two opposed substances which can affect each other only through
the medium of a _deus ex machina_. Locke, on the other hand, took the
Cartesian principle for granted, and thus enveloped himself in all the
difficulties which surround the question of "mind and matter." Locke
wavers between two positions, one of which is that there are two
unknown substances,--the soul and the object in itself,--which, coming
in contact, produce sensations; while the other takes the hypothetical
attitude that there may be but one substance,--matter,--and that
God, out of the plenitude of his omnipotence, has given matter a
capacity which does not naturally belong to it,--that of producing
sensations. In either case, however, the final recourse is to the
arbitrary power of God. There is no natural--that is, intrinsic and
explicable--connection between the sensation and that which produces
it. Sensation occupied the hard position which the mechanical school
of to-day still allots it. It is that "inexplicable," "mysterious,"
"unaccountable" link between the domains of matter and mind of which no
rational account can be given, but which is yet the source of all that
we know about matter, and the basis of all that is real in the mind!

Leibniz, recognizing that reality is an organic whole,--not two parts
with a chasm between them,--says that "God does not arbitrarily give
substances whatever qualities may happen, or that he may arbitrarily
determine, but only such as are natural; that is, such as are
related to one another in an _explicable_ way as modifications of
the substance." Leibniz feels sure that to introduce the idea of the
inexplicable, the purely supernatural, into the natural is to give up
all the advantages which the modern mechanical theory had introduced,
and to relapse into the meaningless features of scholasticism. If the
"supernatural"--that is, the essentially inexplicable--is introduced
in this one case, why should it not be in others; why should we not
return outright to the "fanatic philosophy which explains all facts by
simply attributing them to God immediately or by way of miracle, or to
the barbarian philosophy, which explains phenomena by manufacturing,
_ad hoc_, occult qualities or faculties, seemingly like little
demons or spirits capable of performing, without ceremony, whatever
is required,--as if watches marked time by their horodeictic power,
without wheels, and mills ground grain, without grindstones, by their
fractive power"? In fact, says Leibniz, by introducing the inexplicable
into our _explanations_ "we fall into something worse than occult
qualities,--we give up philosophy and reason; we open asylums for
ignorance and laziness, holding not only that there are qualities which
we do not understand (there are, indeed, too many such), but qualities
which the greatest intelligence, if God gave it all the insight
possible, could not understand,--that is, such as are _in themselves_
without rhyme or reason. And indeed it would be a thing without
rhyme or reason that God should perform miracles in the ordinary
course of nature." And regarding the whole matter of introducing the
inconceivable and the inexplicable into science, he says that "while
the conception of men is not the measure of God's power, their capacity
of conception is the measure of _nature's_ power, since everything
occurring in the natural order is capable of being understood by the
created intelligence." Such being the thought of Leibniz regarding the
virtual attempt to introduce in his day the unknowable into philosophy,
it is evident that he must reject, from the root up, all theories of
sensation which, like Locke's, make it the product of the inexplicable
intercourse of two substances.

For this doctrine, then, Leibniz substitutes that of an infinite number
of substances, all of the same kind, all active, all developing from
within, all conspiring to the same end, but of various stages of
activity, or bearing various relations of completeness to the one end.

Indeed, one and the same monad has various degrees of activity in
itself; that is, it represents more or less distinctly the universe
according to its point of view. Its point of view requires of it, of
course, primarily, a representation of that which is about it. Thus
an infinity of states arises, each corresponding to some one of the
multitude of objects surrounding the monad. The soul has no control,
no mastery, over these states. It has to take them as they come; with
regard to them, the soul appears passive. It appears so because it does
not as yet clearly distinguish them. It does not react upon them and
become conscious of their meaning or thoroughly rational character. We
shall afterwards see that "matter" is, with Leibniz, simply this
passive or confused side of monads. It is the monad so far as it has
not brought to light the rational activity which is immanent in it. At
present we need only notice that the body is simply the part of matter
or of passivity which limits the complete activity of any monad. So
Leibniz says, "in so far as the soul has perfection, it has distinct
thoughts, and God has accommodated the body to the soul. So far as it
is imperfect and its perceptions are confused, God has accommodated the
soul to the body in such a way that the soul lets itself be inclined by
the passions, which are born from corporeal representations. It is by
its confused thoughts (sensations) that the soul represents the bodies
about it," just as, we may add, its distinct thoughts represent the
monads or souls about it, and, in the degree of their distinctness,
God, the monad which is _purus actus_.

Following the matter into more detail, we may say that since God alone
is pure energy, knowing no limitation, God alone is pure spirit. Every
finite soul is joined to an organic body. "I do not admit," says
Leibniz, "that there are souls entirely separate from matter, nor
created spirits detached from body. . . . It is this body which
the monad represents most distinctly; but since this body expresses the
entire universe by the connection of all matter throughout it, the soul
represents the entire universe in representing the body which belongs
to it most particularly." But according to the principle of continuity
there must be in the least apparent portion of matter still "a universe
of creatures, of souls, of entelechies. There is nothing sterile,
nothing dead in the universe. It is evident from these considerations
that every living body has a dominant entelechy, which is the soul in
that body, but that the members of this living body are again full of
other living beings and souls," which, however, since not of so high
a grade, that is, not representing the universe so fully, appear to be
wholly material and subject to the "dominant" entelechy; namely, to the
one which gives the law to the others by expressing more adequately
the idea at which they only confusedly aim. Owing to the constant
change of activity, however, these particles do not remain in constant
subordination to the same entelechy (that is, do not form parts of the
same body), but pass on to higher or lower degrees of "evolution,"
and have their places taken by others undergoing similar processes
of change. Thus "all bodies are in a perpetual flux, like rivers,
with parts continually leaving and entering in." Or, interpreting
this figurative language, each monad is continually, in its process
of development, giving law to new and less developed monads, which
therefore appear as its body. The nature of matter in itself, and of
its phenomenal manifestation in the body, are, however, subjects which
find no explanation here, and which will demand explanation in another

We may sum up Leibniz's theory of sensation by saying that it is a
representative state developed by the self-activity of the soul; that
in itself it is a confused or "involved" grade of activity, and in
its relation to the world represents the confused or passive aspects
of existence; that this limitation of the monad constitutes matter,
and in its necessary connection with the monad constitutes the body
which is always joined to the finite soul; that to this body are joined
in all cases an immense number of monads, whose action is subordinate
to that of this dominant monad, and that it is the collection of these
which constitute the visible animal body. Thus if we look at sensation
with regard to the monad which possesses it, it is a product of the
body of the monad; if we look at it with reference to other monads,
it represents or reflects their passive or material side. This is
evidently one aspect again of the pre-established harmony,--an aspect
in which some of the narrower of Leibniz's critics have seen the whole
meaning of the doctrine exhausted. It is, however, simply one of the
many forms in which the harmony, the union of spiritual and mechanical,
ideal and material, meets us. In truth, while in other systems the fact
of sensation is a fact demanding some artificial mode of reconciling
"mind" and "matter," or is else to be accepted as an inexplicable fact,
in the system of Leibniz it is itself evidence that the spiritual
and the mechanical are not two opposed kinds of existence, but are
organically united. It is itself the manifestation of the harmony
of the ideal and the material, not something which requires that
a factitious theory be invented for explaining their appearance of
harmony. Sensation has within itself the ideal element, for it is the
manifestation, in its most undeveloped form, of the spiritual meaning
of the universe. It has a mechanical element, for it expresses the
limitation, the passivity, of the monad.

It is from this standpoint that Leibniz criticises what Locke says
about the relation of sensations to the objects which produce
them. Leibniz holds that all our sensations have a definite and
natural connection with the qualities of objects,--the "secondary"
as well as the "primary." They all represent certain properties of the
object. Even the pain which the thrust of a needle gives us, while it
does not resemble anything in the needle, does in some way represent
or resemble motions going on in our body. This resemblance is not
necessarily one of exact form, but just as the ellipse, hyperbola,
and parabola are projections of the circle in the sense that there
is a natural and fixed law of connection between them, so that every
point of one corresponds by a certain relation with every point of the
other, so the resemblance between the sensation and the quality of the
object is always in the form of a fixed law of order, which, however
unknown to us it may now be, is capable of being found out. If we are
to make any distinction between "secondary" and "primary" sensations,
it should be not that one presents qualities that are in the objects,
and the other affections which exist only in us, but that the primary
sensations (of number, form, size, etc.) represent the qualities in
a distinct way, appealing to the rational activity of intelligence,
while the secondary represent the qualities in a confused way, a way
not going beyond the effect upon the mind into relations, that is, into
distinct knowledge.

This brings regularly before us the question of the relation of
sensations to knowledge. We have seen enough already to know that
Leibniz does not believe that knowledge begins with the simple (that
is, unrelated), and then proceeds by a process of compounding. The
sensation is not simple to Leibniz, but thoroughly complex, involving
confusedly within itself all possible relations. As relations are
brought forth into distinct light out of this confusion, knowledge
ends rather than begins with the simple. And again it is evident that
Leibniz cannot believe that knowledge begins and ends in experience,
in the sense in which both himself and Locke use the word; namely, as
meaning the combination and succession of impressions.

"Experience," as they use the term, consists in sensations and their
association,--"consecution" as Leibniz calls it. Experience is the
stage of knowledge reached by animals, and in which the majority
of men remain,--and indeed all men in the greater part of their
knowledge. Leibniz takes just the same position regarding the larger
part of our knowledge which Hume takes regarding it all. It consists
simply in associations of such a nature that when one part recurs
there is a tendency to expect the recurrence of the other member. It
resembles reason, but it is based on the accidental experience of
events in a consecutive order, and not on knowledge of their causal
connection. We all expect the sun to rise to-morrow; but with all of
us, excepting the astronomer, such expectation is purely "empirical,"
being based on the images of past experiences which recur. The
astronomer, however, sees into the grounds, that is, the reasons, of
the expectation, and hence his knowledge is rational.

Thus we have two grades of knowledge,--one empirical, consisting
of knowledge of facts; the other rational, being of the truths
of reason. The former is contingent and particular, the latter is
necessary and universal. Leibniz insists, with a pertinacity which
reminds us of Kant, that "experience" can give instances or examples
only, and that the fact that anything has happened in a given way
any number of times in the past, can give no assurance that it will
continue to do so in the future. There is nothing in the nature
of the case which renders its exact opposite impossible. But a
rational truth is necessary, for its opposite is impossible, being
irrational or meaningless. This may not always be evident in the
case of a complex rational truth; but if it be analyzed into simpler
elements, as a geometrical proposition into definitions, axioms, and
postulates, the absurdity of its opposite becomes evident. Sensation,
in conclusion, is the having of confused ideas,--ideas corresponding
to matter. Experience is the association of these confused ideas, and
their association according to their accidental juxtaposition in the
life of the soul. It therefore is not only thoroughly sensible, but is
also phenomenal. Its content is sensations; its form is contingent and
particular consecution. Both form and content, accordingly, need to be
reconstructed if they are to be worthy of the name of science or of
knowledge. This is the position which Leibniz assumes as against the
empiricist, Locke. The details of this reconstruction, its method and
result, we must leave till we come in the course of the argument again
to the subject of knowledge.



Locke, after discussing the subject of innate ideas in their relation
to knowledge, goes on to discuss their practical side, or connection
with will. We shall follow him in this as Leibniz does; but we shall
consider in connection with this, Leibniz's general theory of will,
which is developed partially in this chapter, but more completely
in his critical remarks upon what Locke has to say of the notion of
"power." Since the theory of morals is as closely connected with will
as the theory of knowledge is with the intellect, we shall supplement
this discussion with what Leibniz says upon the ethical question,
drawing our material somewhat freely from his other writings.

The doctrine of will which Leibniz propounds is in closest harmony
with his conception of intelligence, and this not merely in the way
of empirical juxtaposition, but as the result of his fundamental
principles. If we recall what has been said concerning the monad,
we shall remember that it is an activity, but an activity with a
content. It is a force, but a force which mirrors the universe. The
content, that portion of reality which is reflected in the action,
is knowledge, or the idea; the activity which brings this about is
will, or the volition. They are related to each other as form and
content. There is, strictly speaking, no "state" of mind; there is
only a tension, a pushing forward of mind. There is no idea which
is not a volition. Will is thus used, in a very broad sense, as
equivalent to action. Since, however, the activity of the monad is
in no case aimless, but has an end in view, the will is not _mere_
activity in general, it is action towards some definite end. And since
the end at which the monad aims is always the development of an idea,
the reflection of some constituent of the universe, the will is always
directed towards and determined by some idea of the intellect.

We have seen, however, that there are various stages in the reflecting
power of the soul, or in the realization of intellect. Taking
only the broadest division, there are perception and apperception;
that is, there are the conscious and the unconscious mirroring of
reality. We shall expect, then, to find two corresponding stages of
volition. Leibniz calls these stages "appetition" and "volition"
in the narrower sense. The constant tendency in every monad to go
from one perception to another,--that is, the following of the law
of development,--constitutes appetition. If joined to feeling,
it constitutes instinct. Since, again, there are two degrees of
apperception, one of empirical, the other of rational, consciousness,
we shall expect to find two grades of volition proper,--one
corresponding to action for conscious particular ends; the other
for ends which are proposed by reason, and are hence universal. In
this chapter we shall simply expand and illustrate these various

Sensations, looked at not as to what they represent, but in
themselves, are impulses. As such they constitute the lowest stage
of will. Impulsive action then includes all such as occurs for an
end which is unknown, or at best but dimly felt. Such action may be
called blind, not in the sense that it is without reason, but in the
sense that reason is not consciously present. We are not to think of
this instinctive action, however, as if it were found simply in the
animals. Much of human action is also impulsive; probably, indeed,
an impulsive factor is contained in our most rational willing. We are
never able to take complete account of the agencies which are acting
upon us. Along with the reasons of which we are conscious in choosing,
there are mingled faint memories of past experience, subconscious
solicitations of the present, dim expectations for the future. Such
elements are decisive factors far more than we realize.

Indeed, it is because of the extent to which such unconscious
influences bear upon us and move us that there arises the idea
of indifferent or unmotivated choice. Were both motive and choice
unconscious, the question as to whether choice were antecedently
determined would not arise; and were our motives and their results
wholly in consciousness, the solution of the question would be
evident. But when we are conscious of our choice, but are not conscious
of our impulses and motives, we get the impression that our choice is
unmotived, and hence come to believe in "indifferent freedom,"--the
ability to choose as we will.

We shall shortly take up in more detail the theory of Leibniz regarding
the freedom of will; and it is needful here to remark only that the
conception which makes it consist in ability to choose without reason
is in direct contradiction to his fundamental thought,--namely, that
there can be no activity which does not aim at some reflection of the
universe, by which, therefore, it is determined. From the psychological
point of view, it is interesting also to notice how Leibniz's theory
of unconscious ideas enables him to dispose of the strongest argument
for indifferent choice,--that drawn from the immediate "testimony"
of consciousness.

Upon the origin and nature of desires Leibniz has much more to say
than about the impulses. His account of the transition from impulse
to desire is based upon the conception of unconscious ideas. Slight
and imperceptible impulses are working upon us all the time. Indeed,
they are a necessity; for the actual state of a soul or monad at any
time is, of course, one of incompleteness. Our nature must always work
to free itself from its hindrances and obtain its goal of complete
development. But it will not do this unless there is some stimulus,
some solicitation to induce it to overcome its limitation. There is
found accordingly in our every condition a feeling of dissatisfaction,
or, using Locke's word, of "uneasiness;" and it is this which
calls forth that activity which brings about a nearer approach to
the soul's real good. But Leibniz differs from Locke in saying that
this feeling of uneasiness is not a distinct, or even in most cases a
conscious, one. It is not pain, although it differs from pain only in
degree. Uneasiness and pain are related to each other as appetite for
food is to hunger,--the first suffices to stimulate us to satisfaction,
but if the want is not met, results in actual pain; if met, these "half
pains" become tributary to pleasure itself. These unconscious stimuli
to action result in actions which meet the want, and the aggregation of
these satisfactions results in pleasure. In Leibniz's own words:--

"If these elements of pain were themselves true pains, we should
always be in a state of misery, even in pursuing the good. But since
there is always going on a summation of minute successes in overcoming
these states of uneasiness, and these put us more and more at ease,
there comes about a decided pleasure, which often has greater value
even than the enjoyment of the good. Far, then, from regarding this
uneasiness as a thing incompatible with happiness, I find that it is
an essential condition of our happiness. For this does not consist
in perfect possession, which would make us insensible and stupid, but
in a constant progress towards greater results, which must always be
accompanied, accordingly, by this element of desire or uneasiness."

And again he says that "we enjoy all the advantages of pain without any
of its inconveniences. If the uneasiness should become too distinct,
we should be miserable in our awaiting the good which relieves it; but
as it is, there is a constant victory over these half-pains, which we
always find in desire, and this gives us a quantity of half-pleasures,
whose continuance and summation (for they acquire force like a moving
body as it falls) result in a whole and true pleasure." In short,
there is indeed an element of pain in all desire which stimulates
us to action, and therefore to higher development. But ordinarily
this element of pain is not present as such in consciousness, but
is absorbed in the pleasure which accompanies the realization of the
higher good. Thus Leibniz, accepting and emphasizing the very same fact
that served Schopenhauer as a psychological base of pessimism, uses it
as a foundation-stone of optimism.

But desire, or the conscious tendency towards something required as a
good, accompanied by the dim feeling of uneasiness at its absence, does
not yet constitute the complete act of volition. "Several impulses and
inclinations meet in forming the complete volition which is the result
of their conflict." In the concrete act of will there are contained
impulses which push us towards some end whose nature is not known;
there is desire both in its inchoate stage, where pleasure and pain
are not in consciousness, and in its formed state, where the pain
and pleasure are definitely presented. Mixed with these desires and
impulses are images of past experiences which call up the feelings
which were formerly attached to them, and thus there are aroused
indirectly additional impulses and desires. Out of this complicated
mass of impulses, desires, and feelings, both original and reproduced,
comes the "dominant effort" which constitutes complete will. But what
governs the production of this prevailing or dominant effort, which we
may interpret as the act of choice? The answer is simple: the result
of the conflict of these various factors, the striking of the balance,
_is_ the choice. Some desire emerges from the confused complex, and
that desire is the final determination of the will. This desire may
not in all cases be the strongest in itself,--that is, the one whose
satisfaction will allay the greatest "uneasiness," for the others,
taken together, may outweigh it; it may, so to speak, have a plurality,
but not a majority, of volitional forces on its side,--and in this case
a fusion of opposing factors may defeat it. But in any event the result
will be the _algebraic_ sum of the various desires and impulses.

It is not at all necessary, however, that the net outcome shall make
itself apparent as a mechanical equivalent of the forces at work. The
soul, Leibniz says, may use its skill in the formation of parties,
so as to make this or that side the victor. How is this to be done,
and still disallow the possibility of arbitrary choice? This problem
is solved through action becoming deliberate. Deliberate action is
impossible unless the soul has formed the habit of looking ahead and
of arranging for modes of action which do not present themselves as
immediate necessities. Only in this way can one look at the matter
impartially and coolly; "at the moment of combat there is no time for
discussion. Everything which then occurs throws its full force on the
balance, and contributes to an outcome made up in the same way as in
mechanics." The formation of certain habits beforehand, therefore, is
the secret of translating impulsive action into the deliberate sphere.

Of these habits the simplest consists in thinking only occasionally and
incidentally of certain things. Imagination is the mother of desire. If
we do not allow the imagination to dwell upon certain lines of thought,
the probability of such thoughts acquiring sufficient force to become
motives of weight is small. A still more effective method of regulating
action is "to accustom ourselves to forming a train of thoughts of
which reason, and not chance (that is, association), is the basis. We
must get out of the tumult of present impressions, beyond our immediate
surroundings, and ask: _Dic cur hic? respice finem!_" In other words,
we must cross-question our impulses and desires, we must ask whence
they come, that we may see how valid are the credentials which they
offer. We must ask whither they tend, that we may measure them, not by
their immediate interest, but by their relation to an end. The desires
are not to be taken at their face-value, but are to be weighed and

Such a process will evidently result in arresting instantaneous
action. There will be a pause between the presentation of the
desires and the overt act. During this pause it may well occur that
the examination to which the desires have been subject has awakened
contrary desires. The thought of the ignoble origin of a desire or of
its repulsive, though remote, result will bring into action desires of
an opposed kind. Thus the soul regulates action, not as if, however, it
had any direct influence over desires, but by its ability of bringing
other desires into the field. The will, in short, is not opposed to
desire, though rational desire may be opposed to sensuous desire. "By
various artifices, then," Leibniz concludes, "we become masters of
ourselves, and can make ourselves think and do that which we ought
to will, and which reason ordains." Such is the summary of Leibniz's
analysis of the elements and mechanism of volition. There was not much
psychology existing at the time which could aid him in such an acute
and subtle account; only in Aristotle could he have found much help. On
the other hand, it has been so generally incorporated into current
psychology that we may seem to have wasted space in repeating truisms.

Of moral action, however, we have as yet heard nothing. We have an
account of a psychological mechanism; but for what ethical end does
this work, and by what method? This question may best be answered
by turning in more detail to the question of the "freedom of the
will." Freedom in the sense of arbitrary choice Leibniz wholly
rejects, as we have seen. It is inconsistent with at least two of
his fundamental principles; those, namely, of sufficient reason,
and of continuity. "Everything that occurs must have a sufficient
reason for its occurrence." This oft-repeated dictum of Leibniz, the
logical way of stating the complete rationality of experience, would
be shattered into fragments by collision with groundless choice. It
conflicts equally (indeed for the same reason) with the principle of
continuity. "The present is pregnant with the future." "Nature never
makes leaps." "An absolute equilibrium is a chimera." "The soul is
never wholly at rest." These are only various ways of saying that the
notion of arbitrary or unmotivated choice rests upon the assumption
that there is a complete break in the life of the soul, so that it
is possible for something to happen which bears no organic relation
to anything that precedes. The notion of a state of the soul without
motives, followed by the irruption of a certain line of conduct, the
notion of an equilibrium broken by arbitrary choice, is simply the
counterpart of the idea of a vacuum. All that makes Leibniz reject the
latter conception makes it impossible for him to accept the former.

This should not be interpreted to mean that Leibniz denied the "freedom
of the will." What he denied is a notion of freedom which seemed to him
at once unverifiable, useless, and irrational. There is a conception
of freedom which Leibniz not only accepts, but insists upon. Such a
notion of freedom is indeed his ethical ideal. Its three traits are
contingency, spontaneity, and rationality of action. How action can
be at the same time contingent and determined is perhaps difficult
to understand; but Leibniz takes the position that it is. His first
step is to distinguish between physical, mathematical, metaphysical,
and moral necessity. There are truths which are eternal, truths
which are absolutely necessary, because their opposites involve
contradiction. They cannot be violated without involving us in
absurdity. There are other truths which are "positive," that is,
ordained for good reason. These truths may be _a priori_, or rational,
and not merely empirical; for they have been chosen for reasons of
advantage. God always chooses and ordains the best of a number of
possibilities; but he does it, not because the opposite is impossible,
but because it is inferior. Truths whose opposites are impossible
have metaphysical and mathematical necessity. Positive truths have
moral necessity. The principle of causation _must_ be true; the three
interior angles of a triangle _must_ be equal to two right angles. But
that God shall choose the better of two courses is a moral necessity
only. It invokes no absolute logical contradiction to conceive him
choosing some other way. Upon moral necessity depends the physical. The
particular laws of nature are necessary, not because their opposites
are logically absurd, but because these laws are most in accordance
with the general principles of good and order, in agreement with which
God chooses. Physical and moral action is therefore in all cases
contingent. (Contingency does not of itself, of course, constitute
freedom, but conjoined with the characteristics of rationality and
spontaneity, does so.)

Necessity, in short, is based upon the principle of logical
contradiction; contingency upon that of sufficient reason. Since our
actions are in no case necessitated in such a way that their opposite
is self-contradictory, or, put positively, since our actions are always
determined by the choice of that which seems best, our actions are
contingent. Occasionally Leibniz puts the matter in a much simpler way,
and one which brings out the essential element more clearly than the
foregoing distinction. Some facts are determined by the principle of
physical causation; others by that of final causation. Some, in other
words, are necessary as the mechanical outcome of their antecedents;
others are necessary as involved in the reaching of a given end. It is
simply the Aristotelian distinction between efficient and teleological
causation. Human action is determined, since it always has a motive or
reason; it is contingent, because it springs from this reason and not
from its temporal antecedents. It is, in short, determined, but it is
also free.

It does not require much analysis, however, to see that this
distinction, in whatever way it be put, really has no significance,
except as it points to the other marks of freedom,--spontaneity
and rationality. As we shall see, Leibniz makes and can make
no absolute distinction between truths of reason and truths of
fact. The contingent and the necessary are one at bottom. To us
with our limited intelligence it does indeed often appear as if no
contradiction were involved in the former,--as if, for example, a man
could turn either to right or left without there being any logical
contradiction in either case; but this is because of our defective
insight. An intelligence cognizant of the whole matter could see that
one action would contradict some truth involved in the constitution
of the universe. The source of the contingent and changing is in the
necessary and eternal. Thus it is that although Leibniz at one time
says that "neither one's self nor any other spirit more enlightened
could demonstrate that the opposite of a given action (like going out
in preference to staying in) involves contradiction," at another time
he says that "a perfect knowledge of all the circumstances, internal
and external, would enable any one to foresee" the decision in a given
case. If that be so, any other action must be impossible; that is,
according to Leibniz's invariable logic, imply contradiction.

We get the same result if we consider the relation of final and
efficient causes. It is only when speaking in a very general way that
Leibniz opposes action as determined by precedent activities to that
directed towards the attainment of an end. He does not really mean
that _some_ action is physical, while _other_ is teleological. He
cannot suppose that some action has an antecedent cause, while other
has a purpose. The very essence of his thought is that action is
both mechanical and teleological; that all action follows in a law of
order from precedent action, and that all fulfils a certain spiritual
function. The distinction is not, with Leibniz, one between two kinds
of action, but between two ways of looking at every action. The desire
to go rather than to stay, has its efficient cause; the movements by
which the desire is executed, have their final cause. The truth of
the matter seems to be that Leibniz in his desire to guard against
being thought a fatalist, or one denying all freedom, uses terms
which are compatible only with a freedom of indifference. So in his
statement that man's action is free because "contingent," he seems
actuated rather by a wish to avoid the hateful term "necessity" than by
considerations strictly in harmony with his own principles.

Had he confined his use of the term "contingent," however, simply to
re-stating the fact that human action is spontaneous, no such apparent
contradiction would have presented itself. Human actions may be called
contingent, as physical actions are not, because the latter always
seem to be externally determined, while the former are internally
directed. Motions act from without; motives from within. The cause of
the falling of a stone lies outside it; the source of a desire which
moves to action is from the mind itself. We are thus introduced to
contingency as a synonym of "spontaneity."

Kuno Fischer calls attention to the fact that Spinoza and Leibniz both
use the same sort of illustration to show the non-arbitrary character
of human action, but the same illustration with a difference;
and in the difference he finds the distinction between the two
philosophies. Spinoza says that a stone falling to the ground, if
endowed with consciousness, might imagine itself following its own will
in falling. Leibniz says that a magnetic needle similarly endowed might
imagine that it turned towards the north simply because it wished. Both
examples are used to illustrate the folly of relying upon the immediate
"testimony" of consciousness. But the example of Spinoza is that of an
object, all whose movements are absolutely necessitated from without;
the example of Leibniz is that of an object whose activity, though
following law, and not caprice, is apparently initiated from within. Of
course in reality the movements of the magnetic needle are just as much
externally conditioned as those of the stone; but the appearance of
self-action in the latter case may serve at least to exemplify what is
meant by spontaneity as attributed to human action.

It must be noticed at the outset that spontaneity belongs to every
simple substance. We have only to recall the doctrine of monads. These
suffer nothing from without, all their activity is the expression,
is the unfolding, of their own law. "By nature," Leibniz says, "every
simple substance has perceptions, and its individuality consists in
the permanent law which forms the succession of its perceptions, that
are born naturally one of another. Hence it is not necessary for it to
receive any physical influence from without; and therefore the soul has
in itself a perfect spontaneity in such a way that its actions depend
only upon God and itself." Or if we put the matter in its connection
with his psychology rather than with his metaphysics, it is true that
our actions are determined by our motives; but motives are not forces
without the soul, they are forces _of_ the soul. In acting according to
motives the soul is simply acting according to its own laws. A desire
is not an impulsion from an external cause; it is the expression of an
inward tendency. To say that the soul acts from the strongest desire
is simply to say, from this standpoint, that it manifests the most
real part of itself, not that it obeys a foreign force. Impulses,
desires, motives, are all psychical; they admit of no description or
explanation except in their relation to the soul itself. Thus when
Leibniz compares, as he often does, motives to weights acting upon a
balance, we are to remember that the balance is not to be conceived
as the soul, and the weights as energies outside it, but that this is
only a way of picturing what is going on _within_ the soul itself. The
soul may be a mechanism, but it is a self-directing and self-executing
mechanism. To say that human action is free because it is spontaneous,
is to say that it follows an immanent principle, that it is independent
of foreign influences,--in a word, that it is self-determined.

But here again it seems as if Leibniz had stated a principle
altogether too wide to throw any light upon the nature of moral
freedom. Spontaneity is no more an attribute of human activity than it
is of all real activity. Every monad, even the unconscious, as truly
follows its own law without interference from without as does man
himself. If the spontaneity of action constitutes its morality, we are
not in a condition to ascribe morality to man any more than to any real
thing. We are thus thrown back again upon the conception of rationality
as the final and decisive trait of freedom and of ethical conduct. Just
as "contingency" gets a moral import only in connection with conscious
ends of action, so "spontaneity" comes within the moral realm only when
conjoined to reason.

Why is there this close connection between reason and freedom? The
reader has only to recall what was said of Leibniz's theory of
causality to get a glimpse into their unity. Causality is not a matter
of physical influence, but of affording the reason in virtue of which
some fact is what it is. This applies of course to the relation of the
soul and the body. "So far as the soul is perfect and has distinct
ideas, God has accommodated the body to it; so far as the soul is
imperfect and its ideas are confused, God has accommodated the soul to
the body. In the former case the body always responds to the demands
of the soul; in the latter the soul is moved by the passions which
are born of the sensuous ideas. Each is thought to act upon the other
in the measure of its perfection [that is, degree of activity], since
God has adjusted one thing to another according to its perfection or
imperfection. Activity and passivity are always reciprocal in created
things, because a portion of the reasons which serve to explain what
goes on is in one substance, and another portion in the other. This is
what makes us call one active, the other passive."

If we translate these ideas out of their somewhat scholastic
phraseology, the meaning is that the self-activity of any substance
is accurately measured by the extent to which it contains the reasons
for its own actions; and conversely, that it is dependent or enslaved
just so far as it has its reasons beyond itself. Sensations, sensuous
impulses, represent, as we have seen before, the universe only in a
confused and inarticulate way. They are knowledge which cannot give
an account of itself. They represent, in short, that side of mind
which may be regarded as affected, or the limitation of mind,--its
want of activity. So far as the mind acts from these sensations and
the feelings which accompany them, it is ideally determined from
without; it is a captive to its own states; it is in a condition of
passivity. In all action, therefore, which occurs from a sensuous
basis, the soul is rightly regarded as unfree.

On the other hand, just in the degree in which distinctness is
introduced into the sensations, so that they are not simply experienced
as they come, but are related to one another so that their reason
for existence, their spiritual meaning, is ascertained, just in
that degree is the soul master of itself. In Leibniz's own words:
"Distinct knowledge or intelligence has its place in the true use of
reason, while the senses furnish confused ideas. Hence we can say that
we are free from slavery just in the degree that we act with distinct
knowledge, but are subject to our passions in just the degree that our
ideas are confused;" that is, not really representative of things as
they are. "Intelligence is the soul of liberty."

This psychological explanation rests, of course, upon the foundation
principle of the Leibnizian philosophy. Spirit is the sole reality,
and spirit is activity. But there are various degrees of activity, and
each grade lower than the _purus actus_ may be rightfully regarded as
in so far passive. This relative passivity or unreality constitutes
the material and hence the sensuous world. One who has not insight
into truth, lives and acts in this world of comparative unreality;
he is in bondage to it. From this condition of slavery only reason,
the understanding of things as they are, can lift one. The rational
man is free because he acts, in the noble words of Spinoza, _sub specie
æternitatis_. He acts in view of the eternal truth of things,--as God
himself would act.

God alone, it further follows, is wholly free. In him alone are
understanding and will wholly one. In him the true and the good are
one; while every created intelligence is subject in some degree to
sensuous affection, to passion. "In us, besides the judgment of the
understanding, there is always mixed some unreal idea of the sensation
which gives birth to passions and impulses, and these traverse the
judgment of the practical understanding." Freedom, in fine, is not
a ready made garment with which all men are clothed to do with as
they will. It is the ethical ideal; it is something to be attained;
it is action in conformity with reason, or insight into the spiritual
nature of reality and into its laws; it is not the starting-point, it
is the goal. Only with a great price do men purchase such freedom. It
will be noticed at once that Leibniz comes very close to Plato in his
fundamental ethical ideas. The unity of virtue and reason, of virtue
and freedom,--these are thoroughly Platonic conceptions. To both Plato
and Leibniz reason is the ethical ideal because it is the expression
of, nay, rather, _is_ the reality of the universe; while all else is,
as Leibniz says, imperfect or unreal, since it is not an activity, or,
as Plato says, a mixture of Being and Non-Being. Again, to both man
bears a similar relation to this spiritual reality. In Plato's words,
he participates in the Ideas; in those of Leibniz he reflects, as a
mirror, the universe. To both, in a word, the reality, the true-self
of the individual, is the spiritual universe of which it is an organic
member. To both, therefore, man obtains freedom or self-realization
only as he realizes his larger and more comprehensive identity with the
Reason of the universe. With both, knowledge is the good, ignorance is
the evil. No man is voluntarily bad, but only through lack of knowledge
of the true Good. Leibniz, however, with a more developed psychology,
supplements Plato in the point where the latter had the most
difficulty,--the possibility of the feelings or of a love of pleasure
overcoming knowledge of the good. This possibility Plato was compelled
to deny, while Leibniz, by his subtle identifying of the passions with
lack of knowledge, or with confused knowledge, can admit it. "It is an
imperfection of our freedom," says Leibniz, "which causes us to choose
evil rather than good,--a greater evil rather than the less, the less
good rather than the greater. This comes from the _appearances_ of good
and evil which deceive us; but God, who is perfect knowledge, is always
led to the true and to the best good, that is, to the true and absolute

It only remains briefly to apply these conceptions to some specific
questions of moral actions. Locke asks whether there are practical
innate ideas, and denies them, as he denies theoretical. Leibniz,
in replying, recognizes two kinds of "innate" practical principles,
one of which is to be referred to the class of instincts, the other
to that of maxims. Primarily, and probably wholly in almost all
men, moral truths take the rank of instincts alone. All men aim
at the Good; it is impossible to think of man wilfully seeking
his own evil. The methods, the means of reaching this Good, are
implanted in men as instincts. These instincts, when brought to the
light of reason and examined, become _maxims_ of action; they lose
their particular and impulsive character, and become universal and
deliberate principles. Thus Leibniz is enabled to answer the various
objections which are always brought against any "intuitive" theory
of moral actions,--the variability of men's moral beliefs and conduct
in different countries and at different times. Common instincts, but
at first instincts only, are present in all men whenever and wherever
they live. These instincts may readily be "resisted by men's passions,
obscured by prejudice, and changed by custom." The moral instincts are
always the basis of moral action, but "custom, tradition, education"
become mixed with them. Even when so confounded, however, the instinct
will generally prevail, and custom is, upon the whole, on the side of
right rather than wrong, so that Leibniz thinks there is a sense in
which all men have one common morality.

But these moral instincts, even when pure, are not ethical
science. This is innate, Leibniz says, only in the sense in which
arithmetic is innate,--it depends upon demonstrations which reason
furnishes. Leibniz does not, then, oppose intuitive and demonstrative,
as sometimes happens. Morality is _practically_ intuitive in the sense
that all men tend to aim at the Good, and have an instinctive feeling
of what makes towards the Good. It is _theoretically_ demonstrative,
since it does not become a science until Reason has an insight into the
nature of the Good, and ascertains the fixed laws which are tributary
to it. Moral principles are _not_ intuitive in the sense that they are
immediately discovered as separate principles by some one power of the
soul called "conscience." Moral laws are intuitive, he says, "as the
_consequences_ of our own development and our true well-being." Here we
may well leave the matter. What is to be said in detail of Leibniz's
ethics will find its congenial home in what we have to say of his



Locke's account of innate ideas and of sensation is only preparatory
to a discussion of the ideas got by sensation. His explanation of the
mode of knowledge leads up to an explanation of the things known. He
remains true to his fundamental idea that before we come to conclusions
about any matters we must "examine our own ability." He deals first
with ideas got by the senses, whether by some one or by their conjoint
action. Of these the ideas of solidity, of extension, and of duration
are of most concern to us. They form as near an approach to a general
philosophy of nature as may be found anywhere in Locke. They are, too,
the germ from which grew the ideas of matter, of space, and of time,
which, however more comprehensive in scope and more amply worked out
in detail, characterize succeeding British thought, and which are
reproduced to-day by Mr. Spencer.

"The idea of solidity we receive by our touch." "The ideas we get
by more than one sense are of space or extension, figure, rest,
and motion." These sentences contain the brief statement of the chief
contention of the sensational school. Locke certainly was not conscious
when he wrote them that they were the expression of ideas which should
resolve the world of matter and of space into a dissolving series of
accidentally associated sensations; but such was none the less the
case. When he writes, "If any one asks me what solidity is, I send him
to his senses to inform him," he is preparing the way for Berkeley,
and for a denial of all reality beyond the feelings of the individual
mind. When he says that "we get the idea of space both by sight and
touch," this statement, although appearing truistic, is none the less
the source of the contention of Hume that even geometry contains
no necessary or universal elements, but is an account of sensible
appearances, relative, as are all matters of sensation.

Locke's ideas may be synopsized as follows: It is a sufficient account
of solidity to say that it is got by touch and that it arises from
the resistance found in bodies to the entrance of any other body. "It
is that which hinders the approach of two bodies when they are moved
towards one another." If not identical with matter, it is at all events
its most essential property. "This of all others seems the idea most
intimately connected with and essential to body, so as nowhere else
to be found or imagined, but only in matter." It is, moreover, the
source of the other properties of matter. "Upon the solidity of bodies
depend their mutual impulse, resistance, and protrusion." Solidity,
again, "is so inseparable an idea from body that upon that depends its
filling of space, its contact, impulse, and communication of motion
upon impulse." It is to be distinguished, therefore, from hardness, for
hardness is relative and derived, various bodies having various degrees
of it; while solidity consists in utter exclusion of other bodies from
the space possessed by any one, so that the hardest body has no more
solidity than the softest.

The close connection between solidity and matter makes it not only
possible, but necessary, to distinguish between matter and extension as
against the Cartesians, who had identified them. In particular Locke
notes three differences between these notions. Extension includes
neither solidity nor resistance; its parts are inseparable from one
another both really and mentally, and are immovable; while matter has
solidity, its parts are mutually separable, and may be moved _in_
space. From this distinction between space and matter it follows,
according to Locke, that there is such a thing as a vacuum, or that
space is not necessarily a plenum of matter. Matter is that which fills
space; but it is entirely indifferent to space whether or not it is
filled. Space is occupied by matter, but there is no essential relation
between them. Solidity is the essence of matter; emptiness is the
characteristic of space. "The idea of space is as distinct from that
of solidity as it is from that of scarlet color. It is true, solidity
cannot exist without extension, neither can scarlet color exist without
extension; but this hinders not that they are _distinct ideas_."

Thus there is fixed for us the idea of space as well as of matter. It
is a distinct idea; that is, absolute or independent in itself,
having no intrinsic connection with phenomena _in_ space. Yet it is
got through the senses. How that can be a matter of sensation which is
not only not material, but has no connection in itself with matter,
Locke does not explain. He thinks it sufficient to say that we see
distance between bodies of different color just as plainly as we see
the colors. Space is, therefore, a purely immediate idea, containing
no more organic relation to intelligence than it has to objects. We
get the notion of time as we do that of space, excepting that it is
the observation of internal states and not of external objects which
furnishes the material of the idea. Time has two elements,--succession
and duration. "Observing what passes in the mind, how of our ideas
there in train some constantly vanish, and others begin to appear,
we come by the idea of succession, and by observing a distance in
the parts of this succession we get the idea of duration." Whether,
however, time is something essentially empty, having no relation to the
events which fill it, as space is essentially empty, without necessary
connection with the objects which fill it, is a question Locke does not
consider. In fact, the gist of his ideas upon this point is as follows:
there is actually an objective space or pure emptiness; employing our
senses, we get the idea of this space. There is actually an objective
time; employing reflection, we perceive it. There is not the slightest
attempt to form a philosophy of them, or to show their function in the
construction of an intelligible world, except in the one point of the
absolute independence of matter and space.

It cannot be said that Leibniz criticises the minor points of Locke
in such a way as to throw much light upon them, or that he very
fully expresses his own ideas about them. He contents himself with
declaring that while the senses may give instances of space, time,
and matter, and may suggest to intelligence the stimuli upon which
intelligence realizes these notions from itself, they cannot be the
source of these notions themselves; finding the evidence of this in the
sciences of geometry, arithmetic, and pure physics. For these sciences
deal with the notions of space, time, and matter, giving necessary
and demonstrative ideas concerning them, which the senses can never
legitimate. He further denies the supposed absoluteness or independence
of space, matter, and motion. Admitting, indeed, the distinction
between extension and matter, he denies that this distinction suffices
to prove the existence, or even the possibility, of a vacuum, and ends
with a general reference to his doctrine of pre-established harmony,
as serving to explain these matters more fully and more accurately.

Leibniz has, however, a complete philosophy of nature. In his other
writing, he explains the ideas of matter and force in their dependence
upon his metaphysic, or doctrine of spiritual entelechies. The task
does not at first sight appear an easy one. The reality, according to
Leibniz, is purely spiritual, does not exist in space nor time, and
is a principle of activity following its own law,--that of reflecting
the universe of spiritual relations. How from this world of ideal,
unextended, and non-temporal dynamic realities we are to pass over to
a material world of extension, with its static existence in space,
and transitory passage in time, is a question challenging the whole
Leibnizian system. It is a question, however, for which Leibniz himself
has provided an answer. We may not regard it as adequate; we may think
that he has not truly derived the material world from his spiritual
principles: but at all events he asked himself the question, and gave
an answer. We shall investigate this answer by arranging what Leibniz
has said under the heads of: matter as a metaphysical principle; matter
as a physical phenomenon; and the relation of phenomena to absolute
reality, or of the physical to the metaphysical. In connection with the
second head, particularly, we shall find it necessary to discuss what
Leibniz has said about space, time, and motion.

Wolff, who put the ideas of Leibniz into systematic shape, did it at
the expense of almost all their significance. He took away the air
of paradox, of remoteness, that characterized Leibniz's thought, and
gave it a popular form. But its depth and suggestiveness vanished in
the process. Unfortunately, Wolff's presentations of the philosophy
of Leibniz have been followed by others, to whom it seemed a dull
task to follow out the intricacies of a thought nowhere systematically
expressed. This has been especially the case as concerns the Leibnizian
doctrine of matter. A superficial interpretation of certain passages
in Leibniz has led to an almost universal misunderstanding about
it. Leibniz frequently says that since matter is composite or complex,
it follows that there must be something simple as its basis, and this
simple something is the monad. The misinterpretation just spoken of
consists in supposing that Leibniz meant that matter as composite
is made up of monads as simple; that the monad and matter are facts
of the same order, the latter being only an aggregate, or continued
collection of the former. It interpreted the conception of Leibniz in
strict analogy with the atomic theory of Lucretius, excepting that it
granted that the former taught that the ultimate atom, the component
of all complex forms of matter, has position only, not extension,
its essence consisting in its exercise of force, not in its mere space
occupancy. The monad was thus considered to be _in_ space, or at least
conditioned by space relations, as is a mathematical point, although
not itself spatial in the sense of being extended. Monad and matter
were thus represented as facts of the same kind or genus, having their
difference only in their relative isolation or aggregation.

But Leibniz repudiated this idea, and that not only by the spirit
of his teaching, but in express words. Monads "are not ingredients
or constituents of matter," he says, "but only _conditions_
of it." "Monads can no more be said to be parts of bodies, or to
come in contact with them, or to compose them, than can souls or
mathematical points." "Monads _per se_ have _no_ situation relative
to one another." An increase in the number of created monads, he says
again, if such a thing could be supposed, would no more increase the
amount of matter in existence, than mathematical points added to a
line would increase its length. And again: "There is no nearness or
remoteness among monads; to say that they are gathered in a point or
are scattered in space, is to employ mental fictions, _in trying to
imagine what can only be thought_." The italicized words give the clew
to the whole discussion. To make monads of the same order as corporeal
phenomena, is to make them sensible, or capable of being imaged,
or conditioned by space and time,--three phrases which are strictly
correlative. But the monads can only be thought,--that is, their
qualities are ideal, not sensible; they can be realized only by reason,
not projected in forms having spatial outline and temporal habitation,
that is, in images. Monads and material things, in other words, are
facts of two distinct orders; they are related as the rational or
spiritual and the physical or sensible. Matter is no more composed of
monads than it is of thoughts or of logical principles. As Leibniz says
over and over again: Matter, space, time, motion are only phenomena,
although phenomena _bene fundata_,--phenomena, that is, having their
rational basis and condition. The monads, on the other hand, are not
appearances, they are realities.

Having freed our minds from the supposition that it is in any way
possible to form an image or picture of the monad; having realized that
it is wholly false to suppose that monads occupy position in space,
and then by their continuity fill it, and make extended matter,--we
must attempt to frame a correct theory of the nature of matter and
its relation to the monad. We shall do this only as we realize that
"matter," so far as it has any reality, or so far as it has any real
_fundamentum_, must be something ideal, or, in Leibniz's language,
"metaphysical." As he says over and over again, the only realities
are the substances or spiritual units of activity, to which the name
"monad" is given. In the inquiry, then, after such reality as matter
may have, we must betake ourselves to this unit of living energy.

Although every monad is active, it is not entirely active. There is,
as we have already seen, an infinite scale of substances; and since
substance is equivalent to activity, this is saying that there is an
infinite scale of activities. God alone is _purus actus_, absolute
energy, untouched by passivity or receptivity. Every other being has
the element of incompleteness, of inadequacy; it does not completely
represent the universe. In this passivity consists its finitude, so
that Leibniz says that not even God himself could deprive monads of it,
for this would be to make them equal to himself. In this passivity,
incompleteness, or finitude, consists what we call matter. Leibniz says
that he can understand what Plato meant when he called matter something
essentially imperfect and transitory. Every finite monad is a union of
two principles,--those of activity and of passivity. "I do not admit,"
says Leibniz, "that there are souls existing simply by themselves,
or that there are created spirits detached from all body. God alone is
above all matter, since he is its author; creatures freed from matter
would be at the same time detached from the universal connection
of things, and, as it were, deserters from the general order." And
again, "Beings have a nature which is both active and passive;
_that is_, material and immaterial." And again, he says that every
created monad requires both an entelechy, or principle of activity,
and matter. "Matter is essential to any entelechy, and can never be
separated from it, since matter _completes_ it." In short, the term
"monad" is equivalent to the term "entelechy" only when applied
to God. In every other monad, the entelechy, or energy, is but one
factor. "Matter, or primitive passive power, completes the entelechy,
or primitive active power, so that it becomes a perfect substance, or
monad." On the other hand, of course, matter, as the passive principle,
is a mere potentiality or abstraction, considered in itself. It is
real only in its union with the active principle. Matter, he says,
"cannot exist without immaterial substances." "To every particular
portion of matter belongs a particular _form_; that is, a soul,
a spirit." To this element of matter, considered as an abstraction,
in its distinction from soul, Leibniz, following the scholastics, and
ultimately Aristotle, gives the name, "first" or "bare" matter. The
same influence is seen in the fact that he opposes this element of
matter to "form," or the active principle.

Our starting-point, therefore, for the consideration of matter
is the statement that it is receptivity, the capacity for being
affected, which always constitutes matter. But what is meant by
"receptivity"? To answer this question we must return to what was said
about the two activities of the monad,--representation, or perception,
and appetition,--and to the difference between confused and distinct
ideas. The monad has appetition so far as it determines itself
from within to change, so far as it follows an internal principle
of energy. It is representative so far as it is determined from
without, so far as it receives impressions from the universe. Yet
we have learned to know that in one sense everything occurs from
the spontaneity of the monad itself; it receives no influence or
influxus from without; everything comes from its own depths, or is
appetition. But, on the other hand, all that which so comes forth is
only a mirroring or copying of the universe. The whole content of the
appetition is representation. Although the monad works spontaneously,
it is none the less determined in its activities to produce only
reflections or images of the world. In this way appetition and
representation appear to be identical. The monad is determined from
within, indeed, but it is determined to exactly the same results as if
wholly determined from without. What light, then, can be thrown from
this distinction upon the nature of matter?

None, unless we follow Leibniz somewhat farther. If we do, we shall
see that the soul is regarded as appetitive, or self-active, so far
as it has clear and distinct ideas. If the monad reaches distinct
consciousness, it has knowledge of self,--that is, of the nature of
pure spirit,--or, what again is equivalent to this, of the nature
of reality as it universally is. Such knowledge is knowledge of God,
of substance, of unity, of pure activity, and of all the innate ideas
which elevate the confused perceptions of sense into science. Distinct
consciousness is therefore equivalent to self-activity, and this to
recognition of God and the universal. But if knowledge is confused,
it is not possible to see it in its relations to self; it cannot
be analyzed; the rational or ideal element in it is concealed from
view. In confused ideas, therefore, the soul appears to be passive;
being passive, to be determined from without. This determination from
without is equivalent to that which is opposed to spirit or reason, and
hence appears as matter. Such is in outline the Leibnizian philosophy.

It thus is clear that merely stating that matter is passivity
in the monad is not the ultimate way of stating its nature. For
passivity means in reality nothing but confused representations,--representations,
that is, whose significance is not perceived. The true significance
of every representation is found in its relation to the
ego, or pure self-activity, which, through its dependent
relation upon God, the absolute self-activity and ego, produces
the representation from its own ideal being. So far as the
soul does not have distinct recognition of relation of all
representations to self, it feels them as coming from without; as
foreign to spirit; in short, as matter. Leibniz thus employs exactly
the same language about confused ideas that he does about passivity,
or matter. It is not possible that the monad should have distinct
consciousness of itself as a mirror of the whole universe, he says,
"for in that case every entelechy would be God." Again, "the soul would
be God if it could enter at once and with distinctness into everything
occurring within it." But it is necessary "that we should have
passions which consist in confused ideas, in which there is something
involuntary and unknown, and which represent the body and constitute
our imperfection." Again, he speaks of matter as "the _mixture_
(_mélange_) of the effects of the infinite environing us." In that
expression is summed up his whole theory of matter. It is a mixture;
it is, that is to say, confused, aggregated, irresolvable into simple
ideas. But it is a mixture of "effects of the infinite about us;"
that is, it takes its rise in the true, the real, the spiritual. It
only fails to represent this as it actually is. Matter, in short, is a
phenomenon dependent upon inability to realize the entire spiritual
character of reality. It is spirit apprehended in a confused,
hesitating, and passive manner.

It is none the less a necessary phenomenon, for it is involved in the
idea of a continuous gradation of monads, in the distinction between
the infinite and the finite, or, as Leibniz often prefers to put it,
between the "creator" and the "created." There is involved everywhere
in the idea of Leibniz the conception of subordination; of a hierarchy
of forms, each of which receives the law of its action from the
next higher, and gives the law to the next lower. We have previously
considered the element of passivity or receptivity as relating only
to the monad which manifests it. It is evident, however, that what
is passive in one, implies something active in another. What one
receives, is what another gives. The reciprocal influence of monads
upon one another, therefore, as harmonious members of one system,
requires matter. More strictly speaking, this reciprocal influence
_is_ matter. To take away all receptivity, all passivity, from monads
would be to isolate them from all relations with others; it would
be to deprive them of all power of affecting or being affected by
others. That is what Leibniz meant by the expression already quoted,
that if monads had not matter as an element in them, "they would be,
as it were, deserters from the general order." The note of unity, of
organic connection, which we found to be the essence of the Leibnizian
philosophy, absolutely requires, therefore, matter, or passivity.

It must be remembered that this reciprocal influence is ideal. As
Leibniz remarks, "When it is said that one monad is affected by
another, this is to be understood concerning its _representation_ of
the other. For the Author of things has so accommodated them to one
another that one is said to suffer (or receive from the other) when
its relative value gives way to that of the other." Or again, "the
modifications of one monad are the ideal causes of the modifications
of another monad, so far as there appear in one the reasons on account
of which God brought about in the beginning certain modifications in
another." And most definitely of all: "A creature is called active so
far as it has perfection; passive in so far as it is imperfect. One
creature is more perfect than another so far as there is found in
it that which serves to _render the reason_, _a priori_, for that
occurring in the other; and it is in this way that it acts upon the

We are thus introduced, from a new point of view and in a more concrete
way, to the conception of pre-established harmony. The activity of one,
the energy which gives the law to the other and makes it subordinate in
the hierarchy of monads, is conceived necessarily as spirit, as soul;
that which receives, which is rendered subordinate by the activity
of the other, is body. The pre-established harmony is the fact that
they are so related that one can receive the law of its activity from
the other. Leibniz is without doubt partially responsible for the
ordinary misconception of his views upon this point by reason of the
illustration which he was accustomed to use; namely, of two clocks so
constructed that without any subsequent regulation each always kept
perfect time with the other,--as much so as if there were some actual
physical connection between them. This seems to put soul and body,
spirit and matter, as two co-ordinate substances, on the same level,
with such natural opposition between them that some external harmony
must arrange some unity of action. In causing this common idea of
his theory of pre-established harmony, Leibniz has paid the penalty
for attempting to do what he often reproves in others,--imagining or
presenting in sensible form what can only be thought. But his other
explanations show clearly enough that the pre-established harmony
expresses, not a relation between two parallel substances, but a
condition of dependence of lower forms of activity upon the higher for
the law of their existence and activity,--in modern terms, it expresses
the fact that phenomena are conditioned upon noumena; that material
facts get their significance and share of reality through their
relation to spirit.

We may sum up what has been said about matter as an element in the
monad, or as a metaphysical principle, as follows: The existence of
matter is not only not opposed to the fundamental ideas of Leibniz, but
is a necessary deduction from them. It is a necessity of the principle
of continuity; for this requires an infinity of monads, alike indeed
in the universal law of their being, but unlike, each to each, in
the specific coloring or manifestation of this law. The principle of
organic unity requires that there be as many real beings as possible
participating in and contributing to it. It is necessary, again, in
order that there may be reciprocal influence or connection among the
monads. Were it not for the material element in the monad, each would
be a God; if each were thus infinite and absolute, there would be
so many principles wholly independent and isolated. The principle of
harmony would be violated. So much for the necessity of the material
factor. As to its nature, it is a principle of passivity; that is, of
ideal receptivity, of conformity to a law apparently not self-imposed,
but externally laid down. This makes matter equivalent to a phenomenon;
that is to say, to the having of confused, imperfect, inadequate
ideas. To say that matter is correlative to confused ideas is to say
that there is no recognition of its relation to self or to spirit. As
Leibniz sometimes puts it, since there is an infinity of beings in
the universe, each one of which exercises an ideal influence upon
every other one of the series, it is impossible that this other one
should realize their full meaning; they appear only as confused ideas,
or as matter. To use language which Leibniz indeed does not employ,
but which seems to convey his thought, the spirit, not seeing them as
they really are, does not _find_ itself in them. But matter is thus not
only the confused manifestation or phenomenon of spirit, it is also its
potentiality. Passivity is always relative. It does not mean complete
lack of activity; that, as Leibniz says, is nothingness, and matter
is not a form of nothingness. Leibniz even speaks of it as passive
_power_. That is to say, there is an undeveloped or incomplete activity
in what appears as matter, and this may be,--if we admit an infinity
of time,--must be developed. When developed it manifests itself as it
really is, as spirit. Confused ideas, as Leibniz takes pains to state,
are not a genus of ideas antithetical to distinct; they differ only in
degree or grade. They are on their way to become distinct, or else they
are distinct ideas which have fallen back into an "involved" state of
being. Matter, therefore, is not absolutely opposed to spirit,--on the
one hand because it is the manifestation, the phenomenon, of spirit;
on the other, because it is the potentiality of spirit, capable of
sometime realizing the whole activity implied in it, but now latent.

Thus it is that Leibniz says that everything is "full" of souls or
monads. What appears to be lifeless is in reality like a pond full of
fishes, like a drop of water full of infusoria. Everything is organic
down to the last element. More truly, there is no last element. There
is a true infinity of organic beings wrapped up in the slightest speck
of apparently lifeless matter. These illustrations, like many others
which Leibniz uses, are apt to suggest that erroneous conception of the
relation of monads to spirit which we were obliged, in Leibniz's name,
to correct at the outset,--the idea, namely, that matter is composed,
in a spatial or mechanical way, of monads. But after the foregoing
explanations we can see that what Leibniz means when he says that
every portion of matter is full of entelechies or souls, like a garden
full of plants, is that there is an absolute continuity of spiritual
principles, each having its ideal relation with every other. There
is no point of matter which does not represent in a confused way the
entire universe. It is therefore as infinite in its activities as
the universe. In idea also it is capable of representing in distinct
consciousness, or as a development of its own self-activity, each of
these infinite activities.

In a word, every created or finite being may be regarded as matter or
as spirit, according as it is accounted for by its external relations,
as the reasons for what happen in it are to be found elsewhere than in
its own explicit activity, or according as it shows clearly in itself
the reasons for its own modifications, and also accounts for changes
occurring in other beings. The externally conditioned is matter;
the internally conditioned, the self-explanatory, is self-active, or
spirit. Since all external relations are finally dependent on organic;
since the ultimate source of all explanation must be that which is
its own reason; since the ultimate source of all activity must be that
which is self-active,--the final reason or source of matter is spirit.



We have seen the necessity and nature of matter as deductions from
the fundamental principles of Leibniz. We have seen that matter is
a phenomenon or manifestation of spirit in an imperfect and confused
way. But why should it appear as moving, as extended, as resisting,
as having cohesion, with all the concrete qualities which always mark
it? Is there any connection between these particular properties of
matter as physical, and its "metaphysical" or ideal character? These
are the questions which now occupy us. Stated more definitely, they
take the following form: Is there any essential connection between the
properties of matter as a metaphysical element, and its properties as a
sensible fact of experience? Leibniz holds that there is. He does not,
indeed, explicitly take the ground that we can deduce _a priori_ all
the characteristics of matter as a fact of actual experience from its
rational notion, but he thinks we can find a certain analogy between
the two, that the sensible qualities are images or reflexes of the
spiritual qualities, witnessing, so far as possible, to their origin in
pure energy.

His position is as follows: that which in the monad is activity or
substantial, is, in sensible matter, motion. That which in the monad
is lack of a given activity, that which constitutes its subordinate
position in the hierarchy of monads, is, in the sphere of material
things, inertia. That which in the spiritual world is the individuality
of monads, making each forever ideally distinct from every other, is,
in the phenomenal realm, resistance or impenetrability. The perfect
continuity of monads in the _mundus intelligibilis_ has also its
counterpart in the _mundus sensibilis_ in the diffusion or extension of
physical things.

Instead of following out this analogy directly, it will rather be
found convenient to take up Leibniz's thought in its historical
connection. We have already alluded to the fact that he began as
a Cartesian, and that one of the first ideas which repelled him
from that system of thought was the notion that the essence of
matter is extension. His earliest philosophical writings, as he was
gradually coming to the thoughts which thereafter dominated him,
are upon this point. In general, his conclusions are as follows:
If matter were extension, it would be incapable of passion or of
action. Solidity, too, is a notion entirely opposed to the conception
of mere extension. The idea of matter as extension contradicts some
of the known laws of motion. It requires that the quantity of motion
remain unchanged whenever two bodies come in contact, while as matter
of fact it is the quantity of energy, that which the motion is capable
of effecting, that remains unchanged; or, as he more often puts the
objection, the Cartesian notion of matter requires that matter be
wholly indifferent to motion, that there be nothing in it which resists
motion when imparted. But, says Leibniz, there is something resisting,
that to which Keppler gave the name "inertia." It is not found to be
true if one body impacts upon another that the second moves without
diminishing the velocity or changing the direction of the first. On
the other hand, just in proportion to the size of the second body,
it resists and changes the motion of the first, up to the point of
causing the first to rebound if small in comparison. And when it was
replied that the retardation was due to the fact that the force moving
the first body had now to be divided between two, Leibniz answered
that this was simply to give up the contention, and besides the notion
of extension to use that of force. If extension were the essence of
matter, it should be possible to deduce all the properties of matter,
or at least to account for them all, from it. But since, as just seen,
this does not enable us to account for any of them, since for any of
its concrete qualities we have to fall back on force, it is evident
where the true essence of matter is to be found.

Leibniz has another argument of a logical nature, as those already
referred to are of a physical: "Those who claim that extension is a
substance, reverse the order of words as well as of thoughts. Besides
extension there must be a subject which is extended; that is to
say, something to which it belongs to be repeated or continued. For
extension is nothing but a repetition or continued multiplication
of that which is spread out,--it is a plurality, a continuity, a
co-existence of parts. Consequently, extension does not suffice to
explain the nature of the repeated or manifold substance, of which the
notion is anterior to that of its repetition." Extension, in other
words, is nothing substantial, it is not something which can exist
by itself; it is only a quality, a property, a mode of being. It is
always relative to something which has extension. As Leibniz says
elsewhere: "I insist that extension is only an _abstraction_, and
requires something which is extended. It presupposes some quality,
some attribute, some nature in a subject which is extended, diffused,
or continued. Extension is a diffusion of this quality. For example,
in milk there is an extension or diffusion of whiteness; in the diamond
an extension or diffusion of hardness; in body in general a diffusion
of antitypia or materiality. There is accordingly in body something
anterior to extension."

From the physical side, therefore, we find it impossible to account
for the concrete properties of material phenomena from extension; on
the logical we find that the idea of extension is always relative to
that which is extended. What is that which is to be considered as the
bearer of extension and the source of physical qualities? We are led
back to the point at which we left the matter in the last chapter. It
is force, and force both passive and active. Leibniz uses the term
"matter" in at least three senses: it is the metaphysical element of
passive force _in_ the monad; it is the monad itself considered as,
upon the whole, externally conditioned or unconscious; and it is the
phenomenon resulting from the aggregation of the monads in the second
sense. The first is naked matter, and is a pure abstraction; the second
is the monad as material, as opposed to the monad, as soul; the third
is clothed, or second matter, or, concretely, body, _corpus_. The first
is unreal by itself; the second is one phase of substance; the third
is not substantial, but is a reality, though a phenomenal one. It
is from the substantial monad that we are to explain the two things
now demanding explanation,--that element in _bodies_ (matter in third
sense) which is the source of their physical properties, and that which
is the subject, the carrier, so to speak, of extension.

That of which we are in search as the source of the physical qualities
of bodies is motion. This is not force, but its "image." It is force,
says Leibniz, that "is the real element in motion; that is to say,
it is that element which out of the present state induces a change in
the future state." As force, in other words, is the causal activity
which effects the development of one "representation" of a monad out
of another, so motion, in the realm of phenomena, is not only change,
but change which is continuous and progressive, each new position
being dependent upon the foregoing, and following out of it absolutely
without break.

Motion, therefore, is the manifestation of the ideal unity of
substance,--a unity not of mere static inherence, but of a continuous
process of activity. It is from this standpoint that Leibniz accounts
for the so-called transference of motion from one body to another upon
contact. The ordinary view of this, which looks at it as if one body
loses the motion which another body gains, Leibniz ridicules, saying
that those who hold this view seem to think that motion is a kind of
thing, resembling, perchance, salt dissolved in water. The right view,
on the other hand, does away with all appearance of mystery in the
carrying over of motion from one body to another, for it recognizes
that continuity is the very essence of motion, and that we do not have
two things and a third process, but that the two bodies are phases or
elements in one and the same system of movement.

Starting from this idea of motion, then, Leibniz is to account for
the actual qualities of matter as found in experience. These are
the form, magnitude, cohesion, resistance, and the purely sensible
qualities of objects. "First" matter, that is, abstract matter,
may be conceived, according to Leibniz, as perfectly homogeneous, a
"subtle fluid," in his words, without any distinction of parts or of
solidity. But this _is_ an abstract notion. It is what matter would
be without motion. Motion necessarily differentiates this plenum
of homogeneity, and thus causes distinctions of figure (that is,
boundaries of parts) and varieties of cohesion, or the varying solidity
and fluidity of bodies. The latter difference is indeed the ultimate
one. The principle of continuity or gradation, as applied to motion,
makes it necessary that motions should not be in any two places of
exactly the same energy. The result is that the original fluid matter
is everywhere differently divided. Motion, entering into the uniform
plenum, introduces distinction; it causes so much of the matter as is
affected by a given movement to collect together and form in appearance
a coherent body, as opposed to surrounding bodies which are affected
by different degrees of energy. But even this is only approximate;
the same principle of continuity must be applied within any apparently
coherent body; its parts, while, in relation to other bodies, they have
the same amount of motion, are in relation to one another differently
affected. There are no two having exactly the same motion; if they had,
there would be no distinction between them; and thus, according to the
principle of Leibniz, they would be the same.

It follows at once from this that there is in the universe no body of
absolute hardness or solidity, nor of entire softness or fluidity. A
perfectly solid body would be one whose system of motions could not be
affected by any other system,--a body which by motion had separated
itself from motion, or become absolute. This is evidently an idea
which contradicts itself, for the very essence of motion is continuity
or relation. A body perfectly fluid, on the other hand, would be one
in which there was no resistance offered to other motions,--a body,
in other words, in which there are no movements that, entering into
connection with one another, form a relative opposition to other
movements. It would be a body isolated or out of relation with the
general system of motions, and hence an impossibility. There is no last
term either of solidity or of fluidity.

It equally follows as matter of course that there is no indivisible
particle of matter,--no atom. The infinity of degrees of motion
implies a corresponding division of matter. As already said, it is
only in contrast with other relatively constant systems of motion
that any body is of uniform motion; in reality there is everywhere
throughout it variety of movement, and hence complete divisibility, or
rather, complete division. If Leibniz were to employ the term "atom"
at all, it could be only in the sense of the modern dynamical theory
(of which, indeed, he is one of the originators), according to which
the atom is not defined by its spatial position and outlines, but,
by the range of its effects, as the centre of energies of infinite
circumference. Correlative to the non-existence of the atom is the
non-existence of the vacuum. The two imply each other. The hard,
limited, isolated body, having no intrinsic relations with other
bodies, must have room to come into external relations with them. This
empty space, which is the theatre of such accidental contacts as may
happen, is the vacuum. But if bodies are originally in connection
with one another, if they are in reality but differentiations of
varying degrees of motion within one system of motion, then there
is no necessity for the vacuum,--nay, there is no place for it. The
vacuum in this case could mean only a break, a chasm, in the order
of nature. According to the theory of Leibniz, "bodies" are but the
dynamic divisions of the one energy that fills the universe; their
separateness is not an independent possession of any one of them
or of all together, but is the result of relations to the entire
system. Their apparent isolation is only by reason of their actual
connections. To admit a vacuum anywhere, would thus be to deny the
relatedness of the parts separated by it. The theory of the atom and
the vacuum are the two phases of the metaphysical assumption of an
indefinite plurality of independent separate realities. The theory
of Leibniz, resting as it does on the idea of a perfect unity of
interrelated members, must deny both of these aspects. Were we making
an extended analysis of the opposed view, it would be necessary to
point out that it denies itself. For it is only _through_ the vacuum
that the atoms are isolated or independent, and the sole function of
the vacuum is to serve as the background of the atoms. The atoms are
separated only in virtue of their connection, and the vacuum is what it
is--pure emptiness--only on account of that which is in it. In short,
the theory is only an abstract and incomplete way of grasping the
thought of relation or mediated unity.

We have thus discovered that all motions conspire together, or
form a system. But in their unity they do not cease to be motions,
or variously differentiated members. Through this differentiation,
or mutual reaction of motions, there comes about the appearance of
boundaries, of separation. From these boundaries or terminations
arise the form and size of bodies. From motion also proceeds the
cohesion of bodies, in the sense that each relative system resists
dissolution, or hangs together. Says Leibniz, "The motions, since they
are conspiring, would be troubled by separation; and accordingly this
can be accomplished only by violence and with resistance." Not only
form, size, and stability depend upon motion, but also the sensible,
the "secondary" qualities. "It must not be supposed that color, pain,
sound, etc., are arbitrary and without relation to their causes. It is
not God's way to act with so little reason and order. There is a kind
of resemblance, not entire, but of relation, of order. We say, for
example, 'Light is in the fire,' since there are motions in the fire
which are imperceptible in their separation, but which are sensible
in their conjunction or confusion; and this is what is made known in
the idea of light." In other words, color, sound, etc., even pain,
are still the perception of motion, but in a confused way. We thus see
how thoroughly Leibniz carries back all the properties of bodies to
motion. To sum up, motion is the origin of the relative solidity, the
divisibleness, the form, the size, the cohesion, or active resistance
of bodies, and of their properties as made known to us in immediate

In all that has been said it has been implied that extension is already
in existence; "first matter" is supposed to fill all space, and motion
to determine it to take upon itself its actual concrete properties. But
this "first matter," when thus spoken of, has a somewhat mythological
sound, even if it be admitted that it is an abstraction. For how can
an abstraction be extended in space, and how can it form, as it were,
a background upon which motion displays itself? The idea of "first
matter" in its relation to extension evidently demands explanation. In
seeking this explanation we shall also learn about that "subject" which
Leibniz said was necessarily presupposed in extension, as a concrete
thing is required for a quality.

The clew to the view of Leibniz upon this point may be derived, I
think, from the following quotations:--

"If it were possible to see what makes extension, that kind of
extension which falls under our eyes at present would vanish, and
our minds would perceive nothing else than simple realities existing
in mutual externality to one another. It would be as if we could
distinguish the minute particles of matter variously disposed from
which a painted image is formed: if we could do it, the image, which is
nothing but a phenomenon, would vanish. . . . If we think of two
simple realities as both existing at the same time, but distinct from
one another, we look at them as if they were outside of one another,
and hence conceive them as extended."

The monads are outside of one another, not spatially, but ideally;
but this reciprocal distinction from one another, if it is to appear
in phenomenal mode, must take the form of an image, and the image is
spatial. But if the monads were pure activity, they would _not_ take
phenomenal form or appear in an image. They would always be thought
just as they are,--unextended activities realizing the spiritual
essence of the universe. But they are not pure activity; they are
passive as well. It is in virtue of this passive element that the ideal
externality takes upon itself phenomenal or sensible form, and thus
appears as spatial externality.

Leibniz, in a passage already quoted, refers to the diffusion
of materiality or _antitypia_. This word, which is of frequent
occurrence in the discussions of Leibniz, he translates generally as
"impenetrability," sometimes as "passive resistance." It corresponds to
the solidity or resistance of which Locke spoke as forming the essence
of matter. Antitypia is the representation by a monad of the passive
element in other monads. Leibniz sometimes speaks as if all created
monads had in themselves antitypia, and hence extension; but he more
accurately expresses it by saying that they need (_exigent_) it. This
is a technical term which he elsewhere uses to express the relation of
the possible to the actual. The possible "needs" the actual, not in
the sense that it _necessarily_ requires existence, but in the sense
that when the actual gives it existence, it is the logical basis of the
actual,--the actual, on the other hand, being its real complement. The
passivity of the monad is therefore at once the logical basis and
the possibility of the impenetrability of matter. It is owing to the
passivity of the monad that it does not adequately reflect (that it is
not transparent to, so to speak) the activities of other monads. In
its irresponsiveness, it fails to mirror them in itself. It may be
said, therefore, to be impenetrable to them. They in turn, so far as
they are passive, are impenetrable to it. Now the impenetrable is,
_ex vi terminis_, that which excludes, and that which excludes, not in
virtue of its active elasticity, but in virtue of its mere inertia,
its dead weight, as it were, of resistance. But mutual exclusion of
this passive sort constitutes that which is extended. Extension is
the abstract quality of this concrete subject. Such, in effect, is the
deduction which Leibniz gives of body, or physical matter, from matter
as metaphysical; of matter as sensible or phenomenal, from matter as
ideal or as intelligible.

If we put together what has been said, it is clear that material
phenomena (bodies, _corpora_, in Leibniz's phrase) simply repeat
in another sphere the properties of the spiritual monad. There
is a complete parallelism between every property, each to each,
and this necessarily; for every property of "body" is in logical
dependence upon, and a phenomenalization of, some spiritual or ideal
quality. Motion is the source of all the dynamic qualities of body, and
motion is the reflection of Force, that force which is Life. But this
force in all finite forms is conditioned by a passive, unreceptive,
unresponsive factor; and this must also have its correlate in
"body." This correlate is primarily impenetrability, and secondarily
extension. Thus it is that concrete body always manifests motion,
indeed, but upon a background of extension, and against inertia. It
never has free play; had it an unrestrained field of activity,
extension would disappear, and spatial motion would vanish into
ideal energy. On the other hand, were the essence of matter found in
resistance or impenetrability, it would be wholly inert; it would be a
monotone of extension, without variety of form or cohesion. As Leibniz
puts it with reference to Locke, "body" implies motion, or impetuosity,
resistance, and cohesion. Motion is the active principle, resistance
the passive; while cohesion, with its various grades of completeness,
which produce form, size, and solidity, is the result of their union.

Leibniz, like Plato, has an intermediary between the rational and
the sensible; and as Plato found that it was mathematical relations
that mediate between the permanent and unified Ideas and the changing
manifold objects, so Leibniz found that the relations of space and time
form the natural transition from the sphere of monads to the world
of bodies. As Plato found that it was the possibility of applying
mathematical considerations to the world of images that showed the
participation of Ideas in them, and constituted such reality as they
had, so Leibniz found that space and time formed the element of
order and regularity among sense phenomena, and thus brought them
into kinship with the monads and made them subjects of science. It
is implied in what is here said that Leibniz distinguished between
space and time on the one hand, and duration and extension on the
other. This distinction, which Leibniz draws repeatedly and with great
care, has been generally overlooked by his commentators. But it is
evident that this leaves Leibniz in a bad plight. Mathematics, in its
various forms, is the science of spatial and temporal relations. But if
these are identical with the forms of duration and extension, they are
purely phenomenal and sensible. The science of them, according to the
Leibnizian distinction between the absolutely real and the phenomenally
real, would be then a science of the confused, the imperfect,
and the transitory; in fact, no science at all. But mathematics,
on the contrary, is to Leibniz the type of demonstrative, conclusive
science. Space and time are, in his own words, "innate ideas," and
the entire science of them is the drawing out of the content of these
innate--that is, rational, distinct, and eternal--ideas. But extension
and duration are sensible experiences; not rational, but phenomenal;
not distinct, but confused; not eternal, but evanescent. We may be sure
that this contradiction would not escape Leibniz, although it has many
of his critics and historians.

It is true, however, that he occasionally uses the terms as synonymous;
but this where the distinction between them has no bearing on the
argument in hand, and where the context determines in what sense
the term is used. The distinction which he actually makes, and to
which he keeps when space and time are the subject of discussion,
is that extension and duration are qualities or predicates of
objects and events, while space and time are relations, or orders of
existence. Extension and duration are, as he says, the _immensity_, the
mass, the continuation, the repetition, of some underlying subject. But
space and time are the _measure_ of the mass, the rule or law of the
continuation, the order or mode of the repetition. Thus immediately
after the passage already quoted, in which he says that extension
in body is the diffusion of materiality, just as whiteness is the
diffusion of a property of milk, he goes on to say "that extension is
to space as duration to time. Duration and extension are attributes of
things; but space and time are to be considered, as it were, outside
of things, and as serving to measure them." Still more definitely
he says: "Many confound the immensity or extent of things with the
space by means of which this extent is defined. Space is not the
extension of body, any more than duration is its time. Things keep
their extension, not always their space. Everything has its own extent
and duration; but it does not have a time of its own, nor keep for its
own a space." Or, as he expresses the latter idea elsewhere, space is
like number, in the sense that it is indifferent to spatial things,
just as number is indifferent to _res numerata_. Just as the number
five is not a quality or possession of any object, or group of objects,
but expresses an order or relation among them, so a given space is not
the property of a thing, but expresses the order of its parts to one
another. But extension, on the other hand, is a property of the given
objects. While extension, therefore, must always belong to some actual
thing, space, as a relation, is as applicable to possible things as to
actual existences; so that Leibniz sometimes says that time and space
"express possibilities." They are that which makes it possible for a
definite and coherent order of experiences to exist. They determine
existence in some of its relations, and as such are logically
prior to any given forms of existence; while extent and duration are
always qualities of some given form of existence, and hence logically
derivative. Since time and space "characterize possibilities" as well
as actualities, it follows as a matter of course "that they are of the
nature of eternal truths, which relate equally to the possible and to
the existing." Being an eternal truth, space must have its place in
that which is simply the active unity of all eternal truths,--the mind
of God. "Its truth and reality are based upon God. It is an order whose
source is God." Since God is _purus actus_, he is the immediate, the
efficient source only of that which partakes in some degree of his own
nature, or is rational; and here is another clear point of distinction
between space and extension, between time and duration.

But we must ask more in detail regarding their nature. Admitting
that they are relations, ideal and prior to particular experiences,
the question must be asked, What sort of relations are they; how are
they connected with the purely spiritual on one hand, and with the
phenomenal on the other? Leibniz's most extended answers to these
questions are given in his controversy with Clarke. The latter took
much the same position regarding the nature of space (though not,
indeed, concerning the origin of its idea) as Locke, and the arguments
which Leibniz uses against him he might also have used, for the most
part, against Locke. Locke and Clarke both conceived of space and
time as wholly without intrinsic relation to objects and events. It
is especially against this position that Leibniz argues, holding that
space and time are simply orders or relations of objects and events,
that space exists only where objects are existing, and that it is
the order of their co-existence, or of their possible co-existence;
while time exists only as events are occurring, and is the relation of
their succession. Clarke, on the other hand, speaks of the universe of
objects as bounded by and moving about in an empty space, and says that
time existed before God created the finite world, so that the world
came into a time already there to receive its on-goings, just as it
fell into a space already there to receive its co-existences.

To get at the ideas of Leibniz, therefore, we cannot do better than
follow the course of this discussion. He begins by saying that
both space and time are purely relative, one being the order of
co-existences, the other of successions. Space characterizes in terms
of possibility an order of things existing at the same time, so far as
they exist in mutual relations (_ensemble_), without regard to their
special modes of existence. As to the alternate doctrine that space
is a substance, or something absolute, it contradicts the principle
of sufficient reason. Were space something absolutely uniform, without
things placed in it, there would be no difference between one part and
another, and it would be a matter of utter indifference to God why he
gave bodies certain positions in space rather than others; similarly
it would be a matter of indifference why he created the world when
he did, if time were something independent of events. In other words,
the supposed absoluteness of space and time would render the action of
God wholly without reason, capricious, and at haphazard. Similarly, it
contradicts the principle of "indiscernibles," by which Leibniz means
the principle of specification, or distinction. According to him,
to suppose two things exactly alike, is simply to imagine the same
thing twice. Absolute uniformity, wholly undifferentiated, is a fiction
impossible to realize in thought. "Space considered without objects has
nothing in it to determine it; it is accordingly nothing actual. The
parts of space must be determined and distinguished by the objects
which are in them." Finally, were space and time absolutely real things
in themselves, they would be independent of God, and even limitations
upon him. "They would be more substantial than substances. God would
not be able to change or destroy them. They would be immutable and
eternal in every part. Thus there would be an infinity of eternal
things (these parts) independent of God." They would limit God because
he would be obliged to exist _in_ them. Only by existing through this
independent time would he be eternal; only by extending through this
independent space would he be omnipresent. Space and time thus become
gods themselves.

When Clarke declares that by the absoluteness of space and time he does
not mean that they are themselves substances, but only properties,
attributes of substance, Leibniz advances the same arguments in
different form. If space were the property of the things that are
in space, it would belong now to one substance, now to another, and
when empty of all material substance, even to an immaterial substance,
perhaps to God. "Truly a strange attribute which is handed about from
one thing to another. Substances thus leave their accidents as if they
were old clothes, and other substances put them on." Since these finite
spaces are in infinite space, and the latter is an attribute of God,
it must be that an attribute of God is composed of parts, some of them
empty, some full, some round, some square. So, too, whatever is in time
would help make one of the attributes of God. "Truly a strange God,"
says Leibniz, "this Deity of parts" (_ce Dieu à parties_). Clarke's
reply to this was that space and time are attributes of God and of
God alone, not of things in space and time,--that, indeed, strictly
speaking, there are no parts in space or in time; they are absolutely
one. This was virtually to give up the whole matter. It was to deny
the existence of finite spaces and times, and to resolve them into
an indefinite attribute of God. Such a view, as Leibniz points out,
not only is contrary to experience, but affords no aid in determining
the actual concrete forms and situations of bodies, and durations
and successions of events. The absolute space and time, having no
parts, are wholly out of relations to these concrete existences. The
latter require, therefore, a space and a time that are relations or
orders. Clarke's hypothesis is, as Leibniz says, wholly without use
or function, and requires a theory like that of Leibniz to account
for the actually determinate forms of experience. In his last reply
Clarke shifts his ground again, and says that space and time are
_effects_ of God's existence; "they are the necessary results of his
existence." "His existence is the cause of space and time." The death
of Leibniz prevented any further reply. It is not hard to imagine,
however, that in a general way his reply would have been to ask how
space and time are at once attributes essential and necessary to God,
as constituting his immensity and eternity, and effects dependent upon
his existence. To take this latter position, indeed, seems to abandon
the position that they are absolute, and to admit that, like the rest
of God's creation, they are relative and finite.

So much for Leibniz's polemic. Its meaning is that space and time have
significance only with reference to things and events, that they are
the intellectual, the ideal side of these objects and occurrences,
being the relations which give them order and unity. A space which
is not the space of objects, which is not space in and through
objects, is an inanity; it is not spirit, it is not matter; it is
not a relation of either. It is nothingness magnified to infinity,
and then erected into existence. And all for nothing; for it does not
enable us to account for a single concrete fact of experience. For
this we must have recourse to relations and orders of existence. Space
is therefore to be defined as the order which makes it possible for
objects to have situation; time as that which makes it possible for
events to have dating,--not as if they were actually prior to them,
and although nothings in themselves, yet capable of giving concrete
determination to things, but as _actually_ the relations themselves,
and as _ideally_ necessary for the coherent experience of co-existent
objects and of connected events. As Leibniz puts it epigrammatically:
"Space is the order of possible constants; time the order of inconstant

We have finished the exposition of the views of Leibniz about matter
and material facts. One question, however, remains to be discussed,--a
question which Leibniz's contemporary critics would not allow him to
pass over in silence, even had he been so disposed. What is the reality
of matter, of motion, of space, and of time? Since they are, as Leibniz
says, only phenomena, not absolute realities, what distinguishes them
from dreams, from illusions? What distinguishes sensible phenomena from
capricious fantasies, and gives them reality?

Leibniz begins his answer by pointing out that the mere fact that
bodies are phenomena does not make them unreal. To say that anything
is phenomenal is to say that it is sensible; but "the senses make
no declaration regarding metaphysical matters" such as truth and
reality. The senses, in a word, only inform us that the experiences
are there for the senses, that they are sensible. What is the ultimate
nature of the sensible or the phenomenal, what is their reality,
is a question wholly outside the province of sense. The questions of
ultimate nature, of reality, are questions of metaphysics, and hence
are to be decided by the reason, not by the senses. And Leibniz goes
on to say that the truthfulness of the senses, since it concerns only
the sensible, consists in the reciprocal agreement of sensible facts,
and in that we are not deceived in reasoning from one to another. An
isolated sense-experience could not be said to be either true or
false, real or illusory. It would be true that it was experienced,
and that is all that could be said about it. But since our experiences
are not thus separated, but have a certain order, there arises what
we may call sensible reality and illusion. When the order between
two facts remains the same "in different times and places and in the
experience of different men," we call these facts real. If, however,
our experience cannot be repeated by ourselves or by other men when
the same conditions (that is, connections) are present, it is unreal,
or false. It is thus "the _relation_ of phenomena which guarantees
truth of fact regarding sensible objects." Constancy, regularity,
justify us in ascribing reality; chaotic change and lack of orderly
connection are a sign of unreality. Even our dreams have a reality; for
they have their connections and place in experience. If we understood
their connections we should even be able to explain their apparent
lack of connection with the rest of experience. Leibniz thinks that
both the Academicians and Sceptics and their opponents erred in
attempting to find greater reality in sensible things than that of
regular phenomena. Since our observations and judgments upon sensible
phenomena are of such a nature that we can predict future phenomena and
prepare for them, we have all the reality in them that can be had or
asked for. Even if it be granted possible (as it must be on this basis)
that, metaphysically speaking, sense-experience is only a connected
dream, it yet has a sufficient reality; for we are not deceived in
the measures taken with reference to phenomena, provided that we act
on the ground of their observed harmonies and relations. Thus while
we are obliged to admit that our senses inform us that there are hard,
passive, extended, indivisible things, not perfectly continuous and not
intellectual in their nature, and we know on metaphysical grounds that
this information is not correct, we cannot say that our senses deceive
us, for sense makes no statements regarding such matters. It is our
reason that errs if it takes the information that the senses give as if
it were a declaration of reason itself. Sensible things have all the
reality necessary for this range of experience,--_practical_,--such
regularity of co-existence and sequence as allows us to act without
being led astray.

But if we regard sense-phenomena not merely in their connection with
one another, but in their dependence upon the absolute realities, we
have still better justification for their comparative reality. These
phenomena are consequences of necessary and eternal truths. One endowed
with a perfect knowledge of such truths would be able to deduce, _a
priori_, the phenomena from them. The reality of sensible phenomena
thus consists not merely in their connection with one another, but in
the fact that they are connected as the laws of the intelligible world
require. They follow not only rules of co-existence and sequence;
but these rules may be brought under general laws of motion, which
in turn may be deduced from geometrical principles. These latter,
however, are _a priori_; they are truths which are grounded in the very
intelligence of God. The sensible has its basis in the ideal. To state
the same fact in another way, all sensible phenomena occur in time
and space; or rather, time and space are the orders, the relations,
of phenomena occurring and existing. But, as we have just seen, time
and space are ideal. A relation, as Leibniz points out, being neither
attribute nor accident, cannot be _in_ the things which it relates,
as their possession. In his own words, it cannot be conceived as if
it had one leg in one object, the other leg in the other. A relation
is not a material bond, running through or cementing objects; it
is ideal, existing in the mind. And while it is true that space and
time are the relations of objects and events, it is also true that
if all objects and events were annihilated, space and time would
continue to have their ideal existence in the intelligence of God as
the eternal conditions of phenomena. They thus form the links between
absolute reality and the reality of sensible existence. The principle
of sufficient reason forms another link. It may be recalled that in
discussing Leibniz's theory of volition we found that the will of God
in relation to the sensible world is always determined by the choice of
the better; that in this consists the controlling reason and regulative
principle of all that occurs and exists. Thus for every fact in the
sensible world there is connection with "metaphysical," or absolute,
reality, not only through the medium of the intellectual relations
of time and space, but through the dynamic intermediary of the divine
will acting in accordance with the divine reason. Sensible facts have,
then, a reality, but a dependent one. There would be no _contradiction_
involved if they were not what they actually are.

We may sum up the matter by saying that the reality of sensible
phenomena consists in the constancy of the mutual order in which they
exist, and in the dependence of this order upon the divine Intelligence
and Will. In this respect, at least, Leibniz resembles the young Irish
idealist, Berkeley, who only seven years after Leibniz wrote the "New
Essays" composed his "Principles of Human Knowledge," urging that the
immediate reality of sense-phenomena consists in their "steadiness,
order, and coherence," "in a constant uniform working," and that this
"gives us a foresight which enables us to regulate our actions for the
benefit of life." It was Berkeley also who wrote that their ultimate
reality consists in their being ideas of a Divine Spirit. This was six
years before the death of Leibniz. Yet it does not appear that Berkeley
knew of Leibniz, and the only allusion to Berkeley which I have
found in the writings of Leibniz shows that Leibniz knew only of that
caricature of his views which has always been current,--that Berkeley
was one who denied the existence of any external world. What he writes
is as follows: "As for him in Ireland who questions the reality of
'bodies,' he seems neither to offer what is rational, nor sufficiently
to explain his own ideas. I suspect that he is one of those men who are
desirous of making themselves known through paradoxes."



The fundamental category of Locke, as of all who take simply a
mechanical view of experience, is that of substance. He had good reason
to be surprised when the Bishop of Worcester objected that Locke wished
"to discard substance out of the world." How can that be so, Locke
asks, when I say that "our idea of body is an extended solid substance,
and our idea of soul is of a substance that thinks." And he adds, "Nay,
as long as there is any simple idea or sensible quality left, according
to my way of arguing, substance cannot be discarded." Everything
that really exists, is, according to Locke, substance. But substance
to Locke, as again to all who interpret the universe after sensible
categories, is unknowable. For such categories allow only of external
relations; they admit only of static existence. Substance, in this
way of looking at it, must be distinct from its qualities, and must be
simply the existing substratum in which they inhere.

Locke's account of the way in which we get the idea, and of its nature,
is as follows: "All the ideas of all the sensible qualities of a
cherry come into my mind by sensation. The ideas of these qualities
and actions, or powers, are perceived by the mind to be by themselves
inconsistent with existence. They cannot subsist of themselves. Hence
the mind perceives their necessary connection with inherence, or with
being supported." Correlative to the idea of being supported is, of
course, the idea of the support. But this idea "is not represented
to the mind by any clear and distinct idea; the obscure and vague,
indistinct idea of thing or something, is all that is left." Or yet
more simply, "Taking notice that a certain number of simple ideas
go together, and not imagining how these simple ideas can subsist by
themselves, we accustom ourselves to suppose some substratum wherein
they do subsist, and from which they do result." Hence the only idea we
have of it is of something which underlies known qualities. It is their
"supposed, but unknown, support."

If we translate these expressions into the ideas of to-day,
we see that they are equivalent to the view of the world which
is given us by scientific categories when these categories are
regarded not merely as scientific, but also as philosophic; that
is, capable of interpreting and expressing the ultimate nature of
experience. This modern view uses the words "things-in-themselves"
(or absolute realities) and "phenomena." It says that we know nothing
of existence as it is in itself, but only of its phenomena. Mind,
matter, objects, are all substances, all equally substances, and all
have their unknown essence and their phenomenal appearance. Such a
distinction between the known and the unknown can rest, it is evident,
only upon a separation between reality and phenomena similar to that
which Locke makes between substance and qualities. In knowing the
latter, we know nothing of the former. Although the latter are called
"phenomena," they do not really manifest the substantial reality; they
conceal it. This absolute distinction between substance and quality,
between reality and phenomenon, rests, in turn, upon the hypothesis
that reality is _mere_ existence; that is, it is something which is,
and that is all. It is a substratum; it lies under, in a passive way,
qualities; it is (literally) substance; it simply stands, inactively,
under phenomena. It may, by possibility, _have_ actions; but it _has_
them. Activities are qualities which, like all qualities, are in
external relation to the substance. Being, in other words, is the
primary notion, and "being" means something essentially passive and
merely enduring, accidentally and secondarily something acting. Here,
as elsewhere, Locke is the father of the mechanical philosophy of

We have already learned how completely Leibniz reverses this way of
regarding reality. According to Locke, reality essentially is; and in
its being there is no ground of revelation of itself. It then acts; but
these actions, "powers, or qualities," since not flowing from the very
being of substance, give no glimpse into its true nature. According to
Leibniz, reality acts, and _therefore_ is. Its being is conditioned
upon its activity. It is not first there, and secondly acts; but its
"being there" is its activity. Since its very substance is activity,
it is impossible that it should not manifest its true nature. Its every
activity is a revelation of itself. It cannot hide itself as a passive
subsistence behind qualities or phenomena. It must break forth into
them. On the other hand, since the qualities are not something which
merely inhere in an underlying support, but are the various forms
or modes of the activity which constitutes reality, they necessarily
reveal it. They _are_ its revelations. There is here no need to dwell
further on the original dynamic nature of substance; what was said in
the way of general exposition suffices. It is only in its relations to
Locke's view as just laid down that it now concerns us.

In the first place, Leibniz points out that qualities are "abstract,"
while substance is "concrete." The qualities, from the very fact
that they have no self-subsistence, are only relations, while the
substance, as that of which they are qualities, or from which they
are abstractions, is concrete. It is, Leibniz says, to invert the
true order to take qualities or abstract terms as the best known
and most easily comprehended, and "concretes" as unknown, and as
having the most difficulty about them. "It is abstractions which
give birth to almost all our difficulties," and Locke's error here
is that he begins with abstractions, and takes them to be most open
to intelligence. Locke's second error is separating so completely
substance and attribute. "After having distinguished," says Leibniz,
"two things in substance, the attributes or predicates, and the common
subject of these predicates, it is not to be wondered at that we
cannot conceive anything in particular in the subject. This result is
necessary, since we have separated all the attributes in which there is
anything definite to be conceived. Hence to demand anything more than a
mere unknown somewhat in the subject, is to contradict the supposition
which was made in making the abstraction and in conceiving separately
the subject and its qualities or accidents." We are indeed ignorant
of a subject from which abstraction has been made of all defining
and characteristic qualities; "but this ignorance results from our
demanding a sort of knowledge of which the object does not permit." In
short, it is a credit to our knowledge, not an aspersion upon it, that
we cannot know that which is thoroughly unreal,--a substance deprived
of all attributes. This is, indeed, a remark which is applicable to
the supposed unknowableness of pure Being, or Absolute Being, when it
is defined as the absence of all relations (as is done, for example,
by Mr. Spencer to-day).

Closely connected with the notion of substance are the categories
of identity and diversity. These relations are of course to Locke
thoroughly external. It is "relation of time and place which always
determines identity." "That that had one beginning is the same thing;
and that which had a different beginning in time and place from that,
is not the same, but diverse." It is therefore easy to discover the
principle of individuation. It "is existence itself, which determines
a being of any sort to a particular time and place, incommunicable to
two beings of the same kind." He applies this notion to organic being,
including man, and to the personal identity of man. The identity of an
organism, vegetable, brute, or human, is its continuous organization;
"it is the participation of the same continued life, by constantly
fleeting particles of matter in succession vitally united to the same
organized body." _Personal_ identity is constituted by a similar
continuity of consciousness. "It being the same consciousness that
makes a man be himself to himself, personal identity depends on that
only." It "consists not in the identity of substance, but in the
identity of consciousness." It will be noticed that Locke uses the
notion of identity which he has already established to explain organic
and personal unity. It is the "_same_ continued life," "_identity_ of
consciousness," that constitute them. We are, hence, introduced to no
new principle. Identity is even in personality a matter of temporal and
spatial relations.

In the general account of the system of Leibniz it was pointed out that
it is characteristic of his thought to regard identity and distinction
as internal principles, and as necessarily implied in each other. We
need not go over that ground again, but simply see how he states
his position with reference to what is quoted from Locke. These are
his words: "Besides the difference of place and time there is always
necessary an _internal principle_ [or law] of distinction, so that
while there may be several things of the same species, there are no two
things exactly alike. Thus, although time and place (that is, relations
to the external) aid us in distinguishing things, things do not
cease to be distinguished in themselves. The essence of identity and
diversity does not consist in time and place, although it is true that
diversity of things is accompanied with that of time and place, since
they carry along with them different impressions upon the thing;" that
is, they expose the thing to different surroundings. But in reality
"it is things which diversify times and places from one another, for
in themselves these are perfectly similar, not being substances or
complete realities."

The principle of individuation follows, of course, from this. "If
two individuals were perfectly similar and equal, that is,
indistinguishable in themselves, there would be no principle of
individuation; there would not be two individuals." Thus Leibniz
states his important principle of the "identity of indiscernibles,"
the principle that where there is not some internal differentiating
principle which specifies the existence in this or that definite
way, there is no individual. Leibniz here states, in effect, the
principle of organic unity, the notion that concrete unity is a
unity _of_ differences, not _from_ them. It is the principle which
allows him at once to accept and transform the thought of Spinoza
that all qualification or determination is negation. Spinoza, in
spite of his intellectual greatness, conceived of distinction or
determination as external, and hence as external negation. But since
ultimate reality admits of no external negation, it must be without
distinction, an all-inclusive one. But to Leibniz the negation is
internal; it is determination of its own being into the greatest
possible riches. "Things that are conceived as absolutely uniform and
containing no variety are pure abstractions." "Things indistinguishable
in themselves, and capable of being distinguished only by external
characteristics without internal foundation, are contrary to the
most important principles of reason. The truth is that every being is
capable of change [or differentiation], and is itself actually changed
in such a way that in itself it differs from every other."

As to organic bodies, so far as they _are_ bodies, or corporeal, they
are one and identical only in appearance. "They are not the same an
instant. . . . Bodies are in constant flux." "They are like a
river which is always changing its water, or like the ship of Theseus
which the Athenians are constantly repairing." Such unity as they
really possess is like all unity,--ideal or spiritual. "They remain the
same individual by virtue of that same soul or spirit which constitutes
the 'Ego' in those individuals who think." "Except for the soul,
there is neither the same life nor any vital union." As to personal
identity, Leibniz distinguishes between "physical or real" identity
and "moral." In neither case, however, is it a unity which excludes
plurality, an identity which does not comprehend diversity. "Every
spirit has," he says, "traces of all the impressions which it has ever
experienced, and even presentiments of all that ever will happen. But
these feelings are generally too minute to be distinguished and brought
into consciousness, though they may be sometime developed. This
_continuity_ and _connection_ of _perceptions_ makes up the real
identity of the individual, while _apperceptions_ (that which is
consciously apprehended of past experiences) constitute the moral
identity and make manifest the real identity." We have had occasion
before to allude to the part played in the Leibnizian philosophy by
"minute perceptions" or "unconscious ideas." Of them he says, relative
to the present point, that "insensible perceptions mark and even
constitute the sameness of the individual, which is characterized
by the residua preserved from its preceding states, as they form
its connection with its present state." If these connections are
"apperceived" or brought into distinct consciousness, there is moral
identity as well. As he expresses it in one place: "The self (_soi_)
is real and physical identity; the appearance of self, accompanied with
truth, is personal identity." But the essential point in either case is
that the identity is not that of a substance underlying modifications,
nor of a consciousness which merely accompanies all mental states,
but is the connection, the active continuity, or--in Kant's word--the
synthesis, of all particular forms of the mental life. The self is not
the most abstract unity of experience, it is the most organic. What
Leibniz says of his monads generally is especially true of the higher
monads,--human souls. "They vary, up to infinity itself, with the
greatest abundance, order, and beauty imaginable." Not a mathematical
point, but life, is the type of Leibniz's conception of identity.

In the order in which Locke takes up his topics (and in which Leibniz
follows him) we have omitted one subject, which, however, may find its
natural place in the present connection,--the subject of infinity. In
Locke's conception, the infinite is only a ceaseless extension or
multiplication of the finite. He considers the topic immediately after
the discussions of space, time, and number, and with good logic from
his standpoint; for "finite and infinite," he says, are "looked upon by
the mind as the modes of _quantity_, and are attributed, in their first
designation, only to those things which have parts and are capable
of increase and diminution." This is true even of the application
of the term "infinite" to God, so far as concerns the attributes of
duration and ubiquity; and as applied to his other attributes the
term is figurative, signifying that they are incomprehensible and
inexhaustible. Such being the idea of the infinite, it is attained as
follows: There is no difficulty, says Locke, as to the way in which
we come by the idea of the finite. Every obvious portion of extension
and period of succession which affects us is bounded. If we take one of
these periods or portions, we find that we can double it, or "otherwise
multiply it," as often as we wish, and that there is no reason to stop,
nor are we one jot nearer the end at any point of the multiplication
than when we set out. "By repeating as often as we will any idea of
space, we get the idea of infinity; by being able to repeat the idea
of any length of duration, we come by the idea of eternity." There
is a difference, then, between the ideas of the infinity of space,
time, and number, and of an infinite space, time, and number. The
former idea we have; it is the idea that we can continue without end
the process of multiplication or progression. The latter we have not;
it would be the idea of having completed the infinite multiplication,
it would be the result of the never-ending progression. And this is
evidently a contradiction in terms. To sum the matter up, the term
"infinite" always relates to the notion of quantity. Quantity is that
which is essentially capable of increase or decrease. There is then an
infinity of quantity; there is no quantity which is the absolute limit
to quantity. Such a quantity would be incapable of increase, and hence
contradictory to quantity. But an actual infinite quantity (whether
of space, time, or number) would be one than which there could be no
greater; and hence the impossibility of our having a positive idea of
an actual or completed infinite.

Leibniz's reply consists simply in carrying out this same thought
somewhat further. It is granted that the idea of an infinite quantity
of any kind is absurd and self-contradictory. But what does this prove,
except that the notions of quantity and infinity are incompatible with
each other, that they contradict each other? Hence, instead of the
infinite being a mode of quantity, it must be conceived as essentially
distinct from and even opposed to quantity. Locke's argument is
virtually a _reductio ad absurdum_ of the notion that the infinite
is capable of parts. In the few pages of comment which Leibniz in
1696 wrote upon Locke, this topic of the infinite is one of the few
touched upon. His words upon that occasion were as follows: "I agree
with Mr. Locke that, properly speaking, there is no space, time, nor
number which is infinite; and that it is only true that however great
be a space, a time, or a number, there is always another which is still
greater, and this without end; and that, _therefore_, the infinite
is not to be found in a whole made up of parts. But it does not cease
to exist: it is found in the absolute, which is without parts, and of
which compound things [phenomena in space and time, or facts which may
be numbered] are only limitations. The positive infinite being nothing
else than the absolute, it may be said that there is, in this sense,
a positive idea of the infinite, and that it is anterior to the idea
of the finite." In other words, while the infinite is to Locke an
indefinite extension of the finite, which alone is positively "given,"
to Leibniz the infinite is the positive and real, and the finite is
only in and by it. The finite is the negative.

Leibniz amplifies this thought upon other occasions, as in his present
more extended examination. "There is no infinite number, line, or
quantity, if they are taken as true wholes." "We deceive ourselves in
trying to imagine an absolute space which should be an infinite whole,
composed of parts. There is none such. It is an idea which implies
contradiction; and all these 'infinites' and 'infinitesimals' are of
use only in geometry, as imaginary roots are in algebra." That which
is ordinarily called the infinite, that is, the quantitative infinite,
is in reality only the indefinite. "We involve ourselves in difficulty
when we talk about a series of numbers extending _to_ infinity; we
imagine a last term, an infinite number, or one infinitely little. But
these are only fictions. All number is finite and assignable, [that is,
of a certain definite quantity]; every line is the same. 'Infinites'
and 'infinitesimals' signify only quantities which can be taken as
large or as small as one wishes, simply for the purpose of showing that
there is no error which can be assigned. Or we are to understand by the
infinitely little, the state of vanishing or commencing of a quantum
after the analogy of a quantum already formed." On the other hand,
the true infinite "is not an aggregate, nor a whole of parts; it is not
clothed with magnitude, nor does it consist in number. . . . The
Absolute alone, the indivisible infinite, has true unity,--I mean
God." And as he sums up the matter: "The infinite, consisting of parts,
is neither one nor a whole; it cannot be brought under any notion of
the mind except that of quantity. Only the infinite without parts is
one, and this is not a whole [of parts]: this infinite is God."

It cannot be admitted, however, that Locke has given a correct account
of the origin of the notion of the quantitative infinite, or--to
speak philosophically, and not after the use of terms convenient in
mathematics--the indefinite. According to him, its origin is the mere
empirical repeating of a sensuous datum of time and space. According
to Leibniz, this repetition, however long continued, can give no
idea beyond itself; it can never generate the idea that the process
of repetition may be continued without a limit. Here, as elsewhere,
he objects that experience cannot guarantee notions beyond the limits
of experience. Locke's process of repetition could tell us that a
number _had_ been extended up to a given point; not that it could be
extended without limit. The source of this latter idea must be found,
therefore, where we find the origin of all extra-empirical notions,--in
reason. "Its origin is the same as that of universal and necessary
truths." It is not the empirical process of multiplying, but the fact
that the _same reason_ for multiplying always exists, that originates
and guarantees the idea. "Take a straight line and prolong it in such
a way that it is double the first. It is evident that the second,
being perfectly _similar_ to the first, can be itself doubled; and we
have a third, which in turn is _similar_ to the preceding. The _same
reason_ always being present, it is not possible that the process
should ever be brought to a stop. Thus the line can be prolonged
'to infinity.' Therefore the idea of 'infinity' comes from the
consideration of the identity of relation or of reason."

The considerations which we have grouped together in this chapter
serve to show the fundamental philosophical difference between Locke
and Leibniz. Although, taken in detail, they are self-explanatory, a
few words may be permitted upon their unity and ultimate bearing. It is
characteristic of Locke that he uses the same principle of explanation
with reference to the conceptions of substance, identity and diversity,
and infinity, and that this principle is that of spatial and temporal
relation. Infinity is conceived as quantitative, as the successive
addition of times and spaces; identity and diversity are oneness and
difference of existence as determined by space and time; substance
is the underlying static substratum of qualities, and, as such, is
considered after the analogy of things existing in space and through
time. It must not be forgotten that Locke believed as thoroughly as
Leibniz in the substantial existence of the world, of the human soul,
and of God; in the objective continuity of the world, and the personal
identity of man, and in the true infinity of God. Whatever negative
or sceptical inferences may have afterwards been drawn from Locke's
premises were neither drawn nor dreamed of by him. His purpose was in
essence one with that of Leibniz.

But the contention of Leibniz is that when substance, identity, and
infinity are conceived of by mechanical categories, or measured by the
sensible standard of space and time, they lose their meaning and their
validity. According to him such notions are spiritual in their nature,
and to be spiritually conceived of. "Spiritual," however, does not mean
opposed to the sensible; it does not mean something to be known by a
peculiar kind of intuition unlike our knowledge of anything else. It
means the active and organic basis of the sensible, its significance
and ideal purpose. It is known by knowing the sensible or mechanical
as it really is; that is, as it is completely, as a _concretum_,
in Leibniz's phrase. Leibniz saw clearly that to make the infinite
something at one end of the finite, as its mere external limit, or
something miraculously intercalated into the finite, was to deprive
it of meaning, and, by making it unknowable, to open the way for its
denial. To make identity consist in the removal of all diversity
(as must be done if it be thought after the manner of external
relations), is to reduce it to nothing,--as Hume, indeed, afterwards
showed. Substance, which is merely a support behind qualities, is
unknowable, and hence unverifiable. While, then, the aim of both Locke
and Leibniz as regards these categories was the same, Leibniz saw what
Locke did not,--that to interpret them after the manner of existence
in space and time, to regard them (in Leibniz's terminology) as
mathematical, and not as metaphysical, is to defeat that aim. The sole
way to justify them, and in justifying them to give relative validity
to the sensible and phenomenal, is to demonstrate their spiritual and
dynamic nature, to show them as conditioning space and time, and not as
conditioned by them.



The third book of Locke's Essay is upon words and language; and in the
order of treatment this would be the next topic for discussion. But
much of what is said in this connection both by Locke and by Leibniz is
philological, rhetorical, and grammatical in character, and although
not without interest in itself, is yet without any especial bearing
upon the philosophical points in controversy. The only topics in
this book demanding our attention are general and particular terms;
but these fall most naturally into the discussion of general and
particular knowledge. In fact, it is not the terms which Locke
actually discusses, but the ideas for which the terms stand. We
pass on accordingly, without further ceremony, to the fourth book,
which is concerning knowledge in general. Locke defines knowledge
as "nothing but the perception of the connection and agreement, or
disagreement and repugnancy, of any of our ideas." These agreements or
disagreements may be reduced to four sorts,--Identity, or diversity;
Relation; Co-existence, or necessary connection; Real existence. The
statement of identity and diversity is implied in all knowledge
whatsoever. By them "the mind clearly and infallibly perceives each
idea to agree with itself and be what it is, and all distinct ideas to
disagree; _i. e._, the one not to be the other." The agreement of
relation is such knowledge as the mind derives from the _comparison_
of its ideas. It includes mathematical knowledge. The connection of
co-existence "belongs particularly to substances." Locke's example
is that "gold is fixed,"--by which we understand that the idea of
fixedness goes along with that group of ideas which we call gold. All
statements of fact coming under the natural sciences would fall into
this class. The fourth sort is "that of actual and real existence
agreeing to any idea."

Leibniz's criticism upon these statements of Locke is brief and to
the point. He admits Locke's definition of knowledge, qualifying it,
however, by the statement that in much of our knowledge, perhaps in all
that is merely empirical, we do not know the reason and connection
of things and hence cannot be said to _perceive_ the agreement
or disagreement of ideas, but only to feel it confusedly. His
most important remark, however, is to the effect that relation is
not a special kind of knowledge, but that all Locke's four kinds
are varieties of relation. Locke's "connection" of ideas which
makes knowledge is nothing but relation. And there are two kinds of
relation,--those of "comparison" and of "concourse." That of comparison
states the identity or distinction of ideas, either in whole or in
part. That of concourse contains Locke's two classes of co-existence
and existence. "When we say that a thing really exists, this existence
is the predicate,--that is to say, a notion connected with the idea
which is the subject; and there is connection between these two
notions. The existence of an object of an idea may be considered as
the concourse of this object with me. Hence comparison, which marks
identity or diversity, and concourse of an object with me (or with the
_ego_) are the only forms of knowledge."

Leibniz leaves the matter here; but he only needed to develop what is
contained in this statement to anticipate Berkeley and Kant in some of
the most important of their discoveries. The contradiction which lies
concealed in Locke's account is between his definition of knowledge
in general, and knowledge of real existence in particular. One is the
agreement or disagreement of _ideas_; the other is the agreement of
an idea _with an object_. Berkeley's work, in its simplest form, was
to remove this inconsistency. He saw clearly that the "object" was an
intruder here. If knowledge lies in the connection of _ideas_, it is
impossible to get outside the ideas to find an object with which they
agree. Either that object is entirely unknown, or it is an idea. It
is impossible, therefore, to find the knowledge of reality in the
comparison of an idea with an object. It must be in some property of
the ideas themselves.

Kant developed more fully the nature of this property, which
constitutes the "objectivity" of our ideas. It is their connection
with one another according to certain _necessary_ forms of perception
and rules of conception. In other words, the reality of ideas lies in
their being connected by the necessary and hence universal relations
of synthetic intelligence, or, as Kant often states it, in their
agreement with the conditions of self-consciousness. It is not, I
believe, unduly stretching either the letter or the spirit of Leibniz
to find in that "concourse of the object with the ego" which makes
its reality, the analogue of this doctrine of Kant; it is at all
events the recognition of the fact that reality is not to be found
in the relating of ideas to unknown things, but in their relation to
self-conscious intelligence. The points of similarity between Kant
and Leibniz do not end here. Leibniz's two relations of "comparison"
and "concourse" are certainly the congeners of Kant's "analytic"
and "synthetic" judgments. But Leibniz, as we shall see hereafter,
trusts too thoroughly to the merely formal relations of identity and
contradiction to permit him such a development of these two kinds of
relation as renders Kant's treatment of them epoch-making.

The discussion then advances to the subject of degrees of knowledge,
of which Locke recognizes three,--intuitive, demonstrative, and
sensitive. Intuitive knowledge is immediate knowledge,--recognition
of likeness or difference without the intervention of a third idea;
it is the most certain and clear of all knowledge. In demonstrative
knowledge the agreement or disagreement cannot be perceived directly,
because the ideas cannot be put together so as to show it. Hence
the mind has recourse to intermediaries. "And this is what we call
reasoning." Demonstrative rests on intuitive knowledge, because each
intermediate idea used must be immediately perceived to be like or
unlike its neighboring idea, or it would itself need intermediates for
its proof. Besides these two degrees of knowledge there is "another
perception of the mind employed about the particular existence of
finite things without us, which, going beyond bare probability, and yet
not reaching perfectly to either of the foregoing degrees of certainty,
passes under the name of knowledge."

Leibniz's comments are again brief. The primitive truths which are
known by intuition are to be divided into two classes,--truths of
reason and of fact. The primitive truths of reason are necessary, and
may be called identical, because they seem only to repeat the same
thing, without teaching us anything. A is A. A is not non-A. Such
propositions are not frivolous or useless, because the conclusions
of logic are demonstrated by means of identical propositions, and
many of those of geometry by the principle of contradiction. All the
intuitive truths of reason may be said to be made known through the
"immediation" of ideas. The intuitive truths of fact, on the other
hand, are contingent and are made known through the "immediation"
of feeling. In this latter class come such truths as the Cartesian,
"I think, therefore I am." Neither class can be proved by anything more

Demonstration is defined by Leibniz as by Locke. The former recognizes,
however, two sorts,--analytic and synthetic. Synthesis goes from the
simple to the complex. There are many cases, however, where this is
not applicable; where it would be a task "equal to drinking up the sea
to attempt to make all the necessary combinations. Here the method
of exclusions should be employed, cutting off many of the useless
combinations." If this cannot be done, then it is analysis which gives
the clew into the labyrinth. He is also of the opinion that besides
demonstration, giving certainty, there should be admitted an art of
calculating probabilities,--the lack of which is, he says, a great
defect in our present logic, and which would be more useful than a
large part of our demonstrative sciences. As to sensitive knowledge,
he agrees with Locke that there is such a thing as real knowledge
of objects without us, and that this variety does not have the same
metaphysical certainty as the other two; but he disagrees regarding
its criterion. According to Locke, the criterion is simply the greater
degree of vividness and force that sensations have as compared with
imaginations, and the actual pleasures or pains which accompany
them. Leibniz points out that this criterion, which in reality is
purely emotional, is of no great value, and states the principle of the
reality of sensible phenomena which we have already given, repeating
that it is found in the _connection_ of phenomena, and that "this
connection is verified by means of the truths of reason, just as the
phenomena of optics are explained by geometry."

The discussion regarding "primitive truths," axioms, and maxims,
as well as the distinction between truths of fact and of reason, has
its most important bearing in Locke's next chapter. This chapter has
for its title the "Extent of Human Knowledge," and in connection with
the sixth chapter, upon universal propositions, and with the seventh,
upon axioms, really contains the gist of the treatment of knowledge. It
is here also that are to be considered chapters three and six of book
third, having respectively as their titles, "Of General Terms," and "Of
the Names of Substances."

To understand Locke's views upon the extent and limitations of our
knowledge, it is necessary to recur to his theory of its origin. If
we compare what he says about the origin of ideas from sensations
with what he says about the development of general knowledge from
particular, we shall find that Locke unconsciously puts side by side
two different, and even contradictory, theories upon this point. In the
view already given when treating of sensation, knowledge originates
from the combination, the addition, of the simple ideas furnished
us by our senses. It begins with the simple, the unrelated, and
advances to the complex. But according to the doctrine which he
propounds in treating of general terms, knowledge begins with the
individual, which is already qualified by definite relations, and
hence complex, and proceeds, by abstracting some of these qualities,
towards the simple. Or, in Locke's own language, "ideas become general
by separating from them the circumstances of time and place and any
other ideas that may _determine_ them to this and that particular
existence." And, still more definitely, he says that general ideas
are framed by "leaving out of the _complex_ idea of individuals that
which is peculiar to each, and retaining only what is common to them
all." From this it follows that "general and universal belong not to
the real existence of things, but are the inventions and creatures of
the understanding." "When we quit particulars, the generals that rest
are only creatures of our own making. . . . The signification
they have is nothing but a relation that by the mind of man is added
to them." And in language which reminds us of Kant, but with very
different bearing, he says that relations are the workmanship of the
understanding. The abstract idea of what is common to all the members
of the class constitutes "nominal essence." This nominal essence, not
being a particular existence in nature, but the "workmanship of the
understanding," is to be carefully distinguished from the real essence,
"which is the being of anything whereby it is what it is." This real
essence is evidently equivalent to the unknown "substance" of which we
have heard before. "It is the real, internal, and unknown constitution
of things." In simple or unrelated ideas and in modes the real and
the nominal essence is the same; and hence whatever is demonstrated of
one is demonstrated of the other. But as to substance it is different,
the one being natural, the other artificial. The nominal essence always
relates to sorts, or classes, and is a pattern or standard by which we
classify objects. In the individual there is nothing essential, in this
sense. "Particular beings, considered barely in themselves, will be
found to have all their qualities equally essential to them, or, which
is more, nothing at all." As for the "real essence" which things have,
"we only suppose its being without precisely knowing what it is."

Locke here presents us with the confusion which, in one form or
another, is always found in empiricism, and which indeed is essential
to it. Locke, like the ordinary empiricist, has no doubt of the
existence of real things. His starting-point is the existence of two
substances, mind and matter; while, further, there is a great number of
substances of each kind. Each mind and every separate portion of matter
is a distinct substance. This supposed deliverance of common sense
Locke never called into question. Working on this line, all knowledge
will consist in abstraction from the ready-made things presented to us
in perception, "in leaving out from the complex idea of individuals"
something belonging to them. But on the other hand, Locke never doubts
that knowledge begins with sensation, and that, therefore, the process
of knowledge is one of adding simple, unrelated elements. The two
theories are absolutely opposed to each other, and yet one and the
same philosophical inference may be drawn from each; namely, that only
the particular is real, and that the universal (or relations) is an
artificial product, manufactured in one case by abstraction from the
real individual, in the other by compounding the real sensation.

The result is, that when he comes to a discussion of the extent of
knowledge, he admits knowledge of self, of God, and of "things,"
only by a denial of his very definition of knowledge, while knowledge
of other conceptions, like those of mathematics, is not knowledge of
reality, but only of ideas which we ourselves frame. All knowledge,
that is to say, is obtained only either by contradicting his own
fundamental notion, or by placing it in relations which are confessedly
artificial and superinduced. It is to this point that we come.

The proposition which is fundamental to the discussion is that we
have knowledge only where we perceive the agreement or disagreement
of ideas. Locke then takes up each of his four classes of connection,
in order to ascertain the extent of knowledge in it. Our knowledge
of "identity and diversity extends as far as our ideas," because we
intuitively perceive every idea to be "what it is, and different from
any other." Locke afterwards states, however, that all purely identical
propositions are "trifling," that is, they contain no instruction;
they teach us nothing. Thus the first class of relations cannot be
said to be of much avail. If we consider the fourth kind of knowledge,
that of real existence, we have an intuitive knowledge of self, a
demonstrative knowledge of God, and a sensitive knowledge of other
things. But sensitive knowledge, it must be noted, "does not extend
beyond the objects _actually present_ to our senses." It can hardly
be said, therefore, to assure us of the existence of _objects_
at all. It only tells us what experiences are being at the time
undergone. Furthermore, knowledge of all three (God, self, and matter),
since of real being, and not of relations between ideas, contradicts
his definition of knowledge. But perhaps we shall find knowledge more
extended in the other classes. And indeed Locke tells us that knowledge
of relations is the "largest field of our knowledge." It includes
morals and mathematics; but it is to be noticed that, according to
Locke, in both of these branches our demonstrations are not regarding
facts, but regarding either "modes" framed by ourselves, or relations
that are the creatures of our minds,--"extraneous and superinduced"
upon the facts, as he says. He thus anticipates in substance, though
not in phraseology, Hume's distinction between "matters of fact" and
"connections of ideas," in the latter of which we may have knowledge,
but not going beyond the combinations that we ourselves make.

This leaves one class, that of co-existence, to be examined. Here,
if anywhere, must knowledge, worthy of being termed scientific, be
found. This class, it will be remembered, comprehends our knowledge
concerning substances. But this extends, according to Locke, "a
very little way." The idea of a substance is a complex of various
"simple ideas united in one subject and co-existing together." When we
would know anything further concerning a substance, we only inquire
what other simple ideas, besides those already united, co-exist with
them. Since there is no _necessary_ connection, however, among these
simple ideas, since each is, by its very simplicity, essentially
distinct from every other, or, as we have already learned, since
nothing is essential to an individual, we can never be sure that any
idea really co-exists with others. Or, as Locke says, in physical
matters we "can go no further than particular experience informs us
of. . . . We can have no certain knowledge of universal truths
concerning natural bodies." And again, "universal propositions of whose
truth and falsehood we have certain knowledge concern not existence;"
while, on the other hand, "particular affirmations are only concerning
existence, declaring only the _accidental_ union or separation of ideas
in things existing." This particular knowledge, it must be recalled,
is, in turn, only sensitive, and thus extends not beyond the time when
the sensation is had.

We are not surprised then at learning from Locke that regarding bodies
"we are not capable of scientific knowledge." "Natural philosophy is
not capable of being made a science;" or, as Locke elsewhere states it,
knowledge regarding the nominal essence is "trifling" (Kant's analytic
judgment); regarding the real essence is impossible. For example,
when we say that all gold is fusible, this means either simply that
fusibility is one of the ideas which we combine to get the general
idea of gold, so that in making the given judgment we only expand
our own notion; or it means that the "real" substance gold is always
fusible. But this is a statement we have no right to make, and for two
reasons: we do not know what the real substance gold is; and even if we
did, we should not know that fusibility _always_ co-exists with it. The
summary of the whole matter is that "general certainty is to be found
only in our ideas. Whenever we go to seek it elsewhere, in experiment
or observations without us, our knowledge goes not beyond particulars."

It has been necessary to give an account of Locke's views at this
length because it is in his discussion of the limitations and extent
of knowledge that his theory culminates. While not working out his
sensationalism as consistently as did Hume, he yet reduces knowledge
to that of the existence of God and ourselves (whose natures, however,
are unknown), and to a knowledge of mathematical and moral relations,
which, however, concerns only "the habitudes and relations of abstract
ideas." We have now to see by what means Leibniz finds a wider sphere
for certain and general knowledge by his theory of intellectualism than
Locke can by his sensationalism.

Leibniz's theory of knowledge rests upon a distinction between truths
of fact, which are _a posteriori_ and contingent, and truths of
reason, which are _a priori_ and necessary. In discussing his views
regarding experience, we learned that, according to him, all judgments
which are empirical are also particular, not allowing any inference
beyond the given cases experienced. Experience gives only instances,
not principles. If we postpone for the present the discussions of
truths of reason, by admitting that they may properly be said to be
at once certain and universal, the question arises how in matters
of fact there can be any knowledge beyond that which Locke admits;
and the answer is, that so far as the mere existence and occurrence
of these facts is concerned, there is neither demonstrative nor
general knowledge. But the intelligence of man does not stop with the
isolated fact; it proceeds to inquire into its cause, to ascertain
its conditions, and thus to see into, not merely its actual existence,
but its _possibility_. In Leibniz's language: "The real existence of
things that are not necessary is a point of fact or history; but the
knowledge of possibilities or necessities (the necessary being that
whose opposite is not possible) constitutes demonstrative science." In
other words, it is the principle of causality, which makes us see a
fact not as a mere fact, but as a dependent consequence; which elevates
knowledge, otherwise contingent and particular, into the realm of the
universal and apodictic. Underlying all "accidental union" is the real
synthesis of causation.

If we follow the discussion as it centres about the terms "nominal"
and "real," it stands as follows: Leibniz objects to the use of the
term "essence" in this connection, but is willing to accept that of
"definition;" for, as he says, a substance can have but one essence,
while there may be several definitions, which, however, all express
the same essence. The essence is the _possibility_ of that which is
under consideration; the definition is the statement of that which is
supposed to be possible. The "nominal" definition, however, while it
implies this possibility, does not expressly affirm it,--that is to
say, it may always be doubted whether the nominal definition has any
possibility (or reality) corresponding to it until experience comes
to our aid and makes us know it _a posteriori_. A "real" definition,
on the other hand, makes us know _a priori_ the reality of the thing
defined by showing us the mode of its production, "by exhibiting its
cause or generation." Even our knowledge of facts of experience cannot
be said, therefore, to be arbitrary, for we do not combine ideas just
as we please, but "our combinations may be justified by reason which
shows them to be possible, or by experience which shows them to be
actual, and consequently also possible." To take Locke's example about
gold, "the essence of gold is that which constitutes it and gives it
its sensible qualities, and these qualities, so far as they enable
us to recognize it, constitute its nominal essence, while a real
and causal definition would enable us to explain the contexture or
internal disposition. The nominal definition, however, is also real in
one sense,--not in itself, indeed, since it does not enable us to know
_a priori_ the possibility or production of the body, but empirically

It is evident from these quotations that what Leibniz understands
by "possibility" is the condition or cause of a given fact; and
that, while Locke distinguishes between particular, accidental and
demonstrative, general knowledge as two opposed kinds, concerned with
two distinct and mutually exclusive spheres, with Leibniz they are
distinctions in the aspect of the same sphere of fact. In reality there
is no combination of qualities accidental, as Locke thought that by
far the greater part were; in every empirical fact there is a cause or
condition involved that is invariable, and that constitutes the reason
of the fact. The "accidental" is only in the relation of our ideas
to objects, not in the objects themselves. There may be accidental
mental associations; there are no accidental relations. In empirical,
or _a posteriori_, knowledge, so-called, the reason is there, but
is not known. _A priori_ knowledge, the real definition, discovers
and explicitly states this reason. Contingent knowledge is therefore
potentially rational; demonstrative knowledge is the actual development
of the reasons implicitly contained in experience.

We may with advantage connect this discussion with the fundamental
doctrine of Locke and Leibniz regarding intelligence and reality. To
Locke, as we have seen, knowledge is essentially a matter of relations
or connections; but relations are "superinduced" and "extraneous" as
regards the facts. Every act of knowledge constitutes, therefore, in
some way a departure from the reality to be known. Knowledge and fact
are, by their very definition, opposed to one another. But in Leibniz's
view intelligence, or reason, enters into the constitution of reality;
indeed, it is reality. The relations which are the "creatures of the
understanding" are, therefore, not foreign to the material to be known,
but are organic to it, forming its content. The process, then, in which
the mind perceives the connections or relations of ideas or objects,
is simply the process by which the mind comes to the consciousness
of the real nature of these objects, not a process of "superinducing"
unreal ideas upon them. The difficulty of Locke is the difficulty of
every theory of knowledge that does not admit an organic unity of the
knowing mind and the known universe. The theory is obliged to admit
that all knowledge is in the form of relations which have their source
in intelligence. But being tied to the view that reality is distinct
from intelligence, it is obliged to draw the conclusion that these
relations are not to be found in actual existence, and hence that all
knowledge, whatever else it may be, is unreal in the sense that it does
not and cannot conform to actual fact. But, in the theory of Leibniz,
the process of relating which is the essence of knowledge is only the
realization on the part of the individual mind of the relations or
reasons that eternally constitute reality. Since reality is, and is
what it is, through intelligence, whatever relations intelligence
rightly perceives are not "extraneous" to reality, but are its
"essence." As Leibniz says, "Truth consists in the relations between
the objects of our ideas. This does not depend upon language, but is
common to us with God, so that when God manifests a truth to us, _we
acquire what is already in his understanding_. For although there is an
infinite difference between his ideas and ours as to their perfection
and extent, yet it is always true that as to the same relation they are
identical. And it is in this relation that truth exists." To this may
be added another statement, which throws still further light on this
point: "Ideas are eternally in God, and are in us before we perceive

We have now to consider somewhat more in detail the means by
which the transformation of empirical into rational knowledge
is carried on. Leibniz points out that the difficulty concerning
scientific knowledge of sensible facts is not lack of data, but,
in a certain sense, superfluity of data. It is not that we perceive
no connections among objects, but that we perceive many which we
cannot reduce to one another. "Our experiences," says Leibniz,
"are simple only in appearance, for they are always accompanied by
circumstances connected with them, although these relations are not
understood by us. These circumstances furnish material capable of
explanation and analysis. There is thus a sort of _pleonasm_ in our
perceptions of sensible objects and qualities, since we have more
than one idea of the same object. Gold can be nominally defined in
many ways. Such definitions are only _provisional_." This is to say,
empirical knowledge will become rational when it is possible to view
any subject-matter as a unity, instead of a multiplicity of varied
aspects. And on this same subject he says, in another connection: "A
great number of experiences can furnish us data more than sufficient
for scientific knowledge, provided only we have the art of using these
data." The aim of science is therefore, to discover the dynamic unity
which makes a whole of what appears to be a mere mass of accidentally
connected circumstances. This unity of relations is the individual.

It is thus evident that to Leibniz the individual is not the
beginning of knowledge, but its goal. The individual is the organic,
the dynamic unity of the variety of phases or notions presented
us in sense-experience. Individuality is not "simplicity" in
the sense of Locke; that is, separation from all relations. It
is complete connection of all relations. "It is impossible for
us to have [complete] knowledge of individuals, and to find the
means of determining exactly the individuality of anything; for
in individuality all circumstances are combined. Individuality
envelops the infinite. Only so far as we know the infinite do we
know the individual, on account of the influence (if this word be
correctly understood) that all things in the universe exercise upon
one another." Leibniz, in short, remains true to his conception of the
monad as the ultimate reality; for the monad, though an individual,
yet has the universe as its content. We shall be able, therefore, to
render our sensible experiences rational just in the degree in which we
can discover the underlying relations and dependencies which make them
members of one individual.

For the process of transformation Leibniz relies especially upon two
methods,--those of mathematics and of classification. Of the former
he here says but little; but the entire progress of physical science
since the time of Leibniz has been the justification of that little. In
the passage already quoted regarding the need of method for using our
sensible data, he goes on to say that the "infinitesimal analysis has
given us the means of allying physics and geometry, and that dynamics
has furnished us with the key to the general laws of nature." It is
certainly competent testimony to the truth of Leibniz's fundamental
principles that he foresaw also the course which the development
of biological science would take. No classification based upon
resemblances, says Leibniz in effect, can be regarded as wholly
arbitrary, since resemblances are found in nature also. The only
question is whether our classification is based upon superficial or
fundamental identities; the superficial resemblances being such as are
external, or the effects of some common cause, while the fundamental
resemblances are such as are the cause of whatever other similarities
are found. "It can be said that whatever we compare or distinguish with
truth, nature differentiates, or makes agree, also; but that nature has
differences and identities which are better than ours, which we do not
know. . . . _The more we discover the generation of species_,
and the more we follow in our classifications the conditions that
are required for their production, the nearer we approach the natural
order." Our classifications, then, so far as they depend upon what is
conditioned, are imperfect and provisional, although they cannot be
said to be false (since "while nature may give us those more complete
and convenient, it will not give the lie to those we have already");
while so far as they rest upon what is causal and conditioning, they
are true, general, and necessary. In thus insisting that classification
should be genetic, Leibniz anticipated the great service which the
theory of evolution has done for biological science in enabling science
to form classes which are "natural;" that is, based on identity of

Leibniz culminates his discussion of classification as a method of
translating the empirical into the rational, by pointing out that
it rests upon the law of continuity; and that this law contains two
factors,--one equivalent to the axiom of the Realists, that nature
is nowhere empty; the other, to that of the Nominalists, that nature
does nothing uselessly. "One of these principles seems to make nature
a prodigal, the other a miser; and yet both are true if properly
understood," says Leibniz. "Nature is like a good manager, sparing
where it is necessary, in order to be magnificent. It is magnificent
in its effects, and economical in the causes used to produce them." In
other words, classification becomes science when it presents us with
both unity and difference. The principle of unity is that of nature
as a miser and economical; that of differentiation is the principle of
nature as prodigal and magnificent. The thoroughly differentiated unity
is nature as self-specifying, or as an organic, not an abstract, unity.

The gist of the whole matter is, then, that experience presents us
with an infinity of ideas, which may appear at first sight arbitrary
and accidental in their connections. This appearance, however, is
not the fact. These ideas are the effects of certain causes; and in
ascertaining these conditions, we reduce the apparently unrelated
variety of experiences to underlying unities, and these unities,
like all real unities or simple beings, are spiritual and rational in
nature. Leibniz's ordinary way of stating this is that the principle
of truths of fact is that of _sufficient reason_. This principle
Leibniz always treats as distinguished from that of identity (and
contradiction) as the ruling category of truths of reason. And we shall
follow him in discussing the two together.

"Our reasonings are based on two leading principles,--that of
contradiction, in virtue of which we judge false all which contains
contradiction, and true that which is opposed or contradictory to that
which is false; and that of sufficient reason, in virtue of which we
judge that no fact is true or actual, no proposition veritable, unless
there is a sufficient reason why it is as it is, and not otherwise,
although these reasons are generally unknown to us. Thus there are
two sorts of truths,--those of reason, and those of fact. The truths
of reason are necessary, and their opposites impossible; while those
of fact are contingent, and their opposites possible. When a truth
is necessary, its reason can be discovered by analysis, resolving
it into ideas and truths that are simpler, until the primitive
truths are arrived at. It is thus that the mathematicians proceed in
reducing by analysis the theorems of speculation and the canons of
practice into definitions, axioms, and postulates. Thus they come to
simple ideas whose definition cannot be given; primitive truths that
cannot be proved, and which do not need it, since they are identical
propositions, whose opposite contains a manifest contradiction."

"But in contingent truths--those of fact--the sufficient reason must
be found; namely, in the succession of things which fill the created
universe,--for otherwise the analysis into particular reasons would
go into detail without limit, by reason of the immense variety of
natural things, and of the infinite divisibility of bodies. There
are an infinity of figures and of past and present movements which
enter into the efficient cause of my present writing, and there are
an infinity of minute inclinations and dispositions of my soul which
enter into its final cause. And since all this detail contains only
other contingent and particular antecedents, each of which has need
of a similar analysis to account for it, we really make no progress by
this analysis; and it is necessary that the final or sufficient reason
be outside the endless succession or series of contingent particulars,
that it consist in a necessary being, in which this series of changes
is contained only _eminenter_, as in its source. This necessary being
and source is what we call God."

In other words, the tracing of empirical facts to their causes and
conditions does not, after all, render them wholly rational. The series
of causes is endless. Every condition is in turn conditioned. We
are not so much solving the problem of the reason of a given fact,
as we are stating the problem in other terms as we go on in this
series. Every solution offers itself again as a problem, and this
endlessly. If these truths of fact, then, are to be rendered wholly
rational, it must be in something which lies outside of the series
considered as a series; that is, something which is not an antecedent
of any one of the series, but is equally related to each and to
all as their ground and source. This, considered as an argument
for the existence of God, we shall deal with hereafter; now we are
concerned only with its bearing upon the relation of experience to
the universality and necessity of knowledge. According to this, the
ultimate meaning of facts is found in their relation to the divine
intelligence; for Leibniz is emphatic in insisting that the relation
of God to experience is not one of bare will to creatures produced by
this will (as Descartes had supposed), but of a will governed wholly
by Intelligence. As Leibniz states it in another connection, not only
matters of fact, but mathematical truths, have the same final basis in
the divine understanding.

"Such truths, strictly speaking, are only conditional, and say that
in case their subject existed they would be found such and such. But
if it is again asked in what consists this conditional connection
in which there is necessary reality, the reply is that it is in
the relation of ideas. And by the further question, Where would
be the ideas if no spirit existed; and what would then become of
the foundation of the certainty of such truths?--we are brought to
the final foundation of truths; namely, that supreme and universal
spirit, which must exist, and whose understanding is, in reality, the
region of the eternal truths. And in order that it may not be thought
that it is not necessary to have recourse to this region, we must
consider that these necessary truths contain the determining reason and
regulative principle of existence, and, in a word, of the laws of the
universe. Thus these necessary truths, being anterior to the existences
of contingent beings, must in turn be based upon the existence of a
necessary substance."

It is because facts are not _mere_ facts, in short, but are the
manifestation of a "determining reason and regulative principle" which
finds its home in universal intelligence, that knowledge of them can
become necessary and general.

The general nature of truths of reason and of their ruling principle,
identity and contradiction, has already been given in the quotation
regarding the principle of sufficient reason. It is Leibniz's
contention that only in truths whose opposite is seen to involve
self-contradiction can we have absolute certainty, and that it is
through connection with such eternal truths that the certainty of
our other knowledge rests. It is thus evident why Leibniz insists, as
against Locke, upon the great importance of axioms and maxims. They are
important, not merely in themselves, but as the sole and indispensable
bases of scientific truth regarding all matters. Leibniz at times,
it is true, speaks as if demonstrative and contingent truths were
of themselves, in principle, distinct, and even opposed. But he also
corrects himself by showing that contingency is rather a subjective
limitation than an objective quality. We, indeed, do not see that the
truth "I exist," for example, is necessary, because we cannot see how
its opposite involves contradiction. But "God sees how the two terms
'I' and 'exist' are connected; that is, _why_ I exist." So far as we
can see facts, then, from the standpoint of the divine intelligence,
so far, it would appear, our knowledge is necessary.

Since these axioms, maxims, or first truths are "innate," we are
in a condition to complete (for the first time) the discussion
of innate ideas. These ideas constitute, as we have learned, the
essential content of the divine intelligence, and of ours so far
as we have realized our identity with God's understanding. The
highest form of knowledge, therefore, is self-consciousness. This
bears the same relation to necessary truths that the latter bear to
experience. "Knowledge of necessary and eternal truths," says Leibniz,
"distinguishes us from simple animals, and makes us have reason and
science, _elevating us to the knowledge of ourselves_. We are thus
developed to self-consciousness; and in being conscious of ourselves we
are conscious of being, of substance, of the simple, of the spiritual,
of God." And again he says that "those that know necessary truths are
rational spirits, capable of self-consciousness, of recognizing what is
termed Ego, substance, and monad. _Thus_ they are rendered capable of
demonstrative knowledge." "We are innate to ourselves; and since we are
beings, being is innate to us, for knowledge of it is implicit in that
which we have of ourselves."

Knowledge, in fine, may be regarded as an ascending series of four
terms. The first is constituted by sensations associated together
in such a way that a relation of antecedence and consequence exists
between them. This is "experience." The second stage comes into
existence when we connect these experiences, not by mere relations of
"consecution," but by their conditions, by the principle of causality,
and especially by that of sufficient reason, which connects them with
the supreme intelligence, God. This stage is science. The third is
knowledge of the axioms and necessary truths in and of themselves,
not merely as involved in science. The fourth is self-consciousness,
the knowledge of intelligence, in its intimate and universal nature,
by which we know God, the mind, and all real substance. In the order of
time the stage of experience is first, and that of self-consciousness
last. But in the lowest stage there are involved the others. The
progress of knowledge consists in the development or unfolding of
this implicit content, till intelligence, spirit, activity, is clearly
revealed as the source and condition of all.



One of the chapters concerning knowledge is entitled, "The Knowledge
that we have of God." This introduces us to the theology of Leibniz
and indirectly to the completion of those ethical doctrines already
outlined in the chapter on will. Leibniz employs three arguments to
prove the existence of God: that of God as the sufficient reason of the
world (substantially the cosmological proof); of God as the source of
the pre-established harmony (an extension of the teleological proof);
and the ontological. The latter he accepts as it came from the hands
of Descartes, but insists that it requires an added argument before it
ranks as anything more than presumptive proof. The Anselmic-Cartesian
argument, as stated by Leibniz, is as follows: "God is defined as
the greatest, or most perfect, of beings, or as a being of supreme
grandeur and perfection. But in the notion of a perfect being,
existence must be included, since it is something more to exist than
not to exist. Or existence is a perfection, and hence must belong to
the most perfect being; otherwise some perfection would be lacking,
which is contrary to the definition." Or as Descartes sometimes puts
it, in the notion of anything like a tree, a mountain, a triangle,
contingency is contained. We may conceive such an object to exist or
not, as we like. There is no necessity involved in our thought. But we
cannot think of a perfect being except as existing. It does not rest
with the decision of our thinking whether or not to include existence
in this notion. We must necessarily think existence as soon as we think
such a being.

Leibniz takes a middle position, he says, between those who
consider this a demonstrative argument, and those who regard it
as a mere paralogism. It is pre-supposed by this argument that the
notion of a Supreme Being is possible, or that it does not involve
contradiction. This pre-supposition is to be proved. First, it is
well to simplify the argument itself. The Cartesian definition may
be reduced to this: "God is a being in whom existence and essence are
one. From this definition it follows as a corollary that such a being,
if possible, exists. For the essence of a thing being just that which
constitutes its possibility, it is evident that to exist by its essence
is the same as to exist by its possibility. Being in itself, then,
or God, may be most simply defined as the Being who must exist if he
is possible."

There are two ways of proving this last clause (namely, that he
is possible) the direct and the indirect. The indirect is employed
against those who assert that from mere notions, ideas, definitions or
possible essences, it is not possible to infer actual existence. Such
persons simply deny the possibility of being in itself. But if
being-in-itself, or absolute being, is impossible, being-by-another,
or relative, is also impossible; for there is no "other" upon which
it may depend. Nothing, in this case, could exist. Or if necessary
being is not possible, there is no being possible. Put in another way,
God is as necessary for possibility as for actual existence. If there
is possibility of anything, there is God. This leads up to the direct
proof; for it follows that, if there be a possibility of God,--the
Being in whom existence and essence are one,--he exists. "God alone
has such a position that existence is necessary, if possible. But
since there can be nothing opposed to the possibility of a being
without limit,--a being therefore without negations and without
contradiction,--this is sufficient to prove _a priori_ the existence
of God." In short, God being pure affirmation, pure self-identity,
the idea of his Being cannot include contradiction, and hence is
possible,--and since possible, necessary. Of this conception of God as
the purely self-identical, without negation, we shall have something to
say in the next chapter.

The cosmological proof is, as we have already seen, that every cause in
the world being at the same time an effect, it cannot be the sufficient
reason of anything. The whole series is contingent, and requires a
ground not prior to, but beyond, the series. The only _sufficient_
reason of anything is that which is also the sufficient reason of
itself,--absolute being. The teleological argument Leibniz invariably,
I believe, presents in connection with the idea of pre-established
harmony. "If the substances of experience," runs the argument,
"had not received their being, both active and passive, from one
universal supreme cause, they would be independent of one another,
and hence would not exhibit that order, harmony, and beauty which
we notice in nature. This argument possesses only moral certainty
which becomes demonstrative by the new kind of harmony which I have
introduced,--pre-established harmony. Since each substance expresses in
its own way that which occurs beyond it, and can have no influence on
other particular beings, it is necessary that each substance, before
developing these phenomena from the depth of its own being, must have
received this nature (this internal ground of external phenomena) from
a universal cause from whom all beings depend, and which effects that
one be perfectly in accord with and corresponding to every other. This
cannot occur except through a being of infinite knowledge and power."

Having determined the existence of God, Leibniz states his
attributes. These may be reduced to three. He is perfect in power, in
wisdom, and in goodness. "Perfection is nothing other than the whole of
positive reality separated from the limits and bounds of things. Where
there are no limits, as in God, perfection is absolutely infinite." "In
God exists _power_, which is the source of all _knowledge_,--which
comprehends the realm of ideas, down to its minutest detail,--and
_will_, which directs all creations and changes according to the
principle of the best." Or as he expands it at another time: "The
supreme cause must be intelligent, for the existing world being
contingent, and an infinity of other worlds being equally possible,
it is necessary that the cause of the world take into consideration
all these possible worlds in order to decide upon one. Now this
relation of a substance to simple ideas must be the relation of
understanding to its ideas, while deciding upon one is the act of will
in choosing. Finally it is the power of this substance which executes
the volition. Power has its end in being; wisdom, or understanding,
in truth; and will in good. Thus the cause must be absolutely perfect
in power, wisdom, and goodness. His understanding is the source of
essences, and his will the origin of existences."

This brings us to the relation of God to the world, or to an
account of the creating activity of God. This may be considered to
be metaphysically, logically, or morally necessary. To say that it is
metaphysically necessary is to say that it is the result of the divine
essence, that it would imply a contradiction of the very being of God
for the world not to be and not to be as it is. In short, the world
becomes a mere emanation of power, since, as we have just learned,
power and being are correlative. But this leaves out of account the
divine understanding. Not all possible worlds emanate from God's
being, but there is recognition of them and of their relations to one
another. Were the world to proceed from the divine understanding alone,
however, it would be logically necessary,--that is, it would bear
the same relation to his understanding that necessary truths do. Its
opposite would imply contradiction, not indeed of the being of God,
but of his understanding. But the will of God plays the all-important
part of choosing among the alternative worlds presented by reason,
each of which is _logically_ possible. One of these worlds, although
standing on the same intellectual plane as the others, is _morally_
better,--that is, it involves greater happiness and perfection to the
creatures constituting it. God is guided then by the idea of the better
(and this is the best possible) world. His will is not arbitrary in
creating: it does not work by a _fiat_ of brute power. But neither
is it fatalistic: it does not work by compulsory necessity. It is
both free and necessary; free, for it is guided by naught excepting
God's own recognition of an end; necessary, for God, being God, cannot
_morally_ act otherwise than by the principle of the better,--and this
in contingent matters is the best. Hence the optimism of Leibniz, to
which here no further allusion can be made.

Since the best is precisely God himself, it is evident that the created
world will have, _as far as possible_, his perfections. It would thus
be possible to deduce from this conception of God and his relation to
the world all those characteristics of the Leibnizian monadology which
we formerly arrived at analytically. God is individual, but with an
infinite comprehensiveness. Each substance repeats these properties
of the supreme substance. There is an infinity of such substances, in
order that the world may as perfectly as possible mirror the infinity
of God. Each, so far as in it lies, reflects the activity of God;
for activity is the very essence of perfection. And thus we might go
through with the entire list of the properties of the monad.

To complete the present discussion, however, it is enough to notice
that intelligence and will must be found in every creature, and
that thus we account for the "appetition" and the "perception" that
characterize even the lowest monad. The scale of monads, however,
would not be as complete as possible unless there were beings in
whom appetition became volition, and perception, self-conscious
intelligence. Such monads will stand in quite other relation to God
than the blind impulse-governed substances. "Spirits," says Leibniz,
"are capable of entering into community with God, and God is related
to them not only as an inventor to his machine (as he is to other
creatures) but as a prince to his subjects, or, better, as a father
to his children. This society of spirits constitutes the city of
God,--the most perfect state under the most perfect monarch. This city
of God, this truly cosmopolitan monarchy, is a moral world within
the natural. Among all the works of God it is the most sublime and
divine. In it consists the true glory of God, for there would be no
glory of God unless his greatness and goodness were known and admired
by spirits; and in his relation to this society, God for the first
time reveals his goodness, while he manifests everywhere his power and
wisdom. And as previously we demonstrated a perfect harmony between
the two realms of nature,--those of efficient and final causes,--so
must we here declare harmony between the physical realm of nature and
the moral realm of grace,--that is, between God as the architect of
the mechanical world-structure, and God as the monarch of the world
of spirits." God fulfils his creation, in other words, in a realm
of spirits, and fulfils it because here there are beings who do not
merely reflect him but who enter into relations of companionship with
him, forming a community. This community of spirits with one another
and with God is the moral world, and we are thus brought again to the
ethics of Leibniz.

It has been frequently pointed out that Leibniz was the first to give
ethics the form which it has since kept in German philosophy,--the
division into _Natur-recht_ and _Natur-moral_. These terms are
difficult to give in English, but the latter corresponds to what is
ordinarily called "moral philosophy," while the former is political
philosophy so far as that has an ethical bearing. Or the latter may be
said to treat of the moral ideal and of the moral motive and of duty in
themselves, while the former deals with the social, the public, and in
a certain sense the external, aspects of morality.

Puffendorf undoubtedly suggested this division to Leibniz by
his classification of duties as external and internal,--the first
comprehending natural and civil law, the second moral theology. But
Puffendorf confined the former to purely external acts, excluding
motives and intentions, and the latter to divine revelation. Both are
"positive," and in some sort arbitrary,--one resting merely on the fact
that certain institutions obtain, the other on the fact that God has
made certain declarations. To Leibniz, on the other hand, the will of
God is in no sense the source of moral truths. The will of God does
not create truth, but carries into effect the eternal truths of the
divine understanding. Moral truths are like those of mathematics. And
again, there is no such thing as purely external morality: it always
contains an inner content, of which the external act is only the
manifestation. Leibniz may thus be said to have made two discoveries,
or rather re-discoveries: one, that there is a science of morals,
independent of law, custom, and positive right; the other, that the
basis of both "natural" and "positive" morals is not the mere will of
God, but is reason with its content of eternal truths.

In morals the end is happiness, the means wisdom. Happiness is defined,
not as an occurrence, but as a condition, or state of being. "It is
the condition of permanent joy. This does not mean that the joy is
actually felt every moment, but that one is in the condition to enjoy
whenever he thinks of it, and that, in the interval, joyfulness arises
from his activity and being." Pleasure, however, is not a state, but
a feeling. It is the feeling of perfection, whether in ourselves or
in anything else. It does not follow that we perceive intellectually
either in what the perfection of the pleasant thing consists or in
what way it develops perfection within us. It is enough that it be
realized in feeling, so as to give us pleasure. Perfection is defined
"as increase of being. As sickness is, as it were, a lowering and a
falling off from health, so perfection is something which mounts above
health. It manifests itself in power to act; for all substance consists
in a certain power, and the greater the power the higher and freer the
substance. But power increases in the degree that the many manifests
itself from one and in one, while the one rules many from itself and
transforms them into self. But unity in plurality is nothing else than
harmony; and from this comes order or proportion, from which proceeds
beauty, and beauty awakens love. Thus it becomes evident how happiness,
pleasure, love, perfection, substance, power, freedom, harmony,
proportion, and beauty are bound up in one another."

From this condensed sketch, taken from Leibniz himself, the main
features of his ethical doctrine clearly appear. When we were studying
freedom we saw that it was not so much a starting-point of the will
as its goal and ideal. We saw also that true freedom is dependent upon
knowledge, upon recognition of the eternal and universal. What we have
here is a statement of that doctrine in terms of feeling and of will
instead of knowledge. The end of man is stated to be happiness, but
the notion of happiness is developed in such a way that it is seen to
be equivalent to the Aristotelian notion of self-realization; "it is
development of substance, and substance is activity." It is the union
of one and the many; and the one, according to the invariable doctrine
of Leibniz, is the spiritual element, and the many is the real content
which gives meaning to this rational unity. Happiness thus means
perfection, and perfection a completely universalized individual. The
motive toward the moral life is elsewhere stated to be love; and love
is defined as interest in perfection, and hence culminates in love
of God, the only absolute perfection. It also has its source in God,
as the origin of perfection; so that Leibniz says, Whoso loves God,
loves all.

Natural right, as distinguished from morals, is based upon the
notion of justice, this being the outward manifestation of wisdom, or
knowledge,--appreciation of the relation of actions to happiness. The
definitions given by Leibniz are as follows: Just and unjust are what
are useful or harmful to the public,--that is, to the community of
spirits. This community includes first God, then humanity, then the
state. These are so subordinated that, in cases of collision of duty,
God, the universe of relations, comes before the profit of humanity,
and this before the state. At another time Leibniz defines justice
as social virtue, and says that there are as many kinds of "right"
as there are kinds of natural communities in which happiness is an
end of action. A natural community is defined as one which rests
upon desire and the power of satisfying it, and includes three
varieties,--domestic, civil, and ecclesiastic. "Right" is defined
as that which sustains and develops any natural community. It is, in
other words, the will for happiness united with insight into what makes

Corresponding to the three forms of the social organism (as we should
now call the "natural community"), are the three kinds of _jus_,--_jus
strictum_, equity, and piety. Each of these has its corresponding
prescript. That of _jus strictum_ is to injure no one; of equity,
to render to each his own; and of piety, to make the ethical law the
law of conduct. _Jus strictum_ includes the right of war and peace. The
right of peace exists between individuals till one breaks it. The right
of war exists between men and things. The victory of person over thing
is _property_. Things thus come to possess the right of the person to
whom they belong as against every other person; that is, in the right
of the person to himself as against the attacks of another (the right
to peace) is included a right to his property. _Jus strictum_ is,
of course, in all cases, enforceable by civil law and the compulsory
force which accompanies it. Equity, however, reaches beyond this to
obligation in cases where there is no right of compulsion. Its law
is, Be of aid to all, but to each according to his merits and his
claims. Finally comes piety. The other two stages are limited. The
lowest is negative, it wards off harm; the second aims after happiness,
but only within the limits of earthly existence. That we should
ourselves bear misery, even the greatest, for the sake of others,
and should subject the whole of this existence to something higher,
cannot be proved excepting as we regard the society, or community,
of our spirits with God. Justice with relation to God comprehends all
virtues. Everything that is, is from God; and hence the law of all
conduct is to use everything according to its place in the idea of God,
according to its function in the universal harmony. It thus not only
complements the other two kinds of justice but is the source of their
inner ethical worth. "Strict justice" may conflict with equity. But God
effects that what is of use to the public well-being--that is, to the
universe and to humanity--shall be of use also to the individual. Thus
from the standpoint of God the moral is advantageous, and the immoral
hurtful. Kant's indebtedness to Leibniz will at once appear to one
initiated into the philosophy of the former.

Leibniz never worked out either his ethics or his political philosophy
in detail; but it is evident that they both take their origin and
find their scope in the fact of man's relationship to God, that they
are both, in fact, accounts of the methods of realizing a universal
but not a merely formal harmony. For harmony is not, with Leibniz,
an external arrangement, but is the very soul of being. Perfect
harmony, or adaptation to the universe of relations, is the end of the
individual, and man is informed of his progress toward this end by an
inner sentiment of pleasure.

It may be added that Leibniz's æsthetic theory, so far as developed,
rests upon the same basis as his ethical,--namely, upon membership
in the "city of God," or community of spiritual beings. This is
implied, indeed, in a passage already quoted, where he states the
close connection of beauty with harmony and perfection. The feeling
of beauty is the recognition in feeling of an order, proportion, and
harmony which are not yet intellectually descried. Leibniz illustrates
by music, the dance, and architecture. This feeling of the harmonious
also becomes an impulse to produce. As perception of beauty may be
regarded as unexplained, or confused, perception of truth, so creation
of beauty may be considered as undeveloped will. It is action on its
way to perfect freedom, for freedom is simply activity with explicit
recognition of harmony.

We cannot do better than quote the conclusion of the matter from
Leibniz's "Principles of Nature and of Grace," although, in part,
it repeats what we have already learned. "There is something more
in the rational soul, or spirit, than there is in the monad or even
in the simple soul. Spirit is not only a mirror of the universe of
creatures, but is also an image of the divine being. Spirit not only
has a perception of the works of God, but is also capable of producing
something which resembles them, though on a small scale. To say nothing
of dreams, in which we invent without trouble and without volition
things upon which we must reflect a long time in order to discover in
our waking state,--to say nothing of this, our soul is architectonic in
voluntary actions; and, in discovering the sciences in accordance with
which God has regulated all things (_pondere_, _mensura_, _numero_), it
imitates in its department and in its own world of activity that which
God does in the macrocosm. This is the reason why spirits, entering
through reason and eternal truths into a kind of society with God,
are members of the city of God,--that is, of the most perfect state,
formed and governed by the best of monarchs, in which there is no crime
without punishment, and no good action without reward, and where there
is as much of virtue and of happiness as may possibly exist. And this
occurs not through a disturbance of nature, as if God's dealing with
souls were in violation of mechanical laws, but by the very order of
natural things, on account of the eternal, pre-established harmony
between the kingdoms of nature and grace, between God as monarch and
God as architect, since nature leads up to grace, and grace makes
nature perfect in making use of it."

No better sentences could be found with which to conclude this analysis
of Leibniz. They resound not only with the grandeur and wide scope
characteristic of his thought, but they contain his essential idea,
his pre-eminent "note,"--that of the harmony of the natural and the
supernatural, the mechanical and the organic. The mechanical is to
Leibniz what the word signifies; it is the _instrumental_, and this
in the full meaning of the term. Nature is instrumental in that it
performs a function, realizes a purpose, and instrumental in the sense
that without it spirit, the organic, is an empty dream. The spiritual,
on the other hand, is the meaning, the _idea_ of nature. It perfects
it, in that it makes it instrumental to itself, and thus renders it not
the passive panorama of _mere_ material force, but the manifestation of
living spirit.



In the exposition now completed we have in general taken for granted
the truth and coherency of Leibniz's fundamental ideas, and have
contented ourselves with an account of the principles and notions that
flow from these ideas. The time has come for retracing our steps, and
for inquiring whether the assumed premises can be thus unquestioningly
adopted. This final chapter, therefore, we shall devote to criticism
of the basis of Leibniz's philosophy, not attempting to test it by
a comparison with other systems, but by inquiring into its internal
coherency, and by a brief account of the ways in which his successors,
or at least one of them, endeavored to make right the points in which
he appeared to fail.

The fundamental contradiction in Leibniz is to be found, I believe,
between the method which he adopted--without inquiry into its validity
and scope--and the subject-matter, or perhaps better the attitude,
to which he attempted to apply this method; between, that is to
say, the scholastic formal logic on the one hand and the idea of
inter-relation derived from the development of scientific thought,
on the other. Leibniz never thought of investigating the formal logic
bequeathed by scholasticism, with a view to determining its adequacy
as philosophic method. He adopted, as we have seen, the principles
of identity and contradiction as sole principles of the only perfect
knowledge. The type of knowledge is that which can be reduced to
a series of identical propositions, whose opposite is seen to be
impossible, because self-contradictory. Only knowledge in this form
can be said to be demonstrative and necessary. As against Locke he
justified the syllogistic method of the schoolmen as the typical method
of all rational truth.

On the other hand, Leibniz, as we saw in the earlier chapters,
had learned positively from the growth of science, negatively from
the failures of Descartes and Spinoza, to look upon the universe as
a unity of inter-related members,--as an organic unity, not a mere
self-identical oneness. Failing to see the cause of the failures of
Descartes and Spinoza in precisely their adoption of the logic of
identity and contradiction as ultimate, he attempted to reconcile this
method with the conception of organic activity. The result is constant
conflict between the method and content of his philosophy, between
its letter and its spirit. The contradiction is a twofold one. The
unity of the content of his philosophy, the conception of organism or
harmony, is a unity which essentially involves difference. The unity
of his method is a formal identity which excludes it. The unity,
whose discovery constitutes Leibniz's great glory as a philosopher,
is a unity of activity, a dynamic process. The unity of formal logic
is exclusive of any mediation or process, and is essentially rigid
and lifeless. The result is that Leibniz is constantly wavering
(in logical result, not of course in spirit) between two opposed
errors, one of which is, in reality, not different from Spinozism,
in that it regards all distinction as only phenomenal and unreal,
while the other is akin to atomism, in that attempting to avoid the
doctrine of the all-inclusive one, it does so only by supposing a
multitude of unrelated units, termed monads. And thus the harmony,
which in Leibniz's intention is the very content of reality, comes
to be, in effect, an external arrangement between the one and
the many, the unity and the distinction, in themselves incapable
of real relations. Such were the results of Leibniz's failure, in
Kantian language, to criticise his categories, in Hegelian language,
to develop a logic,--the results of his assuming, without examination,
the validity of formal logic as a method of truth.

So thoroughly is Leibniz imbued with the belief in its validity, that
the very conception, that of sufficient reason, which should have been
the means of saving him from his contradictions, is used in such a way
as to plunge him deeper into them. The principle of sufficient reason
may indeed be used as purely formal and external,--as equivalent to the
notion that everything, no matter what, has _some_ explanation. Thus
employed, it simply declares that everything has _a_ reason, without in
the least determining the _what_ of that reason,--its content. This is
what we mean by calling it formal. But this is not the way in which
Leibniz conceives of it. According to him, it is not a principle
of the external connection of one finite, or phenomenal, fact with
another. It is a principle in the light of which the whole phenomenal
world is to be viewed, declaring that its ground and meaning are to be
found in reason, in self-conscious intelligence. As we have seen, it is
equivalent, in Leibniz's case, to the notion that we have no complete
nor necessary knowledge of the world of scientific fact until we have
referred it to a conditioning "Supreme Spirit."

Looked at in this way, we see that the unity which Leibniz is
positively employing is an organic unity, a unity of intelligence
involving organic reference to the known world. But such a conception
of sufficient reason leaves no place for the final validity of
identity and non-contradiction; and therefore Leibniz, when dealing
with his method, and not, as in the passages referred to, with
his subject-matter, cannot leave the matter thus. To do so indeed
would have involved a complete reconstruction of his philosophy,
necessitating a derivation of all the categories employed from
intelligence itself (that is, from the sufficient or conditioning
reason). But the bondage to scholastic method is so great that Leibniz
can see no way but to measure intelligence by the ready-made principle
of identity, and thus virtually (though not in purpose) to explain
away the very principle of sufficient reason. In Leibniz's words:
"Contingent truths require an infinite analysis which only God
can carry out. Whence by him alone are they known _a priori_ and
demonstratively. For although the reason can always be found for some
occurring state in a prior state, this reason again requires a reason,
and we never arrive in the series to the ultimate reason. But this
_progressus ad infinitum_ takes (in us) the place of a sufficient
reason, which can be found only outside the series in God, on whom
all its members, prior and posterior depend, rather than upon one
another. _Whatever truth, therefore, is incapable of analysis, and
cannot be demonstrated from its own reasons, but has its ultimate
reason and certainty only from the divine mind, is not necessary._
Everything that we call truths of fact come under this head, and this
is the root of their contingency."

The sentences before the one italicized repeat what we have learned
before, and seem to convey the idea that the phenomenal world
is that which does not account for itself, because not itself a
self-determining reason, and which gets its ultimate explanation and
ground in a self-sufficient reason,--God. But notice the turn given to
the thought with the word "therefore." Therefore all truth incapable
of analysis,--that is, of reduction to identical propositions,
whose opposite is impossible because self-contradictory,--all truth
whose meaning depends upon not its bare identity, but upon its
relation to the very content of all intelligence, is not necessary,
but contingent. Leibniz here distinctly opposes identical truths as
necessary, to truth connected with reason as contingent. Synthetic
reference to the very structure of intelligence is thus made,
not the ground of truth, but a blot upon its completeness
and necessity. Perfect truth, it is implied in the argument,
is self-identical, known by mere analysis of itself, and needs
no reference to an organism of reason. The reference, therefore,
to a principle of sufficient reason is simply a concession to the
fragmentary and imperfect condition of all knowledge. Truth in itself
is self-identical; but appearing to us only confusedly, we employ
the idea of sufficient reason as a makeshift, by which we refer, in a
mass, all that we cannot thus reduce to identical propositions, to an
intelligence, or to a _Deus ex machina_ which can so reduce it. This is
the lame and impotent conclusion.

Leibniz's fundamental meaning is, no doubt, a correct one. He means
that contingency of fact is not real, but apparent; that it exists
only because of our inability to penetrate the reason which would
enable us completely to account for the facts under consideration. He
_means_ that if we could understand, _sub specie aeternitatis_,
from the standpoint of universal intelligence, we should see every
fact as necessary, as resulting from an intrinsic reason. But so
thoroughly is he fettered by the scholastic method--that is, the
method of formal logic--that he can conceive of this immanent and
intrinsic reason which makes every fact a truth--that is, self-evident
in its necessity--only as an analytic, self-contained identity. And
herein lies his contradiction: his method obliges him to conceive of
ultimate intelligence as purely formal, simply as that which does not
contradict itself, while the attitude of his thought and its concrete
subject-matter compel him to think of intelligence as possessing a
content, as the organic unity of a system of relations.

From this contradiction flow the other contradictions of Leibniz, which
we are now prepared to examine in more detail. For his ideas are so
much greater than his method that in almost every point there seems to
be contradiction. His ideas _per se_ mean one thing, and his ideas as
interpreted by his method another. Take his doctrine of individuality,
for instance. To some it has appeared that the great defect of the
Leibnizian philosophy is its individualism. Such conceive him simply
to have carried out in his monadism the doctrine of the individual
isolated from the universe to its logical conclusions, and thereby to
have rendered it absurd. In a certain sense, the charge is true. The
monad, according to the oft-repeated statement, has no intercourse
with the rest of the universe. It really excludes all else. It acts
as if nothing but itself and God were in existence. That is to say,
the monad, being the self-identical, must shut out all intrinsic or
real relations with other substances. Such relations would involve a
differentiating principle for which Leibniz's logic has no place. Each
monad is, therefore, an isolated universe. But such a result has no
value for Leibniz. He endeavors to correct it by the thought that each
monad _ideally_ includes the whole universe by mirroring it. And then
to reconcile the real exclusion and the ideal inclusion, he falls back
on a _Deus ex machina_ who arranges a harmony between them, foreign to
the intrinsic nature of each. Leibniz's individualism, it is claimed,
thus makes of his philosophy a synthesis, or rather a juxtaposition,
of mutually contradictory positions, each of which appears true only as
long as we do not attempt to think it together with the other.

There is, no doubt, truth in this representation. But a more
significant way of stating the matter is, I think, that Leibniz's
defect is not in his individualism, but in the defect of his conception
of the individual. His individualism is more apparent than real. It is
a negative principle, and negative in the sense of _privative_. The
individuality of the monad is due to its incompleteness, to its
imperfections. It is really matter which makes monads mutually
impenetrable or exclusive; it is matter which distinguishes them
from God, and thus from one another. Without the material element
they would be lost in an undistinguished identity with God, the
supreme substance. But matter, it must be remembered, is passivity;
and since activity is reality, or substance, matter is unsubstantial
and unreal. The same results from a consideration of knowledge. Matter
is always correlative to confused ideas. With the clearing up of
knowledge, with making it rational, matter must disappear, so that
to God, who is wholly reason, it must entirely vanish. But this
view varies only in words from that of Spinoza, to whom it is the
imagination, as distinguished from the intellect, that is the source of
particular and finite objects.

It is perhaps in his _Theodicée_, in the treatment of the problem of
evil, that his implicit Spinozism, or denial of individuality, comes
out most clearly. That evil is negative, or privative, and consists in
the finitude of the creature, is the result of the discussion. What is
this except to assert the unreality, the merely privative character,
of the finite, and to resolve all into God? To take one instance out
of many: he compares inertia to the original limitation of creatures,
and says that as inertia is the obstacle to the complete mobility
of bodies, so privation, or lack, constitutes the essence of the
imperfection, or evil, of creatures. His metaphor is of boats in
the current of a river, where the heavier one goes more slowly,
owing to inertia. The force of the current, which is the same to all,
and which is positive, suffering no diminution, is comparable to the
activity of God, which also is perfect and positive. As the current
is the positive source of all the movements of the bodies, and is in
no way responsible for the retardation of some boats, so God is the
source only of activities,--the perfections of his creatures. "As the
inertia of the boat is the cause of its slowness, so the limitations
of its receptivity are the cause of the defects found in the action
of creatures." Individuality is thus reduced to mere limitation; and
the unlimited, the real which includes all reality, is God. We are
thus placed in a double difficulty. This notion of an all-inclusive
one contradicts the reality of mutually exclusive monads; and we have
besides the characteristic difficulty of Spinoza,--how, on the basis
of this unlimited, self-identical substance, to account for even the
appearance of finitude, plurality and individuality.

Leibniz's fundamental defect may thus be said to be that, while
he realized, as no one before him had done, the importance of
the conception of the _negative_, he was yet unable to grasp the
significance of the negative, was led to interpret it as merely
privative or defective, and thus, finally, to surrender the very
idea. Had not his method, his presupposition regarding analytic
identity, bound him so completely in its toils, his clear perception
that it was the negative element that differentiated God from the
universe, intelligence from matter, might have brought him to a
general anticipation not only of Kant, but of Hegel. But instead of
transforming his method by this conception of negation, he allowed
his assumed (_i. e._, dogmatic) method to evacuate his conception
of its significance. It was Hegel who was really sufficiently in
earnest with the idea to read it into the very notion of intelligence
as a constituent organic element, not as a mere outward and formal

We have already referred to the saying of Leibniz that the monad acts
as if nothing existed but God and itself. The same idea is sometimes
expressed by saying that God alone is the immediate or direct object
of the monad. Both expressions mean that, while the monad excludes
all other monads, such is not the case in its relation to God, but
that it has an organic relation with him. We cannot keep from asking
whether there is not another aspect of the contradiction here. How is
it possible for the monad so to escape from its isolation that it can
have communication with God more than with other substances? Or if
it can have communication with God, why cannot it equally bear real
relations of community with other monads? And the answer is found in
Leibniz's contradictory conceptions of God. Of these conceptions there
are at least three. When Leibniz is emphasizing his monadic theory,
with its aspects of individuality and exclusion, God is conceived as
the highest monad, as one in the series of monads, differing from the
others only in the degree of its activity. He is the "monad of monads";
the most complete, active, and individualized of all. But it is evident
that in this sense there can be no more intercourse between God and a
monad than there is between one monad and another. Indeed, since God
is _purus actus_ without any passivity, it may be said that there is,
if possible, less communication in this case than in the others. He is,
as Leibniz says, what a monad without matter would be, "a deserter from
the general order." He is the acme of isolation. This, of course, is
the extreme development of the "individual" side of Leibniz's doctrine,
resulting in a most pronounced atomism. Leibniz seems dimly conscious
of this difficulty, and thus by the side of this notion of God he
puts another. According to it, God is the source of all monads. The
monads are not created by a choice of the best of all possible worlds,
as his official theology teaches, but are the radiations of his
divinity. Writing to Bayle, Leibniz expresses himself as follows: "The
nature of substance consists in an active force of definite character,
from which phenomena proceed in orderly succession. This force was
originally received by, and is indeed preserved to, every substance by
the creator of all things, from whom all _actual forces or perfections
emanate by a sort of continual creation_." And in his Monadology
he says: All "the created or derived monads are the productions of
God, and are born, as it were, _by the continual fulgurations of the
divinity from instant to instant_, bounded by the receptivity of the
creature to which it is essential to be limited." What has become of
the doctrine of monads (although the word is retained) it would be
difficult to say. There is certainly no individual distinction now
between the created monads and God, and it is impossible to see why
there should be individual distinctions between the various created
monads. They appear to be all alike, as modes of the one comprehensive
substance. Here we have the universal, or "identity," side of Leibniz's
philosophy pushed to its logical outcome,--the doctrine of pantheism.

His third doctrine of God is really a unity of the two previous. It is
the doctrine that God is the harmony of the monads,--neither one among
them nor one made up of them, but their organic unity. This doctrine
is nowhere expressly stated in words (unless it be when he says that
"God alone constitutes the relation and community of substances"),
but it runs through his whole system. According to this, God _is_
the pre-established harmony. This conception, like that of harmony,
may have either a mechanical interpretation (according to which God is
the artificial, external point of contact of intelligence and reality,
in themselves opposed) or an organic meaning, according to which God
_is_ the unity of intelligence and reality. On this interpretation
alone does the saying that God is the only immediate object of the
monads have sense. It simply states that the apparent dualism between
intelligence and its object which is found in the world is overcome
in God; that the distinction between them is not the ultimate fact,
but exists in and for the sake of a unity which transcends the
difference. According to this view, the opposition between ideal
inclusion and real exclusion vanishes. God _is_ the harmony of the real
and ideal, not a mere arrangement for bringing them to an understanding
with one another. Individuality and universality are no longer opposed
conceptions, needing a _tertium quid_ to relate them, but are organic
factors of reality, and this, at the same time, is intelligence.

But admitting this conception as stating the implicit intention of
Leibniz, the relation of monads to one another is wholly different from
that which Leibniz gives. And to this point we now come. If in God,
the absolute, the real and the ideal are one, it is impossible that in
substances, which have their being and significance only in relation
to God, or this unity, the real and the ideal should be so wholly
separated as Leibniz conceives.

Leibniz's conception relative to this is, as we have seen, that
there is no physical _influxus_, or _commercium_, of monads, but
ideal consensus. _Really_ each shuts out every other; _ideally_,
or representatively, it includes every other. His positive thought
in the matter is that a complete knowledge of any portion of the
universe would involve a perfect knowledge of the whole, so organic
is the structure of the universe. Each monad sums up the past history
of the world, and is big with its future. This is the conception of
inter-relation; the conception of all in one, and one as a member,
not a part of a whole. It is the conception which Leibniz brought
to birth, the conception of the thorough unity of the world. In this
notion there is no denial of community of relation; it is rather the
culmination of relation. There is no isolation. But according to his
presupposed logic, individuality can mean only identity excluding
distinction,--identity without intrinsic relation, and, as Leibniz
is bound at all hazards to save the notion of individuality, he is
obliged to think of this inter-relation as only ideal, as the result of
a predetermined tendency given at its creation to the self-identical
monad by God. But of course Leibniz does not escape the contradiction
between identity and distinction, between individuality and
universality, by this means. He only transfers it to another realm. In
the relation of the monad to God the diversity of its content, the real
or universal element, is harmonized with the identity of its law, its
ideal or individual factor. But if these elements do not conflict here,
why should they in the relation of the monads to one another? Either
there is already an immanent harmony between the individual and
universal, and no external arrangement is needed to bring it about, or
there is no such harmony, and therefore no relation possible between
God and the individual monad. One side of the Leibnizian philosophy
renders the other side impossible.

Another consequence of Leibniz's treatment of the negative as
merely limitative is that he can find no distinction, excepting of
degree, between nature and spirit. Such a conception is undoubtedly
in advance of the Cartesian dualism, which regards them as opposed
realms _without_ any relation; but it may be questioned whether it is
as adequate a view as that which regards them as distinct realms _on
account_ of relation. At all events, it leads to confusion in Leibniz's
treatment of both material objects and self-conscious personalities. In
the former case his method of escape is a metaphor,--that objects
apparently material are full of souls, or spirits. This may mean that
the material is _merely_ material only when considered in implicit
abstraction from the intelligence which conditions it, that the
material, in truth, is constituted by some of the relations which
in their completeness make up intelligence. This at least bears a
consistent meaning. But it is not monadism; it is not the doctrine
that matter differs from spirit only in degree: it is the doctrine
that they differ in kind, as the conditioned from the conditioning. At
times, however, Leibniz attempts to carry out his monadism literally,
and the result is that he conceives matter as being itself endowed,
in some unexplained way, with souls, or since this implies a dualism
between matter and soul, of being made up, composed, of souls. But
as he is obliged to explain that this composition is not spatial, or
physical, but only ideal, this doctrine tends to resolve itself into
the former. And thus we end where we began,--with a metaphor.

On the other hand there is a wavering treatment of the nature
of spirit. At times it is treated as precisely on a level in kind
with the monads that "compose" matter, differing only in the greater
degree of its activity. But at other times it is certainly represented
as standing on another plane. "The difference between those monads
which express the world with consciousness and those which express it
unintelligently is as great as the difference between a mirror and one
who sees." If Leibniz means what he seems to imply by these words,
it is plainly asserted that only the spiritual being is worthy of
being called a monad, or individual, at all, and that material being
is simply a dependent manifestation of spirit. Again he says: "Not all
entelechies are, like our soul, _images of God_,--being made as members
of a society or state of which he is chief,--but all are _images of
the universe_." In this distinction between self-conscious beings as
images of God and unconscious monads as images of the universe there
is again implied a difference of kind. That something is the image
of the universe need mean only that it cannot be explained without
its relations to the universe. To say that something is the image of
God, must mean that it is itself spiritual and self-conscious. God
alone is reason and activity. He alone has his reality in
himself. Self-conscious beings, since members of a community with him,
must participate in this reality in a way different in kind from those
things which, at most, are only substances or objects, not subjects.

Nor do the difficulties cease here. If matter be conceived, not as
implied in the relations by which reason is realized in constituting
the universe, but as itself differing from reason only in degree,
it is impossible to account for its existence. Why should a less
degree of perfection exist than is necessary? Why should not the
perfect activity, God, complete the universe in himself? Leibniz's
answer that an infinity of monads multiplies his existence so far as
possible, may hold indeed of other spirits, who mirror him and live
in one divine society, but is utterly inapplicable to those which fail
to image him. Their existence, as material, is merely privative; it is
merely the absence of the activity found in conscious spirit. How can
this deprivation, this limitation, increase in any way the harmony and
perfection of the universe? Leibniz's theory of the negative, in fine,
compels him to put nature and spirit on the same level, as differing
only in degree. This, so far from giving nature a reality, results in
its being swallowed up in spirit, not as necessarily distinct from
it and yet one with it, but as absorbed in it, since the apparent
difference is only privative. Nor does the theory insure the reality
of spirit. This, since one in kind with matter, is swallowed up along
with it in the one substance, which is positive and self-identical,--in
effect, the _Deus sive Natura_ of Spinoza.

We have to see that this contradiction on the side of existence has
its correlate on the side of knowledge, and our examination of this
fundamental deficiency in Leibniz is ended. Sensation is on the side
of intelligence what matter is on the side of reality. It is confused
knowledge, as matter is imperfect activity or reality. Knowledge is
perfect only when it is seen to be necessary, and by "necessary" is
meant that whose opposite is impossible, or involves contradiction. In
spite, therefore, of Leibniz's thorough conviction that "matters of
fact"--the subject-matter of physical science--are not arbitrary, he
is yet obliged finally to agree with Locke that there is no certainty
to be found in such knowledge, either as a whole or in any of its
details. The element of sensation, of confused knowledge, cannot be
eliminated. Hence it must always be open to any one to object that
it is only on account of this imperfect factor of our knowledge that
there appears to be a physical world at all, that the external world
is an illusion produced by our sensations. And Leibniz himself,
while claiming that the world of fact, as opposed to the realm of
relations, possesses _practical_ reality, is obliged to admit that
_metaphysically_ it may be only an orderly dream. The fact is that
Leibniz unconsciously moves in the same circle, with relation to
sensation and the material world, that confines Spinoza with regard
to imagination and particular multiple existences. Spinoza explains
the latter from that imperfection of our intelligence which leads us
to imagine rather than to think. But he accounts for the existence
of imagination, when he comes to treat that, as due to the plurality
of particular things. So Leibniz, when an account of the existence of
matter is demanded of him, refers to confused knowledge as its source,
while in turn he explains the latter, or sensation, from the material
element which sets bounds to the activity of spirit. Leibniz seems
indeed, to advance upon Spinoza in admitting the reality of the
negative factor in differentiating the purely self-identical, but
he gives up what he has thus gained by interpreting the negation as
passivity, or mere deprivation.

To sum up, it may be doubted whether we have more to learn from
Leibniz's successes or from his failures. Leibniz's positive
significance for us is in his clear recognition of the problems of
modern philosophy, and in his perception of the isolated elements
of their solution. His negative significance is in his clinging to
a method which allowed him only to juxtapose these elements without
forming of them a true synthesis. There are a number of sides from
which we may state Leibniz's realization of the problem. Perhaps that
which distinguishes Leibniz most clearly from Locke is their respective
treatments of the relation of the physical to the spiritual, or, as
the question presented itself mainly to them, of the "natural" to the
"supernatural." To Locke the supernatural was strictly miraculous;
it was, from our standpoint, mere power, or will. It might indeed
be rational, but this reason was incapable of being apprehended by
us. Its distinction from the finite was so great that it could be
conceived only as something preceding and succeeding the finite in
time, and meanwhile as intercalating itself arbitrarily here and
there into the finite; as, for example, in the relation of soul and
body, in the production of sensation, etc. In a word, Locke thought
that the ends of philosophy, and with it of religion and morals,
could be attained only by a complete separation of the "natural"
and the "supernatural." Leibniz, on the other hand, conceived the
aim of philosophy to be the demonstration of their harmony. This is
evidenced by his treatment of the relations of the infinite and finite,
of matter and spirit, of mechanical and final causation. And he found
the sought-for harmony in the fact that the spiritual is the reason,
purpose, and function of the natural. The oft-quoted words of Lotze
express the thought of Leibniz: "The mechanical is unbounded in range,
but is subordinate in value." We cannot find some things that occur
physically, and others that occur supernaturally; everything that
occurs has its sufficient mechanical antecedents, but all that occurs
has its significance, its purpose, in something that does not occur,
but that eternally is--Reason. The mechanical and the spiritual are not
realms which here and there come into outward contact. They are related
as the conditioned and the conditioning. That, and not the idea of an
artificial _modus vivendi_, is the true meaning of the pre-established

In other words, Leibniz's great significance for us is the fact that,
although he accepted in good faith, and indeed as himself a master
in its methods, the results and principles of physical science, he
remained a teleological idealist of the type of Aristotle. But I have
not used the right words. It was not in spite of his acceptance of the
scientific view of the world that he retained his faith in the primacy
of purpose and reason. On the contrary, he was an idealist because of
his science, because only by the idea of an all-conditioning spiritual
activity could he account for and make valid scientific conceptions;
he was a teleologist, because natural processes, with their summing up
in the notion of causality, were meaningless except as manifesting an
immanent purpose.

There are other more technical ways of stating the bearing of Leibniz's
work. We may say that he realized that the problem of philosophy
consisted in giving due value to the notions of individuality and
universality, of identity and difference, or of the real and the
ideal. In developing these ideas, however, we should only be repeating
what has already been said, and so we may leave the matter here. On
the negative side we need only recall what was said a few pages back
regarding the incompatibility of Leibniz's method--the scholastic
formal logic--with the content of his philosophy. The attempt to
find a formal criterion of truth was hopeless; it was worse than
fruitless, for it led to such an interpretation of concrete truths
as to deprive them of their significance and as to land Leibniz in
involved contradictions.

To write a complete account of the influence of Leibniz's philosophy
would be too large a task for these pages. If we were to include under
this head all the ramifications of thought to which Leibniz stimulated,
directly and indirectly, either by stating truths which some one worked
out or by stating errors which incited some one to new points of view,
we should have to sketch German philosophy since his time,--and not
only the professional philosophy, but those wide aspects of thought
which were reflected in Herder, Lessing, and Goethe. It is enough to
consider him as the forerunner of Kant. It has become so customary to
represent Kant as working wholly on the problem which Hume presented,
that his great indebtedness to Leibniz is overlooked. Because Hume
aroused Kant from his dogmatic slumbers, it is supposed that Kant
threw off the entire influence of the Leibnizian thought as vain
dreams of his sleep. Such a representation is one-sided. It is truer
to state that Hume challenged Kant to discover the method by which he
could justify the results of Leibniz. In this process, the results,
no doubt, took on a new form: results are always relative to method;
but Kant never lost sight of the results. In the main, he accepted the
larger features of the Leibnizian conclusions, and, taught by Hume of
the insufficiency of the method that Leibniz followed, searched for a
method which should guarantee them.

This aspect of Kant appears more fully in his lesser and somewhat
controversial writings than in his classic works: and this, no doubt,
is one reason that his indebtedness is so often overlooked. His close
relation to Leibniz appears most definitely in his _brochure_ entitled
"Concerning a Discovery which renders Unnecessary all Critique of Pure
Reason." A Wolffian, Eberhard by name, had "made the discovery" (to use
Kant's words) "that the Leibnizian philosophy contained a critique of
reason just as well as the modern, and accordingly contained everything
that is true in the latter, and much else in addition." In his reply
to this writing, Kant takes the position that those who claimed to be
Leibnizians simply repeated the words of Leibniz without penetrating
into his spirit, and that consequently they misrepresented him on
every important point. He, Kant, on the other hand, making no claim to
use the terminology of Leibniz, was his true continuator, since he had
only changed the doctrine of the latter so as to make it conform to the
true intent of Leibniz, by removing its self-contradictions. He closes:
"'The Critique of Pure Reason' may be regarded as the real apology for
Leibniz, even against his own professed followers."

Kant, in particular, names three points in which he is the true
follower of Leibniz. The professed disciples of the latter insisted
that the law of sufficient reason was an objective law, a law of
nature. But, says Kant, it is so notorious, so self-evident, that
no one can make a new discovery through this principle, that Leibniz
can have meant it only as subjective. "For what does it mean to say
that over and above the principle of contradiction another principle
must be employed? It means this: that, according to the principle
of contradiction, only that can be known which is already contained
in the notion of the object; if anything more is to be known, it
must be sought through the use of a special principle, distinct from
that of contradiction. Since this last kind of knowledge is that of
synthetic principles, Leibniz means just this: besides the principle of
contradiction, or that of analytic judgments, there must be another,
that of sufficient reason, for synthetic judgments. He thus pointed
out, in a new and remarkable manner, that certain investigations
in metaphysics were still to be made." In other words, Kant, by his
distinction of analytic and synthetic judgments, with their respective
principles and spheres, carried out the idea of Leibniz regarding the
principles of contradiction and sufficient reason.

The second point concerns the relation of monads to material
bodies. Eberhard, like the other professed Leibnizians, interpreted
Leibniz as saying that corporeal bodies, as composite, are
actually made up out of monads, as simple. Kant, on the other
hand, saw clearly that Leibniz was not thinking of a relation of
composition, but of condition. "He did not mean the material world,
but the substrate, the intellectual world which lies in the idea
of reason, and in which everything must be thought as consisting
of simple substances." Eberhard's process, he says, is to begin
with sense-phenomena, to find a simple element as a part of the
sense-perceptions, and then to present this simple element as if it
were spiritual and equivalent to the monad of Leibniz. Kant claims to
follow the thought of Leibniz in regarding the simple not as an element
_in_ the sensuous, but as something super-sensuous, the _ground_ of
the sensuous. Leibniz's mistake was that, not having worked out clearly
the respective limits of the principles of identity and of sufficient
reason, he supposed that we had a direct intellectual intuition of this
super-sensuous, when in reality it is unknowable.

The third group of statements concerns the principle of pre-established
harmony. "Is it possible," asks Kant, "that Leibniz meant by this
doctrine to assert the mere coincidence of two substances wholly
independent of each other by nature, and incapable through their own
force of being brought into community?" And his answer is that what
Leibniz really implied was not a harmony between independent things,
but a harmony between modes of knowing, between sense on the one
hand and understanding on the other. The "Critique of Pure Reason"
carried the discussion farther by pointing out its grounds; namely,
that, without the unity of sense and understanding, no experience
would be possible. _Why_ there should be this harmony, _why_ we
should have experience, this question it is impossible to answer,
says Kant,--adding that Leibniz confessed as much when he called it a
"pre-established" harmony, thus not explaining it, but only referring
it to a highest cause. That Leibniz really means a harmony within
intelligence, not a harmony of things by themselves, is made more
clear, according to Kant, from the fact that it is applied also to
the relation between the kingdom of nature and of grace, of final
and of efficient causes. Here the harmony is clearly not between
two independently existing _external things_, but between what
flows from our notions of nature (_Naturbegriffe_) and of freedom
(_Freiheitsbegriffe_); that is, between two distinct powers and
principles _within us_,--an agreement which can be explained only
through the idea of an intelligent cause of the world.

If we review these points in succession, the influence of Leibniz upon
Kant becomes more marked. As to the first one, it is well known that
Kant's philosophy is based upon, and revolves within, the distinction
of analytic and synthetic judgments; and this distinction Kant
clearly refers to the Leibnizian distinction between the principles
of contradiction and of sufficient reason, or of identity and
differentiation. It is not meant that Kant came to this thought through
the definitions of Leibniz; on the contrary, Kant himself refers it to
Hume's distinction between matters of fact and relations of ideas. But
when Kant had once generalized the thought of Hume, it fell at once,
as into ready prepared moulds, into the categories of Leibniz. He
never escapes from the Leibnizian distinction. In his working of it
out consists his greatness as the founder of modern thought; from his
acceptance of it as ultimate result his contradictions. That is to say,
Kant did not merely receive the vague idea of sufficient reason: he
so connected it with what he learned from Hume that he transformed it
into the idea of synthesis, and proceeded to work out the conception of
synthesis in the various notions of the understanding, or categories,
as applicable to the material of sense. What Leibniz bequeathed him was
the undefined idea that knowledge of matters of fact rests upon the
principle of sufficient reason. What Kant did with this inheritance
was to identify the wholly vague idea of sufficient reason with the
notion that every fact of experience rests upon necessary synthetic
connection,--that is, connection according to notions of understanding
with other facts,--and to determine, so far as he could, the various
forms of synthesis, or of sufficient reason. With Leibniz the principle
remained essentially infertile, because it was the mere notion of the
ultimate reference of experience to understanding. In the hands of
Kant, it became the instrument of revolutionizing philosophy, because
Kant showed the articulate members of understanding by which experience
is constituted, and described them in the act of constituting.

So much for his working out of the thought. But on the other hand,
Kant never transcended the absoluteness of the distinction between
the principles of synthesis and analysis, of sufficient reason and
contradiction. The result was that he regarded the synthetic principle
as the principle only of our knowledge, while perfect knowledge he
still considered to follow the law of identity, of mere analysis. He
worked out the factor of negation, of differentiation, contained in
the notion of synthesis, but limited it to synthesis upon material
of sense, presupposing that there is another kind of knowledge,
not limited to sense, not depending upon the synthetic principle, but
resting upon the principle of contradiction, or analysis, and that this
kind is the type, the norm, of the only perfect knowledge. In other
words, while admitting the synthetic principle of differentiation
as a necessary element within _our_ knowledge, he held that on
account of this element our knowledge is limited to the phenomenal
realm. Leibniz's error was in supposing that the pure principles of
the logical understanding, resting on contradiction, could give _us_
knowledge of the noumenal world; his truth was in supposing that
only by such principles _could_ they be known. Thus, in substance,
Kant. Like Leibniz, in short, he failed to transcend the absoluteness
of the value of the scholastic method; but he so worked out another
and synthetic method,--the _development_ of the idea of sufficient
reason,--that he made it necessary for his successors to transcend it.

The second point concerns the relations of the sensuous and
the super-sensuous. Here, besides setting right the ordinary
misconception of Leibniz, Kant did nothing but render him consistent
with himself. Leibniz attempted to prove the existence of God,
as we have seen, by the principles both of sufficient reason and
contradiction. Kant denies the validity of the proof by either
method. God is the sufficient cause, or reason, of the contingent
sense world. But since Leibniz admits that this contingent world may,
after all, be but a dream, how shall we rise from it to the notion
of God? It is not our dreams that demonstrate to us the existence of
reality. Or, again, sense-knowledge is confused knowledge. How shall
this knowledge, by hypothesis imperfect, guarantee to us the existence
of a perfect being? On the other hand, since the synthetic principle,
or that of sufficient reason, _is_ necessary to give us knowledge of
matters of fact, the principle of contradiction, while it may give
us a consistent and even necessary notion of a supreme being, cannot
give this notion reality. Leibniz, while admitting, with regard to all
other matters of fact, that the principles of formal logic can give
no unconditional knowledge, yet supposes that, with regard to the one
unconditional reality, they are amply sufficient. Kant but renders him
self-consistent on this point.

It is, however, with regard to the doctrine of pre-established harmony
that Kant's large measure of indebtedness to Leibniz is most apt to
be overlooked. Kant's claim that Leibniz himself meant the doctrine
in a subjective sense (that is, of a harmony between powers in our
own intelligence) rather than objective (or between things out of
relation to intelligence) seems, at first sight, to go far beyond the
mark. However, when we recall that to Leibniz the sense world is only
the confused side of rational thought, there is more truth in Kant's
saying than appears at this first sight. The harmony is between sense
and reason. But it may at least be said without qualification that
Kant only translated into subjective terms, terms of intelligence,
what appears in Leibniz as objective. This is not the place to go into
the details of Kant's conception of the relation of the material to
the psychical, of the body and the soul. We may state, however, in his
own words, that "the question is no longer as to the possibility of the
association of the soul with other known and foreign substances outside
it, but as to the connection of the presentations of inner sense with
the modifications of our external sensibility." It is a question, in
short, of the harmony of two modes of our own presentation, not of the
harmony of two independent things. And Kant not only thus deals with
the fact of harmony, but he admits, as its _possible_ source, just what
Leibniz claims to be its _actual_ source; namely, some one underlying
reality, which Leibniz calls the monad, but to which Kant gives no
name. "I can well suppose," says Kant, "that the substance to which
through external sense extension is attributed, is also the subject
of the presentations given to us by its inner sense: _thus that which
in one respect is called material being would be in another respect
thinking being_."

Kant treats similarly the problem of the relations of physical and
final causes, of necessity and freedom. Here, as in the case just
mentioned, his main problem is to discover their _harmony_. His
solution, again, is in the union, in our intelligence, of the
understanding--as the source of the notions which "make nature"--with
the ideas of that reason which gives a "categorical imperative." The
cause of the possibility of this harmony between nature and freedom,
between the sense world and the rational, he finds in a being, God,
whose sole function in the Kantian philosophy may be said to be to
"pre-establish" it. I cannot believe that Kant, in postulating the
problems of philosophy as the harmony of sense and understanding,
of nature and freedom, and in finding this harmony where he did,
was not profoundly influenced, consciously as well as unconsciously,
by Leibniz. In fact, I do not think that we can understand the
nature either of Kant's immense contributions to modern thought or
of his inconsistencies, until we have traced them to their source
in the Leibnizian philosophy,--admitting, on the other hand, that we
cannot understand why Kant should have found necessary a new way of
approach to the results of Leibniz, until we recognize to the full
his indebtedness to Hume. It was, indeed, Hume that awoke him to his
endeavors, but it was Leibniz who set before him the goal of these
endeavors. That the goal should appear somewhat transformed, when
approached from a new point of view, was to be expected. But alas! the
challenge from Hume did not wholly awaken Kant. He still accepted
without question the validity of the scholastic method,--the analytic
principle of identity as the type of perfect knowledge,--although
denying its sufficiency for human intelligence. Leibniz suggested, and
suggested richly, the synthetic, the negative aspect of thought; Kant
worked it out as a necessary law of _our_ knowledge; it was left to his
successors to work it out as a factor in the law of _all_ knowledge.

It would be a grievous blunder to suppose that this final chapter
annihilates the earlier ones; that the failure of Leibniz as to
method, though a failure in a fundamental point, cancelled his
splendid achievements. Such thoughts as that substance is activity;
that its process is measured by its end, its idea; that the universe
is an inter-related unit; the thoughts of organism, of continuity,
of uniformity of law,--introduced and treated as Leibniz treated
them,--are imperishable. They are members of the growing consciousness,
on the part of intelligence, of its own nature. There are but three or
four names in the history of thought which can be placed by the side of
Leibniz's in respect to the open largeness, the unexhausted fertility,
of such thoughts. But it is not enough for intelligence to have great
thoughts nor even true thoughts. It is testimony to the sincerity and
earnestness of intelligence that it cannot take even such thoughts as
those of Leibniz on trust. It must _know_ them; it must have a method
adequate to their demonstration. And in a broad sense, the work of
Kant and of his successors was the discovery of a method which should
justify the objective idealism of Leibniz, and which in its history has
more than fulfilled this task.

  [ Transcriber's Note:

    The following is a list of corrections made to the original.
    The first line is the original line, the second the corrected one.

    By S. C Griggs and Company.
    By S. C. Griggs and Company.

  passivity of any kind is a myth, as scholastic fiction. Sensation is
  passivity of any kind is a myth, a scholastic fiction. Sensation is

  the vacuum is to serve as the background of the atoms. The atoms, are
  the vacuum is to serve as the background of the atoms. The atoms are


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