LEIBNIZ

THE MONADOLOGY

AND

OTHER PHILOSOPHICAL WRITINGS

TRANSLATED

WITH INTRODUCTION AND NOTES

Y

ROBERT LATTA, M.A., D.PHIL. (EDIN.)

LECTURER IN LOGIC AND METAPHYSICS AT THE
UNIVERSITY OF ST. ANDREWS

AT THE CLARENDON PRESS
1898

PRINTED AT THE CLARENDON PRESS

BY HORACE HART, M.A.
PRINTER TO THE UNIVERSITY

PREFACE

IN this country Leibniz has received less attention
than any other of the great philosophers. Mr. Merz
has given, in a small volume, a general outline of
Leibniz's thought and work, Professor Sorley has
written for the Encyclopaedia Britannica a remark-
ably clear, but brief, account of his philosophy, and
there are American translations of the Nouveaux
Essais and of some of his philosophical papers. That
is very nearly the whole of English writing about
him. Yet few philosophical systems stand so much
in need of exposition as that of Leibniz. His theories
have to be extracted from seven large volumes of
correspondence, criticism, magazine articles, and other
discursive writings, and it is only in recent years that
this material has been made fully available by the
publication of Gerhardt's edition. No complete and
detailed account of Leibniz's philosophy has hitherto
been published in English, and accordingly I have
written a very full Introduction to this book, with
illustrative foot-notes, consisting mainly of transla-
tions from Leibniz himself.

The endeavour of the book is to make the
Monadology clear to students. I cannot agree with
Dillmann in treating it as of little importance.

A 3

VI PREFACE

Leibniz himself expressly intended it to be a com-
pact and ordered statement of the views he had
expounded in many scattered papers and in his
somewhat desultory The'odicee, the only book he
published. There is evidence of this in his corre-
spondence and in the fact that he annotated the
Monadology with references to passages in the
Tkeodicee. My original intention was to publish
a translation of these passages along with the
Monadology, but on re-consideration it seemed better
to translate several short papers illustrating different
parts of Leibniz's system and explaining its growth.
Thus the Monadology, as being the centre of the
book, is printed first of the translations (although
in date it is last), while the other writings follow in
chronological order. The only disadvantage of this
arrangement is that it places the Principles of Nature
and of Grace, which is most akin to the Monadology,
farthest away from it.

If I might venture to suggest to the student the
way in which the book should be read, I would
recommend him first to read Part I of the Intro-
duction, then the Monadology (without the notes),
afterwards Parts II and III of the Introduction,
the Monadology again (with the notes), the other
translations, and finally Part IV of the Introduction,
in which I have endeavoured to ' place ' the philosophy
of Leibniz in relation to the systems which came
before and after his.

My indebtedness to authors is so great and varied
that I cannot acknowledge it in detail; but I may
mention as specially helpful to me the works of
Boutroux, Dillmann, Nourisson, Nolen, and Stein.
My thanks are due to Professor Jones, of Glasgow,

PREFACE Vll

who read the Introduction in manuscript, for much
valuable suggestion and criticism; and I am more
than grateful to Professor Ritchie, of St. Andrews,
who read the whole book, both in manuscript and in
proof, and to whom it owes numerous improvements
as well in form as in matter.

I have adopted the spelling 'Leibniz' in place of
the traditional 'Leibnitz,' because the former was
invariably used by Leibniz in signing his own name.

It ought perhaps also to be mentioned that Parts
II and III of the Introduction were accepted by the
University of Edinburgh as a thesis for the degree of
Doctor of Philosophy.

ROBERT LATTA.

UNIVERSITY OF ST. ANDREWS,
June, 1898.

TABLE OF CONTENTS

PAGE

PREFACE . . . . . '• v

INTRODUCTION :

Part I. Life and Works of Leibniz i
„ II. General Principles of the Philosophy of

Leibniz 21

„ III. Detailed Statement of the Philosophy of

Leibniz ....... 74

A. Leibniz's Mathematics in relation to his

Philosophy . . . . . 74

B. Matter . 86

C. Organism 108

D. Self-Consciousness ..... i2q
Theory of Knowledge . . . .121
Ethics . . . ' . . . .137

„ IV. Historical and Critical Estimate of the Phi-
losophy of Leibniz . . . .151
APPENDIX A. Explanation of the Pre-established

Harmony 200

„ B. Formation of the Idea of Space . . 202

„ C. Meaning of Cause . . . . . 204

„ D. Leibniz's Logic ..... 206

„ E. Kant on his relation to Leibniz . . 208

THE MONADOLOGY 215

APPENDIX F. Leibniz and Bayle on the multiplicity

in the Monad 272

G. Proof of the Existence of God . . 274

ON THE NOTIONS OF RIGHT AND JUSTICE . . . 281

X CONTENTS

PAGE

NEW SYSTEM OF THE NATURE OF SUBSTANCES AND OF

THE COMMUNICATION BETWEEN THEM . . . 297

EXPLANATION OF THE NEW SYSTEM . . . . 319

APPENDIX H. On the Elements of Extension . . 329

THIRD EXPLANATION OF THE NEW SYSTEM . . . 331

)N THE ULTIMATE ORIGINATION OF THINGS . . . 337
APPENDIX I. Growth of Leibniz's Theories regarding

Force and Motion . . . '.351

NEW ESSAYS ON THE HUMAN UNDERSTANDING— Intro-
duction . ' • . 355

— PRINCIPLES OF NATURE AND OF GRACE . : . . 405

INDEX «• . ' - . . 425

ABBKEVIATIONS

E. God. Guil. Leibnitii opera philosophical quae extant latina, gallica, ger~
manica omnia, ed. J. E. Erdmann. Berlin, 1840.

G. Die philosophischen Schriften von G. W. Leibniz, herausgegeben von
C. J. Gerhardt. Berlin, 1875-90.

G. Math. Leibnizens mathematische Schriften, herausgegeben von C. J.
Gerhardt. Berlin and Halle, 1850-63.

Dutens. G. G. Leibnitii opera omnia, nunc primum collecta, studio
Ludovici Dutens. Geneva, 1768.

Klopp. Die Werke von Leibniz, herausgegeben von Onno Klopp.
Hanover, 1864-77.

Foucher de Careil. (Euvres de Leibniz, publiees pour la premiere fois
d'apres les manuscrits originaux, par A. Foucher de Careil. Paris,
1859-75.

Mollat. Rechtsphilosophisches aus Leibnizens ungedruckten Schriften, von
Dr. Georg Mollat. Leipzig, 1885.

INTRODUCTION

PAKT I.

THE LIFE AND WORKS OF LEIBNIZ.

His Boyhood.

ON June 21, 1646, two years before the close of
the Thirty Years' War, Gottfried Wilhelm Leibniz was
born at Leipzig. His family was of Bohemian origin ;
but his ancestors for several generations had lived in
Saxony and Prussia, and his father was a Professor of
Philosophy in the University of Leipzig. Leibniz was
only six years of age when his father died ; and, though
in his early years he had the training of a pious mother,
she also passed away before he had completed his Univer-
sity studies. The boys of Leipzig in Leibniz's time
appear to have been brought up on ' the picture-book of
Comenius and the little Catechism ' (Luther's) ; but the
soul of Leibniz already sought stronger meat, and having
found in the house an illustrated copy of Livy, of which
he could not thoroughly understand a single line, he
managed to get a tolerable idea of its contents, supple-
menting his scanty Latin by a study of the pictures and
some judicious guessing. As an indirect result of this
precocity, his father's library was thrown open to him,
and he wandered at will from volume to volume, finding
(as was ever characteristic of him) some good in all1.

1 ' It is characteristic of me to hold opposition (Widerlegeri) as of

B

2 INTKODUCTION

Providence or Fortune seemed to say to him, Tolle, lege ;
and it is significant for the philosophy to come that he
turned first to the Ancients, to Cicero, Quintilian, Seneca,
Pliny, Herodotus. Xenophon, Plato, the historians of the
Roman Empire, and the Fathers of the Church. Of these
he tells us that * he understood at first nothing, then
gradually something, and finally enough'; but uncon-
sciously his mind was coloured by their style and thought,
' as men walking in the sun have their faces browned
without knowing it,' and under their inspiration he made
it the rule of his life ever to seek clearness in speaking
and a useful purpose in acting (in verbis daritas, in rebus
usus). Thus at fourteen years of age he was counted by
his fellows a prodigy of learning and ability, and already
his reading of Logic and intense determination towards
clearness of thought and speech had led him to ideas
which were afterwards developed into the suggestion of
a logical Calculus and an 'Alphabet of Concepts' as
means to the discovery of truth 1.

University Life.

At fifteen years of age Leibniz became a student at the
University of Leipzig, and about the same time he became

little account, exposition (Darlegen) as of much account, and when
a new book comes into my hands I look for what I can learn
from it, not for what I can criticize in it.' Schreiben an G. Wagner
(1696) (E. 425 b; G. vii. 526).

1 ' Before I reached the school-class in which Logic was taught,
I was deep in the historians and poets ; for I had begun to read
the historians almost as soon as I was able to read at all, and in
verse I found great pleasure and ease ; but as soon as I began to
learn Logic I found myself greatly excited by the division and
order of thoughts which I perceived therein. I immediately began
to notice, so far as a boy of thirteen could, that there must be a
great deal in it. I took the greatest pleasure in the Predicaments '
(i. e. the Categories) ' which came before me as a muster-roll of all
the things in the world, and I turned to "Logics" of all sorts to
find the best and most detailed form of this list. I often asked
myself and my schoolfellows to which Predicament and also to
which sub-class this or that thing might belong/ Schreiben an
(?. Wagner (E. 420 a ; G. vii. 516).

LIFE AND WORKS 3

acquainted with the works of some of the modern philo-
sophers, beginning with Bacon's De Augmentis Scientiarum.
At this time also, as he himself tells us, he read with
interest the works of Cardan and Campanella and the
suggestions of a better philosophy in Kepler, Galileo, and
Descartes. But he was no l read ing-machine, all wound
up and going/ He thought for himself : he read in order
to ' weigh and consider. ' And thus in after-years he re-
calls how, when he was fifteen years of age, he walked
alone in a wood near Leipzig, called the Rosenthal, to
consider whether or not he should retain in his philo-
sophy the 'Substantial Forms' of the Scholastics1.
Although his favourite teacher at Leipzig was Jacob
Thomasius, a Professor of Philosophy, deeply versed in
ancient and scholastic learning, the private reading of
Leibniz at first prevailed in his thought and he turned
from the older philosophies to * mechanism ' and mathe-
matics. The ' Substantial Forms * were for the time set
aside, to reappear, transmuted, in later years. His
scholastic studies, however, bore fruit in the earliest of
his published writings, a graduation thesis with the
significant title De principle individui, in which he de-
fended the Nominalist position. Intending to devote him-
self to the profession of law, he went for a year (in 1663)
to Jena, where the mathematician, Erhard Weigel, was
lecturing on 'the Law of Nature,' or what we should now
call Jurisprudence in general. Doubtless the influence
of Weigel tended to confirm Leibniz's mathematical
bent, and he still continued his study of history. In
1666 the University of Leipzig, ostensibly on the ground
of his youth, refused to give him the Doctorate in Law ;
but his thesis, De casibus perplexis in jure, was immediately
accepted by the University of Altdorf (near Niirnberg),
where he declined the offer of a professorship. Thus
ended his connexion with Leipzig.

1 Lettre a M. Remond (1714) (E. 7028 ; G. iii. 606).
B 2

4 INTRODUCTION

Boineburg and the Elector of Mainz.
In Niirnberg, at that time the capital of a small
republic, which had suffered less than many other
German States from the Thirty Years' War, Leibniz spent
a year, in the course of which his extensive curiosity led
him to become a member of a secret society of the
Rosicrucians, who were trying to find the philosopher's
stone. Fontenelle tells us that Leibniz's method of
gaining admission to the society was to collect from
books on alchemy all the most obscure phrases he could
find and to make of them an unintelligible letter, which
he produced as evidence of his fitness for membership.
The society was so impressed that it immediately ap-
pointed him to be its secretary. The chief gain to Leibniz
appears to have been that through this society he became
acquainted with Baron von Boineburg, ' one of the most
celebrated diplomatists of his age/ who had formerly
been minister to the Elector and Archbishop of Mainz,
the most powerful man in the Empire. With Boineburg
Leibniz went to Frankfort, where he wrote and pub-
lished a paper on legal education, which was the means
of introducing him to the archbishop, in whose service
he remained for some time. This was the beginning of
his career as a diplomatist. The long war had left
Germany in ruins, and, ere there was time to rebuild,
the whole empire was threatened by the immense power
of Louis XIV, who was dreaming of world-wide sway.
The Elector of Mainz, says Leibniz, 'had seen the miseries
of Germany, whose ruins were still smoking : he was one
of those who had laboured most to bring back rest to the
land, from which life seemed almost to have gone. The
country was (as one might hardly say) " peopled " with
little children, and if war were to break out again (as
might be expected when Sweden was irritated and France
threatening) there was every reason to fear that this seed
of a new population would be destroyed and a great part

LIFE AND WOEKS 5

of poor Germany left almost without inhabitant V The
treaty of Westphalia had secured peace and some measure
of political unity, but it pointed also to an ecclesiastical
reunion, yet to be realized, which to men like the Elector
of Mainz and Boineburg seemed the best means of re-
storing power and happiness to the country. Negotiations
for the reunion of Eoman Catholics and Protestants had
already been begun, and thus early in his diplomatic
career Leibniz took part in the work of conciliation
which in various ways he continued throughout his life.
At the suggestion of Boineburg he made a special study
of the doctrine of transubstantiation, with the result
(expressed in a letter to Arnauld in 1671) that he found
it impossible to reconcile the Cartesian view of material
substance as pure extension either with the Roman
Catholic or with the Lutheran doctrine. He accord-
ingly formed the purpose of discovering a theory of
substance which should satisfy both, and should thus
become a philosophical basis for the reconciliation of the
Churches.

Paris and London.

Presently events occurred which led him away from
Mainz and gave him new opportunities of study and of
intercourse with learned men. Leibniz and his friends
felt strongly the necessity of drawing into safe channels
the military ambitions of Louis XIV, and accordingly
Leibniz prepared a most elaborate work in which he
suggested to the King of France the advantages that
would arise from a conquest of Egypt, and tried to con-
vince him that it was more worthy of a Christian king
to fight the unchristian Turks than to harass a poor
little people like the Dutch2. This book was never

1 From a letter of Leibniz, quoted by Foucher de Careil, vol. iv.
Introduction, p. xx.

2 This Projet de Conquete de I'figypte was published by Foucher de
Careil, vol. v. It shows a most remarkable knowledge regarding
the state of the country and its possibilities, and so clever are the

6 INTRODUCTION

actually presented to King Louis, but Leibniz in 1672
went by invitation to Paris to explain his project. His
advice was not taken ; but he remained in Paris for
four years, during which he devoted himself to the study
of the higher mathematics l and to the discussion of the
Cartesian philosophy. He had already corresponded with
Arnauld, and he now met also Huygens and Male-
branche. At this time, says Leibniz himself, 'law and
history were my forte V But intercourse with Huygens
and the study of the mathematical works of Pascal intro-
duced him to the problems of modern mathematics.
Huygens, he tells us3, 'had no taste for metaphysics,'
but Leibniz learned from him mathematical methods
and principles which influenced the growth of his philo-
sophy, and which set him on the way to the discovery of
the Differential Calculus. At this time also Leibniz in-
vented a calculating machine, superior to that of Pascal,
which could only add and subtract, while his own machine
could also multiply, divide, and extract roots. And in
other ways the residence of Leibniz in Paris greatly
affected his life-work. For instance, it probably led to
his writing so much in French. He had already, in his
essay on the philosophical style of Nizolius (1670), advo-
cated the use of the German language for philosophical
and other works. But in the time of Louis XIV Paris
was the intellectual centre of Europe, and to write for
the world was to write in French. While, therefore,

plans which it suggests that Napoleon was at one time supposed
to have borrowed its ideas for his campaign. Though this has
been shown to be a mistake, the coincidence between the suggested
expedition of Louis XIV and the actual expedition of Napoleon is
sufficiently noteworthy.

1 * The merit of an author in mathematics cannot be disputed, as
it can in other subjects. This is the reason why I remained some
time in France, in order to perfect myself .in mathematics, and
I gave my time to these sciences not on their own account, but in
order to make them contribute to the advancement of piety.' Lettre
au Due Jean Frederic (undated) (Klopp, iv. 450).

2 Lettre a la Comtesse de Kilmansegg (1716) (Dutens, iii. 456).
* E. 702 b ; G. iii. 607.

LIFE AND WORKS 7

Leibniz has rightly been called 'the father of German
philosophy,' he is only to a very small extent a German
author.

The four years' residence of Leibniz in Paris was
broken by a brief visit to England in the early months
of 1673. Leibniz had already sought the favour of Eng-
lish learning by dedicating one of his publications to the
Koyal Society, and he had also been greatly interested in
the philosophy of Hobbes, with which to a great extent
he found himself in agreement, especially as regards
questions of physics, although he was strongly opposed
to his political theories. In 1670 he wrote a letter
to Hobbes, to which he received no answer, and after-
wards he began another letter, but left it unfinished. It
has recently been maintained that, up to the year 1670,
Leibniz was 'more deeply affected by Hobbes than by
any other of the leading spirits of the new time V When
Leibniz visited London, Hobbes was still living there,
but he was eighty-five years of age, and some years
earlier Leibniz had heard from his countryman Olden-
burg, who was secretary of the Koyal Society, that
Hobbes was in his dotage. Accordingly it is not sur-
prising that they did not meet. Apart from Oldenburg,
the man with whom Leibniz seems to have had most
intercourse during this visit to London wasKobert Boyle,
the famous physicist ; but there is no reason to suppose
that Leibniz gained much from his stay in England,
except an additional stimulus to the study of the higher
mathematics, which he carried on more systematically
after his return to Paris. As a fitting conclusion of his
Parisian period came the discovery of the Differential
Calculus, which was practically accomplished by Leibniz

1 See Tonnies in Philos. Monatshefte, vol. xxiii. pp. 557-573. Cf.
Leibniz's Letter to Holies (1670) (G. i. 85): 'I constantly maintain
among my friends, and, with the help of God, I will always publicly
maintain also, that I know no writer who has philosophized more
accurately, more clearly, and more elegantly than you, not even
excepting a man of such excellent genius as Descartes himself.'

8 INTRODUCTION

in 1676. There can be no doubt that Newton was in
possession of a similar method as early as 1665. He at
first made known only some of the results of the method,
and not the method itself. Hence an attempt has been
made to show that Leibniz got hints of the method
during his first visit to England, and that he was thus
more or less a plagiarist of Newton. But there is nothing
to confirm this, and a full consideration makes it much
more likely that each discovered the method indepen-
dently. Leibniz published his account of the method in
1684 : Newton's was first published in 1693. To Newton
belongs the glory of priority, whatever that may be
worth ; while the form which Leibniz gave to the Cal-
culus, the names and the signs which he used, have come
to be universally employed in preference to those of
Newton l.

Visit to Spinoza.

Shortly before Leibniz went to London, Boineburg
died ; and the visit to London was unexpectedly brought
to an end in March, 1673, by the death of the Archbishop
of Mainz. Leibniz was now without an official position,
and during the next few years he made various unsuc-
cessful attempts to obtain a diplomatic appointment. At
last, in 1676, he somewhat reluctantly accepted the post
of librarian to the Duke of Brunswick at Hanover, which
was to be his home during the remainder of his life.
During the earlier years of his residence in Paris, Leibniz
had given much attention to the philosophy of Descartes
and the Cartesians, with the result that he became more
and more convinced of its insufficiency2. In his en-

1 See Merz, Leibniz (Blackwood's Philosophical Classics), ch. iii.
and v. Cf. Guhrauer's Leibnitz, i. 170 sqq.

2 A few years after (in 1679) Leibniz writes to Philipp : 'As to
the philosophy of Descartes I have no hesitation in saying abso-
lutely that it leads to atheism' (G. iv. 281). And in the same
year he writes to Malebranche that, while in many respects he
admires Descartes, he is * convinced that his mechanics is full of

LIFE AND WORKS 9

deavour after a more satisfactory metaphysic he after-
wards made a considerabl_e_jjtady_ ofJPlato, and in 1676
he translated the Phaedo and the Theactetus. Towards
the end of 1675 Leibniz became acquainted with the
young Bohemian nobleman, Tschirnhausen, Spinoza's
acute critic and correspondent, who was at that time in
Paris, and who had earlier in the same year written
some of the remarkable letters on account of which his
name will always be associated with that of Spinoza1.
Leibniz had already (in 1671) written to Spinoza from
Frankfort about a question of optics ; but now Tschirn-
hausen seems to have aroused in him the hope that
a solution of the difficulties of Cartesianism might be
found in the unpublished system of Spinoza. In
November, 1675, a medical friend of Spinoza in Amster-
dam (G. H. Schuller) wrote to him: * Von Tschirnhausen
further mentions that he has found at Paris a man called
Leibniz, remarkably learned and most skilled in various
sciences, as also free from the vulgar prejudices of
theology. With him he has formed an intimate acquain-
tance, founded on the fact that Leibniz labours with him
to pursue the perfection of the intellect, and, in fact,
reckons nothing better or more useful. Von Tschirnhausen
says that he is most practised in ethics, and speaks with-
out any impulse derived from the passions, but by the
sole dictate of reason. He adds that he is most skilled in
physics, and also in metaphysical studies concerning God
and the soul. Finally, he concludes that he is most
worthy of having communicated to him the master's
writings, if you will first give your permission, for he
believes that the author will thence gain a great ad-
vantage, as he promises to show at length, if the master
be so pleased. But if not, do not doubt in the least that

errors, his physics is too hasty, his geometry is too limited, and
his metaphysics has all these faults combined' (G. i. 328).

1 Letters, 57 sqq. Van Vloten and Land, vol. ii. p. 204 ; Bruder,
vol. ii. p. 321 (Letters, 61 sqq.).

10 INTKODUCTION

he will honourably keep them concealed as he has
promised, as in fact he has not made the slightest men-
tion of them. Leibniz also highly values the Theologico-
Political Treatise, on the subject of which he once wrote
the master a letter, if he is not mistaken V Spinoza, in
reply, recollects having some correspondence with Leibniz,
but Leibniz was at that time a counsellor at Frankfort,
and Spinoza would like to know, before entrusting his
writings to him, what he is doing in France, and he
would also like to have Tschirnhausen's opinion of
Leibni/, after a longer and more intimate acquaintance.
Spinoza's shyness had probably no other effect than to
whet the curiosity of Leibniz, and accordingly, when he
left Paris in October, 1676, he went for a week to
London (where he met for the first time Newton's friend
Collins) and then crossed to Amsterdam, where he stayed
four weeks with Schuller, eagerly reading and criticizing
every writing of Spinoza's which Schuller could give
him. At last, in November, Leibniz obtained an inter-
view with Spinoza at the Hague, where he seems to have
spent some time. They had many conversations together
regarding philosophical matters, of which Leibniz has
left hardly any record except the remark that i Spinoza
did not quite clearly see the defects of Descartes'
laws of motion : he was surprised when I began to show
him that they were inconsistent with the equality of
cause and effect3.' The persistence of Leibniz ultimately
induced Spinoza to show him the MS. of the Ethics
(or at least a portion of it), and he seems even to
have- had permission to make a copy of the leading
definitions, axioms, and propositions3. What at this time
most dissatisfied Leibniz was Spinoza's treatment of
Final Causes. His recent study of Plato had impressed

1 Letter 70, Van Vloten and Land, vol. ii. p. 235.
Foucher de Careil, Refutation inedite de Spinoza, p. Ixiv.
Spinoza died in the following year, and soon afterwards the
Ethics was published.

LIFE AND WORKS II

Leibniz with the value of teleological considerations, and
he was already seeking in that direction an escape from
the imperfections of the mechanical view of things. But
his general hostility to Spinoza's system did not show
itself until ten years later, when he had settled the
essential points of his own doctrine of substance. At
this time Leibniz was still seeking light in every
quarter.

Residence in Hanover. Correspondence and Growth of
his System.

Leibniz arrived at Hanover in the last days of 1676.
Efforts had already been made to convert him to the
Roman Catholic faith, and he had begun a correspondence
with Pellisson (a distinguished convert from Protes-
tantism) in the hope of finding some means of Church
reunion. This correspondence led to others, of which the
most important was one with Bossuet. But, though
Leibniz was more or less occupied with these discussions
throughout the rest of his life, nothing practical came of
them. Bossuet's attitude in the discussion was only too
well expressed in his exclamation regarding Leibniz :
Utinam ex nostris esset ! ; Would that he were one of
us ! ' And Leibniz was too much of a scientific inquirer
to unite two opposed religious communions. He might
draw up a statement of dogma to which both sides could
assent *, but inevitably it would express the real belief of
neither. The endeavour to convert Leibniz was not given
up for a very long time, and a brief visit of his to Rome
in 1689 seems to have caused a flutter of excitement.
He was offered the librarianship of the Vatican and other
posts with a vista of preferment ; but conversion was so
far from his mind that we hear of him bringing from
the Catacombs a piece of glass, reddened with the blood
of martyrs, in order to submit it to chemical analysis !

1 He actually attempted this, in what has been grandiloquently
called the Systema Theologicum, written in 1686.

12 INTRODUCTION

It was during the early years of his residence in
Hanover that Leibniz worked out the leading ideas of
his system. Disappointed in his hope of finding in
Spinoza a saviour from the errors of Descartes, and being
the rather confirmed, by Spinoza's conclusions, in his
conviction of the insufficiency of any merely mechanical
interpretation of things, he turned with renewed interest
to Plato1, with the result that towards 1680 he had
reached the conception of substance as essentially active
force. It is possible also that, in spite of his general
dissatisfaction with Spinoza's position, some of Spinoza's
ideas (such as that of the conatus or self-preserving
tendency of things) may have contributed to the develop-
ment of his new view of substance. One further step
was needed to complete the theory, namely, the recogni-
tion that the force constituting a substance is not a
universal world-principle, but something individual—
that there are substances which are forces. To this position
he seems to have attained about 1684 or a little later,
through a return to the consideration of Aristotle and the
Peripatetic Schools, whose views he had set aside in his
boyhood, nearly twenty-five years before. The main ideas
of his philosophy (such as his conception of ' simple
substance' and his pre-established harmony) . were first
stated in the correspondence with Arnauld, which took
place between 1686 and 1690. This correspondence,
however, was not published as a whole until 1846 ; and
the learned world was first made aware that Leibniz had
worked out a philosophical system of his own by two
papers which he published in 1695— one (the Specimen
Dynamicum) in the Leipzig Acta Eruditontm, and the
other (the Systeme Nouveau) in the French Journal des
Savants. Leibniz uses the term 'monad' for the first
time in 1697.

1 ' Of all the ancient philosophers I find Plato the most satis-
factory in regard to metaphysics.' Letlre a M. Bourguet (1714) (E.
723 a ; G. iii. 568).

LIFE AND WOKKS 13

The 'Nouveaux JEssais' and the l Tfieodicee.'

Having thus definitely fixed his philosophical system-1,
and having published its leading principles, Leibniz
gradually expounded it in detail, for the most part by
means of correspondence and criticism. Hitherto he
had given most attention to ontological or purely meta-
physical problems. But now he began to consider more
carefully the theory of knowledge and the psychological
questions that are connected with it. Locke's Essay was
published in 1690, and a few years afterwards Leibniz
read it, writing (as was his custom) notes and comments
as he read. Some of these criticisms were in 1697 sen^
to Locke, who treated them with contempt, and made no
reply2. In 1703 Leibniz wrote the Nouveaux Essais sur
I'Entendement humain, a long dialogue, in which the views
of Locke and of himself are set in contrast throughout
a discussion dealing with the subjects of Locke's Essay
chapter by chapter. This book was evidently intended
to call forth a rejoinder from Locke. But before it was
ready for publication Locke died (in 1704) ; and Leibniz,
saying that he ' greatly disliked publishing refutations of
dead authors,' and that he now 'preferred to publish his
thoughts independently of another person's,' allowed the
Nouveaux Essais to remain in manuscript, so that the
book was first published by Kaspe in 1765, nearly fifty
years after Leibniz's death.

After writing some other papers on psychological and

1 In 1697 he writes to Thomas Burnet of Kemnay : ' I have
changed and changed again, according as new light came to me ;
and it is only about twelve years since I found what satisfies me, and
arrived at demonstrations regarding matters which did not seem
capable of demonstration/ (G-. iii. 205.)

* Leibniz (in 1714) says that he was not surprised at Locke's
disdain. 'The difference between our principles was somewhat
too great, and what I maintained seemed to him to be paradox.'
He adds that Locke ' had subtlety and dexterity, and he had
a kind of superficial metaphysics which he knew how to make the
most of; but he did not know the method of mathematicians.'
Ltttre a Eemond (E. 703 b ; G. iii. 612).

14 INTRODUCTION

epistemological subjects, Leibniz, in 1710, published his
Tfieodicee, the one great work of his which was printed
in his lifetime. It was written, not continuously, but at
intervals, in a very diffuse and discursive style, and its
purpose was to develop the principles of its author's
philosophy in maintaining, against the 'arguments of
Pierre Bayle, the harmony of faith and reason, and to
'vindicate the ways of God to man/ The writing of
the Theodicee was suggested to Leibniz as the result of
conversations with Queen Sophia Charlotte of Prussia,
who also induced him to write various other philo-
sophical papers, and who encouraged him in his plans
for the founding of an Academy at Berlin. Besides the
exposition of his system which he gives in such elaborate
works as the Nouveaux Essais and the Theodicee, Leibniz
met the objections of critics and suggested new applications
of his principles in the course of a varied correspondence.
On questions of mathematics and physics in their con-
nexion with metaphysics, he corresponded with John
Bernouilli for more than twenty years (from 1694 to
1716), and for ten years (1706-1716) he discussed with
Des Bosses the possibility of combining his philosophy
of substance with the presuppositions of the doctrine
of transubstantiation. Further, among many other epi-
stolary discussions, mention may be made of Leibniz's
correspondence, during the last two years of his life,
with Bourguet on the chief doctrines of his philosophy,
with special reference to biological questions, and with
Clarke on space and time and the Divine attributes.

Founding of Academies. Closing Tears.
The amazing intellectual activity of Leibniz found
expression in many other writings. During the greater
part of his residence at Hanover he worked at a history
of the house of Brunswick, in connexion with which he
travelled much and ransacked the libraries of Germany
and Italy. He suggested the development of mining in

LIFE AND WORKS 15

the Harz Mountains, and in connexion with this he
studied and wrote on geological subjects and on the
currency. But, above all, the interest of Leibniz in these
later years lay in the endeavour to extend science and
civilization throughout Europe. With this end in view,
he, who (according to Frederick the Great) was an
Academy in himself, succeeded after much effort in
obtaining the foundation of an Academy at Berlin, of
which he himself was appointed the first president
(1700). Afterwards he made long-continued but un-
successful attempts to induce the King of Poland, the
Czar, and the Emperor to found similar Academies at
Dresden, St. Petersburg, and Vienna. He had Inter-
views with Peter the Great, whom he expected to
become 'the Solon of Russia,' and he lived for some
time in Vienna, where he tried to bring about an alliance
between the Czar and the Emperor. Charles VI favoured
his projects for the founding of learned societies, and he
was also strongly supported by Prince Eugene of Savoy,
for whom in 1714 he wrote the Monadologie (or, as
Gerhardt maintains, the Principes de la Nature et de la
Grace). But Europe was full of wars and rumours of
wars, and the peaceful plans of Leibniz were set aside.
The Berlin Academy had a struggling existence, and no
other was founded until long after Leibniz's death.

The happiest years of the life of Leibniz were now
over. The Duke of Brunswick1 died in 1698, and
Leibniz seems gradually to have lost favour with his son
and successor, our George I. After the death of his
friends, 'the two Electresses,' Sophia and Sophia Charlotte
(the mother and the sister of George I), Leibniz's position
became intolerable. George I succeeded to the English
crown in 1714, and his prejudices against Leibniz, shown
in his displeasure on account of the latter 's residence in
Vienna, were encouraged by some of Newton's friends,

1 Successor of the duke who had originally appointed Leibniz to
the librarianship at Hanover.

l6 INTRODUCTION

whom he met in England. Leibniz thought of leaving
Hanover ; but in later years his health had been some-
what broken, and on November 14, 1716, he died during
an attack of gout. His secretary, Eckhart, invited all
the people of the Court to his funeral, but not one of
them came, and Eckhart alone followed his master's body
to the grave. An acquaintance of Leibniz, John Ker of
Kersland1, who had come to Hanover on the very day
of Leibniz's death, says that he was buried ' more like
a robber than, what he really was, the ornament of his
country.' No minister of religion was present ; for
Leibniz was parcus deorum cultor et infrequens, and his
absence from church was counted to him for irreligion,
so that from priests and people he got the nickname
Ajjdvenix (the Low German for Glaubet nichts, believer in
nothing). The Berlin Academy and the Koyal Society
of London took no notice of his death ; but a year
afterwards Fontenelle commemorated it in a fine oration,
delivered before the Parisian Academy.

Personal Characteristics. ,

As to the personal characteristics of Leibniz, Eckhart
tells us that he was of middle height, with a somewhat
large head, dark-brown hair, and small but very sharp
eyes. He was near-sighted, but had no difficulty in
reading, and himself wrote a very small hand. His lungs
were not strong, and he had a thin but clear voice, with
a difficulty in pronouncing gutturals. He was broad-
shouldered and always walked with his head bent for-
ward, so that he looked like a man with a humped back.
In figure he was slim rather than stout, and his legs

1 A leader of the Scottish Cameronians. He lived on political
intrigue, and when his resources in England were failing him he
presented to the Emperor, through Leibniz, a project for privateer-
ing and buccaneering against the Spaniards in the Pacific. In
the Political Memoir containing Ker's proposals there is a curious
medley of religious considerations and the hope of gain. Cf. Foucher
de Careil, iv. 272 sqq.

LIFE AND WORKS 17

were crooked. His household arrangements (if they can
be called * arrangements ') were very irregular. He had
no fixed hours for meals, but, when a convenient oppor-
tunity came in the course of his studies, he sent out for
something to eat. He once made a proposal of marriage
(when he was fifty years of age), but the lady took time to
consider, and (Fontenelle says) i this gave Leibniz also
time to consider, and he never married.' He slept little,
but well : he often spent the night in his chair, and
sometimes he would remain in it for several days at a
time. This enabled him to do a great deal of work ; but
it led to illness, for which, disliking physicians, he em-
ployed remedies more ' heroic ' than wise. He enjoyed
intercourse with all sorts and conditions of men, believing
that he could always learn something even from the
most ignorant. ' Cum Socrate semper ad disc endum par atus
sum.9 l He spoke well of everybody,' says Eckhart, 'and
made the best of everything ' (er kelwte alles zum Besten).
He often congratulates himself on being self-taught
(avroSt'SaKTos), and thus able to avoid acquiescence in super-
ficial, ready-made knowledge and to strike out paths of
his own. For he is ever (he teljs us) ' eager to penetrate
into all things more deeply than is usually done and to
find something new.'

'When,' says Diderot, 'one considers oneself and
compares one's talents with those of a Leibniz, one is
tempted to throw books away and seek some hidden
corner of the world where one may die in peace. < This
man's mind was a foe of disorder : the most entangled
things fell into order when they entered it. He com-'
bined two great qualities which are almost incompatible
with one another — the spirit of discovery and that of
method ; and the most determined .and varied study,
through which he accumulated knowledge of the most
widely differing kinds, weakened neither the one quality
nor the other. In the fullest meaning these words can
bear, he was a philosopher and a mathematician V
1 Encyclopedic, (Euvres (Assezat's ed.), vol. xv. p. 440.
C

1 8 INTRODUCTION

The Works of Leibniz.

Many of the most important philosophical works of
Leibniz were not published till after his death. Large
quantities of manuscript were preserved in the Royal
Library at Hanover, and successive editors have con-
tinually drawn upon it for publication. The chief editions
of the philosophical works are that of Erdmann (1840)
and that of Gerhardt (1875-90), the latter being the
most complete. In 1866 Janet published an edition in
French, containing the principal works as they are given
in Erdmann, with the addition of the correspondence
between Leibniz and Arnauld, which had not been pub-
lished when Erdmann's edition appeared. The mathe-
matical works were published by Gerhardt in seven
volumes (1850-63). Of the historical and political works
Onno Klopp published ten volumes (1864-77). Toucher
de Careil also published in seven volumes (1859-75)
some of Leibniz's political works, along with his corre-
spondence on the reunion of Christendom and his writings
in connexion with the founding of academies. In addition
to these may be mentioned the old edition of Dutens in
six volumes (1768), which contains some things not in-
cluded in any of the others, and the booklet of Mollat
(1885), containing some papers of Leibniz on ethics and
jurisprudence.

The following are the principal philosophical works of
Leibniz, with the dates at which they were written or
published. The letters J. S. indicate those which appeared
in the Journal des Savants, and the letters A. E. those
which appeared in the Acta Eruditorum. Those marked
with an asterisk were published in Leibniz's lifetime.

Correspondence with Philipp and others regarding the Philosophy of Descartes,
1679-80. (In French.) G. iv. 281 sqq.

*Medifationes de Cognitione, Vcritate et Ideis, A. E. 1684. G. iv. 422 ; E. 79.

Correspondence icith Arnauld, 1686-90. (In French.) G. ii. i. Pub-
lished by Grotefend, 1846.

LIFE AND WORKS 19

*Extrait d'une Lettre a M. Bayle. Published in the Nouvelks de la

Republique des Lettres, 1687. G. iii. 51 ; E. 104.

De Vera Methodo Philosophiae et Theologiae, 1690. G. vii. 323 ; E. 109.
*Si I'Essence du Corps consiste dans I'Etendue, J. S. 1691 and 1693.

G. iv. 464; E. 112.
Animadversiones in partem generalem Principiorum Cartesianorum, 1692.

Published by Guhrauer, 1844. G. iv. 350. Mentioned by

Leibniz in a letter to Bernouilli, 1697.
*De Notionibus Juris et Justitiae, preface to Codex Juris Gentium Diplo-

maticus, published in 1693. E. 118.
*De Primae Philosophiae Emendatione et de Notione Substantiae, A. E. 1694.

G. iv. 468 ; E. 121.
*Systeme Nouveau de la Nature et de la Communication des Substances,

J. S; 1695. G. iv. 471 ; E. 124. Also three Eclaircissements du

Nouveau Systeme, J. S. 1696.
Schreiben an Gabriel Wagner vom Nutzen der Vernunftkunst oder Logik,

1696. Published by Guhrauer, 1838. G. vii. 514 ; E. 418.
De Eerum Originatione radicali, 1697. G. vii. 302; E. 147. Published

by Erdmann, 1840.
*De ipsa Natura, sive de Vi insita Actionibusque Creaturarum, A. E. 1698.

G. iv. 504 ; E. 154.
Various papers (without titles) on Cartesianism, written between

1700 and 1702. G. iv. 393 sqq. ; E. 177.
Considerations sur la Doctrine d'un Esprit Universel unique, 1702. G. vi.

529 ; E. 178. Published by Erdmann, 1840.
Sur ce qui passe les Sens et Id Matiere (Letter to Queen Sophia Charlotte

of Prussia), 1702. G. vi. 488.
Nouveaux Essais sur VEntendement humain, 1704. G. v. 41 ; E. 194.

Published by Raspe, 1765.
* Considerations sur les Principesde Vie et sur les Natures plastiques (Histoire

des Ouvrages des Savants, 1705). G. vi. 539 ; E. 429.
Ad rev. Patrem des Bosses Epistolae 71, 1706-16. G. ii. 291 ; E. 434, &c.

E. gives 29 only. Dutens gives 70.
De Modo distinguendi Phaenomena realia ab imaginariis. G. vii. 319 ;

E. 443-
Animadversiones ad Joh. G. Wachteri Librum de recondita Hebraeorum philo-

sophia, c. 1708 (including the 'Refutation of Spinoza'). Pub-
lished by Foucher de Careil, 1854.
Commentatio de Anima Brutorum, 1710. G. vii. 328 ; E. 463. Published

by Kortholt, 1735.
* Essais de Theodicee sur la Bonte de Dieu, la Liberte de I'Homme et I'Origine

du Mai, 1710. G. vi. i ; E. 468.
Von der Gluckseligkeit, 1710 (?). G. vii. 86 ; E. 671. Published by

Guhrauer, 1838.

C 2

20 INTRODUCTION

Principes de la Nature et de la Grace, fondes en Raison, 1714. G. vi. 598 ;

E. 714. First published in L'Europe Savante, Nov. 1718.
La Monadologie, 1714. G. vi. 607 ; E. 705. Germ, trans. Kohler

(Jena), 1726. Lat. trans. A. E. 1721. Original French in E.

1840.
Correspondence with Nicholas Remond, 1713-16. (In French.) G. iii.

599 ; E. 701, &c.
Correspondence with Bourgiiet, 1709-16. (In French.) G. iii. 539;

E. 718, &c.
Correspondence with Clarke, 1715-16. (In French.) G. vii. 347 ;

E. 746.

PART II.

GENERAL PRINCIPLES OF THE PHILOSOPHY OF LEIBNIZ.

Statement of Leibniz's Problem : How can that which is
continuous consist of indivisible Elements ?

IN the preface to his The'odice'e1 Leibniz declares that
* there are two famous labyrinths, in which our reason
often goes astray : the one relates to the great question
of liberty and necessity, especially in regard to the
production and origin of evil ; the other consists in the
discussion of continuity and of the indivisible points which
appear to be its elements, and this question involves the
consideration of the infinite. The former of these perplexes
almost all the human race, the latter claims the attention
of philosophers alone/ Accordingly, while a right under-
standing of the principle of continuity is of the utmost
speculative importance, the practical value of a true
knowledge of necessity is equally great. Thus, Leibniz
makes his Theodicee an investigation of the meaning of
liberty and necessity, while in others of his writings he
oifers a solution of the problem which he describes as the
special perplexity of philosophers.

It is this latter problem with which we are here mainly
concerned. The philosophical work of Leibniz was an
endeavour to reconcile the notion of substance as con-
tinuous with the contrary notion of substance as consisting
of indivisible elements. The opposition of these two notions
1 E. 470 a ; G. vi. 29.

22 INTRODUCTION

seemed to him to arise from an inadequate conception of
substance, and the task he set himself was that of
deepening the current notion of substance, or, as he him-
self would have put it, finding a better hypothesis than
that which had satisfied his Cartesian predecessors.

Stated in another way the problem is : How are we to
interpret the relation of whole and parts so that the
continuity or complete unity of the whole shall not be in
conflict with the definiteness or real diversity of the
parts ? To say that the whole is continuous or really one
seems to mean that, if it is divisible at all, it is infinitely
divisible. If it were not infinitely divisible, it would
consist of insoluble ultimate elements, and would thus be
discontinuous. Accordingly, if the whole be really con-
tinuous there seem to be no fixed boundaries or lines of
division within it, that is to say, no real, but only
arbitrary parts \

On the other hand, if the whole consists of real parts
and not merely possible subdivisions, these parts must
be definite, bounded, separate from one another, and
consequently the whole which they constitute must be,
not a real continuous unity, but a mere collection or
arbitrary unity. Nevertheless, we cannot hold either that
the whole is real and the parts unreal, or that the parts
are real and the whole unreal.

Quantitative or extensive Notion of Substance held ly Des-
cartes and Spinoza, on the one hand, and ly the Atomists
on the other.

The philosophy of Spinoza, with its cardinal principle
that * Determination is negation,' practically amounted
to an assertion of the unity and continuity of the whole
at the expense of the reality of the parts. According to

1 For instance, the spectrum is continuous. There is no limit
to the number of varieties of colour that may be discriminated in
the rainbow : the usual division into seven colours is an arbitrary
arrangement made by observers. It probably originated in a sug-
gested analogy with the musical scale.

GENERAL PRINCIPLES 23

Spinoza, 'substance ' is ' that which is in itself and is
conceived through itself; in other words, that, the
conception of which does not need the conception of
another thing from, which it must be formed V That
is to say, substance is the unconditioned, or that which
is not conditioned or determined by anything other
than itself. There is ambiguity in the statement. It
may mean e'ither that substance is sel£conditioned or
that it is absolutely unconditioned, to the exclusion of all
determination. In the one case substance would be a
real system of reciprocal determinations ; in the other, it
would be unbroken being, to which every determination
is foreign. The latter is the dominant aspect of substance
in the philosophy of Spinoza. That aspect alone is con-
sistent with the principle that i Determination is negation.'
Consequently his position amounts to saying that sub-
stance can have no real parts. For the very meaning of
a part implies that it must be determined or conditioned
by other parts 2.

In contrary opposition to this, there is the theory of
atoms and the void, which Leibniz tells us at one time
charmed his imagination 3. To affirm the real existence
of indivisible material atoms is to deny the infinite
divisibility of matter. Accordingly, if the atoms con-
stitute the ultimate reality of the world, its unity is
destroyed, its continuity becomes an illusion. However
numerous the atoms may be, they can together constitute
no true unity, i but only a collection or heaping up of
parts ad infinitum4.' Atomism thus endeavours to establish
the reality of the parts at the expense of the whole.

It is necessary, then, to lay bare the presuppositions
of these contrary theories in order to find the elements of
truth in each and to reconcile them in a more compre-
hensive view. The doctrine of Spinoza is the consistent

1 Ethics, Part i. def. 3, Hale White's Tr.

2 Ibid. Part i. prop. 12 and 13.

3 New System, § 3. * Loc. cit.

24 INTRODUCTION

logical development of the principles involved in the
position of Descartes1. In this connexion it is Descartes's
special theories that Leibniz has mostly in view, although
his arguments are equally applicable to the more thorough
metaphysic of Spinoza. ' Spinoza,' he tells us, 'has done
nothing but cultivate certain seeds of the philosophy of
M. Descartes2.' Descartes endeavoured to reach absolute
metaphysical certainty by a method which was after-
wards more clearly and fully applied by Spinoza, who
denned it in his great principle that l Determination is
negation/ The essence of Descartes's method of doubt
is the endeavour to attain certainty by stripping from
experience (as it is given in common consciousness) all
specific qualities or determinations, on the ground that
no contradiction in terms is involved in regarding each of
these qualities by itself as non-existent or other than it
is. The result of the method is to give, as the residual
ultimate certainty, nothing but the instrument by which
the process of stripping has been carried out, viz. the

1 ' Cartesianae disciplinae intemperantia Spinozae doctrinam par it ; in
hoc sententia totum reperire est Leibnitium ' (Lemoine, Quid sit materia
apud Leibnitium, p. 52). ; The philosophy of Descartes . . . seems to
lead straight to the opinions of Spinoza, who dared to say what
Descartes carefully avoided.' (G. iv. 3464)

a Lettre a I' Abbe Nicaise (1697) (E. 139 h; G. ii. 563). Leibniz,
especially in his earlier days, recognized that his philosophy had
much in common with that of Spinoza., although, as time went on,
it became more and more evident to him that they were funda-
mentally at variance. Thus, in an early letter (February, 1678), we
find Leibniz writing: 'I find in it' [the Ethics] 'plenty of fine
thoughts agreeing with mine, as is known to some of my friends
who are also friends of Spinoza. But there are also paradoxes
which seem to me unreal and not even plausible. As, for example,
that there is only one substance, namely God ; that created things
are modes or accidents of God ; that our mind has no wider outlook
[nihil amplius percipere~\ after this life ; that God Himself thinks
indeed, but nevertheless neither understands nor wills , that all
things happen by a certain necessity of fate ; that God acts not for
an end but by a certain necessity of nature, which is verbally to
retain, but really to give up, providence and immortality^; I regard
this book as a dangerous one for people -yrho will give themselves
the trouble to go deeply into it, for others do not care to under-
stand it.' Archivfur Geschichte d. Philosophic, vol. iii. p. 75.

GENERAL PRINCIPLES 25

thinking Ego, without any specific thought. If we
challenge the reality of this instrument, we do so by
means of the instrument itself, and so involve ourselves
in self-contradiction. The thinking Ego cannot be thought
non-existent : to think its non-existence would be a con-
tradiction in terms-. Spinoza's advance upon1 this was
merely to pass from Descartes's practical method of
attaining truth (namely, the discarding: of specific deter-
minations) to the general metaphysical principle which
the method implied, the principle, namely, that the
essence or reality of a thing is that which remains after
the differences in its states and qualities have been
thought away, or that which is common to all its forms
and manifestations, and consequently that the ultimate
reality or substance is that which is free from all specific
determinations, that which includes or is common to
everything because it is not (specially) anything.

Now when we rigorously apply this principle,, that the
reality of substance is that which remains after all
specific or differential qualities have been removed, we
are left with nothing but quantity — either, as in. the case
of Spinoza, quantity of substance in general l ; or, as
in the case of Descartes, quantity of a specific substance,
that is to say quantity of one quality. Thus Descartes's
position is that in addition to the one true and perfect
substance, God, whose existence is externally uncon-
ditioned, there are two created substances, whose exis-
tence is not conditioned by anything finite, but by infinite

1 It is true that Spinoza regards substance as indivisible, in the
sense that it has no real parts ; and this may seem inconsistent
with the contention that Spinoza's substance is merely quantita-
tive. But the contradiction is Spinoza's : it is a fragment of the
great fissure of inconsistency that traverses his whole system,
namely, the confounding of a substance possessing infinite attri-||
butes with a substance whose reality is reached by the exclusion |1
of all specific determinations. If we hold strictly to the second of
these views of substance, then substance can be said to be in-
divisible only on the ground that there is nothing to divide. Cf.
Spinoza, Ethics, Part i. prop. 12 and 13, with Tractatus de Intettectus
Emendations, 108, ii. iii.

26 INTRODUCTION

substance alone. These are bodily substance and think-
ing substance. They are mutually opposite : the one is
what the other is not. Neither is conditioned by the
other nor dependent upon it. The essential attribute
of bodily substance is extension, that of thinking sub.
stance is thought. All the specific qualities of created
things are reducible to one or other of these as a common
quality ; and consequently the essence or reality of
created substance comes to be either extension without
specific contents or thought without a specific object.
In other words, bodily substance is quantity of one
determination, namely extension ; while thinking sub-
stance is quantity of one other determination, namely
thought. Thus the presupposition of the Cartesian
systems is a purely quantitative relation of whole and
parts \

The same presupposition in another form underlies
the Atomist philosophy. The atoms are material par-
ticles, and the whole consists of their aggregation. If
the theory is self-consistent they must be regarded as

1 Cf. Descartes, Principia, Part ii. § 8 : ' Quantity and number
differ only in thought [ratione] from that which has quantity and
is numbered.' § 1 1 : 'It will be easy to discern that it is the same
extension which constitutes the nature of body as of space, and
that these two things are mutually diverse only as the nature of
the genus and species differs from that of the individual, provided
we reflect on the idea we have of any body, taking a stone for
example, and reject all that is not essential to the nature of body.
In the first place, then, hardness may be rejected, because if the
stone were liquefied or reduced to powder it would no longer
possess hardness, and yet would not cease to be a body ; colour also
may be thrown out of account, because we have frequently seen
stones so transparent as to have no colour ; again, we may reject
weight, because we have the case of fire, which, though very light.
is still a body ; and finally, we may reject cold, heat, and all the
other qualities of this sort, either because they are not considered
as in the stone, or because, with the change of these qualities, the
stone is not supposed to have lost the nature of body. After this
examination we shall find that nothing remains in the idea of
body, except that it is something extended in length, breadth, and
depth ; and this something is comprised in our idea of space, not
only of that which is full of body, but even of what is called void
space' (Veitch's Tr.). Cf. Principia, Part i. §§ 51-53, 63-65.

GENERAL PRINCIPLES 27

homogeneous, and the specific qualities of things must
arise from the variety of their combinations. They could
not all really exist and be different from one another
without some of them being complex. And in any case
the very essence of the theory is that the whole should
be taken as a sum or totality, a quantity of parts.

Leibniz's non-quantitative or intensive Notion of Substance,

developed through criticism of Cartesian andAtomist views

regarding material Substance.

Accordingly, the essence of Leibniz's argument is
that a quantitative conception of the relation of whole
and parts aifords an inadequate theory of substance.
The common element in the contrary positions of the
Cartesians and the Atomists is the explicit or implicit
reduction of qualitative to quantitative differences \ And
it appears to Leibniz that the solution of the dilemma , /
is to be found in the opposite hypothesis, namely, that
the essence of substance is non-quantitative, and that
the relation of whole and parts must be conceived as <jO
intensive rather than extensive. Thus a 'simple sub-
stance' has no parts, i.e. no quantitative elements2, ^
and yet it must comprehend a manifold in unity 3 ; that
is to say, it must be real, it must be something, it must
be qualitative, specifically determined.

While the general principle of Leibniz's argument
may be stated in this way, he actually develops it through
criticism of Descartes's theory of material substance. To
regard matter as ultimately pure extension is to make
it essentially a substance with nothing more than a
shadow of quality. An extended nothing is meaningless.
An extended something must have quality. And to call

1 The mechanical view of things 'has two forms: Cartesianism
and Atomism. . . . The one, which makes matter continuous, may
be called geometrical mechanism ; the other, which makes it dis-
continuous, may be called arithmetical mechanism.' E. Boutroux,
La Monadologie de Leibnitz, &c., p. 36.

2 Monadology, § i. 3 Ibid. § ra.

28 INTRODUCTION

that quality extension itself is merely to cover up the
difficulty with a name : an extended extension is much
the same as a shaded shadow of nothing. 'In my
opinion corporeal substance consists in something quite
other than being extended and occupying a place : we
must, in fact, ask ourselves what it is that occupies the
place1.' 'Those who hold that the extended is itself
a substance transpose the order of the words as well as
of the thoughts. Besides extension there must be an
object which is extended, that is to say a substance
which can be repeated or continued. For extension
means nothing but a repetition or a continued multi-
plicity of that which is spread out, a plurality, continuity,
and coexistence of parts ; and consequently it [extension]
is not sufficient to explain the very nature of extended
or repeated substance, the notion of which is anterior
to that of its repetition V

Again, it cannot be said that pure extension has any
real parts. There can be no real unit of mere extension 8.
It would be an erroneous conception to regard mathe-
matical surfaces as made up of real lines, and these lines
as made up of real points. The line is the limit of the
surface, and the point is the limit of the line. A mathe-

1 Epistolaad Schuleriburgium (1698) (G. Math. vii. 242).

3 Extrait d'une lettre (1693) (E. u^b ; G. iv. 467). Cf. Lotze, Micro-
cosmws, bk. iii. ch. 4, § 2 t^Eng. Trans, vol. i. p. 356). Cf. also Examen
des principes du R. P. Malebranche (c. 1711) (E. 691 a ; G. vi. 580):
' Ariste. But do you not think that the destruction of extension,
which carries with it that of body, proves that body consists only
in extension ? Philarete. It proves only that extension enters into
the essence or nature of body ; but not that it constitutes its whole
essence. Similarly, magnitude enters into the essence of extension,
but is not equivalent to it ; for number, time, motion have also
magnitude, and yet they are not extension.' Also (E. 693 -b ; G. vi.
584) : ' Extension is nothing but an abstraction and requires some-
thing which is extended. ... It presupposes some quality, some
attribute, some nature in the thing, which quality extends or
diffuses itself along with the thing, continues itself.'

3 'You are right in saying that all magnitudes [grandeurs'] may
be divided ad infinitum. None of them is so small that we cannot
conceive in it an infinity of divisions which will never be exhausted.'
Lettre a Foucher (1692) (E. 115 a ; G. i. 403).

GENERAL PRINCIPLES 29

matical point may, then, be regarded as indivisible, but
only because there is nothing in it to divide. It cannot
be a real unit, for there is nothing to determine its unity.
We should have to conceive it as the unit of that whose
sole characteristic is to consist of units, to be a quantity.
For such is, strictly speaking, the nature of Descartes's
' extension.' Thus, as Leibniz puts it, ' mathematical
points are exact ' [i. e. indivisible] ; * but they are only
modalities1,' that is to say abstractions and not real
existences 2.

Now, while Leibniz regards the parts of Cartesian
extension as thus indivisible without being real, he
maintains on the other hand that the parts to which
Atomism reduces material substance are real only if
they are not indivisible. Their claim to be indivisible
rests upon the supposition that they are infinitely hard.
But hardness is a relative term. There is no absolute
hardness, as there is no absolute motion or rest. And
thus infinite hardness is a self-contradictory conception.
'By an atom,' says Leibniz, 'I understand a corpuscle,

1 New System, § n.

2 Cf. Epistola ad Bernoullium (1698) (G. Math. iii. 535) : 'Indeed
many years ago I proved that a number or sum of all numbers
involves a contradiction, if it be taken as one whole. And the
same- is true of an absolutely greatest number and an absolutely
least number or an absolutely smallest fraction. . . . Now, just as
there is no (given) numerical element or smallest part of unity or
least among numbers, so there is no (given) least line or lineal
element ; for a line, as a unity, can be cut into parts or fractions. . . .
Suppose that in a line there are actually £, £, |, ^ ^, &cv an<*
that all the terms of this series actually exist. You infer from
this that there is also an absolutely infinite term, but I think
nothing else follows from it than that there actually exists any
assignable finite fraction, however small. . . . And indeed I conceive
points, not as elements of a line, but as limits, or negations of
further progress, or as ends [termini] of a line.' Cf. Lettre a Foucher
(1693) (E. n8a; G. i. 416). 'As to indivisible points in the sense •
of the mere extremities of a time or a line, we cannot conceive in
them new extremities, nor parts, whether actual or potential.
Thus points are neither large nor small, and no leap is needed to
pass them. Yet the continuous, though it has everywhere such
indivisible points, is not composed of them.' Cf. Explanation of the
New System, i, note.

30 INTRODUCTION

mentally divisible indeed, but which actually neither is
nor has been divided. Not that it cannot be actually
divided ; for such atoms do not occur, since they would
demand perfect hardness. But it suffices for my defini-
tion that there should be corpuscles, whose particles have
never been separated, from the foundation of the world
to the present day1/ Every material atom must be at
least ideally divisible, if it be real. ' The atoms of matter
... are still composed of parts, since the invincible
attachment of one part to another (if one could rationally
conceive or suppose it) would in no way destroy their
diversity2.'

How the Relation of Whole and Parts is to ~be conceived.
The real and indivisible Unit of Substance (Monad\
'Perception ' and l Appetition.'

Leibniz's problem thus takes the form of an attempt
to find a unit of substance which shall avoid the imper-
fections of both the Cartesian and Atomist theory. This
unit must be at once real and indivisible. Its reality
must be of such a kind that it does not conflict with its
indivisibility, and it must be indivisible in a sense which
is consistent with the continuity of the whole. The basis
of its reality cannot be quantity, for no quantity is
indivisible. And its indivisibility cannot be exclusive
particularity in space or time, for indivisible points in
space or time may form an aggregate but cannot become
a continuum. The unit of substance must then be inten-
sive rather than extensive, and the continuity of the
whole must be not a mere empty homogeneity, but a

1 Epistola ad Bernoullium (1697) (G. Math. iii. 443).

8 New System, § n. Cf. Lettre a Hartsoeker (1710) (G. iii. 507) :
'Nothing is large or small, except hy comparison, so that such
a particle as an atom is as considerable in itself, and in relation to
others proportionately less (and consequently, in the sight of God),
as our visible system is considerable in relation to it. Atoms are
the effect of the weakness of our imagination, which likes to rest
and to hasten to an end in subdividing or analyzing. It is not so
in nature, which comes from infinity and goes to infinity.'

GENEKAL PKINCIPLES 31

continuity through infinite degrees of intension. The
word 'intension,' however, does not help us much. It
must be more precisely defined.

The antinomy between whole and parts, which was
the issue of the quantitative or extensive view of sub-
stance, had its roots in the conception of whole and parts
as inevitably exclusive of one another, the whole being
regarded as prior to the parts or the parts as prior to the
whole. That is to say, either, as in the view of Spinoza,
the parts are to be deduced, in a purely analytic way,
from the whole as self-evidently given, or, as in the
Atomist doctrine, the whole is a secondary construction,
of a purely synthetic kind, from the primary parts. In
contrast with this the intensive doctrine of substance
which regards determination as primary or essential
amounts to a declaration that whole and part are in-
separable. All specific determinations, states, or func-
tions are determinations, states, or functions of the whole,
not in the sense that they are ultimately reducible to one
vague determination which is common to everything, but
in the sense that the whole is expressed, symbolized, and
therefore in some way included in each, however specific,
individual, limited it may be. Thus the parts are not
determined or characterized without reference to the
whole, and the whole is not a mere vague aggregate of
independent parts. In some sense each part must con-
tain the whole within itself, each unit must include an
infinite manifold. The whole stands not merely in a
mechanical, but in a dynamic relation to the part. The
whole is not merely other than the part, but in some
way passes into it and expresses itself through it. That,
in general, is the conception of substance as essentially
intensive rather than extensive.

There is here an approach to the modern conception of
organism as more adequate to the expression of substance
than are merely mechanical conceptions \ But the special

1 Leibniz does hold that all real substances are organic (cf. p. 108).

32 INTRODUCTION

angle at which Leibniz regards his problem prevents him-,
from developing this. His early imaginative liking for
'atoms and the void,' when first he 'freed himself from
the yoke of Aristotle1,' the love of historical system and
of well-grounded hypothesis which set his whole intel-
lectual character in revolt against Spinoza's abstract unity
and his purely a priori deductions, probably also the
influence of his Scholastic training with its suggestions
of an infinite multiplicity of 'substantial forms' — all
resulted in a tendency to emphasize rather the elements
of reality than its wholeness. That there can be no real
whole without real units, is Leibniz's guiding thought 2,
and accordingly his question does not primarily take the
form : ' What must be the nature of a whole which
expresses itself in each of its parts ? ' It rather is :
' What must be the nature of a part or unit which can in
some way contain or express the whole within itself ? '

Now the part cannot contain the whole within itself
actually and fully, in all its realized completeness ; for
thus the distinction between whole and part would
vanish. The part must, therefore, contain the whole
potentially and ideally or by means of representation.

The relation of whole and parts is not to be conceived
as one of greater and less, of thing containing and things

But the notion of organism, as .he uses it, is much more vague than
it has since become. According to Leibniz anything is an organism
if it has a ' soul ' or principle of unity, that is to say, if it is other
than a mere aggregate of independent elements.

1 New System, § 3.

2 Cf. Lettre a Arnauld (1687) (G. ii. 97) : < Every machine pre-
supposes some substance in the pieces from which it is made, and
there is no manifold without real units. In short, I take as
axiomatic this identical proposition, in which the difference is
entirely a matter of accent, namely, that what is not really one
On] being is^not really a [un~\ being. It has always been thought
that unity [run] and being are reciprocal things. " Being" is one
thing, « beings" is another; but the plural presupposes the
singular, and where there is not one being there will still less be
several, beings.' « Being and unity are convertible terms [ens et
unum convertuntur]: Epist. ad des Bosses (1706) (E. 435 b ; G. ii. 304).
The phrase is used by Nicholas of Cusa, De docta ignorantia (1440), ii. 7.

GENERAL PRINCIPLES 33

contained, but rather as a relation of symbolized and
symbols, sign and thing signified. That is to say, the
part must be a representation of the whole from some
particular point of view, a symbol or expression of the
whole, and the part must .contain the whole in such
a way that the whole might be unfolded entirely from
within it \

Thus the part must have a certain spontaneity or power
of acting from within itself, and in virtue of this Leibniz
describes the individual substance as essentially a * force*
rather than a quantity. This intensive essence or force
in the part (or individual substance) .appears in two ways.
As representative or symbolic of the whole, the part, in
Leibniz's terminology, has 'Perception,' while, in so far
as in the part the potential whole tends to realize itself,
the part is said -to have ' Appetition.' Both of these
characteristics must belong to it, for, if it had perception
alone, the part would merely represent one aspect of the
whole, like an unchanging picture. It is in virtue of its
appetiti6n that the part is able to realize the life of the
whole, to unfold spontaneously from within itself all the
variations of that which it represents 2.

This new atom or unit of substance (the 'simple
substance' in his own phrase) Leibniz calls ,a Monad3.

1 Although, as a matter of fact, it never is so unfolded. Prae-
dicatum inest subjecto ; but, in the case. of any actual thing, to develop
the predicate out of the subject would involve an infinite analysis.
We here touch a fundamental inconsistency in Leibniz's thought.

2 Cf. De Anima Brutorum, 12 (E. 464 b ; G. vii. 330) : ' Not only is
the variety of the object represented in that which has perception ;
but there is also variation in the representation itself, since that
which is to be represented varies.'

3 Cf. Epistola ad R. C. Wagnerum (1.710) (E. 466 a ; G. vii. 529) :
'. . . Monads, and, so to speak, metaphysical atoms, without parts.'
Also Replique aux Reflexions de Bayle (1702) (E. 186 b ; G. iv. 561) :
'In fact, I regard souls, or rather Monads, as atoms of substance,
since, in my opinion, there are no atoms of matter in nature and the
smallest portion of matter has still parts.' See also New System,
§§3 and n. Leibniz says that he applies the term ' Monad' to the
simple substance, because it is unum per se. De ipsa natura (1698)
(E. 158 a ; G. iv. 511). But * Monads are not to be confounded with
atoms. Atoms (as people imagine them) have shapes; Monads no

34 INTRODUCTION

The word is almost as old as European philosophy, and
has varied greatly in meaning and application. • Shortly
before the time of Leibniz the term was used by Giordano
Bruno, whose Monads were ultimate spherical points,
regarded as possessing both spiritual and material charac-
teristics. There are some parts of the philosophy of
Bruno with which the doctrine of Leibniz has affinity,
as, for instance, Bruno's contention that there is nothing,
however little or valueless, that does not contain in it
life or soul. But Leibniz repeatedly attacks the doctrine
of a world-soul, which is Bruno's central conception.
Thus, in adopting the term 'Monad,' Leibniz may be said
to have taken from Bruno little more than the name \

The Monad, then, has perception, but not necessarily
in the sense of consciousness. For consciousness is not
the essence of perception, but merely an additional
determination belonging to certain kinds or degrees of
, perception. Conscious perception is called by Leibniz
' Apperception.' But the essence of perception in general
is that in it we have a unity variously modified or a unity
.which appears in a multiplicity of relations. 'I have
many ideas [ Vorstellungen], wealth of thoughts is in me ;
and yet I remain, in spite of this variety, one2.' But
it is not necessarily because I am conscious of many
thoughts or many objects that I 'perceive' and thus
exhibit a multiplicity in unity. All representation is

more have a shape than souls have. They are not parts of bodies,
but presuppositions of them.' Epistola ad Bierlingium (1712) (G-.
vii. 503).

1 Professor Ludwig Stein, in his Leibniz und Spinoza, has shown
that the term * Monad ' was actually suggested to Leibniz, not by
the writings of Bruno, but by Leibniz's contemporary, Fra^ois
Mercure Van Helmont (1618-1699), with whom he had much
intercourse and considerable correspondence. 57 novas to the Greek
meant simply the unit in arithmetic. Leibniz himself attributes
the term to Pythagoras. In the sense of a numerical unit it occurs
in Plato (Philebus, 15 B ; Phaedo, 105 C, 101 E). But Leibniz's chief
forerunner in the use of the term was Bruno. It is also used by
Nicholas of Cusa.

3 Hegel, Geschichte der Philosophic, iii. 412.

GENERAL PRINCIPLES 35

perception \ Similarly, the Monad has appetition, but
not necessarily in The sense of conscious desire or will. 4
As the essence of perception is multiplicity in unity, so
the essence of appetition is change jwithin the identity
or permanence of a simple substance. Appetition is ' the ^
action of the internal principle which produces change
or passage from one perception to another2.' As the
Monads alone are real, every change in nature must be
change within a Monad. This change, as we have seen,
must be the unfolding of the whole which the Monad
potentially contains or represents. That is to say, it
must be the passing from one perception (or state of
representation, whether conscious or unconscious) to
another. And thus, wherever there is change there is
appetition. It is simply another name for the spon-
taneity of the Monad, its power of unfolding its whole
nature and experience from within itself. The Monad
as perceptive is thus a universal within, rather than
exclusive of, the particular, while as appetitive it is
dynamic and not static 3.

1 Cf. p. 135. Also Epistola ad E. C. Wagnerum (1710) (E. 466 a ;• '
G. vii. 529) : l This correlation of the internal and external, or
representation of the external in the internal, of the compound in
the simple, of multiplicity in unity, really constitutes perception.'
In a letter to Arnauld (1687) (G. ii. 112) Leibniz says that 'ex-
pression is a genus of which natural perception, animal feeling,
and intellectual knowledge are species. In natural perception
and feeling, it is enough that what is divisible and material, and
is actually dispersed among several beings, be expressed or repre-
sented in a single indivisible being or in substance which has
a genuine unity.'

a Monadology, § 15.

3 'We could not say in what the perception of plants consists,
and even that of animals is not well conceived by us. Yet,
according to the general sense I give to these words, in order that
there may be a perception, it is enough that there should be
a variety in unity ; and in order that there may be appetition it is
enough that there should be a tendency to new perceptions.'
Letlre a Bourguet (1715) (E. 732 b ; G. iii. 581). ' The soul has
perceptions and appetitions, and its nature consists in these.
And as in body there are understood to be avrnvma. and figure of
some kind, although we do not know what are the figures of
imperceptible bodies ; so in the soul there are understood to be

36 INTRODUCTION

As the Monads are purely intensive centres or units,
each must be absolutely exclusive of all others. Not
being quantitative, they are simple, in the sense of
having no parts1; and thus no one Monad can include
another. Further, no Monad can really influence another
or produce any change in it. For that would mean
a transference of quality from one to the other. But
as the quality of a substance, being its very essence, is
inseparable from it, such a transference is impossible2.
The Monads are also real ultimate elements, because,
being entirely non- quantitative, they cannot have been
formed out of any combination of simpler elements, nor
is it possible in any way to dissolve them, as they are
without parts3. The point which is at once real and
indivisible has thus (Leibniz thinks) been found in the
Monad, as contrasted, on the one hand, with the mathe-
matical point of Descartes, which is indivisible only
when it ceases to be real, and, on the other hand, with
the physical point of the Atomists, which, if it is real,
must always be divisible l.

>L The Identity of Indiscernibles and the Law of Continuity.

The indivisible having thus been established, there
remains the question of continuity and the infinite. As
we have seen, a quantitative continuum cannot have
indivisible parts. But, as the actual indivisible elements
of reality are essentially perceptive, real continuity must
also be a continuity of perception. As each Monad is
a part or element of the universe, in the sense that each
represents it or reflects it as in a mirror from some
particular angle, in some special aspect, the whole must

perception and appetition, although we do not distinctly know
the imperceptible elements of the confused perceptions, by which
the imperceptible elements of bodies are expressed.' Epistola ad
Bierlingntm (1711) (E. 678 a ; G. vii. 501).

1 Monadology, § i. 2 Ibid. § 7.

3 Ibid. §§ 3-6.

* As to the contrast between Leibniz's view of substance and
that of Locke, see Locke's Essay, Fraser's ed, . vol. i. pp. 399 sqq.

ty

GENERAL PRINCIPLES 37

be the infinite totality of Monads, representing the
universe from every possible point of view. And thus,
while the Monads are entirely separate from one another,
each must represent the universe in a way which differs
to the least possible extent from the representation given
by some other. No two Monads (and a fortiori no two Y
things, which are all aggregates of Monads; can be exactly y
the same : no thing can have a merely numerical differ- *"""
ence from another. The Monads are essentially non-
quantitative, and number by itself is merely a measure
of quantity. The Monads differ from one another in
quality or intension alone, so that two Monads not
differing in quality are impossible. This is the doctrine
of Leibniz which is usually called the

cerniblesV It is simply his law of continuity in a ^
negative form. The number of Monads must be in-
finite 2 : otherwise the universe would not be represented
from every possible point of view, and would thus be
imperfect. But if the number of Monads is infinite, and
if every Monad differs in quality from every other, then
the Monads must be such that they might be considered
as a series, each term or member of which differs from
the next by an infinitely small degree of quality, i. e. by
a degree of quality less than any which can be assigned. •1>-
Leibniz explains his principle of continuity in a letter y
quoted by his biographer, Guhrauer3. *I think, then,'

1 < There are no two indiscernible individuals. A clever gentle-
man of my acquaintance, talking with me in presence of Mme. the
Electress, in the garden of Herrenhausen, was of opinion that he
could quite well find two leaves entirely alike. Mnie. the Electress
would not believe it, and he spent a long time vainly seeking them.
Two drops of water or of milk, looked at through a microscope, will
be found discernible. This is an argument against atoms, to which,
no less than to the void, the principles of true metaphysic are
opposed ... To suppose two indiscernible things is to suppose the — •
same thing under two names.' IF"*5 Lettre a Clarke, §§4 and 6
(E. 755 b, 756 a ; G. vii. 372). Cf. Nouveaux Essais, bk. ii. ch. 27, § 3
(E. 277 b ; G. v. 214).

2 Du Bois-Reymond compares the infinite series of Monads to
the ordinates of a curve, which grow from nothing to infinity.

3 G. W. F. von Leibnitz, eine Biographic, vol. i., Anmerkungen, p. 32.

38 INTRODUCTION

he says, ' that I have good reasons for believing that all
the different classes of beings, the totality of which forms
the universe, are, in the ideas of God, who knows
distinctly their essential gradations, merely like so many
ordinates of one and the same curve, the relations of
which do not allow of others being put between any two
of them, because that would indicate disorder and imper-
fection. Accordingly men are linked with animals, these
with plants, and these again with fossils, which in their
turn are connected with those bodies which sense and
imagination represent to us as completely dead and inor-
ganic [informes]. But the law of continuity requires that,
when the essential determinations of any being approximate to
those of another, all the properties of the former must gradually
approximate to those of the latter. Therefore all the orders
of natural beings must necessarily form only one chain,
in which the different classes, like so many links, are so
closely connected with one -another that it is impossible
for sense or imagination to determine exactly the point
where any one of -them begins or ends ; all the species
which border upon or which occupy, so to speak, dis-
putable territory [regions d" inflexion et de rebroussement ']
being necessarily ambiguous and endowed with charac-
teristics which may equally be ascribed to neighbouring
species. Thus, for instance, the existence of zoophytes,
or, as Buddeus2 calls them, Plant- animals, does not imply
monstrosity, but it is indeed agreeable to the order of
nature that they should exist. And so strongly do I hold

The Academy of Berlin declared this letter to be spurious ; but
there seems no good reason to doubt its genuineness. All they
proved was that the letter had not been addressed to the person to
whom it was said to have been addressed. See also Introduction,
Part iii, p. 83 note, and New Essays, Introduction, p. 376. Cf. Locke,
Essay, bk. iiL ch. 6, § 12, Eraser's ed., vol. i. p. 67 ; cf. note on
p. 380.

1 Literally, places where the curve or chain turns back upon
itself.

2 Probably Johannes Franciscus Buddaeus (1667-1729), Professor
of Philosophy at Halle, and afterwards of Theology at Jena. Ho
published many books, mostly on moral philosophy.

GENERAL PRINCIPLES 39

to the principle of continuity that not only should I not
be astonished to learn that there had been found beings
which, as regards several properties — for instance, those
of feeding or multiplying themselves — might pass for
vegetables as well as for animals, and which upset the
common rules, founded upon the supposition of a complete \
and absolute separation of the different orders of beings
which together fill the universe : I say, I should be so
little astonished at it that I am even convinced that there
must be such beings, and that natural history will perhaps
some day come to know them, when it has further studied
that infinity of living beings whose smallness conceals
them from ordinary observation, and which lie hid in the
bowels of the earth and in the depths of the waters * . . . '

T}ie pre-established Harmony between Substances.

There is, then, in the system of the Monads a perfectly
continuous and infinite gradation of intension, that is to
say, of perception or representation, combined with appe-
tition or spontaneous change. And thus the universe is
at once continuous and not only infinitely divisible, but
infinitely divided, consisting of an infinity of real ele-
ments 2. But we still have to consider how the principle I
of continuity, as thus interpreted, is consistent with the B
changes which take place in real things. In the system
of Monads the principle of continuity corresponds to the

1 <M. Malpighi, founding upon very considerable analogies in A
anatomy, is much inclined to think that plants may be included ji
in the same genus as animals, and that they are imperfect animals.' ft
Lettre a Arnauld (1687) (Q-. ii. 122). **

2 Cf. Lettre a Foucher (1693) (G-. i. 416) : 'I hold by the actual
infinite to such an extent that, in place of admitting that nature
abhors it, as is commonly said, I maintain that nature affects it
everywhere, so as the better to indicate the perfections of its
Author. Thus I think that there is no part of matter which is
not, I do not say merely divisible, but actually divided ; and
consequently the smallest particle must be regarded as a world
filled with an infinity of different creatures.' Also Lettre a Arnauld
(1686) (G. ii. 77) : * Not only is the continuous infinitely divisible ;
but every part of matter is actually divided into other parts.' See
Monadology, § 65 note.

4O INTRODUCTION

'void' in the older Atomism. Each is the necessary
correlative of the indivisible and impenetrable elements.
The conception of continuity, however, by implying
a plenum, escapes the contradictions that are involved
in the idea of a void. But it has still to be shown how
change is possible within a plenum, or how change can
take place without disturbing the continuity of the
infinite series of Monads. Any change within a plenum
affects eveiy part of it. This is the principle involved
in the scientific point of view regarding the universe,
which became current with the rise of modern philosophy.
Everything in the world acts and reacts upon everything
else. However separate things may be, no change can
take place in any one without affecting every other. The
influence may in some cases be imperceptible, infinitely
, small; but it exists. If, however, the universe be a
quantitative plenum, it is impossible to understand how
any change could originate within it. It must receive its
motion from outside, and must thus be regarded as finite,
which again is inconsistent with its reality as a plenum.
Leibniz overcomes this difficulty by regarding the uni-
verse, not as an infinite mass occupying all that there is
to occupy, but as a continuity or infinite gradation of
^J fjtplitntiVe differences., each containing within itself the
principle of its own changes. He substitutes for an
extensive plenum of mass an intensive continuum of force
or life.

But if the universe consists of an infinity of Monads,
each independent of the rest, impenetrable and unaffected
by them, and each containing within itself the principle
of all its changes, how is it possible for a change to take
place in any one of them without destroying the con-
tinuity of the series1? Each Monad contains within

1 How the perfect independence of the Monads is to be reconciled
with the continuity of their series is a question which Leibniz does
not answer. For him the ideal unity of the Monads (as each repre-
senting the same universe) does not make their mutual indepen-
dence any the less complete. To give up the independence of the

GENERAL PRINCIPLES 41

itself a representation of the whole universe from one
particular point of view, which differs to an infinitely
small degree from the representations contained in some
other Monad. If, then, any change, however slight,
takes place in the perception or representation of one
Monad, the continuity of the series will be broken and
we shall have two indiscernible Monads. But it is of
the very essence of the Monads to be ' living mirrors/
'forces' (as distinct from masses), centres of appetition,
spontaneously unfolding a sequence of perceptions. Ac-
cordingly this change within the Monad does take place :
it is essential to its nature. The continuous order or
system of the Monads must therefore be destroyed, unless
we can say that any change within one Monad produces,
or is invariably accompanied by, correlative changes in
other Monads, of such a kind that the equilibrium of the
whole system is maintained. In other words, there must
be something of the nature of mutual influence, action
and reaction, between the various elements in the system.
If the system were a plenum of mass, this interaction
would be intelligible without further explanation. But,
as the Monads form a qualitative continuum of such a
kind that no part can really act upon another, a further
hypothesis is required to complete the theory.

This hypothesis is Leibniz's system of the pre-estab-
lished harmony between substances. Though no true
substance can really act upon another, everything in the
universe takes place as if this mutual interaction were
real. Substances form a system, not of physical relations,
but of harmony or mutual compatibility. In the creation
of the world, the inner development of each Monad has
been so prearranged that all its changes are accompanied
by corresponding changes in others. The succession of

Monads would for him have meant to fall into Spinoza's pantheism,
while, on the other hand, to give up the continuity of their series
would have meant having recourse to Atomism. And these he
regarded as equally irrational alternatives. Cf. this Introduction,
Part iv. p. 1 88.

42 INTRODUCTION

changes in each Monad is different from that in every
other, and yet all are in harmony, the perfections of one
being accompanied by counterbalancing imperfections in
others. One Monad influences another ideally \ that is to
say, not db extra, but through an inner pre-established
conformity \

Relation of the System of pre-established Harmony to
Scholastic and Occasionalist Theories.

Like most of the other doctrines of Leibniz, this system
of the pre-established harmony is a new hypothesis
devised to remedy the imperfections of previous theories.
The general problem which it is meant to solve appeared
at first for Leibniz in a particular form, that of the rela-
tions between soul and body. The usual pre-Cartesian
solution of this special problem was the theory of an
influxus physieus or actual passage of elements from the one
substance to the other. Descartes's complete separation
of soul from body, of thinking substance from extended
substance, was in total opposition to the earlier theory 3.

1 Monadology, § 51.

3 Cf. Nouveaux Essais, bk. iv. ch. 10, § 10 (E. 376 a ; GL v. 421) :
1 As each of these souls expresses in its own way what takes place
outside of it, and is unable to have any influence upon other par-
ticular beings, or rather, as each must draw this expression entirely
from within its own nature, each soul must necessarily have received
this nature (or this internal ground of its expressions of what is
external) from a Universal Cause, upon which these beings are all
dependent, and which makes each of them to be perfectly in agree-
ment and in correlation with every other. This implies the use of
infinite knowledge and power and great ingenuity, especially with
reference to the spontaneous agreement of a mechanism with the
activities of the rational soul.' Also Monadology, §§51 sqq. and 81 ;
New System, §§ 14 and 15.

3 CLTheodicee, Part i. § 59 (E. 519 b ; G. vi. 135) : — 'The scholastic
philosophers believed that there is a reciprocal physical interaction
between body and soul ; but since a thorough investigation has
shown that thought and extended mass have no connexion with
one another, and that they are created things which differ toto
genere, several modern writers have recognized that there is no
physical communication between soul and body, although there
always remains the metaphysical communication, which makes of
soul and body one and the same agent, or what is called one
person.'

GENERAL PRINCIPLES 43

The problem itself is left by him without any satisfactory
solution ; but his followers made a definite attempt to
solve it by the theory of 'Occasionalism/ in which they
developed a suggestion that had been made by Descartes
when he spoke of thinking and extended substance as
alike dependent on nothing but the 'ordinary co-operation '
(concours ordinaire) or l assistance ' of God. The Occa-
sionalist theories varied to some extent, but in its most
consistent form the hypothesis is that God is the sole
real Cause, that finite substance has no power or activity
of its own, and consequently that the changes which take
place in soul and body are both directly produced by
God. Consequently on the occasion of the appearing
of a phenomenon in the one substance God produces
a corresponding phenomenon in the other. The two
phenomena are quite independent, except for the fact
of their contemporaneous production by God, the one
real Cause.

Leibniz's pre-established harmony has sometimes been
regarded as merely another variety of Occasionalism, in
spite of his frequent criticisms of the Occasionalist theory.
And he has been accused of borrowing (without acknow-
ledgement) from the Occasionalist Geulincx the well-
known illustration of the two clocks which he uses
in explaining his pre-established harmony. But Dr.
Edmund Pfleiderer has clearly shown l that Leibniz, who

1 Leibniz und Geulincx mit besonderer Besiehung auf ihr beiderseitiges
Uhrengleichniss (Tubingen, 1884). Zeller comes to the same con-
clusion. The illustration appears in a note to Geulincx's Ethica,
Tract, i. cap. ii. § 2, note 19 ; Land's ed., vol. iii. p. an. Cf. Third
Explanation of the New System, note 3. The notes are not in the first
edition of the Ethica, and they do not seem to have been known to
Leibniz. He received the illustration from Foucher, who probably
arrived at it independently, not knowing that it was used by
Geulincx. Cf. E. 130 a ; G. iv. 488.

L. Stein holds that Leibniz was unaware of the source of the
illustration, and may have considered it superfluous to assign any
special source for it, inasmuch as it was a universally used simile,
characteristic of the Cartesian school (a Schulbeispiel*). With other
references the illustration is used both by Descartes and by
Cordemoy. See Archivftir Geschichte d. Philosophic, i. 59.

44 INTRODUCTION

never mentions Geulincx in his writings, must have been
quite unaware of Geulincx's use of the illustration. And
in any case there is this essential difference between the
Occasionalist theory and that of pre-established harmony,
that the former regards finite things as empty of all
activity except that which is immediately communicated
to them by God, while the latter is founded on the
conception of finite things as in reality forces, Monads
with spontaneous activity '. Thus, the Occasionalist
theory is open to the criticism which Leibniz repeatedly
// brings against it, namely, that it involves the supposition
of perpetual miracle, or, in other words, that, if it be true,
the connexion between soul and body must be a purely
arbitrary one, there being nothing in the nature of either
which can serve as a reason why this phenomenon of soul
should accompany that phenomenon of body and not some
other. The Monads, on the other hand, have at least this
in common, that it is of the essence of each to represent
the same world from a particular point of view, and that
each unfolds the series of its perceptions or representa-
tions in an intelligible order. The whole is potentially
present and seeks its realization in each of the parts.
Consequently, the pre-established harmony is not arbi-
trary, but rational : no Deus ex machina is invoked. Thus
it is impossible to regard Leibniz's theory as the com-
pletion of the Occasionalist doctrine, unless in the sense

1 'When I speak of the force and action of created beings, I mean
that each created being is pregnant with its future state, and that
it naturally follows a certain course, if nothing hinders it ; and
that the Monads, which are the true and only substances, cannot
be naturally hindered in their inner determinations, since they
include the representation of everything external [to them]. But,
nevertheless, I do not say that the future state of the created being
follows from its present state without the co-operation [concours] of
God, and I am rather of opinion that preservation is a continual
creation with an orderly change. Thus Father Malebranche might
perhaps approve the pre-established harmony without giving up
his own hypothesis, to the effect that God is the sole Agent [acteur] ;
though it is true that otherwise it [his hypothesis] does not appear
to me well founded.' Lettre a Bourguet ^1714) (E. 722 a ; G. iii. 566).

GENERAL PRINCIPLES 45

that it is an hypothesis which seeks to reconcile the
contrary views of Scholastics and Cartesians l.

The scholastic theory of an in/luxus physi cus connected
soul and body in a way which ultimately confounded
them, making it impossible to draw any clear line
between them. The Cartesian or Occasionalist view, on
the other hand, separated them so absolutely that nothing
but a purely arbitrary connexion could be supposed — a
connexion external to the nature of both. The Scholastics
seemed to Leibniz to be right in holding that the con-
nexion is a real one, grounded in the nature of the
substances ; the Cartesians seemed right in maintaining
that the substances are mutually exclusive. And the
antinomy is solved for Leibniz by the supposition of a
mutual 'ideal influence/ a relationship of perception or
representation, between independent self-active Monads,
the harmony of whose inner developments has been
established before their creation 2.

Leibniz's Illustrations of the pre-established Harmony —
the Clocks and the Choirs.

The simile of the clocks, by means of which Leibniz
illustrates his theory in relation to the Scholastic and
Cartesian views, is given in the Tliird Explanation of his
New System. Two clocks may be made to keep perfect
time with one another in three different ways. They
may be actually connected together, for instance by
a piece of wood, in such a way that there is a mutual
transference of vibrations between them, resulting in a
perfect agreement of the motions of the pendulums 3. Or,

1 Of. H. C. W. Sigwart, Die Leibnizsche Lehre von *der prastablirten
Harmonic in ihrem Zusammenhange mit fruheren Philosophemen betrachtet
(Tubingen, 1822), pp. 107 sqq.

2 For an application of the doctrine of pre-established harmony
to a particular case, see Appendix A, p. 200.

3 This was suggested to Leibniz by an experiment of Huygens,
who hung two pendulums on a bar of wood, and found that, though
they were set swinging out of time with one another, the vibra-
tions which each gave to the bar of wood caused them ultimately
to swing in harmony. Cf. Third Explanation of the New System, p. 332.

46 INTRODUCTION

in the second place, they may be supposed to be kept
in time with one another from moment to moment by
a skilled workman. Or, finally, they may have been so
perfectly constructed that they keep time of themselves,
without any mutual influence or assistance. If we com-
pare soul and body to the two clocks, the first of these
ways of connexion corresponds to the doctrine of an
mfluxus physicus, the second to the Occasionalist view, and
the third to the pre-established harmony.

It is, however, misleading to suppose, as has too often
been done, that this is Leibniz's favourite simile for
explaining his system of pre-established harmony \ He
uses the illustration, not so much to explain his own
theory as to make clear the relation in which it stands to
previous hypotheses. He accepts for the moment the
limited problem which these hypotheses endeavour to
solve. But his own problem is larger and his own hypo-
thesis is therefore more comprehensive than those of his
predecessors. Body, for Leibniz, is nothing but a collection x
of Monads (or phenomena of Monads), and consequently
the question of the connexion between soul and body is
only a confused and imperfect form of the question as
to the relation between any one Monad and another. The
larger problem thus deals with the relations of body to
body and soul to soul as well as the relations of soul and
body, with which alone the earlier theories were concerned.

Leibniz would maintain that, as substances (Monads)
are not physical but metaphysical, it is impossible for us
to realize the true relations between them by conceptions
of sense or imagination. These relations are metaphysical
or ideal, and are therefore only intellectually apprehended.

1 The somewhat misleading prominence which has been given
to this illustration is to be attributed to Wolff and his school, who
represented the metaphysics of Leibniz in a very imperfect way.
Too many historians and teachers have been content with a Wolffian
Leibniz ; though for this there was doubtless some excuse in the
imperfection of the editions of his writings. For instance, the
Correspondence with Arnauld, in which the illustration of the choirs
occurs, was first completely published by Grotefend in 1846.

GENERAL PRINCIPLES 47

But he elsewhere uses a simile for the pre-established
harmony more adequate than that of the two clocks,
when he compares the Monads to completely independent
bands of musicians playing in perfect harmony. 'In
short, to use an illustration, I will say that this con-
comitance, which I maintain, is comparable to several
different bands of musicians or choirs, playing their parts
separately, and so placed that they do not see or even
hear one another, which can nevertheless keep perfectly
together by each following their own notes, in such a way
that he who hears them all finds in them a harmony
that is wonderful and much more surprising than if there
had been any connexion between them. It would even
be possible that some "one, being beside one of two such
choirs, should by means of the one judge what the other
is doing, and should even acquire such a habit of doing
this (particularly if we suppose that he could hear his
own without seeing it, and see the other without hearing
it) that, with the help of his imagination, he should no
longer think of the choir beside which he is, but of the
other, or should take his own merely for an echo of the
other \ ' &c. The analogy must not be pressed to an
extreme ; but the simile is much better than that of the
clocks. The clocks are too much alike to represent the ,
Monads, and the harmony of their movement is too empty
and almost meaningless. But in the case of the bands
there is a real harmony formed out of the complementary
movements of several self-acting units, and there is also
the spontaneous development from the written notes of
the score to the system of sounds which they signify.
This development from the written signs to the sounds
signified might be said to correspond to the passage from
unconscious to conscious perception in the Monad2.
An unconscious perception is, for Leibniz, a symbol of
the corresponding conscious perception.

We have now considered the three chief conceptions of
1 Lettre a Arnauld (1687) (G. ii. 95). 2 Cf. G. ii. 74.

48 INTRODUCTION

the metaphysic of Leibniz, and we have seen how they
arise as the solution of his problem in the form which is
given to it by its historical setting. In the first place,
intension, force, or life, .in the form of perception and
appetition, is the essence of real, individual substance.
In the second place, the principle of continuity or the
identity of indiscernibles is the hypothesis by which
Leibniz endeavours to explain the system or inter-relation
of strictly individual substances. And, in the third place,
the pre-established harmony is introduced to account for
the possibility of change in elementary substances without
prejudice to the whole.

Clear and confused Perception and Degrees of Appetition.

We must now consider more fully the varieties of per-
ception and appetition which constitute the differences
amongst Monads. In regard to perception Leibniz adopts
the Cartesian distinction among ideas, with considerable
modifications. Descartes divided ideas into those which
are obscure, those which are clear, and those which are
distinct as well as clear. 'I call that clear,' he says,
' which is present and manifest to the attentive mind, as
we say we see an object clearly when it is present to the
eye looking on, and when" it makes on the sense of sight
an impression sufficiently strong and definite ; but I call
that distinct which is clear and at the same time so
definitely distinguished from everything else that its
essence is evident to him who properly considers it1.'
And ' all the things which we clearly and distinctly con-
ceive are true2.' Leibniz follows Descartes in regarding
clearness and distinctness as the marks of perfection in
ideas or perceptions 3 ; but he does not limit the dis-

1 Principia, i. 45. a Method, Part iv.

3 Leibniz, however, interprets clearness and distinctness some-
what differently from Descartes. The distinction of one idea from
all others is emphasized by Descartes, while Leibniz rather lays
stress upon the internal distinctness of the idea, the distinctness
of its elements. Cf. Meditationes de Cognitione, Veritate et Ideis (1684)

GENERAL PRINCIPLES 49

tinction betweeja distinct and confused ideas to the ideas
which we consciously possess, nor does he draw a sharp
line between ideas which are perfectly clear and distinct,
and all others, which are confused or obscure. Confused
perceptions are not for Leibniz, as for Descartes, mere
mistakes and illusions ; but they belong to the real order
of things, which without them could not be what it is.
And there is no question, as in Descartes, regarding the
correspondence of perceptions to reality, clear and distinct
ideas representing their objects with perfect truth, while
obscure and confused ideas are ' of no avail in affording
us the knowledge of anything out of ourselves, but serve
rather to impede it l. ' According to Leibniz all perceptions
are more or less perfect representations of objects ; but
they vary infinitely in their degrees of distinctness or
confusedness. Confusedness is simply a low degree of
distinctness : the more perfect any perception or repre-
sentation is, the more distinct is it, while the less perfect it
is, the more is it confused. Thus the differences among the
Monads consist entirely in the various degrees of perfec-
tion or distinctness with which they perceive or represent

(E. 79 a ; Q-. iv. 422) : ( A notion is obscure when it does not suffice
for the recognition of the thing represented, as for instance when
I remember some flower or animal formerly seen, but not so well
as to be able to recognize it when it appears and to distinguish it
from some other near it, or when I think of some scholastic term
insufficiently explained, like the "entelechy" of Aristotle, or
" cause" in so far as the name is applied indifferently to material,
formal, efficient, and final causes. . . . Thus knowledge is clear
when it enables us to recognize the thing represented, and clear
knowledge again is either confused or distinct. It is confused
when I cannot separately enumerate the marks which are sufficient
for distinguishing the thing from others, although the thing really
has such marks and essential elements, into which its notion may
be analyzed. . . . So we see painters and other artists knowing
rightly what is well and what is badly done, but often unable to
give a reason for their opinion and saying that the thing they
dislike is lacking in something, they know not what. ' But a distinct
notion is such an one as the assayers have regarding gold, namely
one acquired through marks and tests sufficient for the discerning
of the thing from all other similar bodies.' For Locke's views, cf.
Essay, bk. ii. ch. 29, §§ i sqq. (Fraser's ed., vol. i. p. 486).
1 Principia, Part iv. § 203.

50 INTRODUCTION

the universe. But as each Monad actually represents
the whole universe, however confusedly or imperfectly,
and as each is essentially a force or living principle,
proceeding, by its own spontaneous activity, from one
perception to another, the distinct and the confused are
not essentially separate from one another, but it is possible
for the confused perception to unfold into distinctness.
Each Monad contains the whole more or less confusedly
within itself l, and by its appetition may rise to a more
perfect state. Each Monad contains as it were enfolded
within itself all that it is to be. It is ' big with the
future.' It is like an exceedingly condensed algebraical
statement which can be indefinitely expounded : some-
what like the symbol n in the problem of determining
the relation between the lengths of the diameter and
circumference of a circle, with this very important differ-
ence, that the Monad ' reads itself off.' An omniscient
Being could see the reality and history of the whole
universe within the lowest Monad.

Three Classes of created Monads — (i) unconscious,

(2) conscious, (3) self-conscious.

While there is thus a perfect continuity in the degrees
of perfection with which the Monads represent the
universe, Leibniz has roughly distinguished created
Monads into three main classes — (i) unconscious or bare
Monads (monades nues), (2) conscious Monads, and (3)
rational or self-conscious Monads. As we have seen,
every Monad or simple substance has a certain degree of
perfection or completeness, inasmuch as it ideally or
potentially contains 'the whole within itself. Thus the
Aristotelian name of Entelechies might be given to all
Monads, since they have each 'a certain perfection*
(exovo-i TO eWeAe'y), and 'a certain self-sufficiency (avrapKeia)
which makes them the sources of their internal actions,

1 ' The world is entirely in each of its parts, but more distinctly
in some than in others.' Lettre a la Princesse Sophie (1696) ,G. vii.

GENERAL PRINCIPLES 51

and, so to speak, incorporeal automata V That is to say,
each is, in its own way, complete in itself as representing
the universe and complete in itself as an active living
being or force. On the other hand, every Monad might
be called a 'soul,' inasmuch as it has both perception
and appetition, in the general sense of these words
which has been already explained. Nevertheless, in spite
of this essential unity of nature in the Monads, it is
possible to draw broad lines of division among them.
Conscious sensation or feeling, accompanied by the
simpler forms of memory, clearly marks off certain
Monads from those which have merely unconscious or
confused perception. To the former class the name
' souls ' may be specially applied, while for the latter the
general name of Entelechies or Monads will suffice. And
as there are still higher Monads which have self-conscious-
ness and reason or thought proper, in addition to uncon-
scious and conscious perception and memory, we may
call these ' rational souls ' or ' spirits ' (intelligences,
esprits) 2. The class of rational souls or spirits includes
men and higher intelligences. The intermediate i soul '-
class is that of animals, and the class of Entelechies or
bare Monads includes all real beings that have not
reached the stage of consciousness.

The differences of appetition in the three classes of
created Monads (corresponding to the three grades of
perception which characterize them) may be expressed
as mere impulse, animal instinct or blind desire governed
by mere feeling, and self-conscious desire or will.

Each of the two higher classes possesses, in addition
to its own specific qualities, the characteristics of the

1 Monadology, § 18.

2 Cf. De Anima Brutorum (1710), §§ 10 and 13 (E. 464 b; G. vii.
330) : ' Sense is perception which contains something distinct and
is combined with attention and memory. . . . Besides the lowest
degree of perception, which also occurs in those who are stunned,
and the intermediate degree, which we call sense . . . there is a
certain higher degree which we call thought. Now thought is
perception combined with reason.'

E 2

52 INTRODUCTION

inferior Monads. Thus both animals and men have
unconscious as well as conscious perceptions, for ex-
ample, when they fall into a faint or have a profound
and dreamless sleep1. In such a case they are not
entirely destitute of perceptions, for the Monad is inde-
structible (being indivisible) and it cannot exist without
perception of some kind. The changes of the Monad
are entirely from within, so that when the man or
animal awakes out of a sleep or trance his conscious
perceptions must have unfolded themselves out of imme-
diately preceding perceptions of an unconscious kind2.
Again, men share with the animals both sense-perception
and the empirical sequence of memory and imagination,
which bears a resemblance to the concatenation of rational
thought, but may be sufficiently distinguished from it 3.
Indeed, in most of our actions and beliefs we are empi-
rics, as for instance when we expect the dawn, not
because we know the cause of it, but because it has
happened regularly in the past4.

Self-consciousness in the Philosophy of Leibniz and in
that of Descartes.

The significance of this may be brought out by a
reference to the position of Descartes, which Leibniz
probably had in view. According to Descartes, the
rational soul is the mind and its reality comes only from
its conscious certainty of itself. Thus without self-con-
sciousness there is no mind or soul. Animals have no
self-consciousness and therefore they have no souls — they
are mere machines. But animals have sensations and
impulses, and consequently sensation and impulse are
not functions of self-consciousness, acts of the soul, but
are purely physical and mechanical processes, whether
they occur in man or in the lower animals. It is in

1 Monadology, § 20. 2 Ibid. §§22 and 23.

8 Ibid. §§26 sqq. Cf. Nouveaux Essais, bk. ii. ch. n (E. 237 ;
G. v. 129), and Eraser's ed. of Locke's Essay, vol. i. p. 208.
* Monadology, § 28.

GENERAL PRINCIPLES 53

self-consciousness alone that we have immediate self-
certainty, from which we may proceed outward to the
certainty of other things. Thus for Descartes the line
between consciousness and unconsciousness on the one
side and self-consciousness on the other must be very
sharply drawn : the complete independence of self-con-
sciousness is the root of the Cartesian dualism.

Now7 Leibniz desires to preserve the independence of
self-consciousness or the self-certainty and self-sufficiency
of the mind. The validity of thinking must not be made
to depend on reference to a reality external to it \ But,
on the other hand, the mechanical dualism of Descartes
must be avoided. The independence of self-consciousness
is preserved through the conception of the Monads as
a plurality of real, independent substances. Mind is not
merely a modification of substance, an attribute (as
Spinoza made it) ; it is an independent substance, in
its various forms one or other of the infinite number.
But, on the other hand, mind must not be regarded as
identical with self-consciousness alone : self-consciousness
must not be taken as entirely exclusive of mere con-
sciousness or of unconsciousness. Otherwise we have
returned to the Cartesian dualism. There must some-
how be an unconscious activity of mind, and the oppo-
sition between mind and body becomes a difference, not
of kind but of degree.

1 Cf. Remarques sur le sentiment du P. Malebranche (1708) (E. 452 b ;
G. vi. 578) : ' The truth is that we see all things in ourselves and
in our souls, and that the knowledge we have of the soul is very
real and correct, provided we have given some attention to it.
And further, it is through the knowledge which we have of the
soul that we know being, substance, God Himself, and it is
through reflexion upon our thoughts that we know extension and
bodies. Yet it is true that God gives us all that is positive in this, —
and all the perfection involved in it, through an immediate and /
continual emanation, in virtue of the dependence of all created f
beings upon Him. In this way it is possible to give a good
meaning to the phrase that God is the object of our souls and that
we see all things in Him.' Cf. also Part iii. of this Introduction,
p. 136.

54 INTRODUCTION

Self-consciousness in the philosophy of Leibniz is,
however, a very different thing from self-consciousness
in the philosophy of Descartes. The latter arrives at
the self-conscious Ego as the result of a rigorous analysis,
whose instrument is doubt *. It is an ultimate fact, the
fact of a subject thinking, without regard to any specific
object of its thought. Self-consciousness is the bare
witness of consciousness to itself, its empty self-con-
sistency. In the certainty of self-consciousness Descartes
(justifiably or not) finds involved the certainty of God.
the Perfect Being, and from this he proceeds to the
certainty of the external world and to the principle that
clear and distinct ideas are characteristic of self-conscious-
ness and are a sufficient warrant for the reality of their
objects. For Leibniz, on the other hand, the Ego is
not a pure subject, whose essence is immediate self-con-
sciousness. No Monad can be a pure subject. ' Not only
is it immediately clear to me that I think, but it is quite

1 Leibniz seems strangely to have missed the significance of
Descartes's method of doubt, probably because his interest lay
more in Descartes' s doctrines than in his way of reaching them.
' M. Descartes,' he says, ' has acted like the quacks [charlatans] who,
in order to attract people and get a sale for their remedies, set up
open theatres in which they show farces and other extraordinary,
but not very necessary, things. Thus all that he says about the
necessity of doubting everything and of treating doubtful things as
false has had no other use than to get him a hearing, to raise
a comniotion, to draw the crowd by its novelty, and even to get
himself contradicted, that he may be the more famous. But he
has taken care to reserve for himself a way of rationally explaining
his paradoxes.' Foucher de Careil, Nouvelles Lettres et Opuscules inedits,
p. 12. Leibniz elsewhere speaks of Descartes's Cogito, ergo sum and
his method of doubt as ' trappings to appeal to the people ' (phaleras
adpopulum), and he pictures Descartes as * throwing balls to plebeian
minds to play with,' so that 'they seem to have got something
great, like boys with a nut or a bean' (G. iv. 327). We must, of
course, remember how different is the problem of Descartes from
that of Leibniz. Descartes lays special stress upon self- conscious-
ness because he regards himself as having found a principle by
means of which to distinguish absolutely the true from the false or
doubtful. On the other hand, for Leibniz as for Spinoza, the
problem of philosophy is not primarily a problem of knowledge.
Leibniz's theory of knowledge follows from his answer to the
question — ' What in reality is substance ? '

GENERAL PRINCIPLES 55

as clear to me that I have different thoughts; that now
I think of A, now of JB, (fee.1' An Ego is one of an
infinite number of substances, and its self-consciousness
is thus not the ground of its existence, but a difference
in degree of quality between it and others2. The self-
conscious Monad is merely one which has developed its
representative or perceptive nature more fully than those
which we describe as animal souls or bare Monads. In
other words, we are i Egos ' before we think of ourselves,
realize ourselves, or reflect upon ourselves as Egos. We
are l raised to the knowledge of ourselves and of God 3. '

The difference between the self-conscious Monad and
others consists in the greater clearness and distinctness
of its perceptions and ideas. But, as clearness and dis-
tinctness are relative terms (every Monad having percep-
tions in some degree clear and distinct), the specific
perceptions of a self-conscious being must be further
defined. Leibniz, as we have seen, cannot accept the
Cartesian view which totally rejects confused and obscure
ideas and makes clearness and distinctness the sole criteria
of truth *. In addition to being clear and distinct, the

1 Nouveaux Essais, bk. iv. ch. 2, § i (E. 341 a ; G. v. 348). Cf. G.
iv. 327 : ' These two things I regard as mutually independent of
one another and as equally original.' Also Lettre a Foucher (1676)
(G. i. 370) : * There are two absolute general truths, that is to say,
general truths which speak of the actual existence of things : the
one is that we think, the other that there is a^great variety in our
thoughts. From the first it follows that we are, from the second
it follows that there is something other than ourselves, that is to
say something other than that which thinks, something which is
the cause of the variety in what appears to us. Now the one of
these truths is as unquestionable, as independent as the other, and
M. Descartes, having in the order of his meditations taken account
only of the first of them, has failed to reach the perfection he set
before himself.'

2 * To say, I think, therefore I am [exist] is not strictly to prove
existence by thought, since to think and to be thinking are the
same thing ; and to say I am thinking is already to say I am.'
Nouveaux Essais, bk. iv. ch. 7, § 7 (E. 362 a ; G. v. 391).

3 Monadology, § 29.

* Cf. Meditationes de Cognitione, Veritate et Ideis (1684) (E. Sob ; G. iv.
425), translated in Appendix to Baynes's ed. of Port-Royal Logic :
'And I also see that the men of our time abuse that vaunted

56 INTRODUCTION

ideas which are characteristic of a rational being must
be analyzed, so that their grounds or premises may be
as fully exhibited as possible. And thus the specific
quality of a rational soul or self-conscious Monad is * the
knowledge of necessary and eternal truths,' that is to
say, of the ultimate grounds or premises of all knowledge.
The self-conscious Monad represents or perceives the
universe in an articulate way. It has carried the internal
evolution or realization of the universe so far that its
underlying principles have clearly revealed themselves.
' It is by the knowledge of necessary truths and by their
abstract expression [leurs abstractions] that we are raised
to acts of reflexion which make us think of what is called
"I," and observe that this or that is within us : and thus,
in thinking of ourselves, we think of being, of substance,
of the simple and the compound, of the immaterial and
of God Himself, conceiving that what is limited in us
is in Him without limits. And these acts of reflexion
furnish the chief objects of our reasonings V

This at once suggests Descartes, but Descartes with
a difference. For Leibniz, as for Descartes, the idea of

principle : whatever I dearly and distinctly perceive regarding anything,
that is true or (rightly} predicdble [enuntiabile] of it. For often things
which are really obscure and confused seem clear and distinct to
men judging hastily. The axiom, therefore, is useless, unless there
be added such criteria of the clear and distinct as we have given,
and unless there is certainty [constet] regarding the truth of the
ideas. For the rest, the rules of common Logic, which are also
used in Geometry, are not to be despised as criteria of true state-
ments, such rules, for instance, as that nothing should be admitted
as certain unless it has been proved by accurate observation
[experientid] or by strict demonstration. But strict demonstration
is that which keeps to the form prescribed by Logic, not necessarily
always in syllogisms set out in order according to the custom of
the schools . . . but at least in such a way that the conclusion of
the argument follows from its very form. Any right calculation
might be taken as an example of an argument of this kind, con-
ceived in due form. Therefore no necessary premise must be left
out, and all the premises must first have been either proved or
assumed by way of hypothesis, in which case the conclusion also is
hypothetical. Those who will diligently observe these things will
easily guard themselves against deceptive ideas.'
1 Monadology, § 30.

GENERAL PRINCIPLES 57

God or the most Perfect Being is involved in that of
an imperfect self-conscious being. Yet Leibniz regards
the idea of God as contained, not in the self-conscious
being alone, but, in one way or another, in every real
being. Thus it is of less consequence for Leibniz than
for Descartes that the idea of God is pre-supposed in the
consciousness of self. That which is of most importance
to Leibniz is that self-consciousness pre-supposes a know-
ledge of necessary truths in general. Thus, for Leibniz,
God is not merely the eternally necessary Being whose
very idea (or essence) involves existence and who is in
that way the ground of existence to all other things : He
is also the greatest of beings, the highest of Monads
(Monas monadum ]), whose own existence is one among
many necessary and eternal truths. l We must not
imagine, as some do, that eternal truths, being dependent
on God, are arbitrary and depend on His will, as Des-
cartes, and afterwards Monsieur Poiret, appear to have
held2.' There are truths or facts which are dependent
on the will of God, but these are not necessaiy and
eternal.

The Kinds of Truth according to Leibniz. Necessary and
eternal Truths and contingent Truths.

Accordingly as, on Leibniz's view, the self-conscious
being has not a primary and independent reality, based
on a complete difference in kind between itself and other
beings, so the special kind of knowledge (that of eternal
and necessary truths) which belongs to a self-conscious
being is not to be regarded as the only absolutely certain
truth, to the form of which all other real knowledge
must be reduced. ' There are two kinds of truths, those
of reasoning and those of fact V The former are the
eternal and necessary truths, the latter are contingent.

1 Giordano Bruno, as well as Leibniz, speaks of God as Monas
monadum.

Monadology, § 46. 3 Ibid. § 33.

58 INTRODUCTION

And the difference between them is that the truths of
reasoning are either ultimate self-evident principles or
truths which are reducible to such first principles by
a process of strict logical analysis, while any attempt to
analyze truths of fact into their ultimate grounds leads
to an infinite process, and they must finally be referred
to God as their ground eminenter1.

Logical Principles of the Philosophy of Leibniz, (a)
Principle of Identity or Contradiction.

With this division of human knowledge into two great
kinds we come in sight of the guiding principles of
Leibniz's philosophy, its logical pre-suppositions as dis-
tinct from its specific metaphysical doctrines. The logic
underlying the philosophies of Descartes and Spinoza
was a logic of abstract self-consistency 2. In their view
all real knowledge must be ultimately of one kind. All
apparent knowledge that is not of that kind must be
regarded as entirely unreal and illusory. This was neces-
sarily involved in the position that there is no appeal
beyond the witness of consciousness to itself. ' The order
and connexion of ideas is the same as the order and
connexion of things3.' And, as all things must be re-
garded as ultimately referable to one ground or cause, so
all ideas must ultimately be referable to one standard ;
that is, must be linked together by one principle. The
standard must be that of self-evidence or absence of self-
%

1 Cf. Monadology, §§ 35~38-

2 Not that this was perfectly evident to themselves. Descartes,
for instance, regards his method of doubt as superior to a logical
deduction, based on the principle of contradiction. * Here, if I am
not wrong,' says Eudoxus, ' you must be beginning to see that he
who can make a proper use of doubt will be able to deduce from
it very certain truths, nay rather, more certain and more useful
truths than those which we derive from the great principle we
usually lay down as the basis or centre to which all other principles
may be referred, "it is impossible that one and the same thing can both be
and not be." ' Recherche de la Verite par les lumieres natureUes, (Euvres de
Descartes (Cousin), vol. xi. p. 366.

3 Spinoza, Ethics, Part ii. Prop. 7.

GENERAL PRINCIPLES 59

contradiction in the ideas, which is simply another way
of describing the immediate witness of consciousness to
itself. True ideas must be clear and distinct in order
that it may be manifest that they are free from self-
contradiction. All real knowledge must either be imme-
diately recognizable as eternal and necessary truth, or
must be deducible from such truth by a formally or
mathematically conclusive process. Thus the philosophies
of Descartes and Spinoza were ruled by the principle of
contradiction, that A cannot both be A and not A, or
that necessary truths are 'identical propositions, whose
opposite involves an express contradiction1.' In other
words, they held that self-consciousness is self-consistent,
that it never absolutely contradicts itself.

Now this is, so far as it goes, a perfectly sound doctrine.
Its fault is that it does not go far enough. Self -con-
sciousness is much more than merely self-consistent. Its
self-consistency is not immediate and on the surface. It
is not a mere negative self-identity of parts, without
regard to their specific content. To be self-consistent,
according to the principle of contradiction, is for a thing
to be itself, that is, to be 'not anything else.' But a
thing whose ultimate essence is to be l not anything else '
is nothing. 'Nothing' is immediately self-consistent
quite as much as l something2.' In other words, all real
(not merely formal) self- consistency must be mediate, it
must have grounds. It must spring from the specific
nature of the self-consistent thing3. And thus, as Leibniz
contended, even axioms may require proof 4. Their self-

1 Monadology, § 35. Cf. ibid. § 31. The principle of contra-
diction is that ' in virtue of which we judge false that which
involves a contradiction, and true that which is opposed or contra-
dictory to the false.'

2 Cf. Locke's Essay, bk. iv. ch. 8, § 3 ; Eraser's ed., vol. ii. p. 293.

3 Cf. Nouveaux Essais, bk. iv. ch. 7, § 9 (E. 362 a ; G. v. 392) : ' In
the natural ' [i. e. logical] ' order, the statement that a thing is what
it is, is prior to the statement that it is not another thing.'

4 Cf. Nouveaux Essais, bk. i. ch. 3, § 24 (E. 222 a ; G. v. 98) : ' It
is one of my great maxims, that it is good to work out proofs of

60 INTRODUCTION

evidence requires elucidation : the basis of it must be
made manifest \ Self-consciousness, then, is really self-
consistent only in virtue of its being a definite system,
a self-revealing process or development, which contains
within itself the ground or reason of its self- consistency,
and the ground or reason of existence. Accordingly, to
treat it in philosophical investigation as if it were merely
superficially self-consistent, as if the law which expresses
its whole nature were the law of contradiction, would be
to arrive at an empty and abstract result.

Leibniz, however, while recognizing the inadequacy of
the principle of contradiction as thus interpreted, did not
clearly enough perceive the reason for this inadequacy.
He regarded the principle of contradiction, not as an
imperfect interpretation of the one principle of all truth,
to be made perfect by further definition, but as an in-
dependent principle, adequate to a certain kind of truth,
yet requiring to be supplemented by another co-ordinate
principle, which should be the standard of another kind
of truth. If the principle of contradiction be the sole
principle of knowledge, whatever is not self-contradictory
is true ; and nothing is true unless it can be shown that
it is not self-contradictory. But how are we to determine
what is or is not self-contradictory ? According to the
Cartesians this is to be done by analytically reducing the
doubtful statement to one or more self-evident propo-
sitions, or, in other words, by showing that the state-
ment is ultimately involved in one or more propositions,
of such a kind that their predicate is manifestly contained
in their subject2. But Leibniz maintains that there are

the axioms themselves.' Cf. Eraser's ed. of Locke s Essay, vol. ii.
p. 267, note.

1 Cf. Noureaux Essais, bk. iv. ch. n, § 14 (E. 379 b ; G. v. 428) :
' As to eternal truths, it is to be noted that at bottom they are all
conditional and say in effect : such a thing being supposed, such
another thing is.'

3 According to Leibniz, all true propositions must be such that
their predicate is really contained in their subject, although this
may not be self-evident. This is simply expressing in another

GENERAL PRINCIPLES 6 1

many statements to which it is impossible satisfactorily
to apply this test. Their very nature is such that the
process of analysis cannot in their case be brought to an
end, and consequently we remain unable to say whether
they are really self-contradictory or not. At any rate,
their self-contradiction, or the absence of it, cannot be
made self-evident. For instance, the statement that
'I took a long walk yesterday' may be perfectly true,
but by no amount of analysis is it possible for us to test
its truth by reducing it to self-evident propositions. It is
not necessarily but contingently true. Its truth is not
directly grounded in the eternal nature of things, but is
determined by a multitude of other truths, which may
each in their turn demand an infinite analysis l. These

form his view that ' in the notion of each individual substance all
its events are contained, along with all their circumstances and
the whole sequence of external things.' Lettre au Prince Ernest
(1686) (G. ii. 12). 'Always in every true affirmative proposition,
whether necessary or contingent, universal or singular, the notion
of the predicate is in some way comprehended in that of the
subject, praedicatum inest subjecto ; otherwise I know not what truth
is. But I require no more connexion here than that which exists
a parte rei between the terms of a true proposition, and it is only in
this sense that I say that the notion of the individual substance
includes all its events and all its characteristics, even those that
are commonly called extrinsic (that is to say, those which belong
to it only in virtue of the general connexion of things and on
account of its expressing the whole universe in its own way).
u For there must always be some foundation for the connexion of
;the terms of a proposition, and this is to be found in their notions."
That is my great principle, as to which I think all philosophers
should be at one, and of which one of the corollaries is the common
axiom that nothing happens without it being possible to give a
reason why things should have gone thus rather than otherwise,
although this reason often inclines without necessitating, a perfect
indifference being a chimerical or incomplete supposition/ Lettre
a Arnauld (1686) (G. ii. 56).

1 Cf. De Sdentia Universali sen Calculo Philosophic? (E. 83 b ; G. vii.
200) : ' The difference between necessary and contingent truths is
indeed the same as that between commensurable and incommen-
surable numbers. For the reduction of commensurable numbers
to a common measure is analogous to the demonstration of necessary
truths, or their reduction to identical truths. But, as in the case
of surd ratios the reduction involves an infinite process and yet
approaches a common measure so that a definite but unending
series is obtained, thus also contingent truths require an infinite

62 INTRODUCTION

contingent truths, however (if they are to be truths at
all, and not merely false or doubtful statements), must
have some ground or reason \ If the truth is such that
it is impossible to find for it an absolute and eternal
reason in the first principles of things, there must at
least be some satisfactory or sufficient reason why it
should be so and not otherwise.

Logical Principles of the Philosophy of Leibniz. (fc) Principle

of Sufficient Eeason.

Thus Leibniz supplements the principle of contra-
diction by the addition of the principle of sufficient
reason. The name has a makeshift sound — as if one
should say, ' We must be content with a sufficient reason
in cases where a perfect reason is not to be found.' But
in the philosophy of Leibniz it is much more than a
makeshift. This principle is essential to his system and,
indeed, gives it the greater part of its value. In the
Monadology, Leibniz defines this principle as that ' in
virtue of which we hold that no fact can be found real or
existing, no statement true, unless there be a sufficient
reason why it should be so and not otherwise, although
these reasons very often cannot be known by us2.' As
thus defined, the principle of sufficient reason might
almost be regarded as including the principle of contra-
diction, inasmuch as the self-consistency of necessary
truths is their sufficient reason. Self-consistency or.

analysis, which God alone can accomplish. Accordingly it is by
Him alone that these truths are known a priori and with certainty.
For, although the reason of any succeeding state might be found in
that which precedes it, yet a reason for this preceding state can
again be given, and so we never come to the final reason in the
series. But this infinite process itself takes the place of a reason,
because in its own special way it might from the beginning have
been immediately understood outside of the series, in God, the
Author of things, on whom both antecedent and consequent states
are dependent, even more than they are dependent upon one
another.'

1 Monadology, §§ 36, 37.

2 Ibid. § 32. In the Theodicee, § 44 (E. 515 ; G. vi. 127), he calls
it 'Determining [deciding] Reason.'

GENERAL PRINCIPLES 63

absence of self-contradiction is one test of the sufficiency
of the reason. But, on the other hand, the principle of
contradiction has ail independent and, in some sense,
superior position, for in the case of necessary truths the
reason can always be given, that is, can be made explicit,
while in the case of contingent truths we often can only
say that there must be a sufficient reason, without know-
ing fully what the reason is.

/The Possible and the Compossible. The lest of all
possible Worlds.

The value and importance of the principle of sufficient
reason become more manifest when we inquire further —
'In what does the sufficiency of the reason consist?'
We have seen that the grounds of any contingent truth
or fact are to be sought in other contingent truths or
facts, and that an attempt to analyze a contingent truth
or fact into its grounds thus leads to an infinite process.
Accordingly it seems to Leibniz that the final reason of I •
contingent truths must be sought in something outside 1
of the system of contingent things, viz. in an eternal and I
necessary Substance or God, who is their source. But \
this requires some further explanation. In the case of
the principle of contradiction, what may be called the
sufficiency of the reason consisted in the absence of
self-contradiction in the thing or proposition. But to
say that a thing is in itself free from contradiction is the
same as to say that, by itself and without reference to
other things, it is possible *. Accordingly, to say that
everything which is not self-contradictory is true or real
is to say that everything possible is true or real. ' I call
possible everything which is perfectly conceivable and
which has consequently an essence, an idea, without
considering whether the remainder of things allows it to
become existent V But the opposite of every particular

1 Cf. Meditationes de Cognitione, &c. (1684) (E. 80 b ; G. iv. 425 ;
Baynes, Port-Royal Logic, 428).

a Lettre a Bourguet (1714) (E. 720 a ; G. iii. 573).

64 INTRODUCTION

event or contingent truth is possible in this sense : it does
not necessarily imply a self-contradiction. The opposite
of the axiom, ' Things that are equal to the same thing-
are equal to one another,' is not possible, for it involves
an immediate self-contradiction. The opposite of the
truth, ' I am sitting here at this moment,' is possible, for it
does not involve a direct self-contradiction. Accordingly,
the truth of contingent things is not grounded in their
possibility \ It is not in virtue of their very essence or
idea that they, and not their opposites, are true or real.
Their sufficient reason lies beyond themselves, in their
relation to other things. In themselves, the contingent
truths and their opposites are alike possible : considered
in relation to other things, the truths alone are possible.
For instance, if we consider the truth that 1 1 am sitting
here at this moment/ not in itself alone, but in relation
to an indefinite number of other truths regarding (say)
my habits, character, work, the hour of the day, &c., we
shall see that the truth alone is possible, that in this
connexion its opposite is impossible. The opposites of
contingent truths, though not self-contradictory, are in
contradiction with the general system. Each is possible,
but 'they are not jointly possible, mutually compatible,
or, in Leibniz's phrase, ' compossible.' Accordingly,
' compossibility,' or conformity with the actual system of
.things, is the true test of reality, the sufficient reason.
/Everything which is possible has an essence or meaning,
| but only that which is also compossible has existence 2.

1 Descartes did not admit that everything which is possible is
realized, but assigned the choice among possible things to the mere
will of God. But this is practically to make the choice arbitrary
and consequently to make the contingent (which is the result of
choice) fortuitous. Spinoza, on the other hand, by holding that
everything possible is realized, made the contingent necessary.
Leibniz, however, points out that Descartes in one passage ( Principia,
iii. 47) says that ' Matter must successively take all the forms of
which it is capable/ an approach to Spinoza's view. Reponse aux
Reflexions, &c. (1697) (E. 144 a ; G. iv. 340).

2 Cf. Lettre a Bourguet (1714) (E. 719 b; G. iii. 572): 'I do not
admit that, in order to know whether the romance of Astraea is

GENERAL PRINCIPLES 65

But, while the ground of the individual thing's reality
is its compossibility with the actual system of things, /
Leibniz does not admit that mere compossibility with \
any system whatever implies the existence of the com- .
possible essences. The principle of sufficient reason is
not interpreted by him as a general reference to system
or as reference to a system which is held to be the only
one possible, to an all-inclusive system1. There are
several possible systems or universes, each of which
consists of a collection of compossible elements. Indeed •
it must be supposed that there is an endless series of such I
possible universes, of which one only has existence as '
well as essence. But the principle of sufficient reason

possible, it would be necessary to know its connexion with the rest
of the universe. That would be necessary in order to know
whether it is compossible with it, and, consequently, whether this
romance has been, is now, or shall be [realized] in any corner of
the universe. For assuredly, without that, there will be no place
for it. And it is very true that what does not exist, has never
existed, and never shall exist, is not possible, if by possible we
mean compossible, as I have just said. . . . But it is another
question whether Astraea is absolutely possible. I say "yes,"
because it involves no contradiction. But, in order that it may
actually exist, the rest of the universe would have to be quite
other than it is, and it is possible that it may be otherwise.'
L'Astree was the first French pastoral romance, modelled on such
works as the Aminta of Tasso or the Pastor Fido of Guarini. It was
written by Honore d'Urfe (1568-1625) and was published in parts
between the years 1610 and 1619. It is a strange medley of his-
torical and imaginary events and characters, and the Court society
of Europe for a long time amused itself by trying to ' identify ' the
characters of the story. It was translated into almost every European
language, many ' kevs ' to it were written, plays were founded upon
it, and it was read with much appreciation by such writers as
La Rochefoucauld, La Fontaine, and Rousseau.

1 Remarques sur la lettre de M. Arnauld (1686) (G. ii. 45) : ' If we
were to reject absolutely things which are merely possible, we
should do away with the contingent, for, if nothing is possible
except what God has actually created, whatever God has created
would be necessary— supposing that God has resolved to create
anything/ Nolen (La Critique de Kant et la Metaphysique de Leibniz,
p. 24) remarks that ' the relation between the world of possibles
and the world of existences remains one of the obscure points in
the philosophy of Leibniz. The correspondence with Arnauld . . .
shows that Leibniz was conscious of the insufficiency of his explana-
tions and of the difficulty of the problem/

66 INTRODUCTION

still requires that a cause or reason be assigned for the
existence of the actual universe rather than any other
among those which are possible. The existence of the
actual universe is its creation by God, that is to say, its
being not merely in the region of ideas, or essences, or
possibilities, which is the pure understanding of God.
but also in the sphere of final causes, in which the will
of God operates \ In other words, the actual universe
is the result of a free choice of God amongst all possible
universes. While the choice of God is free, being un-
limited in its application, it _js_no_t__an arbitrary choice,
but_a_choiiifi.-according to. reason. God chooses as the
Victual universe that whose compossible elements admit
pf the greatest amount of perfection or reality, that is to
pay, the fullest and most complete essence. Thus the

(actual universe is ' the best of all possible worlds ' — of
all worlds which are really worlds or systems, that is,
in Leibniz's language, of all worlds whose elements are
compossible. God makes this choice because, being
omnipotent, His choice is unlimited, He may create any
possible world ; being omniscient, He contains all possible

1 worlds in His understanding and perceives that which is
best ; and, being perfect in goodness of will, He chooses
the best. Thus the Divine Nature is ultimately the
sufficient reason of all particular things, since it is the
ground both of the essence and of the existence of the
actual universe 2, which, in its turn, as a system of corn-
possibles, is the immediate ground of its individual ele-
ments.

Accordingly, the principle of contradiction and the
principle of sufficient reason remain side by side in the

1 According to Leibniz, existence (or the creation which produces
existence) involves no change in the essence of a thing. Its essence
is the same, whether it be in the actual world or merely in the
region of the Divine ideas. Cf. Monaddogy, §§43 and 47, notes.

a Cf. Theodicee, § 7 (E. 506 a ; G-. vi. 107) : ' His understanding is
the source of essences, and His will is the origin of existences.'
Also Monadology, §§ 53-55, and Theodicee, § 201 (E. 565 b ; &. vi. 236).

GENERAL PRINCIPLES 67

philosophy of Leibniz, each having its specific function,
but neither reducible to the other, while no attempt is
made to find a more comprehensive principle which may
include both. There are certain eternal and necessary
truths which are independent of the will of God, existing
in His understanding alone, and these are subject to the
principle of contradiction ; but the reality of all indi-
vidual substances and their changes is dependent on the
will as well as the understanding of God, and they are
all subject to the principle of sufficient reason. Each
principle expresses a certain necessity ; but the necessity
of the principle of contradiction differs in kind from
that of the principle of sufficient reason, the former
being an absolute, compelling, or metaphysical necessity,
whose opposite is impossible, involving self-contradiction,
while the latter is a relative, inclining, or moral neces-
sity, whose opposite is not impossible, but incompossible,
inconsistent not with itself but with the system of which
it is a part, inconsistent not so much with the eternally
true as with the best possible.

The leading Characteristics of Leibniz" s Philosophy as
Results of the two great logical Principles.

We are now in a position to see how the main features
of the Metaphysics of Leibniz are determined by these
great logical principles which underlie it \ The principle
of contradiction, taken by itself, is a principle of exclu-
sion. A is A (every real thing is identical with itself)
at all times, in all circumstances, throughout all changes,
in every variety of relations. Strictly speaking, then,
A can never become B. A is always A, B is always B ;
each is for ever exclusive of the other. ' Black is black,
furieusement black ; white is white, furieusement white. '
The principle of contradiction, as thus interpreted, is

1 What follows is, of course, not an exposition of Leibniz's explicit
doctrine, but an analytic investigation of the way in which his
logical principles fix the main lines of his philosophy.

F 2

68 INTRODUCTION

a principle of pure self-identity which asserts permanence
to the exclusion of change or, in general, unity to the
exclusion of difference. In other words, it insists on
the reality of Terms, making relations subordinate or
fictitious. Consequently a philosophy whose dominant
principle is that of contradiction, in this sense, must
(consciously or unconsciously) treat whole and parts as
exclusive of one another, asserting the reality of the one
as against that of the other. For if the whole be real
it must be simple, it must exclude as unreal all relations
or differences. Otherwise it will not be purely self-
identical, but may receive a variety of real predicates.
And as it is simple it can have no real parts. Since A
cannot be not- A, and since not-A includes B, C, &c.,
it cannot be true that some A is B or C. Some A can
only be A without further distinction,, On the other
hand, if the parts be real and purely self-identical, if the
reality of each is self-centred and is determined without
regard to its relations to the others, then there is no
real whole, but only a numerical collection of individuals
which may even be contradictory of one another. The
principle of contradiction, considered as meaning merely
that the real is that which is not self-contradictory, yields
either a whole, which has no real parts or determinations
because it is equally indifferent to all possible determina-
tions, or a bare collection of severally possible, but jointly
' incompossible ' parts.

Now, it is the influence of the principle of contra-
diction, thus abstractly interpreted, that leads Leibniz
to the conception of real substance as simple, i. e. as
without parts, indecomposable. And it is the same
principle that accounts for the infinite plurality of simple
substances and their complete isolation from one another.
For Leibniz, in order to give due value to the differences
in the universe, holds the principle of contradiction as
ensuring reality to the parts, leaving the whole to be
otherwise accounted for. And, on the other hand, the

GENERAL PRINCIPLES 69

mutual isolation of simple substances is but another
name for their abstract self-identity. A can never become
B, and, as A and B are simple, no part of A can ever
become B, or a part of B. One Monad can never become
another, and no quality of one Monad can ever become
a quality of another.

The principle of sufficient reason in combination with
the principle of contradiction yields the idea of the
Monad as itself the source of all the differences it con-
tains, the whole variety of its existence 1. The principle
of contradiction requires that real substance must con-
tain its whole nature within itself in such a way that
it may be analytically deduced. The notion of substance
is self-explicative. Every true proposition must be ana-
lytic. Thus the Monad must be self-sufficient. But
now the principle of sufficient reason is added to explain
that the analysis is not necessarily completed in every
case, that, while substance must be self-sufficient and self-
explicative, its self-sufficiency is not necessarily in every
case fully realized. Its self-identity is not static but
dynamic : it is not immediately self-explaining, but pro-
gressively self-revealing. Many true propositions are not
actually but potentially analytic. While the predicate
of every true proposition must in some way be contained
in the subject, it does not follow that in each particular
case the relation can be made perfectly and self-evidently
clear2. The predicate must have a sufficient ground or
reason in the subject, but not necessarily a self-evident
one. The Monad must be conceived as sufficiently the
reason of its changes or varieties, though not self-evidently
the reason of each. In other words, the various per-
ceptions which are the variety or change in the Monad,
the manifold [multitude] in the simple substance, have

1 The problem how the simple substance can contain differences is
the same as the problem how the principles of contradiction and
sufficient reason can be treated as independent and co-ordinate.
Of this Leibniz offers no clear solution.

2 Cf. this Introduction, Part ii. p. 60, note 2.

70 INTRODUCTION

reality even though they are not all perfectly clear and
distinct. Thus Spinoza, under the guidance of the prin-
ciple of contradiction, rejected merely empirical know-
ledge, the contingent sequence of ideas that comes ab
experientia vaga, as confused and therefore unreal and
illusory, a work of imagination. On the other hand,
Leibniz (for whom this empirical sequence is the series
of perceptions in Monads that have not reached the self-
conscious stage) attributes to this sequence a relative
reality, inasmuch as it is potentially, though not actually,
clear and distinct.

Further, we see the influence of the principle of suffi-
cient reason in the conception of the Monads as each
representative of the whole universe from its particular
point of view. The Monads are indeed Terms or absolute
points, centres exclusive of one another ; but they are
not Terms exclusive of relations. It is a part of their
essential reality to contain within themselves a multi-
plicity of relations. The Monad may be likened to ' a
centre or point in which, quite simple though it is, there
exists an infinite number of angles, formed by the lines
which meet in it1.' The principle of contradiction
requires nothing but a pure simplicity in the individual
substance ; any kind of simple substance would satisfy
it. But the principle of sufficient reason imposes the
further condition that the simple substance must have
relations to other simple substances and to the whole,
and that only those simple (self-consistent) substances
are real which are also consistent with the real unity
of the whole. For otherwise every real substance would
have its ground or reason wholly in se, and those things
for which we must be content with a ground or reason
in olio would be entirely illusory. Thus the combination
of self-consistency with consistency in relation to the

1 Principles of Nature and of Grace, § 2. Of. Extrait du Dictionnaire de
Bayk, &c. (1702) (G. iv. 542) : 'God has put in each soul a concentra-
tion of the world.'

GENERAL PRINCIPLES 7!

whole is what Leibniz means by the character of the
Monad as at once exclusively individual and represen-
tative or perceptive of the whole universe from its par-
ticular point of view.

Again, the appetition of the Monads is due entirely
to the principle of sufficient reason. A substance which
is real in virtue of its mere possibility can have no ten-
dency to a change of state 1. If it were really to change
it would cease to be itself. But the appetition of the
Monads is ruled not by the principle of realizing the self-
consistent or the abstractly possible, but by the principle
of realizing the best or the full harmony of a system.
The pre-established harmony of the universe as a
system of l compossible ' substances is the ground or
reason of the appetition in each, the principle of its
changes. But this, as we have seen, is a consequence
of admitting the principle of sufficient reason.

Lastly, a very slight consideration will show that the
law of continuity (with its obverse, the identity of in-
discernibles) is a particular application of the principle
of sufficient reason. A breach in the continuity of the
series of simple substances would mean a void in nature.
Such a void is not inconsistent with the principle of
contradiction : it is not self-evidently impossible. But
it is inconsistent with the principle of the best or most
fitting which governs the actual system of things, that
is to say, it is inconsistent with the principle of sufficient
reason. That one possible thing is in itself more perfect
than another is no sufficient reason for the existence of
the former rather than the latter ; the former might
perhaps be incompatible, while the latter is compatible,
with the rest of the world. But it is inconsistent

1 Cf. Spinoza's Conatus, the ' effort by which each thing endeavours
to persevere in its own being,' and which is ' nothing but the actual
essence of the thing itself.' Ethics, Part iii. Prop. 7. Leibniz
might say that, on Spinoza's principles, to call this an * effort ' is to
beg the question, because effort implies tendency towards some-
thing.

72 INTRODUCTION

with the principle of sufficient reason that nothing
should exist where something is possible ; for the prin-
ciple of sufficient reason requires the existence of a
complete world, that is to say, of that entire system of
compossible things which contains the fullest reality or
the greatest amount of essence l. Consequently the law
of continuity derives its force from the principle of
sufficient reason. And thus, in general, Leibniz's solu-
tion of his main problem is accomplished by the com-
bination of the principles of contradiction and sufficient
reason, giving, on the one hand, real units of substance,
even more thoroughly impenetrable and indivisible than
physical atoms ; and, on the other hand, in consistency
with these, a real whole, which is not a mere aggregate
of independent and perhaps mutually contradictory ele-

i cf Ivme LMre ^ Qfafo (I^I6), Apostate (E. 758 b ; G. vii. 378)
(Clarke's translation) : ' In like manner, to admit a vacuum in
nature is ascribing to God a very imperfect work ; 'tis violating
the grand principle of the necessity of a sufficient reason ; which
many have talked of, without understanding its true meaning. . . .
To omit many other arguments against a vacuum and atoms, I shall
here mention those which I ground upon God's perfection and
upon the necessity of a sufficient reason. I lay it down as a prin-
ciple that every perfection which God could impart to things
without derogating from their other perfections has actually been
imparted to them. Now let us fancy a space wholly empty.' God
could have placed some matter in it, without derogating in any
respect from all other things ; therefore He hath actually placed
some matter in that space : therefore there is no space wholly
empty : therefore all is full. ... I shall add another argument,
grounded upon the necessity of a sufficient reason. 'Tis impossible
there should be any principle to determine what proportion of
matter there ought to be, out of all the possible degrees from
a plenum to a vacuum, or from a vacuum to a plenum.' [? The pro-
portion of either plenum to vacuum or of vacuum to plenum.'] ' Perhaps
it will be said that the one should be equal to the other; but,
because matter is more perfect than a vacuum, reason requires that
a geometrical proportion should be observed, and that there should
be as much more matter than vacuum as the former deserves to
have the preference before the latter. But then there must be no
vacuum at all ; for the perfection of matter is to that of a vacuum as
something to nothing.' Cf. also the beginning of Leibniz's second
letter (,E. 748 b ; G. vii. 356) : « The more matter there is, the more
opportunity is there for God to exercise His wisdom and His power ;
and for this reason, among others, I hold that there is absolutely
no void.' ,

GENERAL PRINCIPLES 73

ments, but the most perfect system of mutually consistent
or compossible substances, in each of which the whole is
in some way ideally contained l.

1 Further consideration of the relation between these two great
principles in the philosophy of Leibniz is given in the Fourth Part
of this Introduction, p. 174.

PART III.

DETAILED STATEMENT OF THE PHILOSOPHY OF LEIBNIZ.

PASSING from the general consideration of the doctrines
of Leibniz, we now come to their more specific develop-
ment. We shall, in the first place, examine the relation
between his philosophical principles and the ruling con-
ceptions of his Mathematics, and we shall aftenvards
endeavour to trace the principles of the Monadology in
the various departments of knowledge which are con-
cerned with Matter, with Organism, and with Self-
consciousness. This review of human knowledge, pro-
ceeding from the most abstract or simple to the most
concrete or complex of the sciences1, will reveal to us
the interpretation which Leibniz's conception of Sub-
stance requires us to give to the judgments of common
consciousness. From another point of view, we may
consider ourselves as inquiring : — * What are the answers
which Leibniz would make to objections against his
system, based upon facts, hypotheses, or common beliefs
in mathematical and physical, biological and mental
science ? '

A. LEIBNIZ'S MATHEMATICS IN RELATION TO HIS

PHILOSOPHY.

It was partly through Mathematics that Leibniz
arrived at the notion of Substance which is the core of
his philosophy. Dissatisfaction with the Mathematics
of Descartes and with its consequences in Physics led
him to reject the Cartesian theory of matter and motion

1 The consideration of Leibniz's Theology or Philosophy of Reli-
gion is beyond the scope of the present volume.

STATEMENT OF LEIBNIZ S PHILOSOPHY 75

and to substitute for it a more adequate theory of Force
and a higher Mathematics. Both the Mathematics and
the Physics of the time appeared to Leibniz to be too
abstract, and the great object of his speculations was to
bring them more into touch with concrete reality.

The Transition from Synthetic to Analytic Geometry.

Early in the seventeenth century a considerable ad-
vance was made in the science of Mathematics, mainly
through the work of Kepler, Cavalieri, and Descartes.
The Geometry of the Greeks was synthetic or synoptic.
It dealt with ideal figures as discrete wholes, not taking
into consideration the possibility of their being analyzed
into elements, of which they are combinations or func-
tions. Thus the relations of the figures to one another
are considered as external. Each is what it is : no one
is regarded as having in it the possibility of passing into
another. A rectilineal figure is one thing ; a curvilinear
figure is another. The barriers between them are re-
garded as insurmountable, at least by the methods of
exact or demonstrative science. Thus a curve is still
a curve, however small may be its curvature. A polygon
is still a polygon, however numerous may be its sides.
And the kinds of curves are each independent of the
others. An ellipse is still an ellipse, however distant
one focus may be from the other.

Kepler's introduction of the notion and the name of
infinity into Geometry was the beginning of a great
change in mathematical methods. The geometrical
figures of the Greeks were all finite, and therefore
capable of representation to the eye, or, in other words,
capable of being pictured. Every curve must have
a definite curvature. Every polygon must Ijave a de-
finite number of sides. Kepler, in order to attain to
greater exactness in the statement of mathematical
relations, suggested that finite (or definite) figures might

76 INTRODUCTION

be regarded as consisting of an infinite (or indefinite)
number of elements. Thus he considered a circle to be
composed of an infinite number of triangles, having
their common vertex at the centre and forming the
circumference by their bases1. Such an analytic con-
ception of the figure is, of course, not capable of being
pictured. But it at once suggests the possibility of
representing the figure, not by a rough drawing or
image, but by an infinite numerical series the terms
of which are so related to one another that their sum is
finite. Accordingly, in thus considering the finite as
made up of an infinite number of elements, we have
promise of a connexion between Geometry and Algebra,
of such a kind that geometrical relations may be sym-
bolized algebraically and the knowledge of them may be
extended and generalized by calculation. Such a con-
nexion would mean the reduction of the discontinuous
concepts of Synthetic Geometry to the comparative
continuity of Algebraic Concepts or Numbers. It would
thus lessen the abstractness of Geometry, and make it
more adequate to the continuity of nature, or, looking
at the same thing from the dpposite point of view, it
would enable the continuous system of space-relations
to be more completely brought within the range of
mathematical demonstration. For instance, problems
w^hich the Greeks had to solve by the indirect and
unsuggestive method of reductio ad absurdum would now
be capable of a direct demonstrative solution, and there
would arise many new problems which the old methods
could not touch. /

1 In a similar way Cavalieri afterwards suggested that the area
of a triangle might be conceived as made up of an infinite number
of straight lines, each parallel with the base. The lengths of these
lines he regarded as forming an infinite series in arithmetical pro-
gression, of which the first term is zero. The sum of this series is
equal to half the product of the last term (i.e. the length of the
base of the triangle) and the number of terms (i.e. the altitude of
the triangle). As against this it was pointed out that, since a line
has no breadth, no number of straight lines can ever make up a

STATEMENT OF LEIBNIZ S PHILOSOPHY 77

The Basis of Analytical Geometry.

This connexion between Algebra and Geometry was
definitely established by Descartes in the Analytical
Geometry, of which he was the inventor. The basis of
the Analytical Geometry is/ the finding of a definite
proportion between the space-relations or ratios investi-
gated by Geometry and certain numerical ratios. But
the space-relations of Geometry are not merely quantita-
tive as are the relations of number. To take the simplest
of instances, the square upon a line may be represented
by the square of a number. But the square of a number
n is simply n times n, that is to say, it is the sum of
n n's added together. The square of n is a quantity of
n's or a simple series of homogeneous units, which may
be interchanged within the series without in any way
affecting the result. On the other hand, the relation
of a geometrical square to the line upon which it is
constructed (i.e. to any one of its sides) is not purely
quantitative. The square is not a sum of lengths. It is
a figure with special characteristics. The line cannot
intelligibly be regarded as its unit. It is its side, and
as the side of a square it has properties other than those
which it would have as a mere line. It is, in fact,
part of a unity which is more than merely quantitative.
And yet a quantitative ratio can express the relation
between the square and its side, in such a way that the
properties of the square may be algebraically calculated
without direct reference to the geometrical figure. Thus

plane area. Pascal, however, showed that Cavalieri's method
really implied that the infinite series of straight lines is an • in-
definite ' number of l small ' rectangles, which are so small that
the minute triangles between them and the sides of the given
triangle may be neglected in the computation. This l indefinite '
of Pascal is the l infinite ' of later mathematicians, and his ( small '
is manifestly their ' infinitely little.' Thus we have here the
transition from the ancient to the modern methods. Pascal vindi-
cated Cavalieri's method on the ground that it differed only in
manner of expression from the method of exhaustions, used in the
Greek mathematics.

78 INTRODUCTION

relations of quantity (that is to say, of mere aggregation)
may become signs or symbols of relations which are
more than quantitative, relations in which the part is
not indifferent to the whole but characteristic of it. All
the processes of Algebra, however complex and elaborate,
are forms of the addition and the subtraction (or separa-
tion) of abstract units. Thus the abstract number i
remains the same, into whatever algebraic combination
it may enter as a part. But the conception of a straight
line, for instance, varies (the line has various functions)
according to the nature of the whole into which it enters
as a part, and according to the special way in which it is
related to the whole. Thus in relation to different kinds
of figures (rectilineal, curved, &c.), or on account of the
various forms of its relation to one and the same figure,
a straight line is a side, a tangent, a raclius, a directrix,
an axis, a sine, &c. There is a closer, more real unity
between the part and the whole than in the relation of
mere quantity, where the part is indifferent to the special
character of the whole.

Relations of purely quantitative Unity and geometrical
Unity. Infinite Series and the infinitely little.

But there is no absolute gulf fixed between quantita-
tive unity and geometrical unity. The difference is,
that geometrical unity, while abstract in comparison
with organic unity or with the real concrete unity of all
existence, is less abstract than merely quantitative unity1.
And the bridge between the unity which is expressed in
the Algebra of finite quantities and that which is expressed
in the Geometry of finite space-relations is to be found in
the analysis of a finite quantity into an infinite series.
No finite quantity can be resolved into an infinite series

1 Strictly speaking, a merely quantitative unity is a contradiction
in terms, for mere quantity is pure difference, the absence of unity.
But what I mean here is unity of the lowest degree, unity on the
point of vanishing, or the most indeterminate unity.

STATEMENT OF LEIBNIZ S PHILOSOPHY 79

formed by an addition of independent integers, such as
i + i + i, &c., or even 1 + 2+3, &c-> that is to say, by an
addition not conditioned by any special law. But there
are certain numerical series in which the terms are not
mutually indifferent (nor immediately reducible to a set
of mutually indifferent terms), but are arranged, or rather
proceed from one another, according to. a definite law,
which law is of such a kind that, although it never
brings the series actually to an end, it results in the sum
of the series approaching more and more nearly to some
finite quantity. Accordingly it is held that, if the series
be regarded as consisting of an infinite number of terms,
the difference between the sum of its terms and the finite
quantity will be infinitely little, and therefore practically
negligible.

This ' practically negligible ' is the keystone of the
bridge between algebraic quantity and geometrical,
physical, or any other kind of relation. Strictly speaking,
if the series be regarded as a pure sum, and therefore
ultimately analyzable into an addition of homogeneous
units (i + i + i, &c., or n + n + n, &c.), the finitude of its
sum is incompatible with its having an infinite number
of terms. It is only inasmuch as the series is regarded,
not as a merely quantitative unity, but as a unity deter-
mined by a characteristic law or principle, that we are
entitled to disregard the ' infinitely little ' difference
between the sum of its terms and the finite quantity.
There can be no absolute * infinitely little ' in mere
quantity. The ' infinitely little' here considered is
* infinitely little ' as determined by the law or character
of the particular series. That is to say, we are certain
that the law of the series holds unchangeably, however
far the process of analysis may be carried ; and we have
thus inferential certainty regarding the result of the
analysis (the equation of the sum of the terms to the
whole finite quantity), even although we may be unable
actually to count each one of the terms. It is the law

8o INTRODUCTION

or principle of the series which enables us to say that the
' infinitely little ' difference may be neglected because the
character of the series is not affected by it.

But in neglecting this * infinitely little ' difference,
because of the special character or law of the series, we
have virtually passed from the unity of mere quantity to
a unity of character, a unity in which the parts are not
entirely indifferent to the whole and to one another, but
are connected in accordance with some special principle.
We have thus given an indefinite increase of elasticity to
the formulae of Algebra and have prepared the way for
an algebraic representation and calculus not merely of the
elementary space-unities (figures) of the Greek Geometry,
but also of more comprehensive geometrical unities of
which these are elements, and further of physical unities
and indeed of any unity the elements of which are in
themselves capable of a sufficiently accurate quantitative
expression. For instance, the phenomena with which
Physics deals are differences of a unity, elements in
a whole. But the unity, the whole, is not one of quantity
merely. And yet its elements are capable of quantitative
expression with a degree of accuracy such that its dif-
ference from absolute accuracy may be neglected so far as
physical science is concerned. Consequently it becomes
possible to state and to work out nggfelems of physical
science in terms of Algebra.

The Infinitesimal Calculus and the Principle of Becoming
or System.

The practical development of this possibility is the
function of the Infinitesimal Calculus of Leibniz and
Newton3. As we have already seen, the Analytical

1 A succinct account of the famous controversy regarding the
discovery of this method, and of the different forms in which
Leibniz and Newton expressed it/will be found in Dr. William-
son's article * Infinitesimal Calculus ' in the pth ed. of the Encyclo-
paedia Britannica. Cf. Merz, History of European Thmight in the Nineteenth
Century, i. 100-103.

STATEMENT OF LEIBNIZ'S PHILOSOPHY 8 1

Geometry reduces the discontinuity of Synthetic Geo-
metry to the relative continuity of number, or quantity
of homogeneous units. But number as a sum of finite
units (even though it may take the form of an infinite
series) is still to some extent discontinuous. It may,
however, be made continuous by regarding its elements
not as finite units, but as t infinitesimals ' or infinitely
little quantities. In other words, any numerical unit we
may choose to employ may be subdivided infinitely, and
thus every finite number may be regarded as the sum of
an infinite series of infinitely small terms. This is the
basis of the Infinitesimal Calculus as originally conceived
by Leibniz. It may be otherwise expressed by saying
that the series of finite numbers or quantities is ulti-
mately to be expressed, not as a series of terms which
grow by finite increments (like i-f-(i + i) + (i + i+i)
&c.), but as a series whose terms flow into one another,
their differences being infinitely small. That is to say,
any variable magnitude must be regarded as increasing or
diminishing by infinitely small increments or decrements.
The work of the Calculus is to determine the relations
between unknown quantities or magnitudes, not by
considering them merely as fixed wholes and directly
finding equations between them, but indirectly, by treat-
ing the quantities as variables or as growing, and in the
first place finding equations between their elements or
differences *.

1 From one point of view it may be regarded as the solving of the
problem of Achilles and the tortoise. Cf. Lettre a M. Foucher (1693)
(E. 118 a; G. i. 416) : 'As to indivisibles, in the sense of the mere
extremities of a time or of a line, we cannot conceive new extremi-
ties, nor actual nor potential parts in them. Thus points are
neither large nor small, and no leap is needed to pass them. Yet
the continuous, although it everywhere has such indivisibles, is
not composed of them, as the objections of sceptics seem to suppose.
There is, in my opinion, nothing insurmountable in these objections,
as will be found if they are put into strict form. Father Gregory
of St. Vincent has excellently shown, by the Calculus of infinite
divisibility, the place where Achilles should overtake the tortoise
which starts before him, according to the proportion of their
velocities. Thus Geometry dissipates these apparent difficulties.'

0

82 INTRODUCTION

Accordingly, for instance, Newton regarded all geo-
metrical magnitudes as capable of generation by con-
tinuous motion. Lines may be regarded as generated by
the motion of points, surfaces by that of lines, and solids
by that of surfaces. That is to say, these figures are dis-
tinct from one another, not absolutely, but merely in the
degree in which they possess certain characteristics. The
difference between the point and the line is an infinitely
small degree of length, the difference between the line
and the surface is an infinitely small degree of breadth,
the difference between the surface and the solid is an in-
finitely small degree of depth. * Motion, ' in Newton's way
of putting it, is in this connexion merely a metaphor for
continuity. Again, in physical science we have to deal
with phenomena which not merely are variable but are
continually varying, and the Infinitesimal Calculus is of
the utmost value in enabling us to state the laws of these
variations, that is to say, to establish proportions between
different sets of constantly changing phenomena.

The value of the Infinitesimal Calculus in the interpre-
tation of nature rests ultimately on this, that the con-
ception of ' infinitesimals ' which it employs is a virtual
recognition of System in knowledge or of the principle of
Becoming as distinct from that of abstract Being. When
we say that a thing (a geometrical figure, for instance) has
a certain quality or characteristic in an infinitely small
amount, we mean that it both has and has not that quality
or characteristic, or (to use another metaphor made familiar
by Psycho-physics) that it is on the ' threshold ' of having
it. The identity of the thing is not merely superficial,
of such a kind that when a quality seems to pass away
from it the thing ceases to exist and another thing ap-
pears ; the identity of the thing is maintained through an
indefinite amount of difference. Thus, as we have seen,
the point, the line, the surface, and the solid are all recog-
nized as differences or relations within one system. So in
general, when we have shown that the difference between

STATEMENT OF LEIBNIZ'S PHILOSOPHY 83

one thing and another is infinitely little, we have not
converted each into the other, but have explained them,
both by referring them to a common ground. We can ex-
press each in terms of the other, provided we state expli-
citly their relations to one another within some system.
A parabola is not an ellipse ; but a parabola is an ellipse
with one of its foci at an infinite distance from the other. ,

, Continuity and the Logical Calculus.
Now it cannot be said that all this was fully manifest
to Leibniz himself ; but the truth of it underlies his
thinking. The Infinitesimal Calculus in his mathematics
is an expression of th& same tendency of thought which
makes the principle of sufficient reason so important an
influence in his philosophy — the tendency to a less
abstract, less dogmatic, more intensive way of looking at
things, in contrast with the a priori deductive methods
of the Cartesians. The influence of the mathematics of
Leibniz upon his philosophy appears chiefly in connexion
with his law of continuity and his prolonged efforts to
establish a Logical Calculus. As to the law of continuity
it is unnecessary to say more. It is the law of the end-
less relativity of things, the principle of system, of in-
finite multiplicity in unity, and we have seen that the
Infinitesimal Calculus is an application of it1. On the

1 Cf. Lettre a M. Bayle (1687) (G. iii. 51 ; E. 104 a) : 'I have seen
the reply of Father Malebranche to the remark I made on some laws
of nature which he laid down in the Recherche de la Verite. He
appears somewhat disposed to give them up himself, and his in-
genuousness is most laudable ; but he gives reasons for it and makes
restrictions which would bring us back into the obscurity from
which I think I have delivered this subject, and which conflict
with a certain principle of general order that I have observed. I hope,
therefore, that he will kindly allow me to take this opportunity of
explaining this principle, which is of great use in reasoning, and
which does not yet appear to be sufficiently employed nor known
in all its scope. It has its origin in the conception of the Infinite ;
it is absolutely necessary in Geometry, and it also holds good in
Physics, inasmuch as the Supreme Wisdom, which is the source
of all things, acts as a perfect geometrician, and according to a
harmony which cannot be bettered. . . . The principle may be stated
thus : When the difference between two cases can be diminished below any

G 2

84 INTRODUCTION

other hand, the endeavour to find a Logical Calculus
(implying a universal philosophical language or system
of signs) is an attempt to apply in theological and philo-
sophical investigations an analytic method analogous to
that which had proved so successful in Geometry and
Physics !. It seemed to Leibniz that if all the complex

given magnitude in datis or in the antecedents [ce qui est pose] it will neces-
sarily also be diminished below every given magnitude in quaesitis or in the
consequents [ce qui en resulte]. Or, to put it more simply : when the
cases (or wJiat is given] continually approach and are finally lost in one
another, the consequences or results (or what is required) must do the same.
This again depends upon a more general principle, to wit : datis
ordinatis etiam quaesita sunt ordinata. [If there is order in the grounds
there will also be order in the consequents.] But, for the under-
standing of this, instances are necessary. It is known that the case
or supposition of an ellipse may be made to approximate, as much
as we like, to the case of a parabola, so that the difference between
the ellipse and the parabola may become less than any given differ-
ence, provided that one of the foci of the ellipse be made sufficiently
distant from the other, for then the radii vectores proceeding from
this distant focus will differ from parallel radii vectores as little as
we like. Consequently all the geometrical theorems which may be
proved of the ellipse in general can be applied to the parabola by
considering it as an ellipse one of whose foci is at an infinite
distance, or (to avoid this expression) as a figure which differs
from some ellipse by less than any given difference. The same
principle holds in Physics. For instance, rest may be regarded as
an infinitely small velocity or as an infinite slowness. Accordingly,
whatever is true of slowness or velocity in general ought also to be
true of rest, thus understood ; so that the law of rest should be
regarded as a particular ease of the law of motion. Otherwise, if
this does not hold, it will be a sure sign that these laws are ill-
constructed. In the same way equality may be regarded as an
infinitely small inequality, and inequality may be made to approxi-
mate to equality as much as we like.' See also New Essays, Intro-
duction, p. 376, and Nouveaux Essais, bk. iv. ch. 16, § 12 (E. 392 a ;
G. v. 455) : ' But the beauty of nature . . . requires the appearance
of discontinuity [sauts~] and, so to speak, musical cadences among
phenomena.' In the letter to Bayle above quoted, Leibniz also
remarks (E. 106 a ; G. iii. 54) : ' It is true that in compound
things a small change may sometimes produce a great effect. For
instance, a spark falling upon a large mass of gunpowder might
overthrow a whole town ; but that is not contrary to our principle,
and might indeed be explained on general principles. But in the
case of elements or simple things nothing like this could happen ;
otherwise nature would not be the i-esult of infinite wisdom.'

1 As to the analogy between Symbolic Thought and Algebra, &c.,
cf. Locke, Essay, bk. ii. ch. 29, § 9 (Eraser's ed. vol. i. p. 490).
See also Fraser, vol. ii. pp. 12 and 124, where further references
will be found.

STATEMENT OF LEIBNIZ'S PHILOSOPHY 85

and apparently disconnected ideas which make up our
knowledge could be analyzed into their simple elements,
and if these elements could each be represented by a
definite sign, we should have a kind of 'alphabet of
human thoughts.' By the combination of these signs
(letters of the alphabet of thought) a system of true
knowledge would be built up, in which reality would be
more and more adequately represented or symbolized.
For, according to Leibniz, the progress of knowledge con-
sists in passing from obscure to clear ideas, from clear to
distinct, from distinct to adequate. Ideas are obscure when
analysis has not proceeded so far as to enable us definitely
to distinguish them from others. They are clear when
we can so distinguish them, but are not yet able to
enumerate their particular elements or qualities. They are
distinct when we can enumerate their qualities, and they
are adequate only when the analysis is complete, that is
to say, when all the elements of the clear and distinct
idea are themselves clear and distinct. In many cases
the analysis may result in an infinite series of elements ;
but the principles of the Infinitesimal Calculus in mathe-
matics have shown that this does not necessarily render
calculation impossible or inaccurate l. Thus it seemed to
Leibniz that a synthetic calculus, based upon a thorough
analysis, would be the most effective instrument of
knowledge that could be devised. ' I feel,' he says, ' that
controversies can never be finished, nor silence imposed
upon the Sects, unless we give up complicated reasonings
in favour of simple calculations, words of vague and un-
certain meaning in favour of fixed symbols [characteres]'2.'
Thus it will appear that * every paralogism is nothing but
an error of calculation.' 'When controversies arise, there
will be no more necessity for disputation between two
philosophers than between two accountants. Nothing
will be needed but that they should take pen in hand, sit

1 Cf. this Introduction, Part ii. p. 61 note.

2 De Scientia Universali sen Calculo Phihsophico (E. 83 b ; G. vii. 200).

86 INTRODUCTION

down with their counting-tables, and (having summoned
a friend, if they like) say to one another: Let us
calculate.' This sounds like the ungrudging optimism of
youth ; but Leibniz was optimist enough t9 cherish the
hope of it to his life's end.

This project of the Logical Calculus or philosophical
language connects the mathematics of Leibniz with his
theory of knowledge, while the Calculus of Infinitesimals
finds immediate application in his revision of Descartes's
theories regarding matter and motion. Descartes treated
motion and rest synthetically as constant quantitative
wholes. Leibniz regards them analytically as consisting
of an infinite series of degrees of one constant force.
Accordingly Leibniz admits that the Cartesian laws of
motion have a certain validity in relation to ' abstract '
motion, but denies that they are adequate to the 'con-
crete ' physical phenomena.

B. MATTER.

Descartes 's Theory of Matter and Motion.

As we have already seen, Leibniz's view of matter can
be understood only as it appears in contrast with that of
Descartes. In accordance with his interpretation of the
principle of contradiction, viz. that the essence of a thing
consists in that only which is common to all its manifes-
tations, or (otherwise expressed) in that only which
remains after all varieties or specific determinations have
been excluded, Descartes maintained that matter is essen-
tially extension. Bodily substance and magnitude or
spatial extent are identical. And all the changes in
matter or extension are ultimately reducible to motion.
Motion is regarded by Descartes as being ' the transference
of a portion of matter or a body from the neighbourhood
of those bodies which are in direct contact with it, and
which we consider as at rest, to the neighbourhood of
other bodies or portions of matter V Matter is infinitely

1 Piincipia, Part ii. 25. Descartes adds : ' By a body, or rather

STATEMENT OF LEIBNIZ'S PHILOSOPHY 87

divisible. Its division is due to motion. Its forms arise
solely from the combinations and separations of its parts,
which also are due to motion. ' All the variety of matter,
or the diversity of its forms, depends on motion1.' 'I
frankly avow that I acknowledge in corporeal things no
other matter than that which can be divided, shaped
[figurees], and moved in all kinds of ways, that is to say,
that which mathematicians call quantity, and which they
take as the object of their demonstrations ; and in this
matter I consider only its divisions, shapes [figures], and
motions ; and, in short, regarding this I will accept
nothing as true which is not deduced from it with as
much certainty as belongs to a mathematical demonstra-
tion. And inasmuch as by this means all the phenomena
of nature may be explained ... it seems to me that in
Physics no other principles ought to be accepted, or even
desired, than those which are here expounded V

Conservation of Motion (or Momentum), its Direction being
left out of account.

Again, according to Descartes, the quantity of motion
in the world (or in any material system complete in
itself and apart fr^m all external influences) is constant.
The motion (or momentum), whose quantity is thus con-
stant, is in each particular case directly proportional to
the mass and the velocity of the moving body, and it may

a portion of matter, I mean the whole of what is transferred to-
gether, although this may be composed of several parts which
themselves have other motions. And I say that motion is the
transfr rence and not the force or activity which transfers, in order
to show that motion is always in the moving object and not in that
which moves it ; for it seems to me that these two things are not
usually distinguished with sufficient care. Further, I mean that
motion is a property of the moving thing and not a substance ;
just as form is a property of the thing which has a form, and rest
is a property of that which is at rest.'

1 Principia, Part ii. 23 (Veitch's tr.).

2 Ibid. Part ii. 64 (tr. from Abbe Picot's French). Descartes's
object is to show that all the motion in the world is one, and thus
to get rid of the later Scholastic theories which referred each parti-
cular motion to some unexplained principle in the moving body.

88 INTRODUCTION

be expressed by the formula mv. Now no new motion
can come to any body from itself ; no material body is
self-moved, because its essence is pure extension, and the
idea of extension does not necessarily involve the trans-
ference of parts. To any quantity of matter, whether
large or small, motion comes entirely from without. Thus
at the creation of the world the whole material universe
received a certain fixed quantity of motion, which is con-
served by the * ordinary co-operation ' [concours ordinaire]
of God. Motion is thus a positive thing and not merely
relative to rest. Motion is not opposed to motion, but
to rest. Motions do not cancel one another ; they are
quantities which can merely be combined and separated.
And, on the other hand, each individual portion of matter
must remain in the state in which it is, unless it receives
motion from outside itself. The motion of any one body
is increased only by a corresponding decrease in the motion
of some other ; and the motion of any body is decreased
only by a part of it passing into some other. Motion is
diffused, but never destroyed \

1 Cf. Principia, ii. 36 (Veitch's tr.) : ' With respect to the general
cause of motion, it seems manifest to me that it is none other than
God Himself, who in the beginning created matter along with
motion and rest, and now by His ordinary 'concourse' alone pre-
serves in the whole the same amount of motion and rest that He
then placed in it. For, although motion is nothing in the matter
moved but its mode, it has yet a certain and determinate quantity,
which we easily understand may remain always the same in the
whole universe, although it changes in each of the parts of it. So
that, in truth, we may hold when a part of matter is moved with
double the quickness of another, and that other is twice the size of
the former, that there is just precisely as much motion, but no
more, in the less body as in the greater ; and that, in proportion as
the motion of any one part is reduced, so is that of some other and
equal portion accelerated. We also know that there is perfection
in God, not only because He is in Himself immutable, but because
He operates in the most constant and immutable manner possible ;
so that, with the exception of those mutations which manifest
experience or Divine revelation renders certain, and which we per-
ceive or believe are brought about without any change in the
Creator, we ought to suppose no other in His works, lest there
should thence arise ground for concluding inconstancy in God
Himself. Whence it follows, as most consonant to reason, that
merely because God diversely moved the parts of matter when He

STATEMENT OF LEIBNIZ'S PHILOSOPHY 89

Now it follows from this, that, while the quantity of
motion in the world, or in any isolated system of bodies,
is constant, its direction is variable. For, as all space is
body and is therefore a plenum, moving bodies must con-
tinually impinge upon others ; and if a moving body be
supposed to impinge upon a body at rest, of such mass
that the moving body is unable to overcome the resistance
of the other and to make it move, then the direction of
the moving body is changed ; it rebounds in the direction
from Which it came or is deflected in some other way.
But, as the moving body has been unable to impart any of
its motion to the body at rest, the quantity of its motion
remains unchanged, while its direction changes — it being,
of course, understood that the action of all other bodies,
except the two in question, is left out of account 1.

Leibniz's Theory of Motion. Conservation of Force.

Now, according to Leibniz, motion is simply change of
position. It is not a positive quality belonging, for the
time being, to the moving body ; but motion and rest are
entirely relative to one another. If the relative position
of any two bodies changes, we may regard either as
moving and the other as at rest 2. And, in general, rest
is merely an infinitely small degree of motion ; nothing

first created them, and now preserves all that matter, manifestly
in the same way and on the same principle o~n which He first
created it, He also always preserves the same quantity of motion
in the matter itself.'

1 Cf. Principia, ii. 41 : ' Each thing, whatever it is, always con-
tinues to be as it is in itself simply, and not as it* is in relation to
other things, until it is compelled to change its state by contact
with some other thing. From this it necessarily follows that
a moving body, which meets on its course another body so firm
and impenetrable that it cannot move it in any way, entirely loses
the determination it had of moving in this particular direction,
and the cause of this is evident, namely, the resistance of the body
which prevents it from going further ; but it does not necessarily
on this account lose any of its motion, since it is not deprived of its
motion by the resisting body or by any other cause, and since
motion is not contrary to motion/

2 Cf. Animadversiones ad Cartes ii Principia (1692?), Part ii. § 25
(G. iv. 369 ; Duncan's tr. p. 60).

go INTRODUCTION

in the world is absolutely at rest. Accordingly no body
begins to move from a state of absolute rest, but from
a state which is to be conceived as already one of motion,
however small in amount. Actual motion is not some-
thing added to a body which, to begin with, is bare mass ;
it is always gradual growth or increment of a motion
which is already there. Actual motion always pre-sup-
poses potential motion or a force which, though it may
not be observed, tends to appear as actual motion.
Descartes, then, was right in interpreting actual motion
as change of position, but wrong in overlooking potential
motion and thus in regarding the total quantity of actual
apparent motion in the universe, or in any independent
system, as constant. He was right also in holding that
each body tends to continue in the state in which it is ;
but he was wrong in thinking that a body can ever be in
a state of absolute rest, and thus in supposing that one
motion cannot oppose another, but can only be opposed
by rest. As a matter of fact everything tends to move,
and would move, were it not for counteracting tendencies
to motion in other things 1. That which is conserved, then,
is not actual motion, as an extrinsic property of material
substance, but this intrinsic tendency or potentiality of
motion, which Leibniz calls force. As mere change of
position does not enable us to attribute motion to one of
the two bodies whose position changes, and not to the
other, the body which we call the moving body (as dis-
tinct from the body at rest) is so, not in virtue of its
motion (in the sense of change of position), but because it

1 Cf. Lettre a M. Pelisson (1691) (Foucher de Careil, i. 208 ; Dutens,
i- 733) : ' It must be observed that every body makes an effort to
act on outside things, and would perceptibly act if the contrary
efforts of surrounding bodies did not prevent it. This has not been
sufficiently noticed by our moderns. They imagine that a body
might be perfectly at rest, without any effort. But this is due to
their failure to understand what bodily substance really is ; for in
my opinion substance cannot (at any rate naturally) be without action.
This also disproves the inaction which Socinians attribute to dis-
embodied souls.'

STATEMENT OF LEIBNIZ S PHILOSOPHY 9!

contains within itself the cause of the change, the force or
activity which produces the motion. ' The notion of
force,' says Leibniz, 'is as clear as that of activity and of
passivity, for it is that from which activity follows, when
nothing prevents it. It is eifort, conatus ; and while
motion is a successive thing, which consequently never
exists, any more than time, because all its parts never
exist together — while, I say, that is so, force or eifort, on
the other hand, exists quite completely at every instant
and must be something genuine and real. And, as nature
has to do rather with the real than with that which does
not completely exist except in our mind, it appears (in
consequence of what I have shown) that it is the same
quantity of force, and not (as Descartes believed) the same
quantity of motion, that is preserved in nature V

This force, then, which is constant, is not only an
actual but a potential reality. It is not mere capacity
for motion, mere passive movableness, nor is it actual
manifest motion or activity in general. It is something
between the two, an undeveloped or restrained tendency
to act, which in appropriate circumstances is the producer
of action 2. This force is to be measured by the quantity
of effect it produces. Descartes rightly insisted on the
quantity of effect as the thing to be measured ; but he

1 Lettre a M. Pelisson (no date, probably 1691) (Dutens, i. 719 ;
Foucher de Careil, i. 157). ' The relative velocity of two bodies '
[i. e. their apparent motion] ' may remain the same, although the
real velocities and absolute forces of the bodies change in an infinity
of ways, so that conservation of relative velocity has nothing to do
with what is absolute in the bodies.' Essai de dynamique (Gr. Math,
vi. 216). Cf. Appendix I, p. 351.

2 Cf. De Primae Philosophiae Emendatione, &c. (1694) (E. 122 b ; G. iv
469) : l Active force differs from the bare potency commonly recog-
nized in the Schools. For the active potency of the Scholastics, or
faculty, is nothing but a mere possibility of acting, which neverthe-
less requires an outer excitation or stimulus, that it may be turned
into activity. But active force contains a certain activity [actus]
and is a mean between the faculty of acting and action itself. It
includes effort and thus passes into operation by itself, requiring no
aids, but only the removal of hindrance. This may be illustrated
by the example of a heavy hanging body stretching the rope which
holds it up, or by that of a drawn bow.'

92 INTRODUCTION

conceived the effect in too narrow a way, regarding it
merely as actual motion (i. e. the momentum acquired by a
body) rather than the work done by the force, the kinetic
energy it produces (i.e. the vis viva which the body
acquires, and which Leibniz calls action motrice). The
formula for this action motrice is not mv but mv*. ' In the
uniform motions of one and the same body, (i) the action l
of traversing two leagues in two hours is double the action
of traversing one league in one hour (for the first action
contains the second exactly twice) ; (2) the action of tra-
versing one league in one hour is double the action of
traversing one league in two hours (or, actions which
produce one and the same effect are proportional to their
velocities) : therefore (3) the action of traversing two
leagues in two hours is four times (quadruple) the action
of traversing one league in two hours. This demonstration
shows that a moving body which receives a double or
triple velocity, in order that it may produce a double or
triple effect in one and the same time, receives a quadruple
or nonuple action. Thus actions are proportional to the
squares of the velocities. But most fortunately this
happens to agree with my calculation of force, drawn
both from experiments and from the pre- supposition that
there is no mechanical perpetual motion. For, according
to my calculation, forces are proportional to the heights
by descending from which heavy bodies might have
obtained their velocities, that is to say, as the squares of
the velocities. And, as there is always conserved the total
force for re-ascending to the same height or for producing
some other effect, it follows that there is conserved also
the same quantity of motive " force " [action motrice] in the
world ; that is to say, to put it definitely, that in any one
hour there is as much action motrice in the universe as
there is in any other hour. But at every moment 2 the

1 I. e. the work done or vis viva. For a full explanation of the
whole matter, see Stallo, Concepts of Modern Physics, ch. vi, especially
pp. 71 sqq.

1 * A momentary state of a body in motion cannot contain motion,

STATEMENT OF LEIBNIZ S PHILOSOPHY 93

same quantity of force is conserved. And in fact action
is nothing but the exercise of force, and amounts to the
product of the force into the time1.' Accordingly this
motive force or vis viva, the amount of which is constant,
includes direction, as well as quantity, of motion. For
the measure of it is height, or position relatively to the
surface of the earth. Descartes's l quantity of motion '
(mv) is the effect of a given force regarded merely as acting
during a given time. Leibniz's vis viva (mv2) is the effect
of a given force regarded also as acting through a given
distance. And Descartes did not take account of the
direction of motion, because he did not take into con-
sideration the distance through which the force acts.

Leibniz's Theory of Matter.

(i) Materia prima.

This doctrine of the conservation of force, as Leibniz
conceives it, involves the rejection of the theory that
material substance is nothing but extension 2. Extension

for motion requires time, but it none the less involves force.' Lettre
a Des Maizeaux (1711) (E. 676 a ; G. vii. 534).

1 Lettre a Bayle (undated) (E. 192 a ; G. iii. 60), cf. G. Math,
vi. 117. Of course, from one point of view, Leibniz's statement is
not quite accurate, since there are many forms .of energy of which
it takes no account. It is, however, on right lines. And indeed
(as Du Bois-Keymond and Stallo have pointed out) Leibniz in one
passage anticipates the modern theory of the transformation of
energy (the apparent loss of molar motion being represented by
increase of molecular motion), although the idea was not worked
out until a much more recent time. ' I had maintained,' says
Leibniz, ' that active forces are conserved in the world. It is objected
that two soft, or non-elastic bodies, when they collide, lose some
of their force. I answer, No. It is true that the "wholes" lose
force in respect of their total motion ; but the parts received it,
being agitated within the whole by the force of the collision. Thus
it is only apparently that the loss occurs. The forces are not
destroyed, but dissipated among the particles. That is not losing
them but doing as is done by those who turn large money into
small change.' Cinquieme Lettre a Clarke, 99 (E. 775 a; G. vii. 414).

2 Projet d'une Lettre a Arnauld (1686) (G. ii. 72) : 'Extension is an
attribute which cannot constitute a concrete [accompli'} being. We
cannot draw from it any activity or change. It expresses only
a present state, and not at all the future and the past, which the
notion of a substance ought to express. When two triangles are

94 INTRODUCTION

is mere capacity for receiving motion, bare movableness,
while motion is complete activity and is entirely extrinsic
to that which is moved. Force, on the other hand, is, as we
have seen, something between the two, viz. a potentiality
f- of motion or action that is always passing into actual
action when it is not prevented by a similar tendency in
another body. This force, then, shows itself not merely
in actual, positive motion, but in hindrance or resistance.
And if this force were not of the essence of material
bodies there would be no resistance among bodies and
the absurdity of perpetual motion would be true. For if
material bodies consist solely of extension, and if one
such body moving should come into contact with another
at rest (i. e. destitute of motion), then the former must
carry the latter along with it. For, ex hypothcsi, there is
nothing but space to resist the progress of the moving
body, and, if motion is possible at all, it must be motion
through space, i.e. motion which mere space cannot resist1.
Accordingly, in addition to extension (however it may
be interpreted), eveiy material body must have resistance
or impenetrability. This mere passive resistance Leibniz
on various occasions calls avriTviria. The avTirviria of a
body is simply its need of space. The body is not mere

found joined together, we cannot infer from them how the joining
has taken place. For it may have happened in various ways ; but
nothing which can have several causes is ever a concrete [accompli]
being.'

1 Epistola ad Des Bosses (1706) (G. ii. 295) : 'If, with the Carte-
sians, we were to admit a plenum and the uniformity of matter,
adding only motion, it would follow that there would never be any-
thing in the world but a substitution of equivalents, as if the whole
universe were to reduce itself to the motion of a perfectly uniform
wheel about its axis or to the revolutions of concentric circles of
perfectly homogeneous matter. In that case, it would not be pos-
sible, even for an angel, to distinguish the state of the world at one
moment from its state at another moment. For there could not be
any variety in the phenomena. That is why, in addition to figure,
size, and movement, there must be admitted forms from which
there arises in matter a variety of appearances ; and I do not see
whence we can draw these forms, if they are to be intelligible,
except from Entelechies.' Cf. De Ipsa Natura (1693), § 13 (E. 158 b ;
G. iv. 512).

STATEMENT OF LEIBNIZ S PHILOSOPHY 95

place : but it cannot be a body unless it has a place of its
own. And its avriTviria consists in its .maintaining its
place, staying where it is. Kesistance is thus a passive
force. ' Matter taken by itself or bare matter consists of
avTiTwrrta and extension. By avriTwria I mean that attribute
in virtue of which matter is in space. Extension is con-
tinuation through space, or continuous diffusion through-
out a place \ ' Matter is that which consists in di/TiTwria
or which resists penetration ; and thus bare matter is
merely passive 2. ' In so far, then, as a material body is
extended and occupies a place which cannot be occupied
by any other body at the same time (for this is the
meaning of avrirviria or impenetrability), it consists of
bare matter. Bare or abstract matter, as thus denned
a + extension), Leibniz usually calls materia prima.

(2) Materia secunda.

But we must beware of supposing that this materia
prima is by itself anything actual. As the mathematical
point is nothing actual, but is the indivisible limit of
extension, so materia prima is the indivisible limit of
matter. No portion of matter, no material body, consists
of materia prima alone, just as no portion of extension
is a mere mathematical point. For materia prima is
simply body considered as if it were purely passive : it is
the abstract passivity of body. But, as we have seen,
there is, according to Leibniz, no such thing as absolute
passivity. Passive resistance, impenetrability, inertia,
always involve a real force, a tendency to action, though
that tendency may actually be prevented by counteracting
forces from realizing itself at this or that particular
moment. Passivity is the limit of activity, as rest is the
limit of motion. Every material body, then, is ultimately
something more than avriTinria + extension. It is essen-
tially force or energy, activity of some kind. And

1 De Anima Brutorum (1710), § i (E. 462 a ; G. vii. 328).

2 Epistola ad Bierlingium (1710) (E. 678 a ; G. vii. 501).

96 INTRODUCTION

inasmuch as this force is a potential activity, a force
which tends to realize itself, it is automatic or sponta-
neous, it contains within itself the principle of its future
conditions, it is an Entelechy. Thus every actual
material body is materia secunda, from which materia
prima is merely a mental abstraction \ Every complete
substance is materia prima + Entelechy, i. e. passivity +
activity.

Now while materia prima, being abstract passivity, is not
to be regarded as real substance, materia secunda, inasmuch
as it is matter and is therefore extended and infinitely
divisible, is, on the other hand, not to be confounded
with individual substance. Materia secunda must con-
tain an entelechy, but is not identical with it. Materia
secunda is an aggregate of things : it is to be conceived as
quantitative, consisting of paries extra partes, and is thus
quite distinct from substance, which must be conceived
as striving force, i. e. under the relation of means to end2.

1 Cf. Epistola ad R. C. Wagnerum (1710) (E. 466 a ; G. vii. 529) :
'The active principle is not attributed by me to bare matter or
maieria prima, which is merely passive and consists solely in O.VTL-
jvrria and extension ; but to body or clothed matter or materia
secunda, which contains in addition a primary entelechy or active
principle. . . . The resistance of bare matter is not activity, but mere
passivity, inasmuch as it has avTirvvta or impenetrability, by which
indeed it resists that which would penetrate it. but does not re-act
unless it has in addition an elastic force. This elastic force must
be derived from motion, and thus also from an active force super-
added to matter/ Also De Ipsa Natura (1698), § 12 (E. 158 b ; G.
iv. 512) : ' Matter is understood as either materia secunda or materia
prima ; materia secunda is indeed a complete substance, but not a
merely passive one ; materia prima is merely passive, but is not
a complete substance ; and there must further be added to it a soul,
or form analogous to a soul, ivrt\cx*ia V "purr), that is a certain
effort or primary force of acting, which itself is an indwelling law,
imprinted by Divine decree.' It should be noted that the expres-
sion 'substance,' as here applied to materia secunda, is not to be
taken too strictly. Materia secunda is not so much substantia as sub-
stantiata. This is more clearly brought out in Leibniz's later
writings. See Monadology, note 2, and this Introduction, Part iii.
p. 98 note.

" Cf. Lettre a Remand (1715) (E. 736 a; G. iii. 657): 'Strictly
speaking, materia prima is not a substance, but something in-
complete. And materia secunda (as, for instance, the organic body)
is not a substance, but for another reason : namely, because it is

STATEMENT OF LEIBNIZ S PHILOSOPHY 97

In short, as materia prima is abstract passivity, the limit
of activity, and is thus in reality merely the finitude or
imperfection of a Monad, so materia secunda is mere
abstract quantity, the limit of intension, and is thus a
mere phenomenon of that which is essentially one and
indivisible, of the 'soul' which the body 'contains1.'
Accordingly every created Monad or simple substance
has materia prima in so far as it is not entirely active ; or,
in other words (since activity and passivity are relative
terms), every created Monad must have materia prima,
because its activity is not entirely realized, but is in part
potential, because it is not actus purus, activity without
passivity. ' Materia prima is essential to every entelechy •
and can never be separated from it, since it completes it,
*nd is itself the passive potentiality of the whole complete
substance. . . . God . . . cannot deprive a substance of
materia prima ; for He would thus make it wholly pure
activity [purus actus] wThich He Himself alone is'-'.'
Materia secunda, on the other hand, is not necessarily
attached to any specific entelechy or individual substance.
It is a relationship of Monads imperfectly conceived by us
as a group of things which may vary from time to time,
^and which, as a matter of fact, is constantly varying.
Leibniz compares it to a river 3. i God, by His absolute
power, may be able to deprive substance of materia
secunda*.' In fact, it is not by itself anything real, but is
merely the relation of certain Monads, regarded abstractly
as a temporary aggregation or collocation. The only real
existences are the Monads, which are purely spiritual,
non-spatial existences, but in relatively confused or

a collection of several substances, like a pond full of fish, or a flock
of sheep ; and consequently it is what is called unum per accidens : in
a word, a phenomenon. A real substance (such as an animal) is
composed of an immaterial soul an«d an organic body ; and it is the
combination of these two that is called unum per se.'

1 Cf. this Introduction, Part iii. pp. 78 sqq.

a Epistola ad Des Bosses (1706) (E. 440 b ; G. ii. 324).

3 Ibid. (1706) (E. 436 b ; G. ii. 306). Cf. p. 1 14 and Monadology, § 71.

4 Ibid. (1706) (E. 440 b ; G. ii. 325').

H

98 INTRODUCTION

abstract and imperfect thought (i.e. in 'sense' or
' imagination ' as distinct from thought proper) we are
presented with the phenomena of things variously
grouped in space, and these groups, qua groups, are
materia secunda l.

Phenomena bene fundata.

As materia secunda is always a mere aggregate, while
yet every aggregate pre-supposes as its reality an in-
divisible simple substance or soul, such aggregates or
groups of things, together with their powers, acts, and
affections, are sometimes described by Leibniz as well-
founded phenomena (phenomena bene fundata). They are

1 Cf. Lettre a Arnauld (1686) (G. ii. 75, 76) : ' In my opinion, our
body in itself (setting aside the soul), or the Cadaver, can be called
one substance only by a wrong use of terms, like a machine or
a heap of stones, which are only beings by aggregation ; for regular
or irregular arrangement has nothing to do with unity of sub-
stance. ... I hold that a marble pavement is probably only
like a heap of stones, and thus cannot pass for only one sub-
stance, but is a collection of several. For suppose there are two
stones — for example, the diamond of the Grand Duke and that of
the Great Mogul — we might give them both, in respect of their
value, one and the same collective name, and we might say that
they are one pair of diamonds, although they are actually far
distant from one another. But it will not be said that these
diamonds compose one substance. Now more or less make no
difference here. Accordingly, if we bring them nearer one
another, and even make them touch one another, they will be
none the more united in substance ; and although, after they had
been brought into contact, we were to join to them some other
body in such a way as to prevent them separating again — for
instance, if we were to set them in one ring — all that would make
of them only what is called unum per accidens. For it is as by
accident that they are compelled to share in the same motion.
I hold then that a marble pavement is not one concrete [accomplie~\
substance, any more than would be the water of a pond with all
the fish it holds, even although all the water and the fish were
frozen together ; or than a flock of sheep, in which the sheep
should be supposed to be so bound together that they could only
walk in step, and that one could not be touched without all the
others crying out. There would be as much difference between
a substance and such a being as between a man and a community,
like a people, army, society or college, which are moral beings and
in which there is something imaginary and created by our mind.
Unity of substance requires an indivisible and naturally inde-
structible concrete [accomplie~] being, since the notion of such a
being includes all that is ever to happen to it.'

STATEMENT OF LEIBNIZ S PHILOSOPHY 99

bene fundata in contrast with the phenomena of dreams
or visions, which are phenomena pure and simple, not
having any proper bond or connexion. Phenomena bene
fundata may be distinguished from the phenomena of
dreams, inasmuch as the former are vivid, multiplex (i.e.
varied in their relations and capable of a variety of tests
or observations), and congruous or consistent both with
themselves and with the general course of life or
experience, which we find in other phenomena. The last
of these tests is the most satisfactory, especially when it
is supported by the testimony of other people who have
also applied it. ' But the most powerful proof of the
reality of phenomena (a proof which is, indeed, sufficient
by itself) is success in predicting future phenomena
from those which are past and present, whether the pre-
diction be founded upon the success, so far, of a reason or
hypothesis, or upon custom so far observed1.' In short,
phenomena bene fundata are distinguished from illusions,
inasmuch as they are not merely separate and discon-
nected, but held together in a system so that their ante-
cedents may be traced and their consequents deduced2.
And Leibniz goes so far as to add: — 'Although this
entire life were said to be nothing but a dream, and the
visible world nothing but a phantasm, I should call this
dream or phantasm real enough, if we were never
deceived by it, when we use our reason rightly3.' On

1 De Modo distinguendi phenomena realia ab imaginariis (E. 444 a ;
G. vii. 320).

2 Can this be reconciled with the view that materia secunda is
a mere aggregate or collection ?

3 Loc. cit. Of course it must be remembered that the 'reality'
attributed by Leibniz to phenomena bene fundata is entirely relative
to the illusoriness of ' pure ' phenomena, such as we have in
dreams, and is not to be confounded with the reality of substance.
Cf. Nouveaux Essais, bk. iv. ch. 2, § 14 (E. 344 b ; G. v. 355) : * The
truth of the things of sense consists only in the connexion of the
phenomena, which must have its reason [ground], and that is
what distinguishes them from dreams ; but the truth of our
existence and of the cause of phenomena is of another kind,
because it establishes substances. . . . The connexion of the pheno-
mena which establishes truths of fact in regard to sense-objects

H 2

100 INTRODUCTION

several occasions Leibniz uses the rainbow as a simile by
which to illustrate what he means by a phenomenon bene
fundatum1. He simply mentions it without explanation;
but we may suppose him to have meant that the rainbow
is the type of a phenomenon bene fundatum, inasmuch as.
being merely colour, it exists as a rainbow only for those
who actually behold it, and is thus a mere appearance,
while, being an appearance which results from certain
physical conditions of light and moisture, it has a ground
or cause, it is the phenomenon of something and is there-
fore bene fundatum and not a pure phantasm or illusion.

Thus, in general, the qualities of matter, whether
secondary, as colour, smell, sound, &c., or primary, as
extension, figure, and motion, are phenomena bene fundata.
Taken by themselves, as qualities of a matter which has
no 'soul,' they are not real but merely subjective. But
their order or connexion implies a principle of order (i. e.
a soul), and accordingly they are confused (i. e. not fully
analyzed) representations, perceptions, or symbols of
that which, expressed distinctly, is real substance.
Ultimately ( ' metaphysically ' as Leibniz would say) they
are reducible to non-spatial perceptions or appetitions of
Monads ; but in the form in which they are given to us

outside of us is verified by means of truths of reason ; as the pheno-
mena of optics are explained by geometry. Yet it must be
admitted that this certitude is not of the highest degree. . . . For it
is not impossible, metaphysically speaking, that there is a consecu-
tive dream lasting as long as the life of a man ; but that is a thing
as contrary to reason as would be the fiction that a book could
be formed by chance through throwing down type in confusion.'
Cf. Locke, Essay, bk. iv. ch. 2, § 14 ; Eraser's ed., vol. ii. pp. 185
sqq., with Prof. Eraser's Notes, and also his Notes on pp. 332 and 333.
1 Cf. Epistola ad Des Bosses (,1715) (E. 728 b ; G. ii. 504) : * I prefer
to say that not substances but species' [i.e. sense -qualities]
'remain, and that these are not illusory, like a dream or like
a sword pointing towards us out of a concave mirror, or as
Dr. Faustus ate a cartful of hay, but true phenomena, that is, in
the sense in which a rainbow or a mock sun is a species, indeed
as, according to the Cartesians and in truth, colours are species.'
Also Epistola ad De Voider (1706) (G. ii. 281, note) : * Extension itself,
mass and motion, are no more things than the image in a mirror
or the rainbow in a cloud. . . .They exist vo^y rather than <pvo-(i, to
use the expression of Democritus ' (p. 282, note).

STATEMENT OF LEIBNIZ S PHILOSOPHY 1OI

by our senses or imagination (which perceive things
confusedly) they are mere connected or orderly pheno-
mena, abstractions or incomplete things, which pre-
suppose souls or Monads.

Space and Time.

In one of the Letters to Arnauld\ Leibniz speaks of
space and time as phenomena bene fundata. Probably,
however, he did not intend this statement to be very
rigidly interpreted, and there is much value in the view
of Erdmann that space and time are to be regarded as
purely ideal, entia mentalia 2, while extended bodies and
actual events in time are entia semimentalia 3 or phenomena
bene fundata. In any case, what Leibniz desires specially
to maintain is that space and time are not real substances
nor attributes of real substances. They are nothing but
orders or arrangements of co-existing and successive
things or phenomena. Individual substances or Monads,
which are the sole realities, are not to be conceived as
partes extra paries: the central thought of Leibniz's
philosophy is that this quantitative aspect of things
should be treated as subordinate, as not belonging to the
essence of real things. Hence space is to be regarded,
riot as the mutual exclusiveness of real substances, but as
simply the order of co- existence pre-supposed in the
aggregation or grouping of phenomenal things, while
time is the order of sequence of phenomena. 'Time,
extension, motion, and the continuous in general, in the
way in which they are considered in mathematics, are
only ideal things ; that is to say, things which express
possibilities, just as numbers do. Hobbes has even
denned space as phantasma existentis. But, to speak
more exactly, extension is the order of possible co- existences,
as time is the order of possibilities which are inconsistent,
but which have nevertheless some connexion. Thus

1 G. ii. 118. 2 Hist, of Philosophy (Eng. tr.), vol. ii. p. 185.
3 Cf. Epistola ad Des Bosses (1706^ (E. 436 b ; G. ii. 306).

102 INTRODUCTION

extension relates to simultaneous things or things which
exist together, time to those which are incompatible and
which are nevertheless all conceived as existing, and it is
this that makes them successive. But space and time
taken together constitute the order of the possibilities of
a whole universe, so that these orders (that is space and
time) square not only with what actually exists but also
with whatever might be put in its place, as numbers are
indifferent to whatever can be res numerata1.' Thus
space does not mean any particular situation of bodies, nor
time any particular succession of phenomena. Space is
simply the indefinitely applicable relation of co-existence,
while time is the indefinitely applicable relation of
succession or order of successive positions. In each case
the things or phenomena related might have been other
than they are, and thus the orders are orders of possi-
bilities. But in neither case is the order actual apart from
some ordered or related things. There is no actual empty
space or empty time. These are abstractions, harmless
or possibly useful when recognized as abstractions, but
hurtful if they are regarded as actual things.
^Tjeibniz's disproof of the independent reality of space
and time is directly based by him upon the principle of
sufficient reason. 'I say, then, that if space was an

1 Replique aux Reflexions de Bayle (1702) (E. 189 b ; G. iv. 568).
The translation is from Gerhardt's text. Cf. IIlme Lettre a Clarke,
4 (Clarke's tr.) (E. 752 a ; G. vii. 363): 'I bold space to be some-
thing merely relative, as time is : I hold it to be an order of co-exist-
ences, as time is an order of successions. For space denotes, in terms
of possibility, an order of things which exist at the same time, con-
sidered as existing together ; without inquiring into their particular
manner of existing. And when many things are seen together
one perceives that order of things among themselves.' The corre-
spondence between Leibniz and Clarke is mainly devoted to this
question of the meaning of space and time. Clarke endeavoured
to defend the view of Newton that infinite space is real, and is to
be regarded as a kind of sensorium of God or as His omnipresent
perception of things. Leibniz attacks not merely this particular
view, but all other theories which make space real, as, for instance,
those which confound infinite space with the Immensity of God
or with any other of His attributes. Cf. Eraser's ed. of Locke's Essay,
vol. i. pp. 259, 260. See also Explanation of the New System, i, note.

STATEMENT OF LEIBNIZ S PHILOSOPHY 103

absolute being there would something happen for which
it is impossible there should be a sufficient reason, which
is against my axiom. And I prove it thus. Space is
something absolutely uniform ; and, without the things
placed in it, one point of space does not absolutely diifer
in any respect whatsoever from another point of space.
Now from hence it follows (supposing space to be some-
thing in itself, besides the order of bodies among them-
selves) that 'tis impossible there should be a reason why
God, preserving the same situations of bodies among
themselves, should have placed them in space after one
certain particular manner, and not otherwise ; why every-
thing was not placed the quite contrary way : for instance,
by changing east into west. But if space is nothing else
but that order of relation, and is nothing at all without
bodies but the possibility of placing them, then those two
states, the one such as it now is, the other supposed to
be the quite contrary way, would not at all differ from
one another. Their difference, therefore, is only to be
found in our chimerical supposition of the reality of space
in itself. But in truth the one would exactly be the same
thing as the other, they being absolutely indiscernible;
and consequently there is no room to inquire after a reason
of the preference of the one to the other. The case is the
same with respect to time. Supposing any one should
ask why God did not create everything a year sooner, and
the same person should infer from thence that God has
done something concerning which 'tis not possible there
should be a reason why He did it so and not otherwise ;
the answer is, that his inference would be right if time
was anything distinct from things existing in time. For
it would be impossible there should be any reason why
things should be applied to such particular instants, rather
than to others, their succession continuing the same. But
then the same argument proves that instants, considered
without the things, are nothing at all, and that they
consist only in the successive order of things ; which

104 INTRODUCTION

order remaining the same, one of the two states, namely,
that of a supposed anticipation, would not at all differ,
nor could be discerned from the other which now is V

Accordingly, Leibniz's theory of space and time may
be summarized thus. Phenomena are bem fiwdata in
proportion as they are connected together. Space and
time are orders or systems of connexion between pheno-
mena, the bond being co-existence in the one case,
succession in the other. Apart from the phenomena,
space and time are mere abstractions. Thus pure space
and pure time are at two removes from reality, for
the things which are in space and time are not Monads
but phenomena. Yet ultimately phenomena are imperfect
realities, unanalyzed perceptions. They have a basis in
simple substance. Thus there must be something non-
spatial and non-temporal, of which space and time are
the imperfect expressions. And in a letter to Schulenburg
(1698) Leibniz, after denning space and time in his usual
way, says that * in themselves \per se] they have no reality
beyond the Divine Immensity and Eternity V

1 lllme Lettre a Clarke, 5, 6 (Clarke's tr.) (E. 752 a ; G. vii. 364^).
In answer to this, Clarke, while professedly admitting the prin-
ciple of sufficient reason, really denies its validity by maintaining
that the mere will of God is to be counted as a sufficient reason,
and that therefore Leibniz's application of the principle does not
prove his case. Cf. lVme Lettre a Clarke, 18 (E. 756 b ; G. vii. 374) :
'Space being uniform, there can be neither any external nor
internal reason by which to distinguish its parts and to make
any choice among them. For any external reason to discern
between them can only be grounded upon some internal one.
Otherwise we should discern what is indiscernible, or choose
without discerning. A will without reason would be the ' chance '
of the Epicureans. A God, who should act by such a will, would
be a God only in name.'

With regard to the general question, cf. Vme Lettre a Clarke, 62 (E.
771 b ; G. vii. 406) : <I don't say that matter and space are the
same thing. I only say, there is no space where there is no
matter, and that space in itself is not an absolute reality. Space
and matter differ as time and motion. However these things,
though different, are inseparable.'

2 G. Math. vii. 242. For Leibniz's account of the origin of
our idea of space, see Appendix B. p. 202.

STATEMENT OF LEIBNIZ S PHILOSOPHY 105
>P

Activity and Passivity of the Monads. Mutual Influence

of Substances. Cause and Effect.

So far, then, from space being, as Descartes held, the
essence of matter, it is a purely ideal relation which we
mentally construct between things or phenomena whose
ultimate reality or essence is not quantitative, and is
consequently not material l. But, as we have seen, every
one of the real substances (the Monads), each of which is
the essence or reality of a portion of matter, contains that
which, taken abstractly, may be described as materia
prima. Every created Monad is both active and passive ;
for there is no such thing as absolute passivity, and pure
activity belongs to God alone. As passive the Monad
has materia prima, as jictive it is entelechy. Thus every
soul has a body ; there is no such thing as an absolutely
disembodied spirit, unless it be the Spirit of God. And,
on the other hand, mere soulless body has no real exist-
ence: it is an abstraction. The world is active, living
through and through, even in its infinitesimal parts. It
is compact of souls.

Now this activity and passivity of. the Monads do not
mean that any Monad exerts a real influence outside of
itself or receives any real impression from a substance
external to it. The relations between the Monads are
purely ideal, and their activity and passivity are altogether
internal. As we have seen, a Monad is in itself passive in
so far as its perceptions are relatively obscure or confused,
active in so far as they are relatively clear and distinct.
And similarly, as each Monad perceives or represents the
whole universe from its own point of view, one Monad is
said to be passive in relation to another in so far as certain
perceptions in the former are obscure or confused in com-
parison with the corresponding perceptions in the latter ;

1 In spite, however, of this reduction of space, matter, &c., to
confused perception, Leibniz continues to use the language of
those who speak of them as real, comparing himself to a Copernican
who speaks of sunrise. Cp. Theodicee, § 65 (E. 521 a; G. vi. 138).

106 INTRODUCTION

while, on the other hand, the Monad whose perceptions
are clearer and more distinct is said to be so far active in
relation to the other or (ideally, of course) to act upon
it \ Thus, as we have already seen, the pre-established
harmony is the basis of the inter-relation of the Monads
and of their mutual changes 2. Further, as clear and
distinct perceptions are simply the unfolding (explication)
or explanation of the corresponding more confused per-
ceptions, the action of one substance upon another is to
be regarded as meaning that the active substance, in so
far as it is active, contains within itself (or, simply, is) the
explanation of the passive substance, in so far as it is
passive. Substances acting upon others are, accordingly,
those in which the reason of the changes in the others
may be read more distinctly than in those in which the
changes actually occur3. Thus the connexion between
cause and effect in different substances is a purely ideal
relation, a harmony of internal changes and operations,
implying no physical influence of one substance upon
another. And, further, the cause of any change is not its
obscure antecedent nor any power or activity prior in

1 Cf. Spinoza's views of action and passion hi Ethics, Part iii,
especially Defs. i and 2, and Props, i, 2, and 3. Also Ethics,
Part v. Prop. 40, Corollary.

a Cf. p. 40 ; see also Lettre a Arnauld (1690) (G-. ii. 135 ; E. 107 b), in
which Leibniz gives a summary of his position : ' There must be
everywhere in body substances indivisible, unborn and imperish-
able, having something corresponding to souls. . . . Each of these
substances contains in its own nature " legem continuationis seriei
suarum operationum " [the principle of succession of the series of its
own operations] and all that has happened and shall happen to
.it. All its actions come from its own inner being [fonds], except
Its dependence upon God. Each substance expresses the entire
universe, but one does so more distinctly than another, and each
expresses it more especially with regard to certain things and
according to its own point of view. The_union of soul with body,
and indeed the operation of one substance upon another, consists
only in the perfect mutual accord of substances, definitely estab-
lished through the order of their first creation, in virtue of which
each substance, following its own laws, agrees with the rest,
meeting their demands ; and the operations of the one thus follow
or accompany the operations or change of the other.'

3 Cf. Monadology, §§49 sqq.

STATEMENT OF LEIBNIZ S PHILOSOPHY 107

time to the effect ; the true cause is always the reason or
explanation, the distinct as opposed to the confused per-
ception, whatever may be the time-order of the events or
phenomena \

Mechanical and final Causes. Soul and Body.

Every substance, as we have seen, consists of soul and
body. And the soul, being on the one hand the relatively
distinct perception of the substance, and on the other
hand its activity, is the final cause of the substance, the
end for which it is, the self-development of its nature.
It must be conceived under the notion of Becoming, as ^p
a thing whose essence it is to move towards an end. It
cannot, therefore, be adequately described by purely
mechanical conceptions. It has something more than
a static self-identity ; its unity unfolds itself in the series
of its changes. Its reality is thus not determined merely V
by the principle of contradiction, taken as a principle of ->£-
pure or abstract self- consistency. The body of every J
substance, on the other hand, i. e. its matter, its confused
perception, its passivity, is the physical or mechanical
cause of the substance. Being entirely abstract, and in
itself a bare possibility, body may by itself be adequately
described by mechanical conceptions, under the principle
of contradiction. Thus we may have an abstract science
of physics by which the phenomena of abstract matter
are explained on purely mechanical principles, that is, as
a system of physical or efficient causes. But if we would
explain the concrete reality even of material substance we
must employ dynamical rather than mechanical concep-
tions, or, in other words, we must regard the world as
ultimately and essentially a system of final causes, a
system which is the expression, not of an indifferent all-
powerful Will, but of an all-powerful Will which knows
and decrees the best 2. -

1 See Appendix C, p. 204.

2 Of. Epistola ad Bierlingium (1711) (E. 677 b ; G. vii. 501) : 'You

108 INTRODUCTION

C. ORGANISM.

Organic and inorganic Bodies. Simple and compound
Substances. Dominant Monad.

The notion of body existing by itself and that of soul
existing by itself are results of confused or imperfect

ask about spiritual, or rather incorporeal things, and you say that
we see the mechanical arrangement of the parts but not the
principles of the mechanism. True ; but, when we see motion also,
we understand from this [what we see] the cause of motion, or
force. The source of mechanism is primary force [vis primitiva],
but the laws of motion, according to which impulses [impetus'} or
derivative forces arise out of the primary force, issue from the
perception of good and evil, or from that which is most fitting.
Thus it is that efficient causes are dependent upon final causes,
and spiritual things are in their nature prior to material things,
as also they are to us prior in knowledge, because we perceive
more immediately [interius] the mind (as it is nearest to us)
than the body ; and this indeed Plato and Descartes have
observed.' Also Lettre a Remond (1714) (E. 702 a ; G. iii. 607):
4 1 have found that most of the philosophical sects are right in
a good part of what they maintain, but not to 'the same extent in
what they deny. The Formalists, such as the Platonists and
Aristotelians, are right in seeking the source of things in final
and formal causes. But they err in neglecting efficient and
material causes and in inferring (as did Mr. Henry More in
England, and some other Platonists) that there are phenomena
which cannot be explained on mechanical principles. But, on
the other hand, the Materialists, or those who hold exclusively
to the mechanical philosophy, err in setting aside metaphysical
considerations and in trying to explain everything by that which
is dependent on the imagination. I flatter myself that I have
discovered the harmony of the different systems and have seen
that both sides are right, provided they do not clash with one
another ; that in the phenomena of nature everything happens
mechanically and at the same time metaphysically, but that the
source of the mechanical is in the metaphysical.' Also Lettre a
Arnauld (1686) (G. ii. 77) : * We are obliged to admit many things
of which our knowledge is not sufficiently clear and distinct.
I hold that the knowledge of extension is very much less so'
[than that of substantial Forms, of which he has been speaking],
' witness the remarkable difficulties as to the composition of the
continuous ; and it may even be said that bodies have no definite and
precise shape, because of the actual sub-division of their parts [i. e. their
sub-division ad infinitum]. So that bodies would without doubt be
something merely imaginary and apparent if there were nothing but matter
and its modifications. Yet it is of no use to mention the unity,
notion, or substantial Form of bodies, when we are explaining the
particular phenomena of nature, as it is of no use for mathe-

STATEMENT OF LEIBNIZ S PHILOSOPHY 109

perception. The world consists solely of Monads, each
of which is a concrete unity of soul and body, of entelechy
and materia prima. Thus nature is throughout living ;
there is nothing really inorganic \ What, then, is meant
by the common distinction between organic or living and
inorganic or material bodies? In order to answer this
question, we must consider more fully the nature of
compound substance.

While the simple substances alone are real they appear
as phenomena in groups or aggregates, which we call
compound substances. Indeed, although in reality they
are secondary, compound substances are prior to simple
substances in the order of knowledge. As phenomena
they can be perceived by the senses, while the Monad*
cannot be so perceived. For the Monads are not really
grouped or combined ; the aggregation is purely pheno-
menal. Now each Monad implied in any such aggregate
perceives or represents all the phenomena constituting its
group, since it perceives the whole universe, of which they
are parts. But as each Monad diifers from all the others
in the degree of distinctness of its perceptions there must
in each group be one Monad which represents the group
more distinctly than does any other Monad implied in it.
This Monad of most distinct perception in each compound
substance Leibniz calls the dominant Monad of the
substance 2. It has a formal superiority over the others

maticians to investigate the difficulties de compositione continm when
they are working at the solution of some problem. These things
are none the less important and worthy of consideration in their
own place. All the phenomena of bodies can be explained
mechanically or by the corpuscular philosophy, according to certain
principles of mechanics, which are laid down without taking into
consideration whether there are souls or not ; but in an ultimate
analysis of the principles of physics, and even of mechanics, it
appears that we cannot explain these principles by modifications
of extension alone, and the nature of force already requires some-
thing else.' See also Antibarbarus Physicus, &c. (after 1687) (Or. vii.
343;. For Leibniz's account of (he development of his views, see
Ultimate Origination of Things, Appendix, p. 351.

1 Cf. Monadology, §§63 sqq.

2 Cf . ibid. § 70 ; Principles of Nature and of Grace, § 3.

110 INTRODUCTION

implied in the group, though all are really independent,
Its control or dominance consists solely in the distinctness
of its perceptions. Just as cause is not a real influence of
one substance upon another, but merely the relation of
activity in the one to corresponding passivity in the other,
or of distinct to confused perception, so the central
Monad of any compound substance has no physical con-
trol over the others, but is dominant because of its
activity and distinctness. Thus the relation between the
dominant Monad and the phenomena (implying other
Monads) which, along with it, constitute a compound
substance is similar to the relation between the two
elements, active and passive (entelechy and materia prima),
which together constitute simple substance or the indi-
vidual Monad. The dominant Monad is the entelechy or
soul of the compound substance, while its body is a
phenomenal aggregate, every portion of which in turn
implies a Monad or soul. But this aggregate is materia
secunda ; and thus we have simple substance consisting of
materia prima and entelechy, and compound substance
consisting of materia secunda and dominant Monad.

While observing this analogy, we must not forget the
essential difference between simple and compound sub-
stance. The former alone is really substance : the latter,
in so far as it differs from the former, is merely sub-
stance by courtesy or common usage. Simple substance
is a concrete unity ; compound substance, in so far as it
is compound (i. e. apart from its soul or dominant Monad,
which is non-quantitative, and therefore cannot be an
element in a compound), is merely an aggregate. Thus
the materia prima or passivity of the individual Monad is
a name for its confused, undeveloped or implicit nature
• taken abstractly : it is confused perception in the sub-
stance itself. But the materia secunda or body of the
compound substance is not confused perception in the
substance itself, for the body as compound has no
perception of its own, as distinct from the perceptions

STATEMENT OF LEIBNIZ^ PHILOSOPHY III

of the simple substances which it implies. Materia
secunda, then, is due to the confused perceptions of
those who observe the compound substances. Thus to
the eye of God there can be no materia secunda, no com-
pound substance ; for in Him there is no confused percep-
tion.

The aggregates of phenomena which we call things or
extended bodies are thus the result of confused percep-
tion. And the differences amongst them, which we
describe by the names of organic, inorganic, &c., are
really differences in their dominant Monads. Without
a dominant Monad, body would be mere indeterminate
quantity, 'without form' if not 'void,' a chaos of pure
difference. The dominant Monad is the unity implied
in a* specific or definite aggregate, the unity in virtue of
which an aggregate or compound is one thing as distinct
from other things. If the dominant Monad be a bare
Monad, with unconscious perceptions, we call the body
inorganic. If the degree of distinctness in the perceptions
of the dominant Monad be a little higher, we call the
body a plant and so on. The organic and the inorganic
pass imperceptibly into one another, and the degree of
organic unity possessed by any body is nothing but the
degree of distinctness in the perceptions of its dominant
Monad. Thus the parts of an organism are more closely
connected, more firmly held together, than those of an
inorganic mass, because the dominance of the central
Monad is greater, more complete (that is to say, its per-
ception is more distinct), in the case of the former than
in the case of the latter.

Body without soul, or mere matter considered as inor-
ganic, that is to say, as an aggregate of parts which have
no unity other than their aggregation, is unreal. We
may regard it either as an abstraction from concrete
substance or (more nearly in Leibniz's way of thinking)
as an imperfect perception or representation of concrete
substance. Nature is organic throughout : no real thing

112 INTRODUCTION

is completely inorganic : what we call ' inorganic ' is
really organic in a low degree *.

The body of every created substance is the point of
view of its soul. As there is no vacuum in nature, the
changes in any one body affect every other. Thus in
every body the whole world is represented or expressed.
But in each dominant Monad, or soul, the aggregate
forming its particular body is more distinctly represented
than the rest of the world. Thus each soul perceives or
represents the universe through the medium of its own
body. While it does represent the whole, it represents
it in a form in which its own body is more distinct than
any other2. The body is like a special lens through
which the soul sees the universe. This, of course, fol-
lows from the view that body in general is relatively
confused perception. For each substance represents the
universe 'from its own point of view,' and its point of
view is simply the degree of confusedness (or of distinct-
ness, for they are entirely relative) of its perceptions 3.

1 Cf. Antibarlarus Physicus, &c. (G-. vii. 344) : ' But indeed,
although all bodies are not organic, nevertheless in all bodies,
including the inorganic, organic bodies lie hid, so that every mass
which to outward appearance is formless [rudts] and quite undif-
ferentiated [similaris\ is inwardly not undifferentiated but diver-
sified, and yet its variety is not confused but orderly. Thus there
is everywhere organism, nowhere chaos, which would be unbe-
coming a wise Creator.'

* Monadology, § 62; cf. Spinoza, Ethics, Part ii. Props. 12, 13
(Scholium), 16 (Coroll. i\ 26, &c.

3 Yet it must not be supposed that the soul has perfect knowledge
of all that takes place in its own body. Cf. Lettre ii Arnauld (1687)
(GK ii. 90) : ' It does not follow that the soul must be perfectly
conscious [s'apercevoir'] of what happens in the parts of its body,
since there are degrees of relationship between these parts them-
selves which are not all expressed equally, any more than external
things are. The distance of the latter is balanced by the smallness
or other disadvantages of the former, and Thales sees the stars
when he does not see the ditch before his feet.' Also Lettre a
Arnauld (1687) (G. ii. 112) : « In natural perception and in feeling,
it is enough that what is divisible and material, and is actually
divided among several beings, should be expressed or represented
in one indivisible being or in substance which possesses a genuine
unity. We cannot doubt the possibility of such a representation
of several things in one only, since our soul gives us an instance

STATEMENT OF LEIBNIZ S PHILOSOPHY 113

Changes in compound Substances. Development and

Envelopment.

Every compound substance is in constant change. No
created Monad, as we have seenr. can- ever be entirely at
rest: each, in virtue of its appetition, is continually
either unfolding (developing) itself (i. e. passing from
confused to more distinct perception), or enfolding (en-
veloping) itself (i. e. passing from distinct to more con-
fused perception). And thus, as the dominance of any
dominant Monad consists solely in the degree of distinct-
ness of its perception, the relations of formal dominance
and subordination, which constitute a compound sub-
stance, must be continually varying in particular cases.

of it. But this representation is .accompanied in the rational soul
by consciousness, and then it is called thought. Now this expres-
sion occurs everywhere, because all substances are in sympathy
with one another, and each receives some proportional change,
corresponding to the least change which happens anywhere in the
universe, though this change is more or less observable, according
as other bodies or their actions have more or less relation to ours.
And I think that M. Descartes himself would have admitted this,
for he would doubtless allow that, because of the continuity and
divisibility of all matter, the least motion has its effect upon
neighbouring bodies, and consequently upon one body after another
ad infinitum, the effect proportionally diminishing. Thus our body
must be in some way affected by the changes in all others. Now
to all the motions of our body there correspond certain more or less
confused perceptions or thoughts of our soul. Hence the soul also
will have some thought of all the motions in the universe, and, in
my opinion, every other soul or substance will have some percep-
tion or expression of them. It is true that we are not distinctly
conscious of all the motions of our body, as, for instance, that of
the lymph ; but this may be compared with the fact that I must
have some perception of the motion of each wave on the shore,
in order that I may be conscious [apercevoir] of that which results
from the totality of them, namely the great noise that I hear when
close to the sea. Thus also we experience some confused result
of all the motions which take place in us ; but being accustomed
to this internal motion, we are not distinctly and reflectively
conscious of it, except when there is a considerable change in it,
as at the beginning of an illness. . . . Now since we are conscious
of other bodies only through the relation they have to our own,
I was right in saying that the soul expresses best what belongs
to our own body. Thus we know the satellites of Saturn or of
Jupiter, only in consequence of a motion which takes place in our
eyes.' Cf. Spinoza, Ethics, Part ii. props. 24 and 27.

114 INTRODUCTION

The phenomena which make up the body of a compound
substance must be continually changing according as the
dominant Monad rises or falls in perceptive rank. No
dominant Monad has a changeless body ; because of its
own variations its body 'is in a perpetual flux like a
river, and parts are entering into it and passing out of
it continually V And there is endless room for variation ;
because each compound substance is made up of other
compound substances (each with its dominant Monad),
and these again are made up of others ad infinitum*.
Thus some or all of the things which at one time form
an inorganic body may, in new relations, become parts
of an organic body and vice versa. And the size of any-
body, belonging to a particular dominant Monad, may
increase or decrease indefinitely.

Metamorphosis. Birth and Death.

Accordingly the change in compound substance of
every kind is always metamorphosis rather than metem-
psychosis3. The fundamental element in every com-
pound substance is the dominant Monad, and the matter
or body of the substance is continually changing by a
gradual removal and addition of parts. It is the body
which bit by bit transfers itself from one soul to another.
There is no such thing as the sudden transference of
a soul from one body to another entirely new body.
Such a transference would involve a sudden or discon-
tinuous change in the soul itself, which is impossible.

1 Monadology, § 71. So Lotze compares the life of the parts to
a throng of travellers. Microcosmus, bk. iii. ch. 4, § 4 (Eng Tr,
vol. i. p. 368).

2 Cf. Epistola ad BernouUium (1698) (G-. Math. iii. 560 1 : « I would
readily allow that there are animals (in the ordinary sense) in-
comparably greater than ours ; and I have sometimes said in jest
that there may be some system similar to ours, which is the watch
of a very great giant/ Also Monadology, §§66 sqq. ; cf. Spinoza, Ethics,
Part ii. Lemma vii. Scholium.

3 Cf. EpistoUi ad Bemoullium (1698) (G. Math. iii. 561) : <I do not
admit fttr*/afwx*ott into a new animal, but utTapofxfxuau,

of the same animal.'

STATEMENT OF LEIBNIz's PHILOSOPHY 115

Though, on the one hand, no soul is limited to any
particular phenomenal aggregate as its body, yet on the
other hand, no soul can be completely and instantaneously
severed from its body and transferred to another. Again,
the birth and the death of any organism are simply forms
of this metamorphosis1. There is no absolute birth, that
is to say, no direct and immediate implanting of soul in
body, and there is no absolute death, no complete sever-
ance of soul from body. All the Monads which constitute
the sole reality of a compound substance are alike unborn
(ingenerdble) and imperishable2. They proceed directly
from God : they are produced by ' fulgurations of His
Divinity3.' None of them comes out of anything else.
Thus the phenomena we call 'birth' and 'death' are
transformations, changes in the relations between Monads.
When we speak of an animal being born, we mean that
the body of a microscopic animalcule has enormously
increased in size, and that its dominant Monad has under-
gone a corresponding internal change. The animal was
an animal from the first, even in the microscopic, sper-
matic stage. In being born it has merely become an
animal of a higher kind. In every case the process of
birth is, in fact, similar to the change which takes place
when a caterpillar develops into a butterfly, 'nature being
wont to reveal in some particular cases her secrets, which
she conceals on other occasions4.' Birth is thus indis-
tinguishable from growth, increase, development. And
on the other hand, when we speak of an animal as dying,
we mean that its body has decreased in size or been
broken up into new compounds. The animal has not
ceased entirely to exist, but has been contracted so that
it is no longer perceived. Death is thus the same as
decay, decrease, involution 5. There is no spontaneous

1 Monadology, §§73 sqq. 2 Cf. Principles of Nature and of Grace, § 6.

3 Monadology, § 47 ; see the note to that section.

4 Lettre a Arnauld (1686) (G. ii. 75).

5 Monadology, §§74 and 75. Cf. Theodicee, § 90 (E. 527 b; G. vi.
152).

I 2

1 16 INTRODUCTION

generation and no passing from life to absolute lifeless-
ness. For lifelessness is entirely relative : the very dust
and ashes still have life \

Indestructibility and Immortality of Souls.
Accordingly the souls of all living beings are inde-
structible, while the soul of man is both indestructible
and immortal, since it not merely persists in existence
but continues to have consciousness, memory, and such
other characteristics as constitute personality 2. It^is
apparently, in Leibniz's view, impossible for the mind
of man to degenerate so as to pass into a lower stage of
existence. The possession of self -consciousness is in-
alienable. The rational soul thus differs from all souls
that are beneath it in rank, inasmuch as it does not
experience such wide variations as those to which the
latter are subject. In a letter to Arnauld (1687), Leibniz
says : * Others, not being able to explain otherwise the

1 Cf. Epistola ad Bernouttium (1698) (G. Math. iii. 553) : ' You argue
entirely to my mind when you say that changes do not take place
per saltum. And further. I do not laugh at your conjecture, but
I definitely avow that there are in the world animals as much
larger than ours, as ours are larger than microscopic animalcules.
Nor does nature know any limit. And again it may be, nay it.
must be, that in the very smallest grains of dust, and indeed in
the least atoms \atomulis~\ there are worlds not inferior to our own
in beauty and variety ; nor is there anything to prevent what may
appear a still more wonderful thing, that animals at death are
transferred to such worlds ; for I regard death as nothing else than
the contraction of an animal.'

2 Cf. Lettre a Des Maizeaux (1711) (E. 676 a; G. vii. 534) : 'I am
of opinion that the souls of men pre-existed, not as rational souls,
but merely as ' sensitive ' [sensible] souls, which attained this higher
degree (that is to say, reason) only when the man, whom the soul
is to animate, was conceived. I grant an existence as old as the
world not only to the souls of the lower animals, but in general to
all Monads or simple substances from which compound phenomena
result ; and I hold that each soul or Monad is always accompanied
by an organic body, which is nevertheless perpetually changing ;
so that the body is not the same, though the soul and the animal
are. These rules apply also to the human body, but apparently in
a higher degree than to other animals which are known to us ;
since man must continue to be, not merely an animal but also
a person and a citizen of the City of God, which is the most
perfect possible state, under the most perfect Monarch.'

STATEMENT OF LEIBNIZ'S PHILOSOPHY

origin of forms, have allowed that they have their be-
ginning in a real creation. While I grant this creation
in time only as regards the rational soul, and hold that
all forms which do not think were created with the
world, they believe that this creation happens every day
when the smallest worm is engendered1.' There is,
then, something comparable to a special creation in the
case of every mind or rational soul, although this creation
is practically no more than the promotion of a Monad
to self- consciousness. 'Minds [esprits] are not subject to
these revolutions [of bodies], or rather these revolutions
of bodies are subservient to the Divine economy regarding
minds. God creates them when the time comes and
detaches them from the body, at least from the earthly
[grossier] body, by death, since they must always retain
their moral qualities and their recollection in order to be
perpetual citizens of that universal all-perfect common-
wealth, of which God is the Monarch, which can lose
none of its members and the laws of which are higher
than_those of bodies 2. '

1 G. ii. 117.

2 Lettre a Arnauld (1687) (G. ii. 99). Cf. Theodicee, § 91 (E. 527 b ;
"G. vi. 152): 'Thus I should think that the souls which will some

day be human souls have, like those of other species, been in the
seed and in their ancestors up to Adam, and have consequently
existed, since the beginning of things, always in some kind of
organic body. ... It appears to me also for various reasons probable
that they then existed only as sensitive or animal souls, endowed
with perception and feeling, and devoid of reason ; and that they
remained in this state up to the time of the begetting of the man
to whom they were to belong, but that then they received reason ;
whether we suppose that there is a natural means of raising
a sensitive soul to the rank of a rational soul (which I find it
difficult to conceive), or that God has given reason to this soul by
a special act, or (if you like) by a kind of transcreation. This is the
more easily admitted, as revelation informs us of many other
immediate acts of God upon our souls. . . . And it is much more in
harmony with the Divine justice to give to the soul, already
physically or as an animal corrupted by the sin of Adam, a new
perfection, namely reason, than, by creation or otherwise, to put
a rational soul into a body in which it is to be morally corrupted.'
Also Lettre a Arnauld (1686) (G. ii. 75) : ' The rational soul is created
only at the time when its body is formed, being entirely different
from the other souls we know, because it is capable of reflexion

Il8 INTRODUCTION

Tlie Vinculum Substantiate.

As to organic substance, one other point requires a brief
consideration. In a correspondence with Father Des
Bosses, Leibniz draws a distinction between a compound
substance, strictly speaking, and a mere collection of
things, such as a heap of stones, or a flock of sheep, or
an army. The compound substance has a certain unity ;
it is substantia composita [singular number]. It involves
something which gives a certain reality to its phenomena
(ens realizans phenomena), or, in other words, there is a
genuine bond of connexion between its phenomena (vin-
culum substantiale}. It is unumper se. The mere collection,
on the other hand, is not a substance but substances
( substantiae, substantiatum, semi- substantia). It has no
unity of its own. Whether, as in the case of a heap of
stones, its unity consists in the contact of its parts or, as
in the case of a regiment, it is united by a common
purpose, the bond of connexion is entirely in the mind of
an observer. In short, when we regard such a thing as
a mere collection, we regard it as without a dominant
Monad, and therefore as not having a genuine body. It
is like the l corporation ' which, according to Sydney
Smith, ' has neither a body to be kicked nor a soul to be
damned.' It is unumper accidens, in contrast with unum
per se l.

This distinction, however, is not to be regarded as
absolute. It is, in another form, the distinction which
we have already considered 2 between phenomena bene
fundata and the pure phenomena of imagination and
dreams. The vinculum substantiale is simply the con-
nexion of the phenomena, in virtue of which we describe
them as bene fundata, since this connexion arises from the

and resembles in miniature the Divine nature.' See Monadology.
§ 82 note.

Cf. this Introduction, Part iii. p. 96, notes i and 2.
Cf. this Introduction, Part iii. p. 98.

STATEMENT OF LEIBNIZ'S PHILOSOPHY

mutual relations of the Monads which are implied in the
compound substance. The vinculum substantiate is no-
where mentioned by Leibniz except in the correspondence
with Des Bosses. It is in no way essential to his philo-
sophy ; but it is the suggestion of a way in which his
system might possibly be made consistent with the Roman
Catholic dogma of Transubstantiation, which requires
that bodies should be considered as real substances.

Leibniz tells us plainly that he has no great liking for
the vinculum substantiate, and that it is better to dispense
with it, unless any would-be disciple of his finds it
necessary as an aid to religious faith \ It ought not,
however, to be forgotten that Leibniz was encouraged in
rejecting the Cartesian view that the essence of bodily
substance is extension and motion, by the fact that this

1 Cf. Gr. ii. 499. A. Lemoine, in his thesis entitled Quid sit Materia
apud Leibnitium (Paris, 1850), discusses fully the Letters to Des Bosses,
with the object of showing that the vinculum substantiate is an excres-
cence upon the philosophy of Leibniz, and that the use he makes
of it involves inconsistency with his general position. Erdmann,
in his History of Philosophy (Eng. Tr., vol. ii. p. 188) holds that it
is not to be regarded merely as a concession to the* religious
scruples of Roman Catholics, but that it is really a part of Leibniz's
life-long endeavour to reconcile the Roman Catholic and Lutheran
Churches Cf. Lettre au Due Jean Frederic (no date) (Klopp, iv.
444) : — ' There is also a considerable feature of my philosophy
which will make it somewhat welcome to the Jesuits and other
theologians. It is this, that I re-establish the substantial forms
which the Atomists and Cartesians claim to have exterminated.
Now it is certain that without these forms and the difference there
is between them and real accidents, it is impossible to maintain
our mysteries ; for if the nature of body consists in extension,
as Descartes holds, it undoubtedly involves a contradiction to
maintain that a body exists in many places at once/ Dillmann
(Neue Darstellung der Leibnizischen Monadenlehre, p. 25) has no doubt
that the vinculum substantiate is the same as the ' soul ' of the
body or its dominant Monad. Logically, perhaps, it ought to
be so ; but it is far from clear that Leibniz meant this. For he
several times uses the terms ' soul ' or ' dominant Monad ' in the
same sentence as the term vinculum substantiate without identifying
them. And he speaks of the vinculum substantiate being 'abolished,'
' destroyed,' ' supernatural ly removed,' &c. But he afterwards admits
that the vinculum substantiate cannot come into being or be destroyed.
So that Leibniz's entire treatment of the matter is tentative and
unsatisfactory.

120 INTRODUCTION

theory is inconsistent both with the Eoman Catholic and
with the Lutheran doctrine regarding the Keal Presence
in the Eucharist.

D. SELF-CONSCIOUSNESS.

By means of the different degrees of clearness and
distinctness in the perceptions of their respective souls or
dominant Monads, the organic compound substances of
which the world is composed may be divided into three
main classes, (i) mere living beings, (2) animals, and
(3) men. Substances of the first class, including plants
and all lower forms of existence, have as their soul a bare
Monad, having mere perception or representation, un-
accompanied by consciousness. Animals, on the other
hand, have a higher degree of perception, which appears
as consciousness or feeling (sentiment], including memory.
The soul of man possesses the characteristics of both of
the lower classes, but its perception has a still higher
degree of clearness, appearing now as self-consciousness or
apperception. The self-conscious soul or spirit does not
merely connect its particular perceptions in the empirical
sequence of memory ; but, having a knowledge of eternal
and necessary truths, it can represent things in logical
order, that is to say, in their necessary rational relations.
This is what is meant by its having reason, or being
a rational soul. The possession of reason means the
power of reflexion or self-consciousness, because necessary
and eternal truths are simply perceptions developed to
the highest degree of distinctness, and consequently the
knowledge of such truths is a clear and distinct conscious-
ness of what is in ourselves (of the perceptions which
constitute our nature), and hence indirectly a clear and
distinct knowledge of substance in general1.

1 Monadologij, §§ 18-30 ; Principles of Nature and of Grace, §§4 and 5.
Of course it is not to be supposed that the scale of organic being
ends with man. There must be between man and God a continuous
succession of other embodied souls, each more perfect than the one
beneath it. Otherwise the law of continuity would be broken.

^

^

STATEMENT OF LEIBNIZ'S

Now, as we saw in considering the meaning of life and
death \ while the self-conscious or rational soul really
differs only in degree from the conscious and the uncon-
scious soul, it can never completely lose its rationality.
The animal soul may at death lose memory and descend
to a lower grade. But this is not possible in the case of
the self-conscious soul. And on the other hand, while
an animal soul may be raised to self-consciousness,
Leibniz finds it difficult to conceive that this can take
place without a special act or operation of God. Self-
conscious beings have thus a position of peculiar inde-
pendence, which requires us to devote to them special
consideration. We proceed, then, to consider Leibniz's
account (*a) of the form in which perception appears in
man, and (6) of the form in which appetition appears in
him ; these being the two essential characteristics of the
human soul as well as of every other Monad.

(O) THEORY OF KNOWLEDGE.

Leibniz seeks a Via Media between the Views of Descartes
and of Locke.

Human perception or apperception is knowledge,
strictly speaking. Leibniz's theory of apperception is
thus a theory of knowledge. Now apperception is the
perception of eternal and necessary_,truths. It is clear
and distinct knowledge. But the human soul has also

' It is also reasonable to suppose that there are below us sub-
stances capable of perception, as there are such substances above
us ; and that our soul, far from being the last of all, occupies
a middle position, from which it is possible to go up or down ;
otherwise there would be in the order of things a defect, which
certain philosophers call vacuum formarum.' Sur les Principes de Vic,
(1705) (E. 431 a; G-. vi. 543). Leibniz calls these higher beings
genies (genii). 'It is to be believed that there are rational souls
more perfect than we, which may be called genies, and it is quite
possible that some day we shall be of their number. The order of
the universe seems to require it.' Lettre a la Princesse Sophie (1706)
(G. vii. 569).

122 INTRODUCTION

knowledge which is not clear and distinct, knowledge of
contingent things which it cannot reduce to eternal and
necessary truth. This must be so, for otherwise the
human soul would be perfectly clear and distinct in its
perceptions, complete and unrestrained in its activity,
actus purus. But this characteristic of perfect intuitive
knowledge and absolute activity belongs to God alone ;
the perceptions of man are always at best only relatively
clear and distinct. Accordingly it is impossible for
Leibniz to assent to the Cartesian theory of knowledge,
which gave worth only to the absolutely clear and distinct,
drawing a hard and fast line between self-conscious
thinking and all else. Descartes's use of the principle of
contradiction was inconsistent with the possibility of
relative truth. It explains the universal and necessary,
but only by setting aside the contingent as ultimately
inexplicable.

On the other hand, the theory of Leibniz is equally
opposed to the opposite view, expounded in Locke's Essay
on the Human Understanding. If distinctively human
knowledge does not consist solely in the perception of
universal and necessary truths, neither is the human mind
altogether destitute of such knowledge and dependent for
its ideas entirely upon the contingency of the senses. As
the human soul is a Monad, its knowledge does not come
to it from outside itself, for it cannot be really influenced
by any other substance. It is not originally a tabula rasa
on which externally-produced impressions are made ; for
no Monad can ever be purely passive or absolutely without
perception. The human mind, being spontaneous in all
its activities, must produce its knowledge entirely from
within itself. It is not a vacuum, gradually filled ab extra
with independent ideas ; it is a force or life transforming
itself, a growth, a self-revelation \

1 Cf. Nouveaux Essais, bk. ii. ch. i, § 2 (E. 222 b ; G. v. 99) : 'This
tabula rasa, of which so much is said, is in my opinion nothing but
a fiction, which nature does not allow and which has its grounds

STATEMENT OF LEIBNIZ S PHILOSOPHY 123

Thus in his theory of knowledge, Leibniz may be
regarded as seeking a via media between two extreme
views, the basis of both of which is mechanical rather
than dynamical. Each in its own way fails to do justice
to the relations in knowledge, to its unity as a system.
Each rests on the absolute (not the relative) validity of

only in the incomplete notions of philosophers, like the void,
atoms and absolute or relative rest of two parts of a whole in
regard to one another, or like the maieria prima, which is conceived
as absolutely passive [sans aucunes formes']. Things which are
uniform and contain no variety are never anything but abstractions,
like time, space, and the other beings of pure mathematics. There
is no body whose parts are at rest, and there is no substance
which has nothing to distinguish it from every other. Human
souls differ, not only from other souls, but also from one another,
although the difference is not of the kind that is called " specific."
And I think I can prove that every substantial thing, whether
soul or body, has its own special relation to every other ; and one
must always differ from another by intrinsic characters ; without
mentioning that those who say so much about this tabula rasa, after
having removed from it the ideas, cannot tell what remains of it,
like the Scholastic philosophers who leave nothing in their materia
prima. Perhaps it may be replied, that this tabula rasa of the
philosophers means that the soul has originally and by nature
nothing but bare faculties. But faculties without any activity, in
a word the pure potencies [puissances'] of the Scholastics, are them-
selves only fictions, which nature knows not and which are
obtained only by making abstractions. For where in the world
shall we ever find a faculty which is shut up in mere potency
without any activity? .There is always a particular disposition to
action, and to one action rather than another. And besides the
disposition there is a tendency to action, and indeed there is always
an infinity of these tendencies at once in every object ; and these
tendencies are never without some effect. Experience is necessary,
I admit, in order that the soul should be determined to such and
such thoughts, and in order that it may take notice of the ideas
which are in us. But by what means can experience and the
senses give ideas? Has the soul windows? Is it like a writing-
tablet ? Is it like wax ? It is plain that all those who think thus
of the soul make it at bottom corporeal. There will be brought
against me this axiom, accepted among the philosophers, that
nothing is in the soul that does not come from the senses. But the soul
itself and its affections must be excepted. Nihil est in intellectu, quod
nonfuerit in sensu • excipe : nisi ipse intellectus. But the soul contains
the notions of being, substance, unity, identity, cause, perception,
reasoning and many others, which the senses cannot give. This
agrees well enough with your author of the Essay, who finds the
origin of a considerable section of the ideas in the mind's reflexion
on its own nature.' Cf. New Essays, Introduction, pp. 360, 367 sqq.

124 INTRODUCTION

certain ideas or impressions ; each is a kind of atomism.
The eternal and necessary truths (or clear and distinct
ideas) of Descartes are unconditionally valid ; they are
a priori atoms, forming the totality of knowledge. The
* simple ideas ' of Locke are equally unconditional in their
validity ; they are a posteriori atoms or data of knowledge *.
But, here as elsewhere, Leibniz would rather reconcile
than overthrow. While the mechanical view of things is
not the truest, it nevertheless has value in its own sphere.
Thus he regards the errors of Descartes and Locke as due
in each case to the over-emphasis of one of the two com-
plementary elements in knowledge, the necessary and the
'contingent. Descartes's view might hold if knowledge

1 Locke's opposition to Descartes, great though it was, ought not
~V^ to be emphasized to such an extent as to hide the fact that they
have much in common. For instance, we know that Locke's first
attraction to philosophy came from a reading of Descartes, and he
may perhaps owe the suggestion of some of his leading ideas to
such passages as the following extract from an unfinished dialogue
of Descartes, in which the method of doubt is wittily set in con-
trast with the Scholastic metaphysics. The question is : ' What
is man's first knowledge ? In what part of the soul does it dwell ?
And why is it so imperfect at the beginning?' Epistemon, the
representative of Scholastic learning, says : ' That appears to me
to be very clearly explained, if we liken the imagination of infants
to a tabula rasa on which our ideas, which are as it were the living
image of objects, are to be painted. Our senses, the dispositions of
our mind, our teachers and our intelligence are the different painters
who can execute this work, and those among them which are least
fitted to succeed, begin it ; namely imperfect senses, blind instinct
and foolish nurses. At last comes the best of all, intelligence ; and
yet is it still necessary that it should serve an apprenticeship of
several years and for some time follow the example of its teachers,
before it dare rectify one of their errors. . . . It is like a clever
artist, called to put the finishing touches to a picture sketched by
learners. Though he use all his art, correcting gradually now one
feature, now another, and putting in all that has been omitted,
there must still remain great defects in it, because the picture was
badly drawn at first, the figures were ill- arranged and little atten-
tion was given to proportion.' Recherche de la Verite par les lumieres
natureVes, (Euvres de Descartes (ed. Cousin), vol. xi. p. 345 ; cf. ibid.
P- 375 : ' All truths follow from one another and are united by
a common bond ; the whole secret consists in beginning with the
first and most simple, and rising gradually to the most remote and
most complex.' See also Eraser's ed. of Locke's Essay, vol. i.
Prolegomena, p. ao.

STATEMENT OF LEIBNIZ'S PHILOSOPHY 125

were entirely necessary ; Locke's might hold if knowledge
were merely contingent. But human" knowledge is both ;
it includes both self-evident truths and truths of fact.
A true theory of knowledge must do equal justice to both.
It must have affinity with the views both of Descartes
and of Locke, without altogether accepting either. *<-

Leibniz's Solution of the Question of Innate Ideas and the
Tabula Rasa.

fLocke endeavoured to establish his empiricism as
against the position of Descartes by denying that there
are in the human mind any innate ideas, f- If there be
no innate ideas, all our knowledge must reach us ab
extra, through the senses. And accordingly the only
true theory of knowledge must explain it a posteriori,
entirely from sense-experience. This was the contrary
opposite of the Cartesian view that all our genuine
knowledge comes from pure thought, in complete
independence of the senses (which are bodily, and there-
fore excluded from the sphere of thinking), and that the
only true theory of knowledge must explain it a priori,
as a logical deduction from self-evident innate ideas. To
Leibniz it seems that the conception of the human mind
as a Monad leads to a theory of knowledge which har-
monizes the other two, by combining in a new form the
truth they each contain, and at the same time setting
aside their errors. As a Monad the soul of man is not,
as in Locke's view, a purely passive tabula rasa, continually
receiving external impressions. It is always an active
force, and it is itself the spontaneous source of all its
ideas, i. e. of the entire sequence of its experience. All
its ideas are therefore innate. But none of its ideas is
from the beginning clear and distinct. When they first
appear they are confused and imperfect. The recognition
of their self-evidence is the result of a process, a develop-
ment from relative confusion to distinctness. But what
Locke calls sensation is, according to Leibniz, confused

126 INTRODUCTION

j)ercegtion, the indistinct representation of things external
to the individual niind. Thus the self-evidence of uni-
versal and necessary truths is a result of experience,
though that experience is purely internal. And though
all our ideas are innate, there are many which can never
be reduced to the perfect clearness and distinctness of
self-evident truth, but which we have nevertheless quite
sufficient ground for recognizing as true. Further, though
our experience is entirely internal, it is none the less
objectively real, for it consists in a representation of the
whole universe, in accordance with the pre-established
harmony between substances. Human knowledge is thus
1 at once a priori and a posteriori, innate and experiential ].

Relativity of the Distinction between Perception and
Apperception.

The acceptance of this theory involves a change in the
point of view held both by Descartes and by Locke. They
both argue on the assumption that perception and apper-
ception are quite distinct from one another. Descartes's
theory of innate ideas rests on his doctrine that absolute
certainty belongs to self-conscious thought alone, ex-
eluding all other forms of human experience as pheno-
mena of body, which is the contradictory opposite of

1 ' If all our ideas [connaissances~] are innate in so far as they are
ideas distinct in themselves, they are all acquired in so far as they
are ideas distinct for us.' Boutroux, ed. of Nouveaux Essais, &c.,
Introduction, p. 83. Cf. Lotze, Streitschrift, p. 13 : ' In earlier times
people made too free a use of the name of innate ideas ; but now it
seems to me that they have fallen into an opposite error when they
at once set aside this notion, with a superficial depreciation of its
somewhat inappropriate name. I have never been able to convince
myself that the logical and metaphysical principles regarding the
nature of things, which are necessary to our thought, the aesthetic
feelings and the consciousness of obligation rest upon anything
else than the immediate depth of our spiritual nature, so that they,
under the stimulus of experience, come into our consciousness as
original possessions of our nature, not as complete innate images,
always hovering in our consciousness, but as so grounded in us that
they indeed require the stimulus of experience, but are never given
to us by experience.'

STATEMENT OF LEIBNIZ^ PHILOSOPHY I2J

mind. Locke, on the other hand, denies the existence of
innate ideas on the ground that children, savages and
idiots do not consciously possess them ; an argument
which implies that we have an idea only when we are
fully aware of it, that is to say, that ideas exist only in
self-consciousness^ or apperception. Thus apperception
(in the Leibnitian sense) is regarded by Descartes as
containing absolute, innate first principles, from which
particular truths may be deduced, while by Locke it is
held to give, not first principles, but simple ideas, which
are the elements out of which knowledge is built. In
both cases it is apperception that is appealed to ; mere
perception does not count l.

Now the great central principle of the philosophy of
Leibniz is the idealizing of all substance, by regarding it
as throughout perceptive or representative. Apper-
ception, feeling and bare perception (which is not
necessarily anything more than the mere possession of
real qualities) are not different in kind but merely in

1 Cf. Nouveaux Essais, bk. ii. ch. i, § 19 (E. 226 a ; G. v. 107) : ' Phil-
alethes [representative of Locke]. " That body is extended without
having parts and that a thing thinks without being conscious
[s'apercevoir~\ that it thinks, are two assertions which appear equally
unintelligible." Theophilus [representative of LeibnizJ. " Forgive
me, sir, but I must tell you that in your contention that there is in
the soul nothing of which it is not conscious, there is a petitio prin-
cipii, which has already dominated our first discussion. It was
there used for the overthrow of innate ideas and truths. If we
were to grant this principle, we should not merely find ourselves
in conflict with experience and reason, but we should have without
any reason to give up our opinion, which I think I have made suffi-
ciently intelligible. But our opponents, very clever though they
are, have never produced any proof of what they so often and so
confidently declare regarding this matter, and besides it is easy to
prove to them the opposite, that is to say, that it is not possible we
should always deliberately reflect on all our thoughts. Otherwise
the mind would make a reflexion upon each reflexion ad infinitum,
without ever being able to pass to a new thought. For instance,
in being conscious of .some present feeling, I should always have to
think that I think of it, and again to think that I think of think-
ing of it and so ad infinitum. But I must surely come to an end of
reflecting upon all these reflexions, and there must, in short, be
some thought which we allow to pass without thinking of it ;
otherwise we should always dwell upon the same thing." '

128 INTRODUCTION

degree. One reality pervades them all ; no one of them
is separated from another by any impassable barrier.
Body is confused soul ; soul is clear and distinct body.
Self-consciousness is not a unique certainty or reality,
but a high degree of clearness and distinctness in that
which is already real in lower forms. The self may be
exclusive, self- limited, individual ; but it is so only in
common with every other substance. There is no sub-
stance which is not potentially an Ego, a self-conscious
being. What Descartes and Locke both ignore is the
internal movement, the becoming, the growth_ and
development, which is of the essence of every substance.
For them a thing, a mind, an idea, a principle is what
it is, unchangeably; so that either, as in the case of
Descartes, the variety of real thought is contained, perfect
and entire, within its unity, and is to be set forth by pure
sub-sumption, the lifting out of class from within class, or,
as in the case of Locke, the unity of real thought is a mere
aggregate of its varieties, the elements remaining un-
changeable into whatever groups we may gather them.

As against Descartes, Leibniz denies th-e complete Separation

of Matter and Mind.

Accordingly, Leibniz brings against Descartes's view of
mind essentially the same argument as he used against
Descartes's view of matter. The Cartesian view of sub-
stance as that which is in itself and is conceived through
itself, without need of anything else, resulted in the
complete separation of matter and mind. Leibniz, on
the other hand, unifies without absolutely identifying
them, through his view of substance as that which is
continually in process of perceiving or representing all
things. Thus, against Descartes's view of matter as an
independent substance, Leibniz argues that a true
doctrine of substance makes matter by itself an abstrac-
tion, for it is really the confused perception which is
potentially clear and distinct perception, apperception or

STATEMENT OF LEIBNIZ^ PHILOSOPHY I2Q

mind. And similarly, against the view of Descartes that
mind is an independent substance, opposed to matter,
Leibniz maintains that pure mind belongs to God alone,
and that mind as we have it is inseparable from matter
and is really nothing but matter raised to a higher power,
confused perception that has passed into greater clearness
and distinctness. As among created substances there is
no body without soul, so there is no soul without body.

In opposition to Locke, he holds that the Mind always

thinks.

On the other hand, as against Locke, Leibniz contends
that the mind is never without thought. If mind is
a tabula rasa, receiving all its impressions from outside
itself, a mind without thought is a perfectly natural
supposition. And a posteriori Loeke holds that in dream-
less sleep the mind exists without thinking. Its existence
during such a sleep is, he thinks, assured to us by our
recollection afterwards of what took place in the mind
before the sleep. Further, Locke maintains that,
as body can exist without motion, mind can exist
without thought1. Now the ground of this contention
manifestly is that motion and rest are not relatively
but absolutely distinct from one another and, similarly,
that clear and distinct consciousness is absolutely and
not relatively different from unconsciousness. When
a body has no apparent motion, it is absolutely at rest ;
when a mind has no clear and distinct consciousness or
apperception, it is absolutely without consciousness.
To this the central principles of the philosophy of
Leibniz are in complete opposition2. While motion and

1 Could this be regarded as a strictly logical development of one
side of Descartes's philosophy, thus revealing Descartes's inconsis-
tency ? Descartes would say that, as thinking is the essence of
mind, mind cannot exist without thought and yet it may exist
without any specific thought.

2 Cf. Nouveaux Essais, bk. ii. ch. i, § 10 (E. 223 a; G. v. 101):
1 Philalethes. " But I cannot conceive it to be more necessary for the
soul always to think than for the body to be always in motion, the

K

130 INTRODUCTION

rest are apparently absolute opposites, in reality, when
we regard them not abstractly but concretely in their
relation to the rest of the world, they can be understood
only as relatively distinct. For otherwise, the law_ of
continuity, which is the basis of any workable interpreta-
tion of lihe universe, would be broken. In virtue of this
law, then, rest must be considered as an infinitely small
degree of motion, and every body possesses at least a
tendency to motion or a virtual motion, even if it has no
actual, apparent, complete motion. In the same way,
when mind is considered concretely, as a real substance
related (through its representation of them) to all the
other substances of which the universe is composed, the
distinction between consciousness and unconsciousness is
seen - to be relative.—] There can be no total absence of
perception, for absence of perception (representation)
would mean absence of relation to the rest of the world,
and thus a breach of the law of continuity. Unconscious-
perception of ideas being to the soul what motion is to the body."
. . . Theophilus. l ' You are right, sir. Activity is no more insepar-
able from the soul than from the body, a state of the soul without
thought and absolute rest in the body appearing to me to be things
which are equally contrary to nature and of which there is no
instance in the world. A substance which is once in activity will
be so always, for all its impressions persist and are merely mixed
with other new ones. When we strike a body we arouse in it ;or
rather determine) an infinite number of vortices as in a liquid, for
at bottom every solid has some degree of fluidity, and every fluid
has some degree of solidity, and there is no way of ever entirely
stopping these internal vortices. Now we may believe that, if the
body is never at rest, neither will the soul, which corresponds to
it, ever be without perception." . . . Ph. " But this proposition —
the soul always thinks — is not evident by itself." T7t. " I don't say
it is. It requires a little attention and reasoning to see it. Ordi-
nary people recognize it as little as they recognize the pressure of
the atmosphere or the roundness of the earth." Ph. " I doubt if
I thought last night. This is a question of fact, to be settled by
sense-experience." Th. " We settle it in the same way in which we
prove that there are imperceptible bodies and invisible motions,
although some people regard these things as absurd. In the same
way there are perceptions without much sharpness, which are not
distinct enough for us to be conscious of them or to remember
them ; but they make themselves known by certain consequences
they have."'

STATEMENT OF LEIBNIZ S PHILOSOPHY 131

ness or apparent absence of perception is then merely an
infinitely small degree of perception, and every mind
must possess at least virtual thought or consciousness,
a tendency to clear and distinct perception, even although
it may actually appear to be empty of all thought ]. The
mind is not like a block of veinless marble, from which
the sculptor may take what figure he pleases. It has
veins which give the outline of the statue that is to come
forth from it 2. In other words, it is the nature of the
mind to 'look before and after.' Leibniz regards his
view as expressing the truth that underlies the Platonic
doctrine of reminiscence. The present perceptions of the
mind may be regarded as recollections of the past, inas-
much as they were already virtually contained in these
past perceptions and are developed from them — are,
indeed, these past perceptions grown more distinct. And
again, the present perceptions of the mind are forecasts
or prophecies of the future, since all its future perceptions
are confusedly wrapped up in its present states.

The Petites Perceptions.

Thus in the Monadology3, Leibniz maintains the
existence of unconscious perceptions, on the ground
that perception can only proceed from perception, and
accordingly that in the passage from the unconsciousness
of a swoon or a deep sleep to full waking consciousness
there must be an infinite series of perceptions gradually
rising in degree from infinitely little perceptions, which
are apparently indistinguishable from absence of percep-
tion, upwards to the fuller perceptions of actual waking
life. These little perceptions (petites perceptions, confused
perceptions, or, as we might now call them, sub-conscious
thoughts or mental activities) express the continuity of

1 Cf. Locke, Essay, Eraser's ed., vol. i. p. 80 note.

2 New Essays, Introduction, p. 367. Cf. Locke, Essay, Eraser's ed.,
vol. i. p. 48 note, and p. 60 note.

3 §§ 21 and 23.

K 2

132 INTRODUCTION

all souls, from the soul of the pebble to that of the
angel, as Leibniz puts it in his correspondence with
J. Bernouilli1. The characteristics of these petites
perceptions, which prevent us from being clearly aware of
them, are, he tells us2, their smallness, their number,
or their individual indistinctness. And by means of
them he explains such psychological phenomena as our
ceasing to be aware of the sound of a mill or a waterfall
when we have become accustomed to it. The perceptions
are still there, but ' having lost the attractions of novelty,
they are not strong enough to claim our attention and
memory, which are directed to more interesting objects.
For all attention requires memory ; and often, when we
are not, so to speak, warned and directed to take notice
of certain of our own present perceptions, we let them
pass without reflexion, and even without observing
them ; but if some one immediately afterwards draws our
attention to them, and speaks to us, for instance, of some
noise that has just been heard, we recall it to ourselves
and perceive that a moment ago we had some conscious-
ness of it. Thus there were perceptions of which we
were not aware at the time, apperception arising in this
case only from our attention having been drawn to them
after some interval, however small V The petites perccp-

1 G. Math. iii. 560.

_ a New Essays, Introduction, p. 370. Cf. bk. ii. ch. 9, § i (E. 233 a ;
G. v. 121) : 'We ourselves have also petites perceptions, of which we
are not conscious in our present state. It is true that we might
quite well be conscious of them and reflect upon them, were we
not prevented by their multitude, which distracts our mind, or if
they were not effaced or rather obscured by greater ones. ... I
should prefer to distinguish between perception and apperception.
For instance, the perception of light and colour, of which we have
apperception [are conscious] is made up of a quantity of petites
perceptions, of which we have no apperception [are not conscious] ;
and a noise, of which we have perception but of which we take
no notice, becomes apperceptible by a small addition or increase.
For if what precedes had no effect upon the soul, this little addition
would have none either, and no more would the whole have any.'

3 New Essays, Introduction, p. 371. Cf. Nouveaux Essais, bk. ii.
ch. i, § ii (E. 224 a ; G. v. 103) : 'We think of a number of things
at once, but we take notice only of the thoughts which are most

STATEMENT OF LEIBNIZ S PHILOSOPHY 133

tions, accordingly, are merely the confused perceptions of
the self-conscious Monad, and their function and value in
psychology may be estimated by reference to the im-
portance of confused perception in Leibniz's general
doctrine of substance. However great may be their
degree of confusion, and however little we may be
conscious of them individually or collectively, they are
still perceptions, one in kind with the highest, most
distinct apperception or self-consciousness. The realm of
self-consciousness includes the whole of substance ; it is
by no means limited to man and spirits higher than man.
But in the infinite variety of substances, self-consciousness
exists in an infinite variety of degrees ; and there are
many substances in which its degree is infinitely little,
that is to say, less than any degree that can be assigned
or named.

Leibniz's Theory of Knowledge in relation to the main
Principles of his Philosophy.

Thus Leibniz's theory of knowledge is simply the
epistemological expression of the main principles of his

distinct : and matters cannot be otherwise, for if we were to take
notice of all, we should have to think attentively of an infinity
of things at once, all of which we feel and all of which make
impression on our senses. I say even more : something from all
our past thoughts remains, and none can ever be entirely effaced.
Now when we sleep without dreaming, and when we are stunned
by some blow, fall, illness, or other accident, there appears in us
an infinite number of little confused feelings, and death itself can
produce no other effect on the souls of animals, which must
without doubt, sooner or later, regain distinct perceptions, for
everything in nature happens in an orderly way. . . . Each soul
retains all its preceding impressions, and cannot split itself up.
... In each substance the future has a perfect connexion with the
past. This is what constitutes the identity of the individual.
Yet memory is not necessary nor even always possible, because
of the multitude of present and past impressions, which come
together in our present thoughts, for I do not believe that there
are in man any thoughts which have not at least some confused
effect, or which do not leave some vestige to be combined with
later thoughts. We can certainly forget things ; but we might
also recollect them after a long interval, if only we were reminded
of them in the right way.'

134 INTRODUCTION

philosophy. All truth is innate, virtually if not actually.
But there are two kinds of truth. Eternal and necessary
truth has its ground in the principle of contradiction.
It is either self-evident or the result of strict demonstra-
tion from the self-evident. l Our mind is the source of
necessary truths, and however many particular experiences
we may have of a universal truth, we cannot assure our-
selves of it for ever by induction without knowing its
necessity through reason. . . . The senses may suggest,
support, and confirm these truths, but cannot demon-
strate their infallible and perpetual certainty1.' On the
other hand, truth of fact or contingent truth, while
equally innate, is not demonstrable through the principle
of contradiction, but through that of sufficient reason2.
It is obtained by induction rather than demonstration.
It is truth of experience, or perception which we cannot
analyze into perfect distinctness and self -evidence, because
of the infinite complexity of its relations to the system of

1 Nouveaitx Essais, bk. i. ch. i, § 5 (E. 209 b ; G. v. 76, 77).

2 Thus Leibniz rejects the view of Locke that our real know-
ledge, as distinct from merely probable knowledge, 'extends as
far as the present testimony of our senses, employed about par-
ticular objects that do then affect them, and no farther.' (Essay,
bk. iv. ch. n, § 9 ; Eraser's ed., vol. ii. p. 332.) Cf. the corresponding
passage in the Nouveaux Essais (E. 378 b ; G. v. 426) : 'Yet I think
that we might extend the names of knowledge and certainty to things
other than actual sensations, for clearness and plainness [evidence]
extend further, and I regard them as a kind of certainty : and it
would without doubt be an absurdity seriously to doubt whether
there are men in the world, when we do not see any. To doubt
seriously is to doubt practically, and we might take certainty as
a knowledge of truth which we cannot doubt practically without
madness ; and sometimes we take certainty in a still more general
sense and apply it to cases in which we cannot doubt without
deserving to be greatly blamed. But evidence would be a luminous
certainty, that is to say, a certainty such that, because of the
connexion we see between the ideas, we have no doubt whatever.
According to this definition of certainty, we are certain that
Constantinople is in the world, that Constantine, Alexander the
Great, and Julius Caesar have existed. It is true that some
peasant of the Ardennes might justly doubt these things, from
lack of information ; but a man of letters and of the world could
not do so, without great mental derangement.' Cf. also Locke's
Essay, bk. ii. ch. ai, § 75 (Eraser's ed., vol. i. p. 373).

STATEMENT OF LEIBNIZ S PHILOSOPHY 135

things. This infinitely complex mass of relations, which
it is impossible for us to reduce to perfect order and
simplicity, is our confused perception. Confused percep-
tion is, then, the representation in us not of our own
nature, but of the system of things other than ourselves,
that is to say, the other Monads as they are related to us.
But distinct perception is the representation or perception
of our own nature, of that which is in ourselves, and it is
at the same time the evolving of some of our confused
perceptions into clearness ; it is not something quite
separate from our confused perception. Thus we rise to
a knowledge of ourselves through our knowledge of
external things 1. Self- consciousness implies the con-
sciousness of objects ; apperception is, indeed, the very
flower of perception, the beauty to produce which per-
ception, in all its degrees, is living and growing. In
experience or confused thought, rightly interpreted, there
is the basis of distinct, rational knowledge. Sense,
experience, imagination, must not be derided as fiction-
makers by the intellect which they have nourished 2.

The Meaning which Leibniz attaches to 'Perception' or
'Representation.' How does he endeavour to avoid an
endless Relativity ?

Something remains to be said as to the meaning of this
'perception,' 'representation,' or 'expression,' which is
the key-word to Leibniz's theory of knowledge. There is
a strong suggestion of petitio principii about it. What
exactly does it mean ? What is perceived, represented,
expressed? And what does the perception, representation,
expression consist in ? If the essence of every real sub-

1 Cf. Nouveaux Essais, bk. ii. ch. 21, § 73 (E. 269 b ; G. v. 197) :
'The senses furnish us with material for reflexion, and we should
never even think of thought, if we did not think of something
else, that is to say, of the particular things with which the senses
furnish us. And I am persuaded that souls and created spirits are
never without organs and never without sensations, as they cannot
reason without symbols.'

2 See Appendix D, p. 206.

136 INTRODUCTION

stance is to perceive, represent, or express every other, we
seem to have come upon the doctrine of the relativity of
human knowledge in its worst form. It seems as if
knowledge must be compared to the life of those unhappy
islanders * who earn a precarious livelihood by taking in
one another's washing.'

As to the meaning of the terms, Leibniz says that l one
thing expresses another (in my sense) when there is
a constant and regular [regie] relation between what can
be said of the one and what can be said of the other. It
is thus that a projection in perspective expresses the
original figure V Any two things, then, are related to
one another as perceiver and perceived, when the predi-
cates or qualities of the one (whatever these predicates or
qualities may be) always vary concomitantly with the
predicates or qualities of the other. Perception, repre-
sentation, or expression is then a relation of harmony (or
development according to some law or principle) between
the qualities of individual substances. But these qualities
are themselves perceptions. What, then, is the ultimate
reality of which they are all representations ? Leibniz's
answer is that the ultimate reality is the nature of God or
the ideas of God as an intuitive Knower. God alone has
a knowledge which is entirely adequate, perfectly realized ;
in Him the universe is transparent through and through.
There is no reality beyond thought, to which thought
must correspond. Thought cannot in any way represent
that which is entirely other than itself, that which is
separated from it ' by the whole diameter of being ' (or by
an even greater distance if that were possible). For no
sign can be entirely cut off from the thing signified. Sign
and thing signified must have some ground of unity in
virtue of which this relation between them is possible.

1 Lettre a Arnauld (1687) (G. ii. 112) : 'Expression is common to
all soul-principles [formes]. It is a genus, oT which natural pt-r-
_c§Ption» animal feeling and intellectual knowledge are species.'
Cf. tnis Introduction, Part iii. p. 112, note 3.

STATEMENT OF LEIBNIZ S PHILOSOPHY 137

Thus pure thought cannot symbolize, represent, or per-
ceive that which is absolutely not-thought. Confused
thought is the symbol both of other confused thought and
of clear and distinct thought. Accordingly, as between
confused thoughts the relation of sign and thing signified
is such that that which is now regarded as sign may from
another point of view be taken as the thing signified, and
vice versa. Nevertheless it is evident that the clearer^
and more distinct of any two corresponding perceptions \
will naturally be regarded as the thing signified by the j
more confused perception, that is to say, the thing which •
the more confused perception is trying to express, but is
unable to express adequately. And thus the ultimate
' thing signified,' the fundamental reality, which all other
perceptions in various degrees symbolize or represent,
must be perfectly clear and distinct thought, or, in other
words, the thought of God. So also God is First .Cause as"
welljasJJltimate Beality. For we have already seen l that
cause is always reason or explanation, the relatively clear
and distinct perception as against the corresponding con-
fused perception, which is the effect. Accordingly, as the
nature of God is absolutely clear and distinct perception,
He must be the Ultimate Cause of all things 2.

(&) ETHICS.

Degrees of Appetition in the Monads — Impulse, Instinctive
Desire, Will

Every Monad has appetition as well as perception.
Appetition is the principle of change in the Monad, that

* — l pp. 106, 107.

2 This seems to imply that God is the ultimate reality of whom
all individual created things are modes or manifestations. But
Leibniz endeavours to avoid such a conclusion as this, by main-
taining that the essences of things are independent ideas in the
mind and understanding of God, eternal truths whose nature is
not subject to His will. It is hardly necessary to point out how
unsatisfactory is this explanation ; but it is manifest that the
weakness of Leibniz's theory at this point is the inevitable conse-
quence of his attempt to work with two first principles, the
mutual relations of which he has not thoroughly thought out.

138 INTRODUCTION

in virtue of which the Monad passes from one perception
to another. Like perception it has an infinite series of
degrees ; but three main varieties of it may be noted,
corresponding to the three main varieties of perception.
Thus the appetition of the lowest class of Monads (the
bare Monads) is mere unconscious impulse or tendency,
a potential blind force tending to become actual. It is
the particular appetition or change of perception (repre-
sentation) which has its source or ground in unconscious
perceptions. This bare impulse may 'be compared to a
watch-spring wound up, which tends to unwind itself ' ;
it is a tendency such as that of l the stone which goes by
the most direct but not always the best way towards the
centre of the earth2.' The appetition of animal souls is
instinctive appetite or desire, which proceeds from feeling
or conscious, yet relatively confused, perceptions. Like
the appetition of the bare Monads, it seeks immediate
present satisfaction, having nothing to guide it but the
consciousness and memory of the animal soul. Finally,
the appetition of rational souls is self-conscious desire or
will, a principle of change whose basis is apperception or
clear and distinct rational knowledge 3. Appetition, like
perception, is one and the same throughout all its degrees
and varieties, from bare force to the freest, most rational
volition. And in the nature of man we find all degrees
of it ; he is not a purely rational will, but has instinctive
impulses and passions, which belong to the middle class
of appetitions, and physical powers which belong to the

1 Nouveaux Essais, bk. ii. ch. 20, § 6 (E. 248 b ; G. v. 152, 153).

2 Ibid. bk. ii. ch. 21, § 36 (E. 259 a ; G. v. 175).

3 Cf. ibid. bk. ii. ch. 21, § 42 (E. 261 b ; G. v. 180) : ' There are
unfelt [insensible] inclinations, of which we have no consciousness
[apperception] ; there are felt [sensible] inclinations, whose existence
and object we know, but which are formed without our being
aware of it, and these are confused inclinations, which we attribute
to the body, although there is always in the mind something cor-
responding to them ; and finally, there are distinct inclinations
which reason gives us, and of whose force and formation we are
aware.'

STATEMENT OF LEIBNIZ S PHILOSOPHY 139

lowest class. As on the cognitive, so on the practical side
of his nature, the law of continuity holds.

Feeling. Pleasure and Pain. ' Semi-pains ' and
1 Semi-pleasures.'

The chief features of Leibniz's ethics are fixed by these
general considerations. In applying them it is necessary
for us, who have become familiar with post-Kantian
distinctions, to remember that the usual threefold
division of mental elements into cognition, feeling, and
will, is not of older date than the age of Kousseau *, and
accordingly that Leibniz still works with the Aristotelian
twofold division of the elements into theoretical and
practical. Thus the ' appetition ' of Leibniz covers both
feeling and will (in our sense of the terms), as well as the
lower forms of both, which are conscious and unconscious
forces more or less restrained from full activity, that is
to say, more or less potential or virtual. Accordingly, as
appetition and perception always accompany one another,
Leibniz maintains that there is no perception absolutely
colourless and entirely unchanging or at rest. Eveiy
perception has an element of feeling and activity, although
the degree of it may be infinitely small. If we can be
pardoned the anachronism of using a phrase which Lotze
has made familiar, we may say that every perception has
a ' value ' or ' worth ' ; but it must not be forgotten that
for Leibniz this value is not anything absolute or pre-
eminently real, but merely the unrealized potentiality of
clearness and distinctness in the perception 2.

Speaking then of human nature, which includes all
the varieties of perception and appetition, Leibniz says
that 'there are no perceptions which are entirely indifferent
to us, but when their effect is not observable we can call
them indifferent ; for pleasure and pain seem to consist in

1 It is usually attributed to Tetens (circa 1750). But it first
comes into prominence through Kant.

2 Cf. Lotze, Microcosmus, bk. iii. ch. 4, § 4 (Eng. Tr., vol. i. p. 366).

140 INTRODUCTION

an observable help or hindrance1.' This, he warns us, is
not to be taken as a strict definition of pleasure and pain,
for he does not think it possible to give such a definition.
But his account of these feelings seems to follow directly
from his general point of view. Pain is essentially a
hindrance or restraining of a Monad's appetition, while
pleasure is its free action2. They are thus entirely
relative to one another. And while we speak of the
hindrance or freedom of appetition as pain or pleasure,
only when the appetition has reached the degree of con-
sciousness, yet consciousness is separated from unconscious-
ness by no hard and fast line, and consequently appetitions
of a lower degree may be regarded as minutely painful or
pleasant, according as they are retarded or advanced. Thus
Leibniz speaks of ' semi-pains ' and ' semi-pleasures ' or
' little imperceptible [inaperceptiNes] pains and pleasures, '
corresponding to the petites perceptions in the theory of
knowledge. Like the petites perceptions these semi-pains
and semi-pleasures may. by growing in individual inten-
sity or by combining into one totality, become observable
in consciousness as complete pains and pleasures 3. No
soul can ever be absolutely at rest, absolutely without
appetition. And no created soul can be purely active,
with a perfect freedom. Thus every soul has continual
appetition, which is partly free and partly restrained.
That is to say, every soul has continually pleasure and
pain in some degree.

Accordingly Leibniz takes great interest in the ' un-
easiness' in which Locke finds the first movings of

1 Nouveaux Essais, bk. ii. ch. 20, § i (E. 246 b; G. v. 149). Cf.
Locke's Essay (.corresponding place), with note in Eraser's ed., vol. i.
p. 302.

* Cf. Nouveaux Essais, bk. ii. ch. 21, § 42 (E. 261 b ; G. v. 180) : ' I
think that fundamentally pleasure is a feeling of perfection, and
pain a feeling of imperfection, provided the feeling is sufficiently
marked for us to be definitely conscious of it [s'en apercevoir'}.' Cf.
De tribus juris naturae et gentium gradibus (Mollat, p. 21) : 'Pleasure
is nothing else than the sense of increasing perfection.'

* See Nouveaux Essais,bk. ii. ch. 20, § 6 (E. 248 a; G. v. 151, 152).

STATEMENT OF LEIBNIZ S PHILOSOPHY 141

desire 1. This uneasiness is not exactly pleasure or pain,
but a vague feeling of discomfort or restlessness, that
tends to pass into more definite desire and so to produce
action. It is thus for Leibniz the confused perception
and undeveloped striving or appetition out of which, by
a process of evolution, clear and distinct perception and
free volition arise. In so far as this evolution is re-
strained, we suffer pain : in so far as it proceeds smoothly
without impediment, we enjoy pleasure. Thus every soul
instinctively seeks its own pleasure: it follows the line
of least resistance. This it does in virtue of its own
nature, which is to unfold itself spontaneously from
within, its present state flowing entirely from its past
and holding a prophecy of its future. Soul-activity is
pleasure, soul-restraint is pain ; and it is of the essence
of the soul to be active, for every simple substance is
primarily a force.

Freedom, Liberty of Indifference, and the i Will to will.'

From this Leibniz's view of freedom directly follows.
There can be no such thing as a liberty of indifference,
an absolutely undetermined choice ; for that would imply
discontinuity in the life of the soul. An absolutely un-
determined choice can only mean that the state of the
soul when it makes the choice is not an orderly unfolding
of the state of the soul preceding the choice, but is a
beginning of action de novo. And this is contrary to the

1 Nouveaux Essais, bk. ii. ch. 20, § 6 (E. 247 ; G. v. 150). Cf.
ch. 21, § 36 (E. 258 b ; G. v. 174) : 'If you consider your "un-
easiness " as a real discomfort [deplaisir], I do not admit that in this
sense it is the sole goad to action. Most frequently the goad is
those little unfelt [insensible] perceptions, which we might call im-
perceptible [inaperceptible~] pains, were it not that the notion of pain
implies apperception. These little impulses consist in the continual
freeing of ourselves from little hindrances, at which our nature
works without thinking about it. In this really consists that un-
easiness, which we feel without knowing it, which makes us act in
passion as well as when we appear most tranquil, for we are never
without some activity and motion, which comes merely from this,
that nature is always working so as to put herself more at ease.'

142 INTRODUCTION

very notion of substance. Both in the TJieodicee and in
the Nouveaux Essais, Leibniz freely illustrates his view
by reference to particular instances, such as the parable
of the ass between two equal bundles of hay ; and he
makes it evident that, as a matter of fact, in every case
there is in the state of the soul before the choice is made
some determining element of perception. The extreme
case, of course, is that of 'willing to will,' resolving to do
a thing contrary to our judgment and wishes, merely
because we have the power to do it. Leibniz points out
that even here our volition is determined by a previous
idea, namely that of showing to ourselves or to others
that we possess a certain power1, so that in every case

1 Cf. Nouveaux Essais, bk. ii. eh. 21, § 25 (E. 255 b ; G. v. 168) :
'Men say that, after having known and considered everything, it
is still in their power to will, not only what pleases them most,
but also the opposite of that, just to show their freedom. But it is
to be noticed that this very caprice or obstinacy or, to say the least,
this reason which prevents from obeying other reasons, also comes
into the balance and makes pleasing to them that which otherwise
would not please them at all, and accordingly their choice is
always determined by perception. Thus we do not will merely
what we will, but what pleases us, although the will may indirectly
and, as it were, from afar contribute to make a thing pleasing to
us or not.' See also the corresponding passage in Locke's Essay
(^bk. ii. ch. 21, § 24), Eraser's ed., vol. i. p. 327.

A hint of Leibniz's psychology of volition is given in the
Nouveaux Essais, bk. ii. ch. 2.1, § 39 (E. 260 b ; G. v. 178) : 'Several
perceptions and inclinations conspire towards complete volition,
which is the result of their conflict. There are perceptions and
inclinations which are individually imperceptible, but the totality
of which produces an uneasiness, which impels us without our
seeing the ground of it ; several of these perceptions combined
together, direct us towards some object or away from it, and then
we have desire or fear, also accompanied by an uneasiness, but an
uneasiness which does not always amount to pleasure or pain
\_deplaisir]. Finally there are impulses actually accompanied by
pleasure and pain, and all these perceptions are either new
sensations or images remaining from some past sensation, accom-
panied or unaccompanied by memory which renews the attractions
these same images had in these preceding sensations, and so
renews the old impulses in proportion to the vivacity of the imagi-
nation. From all these impulses there finally results the prevailing
effort, which constitutes the full volition. Yet the desires and
tendencies of which we are conscious are also frequently called
volitions (although less complete') whether or not they prevail and

STATEMENT OF LEIBNIZ S PHILOSOPHY 143

the will is determined by some reason or perception.
The error of abstract indeterminism arises from neglect
of sub-conscious perceptions and appetitions. It is thus
akin to the error of Descartes and Locke with regard to
knowledge, namely that of regarding only self-conscious
knowledge or apperception as real knowledge. We have
seen1 that to regard all thought as self-conscious or reflec-
tive would make any progress in thought impossible,
because it would imply that the mind thinks that it thinks
that it thinks ad infinitum, and is accordingly never able
to go on to any new thought. Similarly, the doctrine of
a liberty of indifference, regarding all volition as neces-
sarily developed and conscious, implies a power of willing
to will that we will ad infinitum. But in fact volition
cannot be restricted to deliberate conscious desire or
intention. We do and experience many things which
ultimately contribute to determine our will, although we

give rise to action. It thus readily follows, that volition can
hardly exist without desire and avoidance \_fuite] ; for I think we may
give this name to the opposite of desire. There is uneasiness not
only in the troublesome passions, like hate, cruelty, anger, envy,
shame, but also in their opposites, such as love, hope, favour and
glory. It may be said that wherever there is desire, there is
uneasiness ; but the contrary is not always true, because often we
have uneasiness without knowing what we want, and then there
is no definite desire. ... As the final determination [to action] is
the result of weighing, I should think it may happen that the
most pressing uneasiness does not prevail [in influencing the will] ;
for even though it might prevail over each of the opposite
tendencies, taken singly, it may be that the others, combined
together, overcome it. The mind may even make use of the
method of dichotomy to make now one and now another set of
tendencies prevail, as in an assembly we can make one or another
party prevail by a majority of votes, according to the order in
which we put the questions. It is true that the mind ought to
make provision for this beforehand ; for at the moment of struggle
there is no time for these artifices. Everything which strikes us
at that moment has a strong influence upon the result and helps
to make up a compound direction, composed almost as in mechanics,
and without some quick turning aside we cannot stop it. Fertur
equis auriga nee audit currus habenas [The driver is borne on by his
horses and the chariot heeds not his guidance].' The quotation is
from Virgil, Georgics, i. 514.

1 Part iii. of this Introduction, p. 127 note.

144 INTRODUCTION

do not at the time deliberately contemplate that they
shall afterwards have this effect *.

Moral and metaphysical Necessity.

On the other hand, volition is not absolutely neces-
sitated as the system of Spinoza requires. Will is not
to be identified with the abstract understanding, whose
principle is that of contradiction. Will does not invari-

1 Cf. Nouveaux Essais, bk. ii. ch. 21, § 23 (E. 255 b ; G. v. 167) :
* We do not will to will, but we will to do, and if we willed to
will, we should will to will to will and that would go on ad
inftnitum. Yet we must not overlook the fact that by voluntary
actions we often contribute indirectly to other voluntary actions,
and though we cannot will what we will, as we cannot even judge
what we will, we may nevertheless so act beforehand that when
the time comes we may judge or will that which we would wish
to be able to will or judge to-day. We devote ourselves to the
people, the kind of reading, the conditions generally that are
favourable to a certain side, we give no heed to what comes from
the opposite side, and by these and many other directions which
we give to our minds, usually without definite intention and
without thinking of it, we succeed in deceiving ourselves or at
least in changing ourselves, becoming converts or perverts, according
to the experiences we have had.'

There is an interesting suggestion of the views of Leibniz in
Montaigne's Essais, bk. ii. ch. 14. Leibniz may quite well have
read it. 'It is a pleasant fancy,' says Montaigne, 'to think of
a mind exactly balanced between two like desires. For it is
indubitable that it will never come to a decision, inasmuch as
determination and choice imply inequality of value ; and if we
should be set between the wine and the bacon, with an equal
desire to drink and to eat, there is doubtless nothing for it but
to die of thirst and hunger. To provide against anything so
inconvenient as this, the Stoics, when they were asked how our
soul comes to make choice between two indifferent things, so that
out of a large number of crowns we take one rather than another,
though they are all alike and there is no reason which disposes
us to a preference—the Stoics reply that this motion of the soul
is extraordinary and exceptional, arising in us from a strange,
accidental and fortuitous impulse. It seems to me they might
rather have said that nothing comes before us in which there is not
some difference, however slight ; and that, to sight or to touch,
there is always some preference which tempts and draws us,
though it be imperceptibly : just as if we suppose a piece of
twine equally strong throughout, it is utterly impossible that it
should ever break. For in what part of it is the breaking to begin,
the flaw to appear ? And for it to break in every part at once is
against all nature.' Cf. New Essays, Introduction, p. 372.

STATEMENT OF LEIBNIZ S PHILOSOPHY 145

ably act from a reason the opposite of which is self-
contradictory : it frequently acts from a sufficient reason,
.that is to say, from an inclining or probable reason. We
do not act merely because we must, because the eternal
nature of things makes it absolutely impossible to do
otherwise. We act towards an end or ideal which is
not a mere fiction of our own imagination, but a recogni-
tion of the fitness of things, a more or less clear perception
of the best among various possible courses of action. Our
will is thus determined by a moral, not a metaphysical
necessity, by the inclination which arises from its re-
cognition of the best, however perfect or imperfect
that recognition may be. Our will (being our conscious
appetition) moves in accordance with our ideals ; for
these ideals are nothing but our perceptions, the potenti-
alities of our nature, and not merely of our own nature,
but of the nature of all things, since our perceptions are
representations of the whole universe.

Freedom is Spontaneity + Intelligence.

Accordingly Leibniz, following Aristotle, regards free-
dom as consisting essentially in spontaneity and intelli-
gence. But intelligence is not to be interpreted merely
as the abstract understanding of pure self- consciousness :
it includes every degree of perception or representation.
There is thus an infinite variety of degrees in freedom,
and no actual concrete substance is subject to an abso-
lutely pure necessity, that is, to a necessity which is other
than an infinitely small degree of freedom. And as all
Monads alike have spontaneity (for they unfold the whole
of their life from within themselves), the degree of freedom
belonging to any Monad depends on the degree of its
intelligence, that is to say, on the^, degree of clearness
and distinctness of its perceptions. Similarly in human
beings, an action is free in proportion to the clearness \
and distinctness of the reasons which determine it. Thus
a capricious or wilful action, far from indicating any

L

146 INTRODUCTION

special freedom of will, is rather lacking in freedom,
since its determining reason is so obscure or confused
that it is hardly possible to describe it. Its obscurity
leads people to overlook it and to fancy that the action
is entirely without reason. No human action is unde-
termined, as none is absolutely necessitated ; but the
highest freedom accompanies the most perfect knowledge,
and God is the freest of beings, not because He can do
whatever He pleases, nor because He always acts spon-
taneously, from the necessity of His own nature, but
because every act of His is determined by infinite wisdom
to 'the best possible ends.

Good and Evil The End of Conduct.

So also good and evil are relative terms. Actions are
good in so far as they are determined by clear and distinct
perceptions, evil in so far as their determining reasons
are confused. As error is confused perception and is thus
imperfect truth, so sin is the action or appetition which
flows from confused perception, and is thus imperfect
righteousness. Now since it is of the essence of the soul
to be continually active, since its activity is more free
the clearer and more distinct are its perceptions, and
since pleasure consists in the freedom of its activity, the
end of conduct is the highest degree of freedom, which is
at once the highest degree of pleasure or felicity and the
highest degree of perception or knowledge. Every soul
more or less blindly seeks pleasure ; but the blinder it is
the more does it tend to seek satisfaction in present,
momentary pleasure. Its blindness or confusedness of
perception means that it does not think the matter out,
that it does not take into account the deeper nature and
connexions of things, and thus fails to find the best way
to freedom, felicity, wisdom. The soul instinctively tries
to take the shortest way to happiness ; but the way that
is really shortest is apt to appear to purblind souls a

STATEMENT OF LEIBNIZ^ PHILOSOPHY 147

roundabout way — an Umweg — and so they fail to achieve
their end. ' The stone goes by the most direct, but not
always the best way towards the centre of the earth, not
being able to foresee that it will meet rocks on which it
will be broken, while it would have more nearly attained
its end, if it had had the intelligence and the means to
turn aside. Even thus, going straight towards present
pleasure, we sometimes fall over the precipice of misery1.'
'We must not abandon those old axioms that the will
follows the greatest good it perceives and shuns the
greatest evil. That the truest good is so little sought
after is mainly due to this, that in matters and on occa-
sions in which the senses have very little influence, most
of our thoughts are, so to speak, insensible [sourdes] (I call
them in Latin, cogitationes caecae [blind thoughts]), that is
to say, they are void of perception and feeling and consist
in the bare use of symbols, like the work of those who
make calculations in algebra, without looking from time
to time at the geometrical figures. In this respect words
usually have the same eifect as arithmetical or algebraic
symbols. We often reason in words, hardly having the
object in mind at all. Now this knowledge cannot move
us : something vivid is required that we may be moved.
Yet it is thus that men most often think of God, of
virtue, of happiness; they speak and reason without
definite ideas. Not that they cannot have these ideas ;
for they are in their minds. But they do not give them-
selves the trouble of carrying on the analysis of their
ideas2.'

1 Nouveaux Essais, bk. ii. ch. 21, § 36 (E. 259 a ; G. v. 175).

2 Ibid. bk. ii. ch. 21, § 35 (E. 257 a ; G-. v. 171). As this
passage suggests, Leibniz is full of moral optimism. Cf. § 38 of
the same chapter (E. 260 a ; G. v. 177^): 'When I consider how
much ambition and avarice can effect in all those who once
set themselves in this line of life, which is almost entirely without

some happy revolution of the human race were some day to give
it vogue and make it fashionable.'

L 2

148 INTRODUCTION

Justice. Self-love, Love of Man and Love of God.

Self-love, more or less enlightened, is the ground of all
our actions. And the more enlightened our self-love is,
the higher is the ethical value of our action and the better
are its results. But as, like all other Monads, our souls
are not mere self-centred atoms but reflect the whole
universe, our self-love is at the same time, according to
its degree, a love for others. To love others is to desire
their good as we desire our own. And as it is the
essence of our souls to represent or perceive all other
souls, the more enlightened our own desire of good is,
the more are we seeking the highest good of others and
fulfilling the ends of God. We can really love others,
and express our love to them only in proportion as we
clearly perceive what is best for them ; and the more
clearly we perceive what is best for ourselves, the more
clearly we perceive what is best for them. This follows
from the very constitution of our being. In other words,
we seek our own perfection, however blindly ; and we
are so united to all other men, that in realizing our own
perfection we are also realizing theirs. Thus the more
enlightened our self-love is the more disinterested does
it become and the more nearly does it approach to a pure
love of God *.

Accordingly love is the root of law. Law is not a
merely external arrangement, an arbitrary command, an
expression of bare power. It is a moral power, and
'moral' means that which is natural to a good man.
t A good man is one who loves all men, so far as reason
allows. Accordingly,' says Leibniz, 'justice (which is
the ruling virtue of that aifection which the Greeks call
<j>LXavOpu7ria.) will, if I mistake not, be most fittingly
defined as the charity of a wise man, that is to say, charity
in obedience to the dictates of wisdom. . . . Charity is

1 Cf. On the Notions of Right and Justice, p. 285 (E. 118 b).

STATEMENT OF LEIBNIZ'S PHILOSOPHY 149

universal benevolence, and benevolence is the habit of
loving1.'

Thus the ethical progress of man is an approach to the
reality that is in God, a bringing forth of the image of
God which is hidden in the soul, through growing en-
lightenment, that is to say, through the appetition of the
soul passing forward to ever clearer and more distinct
perceptions. This feature of the philosophy of Leibniz
leads Windelband to describe his ethics as expressing
1 the philanthropic ideal of morality which was character-
istic of the AufTdarung period ' in Germany. i " Enlighten
thyself, and have a care for the enlightenment of thy fel-
lows : so shall you all be happy ; " that is the philosophy
professed by the whole eighteenth century in Germany2.'

1 On the Notions of Right and Justice (1693), p. 283 (E. 118 a). Cf.
Nouveaux Essais, bk. ii. ch. 28, § 5 (E. 286 b ; G. v. 232) : ' Ac-
cording to this notion' [externally imposed law], 'one and the
same action would be at the same time morally good or morally
bad, under different legislators, just as our able author' [Locke]
' considered virtue as that which is praised, and accordingly one and
the same action would be virtuous or not, according to the different
opinions of men. Now, as that is not the meaning that is usually
given to morally good and virtuous actions, I should prefer for my
part to take as the measure of moral good and virtue the invariable
rule of reason, which it is the office of God to maintain. So we
may be assured that by His means, every moral good becomes also
a physical good, or as the ancients said, every honourable act is
useful ; in place of which, if we would express the view of our
author, we should have to say that moral good or evil is an imposed
or ordained [institutif^ good or evil, which he who has command of
power endeavours by rewards or penalties to make us do or shun.
The good thing is, that what proceeds from the general ordinance
of God is conformable to nature or to reason/

2 Windelband, Geschichte der neueren Philosophie, vol. i. p. 477.
Cf. Von der Gluckseligkeit (E. 673 a ; G. vii. 89) : ' If now a noble \hohe]
person attains to this, that in the midst of all luxury and honours
he yet finds his greatest enjoyment in the activities of his under-
standing and the practice of virtue, then I hold him doubly noble :
in himself, on account of this happiness and true joy of his ; and
for others, since it is most certain that this person, on account of
his power and insight, can and will also impart light and virtue
to many others, for such an imparting means a reflected light
upon the giver, and those who have the same common aim can
help one another and give new light in the investigation of truth,
the increase of human powers, and the promotion of that which
is best for all. Thus the exalted \hohe~] happiness of noble \hohe~]

150 INTRODUCTION

and also enlightened persons appears from this that they can do
as much for their happiness as if they had a thousand hands and
a thousand lives, indeed as if they were to live a thousand times
as long as they do. For our life is to be counted a true life in so
far as we do good in it. Now he who does much good in a shorter
time is the same as him who lives a thousand times longer; which
is the case with those who can get a thousand and more than a
thousand hands to work along with them, and consequently in
a few years more good can happen for their highest peace and
enjoyment than otherwise many centuries could bring to pass.'

PART IV.

HISTORICAL AND CRITICAL ESTIMATE OF THE PHILOSOPHY
OF LEIBNIZ.

Relation of Leibniz to earlier Thinking, especially to the
Peripatetic and Atomist Positions.

No genuine thinker can set himself outside of the
philosophic succession. However protestant or revolu-
tionary he may be, his problem is always to a great extent
determined for him by the systems of the past. Unless
intellect is to be called ' bloodless ' these systems may be
said to be in his blood ; he could not turn against them if
they were not in him, if he had not made them his own.
He may cease to seek for truth in the perplexing world,
and try to find it in what he takes to be the simplicity
and certainty of his own nature ; but, whether he knows
it or not, that very nature of his is to a great extent what
the tiresome world has made it. He may ignore history
or scorn it, but he cannot escape from it.

The conviction of some such truth as this was very
strong in Leibniz. He held it against the fashion of his
time. The early part of the seventeenth century was
a time when the new felt itself to be so very new, the
modern so very modern, that, with the infallibility of
youth, it could aiford to despise what seemed ancient,
worn-out, and superseded. When ' our moderns ' (as
Leibniz frequently calls them) were not contemptuous
of older thought they were unconscious of it. In fact,
history for them meant a blind tradition, which they had

152 INTRODUCTION

cast off. Descartes, for instance, when he turned from
courts and camps to meditation by his own fireside,
professed to renounce entirely the methods and results of
earlier thinkers, and to draw from his own unaided con-
sciousness a system of truth which no learned sophistry
could shake. Descartes was the discoverer of the ' plain
man.' Unsophisticated mother-wit will of itself produce
absolutely certain knowledge, if only we put the right
instrument into its hands, or in other words, if we
suggest to it a right method l. Thinking thus, Descartes

1 Cf. Recherche de la Verite par les Lumieres Naturelles, (Euvres de
Descartes (Cousin), vol. xi. p. 334 : ' My purpose in this work is to
bring to light the wealth of our nature, by throwing open to every
one the way by which he may find in himself, without borrowing
anything from anybody else, the knowledge that is necessary for
the conduct of his life, and by which he may afterwards make use
of this knowledge to master the most abstruse sciences to which
human reason can attain. But lest the magnitude of my plan
should at once fill your mind with such amazement that you can
no longer find it possible to have any confidence in what I say,
I may tell you that what I am undertaking is not so difficult as
might be imagined. In fact, the branches of knowledge which are
not beyond the reach of the human mind are united together by
so wonderful a bond and can be deduced from one another with so
complete a necessity, that not much art and skill are required to find
them out, provided we begin with the most simple and learn to
rise gradually to the most exalted. This I intend to show here, by
means of a succession of reasonings so clear and so commonplace
that every one will see that, if he has not noticed the same things
as I have, it is only because he has not turned his eyes in the right
direction nor given his thoughts to the same objects as I have, and
that I no more deserve glory for having discovered these things
than would a peasant deserve it for having found by chance under
his feet a treasure which had long remained hidden, though
diligently sought after. ... I will not inquire into what others
have known or have not known. Suffice it to observe that,
although all the knowledge we can desire were to be found in
books, yet the good they contain is mixed up with so much that
is useless and is scattered throughout so many big volumes that life
is not long enough to read them, and to recognize what is useful
in them would require more ability than to find it out for our-
selves. So I hope the reader will not be displeased to find here
a shorter way, and that the truths I bring forward will be accept-
able to him, although I do not borrow them from Plato or Aristotle
but offer them as having value in themselves, like money which
has the same worth whether it comes from a peasant's purse or
from the treasury.' Cf. Discourse on Method, Part vi. (Veitch's
Translation, pp. 109 et sqq.). Huet says that 'though Descartes

ESTIMATE OF LEIBNIZ S PHILOSOPHY 153

inevitably turned his back upon the history of thought,
counting it little better than ' old wives' fables1.'

In Leibniz, on the other hand, there is a double re-
action— a reaction against the scorn 'of history, and a
reaction against the extremes to which modern philosophy
had been carried in its opposition to Scholasticism, The
whole bent of Leibniz's thought was against sharp and
absolute divisions. Thought does not proceed per saltum.
In the history of thinking, as in all other history, i the
present is laden with the past and full of the future2.'
Thus, for Leibniz, the Scholastics may have been wrong,
but they were not absolutely wrong. And the moderns
may be right, but they are not entirely right. Nothing
in the past is to be completely set at naught, for out
of the past the present has come. The one cannot be

had carefully studied the ancient philosophers and several of the
moderns, he yet affected to appear ignorant of them, in order that
he might be regarded as the sole discoverer of his doctrine. In
this several of his disciples have too thoroughly followed his
example ; for they have imitated his feigned ignorance by culti-
vating a real ignorance.' Traite philosophique de la faiblesse de I' Esprit
humain, bk. iii. ch. 10. Voltaire also gives point to the general
opinion regarding Descartes by the satirical suggestion that
Descartes had 'never read anything, not even the Gospels.' Les
Systemes, line 37 ; (Euvres Completes, vol. x. p. 169.

1 It was not only the fact of a revolution in thought that gave
rise to the Cartesian disregard of history : the very nature of the
revolution itself contributed to this end. The substitution of
a mechanical for an a priori dogmatic way of explaining things
was inevitably connected with a fresh interest in the study of
mathematics, and this led to a preference of mathematical to
historical methods in philosophy. Cf. Regies pour la Direction de
I' Esprit, (Euvres de Descartes (Cousin), vol. xi. p. 211: 'We shall
never be mathematicians, even although we were to know by
heart all the demonstrations of other people, if we are not capable
of solving by ourselves all kinds of problems. In the same way.
though we have read all the reasonings of Plato and Aristotle, that
will not make us philosophers if we cannot bring to any question
a steady judgment. In such a case we should, indeed, have
learned not a science, but history.' Also, p. 209 : ' Eegarding the
object of our study we must inquire, not what others have thought
nor what we ourselves surmise, but what we can see clearly and
manifestly [avec evidence], or what we can deduce with certainty.
This is the only way to obtain real knowledge [la science'].'

2 Cf. Wallace, Logic of Hegel (2nd ed.) ; Prolegomena, pp. 203 sqq.

154 INTRODUCTION

understood without the other. Leibniz from his earliest
days had been a vast reader of books, and his erudition
tempered his imaginative optimism with reverence and
caution. Thus his philosophizing most often takes the form
of hypothesis or suggestion rather than that of dogma or
demonstration. In the Kantian sense his philosophy is,
of course, * dogmatic ' and not ' critical ' ; but to some
extent he foreshadows the ' critical spirit V As a thinker,
he counts as foreign to him nothing that men have
thought, and his ideal philosophy would be a philosophy
which says clearly all that all previous thinkers have
stammeringly tried to say. So people have called him an
'eclectic,' and possibly his fame has suifered from the
imputation. But there is no lack of originality in the
* metaphysical romance 2 ' he brings us, for he is to be
called an eclectic mainly in contrast with the Cartesian
extremists, who repudiated all obligation to the past.
While convinced of the value of his own hypotheses,
Leibniz rather glories in his indebtedness, rejoicing to
find himself in the philosophic succession. 'I despise
almost nothing,' he says, 'except judicial astrology and
trickeries of that kind3.' 'It happens somehow that the
thoughts of other people are usually not displeasing to me,
and I appreciate them all, though in divers degrees4.'
' There is as much or more reason to beware of those who,
most often through ambition, claim to put forth something
new as to mistrust old impressions. And after having
devoted a great deal of thought both to the old and the
new, I have come to the conclusion that most of the
received doctrines can be taken in a right sense. So that

1 'In Leibniz the dogmatic philosophy comes in all points so
near to the critical that only one step is needed to rise from the
point of view of the one to that of the other.' K. Fischer, Gesch.
d. neueren Phil., vol. ii. ch. 21, § i.

2 Hegel, Gesch. d. Philosophic, vol. iii. p. 408. Kant also speaks of
the universe of Leibniz as 'a kind of enchanted world' [eine Art
von bezauberter Welt]. Rosenkranz, i. 521 ; Hartenstein, iii. 445.

3 Lettre a Bourguet (1714), (G. iii. 562).

4 Specimen Dynamicum (1695) (G. Math. vi. 236).

ESTIMATE OF LEIBNIZ S PHILOSOPHY 155

I wish clever men would seek to satisfy their ambition
rather by building and making progress than by going
back and destroying1.' 'This system' [Leibniz's own]
' appears to combine Plato with Democritus, Aristotle
with Descartes, the Scholastics with the moderns, theology
and ethics with reason. It seems to take the best from
all sides, and then to go further than any one has yet
gone. ... I see now what Plato meant when he regarded
matter as an imperfect and transitory thing ; what Aris-
totle intended by his entelechy; what is that promise
of another life, which Democritus himself made, accord-
ing to Pliny ; how far the Sceptics were right in crying
out against the senses ; how animals are automata, as
Descartes says, and have nevertheless souls and feeling, as
people think ; how a rational explanation is to be given of
the views of those who attribute life and perception to all
things — such people as Cardan, Campanella, and (better
than these) the late Countess of Conway (a Platonist), and
our friend, the late M. Francois Mercure Van Helmont
(though otherwise bristling with unintelligible paradoxes),
with his friend, the late Mr. Henry More V

1 Nouveaux Essais, bk. i. ch. 2, § 21 (E. 219 a ; Gr. v. 92).

z Ibid. bk. i. ch. i (E. 205 a ; G. v. 64). Leibniz might have
added the name of Spinoza, who says that ' all individual bodies
are animate, though in different degrees.' Ethics, Pt. ii. prop. 13,
Scholium. Cf. Lettre a Basnage (1698) (E. 153 b ; G. iv. 523) : « When
we penetrate deeply into things, we observe more reason than
would be believed in most of the sects of the philosophers. The
lack of reality in the things of sense, according to the Sceptics ;
the Pythagorean and Platonist reduction of everything to har-
monies, numbers, ideas, and perceptions; the "One" and even the
one Whole of Parmenides and Plotinus, without any Spinozism ;
the Stoic connexion, compatible with the spontaneity of others ;
the vital philosophy of the Cabbalists and Hermetics, who attri-
bute feeling to everything ; the forms and entelechies of Aristotle
and the Scholastics ; and on the other hand the mechanical
explanation of all particular phenomena, according to Democritus
and the moderns— these are all combined together as in a centre
of perspective, viewed from which the object (confused from every
other point of view) reveals its regularity and the harmony of its
parts. We have failed to accomplish this by our sectarian spirit,
limiting ourselves by rejecting others.' The writings of Leibniz
are full of similar passages.

156 INTRODUCTION

Descartes himself * took a good part of his best thoughts '
from the men of old l. And thus, Leibniz would say, it
is better frankly to own our obligations and to go back to
the past that we may, if possible, draw from it neglected
truths, by the aid of which our present theories may be
improved and thinking may go forward. For the idea
of progress on the basis of history controls the mind
of Leibniz, to whatever objects he directs his think-
ing2. Accordingly, admitting the value of the modern
mechanical philosophy, and yet being conscious of its
imperfections and dissatisfied with some of its results,
Leibniz turns back to Scholasticism and its roots in the
philosophy of Greece, to ' recover the gold from the
mire, ' and so build up a more perfect system 3. Thus
Dillmann rightly contends that Leibniz can be properly
understood only if we recognize that his main endeavour
is to reconcile the modern mechanical view of things with
the ancient doctrine of 'substantial forms.' Yet it must
not be forgotten that Leibniz sought to effect this recon-
ciliation by modifying and reconstructing, and not by
merely dovetailing one system into another.

The way of explaining phenomena by reference to
* substantial forms,' which Descartes and Gassendi rejected
in favour of a mechanical explanation of nature, was a
growth of the Peripatetic philosophy, which in course of
time had run to seed. It sprang originally from the
sound Aristotelian idea that all events or particular things
are to be explained by reference to active principles, not

1 Lettre a Nicaise (1692) (E. 120 a ; G. ii. 534). Cf. De stilo philoso-
phico Nizolii (1670), § 24 (E. 67 a ; G. iv. 154).

2 Thus one of his latest (and not least able) expositors, E. Dill-
mann, offers Leibniz a homage which he himself would at once
have condemned. For Dillmann regards the philosophy of Leibniz
as final and all-sufficient, if only it be rightly understood. ' The
Monadology is the most perfect fruit of philosophical reflexion,
the most complete and brilliant system in the history of philo-
sophy.' (Neue DarsteUung, &c., p. 525.) There is a strange irony
in the fact that so able and devoted a disciple has so completely
missed his master's spirit.

3 Lettre a Remond (1714) (E. 704 b ; G. iii. 625).

ESTIMATE OF LEIBNIZ S PHILOSOPHY 157

entirely external to the events or things, but appearing in
them. But the meaning, the spirit of Aristotle's method
was lost sight of. 'Find a principle, a form, of any kind,'
came to be the rule of explanation. And thus the number
of 'substantial forms' or principles of substance was
multiplied indefinitely, while, in addition, the most
minute changes in substances were each explained by
reference to some ' accidental form ' or principle of
accident. Anything sufficed as an explanation so long
as it was called a form. Thus when no intelligible
account of a phenomenon could readily be given it was
attributed to some hidden principle (qualitas occulta),
which was described by the name of the phenomenon to
be explained. Thus, for instance, Toletus * gives us the
valuable information that ' the substantial form of fire is
an active principle by which fire, with heat as its instru-
ment, produces fire.' After making this amazing state-
ment he recollects that fire is sometimes produced by
things other than fire, and he proceeds with grave
elaboration to prove that 'fire can result from all the
substantial forms capable of producing it in air, in water,
or in anything else. '

This may be the redudio ad absurdum of the Peripatetic
Scholasticism ; for indeed petitio principii could no farther
go. It is almost worse than the virtus dormitiva of
Moliere's satire. But the author does not appear to have
seen the humour of it. Can we wonder, then, that
Descartes turned his back upon history ? To him it
seemed that an explanation to be an explanation must at
least be intelligible. There can be truth and certainty, he
thought, only where there is clearness and distinctness.
Accordingly all these hidden principles and inexplicable
forms must be thrown aside as philosophical lumber, a
screen of ignorance and a source of confusion. In true
explanation there must be no obscurities, fancies, or

1 Francisco de Toledo (1532-1596), a Spanish cardinal and theo-
logian, author of Summa Casuum Conscientiae.

158 INTRODUCTION

guesses ; but it must consist in tracing the necessary
connexions of things or finding definitely measurable
relations between them — connexions and relations which
the understanding can clearly grasp. That is, in brief,
the mechanical view of what explanation ought to be,
as the Cartesians held it in opposition to the Scholastics.

Now Leibniz, as we have seen, is not so exclusively
enamoured of the clear and distinct as Descartes was.
He thinks Descartes has gone too far in the zeal of his
reformation. Doubtless the Scholastics were guilty of
gross absurdities, but if we are to be satisfied with no
explanation which is not absolutely perfect in its intelli-
gibility, we shall have to do without explanations of most
things, and our science will perforce be very abstract and
very limited. For to be perfectly intelligible or clear and
distinct in the Cartesian sense, an explanation must either
be a self-evident truth or must be logically reducible to
such a truth. And Leibniz maintains that, while ideas
or abstractions (' possible ' things) may be capable of such
explanation as this, it is impossible so thoroughly to
explain any actually existing finite thing or phenomenon.
We may ' clearly and distinctly ' explain how such a
thing is possible ; we cannot * clearly and distinctly '
explain why it exists. No absolute reason can be given
for its existence ; we must be content with a sufficient
reason. An examination of the measurable relations or
connexions of things does not yield an exhaustive account
of their nature, and accordingly, while such an exam-
ination is valuable so far as it goes, it requires to be
supplemented by other considerations. The infinite
complexity of things makes a perfect analysis impossible,
and consequently, if we confine ourselves to a strictly
mathematical method, our science must remain a science
of abstractions and not of actual things as they exist.

Leibniz, then, admits the value of the mechanical view
as regards phenomena, considered in abstraction from the
realities of which they are the phenomena, but he returns

ESTIMATE OF LEIBNIZ S PHILOSOPHY 159

to the older philosophy for an explanation of the realities
themselves. Descartes has done well in clearing away
the great mass of forms, which explained nothing, and in
accounting for all the changes in nature by regarding
them as due to variations in the distribution of one
constant quantity of motion. But motion is not a deep
enough principle to explain reality. It is entirely apparent,
phenomenal, on the surface ; and therefore it cannot
explain that which is half-hidden, which comes and goes,
which passes from potentiality into actuality. But this
is the characteristic of every real thing, every res completa.
In so far as it exists, and is not merely possible, it has
come into being ; it is its nature to pass from potentiality
to actuality. We cannot have a better example of this
than the human soul, in which we find continuous process
along with unity and self-identity. Thus it seems to
Leibniz that real things or substances are to be conceived
as analogous to the human soul, as forms or living prin-
ciples in a sense deeper than that of the later Scholastics,
who had, indeed, almost entirely emptied the term
' form ' of signification. Going back to the source of these
views that had so degenerated, Leibniz finds the nearest
approach to what he is seeking in Aristotle's ' entelechy, '
the principle of a thing in the sense of its implicit perfect
realization, what it is in the thing to be or become. Thus
Leibniz supplements the Cartesian physics by the idea
that mere body or matter is an abstraction, existing
nowhere, and that every real existence has a soul or living
principle. And in this way the Monadology restores to
philosophy, with new force and meaning, the infinite
number of forms which was the chief feature of the
Peripatetic philosophy.

Leibniz's relation to Atomist philosophy is for the most
part a negative one, and it is hardly necessary to add
anything to what has incidentally been said regarding it.
He is on the side of modern science in rejecting the idea
of an absolute vacuum. And when he sometimes speaks

l6o INTRODUCTION

of the Monads as atoms his object is probably to show
that the Monadology expresses clearly what the atomists
are groping for. His leading thought in this connexion
is that a real whole presupposes a real unit, that is to say,
a unit which is essentially connected with the whole,
representative of it, and not in a merely accidental or
indeterminate relation to it. The atomists are right, he
would say, in insisting upon a real unit, but, on their
view of reality, it is impossible to find any such unit \

Leibniz's ' Sufficient Reason ' in relation to the ' Cause '
of Descartes and Spinoza.

When we look, not at what Leibniz was himself aware
of doing but at what he actually did without clearly
knowing it, we may regard his use of the principle of
sufficient reason as a development of what was implied in
the use which Descartes and Spinoza made of the notion
of ' cause.' Descartes, as we have seen2, develops his
system under the guidance of the principle of contradiction
alone. But in order to pass from the subjectivity of the
pure Ego to an objective, external reality, he finds it
necessary to have recourse to the principle that everything
must have an efficient cause which is at least as real as the
effect (and may be more real than it). This principle he
assumes without any attempt to demonstrate its validity,
and it is the real basis of his proofs, in the first place, of
the existence of God, and in the second place, of the
existence of an external world 3. The proofs of the
existence of God form the keystone of Descartes's system.
Their function is to make up for the inevitable imper-
fections of a logic based solely on the principle of contra-
diction. Clinging, as he does, to the dualism of mind and

1 Cf. this Introduction, Part ii. pp. 27 sqq.
3 This Introduction, Part ii. pp. 58 sqq.

3 Cf. Meditation III and the mathematically arranged arguments
in the Reponses aux Deuxiemes Objections.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 1 6 1

matter, of thought and external existence, Descartes could
not rest satisfied with the idea of a most perfect being. He
must get beyond the idea to the reality ; he must justify
not one or another idea but thought itself. In the charac-
teristics of * clearness ' and * distinctness ' in ideas he had
found a criterion for the consistency of thought with itself.
A clear and distinct idea completely satisfied thought, but
it still remained to be shown that such an idea has
objective validity ; that there actually exists that which it
represents. Now according to Descartes, it is the truth-
fulness, the consistency, the goodness of an actually
existing God (who would not be perfect had He not these
qualities) that assure to us the validity of our clear and
distinct ideas. ' Even the principle,' says Descartes,
' which I have already taken for a rule, namely, that all
the things which we clearly and distinctly conceive are
true, is certain only because God is or exists, and because
He is a perfect Being, and because all that we possess is
derived from Him. ... If we did not know that all which
we possess of real and true proceeds from a perfect and
infinite Being, however clear and distinct our ideas might
be, we should have no ground on that account for the
assurance that they possessed the perfection of being true '.'
Accordingly, as regards real existence (apart from that of
the pure Ego), everything in Descartes's system ultimately
turns upon this unexplained principle of cause, by means
of which he proves the existence of God, and which he
again employs in establishing the reality of the world.
God must exist, for otherwise no adequate cause can be
assigned for the existence of the idea of God in us. And
again, we must postulate the real existence of external

1 Method, Part iv. (Veitch's Tr., p. 80). Cf. Meditation IV: 'It is
impossible that God should ever deceive me ; since in all fraud
and deceit one meets with some kind of imperfection ; and
although it may seem that to be able to deceive is a mark of clever-
ness or of power, the wish to deceive always indicates, without
a doubt, feebleness or malice ; and accordingly such a wish cannot
exist in God.' Cf. Hegel, Geschichte der Phil. iii. p. 319.

!

1 62 INTRODUCTION

things as the cause of certain ideas in us, unless we are to
suppose that God deceives us l.

Spinoza takes the one substance, God, as his starting-
point of absolute certainty, and accordingly proofs of the
existence of God have for him no meaning. Nevertheless,
he does not altogether dispense with the notion of cause.
Ostensibly he reduces the relation of cause and effect to
a logical connexion, like that between a geometrical figure
and its properties. But he makes use of the notion of
cause to introduce variety into the perfect unity of sub-
stance by describing it as cause of itself (causa sui). And
in his distinction between natura naturans and natura
naturata he endeavours, by a further application of the
notion of cause, to bridge the gulf which his logic has set
between the infinite (as purely indeterminate) and finite
or determinate existence. Natura naturans is substance
expressed in attributes or ' God as the free cause of all that
is.' Natura naturata is ' all that follows from the necessity
of the Divine nature or from any one of the attributes of
God, i. e. all modes of God's attributes, considered as
things which exist in God, and without God can neither
exist nor be conceived V In short, causa sui or substance
is analyzed into two moments, cause (natura naturans) and
effect (natura naturata) ; but both of these are ultimately
the same thing. Apart from this distinction without a
difference it would be impossible for Spinoza to identify
his infinite substance with the actual world. And yet,
in spite of it, for Spinoza the finite, as finite, remains
unreal.

Now this notion of cause, which Descartes and Spinoza
employ without attempting to explain or justify it, is, in
a more general form, acknowledged by Leibniz as an
independent logical principle, that of sufficient reason.
There must be, not merely an adequate cause but a
sufficient reason for the existence of each individual thing.

1 Cf. Meditation VI, passim.

9 Ethics, Part i. prop. 29, Scholium.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 163

And as we have seen *, the sufficiency of the reason rests
ultimately on the nature of God as perfect in wisdom,
goodness, and power. Manifestly there is here a working-
out of what is more vaguely implied in Descartes's
repeated references to the perfection of the character of
God as our warrant for the reality of things. And the
argument of Spinoza (however inconsistent it may be) is
based on the conviction that every finite thing must find
its place in the one all-embracing system, that is to say,
must follow from the nature of God in whom are all
perfections. Thus the addition of the principle of suffi-
cient reason to that of contradiction is not an entirely
novel suggestion on the part of Leibniz, but is an out-
growth of what was already involved in the reasonings of
his immediate predecessors. It is a step towards the
reconciling of their inconsistencies by bringing into clear
consciousness a principle which they blindly and imper-
fectly employed.

The Philosophy of Wolff.

The philosophy of Leibniz suffered grievously at the
hands of his immediate disciples 2. Probably this was
inevitable. Few of his writings were published in his
lifetime, and his philosophical opinions were dispersed
through masses of manuscript which might well be the
despair of his friends. And the philosophical system

J This Introduction, Part ii. p. 66.

2 'It has been with Leibniz as with several philosophers of
antiquity, who might have said : "May God preserve us from our
friends ; as for our enemies, we ourselves shall be able to protect
ourselves from them." ' Kant, Entdeckung nach der alle neue Kritik
der reinen Vernunft durch eine altere entbehrlich gemacht werden soil.
Rosenkranz, i. 478 ; Hartenstein, iii. 390. Cf. Wallace, Logic of
Hegel (snd ed.) ; Prolegomena, ch. 17. Kant himself in one of his
earlier writings (Traume ernes Geistersehers, &c. ; Rosenkranz, vii. 45 ;
Hartenstein, iii. 58) speaks of 'Leibniz's amusing idea, according
to which we might perhaps swallow in our coffee atoms destined
to become human souls.' And a naturalist of the end of last
century, Otto F. Muller, thought that he had discovered Monads
under the microscope !

M 2

164 INTRODUCTION

itself must have seemed as broken as was the expression
of it. The two principles of contradiction and sufficient
reason stood side by side, and there was no clear account
of the relation between them. A system with two
independent principles can have no stability, and this
defect must somehow be removed. On the other hand,
Newton had triumphed in the long controversy, and his
fame had led to Leibniz's discredit. Leibniz's metaphysics
seemed in some points incompatible with the Newtonian
physics, and must therefore to some extent be modified.
This systematizing and modifying of the philosophy of
Leibniz were accomplished by Christian Wolff (1679-
X754)? wno himself, however, strongly objected to being
called a mere disciple .of Leibniz, or an elaborator of the
Leibnitian philosophy.

Wolffs position may be regarded as in some respects
a return to the Cartesian attitude of mind. His solution
of the difficulty arising from the supposition of two co-
ordinate first principles is to make the principle of sufficient
reason a logical inference from that of contradiction, and
thus to make the law of contradiction the one supreme
law of thought. He holds that the difference between
'something' and 'nothing' is absolute, ' something' being
that of which there is some notion, while ' nothing ' is
that of which there is no notion 1. Thus everything must
have a sufficient reason, i. e. some reason why it exists
rather than does not «xist, for otherwise something would
proceed out of nothing. But ex nihilo nihil fit : there is
no middle term between ' something ' and * nothing V So
in Wolff the antithesis of being and not-being is supreme,
to the exclusion of the notion of becoming. ' The impos-
sible is nothing.' And on the other hand, 'the possible
is always something V It ought logically to follow that
everything possible is actual, and that there is no distinc-
tion between essence and existence. But at this point the

1 Oniologia, 57, 59. 2 Ibid. 70.

8 Ibid. 101, 102.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 165

Leibnitian influence reasserts itself, and Wolff becomes
confused. His ruthless logic gives way. * Besides the
possibility of a being, something else is still needed for
its existence.' * Existence or reality is the complement of
possibility1.' As an illustration of what he means he
takes the case of a tree which is potentially in the seed,
but which requires for its actual development (its exis-
tence as a tree) the co-operation or complement of other
existing things. Thus Wolff returns to the Leibnitian
distinction between the ' possible' and the 'compossible,'
after he has emptied of all meaning the principle of
sufficient reason, on which the distinction rests. To put
it otherwise, . if the actual existing ' something ' is more
than a merely possible ' something ' (as Wolff's position
here implies), then there must be a middle term between
the actual 'something' and 'nothing.' And this, of
course, is flatly contradictory of Wolff's original principle.
Thus while Wolff makes a show of logical completeness
and system, he is really hacking in pieces the philosophy
of Leibniz. He is fascinated by its individualist element,
the self-sufficiency and mutual exclusiveness of the Monads,
which we have seen to be connected, in the thinking of
Leibniz, with the survival of a narrow interpretation of
the principle of contradiction2. Wolff carries to an ex-
treme this tendency (which, after all, is not the supreme
power in Leibniz's thought), and gives us, as the outcome
of the bare principle of contradiction, an abstract indi-
vidualism, just as Spinoza had already from the same
principle developed an abstract universalism or pantheism.
It is because of the essentially dogmatic character of the
principle that such extremes can each be represented as
flowing from it. As employed by Spinoza and by Wolff
the principle can legitimately yield nothing but the bare
self-identity of the data or assumptions with which each
begins his work. Accordingly (as in this case) if the

1 Ontologia, 173, 174.

2 This Introduction, Part ii. p. 68.

1 66 INTRODUCTION

presuppositions are in complete opposition to one another,
we may have two contrary philosophical systems, both
apparently flowing from the same first principle.

Wolff, then, rejects the law of continuity and returns
to a position which has some analogy with that of
Descartes. Ostensibly his philosophy is a Monad ology ;
really it is a kind of combination of Monadology with
Atomism \ The Cartesian dualism is restored in the form
of a distinction between spiritual and physical Monads.
The spiritual Monads alone, in Wolff's opinion, deserve
the name of Monads. The others are ' elements of things,'
atomi naturae. These physical atoms or unconscious
Monads are no longer regarded as living mirrors, repre-
senting or perceiving the whole universe. They are still
automata, but they are no longer souls. They have
nothing in common with the spiritual Monads except the
characteristics of unity, simplicity, and activity. Thus
the whole of Leibniz's hypotheses regarding unconscious
thinking, petites perceptions, &c., are thrown aside, and we
have, in place of Descartes's two substances (thought and
extension \ two sets of independent particular substances,
the phenomena of the one set being thoughts and of the
other set motions. As an inevitable consequence of this,
the system of pre-established harmony, as Leibniz con-
ceived it, disappears also. Wolff retains the name, but
he regards the harmony not as a hypothesis by which to
explain the relations of each independent particular sub-
stance to eveiy other, but merely as an explanation of the
connexion between soul and body, between spiritual atoms
or Monads and corporeal atoms. According to Leibniz
there could be no real interaction between Monads. But
Wolff's * atoms of nature,' being1 purely physical, do
really influence one another. He sees no difficulty in

1 Cf. Schelling, SammtUche Werkffj vol. vi. p. 116 : 'As often
happens, the immediate successorsfof Leibniz set aside the really
speculative part of his doctrine, rthe Monadology. For example
the most celebrated of them, Wolff, admits it into his system only
in the guise of a hypothesis.'

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 167

holding that motion can be transferred from one to
another \ His difficulty is the original Cartesian problem —
How can a purely thinking substance influence an abso-
lutely non-thinking substance, or how can motion pass
into thought ? And the pre-established harmony is, in
Wolff's view, preferable to Occasionalism merely because
it means one large and comprehensive initial miracle
rather than an endless series of miraculous interventions
of God.

The natural, physical world is thus, according to Wolff,
entirely subject to mechanical laws. There is, indeed, a
realm of final causes, but the ends of things are com-
pletely external to the things themselves. The final cause
of a physical substance is not, as in the view of Leibniz,
to be found in the nature of the substance itself, in its
tendency towards self-realization, but in a law imposed
upon it from outside. Thus the Wolffian teleology
becomes almost childish, and suggests at times the naive
explanations of things which are to be found in such
writers as Bernardin de St. Pierre, who tells us that the
melon is made large in comparison with other fruits to
indicate that it ought to be eaten not in solitude but en
famille, and that the cow with only one calf has four teats
because the human race is fond of milk. Wolff hardly
rises to this height, but he regards the stars as existing to
give us light at night, and he points out that ' the light
of day is of great advantage to us ; it enables us to carry
on comfortably certain works which comparative darkness
would make impossible or difficult, and also more expen-

1 Here again Wolff's position is glaringly ineon'sistent. His
physical atoms or Monads are supposed to have a unity like that
of the Leibnitian Monads. Yet he denies to them that which, for
Leibniz, is the principle of this unity, viz. a soul differing not in
kind but in degree from the conscious and rational soul. The atomi
naturae are, in short, neither atoms nor Monads, but a contradictory
jumble of the characteristics of both. Wolff regards the atomi
naturae as 'in themselves indivisible,' and thus distinguishes them
from atomi materiales, which are l in themselves divisible,' but which
cannot be actually divided by any natural power. See Cosmologia,
§§ 182 sqq., 186 sqq. and 232.

l68 INTRODUCTION

sive V This doctrine of final causes is a most essential
part of the Wolffian system. For, according to Wolff,
although nature is ultimately explicable by purely
mechanical laws, we cannot actually reduce it to its
ultimate elements, and consequently, in explaining
physical phenomena as they are presented to us, we must
continually have recourse to final causes. So also, while
Wolff, adopting the phrase of Leibniz, speaks of God as
freely choosing to create ' the best of all possible worlds,'
he takes * best ' as meaning not • best on the whole,' but
rather 'best for mankind.' Thus the optimism of Wolff
is as shallow and arbitrary as his teleology, and it is not
surprising that Kant, even in the early years when he
followed Wolff on most points, deserted him in this
matter, and turned back to views more akin to the greater
thoughts of Leibniz.

Relation of the Philosophy of Leibniz to that of Kant.

In the earliest writings of Kant (who, through his
teacher Knutzen, was bred a Wolffian), questions regard-
ing space are discussed — questions, for instance, as to the
reason why our space has three dimensions and as to the
possibility and reality of other spaces having more than
three dimensions. Kant was evidently already some-
what dissatisfied with the current Wolman view of space
and was beginning the course of inquiry that ultimately
led to the doctrine of the Transcendental Aesthetic, a doc-
trine more in harmony with the view of Leibniz than
with that of Wolff2. According to Wolff, 'real' space
must be distinguished from ' imaginary ' space, although

1 Verniinftige Gedanken von den Absichten der naturlichen Dinge. Cf.
Ausfuhrliche Nachricht von seinen eigenen Schriften, §§ 186 sqq.

2 ' Leibniz's doctrine of sense as confused thought — confused in
such a way as to make us represent the world as an order of things
in space and time — though Kant explicitly rejects it, is in fact
rather elaborated than superseded by his doctrine of space and
time as forms of sensibility, under which alone experience is
possible, but which prevent what is true of phenomena from being
true of things in themselves, and knowledge from reaching the
totality which it seeks.' T. H. Green, Works, vol. iii. p. 135.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 169

the results obtained from consideration of the notion of
* imaginary ' space may justifiably be applied to ' real '
space '. 'Real' space is the order of co-existing things2
and is inseparable from the things themselves. God
alone can have a perfectly adequate notion of it and can
thus actually perceive its continuity. But we can form
an abstract or ' imaginary ' notion of space, by thinking
it as distinct from (or indifferent to) the co-existing things
of which it is an * order ' ; and this imaginary space is,
of course, homogeneous and continuous. The space of
mathematics and physics is thus t imaginary space ' ; but
it is such that the laws of mathematics and physics are
valid in relation to 'real' space. Manifestly we have here
neither the view of Leibniz nor that of Newton, but a
doctrine which points to a possible reconciliation between
them. On the one hand, space is not merely confused
perception. As space it has reality : it is a real order in
which physical things exist. But, on the other hand,
this real space is not the space of the mathematician.
He deals with a kind of projection or symbol of it, and
thus the Newtonian position also is without WoliF s
assent. It might easily be shown that the Wolffian
doctrine of space is riddled with inconsistencies, of a kind
similar to those which have been noticed in Wolff's
account of individual substances. But the matter of
main interest is that Kant received the problem of space
in the form which Wolff had given it 3, and that through-

1 Ontologia, 599.

2 In analogy with time which is 'the order of successive things
in a continuous series/ space is defined as 'the order of simul-
taneous things, in so far as they co-exist.' Ontologia, 589. Cf.
Qosmologia, 56.

3 Kant's criticism of Leibniz illustrates this. Cf. Fortschritte der
Metaphysik seit Leibniz und Wolff' (Bosenkranz, i. 516; Hartenstein,
iii. 441) : ' The principle of the identity of indiscernibles (princi-
pium identitatis indiscemibilium) is that, if from A and B, which, in
respect of all their internal characteristics (of quality and of
quantity) are entirely alike, we make a concept as of two different
things, we are in error, and we ought to have taken them for one
and the same thing (numero eadem). Leibniz could not admit that

J 70 INTRODUCTION

out the writings of his pre-critical period, we find Kant
working towards a view of space in which the Leibnitian
and Newtonian positions shall be reconciled. Although
he does not himself express it in this way, his problem
might fairly be regarded as that of finding a single Con-
ception of space which can take the place both of the
* real ' and of the * imaginary ' space of Wolff. In what
sense can space be regarded as at once real and ideal ?
Not in the Wolffian sense ; for that practically involves
a circulus in definiendo : i simultaneous or co-existing '
physical things presuppose space. Nor is the Newtonian
view more satisfactory-, for, while it recognizes that space
is prior to actual cases of spatial existence and while it
maintains the reality of space, it implies that the whole
universe is set in space and that the spatial system of
relations has a real existence independent of the things
related. Accordingly, through a course of thinking which
we need not here trace \ Kant arrives at the position which
he expounds in the Critique of Pure Reason, namely, that
space is a form presupposed in the possibility of our
sense-experience. It is not in any way given ab extra ;
but it is the condition of there being externality for us.
It is not a thing in itself, a real object ; but as it is a per-
fectly pure perception, free from all the contingent detail

we could still distinguish them through their places in space (as it
is possible to perceive quite similar and equal spaces outside of one
another without being able to say that they are one and the same
space, for otherwise we could put the whole of infinite space into
a cubic inch or less). Leibniz could not admit this, for he re-
cognizes no other distinction among things than that which is made
through notions [Begriffe], and refuses to allow any way of repre-
sentation specifically distinct from this, such as intuition [An-
schauung], and more especially intuition a priori. On the contrary
he thought that this must be reduced to pure notions [Begriffe] of
co-existence or succession, and thus he set himself against common
sense, which will never be persuaded that the existence of a drop
of water in one place makes it impossible for a perfectly similar
and equal drop to exist in another place.'

1 For a full account see Caird's Critical Philosophy of Kant, vol. i.
Introduction, ch. 5, especially pp. 164-168 and 178-182. Also
bk. i. ch. 2, pp. 304, 305. Cf. Hutchison Stirling, Text-Book to Kant,
PP- 34-43 and 366 sqq.

ESTIMATE OF LEIBNIZ S PHILOSOPHY 171

of sense, it satisfies the requirements of Newtonian
mathematics even better than if it were an independent
entity. On the other hand, while it belongs to perception
or direct intuition and is therefore not, as Leibniz and
WoMf held, a relation or order among things which are
prior to it, yet it is subjective or ideal, it belongs to our
minds, and accordingly the difficulties inseparable from
the Newtonian view of space (as expounded by Clarke,
for instance) are avoided.

.But mere sense-perception under the forms of space
and time is not, according to Kant, a complete experience.
It requires the complement of conception, which is the
function of the understanding. Here Kant believed him-
self to be in complete opposition to Leibniz, and yet it
may well be doubted whether the opposition is really so
great as Kant supposed it to be. In the Critique of Pure
Reason Kant does draw a much sharper line between per-
ception and conception than Leibniz did. Kant may be
said to regard the difference as one of kind, while for
Leibniz it is a difference of degree. Leibniz, as we have
seen, gave to perception an exceedingly wide meaning,
a meaning which includes conception and representation
of every kind, whether conscious or unconscious. But
Kant's l perception ' is limited to sense-representation.
Nevertheless Kant's t perception ' is avowedly abstract,
and the confused perception, which is Leibniz's name for
sense-knowledge, is abstract also, though in a somewhat
different way. In fact, for Kant the distinction between
perception and conception is a distinction between abstract
elements in a concrete whole of experience, while the
corresponding distinction in Leibniz is a distinction be-
tween degrees of perfection in one quality or function.
Thus for Kant sense-perception is abstract, because its
reality always implies a complementary element, while
for Leibniz it is abstract because it is imperfectly deve-
loped, because it contains the potentiality of greater
perfection. The weakness of the Kantian position is its

172 INTRODUCTION

tendency to over-sharpen the distinction between percep-
tion and conception by ignoring the idea of development,
while the defect of Leibniz is his inclination to define the
common quality or function ('perception') by its lowest
rather than its highest terms, to interpret it, not as essen-
tially self-consciousness, which is its most perfect develop-
ment, but as mere representation or multiplicity in unity,
to which consciousness and self-consciousness are added
characteristics ]. Yet while Kant makes an advance from
the position of Leibniz, they are on similar lines, and we
can read their reconciliation in Hegel 2.

Leibniz does not give any clear account of the relations
between the principle of contradiction and that of suffi-
cient reason, as he uses them in his philosophy ; but it is
evident that he considered them to be, in some way,
ultimately in harmony. The tendency of Kant, on the
other hand, is to emphasize the distinction between them,
while treating each, apart from the other, as abstract.
The course of Kant's pre-critical thinking makes this clear.
He begins with the Wolffian view that the principle of
sufficient reason is reducible to that of contradiction 3, and
accordingly, that the principle of contradiction is the sole
ultimate principle of knowledge. But gradually he comes
to see that the principle of contradiction has to do with
nothing but the form of thought and that it yields merely
a self-consistent system of knowledge, based on dogmatic

1 In this, I think, there is to be found the explanation of the
separation (almost amounting to a distinction of kind) between
rational souls and the other Monads, which Leibniz makes with
such apparent inconsistency. Cf. this Introduction, Part iii.p. 116.

2 ' The doctrines of Leibniz formed the permanent atmosphere
of Kant's mind. His reading of Hume in middle life no doubt
helped to determine the mode in which he absorbed and trans-
formed them ; but it was upon them, as we find in the Critique no
less than in his earlier writings, that his mind constantly worked,
and there would be a better case, at any rate, for describing him
as a corrected and developed Leibniz than for putting him in such
a relation to any one else/ T. H. Green, Works, vol. iii. p. 134.

3 Cf. Principiorum primorum cognitionis metaphysicae nova dilucidatio
(T755) (Rosenkranz, i. 4; Hartenstein, iii. 4).

ESTIMATE OF LEIBNIZ S PHILOSOPHY 173

presuppositions. It ensures order and necessary con-
nexion in thought, but it is inadequate to reality. It
gives the logical ground of things (logisclie G-rund) but
not the ground of their reality (Eeal-grund) \ Thus the
principle of contradiction is insufficient when treated as
the ultimate principle of metaphysics. Kant develops
this position in connexion with the problem of proving
the existence of God. He rejects, as a begging of the
question, the Cartesian demonstration which maintains
that existence is necessarily involved in the perfection of
the most perfect Being. Existence, Kant says, cannot be
a predicate. That is to say, you cannot take out of any
subject more than is contained in it ; the principle of
contradiction will never entitle you to pass from any
mere idea to the reality of that idea. Pure thought,
determined by the principle of contradiction, always
presupposes something 'given,' and thus reality must
ultimately lie outside of pure thought. Thus, for example,
the real cause of anything is always more than a mere
reason : a causal connexion is not a merely logical con-
nexion. It is this line of thinking that leads Kant to
emphasize the distinction between logical understanding
and empirical sense, and to lay stress on l experience ' (un-
rationalized and unexplained) as the ground of reality,
in a way that recalls the position of Locke. Thus, while
admitting the certainty of mathematics, Kant protests
against the use of a purely mathematical method in deal-
ing with metaphysics or with the theory of knowledge,
on the ground that such a method is ' merely synthetic, '
that is to say, on the ground that it does not analyze
actual experience but deduces from (or builds upon) arbi-

1 Cf. Der einzig mogliche Beweisgrund zu einer Demonstration des
Daseins Gottes (1763) (Rosenkranz, i. 161 ; Hartenstein, vi. n). Kant
makes advances towards this position in the Essay on Die falsche
Spitsfindigkeit der vier syllogistischen Figuren (1762) (Rosenkranz, i. 55 ;
Hartenstein, i. i), and in the Versuch den Begriff der negatiren Grossen
in die Weltweisheit einzufuhren (1763) (Rosenkranz, i. 113; Harten-
stein, i. 19).

174 INTRODUCTION

trary or at least mind-made presuppositions \ Finally in
the Critique of Pure Reason we have Kant's solution of the
problem as to the relations between a priori and a posteriori,
thought and experience. And his contention is that the
a priori is not merely that which is self-evident and can
be expressed in an analytic judgment, but that which
experience universally and necessarily involves as the
condition of its possibility.

This, after all, is but the working out of what is out-
lined by Leibniz, when he insists on l compossibility, ' or
necessity arising from the system of things, as the ground
of reality. For Leibniz the real is the 'fitting,' that
which has its place in the best possible system or world :
for Kant the real is that which is in an orderly experience
constituted by principles which are the logical a priori
conditions of its possibility. In the philosophy of Kant,
accordingly, we have a more thorough application of the
principle of sufficient reason, which Leibniz had imper-
fectly applied. Leibniz's explanation of the existence of
the actual system of things as the result of a choice among
all possible worlds is due to the inconsistency in his posi-
tion which comes from working with two co-ordinate first
principles. The totality of possible worlds is at once a
system and not a system. If it were a system, the choice
by God of the best possible world would be determined
by the nature of the whole system of possibles. The best
possible world would be the best world in that system,
and thus the problem of Leibniz would not be solved by
the * choice/ but would merely be carried a stage farther
back. On the other hand, if the totality of possible
worlds were not a system, the choice of God would prac-
tically be arbitrary : at least it would be grounded on no

1 Of. Untersuchung uber die Deutlichkeit der Grundsdtze der naturlichen
Thcologie und der Moral (1764^ (Rosenkranz, i. 75 ; Hartenstein, i. 63).
See also Kant's Inaugural Thesis on becoming Professor in Konigs-
berg, De mundi sensililis atque intelligibilis forma et principiis (1770), in
which the distinction between sense and understanding is brought
to the sharpest point. (Rosenkranz, i. 301 ; Hartenstein, iii. 123.)

ESTIMATE OF LEIBNIZ S PHILOSOPHY 175

reason intelligible to us. God would choose the best
possible world ; but it would be the best possible for no
other reason than that He chose it. Thus the totality of
possible ideal worlds has the appearance of being a system,
while really it is not. It is this ambiguity that conceals
the fundamental inconsistency of Leibniz — the incon-
sistency of regarding God as both within the system of
things and quite outside of it (as the Creator), making
Him at once the source of the whole system of mutually
exclusive Monads and the highest Monad of the series,
without whom the system would itself be incomplete.
The principle of sufficient reason, rightly understood, in-
volves the supposition of one all-embracing system ; but
•though Leibniz had certainly an inkling of the truth
of this, his individualistic tendency and his dread of
Spinozism prevented him from fully realizing it.

For Kant there is but one system of experience, that
which actually exists. The supposition of a choice among
possible worlds is no part of his philosophy. But in
Kant's doctrine the t thing-in-itself ' performs very much
the same function as did the ' choice ' in Leibniz's scheme
of things. Each is a way of allowing for a possible reality
other than the actual system, although the need of this
arises from one cause in Leibniz, and from another in
Kant. Leibniz wishes to avoid a doctrine of blind neces-
sity : Kant is afraid of a pure relativity. They both feel
that the ultimate ground of the system of mutually related
things must be sought in some principle outside the
system itself l. The dogmatism of Leibniz appears in his

1 Cf. Critique of Pure Reason, Eosenkranz, ii. 524 ; Hartensteiii,
ii. 513 (Meiklejohn's Tr., p. 414) : 'The notions of reality, of sub-
stance, of causality, of necessary existence itself, have no signifi-
cance in determining any object, beyond their use in making
possible the empirical cognition of a thing. They may thus be
used to explain the possibility of things in the world of sense, but
they cannot be used to explain the possibility of the unicerse itself;
since in this case the ground of explanation must lie outside the
world, and can therefore be no object of a possible experience.
Now, relatively to the world of sense, I may admit such an incom-
prehensible being, the object of a mere idea ; though I may not

176 INTRODUCTION

making this principle a real and independent 'constitutive '
ground of the world, and he glosses over the difficulty of
explaining its relation to the world by metaphors such as
the ' Divine choice ' and the producing of created Monads
by continual * fulgurations of Divinity/ The criticism of
Kant, on the other hand, leads him to interpret this
ultimate principle negatively, as a merely 'regulative'
idea, of the absolute nature of which the speculative
reason can say nothing. Its reality, however, is assured
to us by the practical reason, and in it we must suppose
that there is a reconciliation of necessity and freedom,
of the kingdom of nature and the kingdom of grace, of
mechanism and teleology. We cannot give a completely
satisfactory account of the phenomenal world as a system
governed by final causes, for we have no speculative
knowledge of the ultimate intelligence and the ends it
sets before itself. We may guess at final causes ; but
we cannot understand their producing anything, apart
from mechanical causes. And on the other hand, while
we cannot help regarding the phenomenal world as a
mechanical system, * absolutely no human reason (in fact
no finite reason like ours in quality, however much it
may surpass it in degree) can hope to understand the
production of even a blade of grass by mere mechanical
causes1.' We must, in certain cases, postulate adaptation
to ends. But we can quite conceive an intelligence which
can think the world, not discursively from part to part as
we do, but immediately and completely, from whole to
part, and for such an intelligence, final and efficient
cause, freedom and necessity, would be harmonized.
For it to know and to create the world would be the

admit its existence in itself. ... It is only a something in general
which I know not in itself, but to which, as a ground of systematic
unity in cognition, I attribute characteristics analogous to the
notions of the understanding in the empirical sphere.'

1 Kant, Critique of Judgment, Part ii. div. ii. § 77 (Rosenkranz, iv.
301 ; Hartenstein, vii. 288 ; Bernard's Tr., p. 326). See the whole
passage.

ESTIMATE OF LEIBNIZ S PHILOSOPHY 177

same thing : creation would be its thought. Thus Leib-
niz and Kant are at one in placing the ultimate synthesis
of things, the sufficient reason of experience, in some-
thing that is beyond experience itself, and that is related
to experience in a way which stands in need of further
explanation. Leibniz, however, falls into a contradiction
which Kant avoids. For Leibniz regards God as at once
the highest of the Monads (the ultimate term in the
series) and the Creator of the Monads, i. e. the sufficient
reason of the world which they constitute. But if God
is one of the series of Monads, it seems impossible to
regard Him as their sufficient reason, as choosing to
create the system of which He is an element. And on
the other hand, if the essence of the Monads is to repre-
sent the universe, and if He factuspurus) perfectly realizes
the universe within Himself, having perfectly clear and
distinct perception, what place is there for a system of
Monads apart from Him ? Kant avoids the difficulty by
the sharp distinction he draws between experience and
the thing-in-itself. He can thus regard God as related
to the world in a way which we may attempt to describe
as causal, creative, or otherwise, but which it is impossible
for us ever with certainty to define \ In short, so far as
our theoretical knowledge of things is concerned, the
account we give of the relation of God to the world is
simply a useful hypottiesis, by means of which we may
give unity to our knowledge, and avoid the fallacies of

1 Cf. Critique of Pure Eeason (Hartenstein, ii. 508 sqq. ; Rosenkranz,
ii. 519 sqq.), Meiklejohn, pp. 410 sqq.: 'The notion of a supreme
intelligence is a mere idea, that is to say, its objective reality does
not consist in its being immediately referable to an object (for
in this sense we cannot establish its objective validity) but it is
merely a schema of the notion of a thing in general, a schema
constructed according to the conditions of the greatest unity of
reason, and serving only to produce the greatest systematic unity
in the empirical use of our reason, inasmuch as we deduce this or
that object of experience from the imagined object of this idea as
the ground or cause of the object of experience.' Cf. also Rosen-
kranz, ii. 598 ; Hartenstein, ii. 581 ; Meiklejohn, p. 471.

N

178 INTRODUCTION

dogmatism1. Yet, while Kant thus escapes the contra-
diction in Leibniz's view, he cannot be said to give us
a satisfactory solution of the difficulty2.

The Influence of Leibniz on Fichte.

In the modern idealism which first took shape in the
writings of Fichte, there may be traced the influence of
certain leading ideas in the philosophy of Leibniz, to
which Kant had inevitably done less than justice. The
work of Fichte is generally regarded as an endeavour to
give systematic unity to the philosophy of Kant by get-
ting rid of the thing-in-itself, regarded as entirely outside
of experience. Indeed, until Kant repudiated his inter-
pretation, Fichte regarded himself as an expositor of the
true Kantian view, and a defender of the critical philo-
sophy against the misunderstandings of its unintelligent
disciples, Fichte's main idea is that experience (in the
Kantian sense) has its basis in a self-consciousness (an
Ich-heit) which is itself the root of the distinction between
the empirical ego and the empirical non-ego, between
subject and object. Both subject and object are logically
involved in the original self-consciousness, out of which
all experience, both in its matter and in its form, may
be deduced. Thus all reference to a reality beyond
experience becomes unmeaning as well as unnecessary.
The unity of the universe is maintained with pantheistic

1 D. Nolen (La Critique de Kant et la Metaphysique de Leibniz, pp. 331
et sqq.) regards the Monadology as a necessary complement to the
' Criticism ' of Kant. It seems to him that the * thing-in-itself has,
in the philosophy of Kant, a function similar to that of the
1 possible thing ' or ' essence ' in the system of Leibniz. An
ingenious attempt has also been make by Otto Riedel (Die Monado-
logischen Bestimmungen in Kants Lehre vom Ding an sicti) to show that
the things-in-themselves, in so far as they are conceived as positive,
have the characteristics of Monads. There is a hint of the same
view in Ueberweg's Commentary on the two editions of the Critique
of Pure Reason.

2 For Kant's account of his own relation to Leibniz see Appendix
E, p. 208.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 179

completeness ; and the system of Fichte has well been
described as t Spinoza in terms of Kant V

Now the need of a thing-in-itself, such as Kant postu-
lates, arises from the thoroughness of his separation
between perception and conception, between sense and
understanding. They are correlative ; yet they are treated
by him as if quite independent, so that the result of
their combination is a merely phenomenal world. Per-
ception cannot evolve from itself the forms of the under-
standing, through which alone it loses its blindness ; and
conception cannot produce for itself the matter of sense
and experience, without which it is empty. But this
dualism indicates, in a negative way, the necessity of a
noumenal world, however completely such a world may
be beyond the reach of our intellectual comprehension
or proof. It is in revulsion from dogmatism that Kant
holds this position. And thus he is continually pointing
out that the great error of Leibniz is that of regarding
experience as a system of concepts, which may constitute
an internally self-consistent whole, but which has no cer-
tain contact with reality. Such a dogmatism, Kant holds,
has no answer to scepticism, and thus to give up the
sharp distinction between perception and conception is
to lose our grasp of reality and truth.

Accordingly it is not surprising to find that, in setting
aside the thing-in-itself (as Kant understood it), Fichte
goes back to the doctrine of Leibniz and proceeds to
develop, under new conditions, some of its leading ideas2.

1 Adamson's Fichte (Blackwood's Philosophical Classics), p. 130.

2 ' The time is come for reviving the philosophy of Leibniz. . . .
Nothing is further removed from the thought of Leibniz than the
speculative dream of a world, of things-in-themselves, which no
mind comprehends or knows, but which nevertheless acts upon us
and produces all our ideas. The first of his thoughts, that which
he makes his starting-point, is, that the representations of external
things arise in the soul in virtue of its own laws, as in an isolated
world, and as if nothing were present in it except God (the Infinite)
and the soul (consciousness of the Infinite). ... In thus expressing
himself Leibniz spoke for philosophers. But now-a-days people
will insist on philosophizing, even when philosophy is the last

K 2

l8o INTRODUCTION

Leibniz, in antagonism to the dualist position of Descartes,
does not lay stress on the distinction of subject and object,
but conceives the universe as an infinity of subjects, each
self-sufficient and 'in the sea of life enisled.' For Kant,
the distinction of subject and object is all in all. Fichte
still gives full weight to the distinction, but conceives it
as overcome in the unity of self-consciousness, or rather
as flowing necessarily from that unity in its most abstract
and indefinite form, and being lost in that unity in its
highest and most perfect form. Thus, according to
Leibniz, the whole succession of a Monad's states,' all its
perceptions of the universe, proceed spontaneously from
within itself, t as if there were only God and itself in the
world l ' ; and every created Monad contains within itself
both matter and form, which are in reality degrees of
one power or function. Similarly, the ego of Fichte, the
primal self-consciousness, is a perfectly spontaneous force,
producing from within itself the empirical ego and non-
ego, subject and object, making its own external world,
projecting that world through the power of imagination,
and continually striving towards the ultimate overcoming
of this distinction between outer and inner in a pure
* intellectual intuition.' Accordingly Fichte throws down
the barriers which Kant had raised between perception
and conception, and returns to the position of Leibniz
that all knowledge is one great process of development,
though, of course, he gives a very different account of
this development from that which we find in Leibniz2.

thing they are fitted for. If anyone tells us that no idea [Vor-
stellung] can arise in us from an external action, there is endless
astonishment. To be a philosopher one must believe that the
Monads have windows, through which things come and go.'
(Schelling, Sammtliche Werke, vol. i. do. Ideen zu einer Philosophic der
Natur, commended by Fichte, Werke, i. 515 note.)

1 Lettre a Foucher (1686), (G. i. 382). Cf. New System. § 14.

3 ' The final notion of Fichte' s philosophy, expressed more clearly
in the later works than in the Wissenschaftslehre, is that of the
divine or spiritual order of which finite spirits are the manifestation
or realization, and in the light of which human life and its
surroundings appear as the continuous progress in ever higher
stages towards realization of the final end of reason. Under this

ESTIMATE OF LEIBNIZ'S PHILOSOPHY l8l

The reality of the world of sense is for Fichte a result of
the activity of imagination. Our mind creates our sensa-
tions ; but it creates them unconsciously, and thus our
imagination attributes them to things outside of us,
objectifies them. Yet imagination does not give us mere
illusions, but truths more or less perfectly expressed. * If
it be shown, as the present system should show, that
upon this activity of imagination rests the possibility of
our consciousness, our life, our being for ourselves, that
is to say, our being as ego [unseres Seyn als Jcfc], this
activity of imagination cannot cease, unless we are to
make abstraction from our ego, which would involve a
contradiction, since that which makes abstraction cannot
make abstraction from itself. This activity of imagina-
tion, then, does not deceive us, but gives us truth, the
only possible truth \ ' There are, as it were, two sides
to our knowledge of things. In so far as it is sensation
(that is to say, an idea unconsciously created by the mind)
it is a product of the non-ego, the object ; while in so far
as it is an idea consciously ' projected ' by us or referred
to something, it is a product of the ego, the subject.
But the action of ego and non-ego is reciprocal, and they
both have their source in the original self-consciousness
from which they necessarily proceed2.

It is, of course, beyond the scope of our intention
to consider the many essential differences between the
systems of Leibniz and of Fichte : to have indicated their
connexion is sufficient. And the words of Schelling may

conception, the oppositions of thought which play so important
a part in philosophy — being and thought, mind and nature, soul
and body, freedom and law, natural inclination and moral effort,
mechanism and teleology — are reconciled. They appear in their
due place as different aspects of the several stages in and through
which the spiritual order is realized.' Adamson, Fichte, pp. 219,
220.

1 Fichte, SammtUche Werke, i. 227.

3 'The ego, as understood in common unscientific language,
posits neither the external object nor itself, but both are posited
through general and absolute thinking, and through this the
object is given for the ego, as well as the ego for itself.' Fichte,
Werke, ii. 562.

I

1 82 INTRODUCTION

be taken as showing that this connexion was from the
first fully realized. 'Since Leibniz/ he says, 'if we set
aside secondary doctrines which do not count, we see
that the real, the finite, is generally placed in the region
of the ideal. The whole real world has no existence in
itself, but only in the representations \_Vorstellungen] of the
soul. . . . Fichte takes up this idealism which is a denial
of the independent being of the real, and, in this regard,
he does not go beyond Leibniz. The only difference
between them is this. Leibniz cannot explain why the
soul or the Monad is subject to affections which produce
in it finite representations ; or, if he tries to find the cause
of this, he is obliged to place it in God, in the Infinite,
which involves him in inevitable contradictions. Fichte,
on the other hand, finds that the finite nature of the soul
has its explanation in the absolutely free activity of the
soul itself and results from this, that the soul by its own
act posits itself for itself as finite, as separated from the
absolute all, and consequently imposes on itself the ne-
cessity of contemplating no longer this absolute all, but
only the negations, limitations, bounds of its infinity V
Accordingly it may be said generally that in the philo-
sophy of Leibniz will and intelligence (appetition and
perception) are co-ordinate principles of things (the will
of God, for instance, not being prior to His understand-
ing nor His understanding to His will), while the
philosophy of Fichte is essentially a practical idealism,
in which will (in however undefined a form) is ultimate
and predominant. The ' principle of the best ' (the ten-
dency to realize the moral order which is the expression
of the infinite good will) is with Leibniz the determining
principle of actual, as distinct from merely possible
existence, while with Fichte it is the ultimate ground
of all reality, of the one system of things2.

1 Schelling, Propaedeutik zur neueren Philosophic. Werke, vol i.
p. 125.

2 An excellent account of Fichte's historical position is given in

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 183

Schopenhauer.

As regards the main principles of his philosophy,
Schopenhauer (however unconsciously) follows Fichte1.
His starting-point is the Kantian distinction between the
intelligible or noumenal and the empirical or phenomenal
character of a real subject2. As in the philosophy of
Fichte, the ultimate reality is will. The l intelligible
character' is a will, which is the source of the 'empirical
character ' ; and in general will is a pure activity which
is the source of the system of phenomena. Thus the
world is will + idea (i. e. Vorstellung, representation, phe-
nomenon). The absolute is the purely practical activity
of will, which gives rise to the relative or mutually
conditioned, in a way which is beyond explanation,
for our understanding cannot pass the limits of the
conditioned, the phenomenal world. But this ultimate
will is essentially destitute of anything that can fairly
be described as ethical character. The world is not a
progress towards the realization of the best, but rather
an unfortunate episode' in the existence of the eternal
will, and the highest good is to be attained not by allow-
ing this will or striving (will to live) to have free course
in us, but by suppressing it as much as possible. The
expression, 'the world as will and idea,' recalls the
Leibnitian view of substance as essentially appetition 4-
perception. But Schopenhauer, like Fichte, gives to
will a metaphysical priority, which is not attributed

Wallace's Logic of Hegel, Prolegomena (and ed.), ch. n. See also
chs. 12 and 13 for an account of Schelling with suggestive references
to Leibniz. In ch. 13 there is a lucid explanation of the various
meanings of the term ' Evolution,' as it is used by Leibniz and by
later writers. Cf. vol. ii. p. 424.

1 ' Except his pessimism, which is no necessary consequence of
the system, there is absolutely nothing in Schopenhauer's philo-
sophy which is not contained in the later works of Fichte.'
Adamson, Fichte, p. 219. Though this is the statement of an expert,
I venture to think it a little too sweeping.

2 Critique of Pure Reason, Rosenkranz, ii. 422 ; Hartenstein, ii. 420 ;
Meiklejohn, p. 333.

184 INTRODUCTION

to it by Leibniz. Again, Schopenhauer, reducing the cate-
gories of Kant to causality ( interpreted in a wide sense),
gives great importance to the principle of sufficient reason
which (in one or other of four different forms) he regards
as the governing principle of the phenomenal world.
'All our ideas \_VorsteUungen] stand to one another in a
regular [gesetzmassig} connexion, which as to its form is
determiiiable a priori, and on account of which nothing
self-sufficient and independent, nothing separate and de-
tached, can become an object for us. It is this connexion
which the principle of sufficient reason, in its univer-
sality, expresses1.' The principle of contradiction is
ostensibly subordinated to that of sufficient reason, it
being regarded as one of the general laws of thinking,
discovered by induction and used as a judgment 'meta-
logically true,' which may be the ground or sufficient
reason of other judgments2. But here there is clearly
an inconsistency between Schopenhauer's logical theory
and his metaphysic. His absolute, the ultimate will, is
(however far he may be from acknowledging it) really
determined by the principle of contradiction, in its
abstract form, for the will is conceived as that which
absolutely is, that which is apart from all relation, that
which may, in some mysterious way, produce a system
of differences, but which has an identity that is perfectly
independent of them. Accordingly, while Schopenhauer
indicates the deeper and more comprehensive interpreta-
tion of the principle of sufficient reason as underlying
that of contradiction, he does not allow it to mould his
system.

Herbart.

Another thinker who owes something to Leibniz and
something more to Kant and to Fichte, is Herbart (1776-
1841). He is not content to subordinate the principle of

1 Ueber die vierfache Wurzel des Satees vom zureichenden Grunde, ch. 3,
§ 16..

2 Cp. Ueber die vierfache Wurzel, &c., ch. 5, § 33.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 185

sufficient reason to that of contradiction, but he practically
endeavours to do without the former principle as far as
possible. The task of philosophy he regards as that of
eliminating the contradictions that appear in common
consciousness by transforming the ideas which are given
in it *. This transformation, for Herbart, practically
means abstraction. Every bit of experience, being given,
has something real in it 2. But its reality is that which
it is, apart from conditions or relations to other things.
The real is always something, a quale, a ' this ' or ' that '
of some kind. But it is absolute position (in the Fichtean
sense) or affirmation without negation ; it has absolute
self-identity, so that it is perfectly simple and not, like
the Monad of Leibniz, a substance involving in its unity
a plurality of qualities ; and it is pure quality, without
any quantitative element or aspect, so that it is neither
a divisible totality nor an unbroken continuum. These
* reals, ' like the Monads, are infinite in number, and each
is different from every other. But they are absolutely
unalterable, they have no characteristic analogous to the
perception of Leibniz, and they are not impenetrable, for
any number of them may equally be thought as occupying
or as not occupying the same point in space. Like the
Monads, no one ' real ' can act upon another ; otherwise
they would cease to be absolute. And each ' real ' is the
immediate cause of one and only one phenomenon of
experience, so that the static variety of the world is due to
the power of 'self-preservation' (SeWsterhaltung) in each
' real. ' The actual changes which we find in experience
are due to the different aspects in which the ' reals ' appear,
when they are in different relations to one another,
although their true natures remain unchanged (as in the
phenomena of colour contrasts). And these 'different

1 ' Mere uncritical experience or merely empirical knowledge
only offers problems ; it suggests gaps, which indeed further re-
flexion serves at first only to deepen into contradictions.' Wallace,
Hegel's Philosophy of Mind, p. Ixiii.

2 * Wieviel Schein, soviel Hindeutung auf s Sein.'

l86 INTRODUCTION

relations of the ' reals ' to one another are, again, due to
the possibility of conceiving the ' reals ' as both together
in one point and apart from one another. Accordingly
the soul, being a ' real/ must not be represented as having
in itself powers, faculties, qualities, &c. It is absolutely
simple, and has nothing but * self-preservation,' which
apparently is little more than a permanent possibility of
relation to other 'reals.' None of the functions and
characteristics of mind belong to it intrinsically. They
are to be ascribed to other things, quite as much as
to the mind or soul itself. They are merely names
for the phenomena or aspects of certain ; reals ' (one of
which is the soul) in certain relations to one another.
These phenomenal (of course, not real) interactions of
the ' reals ' admit of mathematical calculation, and
accordingly Herbart is the father of those who apply
mathematical methods in empirical psychology1. This
is natural in one whose thought is so completely
dominated by the abstract use of the principle of contra-
diction. And, in short, if we leave out of account the
influence of Fichte upon his psychology, we may regard
Herbart's work as a remodelling of that of Leibniz, on the
supposition that the principle of sufficient reason is to be
dropped.

Hegel's Solution of the Dualism in Leibniz.

In the philosophy of Hegel we have a solution of the
dualism between the principle of contradiction and that
of sufficient reason, as they are used and conceived by
Leibniz. The problem indicated by this dualism under-
lies the whole course of German speculation from the
time of Leibniz onwards. Wolff, in a negative way, gave

1 His application of mathematical methods, however, differs
entirely from that which occurs in the psycho-physics of the
Fechner School, and in modern physiological psychology. For
a full explanation, see Wallace, Hegel's Philosophy of Mind, pp. Ixviii
sqq. It may also be noted that Leibniz's theories regarding un-
conscious and petites perceptions are developed and applied in the
psychology of Herbart.

ESTIMATE OF LEIBNIZ^ PHILOSOPHY 187

precision to the problem by suggesting the most superficial
possible solution, reducing the principle of sufficient
reason to that of contradiction. This (though Wolff
perhaps did not realize it) was little better than telling
Leibniz that he had discovered a mare's nest. Kant, on
the other hand, gives positive precision to the problem by
the sharpness of his distinction between the absolute and
the relative, while Fichte and Schelling, in different ways,
endeavour to make explicit the unity to which the Kantian
divisions point. Their re-employment of the principle of
development or progressive self-realization, which is so
important a feature of Leibniz's thinking, brings us to the
verge of Hegel's solution of the problem. Hegel practi-
cally reverses the procedure of Wolff, by showing that the
principle of contradiction presupposes that of sufficient
reason, and that each by itself is an abstract expression
of the principle of self-consciousness1. The real is not
merely in se (as it would be if the abstract principle of
contradiction were ultimate), nor is it merely in alio (as it
would be if the abstract principle of sufficient reason were
ultimate, which, of course, no one maintains). But the
real is that which becomes itself through being in alio,
through being not itself. There is no such thing as a
purely analytic or a purely synthetic judgment ; but
when we attribute any quality to a subject, we attribute
to it not merely a difference from other things but a
oneness with that from which we differentiate it 2. The
universe is a system of such perfect unity that the oppo-
sites it contains are all contraries and never contradictories.
Absolute contradictories or absolute differences are ab-
stractions. To say, as did Leibniz, that no two things are
exactly the same implies that no two things (not even the
most extreme opposites) are entirely different. A must

1 See Caird's Hegel (Blackwood's Philosophical Classics), chs. 7
and 8. Also Wallace, Prolegomena to the Logic of Hegel (and ed.),
ch. 30.

2 Cf. Caird, Critical Philosophy of Kant, vol. ii. pp. 64 sqq.

1 88 INTRODUCTION

have something in common with not-A, if their opposition
is to have any meaning. l The other stands over against
its other1.' That is to say, their difference must have
some ground, some underlying unity. And on the other
hand, every identity, even the identity of a thing with
itself, implies some difference. There is no pure ground,
no absolute first principle, independent of a sufficient
reason. Hegel regards the universe as itself one absolute
system. The world we know is the only world, and it
is not a merely phenomenal system, the expression of
something heterogeneous with it (like the arc electric
light between two opposite points of carbon , nor is it an
inexplicable product of something other than itself, such
as an unconditioned will, nor yet is it the production of
some noumenal absolute. It hangs upon nothing ; it
needs nothing to hang upon. The universe is one system
of endless mutual determinations, yet not a merely static
system nor a system of cyclical revolutions, endlessly
repeated, which would involve the supposition of an
external absolute as the source or support of all. It is
rather an evolution of that whose end is in its beginning,
that whose development is free, because, being all-com-
prehensive, it is perfectly self-determined.

Thus Hegel points out that 'it is the notion which
Leibniz had in his eye when he spoke of sufficient ground
and urged the study of things under its point of view.' By
the notion Hegel means ' a content objectively and intrin-
sically determined and hence self-acting.' This would
sufficiently describe the Monad of Leibniz if we keep out
of view the Monad's absolute particularity, its isolation as
one of an infinite series of independent units, or, in other
words, if we omit from the conception of the Monad all
that is due to the principle of contradiction, interpreted
abstractly as a principle of pure or immediate self-identity.
This isolation, of course, is an essential element in

1 Hegel, Logic, § 119 (Wallace's Tr., and ed., p. 222). See the
whole passage, and also pp. 224 sqq.

ESTIMATE OF LEIBNIZ'S PHILOSOPHY 189

Loibniz's conception of the Monad, and the result is that
while his speculation points to a view of the universe as
one system in which the elements are intrinsically and
not externally combined, he does not go far enough to
secure this metaphysical position, just as he does not
push his logical analysis far enough to reconcile the
principles of contradiction and sufficient reason. The
Hegelian l notion ' is thus the completion of what is
vaguely shadowed forth in the Monad of Leibniz, and
more especially in the Monas Monadum, in which all is
(however unsatisfactorily) brought to unity. For the
notion implicitly contains all in itself, and all is realized
through its logical (not temporal) development. Like
the Monad, the notion is not in time any more than it is in
space ; it comprehends both. The difference is that by
Leibniz the development is conceived as a continuous
growth or increase in a certain fundamental quality
(clearness and distinctness of perception), while by Hegel
it is represented as a dialectic movement from that which
is relatively abstract, through its correlative abstraction
(or its ' negation ') to that which, comprehending or
uniting both, is relatively concrete. For Leibniz develop-
ment is from small to great (witness, for instance, his
petites perceptions) ; for Hegel development is from frag-
ments to wholes, or rather from the vague and undeter-
mined to the definite and determined.

Accordingly what Leibniz means by saying that the
Monad (or its qualities) cannot go out of itself and cannot
be entered or influenced from outside, would by Hegel be
expressed as the doctrine that thought or self-consciousness
is reality, the universe, and that accordingly it can neither
go beyond itself nor have anything beyond it. It may
sunder itself ideally, but it cannot really go out of itself,
for there is no ' out of itself/ In the same way the Monad
may ideally be sundered into active and passive elements
(entelechy and materia prima^, but it can really give
nothing and it can really receive nothing. The difference

190 INTRODUCTION

at this point between the attitude of Hegel and that of
Leibniz is due to the fact that while Leibniz interprets

* perception ' as that which it is in its lowest form (mere
1 representation ' or ' expression '), and regards conscious-
ness and self-consciousness as developments from it by
increase or addition, Hegel interprets ' representation ' or
relation in general as being essentially that which it is
in its highest form (self -consciousness), and regards the
lower forms as * abstract ' or incomplete foreshadowings,
undeveloped expressions of it. For Hegel as for Leibniz
the universe is organic throughout. No part of it is
actually other than self-determined, for the unity of the
whole and its parts is absolutely complete, so that no part
can be conceived as having any reality by itself. Leibniz
holds that the Monads must be conceived on the 'analogy' of
the soul. Hegel insists on a unity which is closer than mere
analogy, and which, at the same time, expresses itself in
the greatest possible variety ; he regards self-consciousness,
explicitly or implicitly, as the reality of every part, every
member or organ, of the whole. In short, it may be
said that in Leibniz's account of simple substance we have
the first suggestion of the transition from substance to
subject (as the ultimate reality of things), which is brought
to completion by Hegel '.

Lotze's Reconstruction of the Hypotheses of Leibniz.

It seemed to Lotze that the ' bold Monism ' of Hegel

* undertook far more than human powers can achieve,'
although 'its leading idea by no means loses its value
through the great defects in its execution V This ' leading
idea ' was in Lotze's opinion the * reconciliation of oppo-
sites,' the overcoming of the contradictions in thought by
bringing all knowledge to systematic unity. But Lotze's

1 Cf. generally Caird, Critical Philosophy of Kant, vol. ii. bk. i.
ch. 12, especially pp. 62 sqq. See also Monadology, § 30.

2 Lotze, Metaphysic, bk. i. ch. 7, § 88 (Eng. Tr., vol. i. p. 206).

ESTIMATE OF LEIBNIZ'S PHILOSOPHY IQI

interpretation of * thought ' is very different from that of
Hegel. Although he expressly repudiated the suggestion
that he is to be counted as a follower of Herbart, Lotze's
position as regards thought and the reconciling of its
contradictions is more akin to the view of Herbart than
to that of Hegel. Like Herbart he regards thought as
essentially analytic, as interpreting rather than constituting
reality, and the work of science or philosophy is thus not
that of laying down an absolute all-comprehensive system,
expressing the whole evolution of reality, but that of
unifying our knowledge, resolving the contradictions that
appear in common experience. Thought cannot pierce to
the inner nature of things, cannot understand them so
thoroughly that it could make them. To use a distinc-
tion which has become a commonplace among writers on
natural science, thought can describe but it cannot explain*.
It can give an account of what happens, can express in the
form of general laws the relations between things, so as to
be able to calculate occurrences, and can possibly reduce
these laws to one general system ; but it cannot tell what
the things themselves really are, how they originally came
into being, and why they are so and not otherwise. In
short, thought is governed solely by the principle of
contradiction ; the principle of sufficient reason (in
Leibniz's sense) is beyond it. ' Reality is infinitely richer
than thought. . . . We know that in fact the nature of
reality yields a result to us unthinkable. It teaches us
that being and not-being are not, as we could not help
thinking them to be, contradictory predicates of every
subject, but that there is an alternative between them,
arising out of a union of the two which we cannot construct
in thought. This explains how the extravagant utterance
could be ventured upon, that it is just contradiction

1 For a fuller account of this distinction, see Merz, History of
European Thought in the Nineteenth Century, vol. i. pp. 337, 382, 383, notes.
Venn (Empirical Logic, ch. 21) minimizes the distinction, holding
explanation to be generalization.

I Q2 INTRODUCTION

which constitutes the truth of the real. Those who used
it regarded that as contradictory which was in fact
superior to logical laws — which does not indeed abrogate
them in their legitimate application, but as to which no
sort of positive conjecture could possibly be formed as
a result of such application1.'

The revolt of Lotze against the idealism of Fichte,
Schelling, and Hegel was due to the bad treatment which
the ' Philosophy of Nature ' had received at their hands.
The self-confidence of a thought which had found itself
absolute resulted in a Naturphilosophie which despised
facts ; and Lotze, as a scientist, felt it necessary to bring
down thought from 'the high horse of idealism,' and
assign to it the humble work of observation and descrip-
tion. ' The study of medicine, which I had chosen as my
life-work, made it necessary for me to acquire a knowledge
of natural science, and hence (in brief) I came to see how
completely untenable is a great part of the views of
Hegel, or rather the whole of them, in the form in which
they are put2.' It was to a large extent through his
medical studies that Lotze arrived at one of the chief
doctrines of his philosophy, viz. the universality of mecha-
nism as an account of the relations between phenomena.
'The father of modern physiology,' Johannes Mtiller
(1801-1858), had changed the whole aspect of biological
science by extending the conception of mechanism to all
the phenomena of life 3. Lotze took a further step in the
same direction when he defined mechanism as * the con-
nexion of all those universal laws, according to which
every individual in the created world acts upon every
other4.' The sphere of mechanism is thus extended so as

1 Lotze. Metaphysic, bk. i. ch. 6, § 76 (Eng. Tr., vol. i. pp. 178,
17.9). See the whole chapter, in which the views of Leibniz and
Herbart are discussed.

8 Lotze, Streitschrift, p. 7.

3 Merz, History of European Thought in the Nineteenth Century, vol. i.
pp. 216 sqq.; cf. Lotze, Metaphysic, bk. ii. ch. 8, §§ 224 sqq. (Eng.
Tr., vol. ii. p. 128).

4 Streitschrift, p. 57.

ESTIMATE OF LEIBNIZ S PHILOSOPHY 193

to include the phenomena not merely of inorganic and
organic bodies, but also of mind. ' The function of
mechanism in the construction of the world is, without
an exception, universal in its extent1.' The conception of
mechanism governs all science, for the principle of all our
thinking is the principle of contradiction, which can
only accept what is given in experience and systematize
its laws.

But Lotze protests strongly against the view that
mechanism gives us a final explanation of the reality of
the world. The laws of science are laws of phenomena ;
they do not account for the things themselves. We may
say that the essence of a thing is to stand in relations to
other things. But the thing itself is more than the
relations, and mechanism gives us an account of the rela-
tions only. Thus while * the function of mechanism in
the construction of the world is universal in its extent, it
is entirely subordinate in its importance*.' As mere
thought is by itself inadequate to reality, so mechanism
(the system of laws which it is the work of science to
discover and express) is not an eternally necessaiy system,
constituting the very nature of things, but is merely the
way in which the ultimate idea, the good, has freely
chosen to realize itself3. Not thought, but goodness is
ultimate, and ' the establishing of mechanism is the first
ethical deed of the Absolute. The fact that there is
a kingdom of universal laws appears to me to be compre-
hensible only in a world whose ultimate principle is an
ethical one ; another world (if I were to try to form for
myself the notion of it, which is for me absurd) might, it

1 Kleine Schriften, iii. 310.

2 Loc. cit., cf. Microcosmus, Introduction (Eng. Tr., vol. i. p. xvi).

3 ' Mechanism is but the collection of all the instrumental forms
in which God has willed that created beings shall act on one another
with their unknown natures, and that all their states shall be
welded into the endless chain of a world-history. This view
explores the sphere of means, not the sphere of ends to which these
minister.' Microcosmus, bk. iii. Conclusion. (Eng. Tr., vol. i.
P- 398.)

0

194 INTRODUCTION

appears to me, have arisen — a world without this thread
of consecutiveness, without this veritas in the sense of the
old metaphysicV Accordingly for Lotze the ultimate
reality is a personal God, who sets before Himself the
highest moral ends, and has established the ' absolutely
valid system of laws which rules the world ' as the best
means of securing these ends. Thought is a means of
attaining to complete experience ; mechanism is a means
of realizing the best. l There is no " nature of things "
outside of God,' limiting the sphere of His choice. But
on the other hand, His choice is not arbitrary, but is
governed by His perfect idea of what is absolutely
best.

In this the influence of Leibniz is so manifest that it
does not surprise us to find Lotze writing to the younger
Fichte : i I went willingly through the splendid gateway
which he [Herbart] is convinced that he has been able to
erect as an entrance to his metaphysic ; the gateway of
the Leibnitian Monad-world V Thus, according to Lotze,
we are constrained to conceive the real world as a world
of Monads, which are ultimately one in nature. In addition
to mechanism, or the system of laws governing (or ex-
pressing) the relations between things, there are the things
themselves, the facts, which may be conceived as Monads.
And both of these (the laws and the facts) presuppose
a universal and all-pervading substance, which is merely
a postulate of thought, but is a reality for feeling, and
which (being intelligible only through the idea of a
personal Deity) realizes the highest moral ends in the
sphere of the facts by means of the laws. Things are to
be thought of as Monads, because nature is to be con-
ceived as animated throughout; all things are endowed
with 'modes of sensation and enjoyment3.' Otherwise

1 Streitschrift, p. 57.

2 Ibid. p. 7.

8 Microcosmus, bk. iii. ch. 4, § 3 (Eng. Tr., vol. i. p. 360). Cf.
Lotze's early writing— Pensees dun Idiote sur Descartes, Spinoza et
Leibnitz. (Kleine Schriften, vol. iii. p. 564.)

ESTIMATE OF LEIBNIZ S PHILOSOPHY 195

we should have to regard all nature as merely machinery
for the drama of human consciousness — a view which
could never satisfy our 'longings' and i cravings.' But
this monadology or t hypothesis of unextended atoms' can
never; for Lotze, be more than a hypothesis. Thought
can never determine its truth, because it is a hypothesis
regarding the nature of things, and thought has to do
only with their relations. The monadology is i a concep-
tion of whose essential truth we are convinced, yet to
which we can hardly expect any further concession than
that, among the dreams of our imagination, it may be
one of those which do not contradict actual facts V

Lotze is here manifestly more in harmony with Kant
than with Leibniz 2. And he further differs from Leibniz
in maintaining that the Monads are not completely isolated
from one another, so that each contains its own relations
within itself. If Leibniz's doctrine be true, * while none
of the members [of the real world] condition each other,
everything goes on as if they all did so ; accordingly,
while it does not really form a whole, yet to an intelli-
gence directed to it, it will have the appearance of doing
so ; and, in one word, its reality consists in a hollow and
delusive imitation of that inner consistency which was
pronounced to be, as such, the ultimate reason why its
realization was possible3.' Accordingly for Lotze 'every
single thing and event can only be thought as an activity,
constant or transitory, of the one existence, its reality
and substance as the mode of being and substance of this
one existence, its nature and form as a consistent phase
in the unfolding of the same4.' The pre-established
harmony of Leibniz is thus set aside by Lotze 5. Its place

1 Microcosmus, bk. iii. ch. 4, § 3 (Eng. Tr., i. 360; cf. i. 363).

2 For an excellent account of the general relation of Lotze to
Kant, see Jones, Philosophy of Lotze, pp. 64 sqq.

8 Metaphysic, bk. i. ch. 6, § 79 (Eng. Tr., vol. i. p. 184). Cf. the
whole context.

* toe. cit.

5 'Only if the course of all, even of the most trivial, events
were fixed by immutable predestination, could the assumption of

O 2

196 INTRODUCTION

is taken by the conception of mechanism, through which
we describe the relations in which things are for thought.
Such relations as those between the phenomena of the
soul and the phenomena of the body can be described on
purely mechanical principles : that is to say, the condi-
tions of their connexion can be stated as laws. And the
theory of a pre-established harmony is not required (not
to say that it is insufficient) to explain how the phenomena
of the soul have any connexion with those of the body —
how, for instance, physical nerve-motion passes into
psychical sensation. It is impossible for our thought to
explain this ; but it is just as impossible for our thought
to explain how one physical phenomenon is invariably
connected with another physical phenomenon — how, for
instance, the burning match is connected with the explod-
ing gunpowder1. In neither case can thought do more
than describe a connexion invariable in our experience.
Science must be content with a ( practical occasionalism '
as distinct from the ' theoretical ' (i. e. absolute ontological)
; occasionalism ' of the Cartesians 2.

Thus in Lotze we find the principles of the philosophy
of Leibniz modified by Kantian influences. Like Leibniz,
Lotze in his application of the principles of contradiction
and of sufficient reason keeps them sharply apart from

a pre-established harmony — not, indeed, explain anything, but—
tolerably well describe the facts. ... It is only if individual things
do not float independent or left to themselves in a vacuum across
which no connexion can reach— only if all of them, being finite
individuals, are at the same time only parts of one single infinite
substance, which embraces them all and cherishes them all within
. itself, that their reciprocal action, or what we call such, is possible.'
Microcosmus, bk. ix. ch. i, § 5 (Eng. Tr., vol. ii. pp. 597, 598).
Cf. Metaphysic, bk. i. ch. 5, §§63 sqq. (Eng. Tr., vol. i. p. 150).

1 ' As in our life we see the physical motions of external nature
employed as stimuli to excite that in ourselves which is far
higher — conscious sensation : so, we think, throughout the universe
mechanical events are but the external tissue of regularly crossing
stimuli, designed to kindle at innumerable points, within in-
numerable beings, the true action of a more intelligent life.'
Microcosmus, bk. iii. Conclusion. (Eng. Tr., vol. i. p. 399.)

2 Streitschrift, p. 96.

ESTIMATE OF LEIBNIZ S PHILOSOPHY 197

one another. But, unlike Leibniz, he regards the principle
of contradiction as, indeed, universally applicable but
completely subordinate in importance. According to
Leibniz, mechanism in the real world is subordinate to
teleology, efficient to final causes. But at least the co-
ordinate priority of the principle of contradiction is secured
by the conception of the ' possible ' things or * essences,'
the realm of ideas, in the understanding of God. Lotze,
on the other hand, does away with this realm of ' possi-
bles,' making the 'principle of the best' absolutely
supreme, allowing the choice of God to be independent
even of the principle of contradiction, independent of all
save the ideal of absolute ethical worth. A violation of
the law of contradiction is an absurdity for us ; but God
might conceivably (if it had been the most perfect means
to the realizing of the best) have made a world in which
the law of contradiction did not hold. But as Leibniz
gave no clear explanation of the relations between the
two principles of contradiction and sufficient reason, so
Lotze does not explain the subordination of the one to
the other, but maintains that any such explanation is
beyond the reach of human thought.

From early years Lotze was familiar with the works of
Leibniz, and his writings continually suggest Leibnitian
ways of looking at things. But, though an inheritor of
Leibniz's ideas, he could not ' take over ' the philosophy
as a whole. ' I have, indeed, in general never had the
presumption to declare myself the successor of Leibniz,
in the sense of being his heir . . . but I must have the
presumption to admit that I could only have entered into
possession of this inheritance cum beneficio inventarii1.'

Other Influences of Leibniz.

It would be impossible briefly to indicate the full
influence of the philosophy of Leibniz in other directions.

1 Kleine Schriften, vol. iii. p. 342.

198 INTRODUCTION

While the academic writers on philosophy missed much
of his best thought, its spirit was felt in the literature of
Germany through the works of Lessing and Herder1.
Nor was Leibniz's thinking altogether without effect upon
English literature ; for, though the doctrine is sadly
straitened into platitude, that sense of the varied whole-
ness and harmonious system of things which pervades the
Theodicee is cleverly expressed in the Essay on Man by
the phrases of which Pope was a master ". Again, with
regard to the influence of Leibniz upon natural science,
reference may be made to the way in which his idea that
the organism is a group of smaller organisms, has been in
various forms developed by naturalists like Buffon 3, and
has finally gained something like scientific verification in
the cell-theory of Schwann. Johannes Muller recognized
this by giving to the cells the somewhat inappropriate
name of * organic monads V Modern psychology also, in
the attention it directs to 'sub-conscious' processes and
in its analysis of sensations and perceptions into elements
which are individually unnoticed (e. g. the * over-tones ' of
Helmholtz and the ' local signs ' of Lotze), owes much to

1 See Merz's Leibniz (Blackwood's Philosophical Classics), pp. 195
sqq. There are also traces of the influence of Leibniz in the works
of Schiller, who is said to have written his poem Die Freundschaft
when his mind was full of ideas suggested by the reading of
Leibniz. This is the poem from which Hegel in his Geschichte d.
Phil., vol. i. p. 91 (ed. 1840), quotes the well-known lines ' Freundlos
war der grosse Weltenmeister,' &c. The poem belongs to Schiller's
' First Period.'

8 See Introduction to the edition by Mark Pattison (Clarendon
Press). Bolingbroke said of Pope that he was • a very great wit,
but a very indifferent philosopher.'

3 Cf. Buffon's Histoire Naturelle, &c. (1787), vol. iv. p. 22 : 'Living
beings contain a large number of living and active molecules.
The life of the animal or of the plant appears to be only the result
of all the activities, of all the little individual lives (if I may so
speak) of each of these active molecules, whose life is underived
[primitive] and appears incapable of destruction.'

4 Weismann regards the unicellular organism as immortal. Cf.
Essays upon Heredity, &c. (Eng. ed. by Poulton, SchOnland, and
Shipley, pp. 25 and 27). For a good account of the relation of
Leibniz's philosophy to modern scientific thought, see Watson,
Comte, Mill and Spencer, pp. 126 sqq.

ESTIMATE OF LEIBNIZ S PHILOSOPHY 199

Leibniz's far-reaching suggestion of the unconsciousness
perceptions. For this suggestion also (if for little else)
Hartmann's Philosophy of the Unconscious is indebted to
Leibniz \ And further, in these days when we are so
persistently assured that 'the real is the individual,'
Monadology may be said to be in the air, and we need
not be surprised to find that, in one form or another, it
has its adherents in theologians like Dorner, philosophical
teachers like Groom Robertson, and expositors like Dill-
mann.

The fruits of the philosophy of Leibniz are as widely
scattered as its roots were far spread. The materials of
his philosophy were derived from every sphere of thought,
from every generation of thinkers, and he gave to the
future as liberally as he borrowed from the past. * Nicht
Vielwisser war er, sondern, soweit der Mensch es kann,
All- und Ganzwisser, und sein Erfassen, sein Erkennen,
war stets zugleich schopferischer Act2.'

1 See Tr. by Coupland, vol. i. pp. 16 sqq.

2 ' He was learned not merely in many things but, so far as
a man can be, in all and everything, and his very comprehending
or acquiring of knowledge was also an act of creating.' E. Du
Bois-Eeymond, Leibnisische Gedanken in der neueren Naturwissenschaft,
in his Eeden, Erste Folge, p. 33.

200 INTRODUCTION

APPENDIX A.

EXPLANATION OF THE PRE-ESTABLISHED HARMONY BY
A SPECIAL INSTANCE.

IN a letter to Arnauld (1687) (G. ii. 113) Leibniz gives an
account of the way in which his theory may be applied to
a particular case (that of the relation between a pin-prick
in the body and pain in consciousness).. 'We have now to
inquire how the soul is conscious of the motions of its body,
since we can see no way of explaining by what channels the
activity of an extended mass can pass into an indivisible being.
Ordinary Cartesians declare that no explanation of this union
can be given. The authors of the hypothesis of occasional
causes think that it is nodus vindice dignus, cui Deus ex Machina
intervenire debeat. For my part I explain it in a natural way.
From the notion of substance or concrete [accompli] being in
general, which declares that its present state is always a natural
consequence of its preceding state, it follows that the nature of
each individual substance, and consequently of every soul, is to
express the universe. Each has been from the first created
such that, in virtue of the laws of its own nature, it must
happen that it is in harmony with what takes place in bodies,
and especially in its own body. We need not then be surprised
to find that it has the power of representing to itself the pin-
prick, when this takes place in its body. And, to complete my
explanation on this point, we have : —

State of the body at moment A. State of the soul at moment A.

State of the body at the following State of the soul at moment B.
moment B.

(Pin-prick.) (Pain.)

1 As, then, the state of the body at moment B follows from the
state of the body at moment A, so the state of the soul B is
a consequence of A, the preceding state of the same soul,
according to the notion of substance in general. Now the

APPENDIX A 201

states of the soul are naturally and essentially expressions of
the corresponding states of the world, and especially of the
bodies which for the time belong to the soul. Accordingly,
since the pin-prick is a part of the state of the body at the
moment B, the representation or expression of the pin-prick
(i. e. the pain) will be a part of the soul at the moment B ; for
as one motion follows from another motion, so one representa-
tion follows from another representation in a substance whose
nature is to be representative. Thus the soul must needs be
conscious of the pin-prick, when the laws of relation require
it to express more distinctly a more observable change in the
parts of its body. It is true that the soul is not always distinctly
conscious of the causes of the pin-prick and of its coming pain,
when these are still hidden in the representation of the state A,
as when we sleep or in some other way are unaware of the
approach of the pin. But that is because the motions of
the pin at that time make too little impression, and though
we are already in some way affected by all these motions and
their representations in our soul, and thus have within us the
representation or expression of the causes of the pin-prick, and
consequently the cause of the representation of the same pin-
prick, that is to say, the cause of the pain— yet we can unravel
them from the multitude of other thoughts only when they
become noticeable. Our soul reflects only upon the more
marked phenomena, which stand out from the others ; not
thinking distinctly of any, when it thinks equally of all. After
this explanation, I cannot imagine where anybody can find the
least shadow of farther difficulty, unless he is prepared to
deny that God can create substances which are so made from
the beginning that each in virtue of its own nature is after-
wards in harmony with the phenomena of all the others. Now
nobody seems to deny this possibility, and since we see that
mathematicians represent in a machine the motions of the
heavenly bodies (as when

Jura poll rerumque fidem legesque deorum
Cuncta Syracosius transtulit arte senex,

which we can do to-day much better than Archimedes could in
his day), why could not God, who excels them infinitely, from
the beginning create representative substances in such a way
that they express by their own laws, according to the natural
change of their thoughts or representations, all that is to

202 INTRODUCTION

happen to every body? This seems to me not only easy
to conceive, but also worthy of God and of the beauty of the
universe, and in a way necessary, since all substances must
have a mutual harmony and connexion and all must express
in themselves the same universe and the universal cause, which
is the will of their Creator, and the decrees or laws which He
has established in order to make them fit into one another as
well as possible. Thus this mutual correspondence of different
substances (which, speaking with metaphysical strictness, can-
not act upon one another, and yet are in harmony as if one
did act upon another) is one of the strongest proofs of the
existence of God or of a common cause which each effect must
always express according to its point of view and its capacity
of expression. Otherwise the phenomena of different minds
would not harmonize, and there would be as many systems as
substances ; or rather, it would be entirely a matter of chance
if they were sometimes in harmony.'

APPENDIX B.

FORMATION OF THE IDEA OF SPACE.

IN § 47 of the fifth letter to Clarke, Leibniz gives an account
of the origin of the idea of space. 'I will here show how
men come to form to themselves the notion of space. They
consider that many things exist at once and they observe in
them a certain order of co-existence, according to which the
relation of one thing to another is more or less simple. This
order is their situation or distance. When it happens that
one of those co-existent things changes its relation to a mul-
titude of others, without their changing their relations among
themselves ; and that another thing, newly come, acquires
the same relation to the others as the former had ; we then
say it is come into the place of the other ; and this change we
call a motion in that body, wherein is the immediate cause
of the change. And though several, or even all the co-existent
things should change according to certain known rules of
direction and velocity, we can always determine the relation of

APPENDIX B 203

situation which each acquires with reference to every other, and
we can even determine the relation which any other [co-existent]
would have [to this], or which this would have to any other, if it
had not changed or if it had changed otherwise. And supposing
or feigning that among those co-existents there is a sufficient
number of them, which have undergone no change, then we
may say that those which now have to those fixed existents
a relation such as that which others formerly had to them,
have the same place which these latter had. And that which
comprehends all these places is called space, which shows that
in order to have an idea of place, and consequently of space,
it is sufficient to consider these relations and the rules of their
changes, without needing to fancy any absolute reality outside
of the things whose situation we consider. And, to give a kind
of definition : place is that which we say is the same for A and
for B, when the relation of co-existence between B and
C, E, F, G, &c., is in perfect agreement with the relation of
co-existence which A formerly had with the same C, E, F, Gr,
&c. ; provided that in C, E, F, G-, &c., there has been no cause

of change Place is that which is the same in

different moments to different existent things, when the re-
lations of co-existence between each and certain other existents,
which are supposed to continue fixed from moment to moment,
agree entirely together. And fixed existents are those in which
there has been no cause of change in the order of their co-
existence with others, or (which is the same thing) in which
there has been no motion. In short, space is that which
results from places taken together. And here it is right to
consider the difference between place and the relation of
situation which is in the body occupying the place. For the
place of A and B is the same ; whereas the relation of A to
the fixed bodies is not exactly and individually the same as
the relation which B (that comes into its place) will have to
the same fixed bodies : these relations are only in agreement.
For two different objects, as A and B, cannot have exactly the
same individual affection ; it being impossible that the same
individual accident should be in two objects or pass from one
object to another. But the mind, not satisfied with mere
agreement, looks for an identity, for something which should
be really the same, and conceives it as outside of the objects :
and this is what we here call place and space. But this can
only be an ideal thing, involving a certain order, in which

204 INTRODUCTION

the mind conceives relations to be applied.' (E. 768 a; G. vii.
400.)

I have made some slight alterations in Clarke's translation
for the sake of clearness. As to other details of Leibniz's
doctrine of space, cf. Eraser's ed. of Locke's Essay, vol. i.
pp. 158 and 1 86.

APPENDIX C.

THE MEANING OF CAUSE.

IN a draft of a letter to Arnauld (1686) (G. ii. 68) Leibniz
expounds his view of cause as follows-: — 'The hypothesis of
concomitance is a consequence of my notion of substance.
For, in my view, the individual notion of a substance includes
all that is ever to happen to it, and it is in this respect that
concrete things [etres accomplis = res completae ?] differ from
those which are not so. Now, the soul being an individual
substance, its notion, idea, essence or nature must include all
that is ever to happen to it ; and God, who sees it perfectly,
sees in it all that it will ever do or suffer and all the thoughts
it will have. Accordingly, since our thoughts are nothing but
the consequences of the nature of our soul and arise in it
in virtue of its notion, it is useless to seek in it the influence
of any other particular substance, besides that such an influence
is absolutely inexplicable. It is true that certain thoughts come
to us when there are certain bodily motions, and that certain
bodily motions happen when we have certain thoughts ; but
that is because each substance expresses the entire universe
in its own way, and that expression of the universe which is
a motion in the body is perhaps a pain in relation to the soul.
But we attribute activity [action} to that substance whose
expression is the more distinct, and we call it cause. Thus
when a body passes through water, there is an infinity of
motions of the parts of the water, such as there must be in
order that the place which the body leaves may be filled up
again by the shortest way. We say that this body is the
cause of the motions, because by its means we can explain
distinctly what happens ; but if we consider what is physical

APPENDIX C 205

and real in the motion, we may equally well suppose that the
body is at rest and that everything else moves, in accordance
with the hypothesis, since the whole motion in itself is only
a relative thing, viz. a change of position [situation] which
we do not know how to explain with mathematical exactness ;
but we do attribute it to a body by means of which all is
distinctly explained ' [i. e. so far sufficiently explained, though
not with mathematical exactness]. 'And in fact, taking all
the phenomena little and great, there is only one hypothesis
which serves to explain the whole distinctly. And we may
indeed say that, although this body may not be an efficient
physical cause of these effects, its idea is at least, so to speak,
their final, or, if you like, archetypal [exemplaire] cause in
the understanding of God. For, if we wish to find whether
there is anything real in the motion, let us imagine that
God wills directly to produce all the changes of situation
in the universe exactly as if this vessel were producing them
in passing through the water ; is it not true that there would
actually happen exactly the same thing ? For it is impossible
to assign any real difference. Thus, in metaphysical strict-
ness, we have no more reason to say that the vessel compels
the water to make this great number of ripples by means
of which the place of the vessel is filled up, than to say that
the water is compelled to make all these ripples and that
it compels the vessel to move in conformity with it; but,
except by saying that God has willed directly to produce
so great a number of motions all tending to this one thing,
we can give no reason for it, and as it is not reasonable to
have recourse to God for the immediate explanation of matters
of detail, we have recourse to the vessel, although actually,
in an ultimate analysis, the agreement of all the phenomena
of the various substances comes only from this, that they
are all productions of one and the same cause, to wit, God;
and consequently each individual substance expresses the re-
solution which God has taken with regard to the whole

universe It is quite right to say that my will is

the cause of the motion of my arm and that a solutio continui
in the matter of my body is the cause of pain, for the one
expresses distinctly what the other expresses more confusedly,
and activity {action} is to be attributed to the substance of
which the expression is more distinct.' (p. 71.)

206 INTRODUCTION

APPENDIX D.
LEIBNIZ'S LOGIC.

IN the Nouveaux Essais, bk . iv. ch. 1 1 , § 14 (E. 379 a ; G. v. 428 ),
there is an interesting passage explaining in more detail a part
of the logic of Leibniz. It contains some remarkable anticipa-
tions of more modern views. ' Propositions of fact also may
become general in a way, but it is by induction or observation ;
so that it ' [the general proposition of fact] * is nothing but
a multitude of similar facts, as when we observe that all
quicksilver evaporates by the force of fire ; and this is not
a perfect generality, because we do not see its necessity.
General propositions of reason are necessary, although reason
also furnishes some which are not absolutely general and are
only probable, as for instance, when we presume that an idea
is possible, until a more strict investigation reveals its contrary.
There are, finally, mixed propositions, which are drawn from
premises, of which some come from facts and observations,
while others are necessary propositions : and such are numerous
geographical and astronomical conclusions about the globe of
the earth and about the course of the stars, which conclusions
are obtained by combining the observations of travellers and
astronomers with the theorems of geometry and arithmetic.
But as, according to the usage of logicians, the conclusion follow*
the weaker of the premises, and cannot have more certainty than
they, these mixed propositions have only the certainty and
generality which belong to observations. As to eternal truths,
it is to be noted, that at bottom they are all conditional and say
in effect : Granted such a thing, such another thing is. For
instance, when I say, Every figure which has three sides will
also have three angles, I say nothing but this, that supposing
there is a figure with three sides, this same figure will have
three angles. I say this same figure, and it is in this respect that
categorical propositions, which can be stated unconditionally

APPENDIX D 207

(although fundamentally they are conditional), differ from
those that are called hypothetical, such as the following: If
a figure has three sides, its angles are equal to two right angles. In
this latter case we see that the antecedent (namely, the figure
with three sides) and the consequent (namely, the angles of the
three-sided figure are equal to two right angles) do not have
the same subject, as they had in the preceding case in which
the antecedent was — This figure has three sides, and the conse-
quent— The said figure has three angles. Nevertheless the
hypothetical might often be transformed into a categorical
by a slight change in the terms, for instance, if in place of the
preceding hypothetical I were to say : The angles of every three-
sided figure are equal to two right angles. The Scholastics have
argued much de constantia subjecti, as they called it, that is to
say, how a proposition regarding a subject can have a real
truth, if the subject has no existence. The fact is that the
truth is only conditional and says that, supposing the subject
ever exists, it will be found to be so-and-so. But it will still
be asked : On what is this connexion founded, since there is
within it reality which does not deceive ? The reply will be, -
that it is in the connexion of ideas. But it will be asked
again : Where would these ideas be, if no mind existed, and
what would then become of the real foundation of this certainty
of eternal truths ? That leads us at last to the ultimate founda-
tion of truths, namely, that supreme and universal spirit, which
cannot but exist, whose understanding, to speak truly, is the
region of eternal truths, as St. Augustine has recognized and
says in a vivid way1. And lest it should be thought unnecessary
to have recourse to this, it is to be noted that these necessary
truths contain the determining reason and regulative principle
of existences themselves, and, in a word, the laws of the
universe. Thus these necessary truths, being anterior to the
existence of contingent beings, must have their foundation in
the existence of a necessary substance. It is here that I find
the original of the ideas and truths which are graven in our
souls, not in the form of propositions, but as sources from which
application and opportunity will produce actual statements.'

1 The reference may be to Augustine, De Genesi ad Litteram, bk. v.
cap. 13 sqq. (Migne's ed., iii. 331 sqq.), or to Enarratio in Psalmum
xlix. (Migne's ed., iv. 576 sqq.). Cf. De diversis Quaestionibus, Q. xlvi.
§ 2 (Migne's ed., vi. 30).

208 INTRODUCTION

APPENDIX E.

KANT ON HIS KELATION TO LEIBNIZ.

THE Wolffians endeavoured to show that Kant's philosophy
was merely a degenerate product of Leibnitian thought. In
reply to Eberhard, Kant in 1790 wrote an interesting account
of his own relation to Leibniz— Uber eine Entdeckung, nach der
alle neue Kritik der reinen Vernunft durch eine altere entbehrlich
gemacht werden soil. See Rosenkranz, i. pp. 478 sqq. ; Harten-
stein, iii. 390 sqq.

'The metaphysic of Leibniz contains three great original
principles: (i) the principle of sufficient reason, especially in
so far as it shows the insufficiency of the principle of contra-
diction for the knowledge of necessary truths ; (2) the monad-

ology ; (3) the doctrine of the pre-established harmony

(i) Is it to be believed that Leibniz desired his principle of
sufficient reason to be understood objectively (as a law of
nature), when he attached a great importance to this principle
as an addition to the principles of earlier philosophy? It
is indeed so universally known and (within proper limits) so
manifestly clear, that the poorest intellect could not imagine
it had made a new discovery in finding it. Thus it is that
critics, who have misunderstood it, have greatly ridiculed it.
But for Leibniz this principle was merely a subjective one, that
is to say, a principle having reference merely to a critique
of reason. For what is meant by saying that, in addition
to the principle of contradiction, there must be other first
principles? It is as much as to say that, according to the
principle of contradiction only that can be known which is
already contained in the notion [Begriff] of the object ; but
if we say anything more about the object, something must
be added to this notion, and thus we must find a special
principle different from that of contradiction, for our assertions
must have their own special reason. Now propositions of thia

APPENDIX E 209

latter kind are now-a-days called synthetic, and thus Leibniz
means nothing but this : " In addition to the principle of
contradiction (as the principle of analytic judgments), there
must be another principle, namely that of synthetic judgments."
This was a new and remarkable suggestion of investigations
in metaphysics which had not yet been undertaken (and which

have actually been undertaken only recently) (2) Is

it to be believed that so great a mathematician as Leibniz
held that bodies are composed of Monads (and consequently
that space is made up of simple parts) ? He referred not to
the corporeal world, but to its substratum imperceptible [uner-
kennbar] to us, namely, the intelligible world which belongs
merely to the idea of reason, and in which doubtless we
must represent to ourselves as made up of simple substances
everything which we think therein as compound substance.
He likewise appears, like Plato, to attribute to the human
mind an original, although at present only obscure, intellectual
intuition [AnscTiauen] of these supersensible realities. But in
this he did not refer to the things of sense, which he attributes
to intuition [Anschauung] of a special kind, of which we are
capable only in relation to things we can really know [fur uns
mogliche ErJcenntnisse], and he regards the things of sense
as mere phenomena (in the strict use of the term), as specific
forms of intuition peculiar to us. With regard to this we
must not allow ourselves to be perplexed by his explanation
of sensation as a confused kind of perception, but must rather
substitute for it another explanation more in harmony with
his main purpose; for otherwise his system would be in-
consistent with itself. To take this defect as a deliberate and
careful speculation on the part of Leibniz (as copiers, in order
to make their copy exactly the same as the original, reproduce
its mistakes of form and language) can hardly be credited to
the disciples of Leibniz as a service done to the fame of their
master. Similarly, if it is taken too literally, a wrong inter-
pretation is given to the view of Leibniz regarding the innate-
ness of certain notions, by which he means a fundamental
faculty to which the a priori principles of our knowledge are
referable : he makes use of this idea merely as against Locke,
who recognized no other than an empirical origin of these
principles. (3) Is it possible to believe that, by his pre-
established harmony between soul and body, Leibniz meant
a mutual conformity of two beings entirely independent of

P

210 INTRODUCTION

one another as regards their nature and incapable of being
brought into connexion through their own forces? That
would have been to proclaim idealism ; for why should the
existence of bodies in general be admitted, if it is possible
to regard everything that takes place in the soul as the effect
of its own powers, which it would exercise even if it were
entirely isolated? The soul and the substratum (entirely
unknown to us) of the phenomena which we call bodies are
indeed two quite different beings, but these phenomena them-
selves, as mere forms of their intuition [Anschammg] depending
upon the nature of the subject (the soul), are mere perceptions
[Vorstellungen]. Hence the connexion between understanding
and sense in the same subject can be understood according
to certain a priori laws, as well as the necessary and natural
dependence of sense upon external things, without sacrificing
external things to idealism. For this harmony between under-
standing and sense, in so far as it renders possible a priori the
knowledge of universal laws of nature, criticism has given
as a reason that without this harmony no experience is pos-
sible But we can give no reason why we have just

such a kind of sense and an understanding of such a nature
that through their combination experience is possible ; and
further we can find no reason why they, as completely
heterogeneous sources of knowledge, always so completely
harmonize in rendering possible experiential knowledge in
general and more especially (as the Critique of Judgment
shows) in rendering possible an experience of nature, under
its manifold special and merely empirical laws, regarding
which the understanding teaches us nothing a priori. Neither
we nor any one else can explain how this harmony is as com-
plete as if nature had been arranged expressly to suit our
power of comprehension. Leibniz called the principle of this
union (especially with reference to the knowledge of bodies
and in particular of our own body as a middle term in this
relation) a pre-established harmony. Manifestly he did not in
this way give an explanation of the union, nor did he profess
to explain it. He merely pointed out that we must regard
the order established by the supreme cause of ourselves as
well as of all things outside of us as involving a certain
conformity to end. This purpose is regarded as present at
creation (pre-established) ; yet as a pre-established agreement,
not between things taken as outside one another, but only

APPENDIX E 211

between our mental powers of sense and understanding, ac-
cording to the special constitution of each in relation to the
other. In the same way criticism teaches that, in order to
a knowledge of things a priori, these powers must stand in
relationship to one another ;n the mind. That this was what
Leibniz really meant, although he did not clearly develop it,
appears from this, that he extends the application of the
pre-established harmony beyond the relation between soul
and body to the relation between the kingdom of nature and
the kingdom of grace (the kingdom of ends in relation to the
supreme end, i. e. man under moral laws). Here the harmony
is to be thought of as a harmony between what follows from
our notions of nature and what follows from our notions of
freedom, and thus as a harmony between two completely
different powers in us, having completely dissimilar principles,
and not between two different things taken as external to one
another. And this harmony, as the Critique teaches, can in
no way be comprehended from the nature of created things
[Weltwesen] but, as it is for us an essentially contingent har-
mony, it can only be understood by referring it to an intelligent
cause of the world.'

p 2

THE MONADOLOGY

THE MONADOLOGY1. 1714.

PREFATORY NOTE.

THE Monadology is one of the latest of the works of Leibniz,
having been written at Vienna in 1714, two years before his
death. On this last visit of his to Vienna he had met the
soldier prince Eugene of Savoy, who (probably through Queen
Sophia Charlotte of Prussia) had heard of the one great work
Leibniz had hitherto published, the Theodicee, which appeared
in 1710. Having read the Theodice'e, Prince Eugene begged
Leibniz to write for him a condensed statement of the main
principles of his philosophy, and having obtained this, in the
form either of what we now call the Monadology or of the
Principles of Nature and of Grace, he was so delighted with it
that he kept it like a jewel in a case, so that his friend, Count
Bonneval, wrote to Leibniz, perhaps with a touch of humorous
exaggeration : — ' He keeps your writing as the priests at Naples
keep the blood of St. Januarius ; he lets me kiss it and imme-
diately shuts it up again in its casket.' (Guhrauer, ii. 287.)

The Monadology was written in French; but it was not
published in its original form until 1840, when Erdinann,
who had discovered the MS. in the Royal Library at Hanover,
printed it in his edition of the philosophical works of Leibniz.
German and Latin translations of it appeared in 1720 and 1721,
and it was for a long time combined with the Principles of

1 Erdinann gave the name ' La Monadologie ' to this work when lie
published it in 1840. Kohler published a German version of it in
1720, under the title: Lehrsatze uber die Monadologie, &c. Dutens
gives a Latin translation of the German and entitles it : Principia
philosophiae seu theses in gratiam Principis Eugenii. The original
MSS. have no title.

2l6 THE MONADOLOGY

Nature and of Grace, there being some doubt as to which of the
two was the treatise written for Prince Eugene. The two
writings are similar in scope and intention, and were probably
written about the same time. Gerhardt holds that the work
written for Prince Eugene was not the Monadology but the
Principles of Nature and of Grace. (See G. vi. 483 and prefatory
note to the Principles of Nature and of Grace in this edition.)
The Principles of Nature and of Grace certainly appears to be
the earlier of the two.

As to its contents, the Monadology is to be regarded, not as
an introduction to the philosophy of Leibniz, but rather as a
condensed statement of the principles expressed in many philo-
sophical papers, and expounded, after a somewhat desultory
fashion, in the Theodicee. Leibniz himself indicated this fact
by putting on the margin of his manuscript of the Monadology
a series of references to sections of the Theodicte in which his
views are more fully expressed. Thus, as Erdmann says, the
Monadology is (in the German sense) an ' Encyclopaedia ' of
the philosophy of Leibniz, and the full understanding of it
presupposes some general knowledge of his thinking. It is not
possible rightly to understand it at a first reading.

The Monadology expounds a Metaphysic of Substance, and it
may for convenience be regarded as consisting of two main
divisions, in the first of which an account is given of the essen-
tial nature of all the substances, created and uncreated, which
constitute the reality of the universe, while the second division
explains the mutual relations through which they form one
world. §§ I to 48 make up the first of these divisions, the
second consisting of §§ 49 to 90. In the first division three
principal parts may be discriminated; (a) §§ 1-18, in which
the nature of Created 'Monads is explained; (b) §§ 19-30, in
which three great classes of Created Monads are discriminated ;
and (c) §§ 31-48, in which transition is made from the highest
class of Created Monads (the self-conscious) to the Uncreated
Monad (God) through the two great principles of Reason, that
of Contradiction and that of Sufficient Reason. Thus a philo-
sophic view is taken of the whole universe, considered as
a hierarchy of individual beings. The second division of the
Monadology, in which the mutual relations of substances are
more fully explained, may also be subdivided into three prin-
cipal parts : (a) §§ 49-60, expounding the general principles

217

of the inter-relation of substances through the hypothesis of
the Pre-established Harmony and the doctrine of 'the best
of all possible worlds' ; (6) §§ 61-82, explaining in more detail
the relations of particular classes of substances to one another,
and dealing with questions of organism and of the relations of
soul and body, including birth and death, &c. ; and (c) §§ 83-90,
in which the whole system of relations is brought to unity in
God, the distinction and harmony between efficient and final
causes (which had been found to be the basis of the distinction
between body and soul), being supplemented by an analogous
distinction and harmony between the ' physical realm of nature
and the moral realm of grace, that is to say, between God,
considered as Architect of the machine of the universe and
God considered as Monarch of the divine City of spirits.' This
brief analysis is to be taken merely as a suggestion of the line
of thought in the Monadology ; the texture of the work is
so close that it is impossible to make perfectly satisfactory
divisions in it.

The translation is made from the text given by M. Boutroux,
who has collated the MSS. at Hanover and corrected some
errors of Erdmann. The Monadology is given in E. 705 sqq. ;
G. vi. 607 sqq.

1. The Monad, of which we shall here speak, is nothing
but a simple substance, which enters into compounds.
By 'simple 'is meant * without parts.' (Theod. 10.)

2. And there must be simple substances, since there
are compounds ; for a compound 2 is nothing but a
collection or aggregatum of simple things3.

2 There is a slight but interesting difference between this and
the corresponding passage in the Principles of Nature and of Grace (see
p. 406). Leibniz speaks here of ' a compound ' in general (le com-
pose') : in the other passage he uses the expression ' compound
substance ' (la composed). In both cases he must be understood to
mean 'body,' which, he -elsewhere tells us, is not a substance,
strictly speaking (Introduction, Part iii. pp. 96 and in). Accord-
ingly, the expression here is more exact than that in the Principles
of Nature and of Grace ; but the difference illustrates the looseness
of Leibniz's terminology in this connexion.

3 If the ' simple things ' are, like the Monads, non-quantitative,
can we attach any intelligible meaning to ' compounds/ which are
mere aggregates of them ? Does not an aggregate always imply

2l8 THE MONADOLOGY

3. Now where there are no parts 4, there can be neither
extension nor form [figure] nor divisibility. These Monads
are the real atoms of nature and, in a word, the elements
of things 5.

4. No dissolution of these elements need be feared,
and there is no conceivable way in which a simple sub-
stance can be destroyed by natural means. (Theod. 89.)

5. For the same reason there is no conceivable way in
which a simple substance can come into being by natural
means, since it cannot be formed by the combination of
parts [composition] 6.

elements which are quantities, however small ? Leibniz elsewhere
makes it perfectly clear that nothing quantitative can ever be
absolutely simple, and thus there seems a weakness in his reasoning
at this point. The difficulty is fundamental and affects the whole
of Leibniz's system : it is, indeed, the crux of every Individualist
or Atomist philosophy. Leibniz's hypothesis of a ' living [formef]
atom,' a ' fertile simplicity,' a ' centre which expresses (or repre-
sents) an infinite circumference ' (Reponse aux Reflexions de Bayle,
1702, E. 187 a ; G. iv. 562), is the suggestion of a way out of
Atomism ; but it does not take us entirely out of the wood. We
have still, in the spirit of much of Leibniz's philosophizing, to
ask ourselves the question — « Are not " simple " and " compound "
purely relative terms, so that to search for an absolutely simple
thing is to explore blind alleys ? ' Kant shows us the blind alleys in
his second Antinomy (Critique of Pure Reason, Meiklejohn's Tr., p. 271).
See also the interesting analysis and criticism of Kant's arguments
in Hegel's Wissenscftaft der Logik. bk. i. div. 2, ch. i. sect. A, note. Cf.
Hegel's Geschichte der Philosophie, vol. iii. p. 525 (Eng. Tr., p. 449).
* i. e. where there are no spatial distinctions.

5 Cf. New System, § 3. Ordinary physical atoms have form and
extension ; and, though they may not be physically divisible, yet
they must be ideally divisible ad infinilum, inasmuch as they
occupy space. Thus for Leibniz all merely physical atoms are
unreal. Cf. Lange's History of Materialism, bk. i. sect. 4, ch. iv.
(Eng. Tr., vol. ii. pp. 124 sqq.).

6 According to Leibniz a thing is produced by nature only when
it comes into being gradually, bit by bit. But the Monads, having
no parts, cannot come into being by the adding of part to part.
Yet it may be pointed out that every Monad has an internal
development, which is gradual. It is not born perfect, fully
realized. Why, then, should it not come into being by natural
means ?

THE MONADOLOGY 219

6. Thus it may be said that a Monad can only come
into being or come to an end all at once ; that is to say,
it can come into being only by creation and come to an
end only by annihilation, while that which is compound
comes into being or comes to an end by parts7.

7. Further, there is no way of explaining how a
Monad can be altered in quality or internally changed 8
by any other created thing ; since it is impossible
to change the place of anything in it or to conceive
in it any internal motion which could be produced,
directed, increased or diminished therein, although all
this is possible in the case of compounds, in which
there are changes among the parts9. The Monads
have no windows, through which anything could come
in or go out. Accidents cannot separate themselves
from substances nor go about outside of them, as the
1 sensible species ' of the Scholastics used to do 10. Thus

7 Consider, by way of analogy and contrast, what Spinoza says
regarding the eternity of the human mind, Ethics, v. prop. 23.
Spinoza dispenses with the idea of creation. But according to
Leibniz there are created Monads, whose creation is, nevertheless,
not an event in time, for time and space have to do merely with
phenomena, and the Monads are not in time and space, but con-
dition them. Cf. § 47 and Introduction, Part iii. p. 101.

8 The meaning is that by other things the Monad can neither
be altered as to its nature, i.e. changed into something else, nor
even affected in those changes of state which it can undergo
without a change of nature.

9 It is implied that all changes in bodies are reducible to traits-
position of parts, and ultimately to changes in the amount alid
direction of motion. See Introduction, Part iii. pp. 89 sqq.''r

10 Leibniz seems here to have in view partly the doctrines of
Thomas Aquinas and partly the scholastic theories which werer ,
based on the system of Democritus. The l species ' are images or
immaterial representations of material qualities. According to
Thomas Aquinas, the accidents of things are known to us by
means of sensible species, or particular images, while we know
the essences of things by means of intelligible species or general I
images. The scholastic theory in general may be said to be t^
the sensible or intelligible ' species ' in us have something
common with the accidents or essences in things, though

220 THE MONADOLOGY

neither substance nor accident can come into a Monad
from outside11.

8. Yet the Monads must have some qualities, otherwise
they would not even be existing things 12. And if simple
substances did not differ in quality, there would be

is a considerable variety of more or less vague opinion as to the
nature of the relation. Leibniz is evidently thinking of a theory
(not that of Thomas Aquinas), according to which sense-perception
means that particles are detached from the body perceived and
pass into the percipient, in whom they are reconstructed into
images or representations of qualities in the thing perceived.
Images of this kind were called efScwAa by Democritus. Of. Ritter
and Preller, Historia Philosophies Graecae, § 155. Atomists felt bound
to explain the action of body upon soul by the suggestion of some
kind of influxus physicus. Descartes has a parallel passage to this
of Leibniz, in which he says that he ' desires to rid people's minds
of all these little images, flying through the air, called intentional
species, which give s'o much work to the imagination of philo-
sophers.' Dioptrique, Discours I. Cf. ether passages quoted by Veitch
in his Translation of Descartes' s Method and Meditations, note 2 — l Idea.'

u Kant pointed out that a thing may have < intensive' as well
as * extensive ' quantity, i. e. quantity which is not divisible into
spatial parts as well as quantity which is so divisible. A stone
descending from a height loses a certain * intensive quantity '
without losing any of its spatial parts. And thus a simple sub-
stance may, in a certain sense, lose and receive quality. Cf.
Critique of Pure Reason (Hartenstein, ii. 178 ; Rosenkranz, ii. 145 ;
Meiklejohn's Tr., p. 125), Kant argues that the simplicity of the
soul (i.e. the absence of parts in it) does not necessarily prove its
indestructibility, for, though it has no parts, it may lose con-
sciousness and the rest of its essential qualities (Hartenstein, ii.
318; Rosenkranz, ii. 792; Meiklejohn's Tr., p. 245). Compare
Kant's 'intensive quantity' with Leibniz's degrees of Perception
and Appetition.

12 After this sentence Leibniz originally wrote, and then deleted,
these words : ' And if simple substances were nonentities [news],
compounds also would be reduced to nothing.' This emphasizes
the point that a being without quality is indistinguishable from
nothing ; cf. Hegel's Logic, Wallace's Tr., pp. 158 sqq. Quantity
always presupposes quality ; see Introduction, Part ii. pp. 27 sqq.
Leibniz seems also to imply that each Monad must have more
than one quality. On the other hand, Herbart (1776-1841), whose
Monadology owes much to that of Leibniz, and who calls his
Monads ' primary qualities ' (Urqualitaten'), holds that a substance
cannot be perfectly simple unless it has only one ultimate quality.

THE MONADOLOGY 221

absolutely no means of perceiving any change in things.
For what is in the compound can come only from the
simple elements it contains, and the Monads, if they had
no qualities, would be indistinguishable from one another,
since they do not differ in quantity13. Consequently,
space being a plenum, each part of space would always
receive, in any motion, exactly the equivalent of what it
already had, and no one state of things would be dis-
cernible from another14.

13 Kant would say that they may differ in ' intensive quantity' ;
see note n. L'eibnfz makes the distinction between quality and
quantity as sharp as the Aristotelian distinction between iroTov
and troffov. Yet in some respects his Law of Continuity suggests
a different view.

" E. reads * one state of things would be indistinguishable from
another.' Cf. Epistola ad Des Bosses (1706) (G. ii. 295) r. 'If we were
to admit, as the Cartesians desire, the plenum and the uniformity
of matter, adding to these motion alone, it would follow that
nothing would ever take place among things but a substitution of
equivalents, as if the whole universe were reduced to the motion
of a perfectly uniform wheel about its axis or, again, to the revolu-

, tions of concentric circles, each made of exactly the same materials.

[The result of this would be that it would not be possible, even for
an angel, to distinguish the state of things at one moment from
their state- at another. For there could be no variety in the phe-
nomena. ^Accordingly, in addition to figure, size, and motion, we
must allow certain Forms, whence there arises a distinction among
the phenomena of matter ; and I do not see whence these Forms
are to be taken, if they are to be intelligible, unless it be from
Entelechies.' To avoid a possible misunderstanding, it should be
noted that for Leibniz, the Monads are not in space, which is a
relation between phenomena ; see Introduction, Part iii. p. 101. Cf.
Epistola ad Des Bosses (1712) (E. 682 b ; G. ii. 450): 'Space is the
order of co-existing phenomena, as time is the order of successive
phenomena. There is no nearness or distance, whether spatial or
absolute, among Monads, and to say that they are collected, together
in one point or dispersed throughout space, is to make use of certain
fictions of our mind, by which we try to represent to ourselves in
imagination what cannot be imagined but only understood.' Kant,
misled by the position of Wolff, does not rightly interpret Leibniz's
view of space, which he discusses in the Critique of Pure Reason,
Hartenstein, ii. 256 sqq. ; Kosenkranz, ii. 216 sqq. ; Meiklejohn's
Tr., pp. 191 sqq., especially p. 199. Cf. Introduction, Part iv.
pp. 1 68 sqq.

222 THE MONADOLOGY

9. Indeed, each Monad must be different from every'
other. For in nature there are never two beings which
are perfectly alike and in which it is not possible to find
an internal difference, or at least a difference founded
upon an intrinsic quality [denomination] 15.

10. I assume also as admitted that every created
being, and consequently the created Monad, is subject
to change, and further that this change is continuous
in each16.

15 This is the principle of the ' identity of indiscernibles ' ; see
Introduction, Part ii. p. 36. Cf. Nouveaux Essais, bk. ii. ch. xxvii.
§ 3 (E. 277 b ; G. v. 214). For Kant's criticism see Critique of Pure
Reason, Hartenstein, ii. 267 ; Eosenkranz, ii. 229 ; Meiklejohn's Tr.,
p. 202. Probably the first statement of the principle is to be found
in the writings of Nicholas of Cusa (14,31-1464). He says that
4 there cannot be several things exactly the same [aequalia~}, for in
that case there would not be several things, but the same thing
itself. Therefore all things both agree with and differ from one
another.' (De Venatione Sapientiae, 23.) Cf. De docta ignorantia, iii. i :
'All things must of necessity differ from one another. Among
several individuals of the same species there is necessarily a
diversity of degrees of perfection. There is nothing in the universe
which does not enjoy a certain singularity, which is to be found in
no other thing.' His theories are full of suggestions of Leibniz. Cf.
Falckenberg, History of Modern Philosophy, English Tr.. pp. 20 sqq.
Reference may also be made to a very interesting article by Zimmer-
mann, Nicolaus Cusanus als Vorlaufer Leibnitzens (Wien. Akad. Sitsungs-
berichte, vol. 8, p. 306). There is no mention of Nicholas of Cusa in
any of Leibniz's philosophical writings ; but in a letter to the Acta
Eruditorum (1697) Leibniz refers to him as a mathematician (cf.
Dutens, iii. 345). — Intrinsic qualities are those which things have
in themselves, e.g. figure, motion, &c., while extrinsic qualities are
those which arise from their relations to other things, e.g. their
being perceived, desired, &c. Cf. Port-Royal Logic, part i. ch. ii.
(Baynes's Tr. , p. 37) : ' There are some modes which may be called
internal, because they are conceived to be in the substance, as round,
square ; d,nd others which may be called external, because they are
taken from something which is not in the substance, as loved, seen,
desired, which are names taken from the actions of another — and
this is what is called in the schools external denomination.'

16 There is constant change in created substances, even though
there may appear to be no change. What appears to us as absence
of change is really a very small degree of change. We have here
an application of the Law of Continuity.

THE MONADOLOGY 223

ii. It follows from what has just been said, that the
natural 17 changes of the Monads come from an internal
principle, since an external cause can have no influence
upon their inner being. (Theod. 396, 400.)

1 2 18. But, besides the principle of the change, there
must be a particular series of changes [un detail de ce qui
change], which constitutes, so to speak, the specific nature
and variety of the simple substances.

13. This particular series of changes should involve a
multiplicity in the unit [unite] or in that which is simple.
For, as every natural change takes place gradually,
something changes and something remains unchanged19;
and consequently a simple substance must be affected and
related in many ways, although it has no parts 20.

17 i. e. other than miraculous changes or than such change as may
be implied in the creation or annihilation of a Monad.

18 At the beginning of § 12 Leibniz originally wrote : 'And gener-
ally it may be said that force is nothing but the principle of the
change.' He seems afterwards to have felt that force was not a deep
enough notion to be an adequate expression of the principle which,
in §§ 14 and 15, he describes under the names of Perception and
Appetition.

19 The Law of Continuity. Everything is continually changing,
and in every part of this change there is both a permanent and a
varying element. That is to say, at any moment everything both
'is' and 'is not,' everything is becoming something else — some-
thing which is, nevertheless, not entirely ' other.'

ao In illustration of this and the following sections, cf. Eeponse aux
Reflexions de Bayle (1702) (E. 186 b ; G. iv. 562) : « The state of the
soul, as of the atom, is a state of change, a tendency. The atom
tends to change its place, the soul to change its thought : each
changes of itself in the simplest and most uniform way, that its
state allows. Whence comes it, then (I shall be asked), that there
is so much simplicity in the change of the atom ' [which is taken
as being always motion in a straight line at a uniform speed] ' and
so much variety in the changes of the soul ? The reason is that the
atom (as it is supposed to be, for there is no such thing in nature),
although it has parts, has nothing which causes any variety in its
tendency, because it is supposed that these parts do not change
their relations ; while on the other hand the soul, though it is
perfectly indivisible, has a composite tendency, that is to say, it
contains a multitude of present thoughts, of which each tends to

224 THE MONADOLOGY

14. The passing condition, which involves and repre-*
sents a multiplicity in the unit [unite~] or in the simple
substance, is nothing but what is called Perception 21,
which is to be distinguished from Apperception or
Consciousness, as will afterwards appear. In this matter
the Cartesian view is extremely defective, for it treats as
non-existent those perceptions of which we are not
consciously aware22. This has also led them to believe
that minds [esprits] alone are Monads, and that there are
no souls of animals nor other Entelechies. Thus, like the
crowd, they have failed to distinguish between a prolonged
unconsciousness and absolute death23, which has made

a particular change, according to the nature of its content, and
which all are present together in the soul; in virtue of the soul's
essential relation to all the other things in the world. It is because
they do not have this relation that the atoms of Epicurus have no
existence in nature. For there is no individual thing, which is
not to be regarded as expressing all others ; and consequently the
soul, in regard to the variety of its modifications, ought to be likened
to the universe, which it represents according to its point of view,
and even in a way to God, whose infinity it represents finitely, because
of its confused and imperfect perception of the infinite, rather than
to a material atom.' Cf. Appendix Fr p. 272.

21 Cf. Epistola ad Des Bosses (1706) (E. 438 a ; G. ii. 311): 'Since
perception is nothing else than the expression of many things in
one, all Entelechies or Monads must necessarily be endowed with
perception.' Also Lettre a Arnauld (1687) (G. ii. 112) : 'Because of
the continuity and divisibility of all matter, the least motion has
its effect upon neighbouring bodies, and consequently upon one
body after another ad infinitum, in a gradually lessening degree ;
and thus our body must in some way be affected by the changes in
all other bodies. Now, to all the motions of our body there corre-
spond certain more or less confused perceptions of our soul, and
accordingly our soul also will have some thought of all the motions
in the universe, and in my opinion every other soul or substance
will have some perception or expression of them.' See Introduction,
Part ii. p. 33.

22 Cf. Method, Part 5, and Meditations, 2 and 6. See also Principia
Philosophiae, i. 48, and cf. Introduction, Part iii. p. 126. The Car-
tesian view is that animals and plants are purely ine'chanical
structures or living automata, parts of extension, entirely separate
from thought.

23 * Sleep, which is an image of death, trances, the burying of

THE MONADOLOGY 225

them fall again into the Scholastic prejudice of souls
entirely separate [from bodies], and has even confirmed
ill-balanced24 minds in the opinion that souls are mortal25.

a silkworm in its cocoon, the resuscitation of drowned flies by
means of a dry powder sprinkled upon them (when they would
remain quite dead, if this were not done), the resuscitation of
swallows which make their winter quarters among the reeds,
where they are found without any appearance of life, the cases of
men frozen to death, drowned, or strangled, who have been brought
to life again ... all these things serve to confirm my opinion that
these different conditions differ only in degree, and if we have not
the means of bringing about resuscitation from death in other
forms, it is either because we do not know what ought to be done
or because, though we do know it, our hands, our instruments, and
our remedies cannot accomplish it, especially when dissolution
takes place too quickly and has gone too far. Accordingly we
must not content ourselves with the notions which the common
people may have about life and death, when we have both analogies
and (what is more) solid arguments which prove the contrary.
Lettre a Arnauld (1687) (G. ii. 123).

2t E. reads mal touches ; G. and Boutroux, mal tournes.

25 Descartes regards the immortality of the soul as ultimately
dependent on the will of God. See the Abrege prefixed to the
Meditations [Synopsis in Veitch's translation]. Cf. Eeponses aux
Deuxiemes Objections, 7. Leibniz thus criticizes the view of Descartes :
' The immortality of the soul, as it is established by Descartes, is
of no use and can give us no kind of consolation. For, granting
that the soul is a substance and that no substance perishes, the
soul then will not be lost, as, indeed, nothing is lost in nature ; but,
like matter, the soul will change in appearance and, as the matter
of which a man is made has at other times belonged to plants and
animals, in the same way the soul may be immortal, indeed, but
it will pass through innumerable changes and will have no re-
collection of its former states. But this immortality without
recollection is ethically quite useless ; for it is inconsistent with
reward and punishment. What good, sir, would it do you to
become king of China, on condition that you forget what you have
been ? Would it not be the same as if God, at the moment He
destroyed you, were to create a king in China ? ' (G. iv. p. 300.)
From his own point of view, however, Descartes can say: 'Al-
though all the accidents of the mind be changed — although, for
example, it think certain things, will others, and perceive others,
the mind itself does not vary with these changes ; while, on the
contrary, the human body is no longer the same if a change take
place in the form of any of its parts.' Abrege des Meditations. It

226 THE MONADOLOGY

15. The activity of the internal principle which pro-
duces change or passage from one perception to another

_may be called Appetition. It is true that desire [I'appetit]
cannot always fully attain to the whole perception at
which it ajms, but it always obtains some of if and
attains to new perceptions26.

1 6. We have in ourselves experience of a multiplicity
in simple substance, when we find that the least thought
of which we are conscious involves variety in its object27.
Thus all those who admit that the soul is a simple
substance should admit this multiplicity in the Monad ;
and M. Bayle 28 ought not to have found "any difficulty

seems to me not improbable that in the last words of this section
Leibniz may have in view, among others, the wandering Irishman,
John Toland (1670-1722), author of Christianity not Mysterious, who
was in Berlin in 1702 and had a brief correspondence with Leibniz,
in which the question of the immortality of the soul is referred to.
Leibniz writes to the Princess Sophia Charlotte with something
like a kindly contempt of Toland's readiness to take either side of
a question. See G. vi. pp. 508 sqq. Of. Principles of Nature and of
Grace, § 4.

-6 See Introduction, Part ii. p. 33. Cf. Principles of Nature and of Grace,
§ 2. In many of his writings Leibniz uses the word ' tendencies '
(tendances} for appetitions. Force is a form of appetition or
tendency, i. e. it is not merely what actually appears as motion, &c.,
but it includes something potential. And it is not really, but only
ideally, an influence of one substance upon another. Cf. appetition,
in respect of likeness and difference, with Spinoza's Conatus.

27 Cf. Nouveaux Essais, bk. ii. ch. 2 (E. 227 a ; G. v. 109).

88 Pierre Bayle, the son of a Protestant clergyman, was born at
Carlat in Languedoc, in 1647. He was educated at the University
of Toulouse, where, under the influence of Jesuit teachers, he
became a Roman Catholic. But his Roman Catholicism was not
lasting and, having returned to his original faith, he avoided the
censures of the Church by going to Geneva. After some years of
wandering he became a Professor of Philosophy in the University
of Sedan (1675). But owing to the < free- thinking ' of Bayle and
others Louis XIV summarily suppressed this Protestant University
in 1681, and Bayle went, as Professor of History and Philosophy, to
a newly established institution at Rotterdam. In 1684 he founded
the Nouvelles de la RepuUique des Lettres, a monthly review of new books,
&c., to which there is frequent reference in the writings of Leibniz.

THE MONADOLOGY 227

in this, as he has done in his Dictionary, article ' Kora-
rius'29.

1 7. Moreover, it must be confessed that perception and
that which depends upon it are inexplicable on mechanical

In 1693, ostensibly on political as well as theological grounds, he
was deprived of his professorship, and he afterwards devoted him-
self to his Dictionnaire Historique et Critique (1695-96), which was the
precursor of the Encyclopaedias and the Encyclopaedist movement
in the following century. Among other writings he also published
a tract against religious persecution and a reply to Maimbourg's
libels upon Calvinism. He died in 1706. The Theoclicee of Leibniz
is to a large extent devoted to answering the arguments of Bayle,
who maintained the impossibility of reconciling faith with reason.
There .is much difference of opinion as to whether Bayle was
sincere in his combination of philosophical scepticism with an
appeal to faith in matters of religion. Probably in this regard he
meant to follow the example of Descartes. Leibniz seems to have
believed in the sincerity of Bayle's religious faith. He always
writes of Bayle with the greatest respect, saying of him (Theod.
§ 174): ' Ubi lene, nemo melius,' and again, after his death: 'We
must believe that Bayle is now enlightened with that light, which
is refused to earth, since, according to all appearance, he has
always been a man of good will.'

29 Like the greater part of Bayle's Dictionary, the article
' Rorarius' may be said to consist mostly of foot-notes. Jerome
Rorarius (1485-1566), an Italian, was Papal Nuncio at the Court
of Ferdinand of Hungary. He was so great an admirer of the
Emperor Charles V that, on hearing a learned man speak of him
as inferior to Otho and to Frederick Barbarossa, he was moved to
write a treatise maintaining that men are less rational than the
lower animals. This treatise (Quod animalia bruta ratione utantur
melius homine) was not published until about 100 years after it was
written, when Descartes's views regarding the souls of animals
were under discussion. Bayle accordingly makes the name of
Rorarius the occasion of a full consideration of the question, in the
course of which he expounds and criticizes the opinions of Leibniz.
Bayle thinks it a pity that the position of Descartes is so difficult
to maintain and so unlikely to be true ; for otherwise it would be
very helpful to the true faith. That is to say, the Cartesian view
is regarded as confirming belief in the immortality of the soul by
making a very great distinction between man and 'the brutes
which perish.' But it seems to Bayle that Leibniz (whom he calls
' one of the greatest minds in Europe ') has made some suggestions
(in regard to the solution of the general problem) which are worthy
of being developed. These suggestions are contained in the New

228 THE MONADOLOGY

grounds, that is to say, by means of figures and motions.
And supposing there were a machine, so constructed as to
think, feel, and have perception, it might be conceived as
increased in size, while keeping the same proportions, so
that one might go into it as into a mill. That being so,
we should, on examining its interior, find only parts
which work one upon another, and never anything by
which to explain a perception 30. Thus it is in a simple
substance, and not in a compound or in a machine, that
perception must be sought for31. Further, nothing but
this (namely, perceptions and their changes) can be found
in a simple substance. It is also in this alone that all

System, which was published in the Journal des Savans of June 27,
1695 (the year before the second vol. of Bay4e's Dictionary appeared).
Bayle's criticism is directed mainly against the pre-established
harmony and the spontaneous development of all their states by
simple substances. Cf. Appendix F. p. 272.

30 That is to say, even if we had microscopes powerful enough to
reveal to us, on a large scale, all the intricacies of nerve-cell and
nerve-fibre in the brain, we should still never get beyond figures and
motions. Cf. Commentatio de Anima Brutorum (1710)^. 463 a ; G. vii.
328) : ' If in that which is organic there is nothing but mechanism, that
is, bare matter, having differences of place, magnitude and figure ;
nothing can be deduced and explained from it, except mechanism,
that is, except such differences as I have just mentioned. For
from anything taken by itself nothing can be deduced and ex-
plained, except differences of the attributes which constitute it.
Hence we may readily conclude that in no mill or clock as such is
there to be found any principle which perceives what takes place
in it ; and it matters not whether the things contained in the
" machine " are solid or fluid or made up of both. Further we know
that there is no essential difference between coarse and fine bodies,
but only a difference of magnitude. Whence it follows that, if it
is inconceivable how perception arises in any coarse "machine,"
whether it be made up of fluids or solids, it is equally inconceivable
how perception can arise from a finer "machine"; for if our
senses were finer, it would be the same as if we were perceiving
a coarse " machine," as we do at present.' See also New Essays,
Introduction, p. 400. (G. v. 59 ; E. 203 a.)

31 Mechanism always means partes extra paries. This is character-
istic of all compounds, but not of any simple substances. Thus it
can never be said that matter thinks. Matter pre-supposes a
thinking or at least a 'perceiving' principle.

THE MONADOLOGY 229

the internal activities of simple substances can consist.
(Theod. Pref. [E. 474 ; G. vi. 37].)

( . 1 8. All simple substances or created Monads might be

•'called Entelechies 32, for they have in them a certain per-

fection (ZXOVO-L TO ZvT€\€<s] ; they have a certain self-sufficiency

(avTapKtLa) which makes them the sources of their internal

activities and, so to speak, incorporeal automata 33. (Theod.

32 li/reAe'xem is probably derived from kv re\et %xfiv> to be complete
or absolute. Leibniz's use of the term differs considerably from
that of Aristotle. €VT€\exeia in Aristotle is the state of perfection
or realization in which IWpycto, as a process, ends, rovvop-a. iy^pytia
At'yercu Kara TO epyov, /cat avvTflvei irpos TT)V tvTeXt\fiav. Melaph. 0, 8,
ic>5oa 22. But the distinction between Iz/TfAexfia and evtpyeia in
Aristotle is not by any means a sharp one. Thus he defines the soul
(fax?]} as €VTt\(xft<*- "n TrpujTrj awfMTOS (pvaiKov dvvdp.fi farjv ZXOVTOS. De
Anima, ii. i. But elsewhere he calls it ovffia Kal tvepyfia owpaTos
TIVOS. Metaph. H, 3, io43a 35. First entelechy is related to second
entelechy as kiriarrip.^ (implicit) is related to Oewpeiv (explicit).
Thus the soul is denned as first or implicit entelechy because it
exists in sleep as well as awake. The entelechy of Leibniz, how-
ever, is to be understood as an individual substance or force,
containing within itself the principle of its own changes. It i»
called entelechy, not because it is a state of perfect realization,
but because it contains in germ an infinity .of perfections, which
it tends to develop. It is thus not so much the final developed
condition of a thing, opposed to its potentiality (Swapis -or vkrj), but
it rather implies the tendency or virtuality, of which Leibniz
speaks as something intermediate between the bare potency (puis-
sance) and the fully developed activity (acte) of the Scholastics.
Cf. Introduction, Part iii. pp. 91, 105. ' The Forms of the Ancients
or Entelechies are nothing but forces.' Lettre au Pere Bouvet, E. 146 a.
Cf. Trendelenbui'g, De Anima, pp. 295, 320. In the eighth book of
Aristotle's Metaphysics there is a remark of much interest, when
considered in relation to Leibniz : rj ovaia €v OUTCWS, a\\' oi>x wj
\cyovcri TtvfS olov poi/ds TIS ovffa r) (nty/J-rj, dAA.' €vrf\e\fia teal (pvffis TIS
ctcdaTr). H, 3, 1044* 7. povds is, of course, used here in its original
sense of a unit.

33 That is to say, not merely machines, such as those made by
man, but entirely self-moving machines or machines which contain
within themselves the ground or principle of all their states or
conditions, in as complete independence of all else as if there were
nothing in the universe but God and themselves. Monads alone
are automata in this sense. Corporeal automata, in so far as they

230 THE MONADOLOGY

19. If we are to give the name of Soul to everything
which has perceptions and desires [appetits] in the general
sense which I have explained, then all simple substances
or created Monads might be called souls ; but as feeling
\le sentiment] is something more than a bare perception,
I think it right that the general name of Monads or
Entelechies should suffice for simple substances which
have perception only, and that the name of Souls should
be given only to those in which perception is more
distinct, and is accompanied by memory34.

20. For we experience in ourselves a condition in which
we remember nothing and have no distinguishable per-
ception ; as when we fall into a swoon or when we are
overcome with a profound dreamless sleep. In this state
the soul does not perceptibly differ from a bare Monad ;
but as this state is not lasting, and the soul comes out of
it, the soul is something more than a bare Monad.
(Theod. 64.)

21. And it does not follow that in this state the simple
substance is without any perception. That, indeed,
cannot be, for the reasons already given ; for it cannot
perish, and it cannot continue to exist without being
affected in some way, and this affection 35 is nothing but
its perception. But when there is a great multitude of
little perceptions, in which there is nothing distinct, one
is stunned ; as when one turns continuously round in the

are corporeal, cannot be said to have this avrapKaa. Cf. § 64.
Spinoza speaks of the soul as * acting according to certain laws and
us if it were a kind of spiritual automaton/ De Intellectus Emenda-
tione, 85 ; Bruder's ed., ii. 34.

34 Memory is thus the sign of consciousness as distinct from
unconscious perception. This is in harmony with the view, em-
phasized by modern writers, that conscious sensation pre-supposes
memory, because we can know one sensation only when it has
been brought into comparison with others. Leibniz in one of his
early writings suggestively remarks that body is 'momentary
mind, i. e. mind without memory ' (mens momentanea, seu carem
recordatione). Theoria Motus Abstracti (1671) (G. iv. 230).

35 Leibniz originally wrote * variation.'

THE MONADOLOGY 231

same way several times in succession, whence comes a
giddiness which may make us swoon, and which keeps
us from distinguishing anything 36. Death can for a time
put animals into this condition 37.

22. And as every present state of a simple substance is
naturally a consequence of its preceding state, in such a
way that its present is big with its future 38 ; (Theod. 350.)

23. And as, on waking from stupor, we are conscious of
our perceptions, we must have had perceptions imme-
diately before we awoke, although we were not at all
conscious of them ; for one perception can in a natural
way come only from another perception, as a motion
can in a natural way came only from a motion 39. (Theod.
401-403.)

24. It thus appears that if we had in our perceptions
nothing marked and, so to speak, striking and highly-
flavoured, we should always be in a state of stupor. And
this is the state in which the bare Monads are.

25. We see also that nature has given heightened
perceptions to animals, from the care she has taken to
provide them with organs, which collect numerous rays
of light, or numerous undulations of the air, in order, by
uniting them, to make them have greater eifect 40. Some-

36 Leibniz's point is that in such states as these we are still mani-
festly in certain peculiar relations to the external world, although
consciousness has, for the time, become so slight as to be imper-
ceptible.

37 Cf. Honadology, § 14, note 23. 38 Cf. §§78 and 79.

39 In virtue of the principle of sufficient reason, every perception
must have a cause, which can be nothing but another perception
(see § 17) ; and if the antecedent perception did not immediately
precede the consequent, there would be a breach of continuity in
the existence of the soul. Ultimately, of course, motions are them-
selves perceptions ; but they are confused perceptions, of such a
kind that their relations to one another can be stated according
to mechanical laws, which, however, are abstract and pre-suppose,
for their full explanation, the system of final causes or the laws of
perception in general.

40 Cf. Helmholtz, Popular Scientific Lectures, vol. i. p. 186. See also
Principles of Nature and of Grace, § 4.

232 THE MONADOLOGY

thing similar to this takes place in smell, in taste and in
touch, and perhaps in a number of other senses, which
are unknown to us 4l. And I will explain presently 42 how
that which takes place in the soul represents what happens
in the bodily organs.

26. Memory provides the soul with a kind of consecu-
tiveness 43, which resembles [imite] reason, but which is to
be distinguished from it. Thus we see that when animals
have a perception of something which strikes them and
of which they have formerly had a similar perception,
they are led, by means of representation in their memory,
to expect what was combined with the thing in this pre-
vious perception, and they come to have feelings similar
to those they had on the former occasion. For instance,
when a stick is shown to dogs, they remember the pain
it has caused them, and howl and run away44. (TJieod.
Discours de la Conformite, &c., § 65.)

2 7. And the strength of the mental image which im-
presses and moves them comes either from the magnitude
or the number of the preceding perceptions. For often
a strong impression produces all at once the same effect
as a long-formed habit, or as many and oft-repeated
ordinary perceptions45.

41 Cf. Lubbock, Ants, Bees and Wasps, ch. 8, especially pp. 220
and 225.

42 See §§ 61 and 62.

43 Consecutio, concatenation or sequence of perceptions. Leibniz
is referring to what would now be called association of ideas.
Cf. Nouveaux Essais, bk. ii. ch. n, § n (E. 237 b; G. v. 130), and
bk. ii. ch. 33 (E. 296 a ; G. v. 252). In the latter of these chapters
(' On the Association of Ideas ') he is thinking mainly of a ' non-
natural connexion of ideas/ as in the case of strange prejudices or
superstitions.

41 Does Leibniz in this section, as some critics maintain, over-
look his * Pre-established Harmony ' and unconsciously adopt tho
ordinary point of view, which implies that substances do really
act upon one another and are not each the cause of all its own
experiences ? ^

45 Cf. Nouveaux Essais, bk. ii. ch. 33 (E. 296 a ; G. v. 252! 'And
as the reasons ' [of the connexion of things] ' are often unknown to

i

THE MONADOLOGY 233

28. In so far as the concatenation of their perceptions
is due to the principle of memory alone, men act like the
lower animals, resembling the empirical physicians46,
whose methods are those of mere practice without theory.
Indeed, in three-fourths of our actions we are nothing
but empirics. For instance, when we expect that there
will be daylight to-morrow, we do so empirically, because
it has always so happened until now. It is only the
astronomer who thinks it on rational grounds47.

29. But it is the knowledge of necessary and eternal
truths that distinguishes us from the mere animals and
gives us Reason and the sciences, raising us to the know-
ledge of ourselves and of God 48. And it is this in us
that is called the rational soul or mind [_esprit\.

us, we must attend to particular instances in proportion to their
frequency ; for then the expectation or recollection of another
perception, usually connected with the perception we are ex-
periencing, is reasonable ; especially in cases where we have to
take precautions. But as the violence [vehemence] of a very powerful
impression often produces all at once as much effect as the fre-
quency and repetition of several moderate impressions could have
done in the long-run, it happens that this violence engraves in the
fancy an image as deep and as vivid as long experience could have
done. Whence it comes that a chance but violent impression
combines in our memory two ideas, which were already together
there, and gives us the same inclination to connect them and to
expect the one after the other, as if long custom had verified their
connexion. Thus association produces the same effect, though the
same reason does not exist. Authority and custom produce also
the same effect as experience and reason, and it is not easy to free
oneself from these inclinations/ Cf. New Essays, Introduction,
p. 364.

46 Until the time of Galen (circa 150 A.D.), there were various
sects of physicians. One of these was the sect of the Empirics,
who laid stress upon observation of the * visible' antecedents of
disease, &c. In later times the name of empiric fell into disrepute
and was given to physicians who despised theoretical study and
trusted to tradition and to their own individual experience.

47 Cf. New Essays, Introduction, p. 365, note 39.

48 The necessary and eternal truths are the first principles of all
rational knowledge. They are innate in us. They are, in fact,
the very principles of our nature, as of the universe, because it is
of our essence to represent the whole universe. Thus conscious-

234 THE MONADOLOGY

30. It is also through the knowledge of necessary
truths, and through their abstract expression, that we
rise to acts of reflexion, which make us think of what is
called J, and observe that this or that is within us :
and thus, thinking of ourselves, we think of being, of
.substance, of the simple and the compound, of the
immaterial, and of God Himself, conceiving that what is
limited in us is in Him without limits. And these acts of
reflexion furnish the chief objects of our reasonings49.
(Theod. Pref. [E. 469 ; G. vi. 27].)

ness or knowledge of these truths is knowledge of ourselves, and
it is at the same time knowledge of God, who is the final reason of
all things. Cf. Nouveaux Essais, bk. i. ch. i, § 4 (E. 207 b ; G. v.
72). 'A pretty general agreement among men is an indication
and not a demonstration of an innate principle ; but the exact and
decisive proof of these principles consists in showing that their
certainty come^ only from what is in us. ... It may be said that
all Arithmetic and all Geometry are innate and are in us in a
virtual manner, so that we could find them by attentively con-
sidering aiid arranging what is already in our mind, without
making use of any truth learned by experience or by external
tradition, as Plato has shown in a dialogue ' [Meno, 82 sqq.] ' in
which he introduces Socrates leading a child to abstruse truths
by questions alone, without giving him any information.' Cf.
Principles of Nature and of Grace, § 5.

49 Thus consciousness becomes self-consciousness (reflective con-
sciousness) when we realize the eternal truths as eternal, that is
to say, as the innate principles of our being and of the whole
world. Substance is always a soul of some kind, because it must
be something analogous to what we find in ourselves. Cf. Nouveaux
Essais, bk. i. ch. i, § 21 (E. 211 b ; G. v. 70). 'Very often know-
ledge of the nature of things is nothing but knowledge of the
nature of our mind [esprit] and of those innate ideas, which there
is no need to look for outside of it/ Cf. also § 23 (E. 212 b ; G. v.
71) : 'Intellectual ideas or ideas of reflexion are derived from our
mind ; and I should like very "much to know how we could have
the idea of being, were it not that we ourselves are beings and thus
find being in ourselves.' We see here (in however imperfect
a form) the germ of the Kantian transition from ' substance ' to
'subject' as the ultimate metaphysical reality. Cf. p. 190.

Boutroux finds in this passage the indication of a succession of
stages in the progress of self-conscious reflexion. The nature
of God is the truth or ultimate reality of our nature. Thus in
1 reflexion, that is to say, in the return of the being towards its

THE MONADOLOGY 235

v^ 31. Our reasonings are grounded upon two great princi-
ples, that of contradiction, in virtue of which we judge
false that which involves a contradiction, and true that
which is opposed or contradictory to the false 50 ; (Theod.
44, 169.)

32. And that of sufficient reason, in virtue of which
we hold that there can be no fact real or existing, no
statement true, unless there be a sufficient reason, why
it should be so and not otherwise, although these reasons
usually cannot be known by us51. (Theod. 44, 196.)

33. There are also two kinds of truths, those of reason-
source, which is God . . . we first of all come upon the ego, or the
being which is in us, in so far as it is limited and distinct from
other beings, and then upon being, substance and the immaterial,
coming ever nearer to the Divine Essence itself. And finally,
through perception which has thus become reflective and conscious,
we reach the Infinite Being, whom, from the first, created beings
are seeking confusedly and unwittingly. Then the circle, so to
speak, closes upon itself : the created being identifies itself with
the Creator in so far as He is in it ; the finite has done all that its
nature allowed in the way of reproducing the infinite.' (Edition
of La Monadologic, p. 156.)

50 Cf. Introduction, Part ii. pp. 58 sqq. Leibniz sometimes
distinguishes between the principle of contradiction and that of
identity (A = A). But he recognizes that they are ultimately one.
Cf. Nouveaux Essals, bk. iv. ch. 2, § i (E. 339 a; G. v. 343). 'The
principle of contradiction is in general : a proposition is either true or
false. This contains two true statements ; (i) that the true and the
false are not compatible in the same proposition or that a proposition
cannot be true and false at the same time ; (2) that the opposites or
negations of the true and the false are not compatible, or that
there is no middle term between the true and the false, or rather
that it is impossible for a proposition to be neither true nor false.' See
Aristotle, Metaph. T, 3, ioo5b 19 and 7, ionb 23.

51 In his earlier writings Leibniz calls the sufficient reason the
determining reason, meaning the reason which determines the exis-
tence of this or that out of a number of possibilities, each of which
involves no self-contradiction. As synonymous with the ' principle
of sufficient 'reason,' he also sometimes uses the phrase, 'principle
of fitness [convenance'] or of harmony.' He thus suggests that the
sufficient reason of a thing is always to be found in its relations to
other things, its place in the general system. We give the sufficient
reason of anything when we show its ' compossibility ' with other

236 THE MONADOLOGY

ing and those of fact 52. Truths of reasoning are necessary
and their opposite is impossible : truthg of fact are con-
tingent and their opposite is possible 53. When a truth is
necessary, its reason can be found by analysis, resolving
it into more simple ideas and truths, until we come to
those which are , primary 5\ (T7ieod. 170, 174, 189, 280-
282, 367. Abrege, Object. 3.)

things in addition to its abstract 'possibility.' The principle of
sufficient reason is the principle of final cause. Leibniz's adoption
of the word ' sufficient ' is supposed to have been suggested by its
use in Mathematics in a sense similar to that in which we say that
a certain magnitude ' satisfies ' a particular equation.

52 Cf. the Scholastic ratio cognoscendi and ratio essendi.

53 Cf. Theodicee, § 174 (E. 557 b ; G. vi. 217). 'It may be said of
M. Bayle : Ubi bene, nemo melius, though it ciould not be said of him,
as it was said of Origen: Ubi male, nemo pejus. . . . Yet M. Bayle adds
at the end ' [of a passage, quoted by Leibniz in the previous section]
'words which somewhat spoil what he has so justly remarked.
" Now what contradiction would there have been if Spinoza had
died at Leyden ? Would nature have been less perfect, less wise,
less powerful ? " He here confounds what is impossible, because it
involves a contradiction, with what cannot happen, because it is
not well fitted to be chosen. It is true that there would have been
no contradiction in the supposition that Spinoza had died at
Leyden and not at the Hague : it was perfectly possible. Accord-
ingly, as regards the power of God, the matter was indifferent.
But it must not be imagined that any event, however insignificant,
can be regarded as indifferent in relation to God's wisdom and
goodness.'

54 Leibniz does not give us a very clear idea of the relations of
the two principles to the two kinds of truths. This is probably
due to his hesitancy regarding the relations of the two principles
to one another. In the Appendix to the The'odicee entitled Remarques
ftur le livre de M. King, Leibniz says (E. 641 b; G. vi. 414): 'Both
principles must apply not only to necessary, but also to contingent
truths, and, indeed, that which has no sufficient reason must
necessarily be non-existent. For it may in a manner be said that
these two principles are included in the definition of the true and
the false. Nevertheless when, by analyzing a suggested truth, we
see that it depends upon truths whose opposite involves a contra-
diction, we can say that it is absolutely necessary. But when,
carrying our analysis as far as we like, we can never reach such
elements of the given truth, it must be said to be contingent, and
to have its origin in a prevailing reason, which inclines without
necessitating.' But on the other hand, at a later date, Leibniz

THE MONADOLOGY 237

34. It is thus that in Mathematics speculative Theorems
and practical Canons are reduced by analysis to Definitions,
Axioms and Postulates.

35. In short, there arejiimple ideas, of which no defini-
tion can be given 55 ; there are also axioms and postulates,
in a word, primary principles, which cannot be proved,
and indeed have no need of proof ; and thesa are identical
propositions56, whose opposite involves an express contra-
diction. (Theod. 36, 37, 44, 45, 49, 52, 121-122, 337,
340-344.)

{36) But there must also be a sufficient reason for con-
tingent truths or truths of fact ^, that is to say, for the
sequence or connexion of the things which are dispersed
throughout the universe of created beings, in which the
analyzing into particular reasons might go on into endless
detail, because of the immense variety of things in nature
and the infinite division of bodies 58. There is an infinity

writes to Clarke (IIme Ecrit de Leibni?, E. 748 a ; G. vii. 355) : ' The
principle of contradiction is by itself sufficient for the demon-
stration of the whole of Arithmetic and Geometry, that is to say,
of all mathematical principles. But in order to pass from Mathe-
matics to Physics, another principle also is needed, the principle
of sufficient reason.' See Introduction, Part ii. pp. 66 sqq. In the
Monadology, Leibniz's position is the same as in the earlier of
the passages quoted.

55 The definition of an idea is, for Leibniz, the statement of the
elements which a complete analysis reveals in it. Cf. Meditationes
de Cogmtione, Veritate et Inez's (1684) (E. 79 b ; G. iv. 423). 'When
everything which is an element in a distinct idea, is in its turn
distinctly known, or when analysis has been completely made,
knowledge is adequate. I know not whether human knowledge
can supply a perfect instance of this : the knowledge of numbers,
however, approaches it.'

56 Leibniz uses the word enondation for enunciatio, which is the
usual Latin translation of Aristotle's airu^iavoLs, or ^670? dntxpavTiicus.

57 Truths of reasoning have their sufficient reason in the self-
evident, identical truths to which they may be reduced by analysis.
Truths of fact can find a sufficient reason only in God.

18 Cf. Lotze, Microcosmus, bk. iii. ch. 5, § i (Eng. Tr., i. 372).
Leibniz says * infinite division' instead of 'infinite divisibility,''
because bodies are infinitely divisible only as phenomena benefundatu
and not as real beings. A real thing or substance must be indi-

238 THE MONADOLOGY

of present and past forms and motions which go to make
up the efficient cause of my present writing ; and there is
an infinity of minute tendencies and dispositions of my
soul, which go to make its final cause 59.

37. And as all this detail again involves other prior or
more detailed contingent things, each of which still needs
a similar analysis to yield its reason, we are no further
forward : and the sufficient or final reason must be out-
side of the sequence or series of particular contingent
things, however infinite this series may be60.

/3§y Thus the final reason of things must be in a neces-
sary substance, in which the variety of particular changes
exists only eminently R1, as in its source ; and this sub-
stance we call God. (Theod. 7.)

visible : it cannot consist of paries extra partes. And the ' infinite
division ' of bodies is merely another way of describing the in-
finite number of particular substances or Monads.

59 See Introduction, Part iii. p. 107. Cf. § 61. Here, in another
form, arises the difficulty as to the relation of Leibniz's 'principles '
to one another. Apparently the efficient and the final cause
combined make up the sufficient reason, neither by itself being
enough. Yet elsewhere Leibniz represents efficient causes as
ultimately depending on final causes. And efficient causes are by
Leibniz usually identified with mechanical causes, whose principle
is that of contradiction. See also Appendix F, p. 272.

50 This is an argument on the same lines as that by means of
which Aristotle infers a ' prime mover.' It depends on his prin-
ciple, dvajKrj arrival, i. e. we must come to a stop somewhere in the
regress of causes or conditions. Cf. Phys. S, 6, 237b 3 ; 0, i, 251* 17 ;
0, 5, 256" 13. Also Kant's Critique of Pure Reason, Transcendental
Dialectic, bk. ii. ch. 2 and 3.

61 Eminently in contrast with formally. The terms are Scholastic
and they were adopted by Descartes. Thomas Aquinas expresses
the difference thus : ' Whatever perfection is in the effect must
also appear in the cause, after the same manner if the agent and
the effect are of the same kind (univocaT) (thus man begets man), or
in a more eminent, that is to say excellent, way, if the agent is of
another kind (equivocal).' Descartes says : * By the objective reality
of an idea, I mean the entity or being of the thing represented by
the idea, in so far as this entity is in the idea ; and in the same way
we may speak of an objective perfection or an objective design, &c.
For all that we conceive as being in the objects of ideas is objectively

THE MONADOLOGY 239

39. Now as this substance is a sufficient reason of all
this variety of particulars, which are also connected
together throughout ; there is only one God, and this God
is sufficient™.

40. We may also hold that this supreme substance,
which is unique, universal c:j and necessary, nothing out-
er by representation in the ideas themselves. The same things are
said to be formally in the objects of the ideas, when they exist in
the objects just as we conceive them to exist ; and they are said
to be eminently in the objects, when they do not really exist as we
conceive them, but when they are so great that their excellence
makes up . for this defect.' Reponses aux Deuxiemes Objections.
Raisons qui prouvent I' existence de Dieu, iii. and iv., cf. note on this
distinction in Veitch's Translation of Descartes. 'Formally' as opposed
to 'objectively' is almost equivalent to our ' objectively' (as opposed to
1 subjectively ') or ' really ' (as opposed to ' in idea '). As opposed
to eminently, formally is secundum eandem formam et rationem, while
eminently is gradu or modo eminentiori.

62 That is to say, all particular things are connected together
in one system, which implies one principle, one necessary
substance, one God. The argument is not merely from the
existence of order in the world to the existence of an intelligence
which produces this order, but from the fact that the whole forms
one system to the existence of one ultimate sufficient reason of the
whole. Otherwise there might be various ' orders ' or ' disorders '
in conflict with one another, each pre-supposing its own first
principle or ' God/ This is Leibniz's form of the Cosmological
proof of the existence of God.

63 l Universal ' in the sense of being equally the cause or first
principle of all things. The whole spirit of Leibniz's philosophy is
opposed to the supposition of a universal substance or spirit, of
which all particular substances are merely modes. Thus in the
Considerations sur la Doctrine d'un Esprit Universel (1702) he endeavours
to refute the view that ' there is but one spirit, which is universal
and which animates the whole universe and all its parts, each
according to its structure and according to the organs it possesses,
as the same blast of wind produces a variety of sounds from
different organ-pipes ' or that ' the universal spirit is like an ocean
composed of an infinite number of drops, which are separated from
it when they animate some particular organic body and which are
reunited with their ocean after the destruction of the organism.'
This is 'the view of Spinoza and of other similar authors, who will
have it that there is only one substance, viz. God, who thinks,
believes and wills one thing in me, and who thinks, believes and
wills quite the opposite in some one else — an opinion the absurdity

240 THE MONADOLOGY

side of it being independent of it, — this substance, which
is a pure sequence of possible being, must be illimitable
and must contain as much reality as is possible 64.

\iy Whence it follows that God is absolutely perfect ;
for perfection is nothing but amount of positive reality,
in the strict sense, leaving out of account the limits or
bounds in things which are limited. And where there
are no bounds, that is to say in God, perfection is abso-
lutely infinite. (Theod. 22, Pref. [E. 469 a; G. vi. 27].)

/4?. It follows also that created beings derive their
perfections from the influence of God, but that their
imperfections come from their own nature, which is
incapable of being without limits. For it is in this that
they differ from God65. An instance of this original
imperfection of created beings may be seen in the natural
imrtia of bodies 66. (Theod. 20, 27-30, 153, 167, 377 sqq.)

of which M. Bayle has well shown in several places in his
dictionary' (E. 178 a, 181 b, 182 a ; G. vi. 529, 535, 537).

64 As God is the sufficient reason of all, nothing is independent
of Him. But if His possibility were in any way limited, it must
be by some possibility outside and independent of Him. Con-
sequently His possibility cannot be limited. And unlimited possi-
bility means unlimited reality and unlimited existence. For that
which is possible must be real, unless there is something else with
which it is not compossible, that is to say, unless there is some other
possible thing, whose nature limits it. Cf. § 54 and Introduction,
Part ii. p. 63. The argument in this and the following sections
will become clear if we keep in view the idea which Leibniz seeks
constantly to emphasize in every department of thought, namely
that possibility or potentiality is never a mere empty capacity,
a tabula rasa, a potentia nuda, but always, in however small a degree,
a tendency to realization, which is kept back only by other similar
tendencies. This is what is meant by the 'claims' and 'aspirations'
of the Monads, mentioned in §§ 51 and 54.

65 Created beings must be essentially limited ; otherwise they
would not be created, but would be identical with God. In the
Theodice'e Leibniz (following the Scholastic principle, ton-urn habet
causam efficientem, malum autem deficientem), uses this as a hypothesis
by which to remove from God the responsibility for the existence
of evil. The origin of evil is the essential imperfection of created
substances ; and God is the cause only of the perfection or positive
reality of created things.

66 This sentence is not given by E. It seems to have been added

THE MONADOLOGY 24!

43. It is farther true that in God there is not only the
source of existences but also that of essences, in so far as
they are real, that is to say, the source of what is real in
the possible67. For the understanding of God is the
region of eternal truths or of the ideas on which they
depend 68, and without Him there would be nothing real
in the possibilities of things, and not only would there
be nothing in existence, but nothing would even be
possible. (Theod. 20.)

by Leibniz in revising the first copy of the Monadology. G. gives it
in a foot-note. The natural inertia of a body is its passivity or
that in it which limits its activity. So far as the passivity of the
body is real (i.e. not a mere appearance to us), it consists of confused
perception. But God is adits purus, entirely without passivity, and
His perceptions are all perfectly clear and distinct.

67 That is to say, God is not only the source of all actual existence,
but also the source of all potential existence, of all that tends to
exist. 'What is real in the possible ' is its tendency to exist. In
a sense, 'essences' or 'possible' things are independent of God.
He does not create them as essences. They are the objects of His
understanding, and ' He is not the author of His own under-
standing' (Theodicee, §380; E. 614 b ; G. vi. 341^ The nature _of
essences or^possibiljties is determined solely by thejgrinciple ^)f
contradiction. And yet, in another sense, they may be said to be
dependent upon God, Inasmuch as they are all expressions of His
nature in one or another aspect or with particular limitations.
His freedom, however, extends only to a choice of those which
shall actually exist, and this choice is determined by His wisdom
and His goodness, having regard to the nature of the ' essences '
themselves. 'Without Him there would be nothing in existence,'
for the existence of things is the result of His will, His choice.
'Without Him nothing would be possible' for all that is possible
is the object of His understanding, and as His understanding is
perfect (i.e. entirely free from confusion in its perceptions), its
object must be the ultimate nature of things, that is, the very
essence of God Himself. Thus in § 44 Leibniz practically identifies
'essences' or 'possibilities' with 'eternal truths.' Cf. Introduction,
Part ii. p. 66.

68 Leibniz connects this part of his system with Plato's world
of ideas. He mentions as one of the ' many most excellent doctrines
of Plato' that 'there is in the Divine mind an intelligible world,
which I also am wont to call the region of ideas.' Epistola ad
Hanschium (1707% E. 445 b.

R

242 THE MONADOLOGY

44. For 69 if there is a reality in essences or possibilities,
or rather in eternal truths, this reality must needs be
founded in something existing and actual, and conse-
quently in the existence of the necessary Being, in whom
essence involves existence, or in whom to be possible is
to be actual70. (Theod. "184-189, 335.)

45. Thus God alone (or the necessary Being) has this
prerogative that He must necessarily exist, if He is pos-
sible. And as nothing can interfere 'with the possibility
of that which involves no limits, no negation and conse-
quently no contradiction, this [His possibility] is sufficient
of itself to make known the existence of God a priori
We have thus proved it, through the reality of eternal
truths. But a little while ago 71 we proved it also a poste-
riori, since there exist contingent beings, which can have
their final or sufficient reason only in the necessary Being,
which has the reason of its existence in itself.

46. We must not, however, imagine, as some do, that
eternal truths, being dependent on God, are arbitraiy
and depend on His will, as Descartes 72, and afterwards

69 G. reads car, E. cependant.

70 See Appendix G, p. 274. 7l §§ 36-39-

72 Cf. Descartes, Lettre au Pere Mersenne (Cousin's ed., vol. vi.
p. 109). * The metaphysical truths which you call eternal have been
established by God and are entirely dependent upon Him, like
all other created things. Indeed, to say that these truths are
independent of God is to speak of God as a Jupiter or a Saturn and
to subject Him to Styx and the Fates. . . . God has established
these laws in nature, just as a king establishes laws in his
kingdom.' Cf. loc. cit., p. 103. ' We cannot without blasphemy say
that the truth of anything precedes the knowledge which God has
of it, for in God willing and knowing are one.' Elsewhere he says
that God was perfectly free to make it untrue that the three angles
of a triangle should be equal to two right-angles. As early as 1671.
in a letter to Honoratus Fabri, Leibniz writes : ' If truths and the
natures of things are dependent on the choice of God, I do not see
how knowledge [scientia] or even will can be attributed to Him.
For will certainly presupposes some understanding, since no one
can will except in view of some good [sub ratione from']. But under-
standing presupposes something that can be understood, that is
to say, some nature. But if all natures are the result of will.

THE MONADOLOGY 243

M. Poiret73, appear to have held. That is true only of
contingent truths, of which the principle is fitness [con-
venance] 74 or choice of the best, whereas necessary truths ;
depend solely on His understanding and are its inner
object. (Theod. 180-184, 185, 335, 351, 380.)

47. Thus God alone is the primary unity or original
simple substance, of which all created or derivative
Monads are products and have their birth, so to speak,
through continual fulgurations 75 of the Divinity from

understanding also will be the result of will. How, then, does
will presuppose understanding?' (G. iv. 259). The point was
much discussed by the Scholastics, with special reference to the
question whether or not the moral law is independent of the will
of God. Descartes's view is in harmony with that of Duns Scotus,
while Leibniz follows Thomas Aquinas. For Descartes, the Divine
and the human understanding differ in kind : for Leibniz they
differ merely in degree.

73 Pierre Poiret (1646-1719), a Calvinist minister, who held
a charge in the Duchy of Zweibriicken, in the Ehine Palatinate.
He was at first a Cartesian and published a book, Cogitatioms
rationales de Deo, Anima et Malo, which Bayle attacked. Afterwards
he came under the influence of Antoinette Bourignon, the Dutch
religious enthusiast, whose life he wrote and whose views he
expounded at very great length. This influence led him to
attack Cartesianism with much fervour, and he is now remembered
as a mystic rather than as a philosopher.

74 By convenance is meant mutual conformity, of such a kind that
things ' fit into ' one another in the most perfect way. Thus the
principle of convenance or of the best is what we should now call
the idea of system. With Leibniz it is the same as the principle
of sufficient reason, which is the principle of conditioned, as distinct
from unconditional reality or truth. Cf. note 85.

'5 That is to say, ' flashings ' or 'sudden emanations/ ' God is the
primary centre from which all else emanates' (G. iv. 553). Cf. the
Stoic rovos which Cleanthes calls a ' stroke of fire ' (71X7777) -nvpos\
Frag. 76. The relation of God to the other Monads is the crux of
Leibniz's philosophy. He wishes to maintain both the individuality
of the Monads and their essential unity with God. Thus he seems
to take fulguration as a middle term between creation and emana-
tion. ' Creation ' would mean too complete a severance between God
and the other Monads ; ' emanation ' would mean too complete an
identity between them. ' Fulguration ' means that the Monad is
not absolutely created out of nothing nor, on the other hand,
merely a mode or an absolutely necessary product of the Divine

K 2

244 THE MONADOLOGY

moment to moment, limited by the receptivity of the
created being, of whose essence it is to have limits. (Theod.
382-391, 398, 395.)

48. In God there is Power, which is the source of all,
also Knoivledge, whose content is the variety of the ideas,
and nnally Will, which makes changes or products
according to the principle of the best76. (Theod. 7, 149,

nature, but that it is a possibility tending to realize itself, yet
requiring the assistance, choice or will of God to set it free from
the counteracting influence of opposite possibilities. As a possibility
it has essential limits (i. e. it is not entirely perfect, actus purus) ;
but it is ready to spring or ' flash ' into being, at the will of God.
If there were no choice of God, possibilities would simply counteract
one another. But His choice means no more than the removal of
hindrances to development, in the case of certain 'elect* possi-
bilities. Creation adds no new being to the universe, and yet it
is not emanation, in the sense of a mere modification of the one
Eternal Being. Thus the ' continual fulgurations ' of Leibniz
are to be distinguished from the ' continual creation ' of Descartes.
According to Leibniz, conservation is not, as with Descartes,
a miraculous renewal of the existence of things from moment
to moment, an absolute re-creation constantly repeated ; but it is
the continuance of the activity, choice or .will of God, by which
certain possible things were set free to exist and through which
alone they can persist. The successive states of any being are
neither completely independent of one another, so that at each
moment there is a new creation (Descartes), nor are they so
absolutely dependent on one another that each proceeds from its
predecessor by a logical or mathematical necessity (Spinoza), but
they are connected together in a sequence which has its ground
in the nature of the being, so that each is automatically unfolded
from its predecessor according to a regular law, provided that God
chooses to allow this unfolding. The * continual fulgurations ' are
the continual exercise of God's will in allowing the Monads of the
actual world to unfold or develop their nature. Cf. On the ultimate
Origination of Things, p. 344.

76 In the Theodicee (§ 150 ; E. 549 a ; G. vi. 199) Leibniz hints at
a connexion between this characterization of God's nature and the
doctrine of the Trinity. ' Some have even thought that there is in
these three perfections of God a hidden reference to the Holy
Trinity : that power has reference to the Father, that is to say, to
the Godhead [Divinite] ; wisdom to the eternal Word, which is
called Ao-yos by the most sublime of the evangelists ; and will or
love to the Holy Spirit.'

THE MONADOLOGY 245

150.) These characteristics correspond to what in the
created Monads forms the ground or basis 77, to the faculty
of Perception and to the faculty of Appetition. But in God
these attributes are absolutely infinite or perfect ; and in
the created Monads or the Entelechies (or perfectihabiae,
as Hermolaus Barbarus translated the word 78) there are .
only imitations of these attributes, according to the degree
of perfection of the Monad. (Theod. "87.)

49. A created thing is said to act outwardly 79 in so far
I as it has perfection, and to suffer [or be passive, pdtir] in

relation to another, in so far as it is imperfect. Thus
activity [action] is attributed to a Monad, in so far as it has
distinct perceptions, and passivity [passion] in so far as its
perceptions are confused. (Theod. 32, 66, 386.)

50. And one created thing is more perfect than another,
in this, that there is found in the more perfect that which
serves to explain a priori what takes place in the less
perfect, and it is on this account that the former is said to
act upon the latter 80.

77 Leibniz does not elsewhere discriminate three elements in the
created Monad, and we must not suppose that the 'ground or
basis' is anything in itself, apart from the two 'faculties.' Leibniz
wishes to emphasize the view that the Monad, whether created
or uncreated, is essentially force or activity, manifesting itself -in
perception and appetition.

78 perfectihabia (from perfecte and habeo} was formed to correspond
to evT(\fxfta (from cfrcAcDs and exftv)' Cf. note 32. Hermolaus
Barbarus or Ermolao Barbaro (1454-1493) was an Italian scholar
who endeavoured, by means of translations of Aristotle and of the
Aristotelian commentaries of Themistius, to make known the true
Aristotelian doctrine as against the degenerate forms which
Scholasticism had given it. He came of a Venetian family and
was Professor of Philosophy at Padua, where he lectured on
Aristotle's Ethics.

79 Of course, no Monad really does act outside itself. This is
merely Leibniz's explanation of what we mean when we speak of
outward action, just as the Copernican system explains what we
mean when we speak of ' sunrise ' and { sunset/ though the sun
neither ' rises ' nor ' sets.'

80 Thus the explanation or reason of an event is its actual cause.
This connects itself with Leibniz's view that the existence of

246 THE MONADOLOGY

51. But in simple substances the influence of one
Monad upon another is only ideal, and it can have its
effect only through the mediation of God, in _so_far_as in
the ideas of God any Monad rightly claims that God, in
regulating the others from the beginning of things, should
have regard to it. For since one created Monad cannot
have any physical influence upon the inner being of
another, it is only by this means that the one can be
dependent upon the other 81. (Theod. 9, 54, 65, 66, 201.
Abrege. Object. 3.^

52. Accordingly, among created things, activities and
passivities are mutual. For God, comparing two simple
substances, finds in each reasons which oblige Him to
adapt the other to it 82, and consequently what is active in
certain respects is passive from another point of view 83 ;

a thing arises solely from the liberating of its essential activities,
and that the Monads claim existence in proportion to their per-
fection, that is to say, to the distinctness of their perceptions.
Cause and effect are relative : every created Monad is both at
once. God alone is pure cause or reason (actus purus). Cause =
relative activity = relative distinctness of perception. This may
instructively be compared and contrasted with the views of
Berkeley and Hume regarding cause and 'necessary connexion.'
See Introduction. Part iii. p. 105. Cf. also Spinoza, Ethics, Part iii.
Def. i and 2, and Prop, i, 2 and 3.

81 We have here the principle of the Pre-established Harmony
(further referred to in §§ 80 and 81). It is a harmony or mutual
compatibility in the very nature of things, anterior to their
creation. Its perfection in the actual world is the ground of God's
choice of that world ; and thus it is not in any sense a created
harmony. In this respect it differs from every form of Occa-
sionalism. See Introduction, Part ii. pp. 39 sqq.

82 No two simple substances are exactly the same, yet all represent
the same universe. Therefore a perception which is comparatively
distinct in one must be comparatively confused in another or
others, and whatever changes take place in one must be accom-
panied by corresponding changes in the others. Thus each fits
into the others.

63 Leibniz's expression here is point de consideration. But he
generally uses the phrase point de vue, which he introduced as
a regular term in philosophical literature. It need hardly be
remarked that the term has a peculiar importance in Leibniz's
philosophy.

THE MONADOLOGY 247

active in so far as what we distinctly know in it serves to
explain [rendre raison de] what takes place in another, and
passive in so far as the explanation [raison] of what takes
place in it is to be found in that which is distinctly known
in another. (Theod. 66.)

53. Now, as in the Ideas of God there is an infinite
number of possible universes, and as only one of them
can be actual, there must be a sufficient reason for the
choice of God, which leads Him to decide upon one rather •
than another84. (Theod. 8, 10, 44, 173, 196 sqq., 225,
414-416.)

54. And this reason can be found only in the fitness
[convenance], or in the degrees of perfection, that these
worlds possess 85, since each possible thing has the right
to aspire to existence in proportion to the amount of per-
fection rTWlfckainsW germ86. (Theod. 74, 167, 350, 201,

130, 352, 345 »qq., 354.)

84 See Introduction, Part ii. p. 65.

85 See Monadology, note 74. God is not compelled by an absolute,
metaphysical necessity, but ' inclined ' by a moral necessity to create
the world which, as one harmonious system, is the best. The
distinction between moral necessity and absolute compulsion is of
Scholastic origin. ' Possible things are those which do not involve
a contradiction. Actual things are nothing but the possible things
which, all things considered, are the best. Therefore things which
are less perfect are not on that account impossible ; for we must
distinguish between the things which God can do and those He
wills to do. He can do everything, He wills to do the best.'
Epistola ad Bernoullium (1699), (G. Math. iii. 574).

86 This aspiration to existence is the tendency to pass into
existence and to proceed from confused to distinct perceptions,
which makes the 'possible* things of Leibniz real essences as
distinct from purely indeterminate capacities. Possibilities, accord-
ing to Leibniz, are never quite empty : they are always realities in
germ. Of. notes 64 and 67. ' From the very fact that there exists
something rather than nothing, we must recognize that in possible
things, or in possibility or essence itself, there is a certain need of
existence [exigentiam existentiae] or (so to speak) a certain aspiration
to exist, and, in a word, that essence by itself tends to existence.
Whence it further follows that all possible things, i. e. things
expressing essence or possible reality, tend with equal right to
existence in proportion to the quantity of essence or reality they

248 THE MONADOLOGY

55. Thus the actual existence of the best that wisdom
makes known to God is due to this, that His goodness
makes Him choose it, and His power makes Him produce
it87. (Theod. 8, 78, 80, 84, 119, 204, 206, 208. Abregt.
Object, i and 8.)

56. Now this connexion or adaptation of all created
things to each and of each to all, means that each simple
substance has relations which express all the others, and,
consequently, that it is a perpetual living mirror of the
universe88. (Theod. 130, 360.)

57. And as the same town, looked at from various sides,
appears quite different and becomes as it were numerous
in aspects [perspectivement] ; even so, as a result of the
infinite number of simple substances, it is as if there
were so many different universes, which, nevertheless are
nothing but aspects [perspectives] of a single universe,
according to the special point of view of each Monad 89.
(Theod. 147.)

. contain or to their degree of perfection ; for perfection is nothing
but quantity of essence.' Ultimate Origination of Things, p. 340.

87 This section states briefly the principles of Leibniz's Optimism,
•which are fully expounded and defended in the Theodicee. A world
entirely free from evil would be indistinguishable from God
Himself. The evil of the world arises entirely from the essential
limitations of created things — their limitations as essences or
possibilities. Consequently evil is not created by God ; but He
creates the universe in which there is the least amount of evil that
is possible in any system of things.

88 Cf. Nicholas of Cusa, Dialogi de ludo gloli (1454-59% i- J57 a :
' The whole is reflected in all the parts ; all things keep their own
relation [habitudo] and proportion to the universe.' Also De docta
ignorantia (1440), i. n : ' Visible things are images of the invisible,
and the Creator can be seen and known by the creatures as in
a mirror darkly [quasi in speculo et aenigmate].'

89 The ' point of view ' of each Monad is its body. But we must
not give a spatial meaning to the expression, as if the Monad's
point of view depended on its having this or that position in
space. For the Monad is absolutely non-spatial, and the nature of
its body depends on the degree of confusedness (or distinctness)
of its perceptions. Thus to say that the body is the point of view
of the soul means simply that the particular way in which the soul
represents or perceives the universe is determined by the degree

THE MONADOLOGY 249

58. And by this means there is obtained as great
variety as possible, along with the greatest possible order ;
that is to say, it is the way to get as much perfection as
possible90. (TJieod. 120, 124, 241 sqq., 214, 243, 275.)

59. Besides, no hypothesis but this (which I venture to
call proved) fittingly exalts the greatness of God ; and
this Monsieur Bayle recognized when, in his Dictionary
(article Eorarius*1}, he raised objections to it, in which

of distinctness of its perceptions. Cf. Theodicee, § 357 (E. 607 b ;
G. vi. 327). ' The projections of perspective, which, in the case of
the circle, are the same as the Conic Sections, show that one and
the same circle can be represented by an ellipse, by a parabola
and by a hyperbola, and even by another circle, by a straight line
and by a point. Nothing seems more different, nothing more
unlike, than these figures ; and yet there is an exact relation
between them, point for point. Thus it must be recognized that
each soul represents to itself the universe, according to its point of
view and by a relation peculiar to itself; but in this there always
continues to be a perfect harmony.'

90 For Leibniz the highest perfection is the most complete unity
or order in the greatest variety. The Monads have the most
complete unity, because the essence of each consists in representing
the same universe, while they have the greatest variety, because
the points of view from which they represent it are infinitely
various. ' For a world to be possible, it is enough that it should
have intelligibility ; but in order to exist it must have a pre-
eminence [prevalence] in intelligibility or order ; for there is order in
proportion as there is much to distinguish in a manifold [multitude].'
Lettre a Bourguet (1712 ?) (E. 718 b ; G. iii. 558).

91 See note 29. Bayle compares Leibniz's theory to the sup-
position that a ship might be constructed of such a kind that
entirely by itself, without captain or crew, it could sail from place
to place for years on end, accommodating itself to varying winds,
avoiding shoals, casting and weighing anchor, seeking a haven
when necessary and doing all that a normal ship can. He admits
that the omnipotence of God could give such a power to a ship, biit
he maintains that the nature of the ship would make it impossible
for it to receive such a power. And ' however infinite be the
knowledge and power of God, He cannot, by means of a machine
which lacks a certain part, do that which requires the help of that
part.' Thus Bayle argues against the possibility of complete
spontaneity in the Monads, and consequently maintains that the
Deus ex machina is involved in Leibniz's Pre-established Harmony
quite as much as in Occasionalism.

250 THE MONADOLOGY

indeed he was inclined to think that I was attributing too
much to God— more than it is possible to attribute. But
he was unable to give any reason which could show the
impossibility of this universal harmony, according to
which every substance exactly expresses all others through
the relations it has with them.

60. Further, in what I have just said there may be
seen the reasons a priori why things could not be other-
wise than they are. For God in regulating the whole has
had regard 92 to each part, and in particular to each Monad,
whose nature being to represent, nothing can confine it to
the representing of only one part of things ; though it is
true that this representation is merely confused as regards
the variety of particular things \le detail] in the whole
universe, and can be distinct only as regards a small part
of things, namely, those which are either nearest or
greatest93 in relation to each of the Monads; otherwise
each Monad would be a deity. It is not as regards their
object, but as regards the different ways in which they
have knowledge of their object, that the Monads are
limited 94. In a confused way they all strive after
[vont a] the infinite, the whole 95 ; but they are limited
and differentiated through the degrees of their distinct
perceptions.

6 1. And compounds are in this respect analogous with

92 So G. E. reads ' has a regard ' [a un egard].

>3 If the Monads are non-spatial, how can we speak of anything
being nearest or greatest in relation to a Monad ? Every Monad
has a body of some kind and this body is confusedly perceived as
spatial in itself and in relation to other bodies, though really it is
nothing but an aggregate of non-spatial Monads. When therefore
it is said that certain things are near or great in relation to
a Monad, what is meant is that they are near or great in relation
to the body of the Monad.

94 That is to say, thought in the widest sense, conscious or un-
conscious, is limited only by itself : there can be nothing that is
not an object of thought, more or less adequate. Contrast with
this the position of Kant. See Introduction, Part iv, pp. 178 sqq.

95 Cf. Nicholas of Cusa, Dialogus de Genesi (1447) 72 b : 'All
things seek the same, which is something absolute.'

THE MONADOLOGY 251

[symbolisent avec %] simple substances. For all is a plenum
(and thus all matter is connected together) and in the
plenum every motion has an effect upon distant bodies in
proportion to their distance, so that each body not only is
affected by those which are in contact with it and in some
way feels the effect of eveiything that happens to them,
but also is mediately affected by bodies adjoining those
with which it itself is in immediate contact. Wherefore
it follows that this inter-communication of things extends
to any distance, however great. And consequently every
body feels the effect of all that takes place in the uni-
verse, so that he who sees all might read in each what is
happening everywhere, and even what has happened or
shall happen, observing in the present that which is
far off as well in time as in place : o-v/zTrvoca Travra, as
Hippocrates said 97. But a soul can read in itself only

9(5 The expression ' symbolize ' suggests the ' calculus ' idea which'
is so continually in Leibniz's mind. As numbers are symbols of
the things numbered, and we make accurate calculations without
referring at every step to the particular things for which our
symbols stand, so in general unanalyzed thoughts may be symbols
of their simple elements. In the same way compound things are
symbols of the simple substances which compose them. What is
perceived confusedly in compounds is not a mere illusion but an
imperfect representation or symbol of the real characteristics of
simple substances. Thus, in this section, Leibniz would say that
the spatial or material plenum (which is a confused perception of
ours) is a symbol of the infinite (or perfectly complete) series of
Monads, which has no gaps, since the Monads differ from one
another by infinitely small degrees. Similarly, the material action
and re-action throughout the universe, such that a change at any
one point affects every other, is a symbol of the Pre-established
Harmony among the Monads. And, again, the fact that every-
thing that happens, has happened or shall happen in the universe
might be read in any one body is a symbol of the representative
character of each Monad as ideally containing the whole within
itself. It is because they are thus symbolic that the phenomena
of the material world are phenomena benefundata.

97 'Svpirvota (the noun) is probably a corruption from ovpirvoa (the
adjective), ' in agreement,' lit. ' breathing together/ conspirantia.
Leibniz makes the same quotation in the New Essays, Introduction,
p. 373. He there translates the phrase by the words 'tout est

252 THE MONADOLOGY

that which is there represented distinctly ; it cannot all at
once unroll everything that is enfolded in it98, for its
complexity is infinite".

The mistake may be due to an imperfect recollection
of the phrase in Hippocrates : £vppoia /Ja, ^v^irvoia juia, £vp.TraOta
iravra. (De Alimento, 4, Littre, (Euvres d'Hippocrate, vol. ix. p. 106).
Cf. Plutarch, De fato, 574 E : TO <f>va(t oioineiaOat rovftf rov nuapov
avfiirvovv, Kal avfjuraBfj, avrbv avrw ovra, For a later statement of the
same position, see Fichte, Werke, ii. 178 sqq. 'In every moment
of her duration, nature is one connected whole : in every moment
each part must be what it is, because all the others are what they
are. . . . You cannot conceive even the position of a grain of sand
other than it is in the present without being compelled to conceive
the whole indefinite past as having been other than it has been,
and the whole indefinite future other than it will be. ... I am
what I am because in this conjuncture of the great whole of nature
only such, and no other, was possible ; and a spirit who could look
through the secrets of nature would, from knowing one single man,
be able distinctly to declare what men had formerly existed and
what men would exist at any future moment ; in one individual he
would cognize all real individuals. My connexion, then, with the
whole of nature is that which determines what I have been, am,
and shall be, and the same spirit would be able, from any possible
moment of my existence, to discover infallibly what I had been
and what I was to become.' [Trans, by Prof. Adamson, Philosophy
of Kant ', p. 221.]

98 E. reads ses regies: G. reads sesreplis. The latter phrase is used
in the Principles of Nature and of Grace, § 13.

y9 Cf. Leibnitiana, Dutens, vol. vi. Part i. p. 332. ' I admit that
after death we do not at first remember what we were, for this is
neither naturally right nor in accordance with the fitness of things
[ni propre ni bienseant dans la nature]. Nevertheless I believe that
whatever has once happened to the soul is eternally imprinted
upon it, although it does not at all times come back to us in
memory ; just as we know a number of things which we do not
always recollect, unless something suggests them and makes us
think aboxit them. For who can remember all things ? But since
in nature nothing is futile and nothing is lost, but everything
tends to perfection and maturity, each image our soul receives will
ultimately become one [un tout] with the things which are to come,
so that we shall be able to see all as in a mirror and thence to
derive that which we shall find to be more fitted to satisfy us.
Whence it follows that the more virtuous we have been and the
more good deeds we have done, the more shall we have of joy and
satisfaction.'

•

, ^^L^^ .

THE MONADOLOGY 253

62. Thus, although each created Monad represents the
whole universe, it represents more distinctly the body
which specially pertains to it, and of which it is the
entelechy100;land as this body expresses the whole uni-
verse through the connexion of all matter in the plenum, j[
the soul also represents the whole universe in representing

this body, which belongs to it in a special way. (Theod.

400.)

63. The body belonging to a Monad (which is its
entelechy or its soul) constitutes along with the ente-
lechy what may be called a living being, and along with
the soul what is called an animal 10LH Now this body of
a living being or of an animal is always organic ; for, as
every Monad is, in its own way, a mirror of the universe,
and as the universe is ruled according to a perfect order,

' there must also be order in that which represents it, i. e.
in the perceptions of the soul, and consequently there
must be order in the body, through which the universe
is represented in the soul 102. ^(Theod. 403.)

100 See note 32. The entelechy or soul is at once the final cause
of the body and the power which controls it or the force which
acts through it. As dominant Monad, the soul has more clearly
the perceptions which are relatively confused in the Monads
implied by the body. The soul is thus relatively the perfection of
the body. And similarly, in the soul is to be read the reason
(i. e. the distinct perception) of what takes place in the body, and
it is therefore the activity or force of the body. Cf. Introduction,
Part iii. p. no.

101 See § 19. Leibniz uses the term living being not as including
all beings which have life, but specifically with reference only to
those whose dominant Monad is unconscious, while in the animal
(as distinct from the living 'being') the dominant Monad has con-
sciousness and memory.

102 Thus order and organism are conceived by Leibniz under the
idea of an infinite series of elements, each differing from its
neighbour to an infinitely small extent. The Monad-series of the
universe, extending from God to the lowest of Monads, is reflected
in the structure of the individual organism, extending from the
dominant Monad downwards, and that again is reflected in the
series of perceptions within each Monad itself, extending from
the most distinct perceptions to which it has attained down to the
most obscure.

254 THE MONADOLOGY

64. Thus the organic body of each living being is a kind
of divine machine or natural automaton, which infinitely
surpasses all artificial automata. For a machine made by
the skill of man is not a machine103 in each of its parts.
For instance, the tooth of a brass wheel has parts or
fragments which for us are not artificial products, and
which do not have the special characteristics of the
machine, for they give no indication of the use for which
the wheel was intended. But the machines of nature,
namely, living bodies, are still machines in their smallest
parts ad infinitum 10*. It is this that constitutes the dif-

103 i. e. not a machine made by man. From another point of view,
as a product of nature, it is (as this section says) a machine in its
smallest parts, for in reality all bodies are living bodies. Thus the
words ' for us ' in the next sentence of this section were added by
Leibniz in a revision of his original manuscript, evidently in order
to suggest that while the fragments of the wheel are not products
of ' human art,' they are yet products of ' divine art.'

104 Cf. Lettre a M. Vfctiqw de Meaiix (Bossuet) (1692), (Foucher de
Careil, i. 277 ; Dutens, i. 531). ' The machines of nature are
machines throughout, however small a part of them we take ; or
rather the least part is itself an infinite world, which even
expresses in its own way all that there is in the rest of the
universe. That passes our imagination, yet we know that it must
be so ; and all that infinitely infinite variety is animated in all its
parts by a constructive [architectonique] wisdom that is more than
infinite. It may be said that there is Harmony, Geometry, Meta-
physics, and, so to speak, Ethics [morale] everywhere, and (what
is surprising) in one sense each substance acts spontaneously as
independent of all other created things, while in another sense, all
others compel it to adapt itself to them ; so that it may be said
that all nature is full of miracles, but miracles of reason, miracles
which become miracles in virtue of their being rational, in a way
which amazes us. For the reasons of things follow one another in
an infinite succession [s't/ pousse a un progres infini\ so that our
mind while it sees that things must be so, cannot follow so as to
comprehend. Formerly people admired nature without in any
way understanding it, and that was supposed to be the right
thing to do. Latterly they have begun to think nature so easy to
understand that they have developed a contempt for it, and some
of the new philosophers even encourage themselves in idleness by
imagining that they know enough about nature already.' See also
Introduction, Part iii. p. 108.

THE MONADOLOGY 255

ference between nature and art, that is to say, between the
divine art and ours 105. (Theod. 134, 146, 194, 403.)

65. And the Author of nature has been able to employ
this divine and infinitely wonderful power of art, because
each portion of matter is not only infinitely divisible, as
the ancients observed 106, but is also actually subdivided
without end 107, each part into further parts, of which

103 Cf. Nicholas of Cusa, Idiotae Libri quatuor, iii. 2, 82 a. 'Humanae
artes imagines Divinae arils'

106 See Aristotle, Phys., Z, 9, 23gb 5. Ov yap avyKfirai 6 xpovos (tc
TU>V vvv a.8iaip(TQJv, uancp ov8' d\Xo yw€-y60o? ovSev. Cf. Phys., Z, I, 23 ib
18 ; Z, 4 (TO Se neral3a\\ov airav avayfcr) Siaipcrov fivai) ; De Caelo, T, I,
298b 33. See also Bayle's Dictionary, article ' Zeno,' notes F and G.

107 Cf. Reponse a la Uttre de M. Foucher (1693), (E. 118 b. ; G. i.
416). ' There is no part of matter which is not, I do not say
divisible, but actually divided ; and consequently the smallest
particle must be considered as a world filled with an infinity of
different creatures.' The paradox in such statements as these
arises from the way in which Leibniz speaks of matter as composed
of non-spatial elements. Leibniz regards matter as a mere aggregate
and as therefore not itself a real substance. But he never explains
what he means by an aggregate of Monads, each of which is non-
quantitative. Again it may be asked whether a real whole can
consist of an infinite number of real parts ? Does not infinite
divisibility mean that it is impossible to bring to an end the
enumeration of parts, because the relation of whole to parts is so
indefinite that we have no means of determining what exactly
is a part? Thus the -term 'infinite' here means that the process
of division is one which can never be completed. Consequently
it seems self-contradictory to speak of things as 'actually sub-
divided without end' or infinitely. (Cf. Kant's Critique of Pure
Reason, First and Second Antinomies. See also Bosanquet's Logic,
vol. i. pp. 172 sqq.) It was Euler, the mathematician, who first
brought this criticism against Leibniz, saying that the existence
of units in the shape of Monads implies the finite divisibility of
matter, while Leibniz at the same time maintains its infinite
divisibility. (Lettres a une Princesse d'Allemagne (1761), Brewster's
Trans , vol. ii. pp. 30 sqq.) Euler's argument is directed mainly
against the Wolffian adaptation of Leibniz's position. Leibniz
might reply that matter as infinitely divisible, is a mere pheno-
menon, resulting from an actual infinity of real Monads. But
even in this explanation the idea of ' infinite ' seems to be used in
two opposite senses (i) as equivalent to 'incapable of completion,"
(2) as equivalent to ' absolutely complete.'

256 THE MONADOLOGY

each has some motion of its own ; otherwise it would be
impossible for each portion of matter to express the whole
universe 108. (Theod. Prelim., Disc, de la Conform. 70, and

195.)

66. Whence it appears that in the smallest particle of
matter there is a world of creatures, living beings, animals,
entelechies, souls.

67. Each portion of matter may be conceived as like
a garden full of plants and like a pond full of fishes. But
each branch of every plant, each member of every animal,
each drop of its liquid parts is also some such garden or
pond.

68. And though the earth and the air which are between
the plants of the garden, or the water which is between
the fish of the pond, be neither plant nor fish ; yet they
also contain plants and fishes, but mostly so minute as to
be imperceptible to us 109.

108 rj^ « p0r{;ions Of matter,' of which Leibniz here speaks, are
ultimately Monads, each of which must ideally contain the whole
universe. The Monads are infinite in number, and each, as it
ideally contains all, must therefore contain an infinity of ' parts.'
Or the argument which Leibniz implies may be otherwise put
thus : If the ' portions of matter ' are not actually subdivided
without end, there must be ultimate undivided atoms. But such
atoms necessarily imply a void ; they are inconsistent with a plenum.
And unless there is a plenum it is impossible for each portion of
matter to ' express ' or be aifected by all the rest.

109 Leibniz had a deep interest in the remarkable development
of microscopic investigation, which took place during his lifetime.
He frequently refers to the work of Leuwenhoek, the discoverer of
spermatozoa, Swammerdam, the entomologist, and Malpighi, who,
among many other works, made a microscopic study of the physio-
logy of animals and plants. In a Meditation sur la notion commune de
la Justice (Moll at, p. 66), Leibniz says : ' It is very necessary to
advance our microscopical knowledge. Scarce ten men in the world
are earnestly devoted to it ; and though there were a hundred
thousand, they would not be too many for the discovery of the
important wonders of this new world which is the inside of the
world we know and which is capable of making our knowledge
a hundred thousand times as extensive as it is. For this reason
I have often wished that great princes might be led to make
arrangements for this and to support people who would devote

THE MONADOLOGY 257

69. Thus there is nothing fallow, nothing sterile, nothing
dead in the universe, no chaos, no confusion save in
appearance n<?, somewhat as it might appear to be in a pond
at a distance, in which one would see a confused move-
ment and, as it were, a swarming of fish in the pond,
without separately distinguishing the fish themselves.
(Theod. Pref. [E. 475 b; 477 b ; G. vi. 40, 44].)

70. Hence it appears that each living body has a domi-
nant entelechy, which in an animal is the soul ; but the
members of this living body are full of other living beings,
plants, animals, each of which has also its dominant
entelechy or soul ln.

themselves to it.' The view of Leibniz also suggests the cell-
theory of modern physiology ; but the analogy must not be pushed
too far. However numerous, for instance, may be the cells in any
portion of an organism, they are not, like Leibniz's 'portions of
matter,' infinitely subdivided in their turn. In fact, the cell-
theory has in many ways a closer relation to the mechanical view
of things than to the position of Leibniz. See Sandeman, Problems
of Biology, pp. 53 sqq.

110 Cf. Epistola ad Bernoullium (1699) (G. Math. iii. 565) : 'God, out
of the infinite number of possible things, chooses by His wisdom
that which is most fitting. . But it is- evident that if there were
a vacuum (and similarly if there were atoms) there would remain
sterile and fallow places, in which, nevertheless, without prejudice
to any other things, something might have been produced. But
it is not consistent with wisdom that such places should remain.
And I think that there is nothing sterile and fallow in nature,
although many things appear to us to be so.'

111 See Introduction, Part iii. p. in. May not the whole world,
then, be conceived as one body, whose dominant soul is God, the
Monad of Monads ?

'All are but parts of one stupendous whole,
Whose body nature is and God the soul.'

Pope, Essay on Man, Epistle' i. 267.

Yet Leibniz maintains that God has no body. Cf. Monadology, § 72.
The difficulty is a fundamental one. Leibniz repeatedly disclaims
the doctrine of a 'world-soul,' if it is understood as in any way
destroying the independence of individual souls. 'Although a soul
may have a body composed of parts, each of which has a soul of its
own, the soul or form of the whole is not composed of the souls
or forms of the parts.' Lettre a Arnauld (1687) (G. ii. 100).

S

258 THE MONADOLOGY

71. But it must not be imagined, as has been done by
some who have misunderstood my thought, that each soul
has a quantity or portion of matter belonging exclusively
to itself or attached to it for ever112, and that it conse-
quently owns other inferior living beings, which are
devoted for ever to its service. For all bodies are in a
perpetual flux like rivers ns, and parts are entering into
them and passing out of them continually.

72. Thus thd sottl changes its body only by degrees,
little by little, so that it is never all a^on^ deprived of
all its organs ; and there is often metaniorpnoBis~~in
animals, but never metempsychosis or transmigration of
souls 1U ; nor are there souls entirely separate [from

112 The misunderstanding probably arose from a confusion of
materia prima, the passive element in the individual created Monad,
which is inseparable from the active or soul element, with materia
secunda, the changing body of a compound substance, which is
phenomenal and not perfectly real, although it is founded upon
reality. Cf. Introduction, Part. iii. pp. 95 sqq.

113 The phrase is as old as Heraclitus, who, according to Plato,
' likened things to the flowing of a river/ Cratylus, 402 A. Cf.
Aristotle, Metaph., A, 6, gQ^ 32. See also Burnet, Early Greek Philo-
sophy, p. 149.

114 While soul and body are quite distinct from one another,
their union is of the closest possible kind. Changes in the one
correspond to changes in the other. But as the perceptions of the
soul are clearer and more distinct than those of the body, the
changes in the soul cause or explain the changes in the body.
Transmigration of souls is inconsistent with this, because it means
that the body remains the same, though the soul is changed.
Accordingly, in Leibniz's view, the identity of any individual
substance means 'the preservation of the same soul.' Nouveaux
Essais, bk. ii. ch. 27, § 6. (E. 278 b ; G. v. 216.) He argues against
Locke that identity is not fixed by time and place, and that the
identity of plant, animal, and man does not consist in the possession
of the same organic body. Thus, according to Leibniz, every soul
or entelechy, whether conscious or not, has what he calls 'real and
physical identity ' (i. e. not a derived identity, but an identity
belonging to its own nature, Qvais}, and is, in virtue of this, im-
perishable (incessable], while the self-conscious soul has in addition
a 'personal* or 'moral' identity, in virtue of which it is immortal.
Neither continued consciousness nor memory is essential to the
maintenance of this ' moral ' identity. ' If I were to forget all the

THE MONADOLOGY 259

bodies] nor unembodied spirits [genies sans corps]. God
"alone is completely without body115. (Theod. 90, 124.)

73- It also follows from this that there never is absolute^]
birth [generation] nor complete death, in the strict sense, \
consisting in the separation of the soul from the body, j
What we call births [generations] are developments and j
growths, while what we call deaths are envelopments and /
diminutions.

74. Philosophers have been much perplexed about the
origin of forms116, entelechies, or souls; but nowadays

past, if I had even to be taught anew my own name and how to
read and write, I could always learn from other people my life in,
former times, just as I should still retain my rights, so that it would
not be necessary to divide me into two people and to make me mjr
own heir. No more is required to maintain the moral identity, which
constitutes the same person' (loc. dk, § 9 ; E. 280 b; G. v. 219).
'An immaterial being or a mind [esprit] cannot le deprived of all
perception of its past existence. It retains impressions of all that
has formerly happened to it ; but these feelings are usually too
small to be capable of being distinguished and of being consciously
perceived, although they may perhaps be developed some day.
This continuing and connexion t)f perceptions makes the being really
the same individual, but apperceptions — that is to say, when one is
conscious \s' aperyoit] of past feelings — prove also a moral identity
and make the real identity apparent ' (toe. tit., § 14 ; E. 281 b ;
G. v. 222). Cf. New Essays, Introduction, p. 373.

115 A soul without body (in the sense of materia secunda} would be
a soul without any relation to other Monads. For a compound
substance (i. e. soul and body) consists ultimately in the relation
of a dominant Monad to subordinate Monads. l Creatures free or
freed from matter would at the same time be separated from the-
universal connexion of things, and, as it were, deserters from the
general order.' Considerations sur les Principes de Vie (1705) (E. 432 b ;
G. vi. 546). Again, a soul without body (in the sense of materia prima)
would be a Monad without passivity or confused perception, i. e. it
would be actus purus or God. Kirchmann (Erlauterungen zu Leibniz*
Schriften) dismisses Leibniz's statement as ' a mere assertion, which
indeed does not necessarily follow from Leibniz's own principles/
The difficulty is the same as that mentioned in note in.

116 The form is the life or vital principle in any organic being.
Cf. Lettre a Arnauld (1687) (G. ii. 116) : 'I proceed to the question
of forms or souls, which I hold to be indivisible and indestructible.
Parmenides (of whom Plato speaks with veneration), as well as
Melissus, maintained that there is no generation nor corruption

S 2

260 THE MONADOLOGY

it has become known, through careful studies of plants,
insects, and animals, that the organic bodies of nature are
never products of chaos or putrefaction, but always come
from seeds, in which there was undoubtedly some pre-
formation m ; and it is held that not only the organic

except in appearance : Aristotle mentions this (De Caelo, bk. iii.
ch. 2). And the author of the De Diaeta, bk. i. (which is attributed
to Hippocrates), expressly says that an animal cannot be engendered
absolutely [tout de nouvcau] nor completely [tout a fait] destroyed.
Albeitus Magnus and John Bacon seem to have thought that sub-
stantial forms were already hidden in matter from the beginning
of time. Fernel makes them descend from heaven, to say nothing
of those who regard them as taken off from the soul of the world.
They have all seen a part of the truth ; but they have not developed
it. Several have believed in transmigration, others in the traduc-
tion of souls' [i.e. in the soul of the offspring being as it were
begotten of the soul of the parent] ' instead of transmigration and
the transformation of an animal already formed. Others, not
being able to explain otherwise the origin of forms, have admitted
that they begin in a real creation, but while I allow that this
creation takes place in time only in respect of the rational soul,
and hold that all forms which do not think were created along
with the world, they believe that this creation takes- place every
day when the smallest worm is begotten.' Cf. New System, notes
43 and 44.

117 ' The living [animee] and organic seed is as old as the world.'
Lettre a la Heine Sophie Charlotte (Gr. vi. 517). Immediately before the
time of Leibniz, the origin of life in the individual plant, animal,
or man was explained either by a theory of traduction or by
a theory of eduction. According to the theory of traduction, the
'form' of the offspring comes from the parental 'form' or 'forms'
in the same way as the body of the offspring comes from the parental
body or bodies. According to the theory of eduction, on the other
hand, life comes from inorganic matter, from 'chaos or putrefaction.'
Eduction thus corresponds to what we now call ' spontaneous gene-
ration.' According to the theory of preformation, adopted by
Leibniz, the germ contains in miniature the whole plant or animal,
point for point, and accordingly the ' form * of the plant or animal
exists in the spermatozoon in a contracted or 'enveloped' state, and
it has existed since the beginning of time. For, as we have seen
(§ 65), there is no limit to the smallness of things, and even a sper-
matozoon may contain an indefinite number of other living beings.
This theory of preformation, which was based on the microscopic
investigations of Malpighi and Leuwenhoek, has now been entirely
abandoned, as the result of more thorough observations. Cf. Sande-

THE MONADOLOGY 261

body was already there before conception, but also a soul
in this body, and, in short, the animal itself ; and that by
means of conception this animal has merely been prepared
for the great transformation involved in its becoming an
animal of another kind. Something like this is indeed
seen apart from birth [generation], as when worms become
flies and caterpillars become butterflies. (Theod. 86, 89.
Pref. [E. 475b; G. vi. 4osqq.]; 90, 187, 188, 403, 86, 397.)

75. The animals, of which some are raised by means of
conception to the rank of larger animals, may be called
spermatic, but those among them which are not so raised
but remain in their own kind (that is, the majority) are
born, multiply, and are destroyed 118 like the large animals,
and it is only a few chosen ones [elus] that pass to a greater
theatre.

76. But this is only half of the truth 119, and accordingly

man, Problems of Biology, p. 92. While rejecting traduction in its
ordinary form, Leibniz recognizes its affinity to his own view, which
he describes as ' a kind of traduction, more satisfactory [traitable]
than that which is commonly taught.' Theodicee, § 397 (E. 618 b ;
G. vi. 352).

118 According to Leibniz, they are not entirely, but only ap-
parently destroyed. The statement is made in the form in which
scientific observers of Leibniz's time would have put it, and it is
subject to the qualification made in § 76. Leibniz's point is that,
just as there is a visible world of larger organisms, so there is
a microscopic world of spermatozoa, undergoing in miniature all
the changes which take place in the larger visible world. The
larger organisms of the visible world are certain elect members of
the spermatic world which, ' by means of conception,' have been
enabled to grow from microscopic minuteness to visibility.

119 The scientific observers have only stated half of the truth ;
but Leibniz thinks that they would have no objection to the other
half. '1 think that if this opinion had occurred to them, they
would not have found it absurd, and there is nothing more natural
than to believe that what does not begin does not perish.' Lettre a
Arnauld (1687) (G. ii. 123). Cf. Plato, Phaedrus, 245 D : 'ETTfiSfj 8i
ayevijTov tart, KOI a8ta<pOopov avro avdyrcrj ftvai. Leibniz elsewhere
speaks of the view of Plato ' that the object of wisdom is ra ovrcas
ovra, that is, simple substances, which are called by me ' [Leibniz]
4 Monads, and which once existing always continue to exist, -npura
SfKTiKa rfjs fays, that is, God and souls, and of these the chief are

262 THE MONADOLOGY

I hold that if an animal never comes into being by natural
means [naturellemeni], no more does it come to an end by
natural means ; and that not only will there be no birth
[generation], but also no complete destruction or death in
the strict sense K0. And these reasonings, made a posteriori
and drawn from experience are in perfect agreement with
my principles deduced a priori, as above121. (Tlieod. 90.)

77. Thus it may be said that not only the soul (mirror
of an indestructible universe) is indestructible, but also
the animal itself122, though its mechanism [machine] may
often perish .in part and take off or put on an organic
slough [des depouilles organiques1-5].

/78. These principles have given me a way of explaining
naturally 124 the union or rather the mutual agreement
[conformite] of the soul and the organic body. The soul
follows its own laws, and the body likewise follows its
own laws ; and they agree with each other in virtue of

minds, images of the Deity, produced by God.' Epistola ad Hanschium
(1707) (E. 445 b). This last passage involves a misunderstanding
of Plato's Ideat, which are universals, not Monads. Democritus
calls his atoms TO 6v.

120 ' There is always going on in the animal what goes on in it at
the present moment ; that is, its body is in a continual change, like
a river ; and what we call generation or death is only a greater and
more rapid change than usual, such as would be the leap or cataract
of a river. But these leaps are not absolute and such as I have
refused to admit, as would be that of a body which should go from
one place to another without going through intervening places
[saws passer par le milieu].' Lettre a Remond (1715) (E. 724 a ; G. iii. 635).

121 Monadology, §§ 3, 4, and 5. This endeavour to show the agree-
ment of a priori with a posteriori conclusions is specially characteristic
of Leibniz. It illustrates his belief in the harmony of the physical
with the metaphysical, the mechanical with the dynamical or
final.

123 Because the soul must always have a body of some kind, whicli
itself ultimately consists of imperishable Monads. Animals, how-
ever, are not immortal. Immortality belongs only to rational souls
or self-conscious Monads.

123 ' As a snake casts its old skin.' Lettre a laPrincesse Sophie (1696)
(G. vii. 544).

124 That is, in contrast to the Occasionalist theory, which accord-
ing to Leibniz implies an endless series of miracles.

THE MONADOLOGY 263

the pre-established harmony between all substances, since
they are all representations of one and the same uni-
verse 125. (Pref. [E. 475 a ; G. vi. 39] ; Theod. 340, 352,
353, 358.)

79. Souls act according to the laws of final causes
through appetitions, ends, and means. Bodies act
according to the laws of efficient causes or motions. And
th6 two realms, that of efficient causes and that of final
causes, are in harmony with one another J26.
\J So. Descartes recognized that souls cannot impart any
force to bodies, because there is always the same quantity

125 That is to say, the problem of the connexion between soul and
body is a special case of the wider problem as to the relation of
any one simple substance or Monad to another.

126 They are in harmony, because ultimately the one is reducible
to the other. When it is said that ' souls act,' what is meant is
that they pass from one perception to another, i. e. that they have
appetition. When it is said that l bodies act/ what is meant is
that they change their state or their relation to other bodies, i. e.
that they have motion. What we call the ' state ' of a bod^v and its
1 relations to other bodies ' ought in strictness to be called the
(unconscious^ perceptions of the

And similarly, the ' motion ' of the body is really the (unconscious)
appetition of its constituent Monads. Thus the difference between
efficient a.ind__pna.|_causes, like that between the unconscious and
the conscious, is merely a dmerence ot clegree. Cf. Principles of
Nature and of Grace , § n. / From a psychological point of view,
Leibniz describes the parallelism of soul and body thus : 1 1 have
carefully examined this matter and I have shown that there are
really in the soul some materials of thought or objects of the
understanding, which the external senses do not supply, namely,
the soul itself and its functions (nihil est in intelleciu quod nonfuerit in
sensu, nisi ipse intellectus) . . . but I find nevertheless, that there is
never an abstract thought which is not accompanied by some
material images or marks [traces'], and I have made out a perfect
parallelism between what passes in the soul and what takes place
in matter, having shown that the soul, with its functions, is some-
thing distinct from matter but yet is always accompanied by
material organs, and also that the functions of the soul are always
accompanied by functions of its organs, which must correspond to
them, and that this is and always will be reciprocal.' Considerations
sur la Doctrine d'un Esprit Universel unique (1702) (E. 180 a ; G. vi.
532).

264 THE MONADOLOGY

of force in matter. Nevertheless he was of opinion that
the soul could change the direction of bodies. But that
is because in his time it was not known that there is
a law of nature which affirms also the conservation of the
same total direction in matter 127. Had Descartes noticed
this he would have come upon my system of pre-estab-
lished harmony128. (Pref. [E. 4? 7 a; G. vi. 44] ; Theod.
22, 59, 60, 61, 63, 66, 345, 346 sqq., 354, 355-)
\/8i. According to this system bodies act as if (to
suppose the impossible) there were no souls, and souls
act as if there were no bodies, and both act as if each
influenced the other 129.

127 See Introduction, Part iii. p. 89. Descartes ' believed he had
found a law of nature, to the effect that the same quantity of
motion is conserved in bodies. He did not think it possible for
the influence of the soul to break this law of bodies ; but he thought
that the soul might nevertheless have the power of changing the
direction of the motions which take place in the body ; somewhat
as a horseman, although he does not give any force to the horse he
rides, nevertheless guides it by directing its force in the way that
he thinks right. As this is done by means of bridle, bit, spurs,
and other material aids, we see how it can take place ; but there
are no instruments which the soul could employ for this purpose
— nothing in soul or in body, that is to say, in thought or in mass,
which could serve to explain this change of one by the other.'
Theodicee, § 60 (E. 519 b ; G. vi. 135).

128 That is to say, Descartes would have seen that neither soul
nor body has any influence whatever upon the other, and that they
must therefore be regarded as acting merely in harmony.

1:9 ' All that ambition or any other passion brings to pass in the
soul of Caesar is also represented in his body, and all the motions
of these passions come from the impressions of objects combined
with internal motions. And the body is so constituted that the
soul never makes any resolution without the motions of the body
agreeing with it. This applies even to the most abstract reasonings,
because of the characters which represent them to the imagination.
In a word, everything takes place in bodies, as regards the par-
ticular series [detail'] of their phenomena, as if the evil doctrine of
those who, like Epicurus and Hobbes, believe that the soul is
material, were true ; or as if man himself were only a body or an
automaton. . . . Those who show the Cartesians that their way of
proving that the lower animals are only automata amounts to
justifying him who should say that all men, except himself, are

THE MONADOLOGY 265

82. As regards minds [esprits] or rational souls, though
I find that what I have just been saying is true of all
living beings and animals (namely that animals and souls
come into being when the world begins and no more
come to an end than the world does), yet there is this
peculiarity in rational animals, that their spermatic
animalcules, so long as they are only spermatic, have
merely ordinary or sensuous [sensitive] souls ; but when
those which are chosen [e7ws], so to speak, attain to human
nature through an actual conception, their sensuous souls
are raised to the rank of reason and to the prerogative of
minds [esprits130]. (The'od. 91, 397.)

also mere automata, have said exactly what I need for that half of
my hypothesis which concerns body. But, apart from the prin-
ciples which make it certain that there are Monads, of which com-
pound substances are only the results, the Epicurean doctrine is
refuted by inner experience, by our consciousness of the Ego which
consciously perceives the things which take place in the body ; and
as perception cannot be explained by figures and motions, the other
half of my hypothesis is established, and we are obliged to recognize
that there is in us an indivisible substance, which must be itself the
source of its phenomena. Consequently, according to this second
half of my hypothesis, everything takes place in the soul as if there
were no body ; just as, according to the first half, everything takes
place in the body as if there were no soul. . . . Whatever of good
there is in the hypotheses of Epicurus and of Plato, of the greatest
Materialists and the greatest Idealists, is combined here.' Keponse
aux Reflexions de Bayle (1702) (E. 185 ; G. iv. 559).

1;0 This elevation of the merely sensuous soul to the rank of
reason might, says Leibniz, ' be attributed to the extraordinary
operation of God.' But he 'prefers to dispense with miracle in the
generation of man as in that of the other animals,' and says that
* among the great number of souls and animals (or at least living
organic bodies) which are in the seed, only those souls which are
destined some day to attain to human nature contain in germ
\_enveloppent~\ the reason which will some day appear in them, and
that only the organic bodies of these souls are preformed and pre-
disposed to take the human form some day, the other animalcules
or seminal living beings, in which nothing of this kind is pre-
established, being essentially different from them and containing
only what is lower.' Theodicee, § 397 (E. 618 a ; G. vi. 352). This
question of the relation of rational to sub-rational souls is treated
by Leibniz in a very unsatisfactory way. If we follow out Leibniz's

266 THE MONADOLOGY

83. Among other differences which exist between
ordinary souls and minds [esprits], some of which
differences I have already noted lsl, there is also this :
that souls in general are living mirrors or images of the
universe of created things, but that minds are also images
of the Deity or Author of nature Himself, capable of
knowing the system of the universe m, and to some
extent of imitating it through architectonic ensamples
\echantillons 133], each mind being like a small divinity in
its own sphere. (Theod. i47.)_

84. It is this that enables spirits [or minds — esprits] to
enter into a kind of fellowship with God, and brings it
about that in relation to them He is not only what an
inventor is to his machine (which is the relation of God
to other created things), but also what a prince is to his
subjects, and, indeed, what a father is to his children 134.

main principles, it ought to be impossible to draw a sharp line
between these two classes of souls. Yet, while not regarding as
absolute the distinction between the rational and the merely sen-
suous, Leibniz is afraid of minimizing this distinction and of thus
putting in jeopardy the pre-eminence of man and the immortality
of the soul. In the draft of a letter to Arnauld (1686) he speaks of
this question as 'a. special point [une particular tie] about which
I have not light enough ' (G. ii. 73). Cf. Introduction, Part iii.
p. 116.

131 §§ 19-30.

132 'The difference between intelligent substances and those which
are not so, is as great as the difference there is between a mirror
and him who looks therein/ Paper without a title (1686) (G. iv.
46o).

133 That is, subsidiary creations or imitative constructions. Man
can not merely express in himself the ' machine ' of the universe,
but he can also make for himself small ' machines,' constructed on
similar principles. Cf. § 64 ; also Principles of Nature and of Grace,
§ 14. An dpxiTtKTcav is literally a 'master of works.'

134 ' Concerning the human soul I dare not assert anything as to
its origin nor as to its state after death, because rational or intelli-
gent souls, such as ours is, having been so fashioned that they have
a peculiar relation to the image of God, are governed by very dif-
ferent laws from those to which souls without understanding are
subject.' Epistola ad Bernoullium (1699) (G. Math. iii. 565). « Spirits
[esprits} alone are made in His image, and are, as it were, of His

THE MONADOLOGY 267

85. Whence it is easy to conclude that the totality
[assemblage] of all spirits [esprits] must compose the City
of God135, that is to say, the most perfect State that is
possible, under the most perfect of Monarchs. (Theod.
146 ; Abrege, Object. 2.)

86. This City of God, this truly universal monarchy,
is a moral world IrTTihe natural world, and is the most
exalted and most divine among the~works of God lse ; and
it is in it that the glory of God really consists, for He
Wouldjhave no glory were not His greatness and His
goodness known and admired by spirits \_esprits™7]. It is

race or like children of the house, since they alone can serve Him
freely and act with knowledge, in imitation of the Divine nature :
one single spirit [esprit] is worth a whole world, since it not only
expresses the world but also knows it and governs itself in the
world [s'y gouverne] after the manner of God. ' Paper without title
(1686) (G. iv. 461).

135 rphe reference js to the civitas Dei of St. Augustine ; but the
difference of meaning is very great. St. Augustine's civitas Dei is
the Christian Church as opposed to the civitas terrena or earthly
state. Leibniz's City of God, on the other hand, is not set in
opposition to an earthly state, but is the moral order of the
universe, as distinct from its natural order. The City of God,
according to Leibniz, includes not Christians alone, but all men.

136 Cf. Fichte, Darstellung der Wissenschaftslehre (Werke, ii. 35) :
' The ground of the universe is ... spirit itself ... a kingdom of
spirits and absolutely nothing else.' Also Werke, v. 188 : ' It is
in no way doubtful, or rather it is the most certain of all things,
and indeed the foundation of all certitude, the sole absolutely
indisputable objective reality, that there is a moral order in the
universe ; that each rational individual has his definite place in
this universal order, a place indicated by his special work ; that
each of the accidents of his existence, in so far as it does not
result from his personal conduct, is a consequence of this general
plan ; that, except in conformity with this plan, not a hair can
fall from his head, any more than a sparrow from its roof ; that
every truly good action succeeds, every bad action fails ; and
that all things necessarily work for the greatest good of those who
only rightly love the good.' See Introduction, Part iv. p. 180
note.

137 Cf. Nicholas of Cusa, Cribratio Alchoran, 16 : < God created
all things for the manifestation of His glory ; an unknown king is
wanting in honour and in beneficence.' Cf. also Excitationes ex

263 THE MONADOLOGY

also in relation to this divine City that God specially
has goodness138, while His wisdom and His power are
manifested everywhere. (Theod. 146 ; Abrege, Object. 2.)
87. As we have shown above that there is a perfect
harmony between the two realms in nature, one* of efficient,
and the other of final causes, we should here notice also
another harmony between the physical realm of nature
and the moral realm of grace 139, that is to say, between
God, considered as Architect of the mechanism [machine]
of the universe and God considered as Monarch of the
divine City of spirits [esprits]. (Theod. 62, 74, 118, 248,
v 112, 130, 247.)

Sermonibus, vi. 112 a: 'God desired to manifest the riches of His
glory, and on this account He created the rational or intellectual
creature, that He might manifest to him the riches of His glory ;
for this creature alone can perceive the glory of God with in-
tellectual appreciation {intellecluali gustu~] ; but these riches [of the
glory of God] are eternal life.' ' God wishes to be known, and
hence on this account all things are' (loc. cit., 1043). Of. also
Schiller's ' Freundlos war der grosse Weltenmeister,' &c. (Die
Freundsckaff) .

138 Because moral distinctions and moral qualities belong specially
to the moral order, i. e. to the society of rational souls.

is9 ipjjg question of the relation between the realm of nature
and that of grace is, in one form or another, perennial. Leibniz
seeks to apply the principles of his philosophy in a reconciling
spirit to the seventeenth-century discussion of the question in its
theological form. The harmony, of which Leibniz speaks, must
not be taken as meaning (like the harmony between the Monads)
that the two realms of nature and of grace are entirely exclusive
of one another. The realm of final causes, for instance, does not
belong entirely to nature : the realm of grace is the realm of
final causes in its highest form. The relation between nature
and grace is analogous to that between body and soul. Just as
body, considered as an aggregate, is merely phenomenal and there-
fore quite distinct from soul or real substance, while yet it is
a phenomenon bene fundatum and its reality is that of its component
Monads or souls ; so nature, considered as subject to the law of
efficient causes, is quite distinct from grace, while yet, since
efficient causes, even in nature itself, derive their meaning and
force from final causes, nature finds its perfection in grace,
which is the highest expression of final cause. §§88 and 89
illustrate this. Cf. Principles of Nature and of Grace, § 15.

THE MONADOLOGY 269

88. A result of this harmony is that things lead to
grace by the very ways of nature, and that this globe,
for instance, must be destroyed and renewed by natural
means at the very time when the government of spirits
requires it, for the punishment of some and the reward of
others. (Theod. 18 sqq., no, 244, 245, 340.)

89. It may also be said that God as Architect satisfies
in all respects God as Lawgiver 14°, and thus that sins
must bear their penalty with them, through the order of
nature, and even in virtue of the mechanical structure of
things ; and similarly that noble actions will attain their
rewards by ways which, on the bodily side, are mechanical,
although this cannot and ought not always to happen
immediately141.

90. Finally, under this perfect government no good
action would be unrewarded and no bad one unpunished,
and all should issue in the well-being of the good, that is
to say, of those who are not malcontents in this great
state, but who trust in Providence, after having done
their duty, and who love and imitate, as is meet, the
Author of all good, finding pleasure in the contemplation
of His perfections, as is the way of genuine ' pure love 142, '

140 That is to say, the world is built on a plan which perfectly
harmonizes with the moral government of its inhabitants.

141 Leibniz regards sin as seeking one's own good in an imperfect,
unenlightened way, without regard to the moral law or order,
which is the only way of securing the highest possible good of all
and of each. Thus sin brings punishment as inevitably as neglect
or defiance of natural laws brings disease and pain. But owing to
the harmony (above explained) between spirit and body, the moral
and the natural worlds, the punishment of sin is not merely
spiritual : the bodily or natural has a share in it. Similarly
virtue has its reward, both spiritual and natural, because it is
enlightened action in accordance with the ultimate law of the
whole universe, the principle of the highest good.

142 That is to say, disinterested love, as distinct from interested
or selfish love. One of the great subjects of theological discussion
in the seventeenth century was the question whether there is such
a thing as purely disinterested love. About this a long pamphlet
controversy (lasting from 1694 to 1699) took place between Bossuet

270 THE MONADOLOGY

which takes pleasure in the happiness of the beloved.
This it is which leads wise and virtuous people to devote
their energies to everything which appears in harmony
with the presumptive or antecedent will of God, and yet
makes them content with what God actually brings to
pass by His secret, consequent and positive [decisive]
will 143, recognizing that if we could sufficiently under-

and Fenelon. Fenelon (partly in defence of Mme. Guyon) main-
tained the possibility of a disinterested love of God, that is, a love
which has no regard to rewards and punishments. Ultimately,
however, Pope Innocent XII condemned the views of Fenelon, at
the same time censuring the controversial methods of Bossuet.
The view of Leibniz is more fully given in his Preface, On the
Notions of Right and Justice (1693), p. 285 ; cf. Butler, Sermons xi,
xiii, and xiv.

143 The distinction between the antecedent and the consequent
will of God is due to Thomas Aquinas. He says : ' This dis-
tinction is not founded upon the Divine will itself, for in it there
is neither before nor after ; but it is founded upon the objects of
His will. ... A thing may be considered either in itself, absolutely,
or with some particular circumstance, which forms a subsequent
consideration. For instance it is good in itself that man should
live and bad that he should he killed, considering the matter
absolutely ; but if we add, with regard to some particular man,
that he is a murderer or that his living is a source of danger to
a large number of people, in this case it will be good that the man
should be killed, and bad that he should live. Accordingly it may
be said that a judge wills with an antecedent will that every man
should continue to live, but wills with a consequent will that
a murderer should be hanged.' Summa Theol. i. Qu. 19, Art. 6 ad
primum. Cf. De Veritate, Qu. 23, Art. 2. Leibniz brings this into
relation with his own hypothesis regarding the region of possible
things and the actual, existing world. ' In a general sense it may
be said that will consists in the inclination to do something in
proportion to the good it contains. This will is called antecedent,
when it is separate [detachee] and has regard to each good by itself,
in so far as it is good. In this sense it may be said that God tends
to all good in so far as it is good, ad perfectionem simpliciter simplicem,
in Scholastic language, and that by an antecedent will. He has
an earnest inclination to sanctify and save all men, to do away
with sin and to prevent damnation. It may even be said that this
will is efficacious in itself (per se), that is to say, so that the effect
would follow, were there not some stronger reason which prevents
it ; for this will does not go to the extreme of effort (ad summum

THE MONADOLOGY 271

stand the order of the universe, we should find that it
exceeds all the desires of the wisest men, and that it is
impossible to make it better than it is U4, not only as a
whole and in general but also for ourselves in particular,
if we are attached, as we ought to be, to the Author of
all, not only as to the architect and efficient cause of our
being, but as to our master and to the final cause, which
ought to be the whole aim of our will, and which can
alone make our happiness. (Theod. 134, 278. Pref. [E.
469 ; G. vi. 27, 28].)

conatum}) otherwise it would never fail to produce its full effect,
since God is master of all things. Complete and infallible success
belongs only to consequent will, as it is called. It is complete, and
this rule applies to it, namely, that we never fail to do what we
will, when we can. Now this consequent, final and decisive will
results from the conflict of all the antecedent volitions [' wills H,
both those which tend towards good and those which oppose evil,
and it is from the concurrence of all these particular volitions
that the total volition comes : as in mechanics the composite
motion is the result of all the tendencies which concur in one and
the same movable body, and equally satisfies each of them so far
as it is possible to do so at once. ... In this sense it may be said
that antecedent will [volition] is in a way efficacious and even
effective and successful. From this it follows that God wills
antecedently the good, and consequently the best.' Theodicee, §§22 and
23 (E. 510 b; G. vi. 115, 116). God antecedently wills the absolute
good of all beings ; but He consequently wills the greatest good of
each that is possible, considering the essential limitations of their
natures and their relations to one another in the system of things.
This greatest possible good is thus compatible with a certain amount
of evil.

14t This is not to be taken as meaning that it is impossible to
make the world better than it is at this or any particular moment of
time. Leibniz is speaking of the world as a system including all
time, and accordingly he does not exclude progress in time.

272 THE MONADOLOGY

APPENDIX F.

THE DISCUSSION BETWEEN LEIBNIZ AND BAYLE REGARDING
THE MULTIPLICITY IN THE MONAD.

THE ' difficulty ' regarding the possibility of a multiplicity in
the Monad, to which Leibniz refers in § 16 of the Monadology,
is variously expressed by Bayle in his Dictionary (article 'Rora-
rius '). He says : 'As Leibniz with much reason supposes that
all souls are simple and indivisible, it is impossible to under-
stand how they can be likened to a clock ' [see Third explana-
tion of the New System, and Introduction, Part ii. p. 45], ' that is
to say, how by their original constitution they can diversify
their operations, by means of the spontaneous activity they
receive from their Creator. We conceive clearly that a simple
being will always act uniformly, if no extraneous cause inter-
feres with it. If it were composed of several pieces, like
a machine, it would act in divers ways, because the special
activity of each piece might change at any moment the course
of the activity of the others ; but in an independent simple
substance [substance unique], where will you find the cause of
any variety in its operation ? ' Leibniz's answer to this appears
in the Reponse aux Reflexions de Bayle ; see Monadology, note 20 ;
cf. Lettre a Bosnage (1698) (E. 153 a; G. iv. 522) : ' I compared
the soul to a clock, only as regards the regulated precision of
its changes. This is but imperfect in the best of clocks, but it
is perfect in the works of God. And the soul may be said to be
an immaterial automaton of the very best kind. When it is
said that a simple being will always act uniformly, a distinction
must be rrade : if acting uniformly means constantly following
the same law of order or varying succession \ continuation], as in
a certain order or series of numbers, I admit that of itself every
simple being, and even every compound being, acts uniformly ;
but if uniformly means exactly in the same way [semblablement],
I do not admit it. . . . The soul, though it is perfectly simple,
has always a feeling [sentiment] composed of several perceptions
at once ; and this is as much to our purpose as if it were com-
posed of pieces, like a machine. For each preceding perception
influences those which follow, according to a law which there
is in perceptions as in motions.' Bayle allows that Leibniz's
view contains the promise of a theory which will solve all diffi-

APPENDIX F 273

culties ; but he still feels dissatisfied as to the power of a simple
substance, like the soul of man, to develop spontaneously all
the variety of thought, &c. It has not ' the necessary instru-
ments' for doing this. * Let us freely imagine an animal created
by God and intended to sing incessantly. It will always sing, that
is indubitable ; but if God assigns to it a certain piece of music
to sing [une certaine tablature], He must necessarily either place
this before its eyes, or imprint it on its memory, or give it an
arrangement of muscles which, in accordance with the laws of
mechanics, shall make one note follow another exactly according
to their order in the musical score [tablature]. Otherwise it is
inconceivable that the animal should ever be able to conform
to the whole succession of notes indicated by God. Let us
apply this to the soul of man. M. Leibniz thinks that it has
received not only the faculty of continually supplying itself
with thoughts, but also the faculty of always following a certain
order in its thoughts, corresponding to the continual changes
of the bodily mechanism. This order of thoughts is like the
musical score assigned to the animal musician of which we have
been speaking. In order that the soul may from moment to
moment change its perceptions or its modifications in accord-
ance with the " score " of thoughts, must not the soul know the
succession of the notes and actually think of it ? Now expe-
rience shows us that it does nothing of the kind. And, failing
this knowledge, must there not at least be in the soul a succession
of special instruments which might each be a necessary cause
of this or that particular thought ? Must not these instruments
be so situated that one acts upon another, in exact accord with
the pre-established correspondence between the changes of the
bodily mechanism and the thoughts of the soul ? Now it is
quite certain that no immaterial, simple and indivisible sub-
stance can be composed of this countless multitude of special
instruments placed one before another in the order required by
the " score " in question. Accordingly it is impossible for the
human soul to carry out this law.' (This illustration of Bayle's
may be compared with Leibniz's simile of the choirs, see Intro-
duction, Part ii. p. 47. The letter containing Leibniz's simile
was written in 1687.) In a paper written in 1702 (G. iv.
549 sqq.) Leibniz makes the following reply to Bayle (referring
in the first place to Bayle's supposition of an animal created by
God to sing incessantly) : ' It is enough if we suppose a singer
paid to sing at certain hours in church or at the opera, and

T

274 THE MONADOLOGY

that he finds there a music-book, in which there are the pieces
of music or the " score " he is to sing on the particular days and
hours. The singer sings with open book [a livre ouvert], his
eyes are directed by the book, and his tongue and throat are
directed by his eyes, but his soul sings, so to speak, by memory
or by something equivalent to memory ; for since the music-
book, the eyes and the ears cannot act upon the soul, it must
by itself, and indeed without trouble or application and without
seeking it, find what his brain and organs find with the help
of the book. The reason is that the whole " score " of the book
or books that shall, one after another, be followed in singing is
potentially [virtuellement] graven in his soul from the beginning
of its existence ; as this "score " was in some way graven in its
material causes before the pieces of music were composed and
the book made out of them. But the soul cannot be conscious
of it [s'en apercevoir\, for it is enveloped in the confused per-
ceptions of the soul, which express all the detail of the universe.
And the soul is distinctly conscious of it only at the time when
its organs are markedly affected by the notes of the " score."
... I have already shown more than once that the soul does
many things without knowing how it does them, when it does
so by means of confused perceptions and unconscious [insensibles]
inclinations or appetitions, of which there is always a very
great number, and which it is impossible for the soul to be con-
scious of, or to unravel distinctly. . . . The soul has all the
instruments which M. Bayle thinks necessary, arranged [place]
as they ought to be. But they are not material instruments.
They are the preceding perceptions themselves, from which
the succeeding perceptions arise by the laws of appetitions
[appetite].'

APPENDIX G.

PROOF OF TrfE EXISTENCE OF GOD.

THE view of Leibniz, expressed in the Monadology (§§ 44 and
45), must be carefully distinguished from the Cartesian argu-
ment (derived from Anselm) that the idea of God involves His
existence, because if He does not exist, a more perfect Being
may be conceived, namely one who does exist. It is also
to be distinguished from the view of Spinoza, which amounts
to saying that the essence of God involves His existence, because

APPENDIX G 275

all essence exists, all that is possible is actual. As against
Descartes's proof Leibniz argues that it is incomplete, for the
idea of a most perfect being might perhaps be self-contra-
dictory, like the idea of the swiftest possible motion or the
greatest possible number. Thus, after stating the Cartesian
argument, Leibniz says : ' But it is to be noted that the only
logical conclusion is : " If God is possible, it follows that He
exists." For we cannot safely use definitions in order to reach
a conclusion, until we know that these definitions are real or
that they involve no contradiction. The reason of this is that
from notions which involve a contradiction opposite conclusions
may be drawn at the same time, which is absurd. To illustrate
this I usually take the instance of the swiftest possible motion,
which involves an absurdity. For, suppose a wheel to revolve
with the swiftest possible motion, is it not evident, that if any
spoke of the wheel be made longer ' [produced, in the mathe-
matical sense] 'its extremity will move more swiftly than
a nail on the circumference of the wheel ; wherefore the
motion of the circumference is not the swiftest possible, as was
supposed by the hypothesis. Yet at first sight it, may appear
that we have an idea of the swiftest possible motion ; for we
seem to understand what we are saying, and nevertheless we
have no idea of impossible things.' Meditationes de Cognitione,
Veritate et Ideis (1684), (E. 80 a ; G. iv. 424.) ' Therefore there is
assuredly reason to doubt whether the idea of the greatest of all
beings is not uncertain, and whether it does not involve some
contradiction. For I quite understand, for instance, the nature
of motion and velocity, and what " the greatest " is. But -I do
not understand whether these are compatible, and whether
it is possible to combine them into the one idea of the greatest
velocity of which motion is capable. In the same way, although
I know what "being" is, and what the "greatest" and the
" most perfect " are, nevertheless I do not therefore know that
there is not a hidden contradiction involved in combining these
together, as there actually is in the instances I have just given
. . . Yet I admit that God has here a great advantage over
all other things. For, in order to prove that He exists, it is
sufficient to prove that He is possible, which is not the case
with regard to anything else that I know of. ... Simple
forms [i. e. living principles] are the source of things. Now
I maintain that all simple forms are compatible with one
another. ... If this be granted, it follows that the nature of

T2

276 THE MONADOLOGY

God, which contains all simple forms taken absolutely, is
possible. Now we have proved above that God is, provided
He is possible. Therefore He exists.' (G. iv. 294 and 296.)
Thus Leibniz, as he himself says (G. iv. 405), holds a middle
position between those who regard the Cartesian proof as a
sophism and those who say that it is a complete demonstra-
tion. God's existence, for Leibniz, follows immediately from
His possibility, for all real possibility includes a tendency to
existence, and there can be nothing to hinder this tendency in
a being supposed to be perfect. In the Reponses aux Deuxiemes
Objections, Descartes maintains the possibility of the idea of
a most perfect being. But he does not make this a prominent
or essential part of his proof, as Leibniz does. Cf. Descartes,
Meditation 5 ; Prindpia Philosophise, Part i. §§ 14 sqq.

In the Animadversiones in partem generalem Principiorum
Cartesianorum (1692) (G. iv. 359) Leibniz suggests that the
argument might be simplified by omitting the reference to
'perfection,' and merely saying 'a necessary Being exists— or
a Being whose essence is existence, or Being in itself [ens a se]
exists — as is evident from the terms. Now God is such a being
(from the definition of God), therefore God exists. This argu-
ment holds if it be granted that a necessary being is possible
and does not involve a contradiction, or, what is the same
thing, that the essence from which existence follows is possible.'
Elsewhere (E. 177 b ; G. iv. 406) Leibniz points out that 'those
who hold that from notions, ideas, definitions or possible
essences alone we can never infer actual existence . . . deny the
possibility of being in itself [ens a se]. But ' if being in itself
is impossible, all beings through another ' [entia ab alio] ' are
also impossible, since indeed they are only through being in
itself: thus nothing can exist.'

As against Spinoza, Leibniz's argument would be that not
all that is possible is actual, but only the compossible or com-
patible. There are unrealized ' possibles,' essences which do
not involve existence, and consequently the necessary being,
whose essence involves existence, is not the all, but is some-
thing distinct from the world of created things. The essence
of a created being does not involve its existence, because it is
limited, and thus its existence depends upon its .' fitting into '
other essences so as to constitute, along with them, the best
possible world. But the essence of a necessary being involves
its existence because it is unlimited. There is nothing to

APPENDIX G 277

hinder or condition its existence, and accordingly, if it be pos-
sible, it must exist. The value of Leibniz's argument depends
on the worth of the distinction he makes between ( possible '
and ' compossible,' that is to say between a metaphysical or
absolute necessity and a moral or inclining necessity. How
are these two kinds of necessity related to one another ? It is
hardly a satisfactory solution of the opposition between them
to refer the one to the understanding and the other to the
will of God. We have here again the fundamental weakness
of Leibniz's philosophy, the uncertainty of the relation between
the principle of contradiction and that of sufficient reason.

Kant rejects the whole argument as a paralogism, on the
ground that ' existence ' can never be a predicate, that is to
say, that we are never justified logically in passing from a
mere idea to the existence of its content. (See Critique of
Pure Reason, Rosenkranz, ii. 462 ; Hartenstein, ii. 456 ; Meikle-
john's Tr., 364.) It is true that we can never pass from a mere
idea to the existence of its content ; but to adduce this as an
argument here is to beg the question. For a mere idea is an
idea of that which may be non-existent ; while the idea of
a necessary being is the idea of that which cannot be non-
existent. Gaunilo in his Liber pro insipiente, anticipates the
objection of Kant, and to this Anselm replied in his Liber
apologeticus contra respondentem pro insipiente, saying, among
other things : * Let us assume that the Summum cogitabile
need not exist merely because it is thought. Mark the con-
sequence. That which can be thought without really existing
would not, if it did exist, be the summum cogitabile ; so that,
by the hypothesis, the summum cogitabile is and is not the
summum cogitabile, which is in the last degree absurd ' (Rigg's
St. Anselm of Canterbury, p. 71. See the whole of his chap. v).
Cf. Introduction, Part iv. p. 173.

OTHER PHILOSOPHICAL WRITINGS
OF LEIBNIZ

ON THE NOTIONS OF EIGHT AND
JUSTICE. 1693.

PREFATORY NOTE.

LEIBNIZ was deeply interested in the maintenance of the
rights of the Empire as against the pretensions of Louis XIV.
He observed that the French took every opportunity of obtain-
ing and preserving documents on which they might found
claims. And accordingly, on behalf of the Empire, he set
himself to make a collection of Treaties and State papers
(international and national) affecting the European nations.
His plan was to publish them in three volumes under the title
Codex Juris Gentium Diplomaticus. In 1693 the first volume
appeared, containing papers of date from noo to 1500 A. D.
The work was never finished ; but an Appendix (mantissa) to
the first volume was published in 1700. Writing to the Count
de Kinsky in 1697, .Leibniz remarks that his book l is a little
less in season than it was at first, for we are assured that
a general peace is on the point of being concluded ' (Klopp,
vi. 454).

To this work Leibniz says he ' contributed only the title, the
preface, and the trouble of reading it over' (Klopp, vi.
441). The preface, however, contains the most convenient
summary of its author's views in an important department of
ethics. The whole preface is given by Dutens (iv. 287) and
by Klopp (vi. 457) ; but Erdmann (118) gives only the para-
graphs dealing with 'the eternal rights [or laws] of a rational
nature,' and Gerhardt includes no part of it in his edition.
I have translated the portion given by Erdmann, adding a few
sentences from the succeeding paragraphs which deal with
'voluntary' and 'divine' right. In the foot-notes will be
found translations of a number of illustrative passages from
the very interesting collection of papers from the Hanover

282 ON THE NOTIONS OF RIGHT AND JUSTICE

MSS. published by Dr. Georg Mollat under the title, Eechts-
philosophisches aus Leibnizens ungedruckten Schriften (Leipzig,
Robolsky, 1885).

The following statement of Leibniz may be used as a sum-
mary of this part of the Preface to the Codex Diplomatlcus :
1 In stating the elements of natural right there must be ex-
pounded, first, the common principles of justice, the charity of
the wise man ; secondly, private right or the precepts of com-
mutative justice, concerning what is observed among men in
so far as they are regarded as equal ; thirdly, public right,
concerning the dispensing of common goods and evils among
unequal people for the greatest common good in this life ;
fourthly, inward right, concerning universal virtue and natural
obligation towards God, that we may have regard to perpetual
happiness. To these must be added the elements of legitimate •
human and divine right : human right both in our own
commonwealth and between nations, divine right in the
universal Church.' (De tribus juris naturae et gentium gradibus,
Mollat, p. 21.)

The ideas expressed in this Preface are to a large extent
derived from Grotius.

The doctrine of right, confined by nature within narrow
limits, has been immensely extended by the human intel-
lect '. I am not sure that, even after so many distinguished
writers have discussed them, the notions of Eight and
Justice may be considered sufficiently clear. Eight is a
certain moral power, and obligation a moral necessity2.
Now by moral I mean that which is equivalent to * natural '
in a good man : for as a Koman lawyer admirably says,
it is not to be believed that we are capable of doing things

1 * Medical science is the science of the pleasant, political science
is the science of the useful, ethical science is the science of the
just.' Juris et aequi elementa (Mollat, p. 23).

2 'Nothing impossible is a duty or, as it is commonly put, of
impossible things there is no obligation. . . . Everything necessary
is permissible or, as it is commonly put, necessity has no law.'
De debitis et illicitis (Mollat, p. 92). 'Necessity is the avoiding of
misery,' which is denned as 'lasting sadness' or 'that state in
which the aggregate of evils preponderates over the aggregate
of goods.' Juris et aequi elementa (Mollat, pp. 32, 33).

ON THE NOTIONS OF RIGHT AND JUSTICE 283

which are contrary to good morals [contra bonos mores] R.
Further, a good man is one who loves all men, so far as
reason allows 4. Justice 5, therefore, which is the virtue 6
governing that disposition of mind [affectus] which the
Greeks call <£iAai/0/o<o7ria, will, if I mistake not, be most
fittingly defined as the charity of the wise man [caritas
sapientis1^ that is to say, charity in obedience to the

3 * When the nature of justice and (as is necessarily involved
in this) the nature of wisdom and charity is understood, it is
manifest that that which to a good man is possible, impossible,
necessary (if he wishes to retain the name), is just or permissible,
unjust, and finally, obligatory [debitum~\. For it is not to be believed
that we are capable of doing things which are contrary to good
morals, and in this sense it may be said that the right we have
of acting or not acting is a certain power or moral liberty, while
obligation is a necessity.' De tribus juris naturae et gentium gradibus
(Mollat, p. 13).

* ' He who loves God, that is he who is wise, will love all men,
but each in proportion as the traces of divine virtue in him shine
out, and in proportion as he hopes to find in him a companion
ready and able to promote the common good, or (what comes to
the same thing) the glory of God, the Giver of good things,' loc. cit.

4 The doctrine of Eight must, according to Leibniz, be deduced
from definitions, for the idea of justice is a priori. l Since justice
consists in a certain congruity and proportion, the just may have
a meaning, although there may neither be any one who practises
justice nor any one towards whom it is practised, just as the ratios
of numbers are true, although there may neither be any one who
numbers nor anything which is numbered, and it may be predicted
of a house that it will be beautiful, of a machine that it will be
effective, of a commonwealth that it will be happy, if it comes into
existence, although it may never come into existence.' Juris et
aequi elementa (Mollat, p. 24). I have in most places translated the
word 'jus' by 'Eight.' Regarding the ambiguities of these words
see E.G. Clark's Practical Jurisprudence, ch. 2 and 6.

6 ' All virtue is the bridling of the desires [affectus] so that
nothing can oppose the commands of right reason.' Juris et aequi
elementa (Mollat, p. 26). Cf. G. vii. 92 sqq.

7 Leibniz gives various longer definitions of justice. In a letter
to Kesner (1709) (Dutens, iv. 261) he says : 'Justice is perfection
in accordance with wisdom, so far as concerns a person's conduct
in relation to the goods and ills of other persons.' Again, ' Justice
is nothing but that which is in conformity with wisdom and
goodness combined ; the end of goodness is the greatest good, but

284 ON THE NOTIONS OF EIGHT AND JUSTICE

dictates of wisdom 8. Therefore the saying attributed to
Carneades 9 that justice is supreme folly, because it bids us
attend to the interests of others, neglecting our own, pro-
ceeds from ignorance of the definition of justice 10. Charity
is universal benevolence, and benevolence is the habit of
loving or esteeming [amandi sive diligendi] u. But to love

in order to recognize it we require wisdom, which is nothing but
the knowledge of the good. . . . Wisdom is in the understanding
and goodness in the will. And justice consequently is in both.'
Meditation sur la notion commune de la justice (Mollat, p. 62). 'The
true and perfect definition of justice is the habit of loving others
or of taking pleasure in the thought of other people's good, as often
as it comes into consideration.' ' Justice is prudence in bringing
about the good of others or not bringing evil upon them for the
sake of bringing about one's own good (by thus manifesting one's
mind), or not bringing evil upon oneself (that is, for the sake of
gaining reward or avoiding punishment).' Juris et aequi elementa
(Mollat, pp. 32 and 35). Eegarding the last statement, it should
be remarked that Leibniz says : ' God Himself is the reward,'
toe. tit.

8 ' . . . even in those who have not attained to this wisdom. For,
setting God apart, the majority of those who would act in
accordance with justice in all things, even against their own
interests, would in fact do what is required by th^ wise man who
finds his pleasure in the general good, but in certain cases they
would not themselves act as wise men, not being sensitive to the
pleasure of virtue.' Meditation sur la notion commune de la justice
(Mollat, p. 75).

9 The saying comes from the Epitome of the Dimnae Institutiones
of Lactantius, ch. i. Cf. Instit. v. 14 and Cicero, De Eep. iii. 23
(Ritter and Preller, Hist. Phil. Graec. §§ 436 and 438). Carneades
(about 213-129 B.C.), a native of Gyrene, was founder of the New
Academy. In 1566.0. he visited Rome as an ambassador from
Athens and caused much astonishment by his skill in arguing
successively for and against justice. Cf. Grotius, De jure belli et
pads, Prolegomena, § 5.

10 ' There cannot be justice without prudence, nor can prudence
be separated from one's own good/ Juris et aequi elementa (Mollat,
p. 26).

11 ' There are two ways of desiring the good of others, the one
when we desire it on account of our own good, the other when
we desire it as if it were our own good. The first is the way
of him who esteems, the second of him who loves ; the first is
the feeling of a master to his servant, the second that of a father
to his son ; the first is the feeling of a man towards the tool he

ON THE NOTIONS OF EIGHT AND JUSTICE 285

or esteem is to take pleasure in the happiness of another,
or what comes to the same thing, to adopt another's happi-
ness as our own. In this way there is solved the difficult
problem, which is also of great importance in theology, how
there can be a disinterested love [amor non mercenarius] 12,
a love apart from hope and fear and every consideration
of advantage ; the solution being that the happiness of
those in whose happiness we take pleasure becomes a part
of our own happiness 13, for things which give us pleasure
are desired for their own sakes u. And as the very con-
requires, the second that of friend to friend ; in the first case the
good of others is sought for the sake of something else, in the
second for its own sake/ Juris et aequi elementa (Mollat, p. 30).
In this note the word translated ' esteem ' is aestimare, while in
the text it is diligere. Benevolence is a f£is in the Aristotelian
sense, l not an act, but a habit or strong inclination of the mind,
which we have acquired either by the fortune of birth, or by
a special gift of God, or by repeated practice/ De justitia (Mollat,

P- 37).

12 Cf. Monadology, § 90, note 142. In the Preface to the second
part of the Codex Juris Gentium Diplomatics, § 10 (Dutens, iv. 313),
Leibniz replies to those who objected to his solution on the ground
that ' it is more perfect to cast oneself entirely upon God, so as
to be moved by His will alone and not by one's own pleasure/
This, says Leibniz, * is contrary to the nature of things : for the
endeavour to act springs from a tendency to perfection, the feeling
of which is pleasure ; and there is no action or volition otherwise/
Cf. a paper on the views of Fenelon (1697) (E. 790 a ; G. ii. 578) :
' We do everything for our own good, and it is impossible for us to
have other opinions, although we can speak about others. But
nevertheless, we do not yet love quite purely, when we do not
seek the good of the loved object for its own sake and because
it pleases us in itself, but because of some advantage which comes
to us from it. But . . . we seek at once our own good for our own
sakes and the good of the loved object for its own sake, when the
good of this object is immediately, finally (ultimata) and by itself
our aim, our pleasure and our good, as happens with regard to all
the things which we desire because they please us in themselves
and are consequently good in themselves without regard to conse-
quences : they are ends, not means.'

13 ' The prerogative of true happiness is that it is increased by
the multitude of those who share it/ De justitia (Mollat, p. 41)-

14 This is a convertible statement. 'Everything pleasant is

286 ON THE NOTIONS OF EIGHT AND JUSTICE

templation of beautiful things is pleasant 15, and a picture
by Raphael moves him who understands it, although it
brings him no gain, so that it becomes dear and delightful
to him, inspiring in him something like love 16 ; so when
the beautiful thing is also capable of happiness, his feeling
for it passes into real love. But Divine love 1T excels
other loves, for God can be loved with the happiest result,
since nothing is happier than God and nothing more
beautiful or more worthy of happiness can be conceived 18.
And since He possesses supreme power and wisdom, His
happiness not only becomes a part of ours (if we are wise,
that is, if we love Him) but even constitutes it 39. But
since wisdom ought to direct charity, wisdom also requires

sought for its own sake, and whatever is sought for its own sake
is pleasant. Other things are sought on account of what is
pleasant, that they may produce it, contribute to it, or remove
what is opposed to it. All men feel this whatever they may say,
or at any rate they do it, whatever they may feel.' Juris et aequi
elementa (Mollat, p. 30).

is i we gggjj beautiful things because they are pleasant. I define
a beautiful thing as that the contemplation of which is pleasant.'
loc. cit (Mollat, p. 31).

16 ' He who finds pleasure in the contemplation of a beautiful
picture and would suffer pain if he saw it spoiled, even though it
belong to another man, loves it so to speak with a disinterested
love ; but this is not the case with him who thinks merely of
making money by selling or getting applause by showing it,
without caring whether it is spoiled or not, when it no longer
belongs to him/ Lettre a Nicaise (1698) (E. 791 b ; G. ii. 581). Cf. Kant,
Critique of Judgment, Part i. div. i. bk. i. §§ 1-5.

17 i.e. love for God.

18 'He Himself is always happy and will never be a cause of
grief to us through His misfortune, nor will He be in need of our
help. And again, since He always does everything in the most
reasonable way, we can act in relation to Him otherwise than
in relation to those who, being carried away by their emotions,
follow no fixed rule of conduct and may even be offended by those
who are most anxious to honour them. But He is always content
with a good will and richly rewards all things well done or
intended, that is, all things which are in harmony with His
presumptive will/ De justitia, 5 (Mollat, p. 38).

19 'The happiness of God constitutes . . . the whole of ours.'
(E. 790 a ; G. ii. 578.)

ON THE NOTIONS OF RIGHT AND JUSTICE 287

to be defined. And I think that the notion men have of
it will best be satisfied, if we say that wisdom is nothing
but the very science of happiness 20. So we are brought
back again to the notion of happiness, which this is not
the place to explain21.

Now from this source flows natural Eight [jus naturae]
of which there are three degrees : Right in the narrow sense
[jus strictum] in commutative justice, equity (or charity
in the narrower sense of the word) in distributive justice 22,
and lastly, piety (or uprightness) in universal justice23.

20 ' Wisdom is the science of the best, as prudence is the science
of the good/ Specimen demonstrationum politicarum (1669), prop. 38
(Dutens, iv. 559).

21 'Happiness is a lasting state of joy/ Initium institutionum juris
perpetui (Mollat, p. 4). ' Nothing contributes more to happiness
than the enlightenment of the understanding and the inclination
of the will always to act according to reason, and such an enlighten-
ment is especially to be sought in the knowledge of those things
which can lead our understanding ever onward to* a higher light ;
because from this there arises a continual progress in wisdom and
virtue, and consequently in perfection and joy, the fruit of which
remains with the soul even after this life.' Van der Gluckseligkeit
(E. 672 b ; G. vii. 88). Cf. E. 793 a ; G. ii. 581.

22 These correspond respectively to Aristotle's TO \v TOIS ffwa\\ay-
}io.ai Sttcaiov or SiKaiov SiopdcariKov and his SiavffiijriKov SiKaiov or Siicaiov
fv TCUS 8iav6fjiais. Ethics, v. 2, H3ob3o; v. 4, H3ib 27 and 33. Cf.
Pol. iii. 9. ' Commutative justice has to do with private right,
distributive with public right.' De tribus juris naturae et gentium
gradibus (Mollat, p. 14). Cf. loc. cit., p. 17, where they are called
'right of property, and right of society/ But Aristotle recognizes
a ' catallactic ' or ' commutative ' justice (T& avriircirovOos) distinct
(at least according to what seems the best interpretation of Eth. v.
5) both from ' corrective ' justice (TO SiopOtuTueov} and ' distributive '
justice (TO SiavffiijTiKov); 'corrective' and 'distributive' justice
pre-supposing the existence of a state (m$A.ty), while 'catallactic'
justice is pre-supposed by the state. See Prof. Ritchie ' On Aristotle's
subdivisions of Particular Justice,' Classical Review, viii. p. 185.

23 ' While justice is only a particular virtue, when we make
abstraction from God or from a government which imitates that
of God ; and while this virtue, thus limited, includes only what is
called commutative and distributive justice, we may say that as
soon as it is founded upon God or upon the imitation of God, it be-
comes universal justice and contains all the virtues/ Meditation sur la
notion commune de la justice (Mollat, p. 75). Cf. infra, note 42.

288 ON THE NOTIONS OF RIGHT AND JUSTICE

Hence come the precepts that we should do injury to no
one, that we should give each his own, that we should
live virtuously (or rather piously), the universal and
commonly accepted precepts of Eight [jus] 24 ; as I
suggested, when a youth, in my little book De Methodo
Juris 25. The precept of bare Eight or Right in the narrow
sense [jus strictum] 26 is that no one is to be injured, lest if
it be within the state, the person should have ground for
an action at law, or if it be without the state, he should
have the right to make war 27. From this there comes
the justice which the philosophers call commutative and
the right which Grotius calls right proper [facultas] 28.

24 The precepts are given by Ulpian. See Justiniani Institutiones,
Lib. i. Tit. i. 3 (Moyle's ed., vol. i. p. 100). In his De tribus juris
naturae et gentium gradibus (Mollat, p. 14), Leibniz says that the three
precepts flow from 'the supreme rule of Right,' which is ' to direct
all things to the greater general good.'

25 Methodus now discendae docendaeque Jurisprudentiae (i667\ §§ 74-76
(Dutens, iv. 213). This was the work through which Leibniz
obtained an introduction to the Elector of Mainz. See Introduction,
Part i. p. 4.

26 Grotius distinguishes between jus strictum and jus laxius, the
latter being moral right. De jure belli etpacis, bk. i. ch. i, § 9, i and 2.
Cf. Prolegomena, § 10. Leibniz holds, as against Hobbes, that ' there
is a right and even a jus strictum before the foundation of the State.
He who produces a new thing or puts himself in possession of an
already existing thing, which no one has already taken possession
of, and who cultivates it and fits it for his use, cannot as a rule be
deprived of it without injustice.' Meditation sur la notion commune de
la justice (Mollat, p. 78).

•s i Against him who knowingly injures without necessity, there
is a right of war.' Juris et aequi elementa (Mollat, p. 33). The object
of this first degree of Right is the preservation of peace, which does
not necessarily secure happiness but is an essential condition of
happiness. ' It is an evil to a man that there is another man who
wishes him ill, and it is a good to a man that there is another man
who wishes him well.' Axiomes ouprincipes de droit (Mollat, p. 54).

28 De jure belli et pads, bk. i. ch. i, §§ 5sqq. Facultas is jus proprie
aut stride dictum. It includes power (potestas) whether over one's
self (which is liberty), or over another (which is authority), also
ownership (dominium), whether full (as of property), or less full
(as of compact, pledge, credit, to which corresponds debt on the
other side). Whewell translate a facultas l jural claim ' in contrast

ON THE NOTIONS OF EIGHT AND JUSTICE 289

The higher degree I call equity™, or if you prefer it,
charity (that is, in the narrower sense), which I extend
beyond the rigour of bare Eight to those obligations also
on account of which those to whom we are obliged have
no ground of action to compel us to perform them, such
as gratitude, pity, and the things which are said by Grotius
to have imperfect right [or fitness, aptitudo] not right
proper [facultas]. And as the precept of the lowest degree
was to do injury to no one, so that of the middle degree
is to do good to everybody 80 ; but that so far as befits
each person or so far as each deserves, since we cannot
equally befriend all men 31. Therefore to this place belong
distributive justice32 and that precept of Eight [jus]
which bids us give to each his own. And to this political
laws in the state are related, laws which have to do with
the happiness of subjects and which usually bring it about
that those who had only moral claim [aptitudo] acquire
a jural claim [facultas]33, that is to say, that they are

with 'moral claim' (aptitudo). 'Commutative justice' (justitia ex-
pletrix) concerns facultas, while 'distributive justice' (justitia attri-
butrix) concerns aptitudo.

29 This degree of Eight presupposes some sort of ' society ' or
social arrangement among men. There may be such a ' society' in
which the first degree of Eight is alone recognized, but it cannot
be a happy state, for there must be ' perpetual quarrels' in it, and
thus the higher degree of Eight comes to be recognized. De tribus
juris naturae et gentium gradibus (Mollat, pp. 17 sqq.)-

30 ' Do not do to others what you do not wish to be done to your-
self, and do not deny to others what you wish to be done to yourself.
It is the rule of reason, and it is our Lord's rule. Put yourself in
the place of others and you will be at the true point of view for
judging what is just or not.' Meditation sur la notion commune de la
justice (Mollat, p. 70).

31 See note 4.

82 'In which I include contributive justice,' that is, not merely
the giving to each his due, but the promoting of the common good
and the averting of the common evil. De tribus juris naturae et gentium
gradibus (Mollat, p. 16).

33 The different degrees of Eight are merely degrees, not absolute
divisions, and thus one passes into another. Thus to refuse to give
a man his due is to injure him, for ' the absence of good is an evil

U

2QO ON THE NOTIONS OF EIGHT AND JUSTICE

enabled to demand what it is fair that others should give.
But while in the lowest degree of Right no regard was
paid to the differences among men (except to those which
arise from the particular matter in hand), and all men
were regarded as equal, now in this higher degree merits
are weighed, and hence privileges, rewards and punish-
ments appear 34. Xenophon has cleverly represented this
difference in the degrees of Right by the case of the young
boy Cyrus S5, who was chosen to decide between two boys
the stronger of whom had forcibly exchanged clothes with
the other, because he had found that the other boy's gown
fitted him better, while his own fitted the other boy
better. Cyrus decided in favour of the robber ; but his
tutor pointed out to him that the question here was not
whom the gown fitted but whose it was, and that some
day he would more rightly make use of this way of judg-
ing when he himself had gowns to distribute. For equity

and the absence of evil is a good/ (Mollat, p. 70.) Thus * the gover-
nors of societies and certain magistrates are obliged not only to
prevent evil but also to promote good.' (Mollat, p. 68.) ' The science
of the just and that of the useful, that is, the science of public and
that of private good are mutually involved, and it is not easy for
any one to be happy in the midst of the miserable/ Juris et aequi
elementa (Mollat, p. 23).

s* Regarding the lowest degree of right, Leibniz says : l This is
that equality which is commonly called arithmetical, that all are so
far regarded as having the same merit, and, no account of persons
being taken, each receives just as much as he gave up/ De tribus
juris naturae et gentium gradibus (Mollat, p. 15). l The distribution of
goods and evils is often made in proportion to people's virtues and
merits, or vices and faults, and this is called geometrical equality,
because in this very inequality an equality of ratios is observed, so
that unequal things are given to unequal persons, the same pro-
portion being kept between the things given as there is between
the persons,' loc. tit., p. 16. The distinction and the names are due
to Aristotle, although Leibniz's application of them is somewhat
different. Cf. Ethics, v. 3, H3ib 12 sqq. and v. 4, H3ib 25 sqq. See
also Plato, Laws, bk. vi. 757 A sqq., and Grotius, De jure belli et pads,
bk. i. ch. i, § 8, 2.

35 Cyropaedia, bk. i. ch. 3, 17. The story is quoted by Grotius.
bk. i. ch. i, § 8.

ON THE NOTIONS OF EIGHT AND JUSTICE 291

itself leads us in business to act upon Eight in the narrow
sense [jits strictum], that is, the equality of men, unless
when a weighty reason of greater good requires us to
depart from it36. Moreover, what is called respect of
persons has place, not in the exchanging of goods with
others, but in the distributing of our own goods or those
of the public.

I have called the highest degree of Eight by the name
of uprightness or rather piety 37. For what has been said
so far may be understood in such a way as to be limited
to the relations of a mortal life. And indeed bare Eight
or Eight in the narrow sense [jus strictum} has its source
in the need of keeping the peace; equity or charity

a6 ' It is not allowable to take from the rich their goods in order
to supply the poor with them. . . . Because the disorder which
would arise from this would cause more evil and inconvenience in
general than the special inconvenience of the present state of
things. . . . Thus the state should maintain individuals in their
possessions. Yet it may make a tolerable breach in them for the
common security, and even for a great common good.' Meditation
sur la notion commune de la justice (Mollat, p. 81).

37 * The third principle of Right is the will of a superior. . . . But
the superior is either superior by nature, as God is : and His will
again is either natural, hence piety, or law, hence positive Divine
Right ; or the superior is superior by agreement [pactum], as a man
is ; hence civil Right. Piety therefore is the third degree of natural
Right, and it gives perfection and effect to the others. For God,
since He is omniscient and wise, confirms bare right and equity ;
and, since He is omnipotent, He carries them out. Hence the
advantage of the human race, and indeed the beauty and harmony
of the world, coincide with the Divine will.' Methodus Nova, &c.
(1667), § 76 (Dutens, iv. 214). Elsewhere Leibniz argues that
there must be a higher degree of right than mere equity, for
' God is supremely just and supremely good,' and the justice of
God differs not in kind but in degree from the justice of man.
' But it is not for his ease nor in order to keep the peace with us,
that God shows us so much goodness ; for we could not make war
upon Him. What, then, will be the principle of His justice and
what will be its rule ? It will not be that equity or that equality,
which has place among men. . . . We cannot regard God as having
any other motive than perfection/ Meditation sur la notion commune
de la justice (Mollat, p. 72).

U 2

292 ON THE NOTIONS OF RIGHT AND JUSTICE

strives after something more, to wit that while each to
other does as much good as possible, each may increase
his own happiness through that of others ; and, to put it
in a word, Eight in the narrow sense [jus strictum] avoids
misery, Right in the higher sense [jus superius~\ tends to
happiness, but of such a kind as falls to our mortal lot.
But that we ought to subordinate life itself and whatever
makes life desirable to the great good of others so that it
behoves us to bear patiently the greatest pains for the sake
of others 38, this is beautifully inculcated by philosophers
rather than thoroughly proved by them. For the moral
dignity and glory and our soul's feeling of joy on account
of virtue, to which philosophers 39 appeal under the name
of rectitude, are certainly good things of thought or of the
mind, and are indeed great goods, but not such as to pre-
vail with all men nor to overcome all the sharpness of
evils, since all men are not equally moved by imagination ;
especially those who have not become accustomed to the
thought of honour or to the appreciation of the good
things of the soul, either through a liberal education, or
a noble way of living, or the discipline of life or of method.
But in order that it may be concluded by a universal
demonstration that everything honourable is- beneficial
[omne honestum utile] and that everything base is hurtful
[omne turpe damnosum]10, we must assume the immor-

38 'The principles of charity are abnegation of self, esteem of
others.' Tabulae duae disciplinae juris, &c. (Mollat, p. 9). ' Love feels
not the wounds which it suffers, but those which it makes,' loc. cit.
p. 12. 'Among true friends all things are common, even to
misery.' Juris et aequi elementa (Mollat, p. 33).

39 ' If you had listened very attentively to Cicero declaiming on
behalf of rectitude as against pleasure, you would have heard him
magnificently perorate about the beauty of virtue, the deformity
of base things, about a conscience at peace with itself in the depth
of a rejoicing soul, about the good of an untarnished reputation,
about an immortal name and the exultation of glory.' Juris et
aequi elementa (Mollat, p. 30).

40 In his Initium institutionum juris perpetui (Mollat, p. 4) Leibniz,
using a similar expression, adds : ' And moral qualities are turned
into natural.' Cf. Monadology, §§ 88-90.

ON THE NOTIONS OF EIGHT AND JUSTICE 293

tality of the soul 41 and the Ruler of the universe, GOD 42.
Thus it is that we think of all men as living in the most
perfect City [civitas] *3, under a Monarch who on account
of His wisdom cannot be deceived \_falli\ and on account
of His power cannot be avoided 44 ; and a Monarch who is
also so loveable that it is happiness to serve such a master.
Therefore he who spends his soul for Him gains it, as
Christ teaches 45. By His power and providence it comes
to pass that every right passes into fact [omne jus in
factum transeat] 46, that no one is injured except by him-

41 If the soul were not immortal, Leibniz thinks it would be im-
possible for even a wise man to have a sufficient regard for his
own perfection. (Mollat, p. 21.) To a similar effect he writes
against the view of Puffendorf, of whom he had a very poor
opinion. (' He is not much of a lawyer and very little of a
philosopher/ Dutens, iv. 261.) Puffendorf limited natural right
to external laws and regarded all virtues or moral qualities as
based on principles not of reason but of revelation. See Nonita
quaedam ad Samuelis Puffendorfii principia (Dutens, iv. 275 sqq., and
262).

4- Grotius held that ; there would be a certain natural obligation,
even if it were granted (which it cannot be) that there is no God.'
De jure belli et pacis, Prolegomena, § n. ' It is true that Aristotle
recognized this universal justice, although he did not refer it to
God, and I think it admirable in him to have had, nevertheless,
so high an idea of it. But this is due to the fact that for him
a well-constituted government or state takes the place of God as
regards earthly things, and such a government will do what it can
to compel men to be virtuous.' Meditation sur la notion commune de
la justice (Mollat, p. 76).

43 ' Finding, as I do, the principle of justice in the good, Aristotle
takes as the rule of expediency [eonvenance] the best, that is to say,
what would be expedient for the best government (quod optimae
reipublicae conveniret), so that, according to this author, natural
right is that which is most expedient for order.' loc. cit. (Mollat,
p. 80). Of. Monadology, § 85.

** ' So that the honourable and the advantageous are the same,
and no sin is without punishment, no noble deed is in vain or
goes without reward.' (Mollat, p. 96.) Cf. Monadologij, § 90.

« St. Luke, ix. 24 ; xvii. 33 ; St. John, xii. 25.

*6 When power is combined with wisdom and goodness 'it
makes right become fact, so that what ought to be really exists, in
so far as the nature of things allows. And this is what God does

2Q4 ON THE NOTIONS OF BIGHT AND JUSTICE

self47, that nothing done rightly is without a reward and no
sin without a punishment. For, as Christ divinely taught,
all our hairs are numbered, and not even a draught of
water is given in vain to one who thirsts, and thus nothing
is disregarded in the commonwealth of the universe48.
It is on this account that justice is called universal and
comprehends all other virtues 49, for things which other-
wise do not seem to concern any one else, as for instance
whether we abuse our own body or our own property, and
which are beyond the range of human laws, are neverthe-
less forbidden by the law of nature [jus naturale] 50, that
is, by the eternal laws of the Divine Monarchy, since we
owe ourselves and all that is ours to God 81. For as it is
of importance to a commonwealth 52, so much more is it
to the universe, that no one should make a bad use of
that which is his own 53. Accordingly from this is derived

in the world/ Meditation sur la notion commune de la justice (Mollat.
p. 62). Cf. Monadology, § 55.

47 * The immortal soul, exposed to no injuries except from itself,
is always in the hand and keeping of God, and Christ has divinely
bidden us not to fear those who can kill the body but cannot harm
the soul.' Dejustitia (Mollat, p. 40).

48 « If a draught of cold water has its reward, what will those
receive, who have done something great in human affairs for the
glory of God and the common good, seeing that those who bring
many to righteousness \justitia] shall shine as the stars.' De tribu*
juris naturae et gentium gradibus (Mollat, p. 20). Cf. G. iv. 462, 463.

49 Cf. Aristotle, Ethics, v. i, H3oa 8.

50 ' Right [jus] cannot be unjust : that would be a contradiction.
But law [lex] may be. For it is power that ordains and upholds
law ; and if this power is lacking in wisdom or goodwill, it may
ordain and uphold very wicked laws. But happily for the universe,
the laws of God are always just, and He is in a position to uphold
them, as He undoubtedly does, although He does not always visibly
and immediately do so, for which He has doubtless excellent
reasons.' Meditation sur la notion commune de la justice (Mollat, p. 61).

51 ' We were not born merely for ourselves, but others claim for
themselves a part of us, and God the whole.' Monita ad Puffendorfii
principia, § 5 (Dutens, iv. 281). l Quicquid sumus Dei sumus' (Mollat,

P- 3).

58 'Saluspublicasupremalex est' (Mollat, p. 3).

53 * For when we are vicious, we not only injure ourselves, but

ON THE NOTIONS OF EIGHT AND JUSTICE 295

the force of that highest precept of Eight, which bids us
live virtuously (that is, piously). And in this sense learned
men have rightly put it down among things to be desired,
that natural law and the law of nations [jus naturae et
gentium] should be formulated in accordance with the
doctrines of Christianity, that is (according to the teach-
ing of Christ) TO, di/wrepa 54, the sublime things, the divine
things of the wise. Thus I think I have very fitly
explained the three precepts of Eight or three degrees of
justice, and have pointed out the sources of natural law.

Besides the eternal rights of a rational nature which
flow from the Divine Source, there is also observed a
voluntary Right, derived from customs or made by a
superior. And indeed in the commonwealth civil Eight
receives its force from him who has the supreme power 55 ;

we also diminish, in so far as it depends upon us, the perfection
of the great commonwealth, of which God is the Monarch.'
Meditation sur la notion commune de la justice (Mollat, p. 76).

54 Possibly Leibniz is thinking of 17 dvoaOev ao<f>ia (St. James, iii.
15, 17). Leibniz seems himself to have intended to supply the
want to which he here refers, for he sketched the outline of
a book on the subject, which is printed by Mollat (pp. 8 sqq.), under
the title Tabulae duae disciplinae juris naturae et gentium secundum
disciplinam Christianorum. In this he refers to St. James as ' calling
charity voftos paei\iK6s, the royal law (ch. ii. 8), inasmuch as it
comes from the supreme King (St. Paul, Romans, i. 32, ducaiajjia rov
foot)).' (Mollat, p. n.)

55 While admitting a right of this kind as distinct from natural
right, Leibniz maintains that the two ought always to be in
harmony. He thus condemns the view of Hobbes, that the basis
of right is power, which he identifies with the view of Thrasymachus
in Plato's Republic, bk. i. (see Mollat, p. 57 sqq.). Cf. Le Portrait
du Prince (Klopp, iv. 461) : 'As the order of States is established
on the authority of those who govern them and on the dependence
of their peoples, nature which destines men for civil life endows
them at birth with different qualities, some for commanding,
others for obeying, in order that the power of the sovereign in
a monarchy and the inequality between those who command and
those who obey in a republic, be no less founded on nature than
on law, on virtue than on fortune. So princes ought to be above
their subjects by their virtue and their natural qualities, as they
are above them by the authority which the laws give them, in

296 ON THE NOTIONS OF EIGHT AND JUSTICE

outside of the commonwealth or among those who are
sharers in supreme power (of whom there are sometimes
several even in the same commonwealth) there is the
sphere of the voluntary law of nations, accepted by the
tacit consent of the peoples. . . .

But Christians have also another common bond, namely
the positive Divine law [jus] which is contained in the sacred
books. To which are to be added the sacred canons
received by the whole Church and afterwards in the West
the Papal law [jures] to which kings and peoples submit
themselves. And in general (and certainly not against
reason) it seems for a long time to have been accepted,
before the schism of last century, that there should be
understood to be a certain general commonwealth of the
Christian nations, the heads of which were in sacred
things the Pope [Pontifex Maximus] and in temporal
things the Emperor of the Romans, who also seemed to
retain so much of the law of the old Roman monarchy
as was needed for the common good of Christendom,
without prejudice to the Right of kings and the liberty
of princes.

order to reign both by natural right and by civil right, like the
first kings in the world, who having been raised to the government
of their peoples by their virtue and their intellectual gifts, com-
nianded as much by nature as by law, by merit as by fortune.'

NEW SYSTEM OF THE NATURE OF SUB-
STANCES AND OF THE COMMUNICATION1
BETWEEN THEM, AS WELL AS OF THE
UNION THERE IS BETWEEN SOUL AND
BODY2. 1695.

PREFATORY NOTE.

IN this paper, which appeared anonymously in the Journal
des Savants of June, 1695, we nave Leibniz's first public state-
ment of his New System (see Introduction, Part i. p. 12). In
character it is much more tentative than his later writings,
and it is only towards the end of the paper (§• 17) that he
ventures to speak of his view as 'more than a hypothesis.'
This is very characteristic of Leibniz : he likes to advance by
suggestion and hypothesis. But he regards hypothesis as
merely a stepping-stone : he will not rest there if it is possible
to go farther. ' In matters where certainty can be obtained,
I will not use hypotheses,' he says to Bernouilli (G. Math. iii.
575). And nearly twenty years after he published the New
System, Leibniz writes of ' this hypothesis, which I venture to
call proved ' (Monadology, § 59). Thus the peculiar interest of
the New System is that it lets us see something of Leibniz's
philosophy in the making. For in this work he writes histori-
cally, indicating to us the course which his thought took.

The New System may be divided into two main parts, in the
first of which (§§ i-n inclusive) Leibniz shows us how he was

1 i. e. inter-relation or interaction.

3 The title in the First Draft is New system for explaining the nature
of substances and their communication with one another, as well as the union
of soul with body.

298 NEW SYSTEM

led to re-introduce into philosophy the ' substantial forms '
of the Scholastics, and in what sense these forms, souls, simple
substances or real units are to be understood ; while in the
second (§§ 12-18) he applies his theory of substance to the
question of the relation between soul and body, mind and
matter, and finds that the problem can be satisfactorily solved
only through the hypothesis of a pre-established harmony
between all simple substances. Analyzing the title of the
paper, we may say that the first part deals with the nature
of substances and the second with their communication.

Erdmann (E. 124 sqq.) gives the New System as it was origin-
ally published. Gerhardt (G. iv. 477 sqq.) gives it as it was
afterwards revised and altered by Leibniz, and he also prints
an interesting First Draft of it. I have translated from
Gerhardt's text, indicating its differences from Erdmann's;
and in the notes will be found some passages from the First
Draft. The paragraphs are numbered in E. ; but not in G.

i. Several years ago I conceived this system and had
communications about it with learned men, especially
with one of the greatest theologians and philosophers of
our time3, who, having been informed of some of my
opinions by a person of the highest rank4, had found
them very paradoxical5. But having received explana-
tions from me, he withdrew what he had said in the

3 * Mons. Arnauld.' Note by Leibniz, who tells us also that with
regard to his New System he ' followed the rule of Horace : nonumque
prematur in annum ' (G. iv. 490). There is an interesting account
of Arnauld and his friends in Stephen's Essays in Ecclesiastical
Biography, vol. i, Essay vi, The Port-Eoyalists.

* Landgraf Ernest of Hesse-Kheinfels (1623-1693), who in 1652,
shortly after the close of the Thirty Years' War, became a Eoman
Catholic and published a justification of the course he had taken.
A copy of this work he sent to the Duke of Brunswick, and he
thus came into communication with Leibniz. They kept up
a correspondence on theological and ecclesiastical subjects until
the death of the Landgraf in 1693.

5 Arnauld writes to the Landgraf : — i I find in these thoughts
so many things which alarm me and at which almost all men,
if I am not mistaken, will be so shocked, that I do not see
what use there could be in a writing which apparently will be
rejected by everybody ' (G. ii. 15). Leibniz felt this very keenly ;
but Arnauld made ample explanations and apologies in a letter to
Leibniz himself. (G. ii. 25.)

NEW SYSTEM 299

most generous and exemplary way ; and having approved
a number of my propositions, he praetermitted his cen-
sure as regards the others, to which he was still unable
to agree. Since that time I have continued my medi-
tations, as I had opportunity, in order that I might give
to the public only well-tested opinions, and I have also
endeavoured to meet the objections raised against my
essays on Dynamics, which have some connexion with
this6. And in short, as some people of consideration
have desired to see my opinions7 more elucidated, I have
ventured upon these meditations, although they are by no
means popular nor such as to be relished by every kind
of mind. I have been led to this mainly in order that
I may profit by the judgment of those who are en-
lightened in these matters ; since it would be too trouble-
some a task to seek out and call to my aid individually
those who might be disposed to give me suggestions,
which I shall always be glad to receive, provided they
are marked by a love of truth rather than by a passion for
preconceived opinions 8.

2. Although I am one of those who have worked much
at mathematics, I have none the less meditated upon
philosophy from my youth up ; for it always seemed to
me that there was a possibility [moyen] of establishing
something solid in philosophy by clear demonstrations.
I had penetrated far into the country of the Scholastics,
when mathematics and modern authors brought me out
again, while I was still quite young. The beauty of
their mechanical explanations of nature charmed me,

6 Leibniz's principal essay on Dynamics is the Specimen Dyna-
micum, published in the Acta Eruditorum for April, 1695. (Gr. Math,
vi. 234.)

7 The First Draft has in addition the words: 'Which they
think may be useful in harmonizing faith with reason as regards
matters of importance.'

8 ' I desire objections to be made against me, which oblige me
to go beyond what I have already said. Objections of this kind
are instructive and I like them because I may profit by them
and make others profit by them ; but it is not easy to make them.'
Lettre a Masson (1716) (G. vi. 629).

300 NEW SYSTEM

and I rightly contemned the method of those who make
use only of forms and faculties, from which we learn
nothing9. But afterwards, having tried to go deeply
into mechanical principles themselves, in order to find
a reason for the laws of nature which experience makes
known, I perceived that the mere consideration of an
extended mass is not sufficient and that use must also be
made of the notion of force, which is very intelligible,
though it belongs to the sphere of metaphysics10. It
appeared to me also that the view of those who trans-
form or degrade the lower animals into mere machines,
although it seems possible, is improbable and indeed is
contrary to the order of things.

3. At first, when I had freed myself from the yoke
of Aristotle, I took to the void and the atoms, for that
is the view which best satisfies the imagination. But
having got over this, I perceived, after much medita-
tion, that it is impossible to find the principles of a real
unity in matter alone, or in that which is only passive,
since it is nothing but a collection or aggregation of parts
ad infinitum". Now a multiplicity [multitude] can derive
its reality only from genuine units [unites] which come
from elsewhere and are quite other than the mathematical
points which are only extremities of the extended and

9 See Introduction, Part i. p. 3, and Part iv. p. 156.

10 The meaning is that, although force is not anything that
can be pictured or represented in imagination, it can nevertheless
be quite well understood. The notion of force is ' metaphysical, '
because force is not merely a physical thing that can be perceived
in the same way as other physical things. For instance, we
can understand, but we cannot perceive, the potential energy
of a mass. In the First Draft, Leibniz says : ' By force or power
[jpuissance] I do not mean the power [powroi'r] or mere faculty,
which is nothing but a near possibility of acting and which, being
as it were dead, never produces an action without being stimulated
from without, but I mean something between power to act [pouwir]
and action, something which includes an effort, an actual working
[acfe], an entelechy, for force passes of itself into action, in so far
as nothing hinders it. Wherefore I regard force as constitutive
of substance, since it is the source [principe~] of action, which is
the characteristic of substance ' (G. iv. 472).

11 Cf. Introduction, Part ii. p. 23.

NEW SYSTEM 301

modifications 12, of which it is certain that the continuous
[continuum] cannot be composed 13. Accordingly, in order
to find these real units [unites] I was constrained to have
recourse to a real and animated point, so to speak, or to an
atom of substance which must contain some kind of form
or active principle, so as to make a complete being u. It
was, then, necessary to recall and, as it were, to rehabili-
tate the substantial forms 15, which are so much decried
now-a-days, but in a way which renders them intelligible
and separates the use to which they should be put from
the abuse which they have suffered. I found, then,
that the nature of the substantial forms consists in force,
and that from this follows something analogous to feeling
[sentiment] and desire [appetit] ; and that thus they must
be conceived after the manner of the notion we have of
souls 16. But as the soul ought not to be used to explain
in detail the structure of the animal's body, I held that
similarly these forms must not be used to solve the par-
ticular problems of nature, although they are necessary
for establishing true general principles 17. Aristotle calls
them first entelechies. I call them (in a way that may

12 That is, not independent beings, but properties or relations,
like the two ends of a stick.

13 E. reads : l quite other than the points of which it is cer-
tain,' &c. See Prefatory Note.

14 E. reads : ' I was constrained to have recourse to a formal
atom, since a material being cannot be at once material and
perfectly indivisible or possessed of a genuine unity/

15 Substantial forms as distinct from accidental forms, the former
being used to explain substances, the latter to explain their
accidents.

16 The transition from point to point is here rather rapid. The
analogy between desire and force is manifest, but that between
feeling and force is more obscure. The essence of feeling, accord-
ing to Leibniz, is not consciousness but the representation or
concentration of many in one ; and similarly the manifold actions
of any substance are ' enveloped ' or potentially contained in its
force or vital principle. Cf. Monadology, §§13 sqq.

17 In the First Draft, Leibniz says : ' In my opinion everything
in nature takes place mechanically, and to give an exact and
complete explanation of any particular phenomenon (such,- for
instance, as weight or elasticity), nothing but figure and motion
need be used' (G. iv. 472.)

302 NEW SYSTEM

perhaps be more easily understood) primary forces1*,
which contain not only actuality [Vacte] or the comple-
ment of possibility, but also an original activity.

4. I saw that those forms and those souls, as well as
our mind [esprit], ought to be indivisible, and in fact
I remembered that this was the opinion of St. Thomas
with regard to the souls of the lower animals19. But
this truth 20 renewed the great difficulty about the origin
and the duration of souls and forms. For, as every
simple*1 substance which has a genuine unity can have
a beginning and an end only by miracle, it follows that
they can come into being only by creation and come to
an end only by annihilation22. Thus I was obliged to
recognize that (with the exception of the souls which
God still intends specially to create) the constitutive
forms of substances must have been created with the
world and must always continue to exist23. So some of
the Scholastics, like Albertus Magnus and John Bacon,
had an inkling of part of the truth regarding the origin
of these forms 24. And all this ought not to appear ex-

18 ' To distinguish it from the secondary, which is called moving
force, and which is an accidental limitation or variation of primary
force.' First Draft (G-. iv. 473).

19 Possibly Leibniz refers to the passage in which Aquinas
says : ' The substantial form, which requires diversity in the
parts, for instance the soul and especially the soul of complete
animals, does not stand in exactly the same relation to the whole
and to the parts. And hence it is not divided per accidensj that
is to say, by a quantitative division.' Summa Theol. i. qu. 76,
art. 8. Elsewhere, however, Aquinas says : ' The sensitive soul
in the lower animals is corruptible ; but in man, since it is the
same in substance as the rational soul, it is incorruptible.' De
Anima, art. 14 ad primum.

20 Janet reads cette nouveaute, ' this new view,' instead of cette verite.

21 E. omits ' simple.'

22 The First Draft has in addition the words : * brought about
expressly by the supreme power of God ' (G. iv. 474).

23 Cf. Principles of Nature and of Grace, § 6 ; Monadology, §§ 4, 5, 6,
and 76. The First Draft has : ' genuine unity is absolutely in-
dissoluble ' (G. iv. 474).

2* Cf. Monadology, note 116. The statement of Leibniz is so
vague that one can hardly fix the passage in Albertus Magnus
of which he is thinking. In his Summa de Creaturis (part ii. qu. 16,
art. 3), Albertus Magnus says : ' We hold that the souls of the

NEW SYSTEM 303

traordinary, for we are only attributing to forms the
duration which the G-assendists 25 accord to their atoms.

5. Nevertheless I held that we must not include
among these, without distinction (or confound with
other forms or souls26), minds [esprits] or rational souls,
which are of a higher rank and have incomparably more
perfection than those forms which are sunk in matter,
which in my opinion are to be found everywhere 27, and

lower animals and plants are educed from the matter of the seed
through generation. But if it be asked whether they are in the
seed or not, we say that they are there in one way, and in another
way they are not. . . . They are not there actually [actu], but they
are there in the potency [potentia] of the efficient cause and the
matter [efficientis et materiae]. And if it be asked : What is this
efficient cause ? Is it the soul or not ? We say . . . that it is not
the soul. . . .' Cf. De Animalibus (xvi. n) : 'The principle of life
is in the seed in the way in which the act is in the instruments
of the act. . . . And in this way also the soul is in the seed like an
act and not like the entelechy of an organic body. . . . That which
is in the seed is something of the soul [aliquid animate] and not the
soul.' See also De Anima, bk. i. Tract. 2, cap. 13: 'The soul is
indivisible, and nothing can be cut off from it.' John Bacon or
Bacho, is better known as John Baconthorp, from the place in
Norfolk where he was born towards the close of the thirteenth
century. He was a Carmelite monk and a schoolman, and in 1329
he became Provincial of the English Carmelites. He lived much
in Oxford and Paris, where he obtained a great reputation for
learning. He was called the Kesolute Doctor. He died in 1346.
Besides a book on the rule of his order, his chief work is the
Commentaria seu quaestiones in quatuor libros Sententiarum. Leibniz
probably refers to a passage in this book, In Secundum, Dist. xii.
Qu. i, Art. 3, § 3.

35 Pierre Gassendi (1592-1655), a French priest and a disciple of
Bacon, expounded the doctrines of Epicurus and endeavoured to
adapt them to the conditions of modern thought. His attitude
was both anti- Scholastic and anti-Cartesian. He severely criticized
Descartes's Meditations and thus began a long controversy with
Descartes regarding the origin of knowledge, Gassendi taking
a purely experiential standpoint as against Descartes's belief in
innate ideas. See Descartes, Meditations, Cinquiemes Objections (by
Gassendi). Gassendi himself does not attribute eternity to his
atoms, which he regards as created by God. The spirit of his
thinking is well expressed in his own words: 'The shadow of
truth which I everywhere pursue suffices to fill me with joy. I say
"the shadow," for, as to truth itself, God alone can know it.'
Lettre a Golius.

26 This clause within brackets is given by G., but not by E.

27 ' Which in my opinion are to be found everywhere ' is given
by G., but not by E. Cf. Monadology, §§65 sqq.

304 NEW SYSTEM

in comparison with which minds or rational souls are
like little gods, made in the image of God and having
within them some ray of the Divine enlightenment
\lumieres]. For this reason God governs minds [esprits]
as a prince governs his subjects, and indeed as a father
looks after his children ; while, on the other hand, He
deals with other substances as an engineer works with his
machines. Thus minds \esprits] have special laws which
put them above the revolutions of matter through the
very order which God has put in them 28 ; and it may be
said that everything else is made only for them, these
revolutions themselves being arranged for the felicity of
the good and the punishment of the wicked 29.

6. However, to return to ordinary forms or material
souls™, the duration which must be attributed to them
(in place of that which used to be attributed to atoms)
might lead to a doubt whether they do not go from body
to body; which would be metempsychosis, something
almost analogous to the transmission of motion and the
transmission of species 31 which certain philosophers have
maintained. But this fancy is very far from the nature
of things. There is no such passing32. And here the
transformations noted by MM. Swammerdam, Malpighi,
and Leuwenhoek 33, who are among the most excellent

28 i Through the very order which God has put in them ' is given
by G., but not by E.

29 Cf. Monadology, §§ 83, 84, 89.

30 E. has dmes materieUes while G. has dmes brutes. Leibniz prob-
ably wrote brutes in order to avoid the ambiguity of the other
expression, which seems to suggest that some souls are 'material,'
while Leibniz, of course, holds that all are 'immaterial.' By
' material or brute souls ' he means the souls which are ' sunk
in matter' (§ 5), i.e. unconscious souls, in which matter as a
phenomenon is bene fundatum.

31 i. e. transference of quality from one body to another, as
when the quality of the leaven is imparted to the whole lump
or the red colour of a drop of wine is diffused throughout water.
Cf. Monadology, note 10.

32 The First Draft says : ' This transmigration of souls is an
absurdity. The principles of substance do not flutter outside of
substances ' (G. iv. 474).

33 ipjie reference is to such changes as that from caterpillar to

NEW SYSTEM 305

observers of our time, have come to my aid and have
led me the more readily to admit that no animal nor any
other organic substance comes into existence at the time
at which we think it does, and that its apparent genera-
tion is only a development and a kind of growth [aug-
mentation]. I have noticed also that the author of the
Eecherche de la Verite™, M. Eegis85, M. Hartsoeker 36,

butterfly. 'God has preformed things, so that new organisms are
nothing but a mechanical consequence of a preceding organic
constitution ; as when butterflies come from silkworms, which
M. Swammerdam has shown to be merely a process of develop-
ment/ The'odicee, Preface (E. 476 a ; G. vi. 41) ; cf. Monadology,
§ 74. John Swammerdam (1637-1680), of Amsterdam, is famous
as an observer of insect life. Marcello Malpighi (1628-1694), of
Bologna, the famous anatomist, is probably mentioned by Leibniz
because of his work on the process of incubation. Anton van
Leuwenhoek (1632-1723), of Delft, did much to support Harvey's
theory of the circulation of the blood. Leibniz refers to him on
account of his investigations regarding spermatozoa, in connexion
with which he may be regarded as one of the founders of the
science of embryology.

31 Nicolas Malebranche (1638-1715) published his De la Recherche
de la Verite in 1674. Descartes had already given a similar title
to one of his writings. While differing greatly from Malebranche's
general theory, Leibniz endeavours to harmonize Malebranche's
view with his own on many particular points. See Foucher de
Careil, Lettres et opuscules inedils de Leibniz, Introduction. Leibniz
corresponded intermittently with Malebranche upon philosophical
and other questions between 1674 and 1711. In his Recherche de
la Verite, bk. ii. ch. 7, § 3 ((Euvres, Jules Simon's ed., vol. iii.
pp. 199 sqq.), Malebranche xises expressions which indicate a belief
in the theory of preformation.

35 Pierre Sylvain Regis or Leroy (Petrus Silvanus Eegius)
(1632-1707) was an exponent of the philosophy of Descartes, which,
in opposition to the idealism of Malebranche, he developed in an
empirical direction. Descartes, however, disowned the views of
Regis. See (Euvres de Descartes (ed. Cousin), vol. x. p. 70. Cf.
"Veitch, Method &c. of Descartes, note vi. on Innate Ideas. Cf. Kuno
Fischer, Descartes and his School, bk. iii. ch. 2. Regis, whose philo-
sophical school at Paris was in 1675 closed by Archbishop Harlay
on account of its Cartesian teaching, wrote a violent attack upon
Leibniz, charging him with injustice towards Descartes. This
attack, anonymously published, will be found, along with Leibniz's
reply, in E. 140 ; G: iv. 333.

^ Nicolas Hartsoeker (1656-1725) was a Dutch physicist, whose
earlier work had mainly to do with the making of microscopes
and telescopes. Leibniz, writing to Des Bosses in 1709, calls him
vir clarissimus in Dioptricis (E. 461 a ; G. ii. 377). In 1694 Hartsoeker
published an atomist philosophy of nature, based on the sup-

306 NEW SYSTEM

and other able men have not been very far from this
opinion.

7. But there still remained the greater question, what
becomes of these souls or forms at the death of the
animal or on the destruction of the individual, of the
organic substance ? This is a most perplexing question,
inasmuch as there seems little reason in thinking that
souls remain uselessly in a chaos of confused matter37.
Accordingly I came to the conclusion that there is only
one view that can reasonably be taken, namely, that
which affirms the conservation not only of the soul but
also of the animal itself and its organic mechanism ;
although the destruction of its grosser parts has reduced
it to a minuteness which makes it as little perceptible
to our senses as it was before its birth 38. Thus no one
can exactly note the real time of death, which for a time
may be taken for a mere suspension of perceptible
activities and which at bottom is never anything else
than this in the case of mere animals : witness the re-
suscitation of flies which have been drowned and then
buried in powdered chalk, and several similar instances
which are sufficient to inform us that there might be
other resuscitations, even when the destruction of the
organic substance had gone much farther, if men were
in a position to reconstruct the [animal] mechanism39.
And apparently it was about something like this that
the great Democritus spoke (thorough atomist as he
was), though Pliny laughs at what he said 40. Accord-
position of perfectly hard atoms in a perfect fluid. In 1704 he
became Professor of Mathematics and Physics at Diisseldorf, and
from 1706 to 1712 he discussed his philosophy of nature with
Leibniz in a correspondence to which Leibniz frequently refers
in his letters to Des Bosses. The correspondence is given by
Gerhardt, iii. 483. Cf. Third Explanation of the New System, p. 334.

87 That is, matter which is (comparatively) inorganic.

38 Cf. Monadology, §§73 and 77.

39 Cf. Monadology, § 14, note 23 and § 21 ; Principles of Nature and
of Grace, §§ 6 and 12.

40 Cf. Lettre a des Naizeaux (1711) (E. 676 b ; G. vii. 535) : 'Plato
believed that material things are in a perpetual flux, but that

NEW SYSTEM 307

ingly it is natural that an animal, having always been
living and organic (as some people of great penetration
are beginning to recognize), should likewise always re-
main so. And thus, since an animal has no first birth
or entirely new begetting [generation], it follows that it
will have no final extinction or complete death, in the
strict metaphysical sense, and that consequently, in
place of the transmigration of souls, there is nothing but
a transformation of one and the same animal, according
as its organs are differently enfolded [plies] and more or
less developed 41.

8. Nevertheless rational souls follow much higher
laws and are exempt from everything which could make
them lose the rank [la qualite] of citizens of the society
of spirits [esprits] ; God having provided for this so care-
fully that all the changes of matter cannot make them
lose the moral qualities of their personality. And it may
be said that everything tends to the perfection, not only
of the universe in general, but also of these created

genuine substances continue to exist. By "genuine substances"
he appears to have meant only souls. But perhaps Democritus,
thorough atomist as he was, believed in the conservation of the
animal also. For he taught that there is resuscitation [reviviscence'],
as Pliny says of him : reviviscendi promissa Democrito vanitas, qui ipse
non revixit' [the false opinion of a coming to life again, put forth
by Democritus, who himself did not come to life again]. 'We
hardly know anything about this great man, except what has
been borrowed from him by Epicurus, who was not capable of
always taking his best things.' The words quoted from Pliny-
occur in his Historia Naturalis, bk. vii. cap. 55. (Sillig's ed., vol. ii.
p. 60.)

u Monadology, §§72 and 73. In the First Draft (G-. iv. 474)
Leibniz writes : ' As the minuteness of organic bodies may be
infinite (which may be seen from the fact that their seeds, enclosed
in one another, contain enfolded a continual succession of organized
and animate bodies), it is easily seen that even fire, which is
the most penetrating and violent agent, will not destroy an
animal, since it will at most reduce it to such a smallness that
fire can no longer act upon it/ In the correspondence with
Arnauld, to which Leibniz refers in § i of the New System, Arnauld
had asked (as an objection to Leibniz's theory of the indestruc-
tibility of animals) what became of the ram which Abraham
sacrificed in place of Isaac. The foregoing passage contains in
brief Leibniz's answer.

X 2

308 NEW SYSTEM

beings in particular, which are destined to such a degree
of happiness that the universe is concerned in it, in
virtue of the Divine goodness which is imparted to each,
so far as supreme wisdom can allow.

9. As to the ordinary body42 of animals and other
corporeal substances, which have hitherto been supposed
to suffer total extinction and whose changes are de-
pendent rather upon mechanical rules than upon moral
laws, I observed with pleasure that the author of the
book De Diaeta (which is attributed to Hippocrates43)
had some inkling of the truth, when he expressly said
that animals are not born and do not die and that
the things which we suppose to come into being and
perish merely appear and disappear. This was also the
opinion of Parmenides and of Melissus according to
Aristotle 44 ; for these men of old had more worth than
we suppose.

10. I am as ready as man can be to do justice to the
moderns, yet I think they have carried reform too far ;
among other things, in confounding natural with arti-

42 G. has corps ordinaire. E. reads cours ordinaire ('usual history ').

43 Hippocrates, 'the father of medicine/ is no longer regarded
as the author of the De Diaeta (trepl Siairr/^. The passage to which
Leibniz refers is most probably the following : dir6\\vTat ptv vvv
ovo€V 6.TravT(av xpr/fMTcav, ov8e yiverai o n pri KOI irpoaOev r/v . . . aal
OVTC, el faov, atroOaveiv olov re, et /«) ueTa irdvTcav TTOV yap diroOaveiTai ;
oijTf T& fj.rj ov yeveaOai' ir60ev yap fffrai ; dAA.' avgerai -navra fifiovrat
teal I? TO fj.r}Kto~Tov KOI [Is TO^ kXa-^iarov^ rcav y€ Svvaraiv, i. 4. 'Now
none among all things is destroyed, and there does not come into
being that which was not in existence before. . . . And neither is it
possible for an animal to die, except along with all things (for
how shall it die ?) ; nor can that which is not come into being
(for whence shall it be?); but all things grow and diminish to
the greatest and to the least that is possible.' See Bywater,
Heraditi Ephesii Reliquiae, Appendix ii.

4t De Cae'o, F I, 298^ 14: of ft€v yap avrSiv o\cos avetXov yevtaiv Kai
<p6opdv ov6(.v yap oijrt ytyvfadai <pa(Tiv ovre <pOdpecr8ai TWJ/ ovrcav, d\Xa
jju'tvov SoKfiv fffjiiv olov ol irfpl MeA.to'O'oi' re teal HapneviSrjv, ouy, et Kal
Ta\Xa \eyovai Ka\S>s, d\\' ov <}>vffiKu>s ye 8ef VOftiffVU \eyeiv. Cf.
Monadology, § 74, note 116. But the views of Parmenides and
Melissus, who deny the reality of change or of becoming, are very
far removed from the position of Leibniz. They deny change or
becoming of TO tv, not of each of a plurality of substances.

NEW SYSTEM 309

ficial things, through not having great enough ideas of
the majesty of nature. They think that the difference
between nature's machines and ours is only a difference
of size. This has lately led a very able man45 (the
author of the Entretiens sur la pluralite des Mondes 46) to
say that, when we look closely at nature, we find it less
wonderful [admirable] than we had thought, it being
merely a kind of workshop. It seems to me that this
is to give an idea of nature which is not quite just nor
worthy of it47, and that it is only our system which
shows how real and immense after all is the distance
between the least productions and mechanisms that are
made by the Divine wisdom and the greatest artistic
masterpieces of a limited mind [esprit] — the difference
being not merely one of degree, but even one of kind.
Accordingly it is to be observed that the machines of
nature have a really infinite number of organs 48 and are
so well equipped and so proof against all accidents that it
is not possible to destroy them. A natural machine still
remains a machine in its smallest parts, and moreover

45 Bernard le Bovier de Fontenelle (1657-1757), a nephew of
Pierre Corneille, was secretary of the Acade'wie des Sciences at Paris
from 1699 to 1741. One of his duties as secretary was to prepare
every year filoges or tributes to the memory of those members of
the academy who had died during the year, and among the ablest
of these papers is his Eloge de Leibniz, published in the Histoire de
I' Academic Royale des Sciences de Paris, anne'e 1716. He wrote a great
deal of indifferent verse ; but his main work consisted in the
popularizing of scientific ideas. There is a saying of his (which
sounds like a parody of Leibniz) that 'everything is possible, and
everybody is right/

*" 'Conversations on the Plurality of Worlds.' This book (pub-
lished 1686) was intended to popularize the astronomical theories
of Copernicus. It has been several times translated into English.

47 E. has merely 'which is not worthy of it.'

48 A machine made by man has a finite number of ' organs ' or
parts having each a definite function in relation to the whole.
The tooth of a wheel is an < organ ' of the wheel and of the whole
machine. But the material particles which make up this tooth
are not 'organs' of the wheel or the machine. Nature, on the
other hand, is organic throughout : no part of it is not an 'organ '
of the whole. Thus a natural machine has 'a really infinite
number of organs.' Cf. Monadology, § 64.

310 NEW SYSTEM

it always remains the same machine it originally was,
being merely transformed through different foldings
[plis] it receives, and sometimes expanded, sometimes
contracted and, as it were, concentrated, when we think
that it is lost.

ii. Further, by means of the soul or form, there is a
real unity which corresponds to what in us is called the
Ego ; but this cannot be the case in regard to the machines
of art or to mere material mass, however well organized
it may be, which can be considered only as an army or
a flock, or as a pond full of fish49, or as a watch com-
posed of springs and wheels. Nevertheless if there were
no real substantial units [unites] there would be nothing
substantial or real in the collection. It was this that
compelled M. Cordemoi 50 to give up .Descartes and to
adopt Democritus's doctrine of atoms in order to find
a real unit [unite]. But atoms of matter are contrary to
reason, besides being still composed of parts, since the
invincible attachment of one part to another (even if
it could rationally be conceived or supposed) would not

49 '"When I say "I," I speak of one substance only; but an
army, a flock, a pond full of fish, even though it were frozen and
had become solid with all the fish in it, will always be a collection
of several substances.' First Draft (G. iv. 473). Cf. Introduction,
Part iii. pp. 96-98.

50 Ge"raud de Cordemoi (born early in the seventeenth century,
died 1684"), a French Cartesian, arrived independently at an
Occasionalist position, about the same time as Geulincx developed
his more famous system. See Kuno Fischer, Descartes and his School,
bk. iii. ch. 2. His most important philosophical work is Le discerne-
ment du corps et de I'dme (1666), and it was in this book that he so far
gave up Descartes as to adopt a theory of atoms. Cf. Leibniz's
Lettre a la Princesse Sophie (1705) (G. vii. 561) : 'M. Cordemoi, seeing
that compound things must be the result of simple things, was
forced, Cartesian though he was, to have recourse to atoms,
abandoning his master. . . .' Also Lettre a Arnauld (1686) (G. ii. 78) :
' M. Cordemoi ... in order to account for the substantial unity in
bodies, felt obliged to admit atoms or indivisible extended bodies
in order to find something fixed to constitute a simple being. . . .
He appears to have recognized something of the truth, but he had
not yet seen in what the real notion of a substance consists.'
Cordemoi, however, was more devoted to history than to philo-
sophy.

NEW SYSTEM 31 1

make one part any the less different from another51.
Only atoms of substance, that is to say real units [unites]
absolutely devoid of parts, are the sources of actions, and
the absolute first principles of the composition of things
and, as it were, the ultimate elements in the analysis of
substantial things 52. They might be called metaphysical
points ; they have something of the nature of life and
they have a kind of perception, and mathematical points
are their points of view53 for expressing the universe.
But when a corporeal substance is contracted, all its
organs together make but one physical point for us54.
Thus physical points are only apparently indivisible.
Mathematical points are indivisible [exacts], but they are
only modalities. None but metaphysical or substantial
points (consisting of forms or souls) are indivisible [m*c£]
and real ; and without them nothing would be real, since
without genuine units [unites] there would be no multi-
plicity 55.

12. Having settled these things, I thought I had
gained my haven, but when I set myself to meditate
upon the union of soul and body I was as it were driven
back into the deep sea. For I found no way of explaining
how the body transmits anything to the soul or vice versa,
nor how one substance can communicate with another
created substance. So far as can be gathered from his
writings, M/ Descartes gave this up56; but his disciples,

61 See Introduction, Part ii. p. 30.

52 E. reads * substances/ In the First Draft, Leibniz says :
' What constitutes corporeal substance must be something which
corresponds to what is called ego in us, which is indivisible and
nevertheless active [agissant], for being indivisible and without
parts, it will no longer be a being by aggregation, but being active
[agissant] it will be something substantial ' (GK iv. 473).

53 E. reads 'point of view.' Mathematical points are merely
positions in space, and when we speak of positions in space, we
are describing in a confused way the essential differences between
Monads. Cf. Monadology, §§ 60-62.

54 Cf. Monadology, §§68 and 69.

65 Cf. Introduction, Part ii. pp. 28 sqq.

66 < The human mind is not capable of distinctly conceiving the
difference of essence between soul and body and, at the same time,

312 NEW SYSTEM

seeing that the common opinion is inconceivable, held
that we are aware of the qualities of bodies, because God
makes thoughts arise in the soul on occasion of the
motions of matter ; and, on the other hand, when our
soul wishes to move the body, they hold that it is God
who moves the body for it. And as communication of
motions also appeared to them inconceivable, they were
of opinion that God gives motion to a body on occasion
of the motion of another body. This is what is called
the system of occasional causes, which has been brought
into wide repute by the excellent reflexions of the author
of the Recherche de la Verite 57.

13. It must be admitted that they have gone far into
the difficulty in telling us what cannot take place ; but
they do not appear to have removed it by their explana-
tion of what actually does happen. It is quite true that
one created substance has, in the strict metaphysical
sense, no real influence upon another, and that all things
and all their reality are continually produced by the
power [vertu^ of God. But to solve problems it is not
enough to make use of a general cause and to introduce
what is called Deus ex machina. For to do this, without
offering any other explanation which can be derived from
the order of secondary causes, is just to have recourse *to
miracle. Ill philosophy wre must endeavour to give a
reason for things by showing how they are carried out
by the Divine wisdom in conformity with the notion of
the matter we are dealing with58.

14. Accordingly, being obliged to admit that it is im-

their union, for it would then be necessary to conceive both as
a single being and at the same time as two different things, which
.is a contradiction.' (Euvres (ed. Cousin), vol. ix. p. 132.

57 Arnold Geulincx (1625-1669) was the real founder of Occa-
sionalism. The first part of his Ethica appeared in 1665, while
Malebranche's great work was published in 1674. See Introduction,
Part ii. pp. 42 sqq. Cf. Kuno Fischer, Descartes and his School, bk. iii.
ch. 3.

58 We must not make a vague reference to the Divine wisdom,
but must show how it is present in particular departments of
experience.

NEW SYSTEM 313

possible the soul or any other real substance should receive
anything from outside, unless through the Divine omni-
potence, I was insensibly led to an opinion which
surprised me, but which seems inevitable and which, in
fact, has very great advantages and very considerable
beauties. It is this, that God at first so created the soul,
or any other real unity, that everything must arise 59 in
it from its own inner nature [fonds] with a perfect
spontaneity as regards itself and yet with a perfect con-
formity to things outside of it. And thus our inner
feelings [sentiments] (that is to say, those which are in
the soul itself and not in the brain or in the finer parts
of the body), being only connected phenomena of external
things or rather genuine appearances and, as it were,
well-ordered dreams60, these internal perceptions in the
soul itself must come to it from its original constitution,
that is to say from the representative nature (capable of
expressing beings outside of it in relation to its organs 61)
which was given to it at creation and which constitutes
its individual character. And accordingly, since each of
these substances accurately represents the whole universe
in its own way and from a certain point of view, and
the perceptions or expressions of external things come
into the soul at their appropriate time, in virtue of its
own laws, as in a world 6'2 by itself and as if there existed
nothing but God and the soul (to adopt the phrase of
a certain person of high intellectual power, renowned
for his piety63), there will be a perfect agreement between
all these substances, which will have the same result as
would be observed if they had communication with one

*

59 E. has 'arises.' As to the 'spontaneity* of the soul and its
'creation,' see Monadology, § 47, note 75.

60 ' And so genuine that they can be successfully foreseen.' First
Draft (G. iv. 477). See Introduction, Part iii. p. 98 sqq.

61 That is, according to the nature and disposition of its organs.

62 E. has 'the world.'

63 Kirchmann suggests that this may perhaps refer to Foucher.
But Leibniz uses the phrase, without any special reference or
acknowledgment, in a letter to Foucher, written in 1686. (G. i. 382.)

314 NEW SYSTEM

another by a transmission of species or of qualities, such
as the mass of ordinary philosophers suppose Gi. Further,
as the organized mass, in which is the point of view of
the soul, is more nearly expressed by the soul65 and,
conversely, is ready of itself to act, according to the laws
of the corporeal mechanism, at the moment the soul
desires it, without either of them interfering with the
laws of the other — the animal spirits \les esprits] 66 and
the blood having exactly at that moment the right
motions to correspond to the passions and perceptions of
the soul — this mutual relationship, prearranged in each
substance in the universe, produces what we call their
communication and alone constitutes the union of soul and
~body. And in this way we can understand how the soul
has its seat in the body through an immediate presence,
which is as near as possible, since the soul is in the
body as the unit [unite] is in the multiplicity which is
the resultant of units [unites] 67.

6* See Monadology, § 7, note 10.

65 E. omits ' by the soul' (par elle).

66 'Animal spirits ' was the name given by Descartes to certain
' very fine particles of the blood,' by means of which he explained
muscular movement. The name was derived from the Stoic
Trvevfta, through the early medical philosophers, such as Galen, who
speaks of l natural spirits ' and ' vital spirits ' ; but Descartes's use
of the term is original. * What I here call " spirits " are only
bodies, and they have no other property except that they are very
small bodies which move very quickly, like the particles of flame
which come from a lighted torch ; so that they do not stay in any
place, and as soon as some of them enter the cavities of the brain,
others go out again through the pores in its substance, which pores
lead them to the nerves and thence to the muscles, by means of
which they move the body in all the different ways it can be
moved.' Les Passions de I'Ame, part i. art. 10. See also articles 11-13,
and Method, part v, where he says that the ' animal spirits ' are ' like
a very subtle wind, or rather a very pure and vivid flame.' The
name survives in common language, and the hypothesis was only
set aside by the results of microscopic study in anatomy. Cf. Kuno
Fischer, Descartes and his School, bk. ii. ch. 9, § a.

67 Descartes also held that the soul must be present to the whole
organism. But he maintained that ' nevertheless there is in the
body a part in which the soul exercises its functions more specially
than in any other part,' this special 'seat of the soul' being the
pineal gland in the brain. (Les Passions, part i. articles 30-33.)

NEW SYSTEM 315

15. This hypothesis is very possible. For why might
not God in the beginning give to substance an inner
nature or force which could regularly produce in it
— as in an automaton that is spiritual or endowed with
a living principle c8, but free in the case of a substance
which partakes of reason 69 — everything that will happen
to it, that is to say, all the appearances or expressions it
will have, and that without the help of any created
thing ? This is the more likely since the nature of sub-
stance necessarily requires and essentially involves a
progress or change, without which it would have no
force to act70. And as the nature of the soul is to
represent the universe in a very exact way (though with
greater or less distinctness), the succession of representa-
tions which the soul produces for itself will correspond
naturally to the succession of changes in the universe itself ;
while, on the other hand, the body has also been adapted
to the soul to fit the circumstances in which the soul is
conceived as acting outwardly. This adaptation of the
body to the soul is the more reasonable inasmuch as
bodies are made only for spirits [esprits] 71, which alone
are capable of entering into fellowship with God and
celebrating His glory. Thus as soon as we see that this
hypothesis of agreements [accords']™ is possible, we see

Leibniz seeks to show that, on his hypothesis, the connexion
between soul and body is much closer. The soul is ' immediately '
present to the body and thus has no special seat but is in every
part (independently of the part's position) as the unit is in every
part of the whole.

68 The French is : un automate spiritual ou formel. Formel conveys
the idea of the form or individual unity of the thing, as in the
phrase ' substantial form.'

69 Every substance has spontaneity, inasmuch as it produces from
within itself the series- of its states or phenomena ; but rational
souls alone have liberty, for liberty is action under the guidance of
right reason.

70 No substance can act upon anything outside of it. Thus its
action must appear in some internal change.

71 That is to say, bodies are entirely subordinate to spirits, as the
realm of efficient causes is to that of final causes. See Monadology,
concluding §§.

72 In the First Draft, Leibniz says : < I call this the system of

31 & NEW SYSTEM

also that it is the most reasonable hypothesis and that
it gives a wonderful idea of the harmony of the universe
and the perfection of the works of God.

1 6. There is also this great advantage in our hypo-
thesis, that instead of saying that we are free only
apparently and enough for practical purposes, as several
clever people have held, we must rather say that we are
only apparently constrained, and that, to use strict meta-
physical language, we possess a perfect independence as
regards the influence of all other created things 73. This
also throws a wonderful light upon the immortality of
our soul and the ever unbroken preservation of our
individuality, which is perfectly well-ordered by its own
nature and independent of all external contingencies,
whatever appearance there may be to the contrary.
Never has any system more completely shown our high
calling. Every spirit [esprit] being like a world apart,
sufficient to itself, independent of eveiy other created
thing, involving the infinite, expressing the universe, is
as lasting, as continuous in its existence and as absolute
as the very universe of created things. Thus we should
hold that each spirit should always play its part \_faire
figure] in the universe in the way that is most fitted to
contribute to the perfection of the society of all spirits,
which constitutes their moral union in the City of God.
There is also here a new and surprisingly clear proof of
the existence of God. For this perfect agreement of so
many substances which have no communication with
one another can come only from their common cause 74.

17. In addition to all these advantages which this

correspondence' (G-. iv. 476). He is still feeling for the name
' Pre-established Harmony,' which he uses for the first time in
the First Explanation of the New System (1696).

73 See Introduction, Part iii. pp. 141 sqq.

74 In the First Draft, Leibniz says : ' It is true that this is only
by a participation, though limited, in the Divine perfections ; for
the agreement among the effects arises from their expressing the
common cause' (G-. iv. 475). Cf. Principles of Nature and of Grace,
§ n, note 49.

NEW SYSTEM 317

hypothesis has in its favour, it may be said that it is
something more than' a hypothesis, since it hardly
appears possible to explain things in any other intelli-
gible way, and since several great difficulties, which
have hitherto perplexed men's minds [les esprits], seem
to disappear of themselves when we rightly comprehend
this hypothesis. The expressions of ordinary language
may also be quite well adapted to it. For we may say
that the substance whose condition [disposition] explains
a change in an intelligible way (so that we may hold
that it is this substance to which tfre others have on this
point been adapted from the beginning, according to the
order of the decrees of God) is the substance which, in
respect of this change, we should consequently conceive
as acting upon the others75. Thus the action of one
substance upon another is not an emission nor a trans-
plantation of an entity as is commonly supposed, and it
can be rationally understood only in the way I have
just mentioned. It is true that we quite well conceive
in matter both the emission and the receiving of parts
through which we are entitled to explain mechanically
all the phenomena of physics ; but as material mass is
not a substance 76, it is evident that action as regards
substance itself can only be what I have just said that
it is.

1 8. These considerations, however metaphysical they
may appear, are also of remarkable service in physics
for establishing the laws of motion, as our Dynamics will
be able to show. For it may be said that in the impact
of bodies each suffers only through its own elasticity,
caused by77 the motion which is already in it78. And

7r> See Introduction, Part iii. pp. 105 sqq.

76 See Introduction, Part iii. p. no.

77 E. has cause du, 'a (or the) cause of the.' G-. has cause du,
' caused by the.' The First Draft has : ' which comes from a motion
already existing in it ' (G. iv. 476).

78 Leibniz opposes the idea that there is a fixed quantity of
motion dispersed throughout the universe and passing indifferently

318 NEW SYSTEM

as to absolute motion, nothing can determine it mathe-
matically, since all ends [se termine] in relations, with
the result that there is always a perfect equivalence of
hypotheses as in astronomy 79 ; so that, whatever number
of bodies we take, we may arbitrarily assign rest or such
and such a degree of velocity to whichever we like, with-
out it being possible for us to be refuted by the pheno-
mena of motion, whether it be in a straight line, in
a circle, or composite. Yet it is reasonable to attribute
to bodies real motions, according to the supposition
which explains the phenomena in the most intelligible
way, for this is in harmony with the notion of activity
[action] which we have here maintained80.

from one body to another. Each body, he would say, has a force,
which is the cause of its actual motions, and when two bodies
collide, there is not a transference of motion from one to the other,
but a certain release of the pent-up force in each, and this release
shows itself in the elasticity of their rebound. See Introduction,
Part iii. pp. 89 sqq.

79 ' Absolute motion ' would be motion that is not in any degree
rest. But motion must always be determined through relation.
One body has motion only in reference to another, and, accordingly,
if we wish to determine which of the two really (i. e. absolutely)
moves, we must refer them both to some third body and so ad
infinitum. The ' equivalence of hypotheses in astronomy' probably
refers to the fact that the hypothesis of Copernicus (1473-1543),
according to which all the planets move round the sun, and the
hypothesis of Tycho Brahe (1546-1601), according to which the sun
moves round the earth and the other planets move round the sun,
equally well explained the phenomena as observed at that time.
Cf. G. iv. 369, and Descartes, Principia, Part iii. §§ 15-18.

80 See Appendix C, p. 204.

EXPLANATION OF THE NEW SYSTEM OF THE
COMMUNICATION BETWEEN SUBSTANCES,
BY WAY OF REPLY TO WHAT IS SAID
ABOUT IT IN THE JOURNAL OF SEPTEM-
BER 12, I6951. 1696.

PREFATORY NOTE.

IN the Journal des Savants for September, 1695, there
appeared a letter to Leibniz from Foucher in which various
objections to the New System were stated. Simon Foucher
(1644-1696) was a Canon of Dijon, who professed philosophical
scepticism and endeavoured to restore the teaching of the later
Academics, somewhat as Gassendi sought to interpret anew
the doctrines of Epicurus. Between 16/6 and 1695 Leibniz
corresponded with Foucher, discussing in the earlier letters
questions regarding the theory of knowledge and in the later
letters questions of Physics. Foucher's comparatively early
death was to some extent due to overwork. In 1697 Leibniz
writes to Nicaise (G. ii. 566) : ' I am grieved at the death of
M. Foucher. His curiosity was limited, and was directed only
to certain somewhat dry matters, and even these he did not
treat with the accuracy they required. Perhaps his aim was
merely to be the resuscitator of the Academics, as M. Gassendi
has resuscitated the Sect of Epicurus. But he ought not to
have confined himself to generalities. Plato, Cicero, Sextua
Empiricus and others might have enabled him to make a real
advance. And under pretext of doubting, he might have
established good and useful truths. I took the liberty of giving

1 The reference is of course to the letter of Foucher in the Journal
des Savants.

320 FIRST EXPLANATION

him my opinion as to this ; but he had perhaps other views of
which I did not know enough. Yet he had much cleverness
and subtlety and he was a most virtuous man, and hence
I lament him.' (Cf. G. i. 365.) Leibniz replied to the objections
of Foucher in an Explanation of the Neiv System, which appeared
in the Journal des Savants for April, 1696. ^A further Explana-
tion (called by Erdmann the Troisieme Eclaircissement} was
published in the Journal for November, 1696. I have translated
these two Explanations, omitting that which Dutens and
Erdmann call Second Eclaircissement (E. 133, J. S. Feb. 1696,
cf. G. iv. 498), as the Troisieme Eclaircissement contains practi-
cally the whole of it.

In Foucher's letter of objections there appears the simile of
the clocks, which Leibniz passes over in his immediate reply
but takes up and develops in the Second and Third Explana-
tions. Foucher writes : ' It will be granted you that God,
the great Artificer of the universe, can so perfectly adjust all
the organic parts of a man's body, that they may be capable
of producing all the motions which the soul combined with
this body will desire to produce in the course of his life, with-
out the soul having the power to change these motions or to
modify them in any way, and that on the other hand God can
make a construction in the soul (be it a mechanism of a new
kind or not), by means of which all the thoughts and modifi-
cations which correspond to these motions might successively
arise at the same moment in which the body performs its
corresponding functions, and it will also be granted you that
this is no more impossible than to make two clocks keep time
[s'accorder] so well and go so uniformly that at the moment
clock A strikes twelve, clock B will strike twelve also, so that
we imagine the two clocks to be kept going by the same
weight or the same spring' (E. 129 b ; G. iv. 488). The
simile was originally applied in this way by Geulincx. See
Introduction, Part ii. p. 43 note ; cf. Third Explanation of the
New System, p. 331 note.

In the translation of the Explanations I follow G.'s revised
text (G. iv. 493, 500 sqq.). E. gives them as they were origin-
ally published (E. 131, 134 sqq.).

I recollect, Sir, that in compliance with what I under-
stood to be your desire, I communicated to you my
hypothesis in philosophy several years ago, although at

OF THE NEW SYSTEM 321

the same time I indicated to you that I had not yet
resolved to make it known. I asked your opinion of it
in exchange ; but I do not recollect having received
objections from you : otherwise, teachable [docile] as
I am, I should not have caused you to offer the same
objections twice over. Nevertheless they still come in
time, although they come after I have published. For
I am not of those with whom the committing of them-
selves to an opinion takes the place of reason, as you will
find when you are able to say that you have brought
forward2 any precise and urgent reason against my
opinions ; which apparently has not been your purpose s.
Your intention was to speak as an able Academic 4, and
thus to give an opportunity for a thorough investigation
of things.

i 6. I intended to explain here, not the principles of
extension [Vetendue], but the principles of that which
is actually extended [Tetendu effectif] or of bodily mass ;
and these principles, in my opinion, are real unities, that
is to say, substances possessing a genuine unity 6.

2. The unity of a clock, which you mention, is in my
view quite other than that of an animal ; for an animal
may be a substance possessing a genuine unity, like what
is called ego [moi] in us ; while a clock is nothing but an
aggregate [assemblage].

3. I do not find the principle of the animal's conscious-
ness \le prindpe sensitif^ in the arrangement [disposition]
of its organs ; and I agree that this arrangement concerns
only the bodily mass 7.

a E. has < when you are able to bring forward.'

8 E. adds ' on this occasion.'

* In reference to Foucher's philosophical position. See Prefatory
Note.

6 In G.'s text the paragraphs are numbered. In E.'s text they
are not numbered, and the paragraphs are differently divided.

6 Foucher had maintained that 'the essential principles of ex-
tension cannot really exist,' i.e. that extension has no ultimate
real elements. (E. 129 a ; G. iv. 487.) Cf. Appendix H, p. 329.

T Foucher had said : * Whatever arrangement [disposition] the
organs of an animal might have, that is not enough to make it

322 FIRST EXPLANATION

4. I notice these things in order to prevent misunder-
standings, and to show that what you say on this point
is by no means contrary to what I have brought forward 8.
Thus it appears that you do not make me out to be
wrong in requiring genuine unities, and in consequently
rehabilitating the substantial forms. But when you
appear to say that the soul of the lower animals must
have reason, if we attribute feeling [sentiment] to it9, that
is an inference10 of which I do not see the proof11.

5. With laudable candour you recognize that my
hypothesis of harmony or concomitance is possible. But
you still have a certain repugnance to it ; doubtless
because you think that it is purely arbitrary, through
not being aware that it follows from my view regarding
unities ; for everything in my theory is connected to-
gether.

6. Accordingly you ask, Sir, of what use is all this
elaborate contrivance which I attribute to the Author of
nature12 ? As if one could attribute too much contrivance
to Him, and as if this exact mutual correspondence of

conscious [sensible] ; for in short this has to do with nothing but
the organic and mechanical structure, and I do not see that you
are right in attributing to the lower animals a principle of conscious-
ness, substantially different from that of men ' (E. 129 b ; G. iv. 488;.

8 E. does not have this sentence.

' Foucher wrote : l After all, it is not without ground that the
Cartesians acknowledge that if we allow to the animals a principle
of consciousness, capable of distinguishing good from evil, we must
also, as a consequence, allow to them reason, discrimination and
judgment ' (E. 129 b ; G. iv. 488). In the Remarques sur Us Objections de
M. Foucher Leibniz replies : ' I do this ' [attribute to the animals
a principle of consciousness, substantially different from that of
men] ' because we do not find that the animals make the reflexions
which constitute reason and which, producing the knowledge of
necessaiy truths or science, make the soul capable of personality.
The lower animals, having perception, distinguish good and evil ;
but they are not capable of moral good and evil, which presuppose
reason and conscience' (G. iv. 492). Cf. Honadology, §§ 25-30.

10 E. reads ' you make use of an inference.'

11 E. reads l force.'

12 Foucher's question is: 'Of what use is all this great elaborate
contrivance among substances, unless to make us believe that they
act upon one another, although this is not the case ? ' (E. 130 a ;
G. iv. 489).

OF THE NEW SYSTEM 323

substances, through the special laws which each has at
the beginning received, were not a thing most admirable
in itself and worthy of its Author ! You ask also what
advantage I find in it.

7. I might refer to what I have already said ; but
I reply, first, that when a thing cannot but be13, there
is no need to ask of what use it is, before we admit it.
Of what use is the incommensurability of the side with
the diagonal ?

8. I reply in the second place, that this correspondence
is of use in explaining the communication of substances
and the union of the soul with the body, through the
laws of nature which have been established from the
first [par avance], without having recourse either to
a transmission of species14 [qualities], which is incon-
ceivable, or to a new intervention of God, which seems
out of accord with the fitness of things. For it is to be
observed that as there are laws of nature in matter, so
there are also laws of nature in souls or forms ; and the
meaning of these laws is that which I have just indicated.

9. Again, I am asked 15 whence it comes that God does
not think it enough to produce all the thoughts and
modifications of the soul, without these useless bodies,
which the soul, it is said, can neither move nor know.
The answer is easy. It was God's will that there should

13 Has Leibniz shown that his pre-established harmony ' cannot
but be ' ? In the Remarques already quoted, he says : ' This elaborate
contrivance, which makes each substance correspond to all others,
is necessary because all substances are the effect of a supreme
wisdom ; and it was not otherwise possible (at any rate in the
order of nature and without miracles) to bring about their inter-
dependence and the changing of one by another or in consequence
of another. It nevertheless remains true that they act upon one
another, provided we give a right sense to these words. . . . God is
not obliged to make a system, about which we are not liable to
make mistakes ; as He was not obliged to avoid the system of the
earth's motion, in order to save us from the error into which
almost all astronomers fell until Copernicus ' (G-. iv. 492).

u See Monadology, § 7, note 10.

15 E. has ' I shall be asked.' The question was put by Foucher
in his letter of objections.

Y 2

324 FIRST EXPLANATION

be more substances rather than fewer, and He thought
it right that these modifications of the soul should corre-
spond to something outside 16.

10. No substance is useless; they are all made to
co-operate 17 towards fulfilling the plan of God.

11. I am also far from admitting that the soul does not
know bodies, although this knowledge arises without any
influence of the one upon the other.

12. I will not even shrink from saying18 that the soul
moves the body ; and as a Copernican speaks truly of the
rising of the sun, a Platonist of the reality of matter, and
a Cartesian of the reality of sensible qualities 19, provided
we rightly understand them, in the same way I hold
that it is most true to say that substances act upon one
another, provided we understand that one is the cause of
changes in the other in consequence of the laws of the
harmony.

13. The objection which is based on the supposed
lethargy of bodies, which would be without activity
[action] while the soul believes them to be in motion,
cannot hold because of this very unfailing correspondence,
which the Divine wisdom has established 20.

18 In the Eemargues Leibniz says : l Bodies were necessary so that
there might be produced not only our unities and souls but also
those of the other corporeal substances, animals and plants, which
are in our bodies and in those which surround us' (G. iv. 493 \
This last sentence indicates Leibniz's real answer to the difficulty
(the answer he would have given in later years\ viz. that ulti-
mately all bodies are souls or Monads, so that to ask why there
are bodies is to ask why there are other souls. Is the answer
sufficient ?

17 E. has ' they all co-operate.'

18 E. has 1 1 will even raise no objection against saying.'

19 i. e. the qualities of bodies, as they are perceived by our senses.
As sensations, facts of consciousness, these are real, according to
Descartes ; but as qualities of bodies they are confused and there-
fore unreal. See Principia, Part i. §§ 66-70.

20 Toucher says that, on Leibniz's hypothesis, ' even although no
motion took place in bodies ' [in harmony with the action of the
soul], ' the soul would nevertheless always think that such a motion
does take place ; in the same way as sleeping people think they are
moving their limbs and walking, while nevertheless their limbs

OF THE NEW SYSTEM 325

14. I have no knowledge of these idle, useless, and
inactive masses, to which reference is made. There is
activity [action] everywhere, and I maintain it even
more fully than does the received philosophy ; because
I hold that there is no body without motion, no sub-
stance without force [effort]*1.

15. I do not understand the nature of the objection
that is contained in the words : — In truth, Sir, is it not
evident that these opinions were formed with a special purpose
in view, and that these systems, appearing by way of after-
thought [venant apres coup], were constructed merely to safe-
guard certain principles? All hypotheses are made with
a special purpose in view, and all systems appear ~by way of
afterthought [viennent apres coup], in order to safeguard
phenomena or appearances ; but I do not see what are the
principles in favour of which I am said to be prejudiced
and which I wish to safeguard.

1 6. If it is meant that I am led to my hypothesis also
by reasons a priori or by fixed principles, as is actually
the case ; this is rather a commendation of the hypo-
thesis than an objection to it. It is usually enough that
a hypothesis be proved a posteriori, by being adequate to
the phenomena ; but when there are in addition other
reasons for it, and these a priori, it is so much the better.

1 7. But perhaps what is meant is that, having invented
a new opinion, I have delighted to make use of it, rather
to give myself airs because of its novelty than because
I have found any usefulness in it. I am not sure, Sir,
that you have so bad an opinion of me as to attribute to
me these thoughts. For you know that I love truth, and
that, if I were so fond of novelties, I should have more

are at rest and do not move at all. So, when wide awake, souls
would always continue to be persuaded that their bodies move in
obedience to their volitions, though nevertheless these idle and
useless masses would be inactive and would remain in a continual
lethargy ' (E. 130 a ; G. iv. 489).

21 That is, force which is not necessarily observed, but includes
tendency or the active potentiality of observed force.

326 FIRST EXPLANATION

eagerness to produce them — especially those whose sound-
ness is recognized. But, lest those who know me less
should give to your words a meaning which we should
not like 22, it will be enough to say, that in my opinion
it is impossible otherwise to explain transeunt activity
\Taction emanente] 23 in conformity with the laws of ntture,
and that I thought that the use of my hypothesis would
be evident, owing to the difficulty which the most able
philosophers of our time have found as to the inter-
relation [communication] of minds [esprits] and bodies,
and even of bodily substances with one another: and
I do not know but that you yourself have found some
difficulty in this.

1 8. It is true that, in my view, there are forces [efforts]
in all substances ; but these forces [efforts] are, rightly
speaking, only in the substance itself, and what follows
from them in other substances takes place only in virtue
of a harmony pre-established 24 (if I may use the word), and
in no wise by a real influence or by the transmission of
some species or quality25. As I have explained what
activity [action] and passivity [passion] are, the nature
of force [effort] and of resistance may be inferred.

19. You say, Sir, that you know there are still many
questions to be put, before those which we have been discussing
can be decided. But perhaps you will find that I have
already put these questions ; and I am not sure that your
Academics have applied what is good in their method
more rigorously and effectively than I26. I strongly

29 E. reads ' contrary to my intentions.'

23 That is, activity which apparently passes beyond the substance
itself and has effects in other substances. It is the same thing as
the ' influence ' of one substance upon another. See De ipsa Nalura
(1698), § 10 (E. 157 b ; G. iv. 510), where Leibniz uses the expression
transeuntes creaturarum actiones.

24 This is the first use of the term by Leibniz.
35 See Monadology, § 7, note 10.

46 Foucher wrote : ' We ought to observe the laws of the
Academics, the second of which forbids us to put in question
matters which we clearly see cannot be settled, as are almost all
those of which we have been speaking ; not that these questions

OF THE NEW SYSTEM 327

approve of seeking to demonstrate truths from first
principles: it is more useful than people think, and
I have often 2V put this precept in practice. Thus I com-
mend what you say on this point, and I would that your
example may lead our philosophers to think of it as they
ought.

20. I will add a further reflexion, which seems to me
helpful in making the reality and use of my system better
understood. You know that M. Descartes believed in
the conservation of the same quantity of motion in bodies.
It has been shown that he was wrong in this ; but I have
shown that it is still true that there is conservation of
the same moving force, instead of which he put quantity
of motion. Nevertheless, he was perplexed by the
changes which take place in the body in consequence
of modifications of the soul, because they seemed to
break this law. But he thought he had found a way
out of it (which is certainly ingenious) in saying that
we must distinguish between motion and direction ; and
that the soul cannot increase nor diminish the moving
force, but that it changes the direction or determination
of the course of the animal spirits, and that it is in this
way that voluntary motions take place 28. It is true that
he made no attempt to explain how the soul acts so as to
change the course of bodies, for there seems as much
difficulty in this as there is in saying that the soul gives
motion to bodies, unless with me you have recourse to
the pre-established harmony ; but it is to be observed
that there is another law of nature, which I have discovered
and proved, and which M. Descartes was unaware of,
namely, that there is conservation not only of the same
quantity of moving force, but also of the same quantity

are absolutely insoluble, but because they are soluble only in
a certain order, which requires that philosophers should begin by
coming to an agreement as to the infallible mark of truth, and
should confine themselves to demonstrations from first principles '
(E. 130 b ; G. iv. 490).

27 E. omits ' often.' Cf. Introduction, Part ii. p. 59.

28 See Monadology, § 80, note 127, and Introduction, Partiii. p. 89.

328 FIRST EXPLANATION

of direction in ivhatever line [de quelque cote] 29 we take it in
the ivorld. That is to say, drawing any straight line you
please, and taking also such bodies and so many of them
as you please, you will find that, considering all these
bodies together, without omitting any of those which act
upon any one of those which you have taken, there
will always be the same amount [quantite] of progression
in the same direction [du meme cote] in all lines parallel
to the straight line you have taken — observing that the
total amount of progression is to be calculated by sub-
tracting from the amount of progression of the bodies
which go in the given direction, the amount of progression
of those which go in the opposite direction 30. This law,
being as good and as general as the other, deserved as

29 E. reads vers quelque cote.

30 See Principles of Nature and of Grace, § n, note 48. Cf. Epistola ad
Bernoullium (1696) (G. Math. iii. 243; E. 108 note): 'In the next
place it is to be observed that I make a distinction between absolute
force and directing force, although I can deduce and demonstrate
directing force from the sole consideration of absolute power. And
indeed I prove that there is conservation not only of the same
absolute force or quantity of action in the world, but also of the
same directing force and the same quantity of direction in the
same lines [ad easdem paries], i.e. the same quantity of progression,
its direction being taken into account and the quantity of pro-
gression being counted equal to the mass multiplied by the
velocity, and not by the square of the velocity' [mv, not ?nt/2].
1 Nevertheless this quantity of progression differs from quantity
of motion in this way, that when two bodies are moving in
opposite directions their total quantity of motion (in the Cartesian
sense) is to be got by adding together the quantity of motion of
each (calculated as the mass into the velocity) ; but the quantity
of progression is to be got by subtracting the one from the other ;
for in such a case the difference between the quantities of motion
will be the quantity of progression. Therefore when Descartes
thought that he could safeguard the soul's power of acting on the
body in this way, that while the soul cannot increase or diminish
the quantity of motion in the world, it can nevertheless increase
or diminish the quantity of direction of the [animal] spirits, he
erred through not knowing this new law of ours regarding the
conservation of the quantity of direction, which is no less beautiful
and inviolable than the law of the conservation of absolute force
[virtus'] or power of action.' The ' quantity of progression ' would
now be called a projection of the quantity of motion. A full
explanation, with diagrams, will be found in the appendix to
Boutroux's edition of the Monadologie.

APPENDIX H 329

little to be broken, and this is so, according to my
system31, in which there is conservation of force and
direction, and none of the natural laws of bodies are
broken, notwithstanding the changes which take place
in body in consequence of changes in the soul.

APPENDIX H.

ON THE ELEMENTS OF EXTENSION.

ONE of Foucher's objections to the New System was based on
the contention that extension has no ultimate real elements
(E. 1 29 a ; Gr. iv. 487). In some Remarques sur les Objections de
M. Foucher (G. iv. 490) Leibniz replies : ' The author of the
objection does not seem to have rightly understood my view.
Extension or space, and the surfaces, lines and points that can
be conceived in it, are nothing but relations of order or orders
of co-existence, both as regards that which actually exists
and as regards the possible thing that might be put in place
of that which exists. Thus they have no ultimate component
elements [principes], any more than number has. And as
a broken number, for instance £, can be further broken into
two-fourths or four-eighths and so on ad infinitum, without our
being able to reach the absolutely smallest fractions or to
conceive the number as a whole formed by the combination of
ultimate elements, so it is with a line which can be divided,
just like this number. Again, strictly speaking, the number ^
in the abstract is a perfectly simple ratio [rapport], not at all
formed by the compounding of other fractions, although in
numbered things there is equality between two -fourths and
one -half. And we may say as much regarding an abstract line,
since compounding takes place only in concrete things, or the
masses of which these abstract lines indicate the relations.
And it is also in this way that mathematical points are to be
regarded : they are merely modalities, that is to say extremi-
ties. And as in the abstract line all is indefinite, it has
reference to everything which is possible, as in the case of

31 E. reads ' and this ' [i. e. the breach of the law] ' is avoided by
my system.'

330 APPENDIX H

fractions of a number, without our troubling about divisions
actually made, which indicate points in the line in various
ways. But in actual substantial things the whole is a sum or
aggregate of simple substances or rather of a multitude of real
units [unites]. And it is the confounding of the ideal and the
actual that has brought the whole matter into confusion and
has produced the labyrinth de compositione continui. Those
who have supposed the line to be made up of points have
sought for the primary elements in ideal things or relations,
which was quite a mistake ; and those who have found that
relations like number or space (which includes the order or
relation of possible co-existent things) cannot be formed by
the aggregation of points, have usually made the mistake of
denying the primary elements of substantial realities, as if
they had no primary unities, or as if ^there were no simple
substances. Nevertheless number and the line are not chimeri-
cal things, although they are not thus compounded, for they
are relations which involve eternal truths, in accordance with
which the phenomena of nature are ordered. Hence it may
be said that, considered in the abstract, \ and \ are indepen-
dent of one another, or rather the total ratio [rapport] \ is
anterior— in the order of reason [dans le signe de la raison], as
the Scholastics say — to the partial ratio ^, since it is by the
subdivision of the half that we come to the fourth, following
the order of what is ideal ; and the same is the case with the
line, in which the whole is anterior to the part because the
part is only possible and ideal. But in realities, in which
there are only divisions actually made, the whole is merely
a sum or aggregate, as in the case of a flock of sheep. It is
true that the number of simple substances which enter into
a mass, however small it be, is infinite, since in addition
to the soul which constitutes the real unity of the animal, the
body of the sheep (for instance) is actually subdivided, that
is to say it is also an aggregate of invisible animals or plants
(which are likewise compound) besides that which constitutes
also their real unity ; and although this proceeds ad infinitum,
it is manifest that ultimately all is reducible to these unities,
the remainder or the aggregates being merely well-founded
phenomena.'

THIED EXPLANATION l— EXTRACT FROM A
LETTER OF M. D. L. REGARDING HIS
PHILOSOPHICAL HYPOTHESIS AND THE
CURIOUS PROBLEM, PROPOUNDED TO
THE MATHEMATICIANS BY ONE OF HIS
FRIENDS, WITH AN EXPLANATION RE-
GARDING SOME DISPUTED POINTS IN
PRECEDING JOURNALS BETWEEN THE
AUTHOR OF.THE PRINCIPLES OF PHYSICS2
AND THE AUTHOR OF THE OBJECTIONS.
1696.

SOME learned and acute friends of mine having con-
sidered my new hypothesis on the great question of the
union of soul and body, and having found it of value,
have asked me to give some explanations regarding the
objections which have been brought against it and which
arose from its not having been rightly understood.
I think the matter may be made intelligible to minds of
every kind by the following illustration.

Suppose two clocks3 or two watches which perfectly

1 E. has ' Third Explanation,' which is omitted by G.

2 Nicholas Hartsocker. ' M.D.L.' is a pseudonym of Leibniz.

3 See Prefatory Note. Geulincx's use of the simile is as follows :
* My will certainly does not move the moving power that it may
move my limbs ; but He who imparted motion to matter and
laid down laws for it, Himself also formed my will. Therefore
He bound together these most diverse things (the motion of
matter and the choice of my will), so that when my will wills,
such a motion as it wills occurs, and on the other hand when

332 THIRD EXPLANATION

keep time together [s'accordenf]. Now that may happen
in three ways. The first way consists in the mutual in-
fluence of each clock upon the other ; the second, in the
care of a man who looks after them ; the third, in their
own accuracy. The first way, that of influence, was
ascertained on trial by the late M. Huygens 4, to his great
astonishment. He attached two large pendulums to the
same piece of wood. The continual swinging of these
pendulums imparted similar vibrations to the particles of
the wood ; but as these different vibrations could not

the motion occurs, the will wills it, without any causality or
influence [influxes] of the one upon the other ; as in the case of
two clocks which are carefully adjusted together to the daily
course of the sun, as often as the one strikes and tells us the
hours, the other strikes in the same way and indicates the hours,
and that apart from any causality, by which the one might produce
this effect in the other, but solely on account of the connexion
which comes from the fact that both were made by the same
art and with similar workmanship. Thus, for example, the
motion of the tongue accompanies our volition to speak, and this
volition accompanies that motion : and the motion does not depend
upon the volition, nor the volition upon the motion, but both
depend upon the same Supreme Artificer, who has so wonderfully
connected and bound them together.' Ethica, Tract. I. cap. 2, § 2,
note 19 ; Land's ed., vol. iii. p. 2-1 1. Cf. ibid, note 48 ; Land, iii. 220.
Cf. also Introduction, Part ii. p. 43.

* Christian Huygens (1629-1695) was a mathematician, phy-
sicist and astronomer, who lived for the most part in Holland,
where he was born, and in France, where Leibniz, coming to
Paris in 1672, met him. Anticipating the revocation of the Edict
of Nantes, the Protestant Huygens left Paris in 1681 and returned
to Holland, but he continued to correspond with Leibniz on
mathematical subjects. In 1673 Huygens published his great
work Horologium OscillatQrium, sive de motu pendulorum ad horologia
adaptatOj in which he gave a full account of a discovery he had
made in 1656, that of the pendulum clock. Among the other
great works of Huygens were discoveries in connexion with the
astronomy of the planets, the undulatory theory of light, and
the use of spiral springs for regulating the balances of watches.
Leibniz frequently acknowledges his great indebtedness to
Huygens in regard to mathematics, and in July, 1695, he writes
to Nicaise : ' Nothing can equal the loss of the incomparable
M. Huygens. Most certainly he ought to be named immediately
after Galileo and Descartes. He might still have given us great
light upon nature' (G. ii. 552). But elsewhere he says that
' M. Huygens had no taste for metaphysics.' Lettre a Eevnond (1714)
(E. 702 b ; G. iii. 607).

OF THE NEW SYSTEM 333

continue in their proper order, without interfering with
one another, unless the pendulums kept time together,
it happened, by a kind of wonder, that even when their
swinging was deliberately disturbed they soon came to
swing together again, somewhat like two stretched strings
that are in unison.

The second way of making two clocks (even though
they be bad ones) constantly keep time together would
be to put them in charge of a skilled workman who
should keep them together from moment to moment.
I call this the way of assistance.

Finally, the third way will be to make the two clocks
[pendules] at first with such skill and accuracy that we
can be sure that they will always afterwards keep time
together. This is the way of pre-established agreement
[consentcmeni],

Now put the soul and the body in place of the
two clocks. Their agreement [accord] or sympathy will
also arise in one of these three ways. The way of in-
fluence is that of the common philosophy; but as we
cannot conceive material particles or immaterial species
or qualities which can pass from one of these substances
into the other, we are obliged to give up this opinion.
The way of assistance is that of the system of occasional
causes ; but I hold that this is to introduce Deus ex
machina in a natural and ordinary matter, in which it is
reasonable that God should intervene only in the way in
which He supports [concourt a] all the other things of
nature. Thus there remains only my hypothesis, that
is to say, the way of the harmony pre-established by a con-
trivance of the Divine foresight, which has from the
beginning formed each of these substances in so perfect,
so regular and accurate a manner that by merely follow-
ing its own laws which were given to it when it came
into being, each substance is yet in harmony with the
other, just as if there were a mutual influence between
them, or as if God were continually putting His hand

334 THIRD EXPLANATION

upon them, in addition to His general support [con-
currence].

I do not think that I need offer any further proof5
unless I should be required to prove that God is in
a position 6 to make use of this contrivance of foresight,
of which we have instances even among men, in pro-
portion to the skill they have. And supposing that
God is able to make use of this means, it is very evident
that this is the best way and the most worthy of Him.
It is true that I have also other proofs of it 7, but they
are deeper and it is unnecessaiy to adduce them here 8.

Let me say a word about the dispute between two very
clever people, the author of the recently-published Prin-
ciples of Physics 9 and the author of the Objections 10 (which
appeared in the Journal of August 13 and else wh ere \
because my hypothesis serves to bring these controversies
to an end. I do not understand how matter can be

5 It should be observed that Leibniz's argument from analogy
proceeds upon the assumption that body and soul, or soul and
soul, are in reality quite independent and separate from one
another. If this be not admitted his ' proof breaks down : the
'three ways' do not exhaust the possible hypotheses. Leibniz
seems rather to have prided himself on emphasizing, by his
hypothesis, the difference between body and soul. In the post-
script to a letter to Basnage de Beauval (1696), part of which is
printed as the Second Edaircissement (E. 134 b; G. iv. 499), Leibniz
says: 'You had a suspicion that my explanation would be irre-
concilable with the great difference which, in our opinion, there
is between mind [esprit] and body. But now you see clearly, Sir,
that no one has established their independence more completely
than I. For since hitherto we have been obliged to explain their
inter-relation [communication] by a kind of miracle, we have con-
stantly given occasion to many people to fear that the' distinction
between mind and body is not so real as people think, since our
reasons for maintaining it are so far-fetched. Now all these scruples

6 The Second Edaircissement reads * is skilful enough.'
T The reference is probably to such arguments as those which
he afterwards gave in the Monadology.

8 I have omitted two paragraphs dealing with a purely mathe-
matical problem.

9 Hartsoeker. See New System, § 6, note 36.

10 Foucher.

OF THE NEW SYSTEM 335

conceived as extended and yet without either actual
or ideal11 parts; and if it is so, I do not know what
is meant by being extended 12. I even hold that matter
is essentially an aggregate, and consequently that there
are always actual parts. Thus it is by reason, and not
merely by the senses, that we judge that it is divided,
or rather that it is ultimately nothing but a collection
[multitude]. I hold it as true that matter (and even each
part of matter) is divided into a greater number of parts
than it is possible to imagine. And accordingly I often
say that each body, however small it may be, is a world
of creatures infinite in number. Thus I do not believe
that there are atoms, that is to say, parts of matter which
are perfectly hard or of invincible solidity ; while, on the
other hand, I as little believe that there is a perfectly
fluid matter 1S, and my opinion is that each body is fluid
in comparison with more solid bodies and solid in com-
parison with the more fluid. I am surprised that it is
still said that an equal quantity of motion, in the Car-
tesian sense, is always conserved ; for I have proved the
opposite, and already excellent mathematicians have
admitted it. Nevertheless I do not regard the solidity
or consistence of bodies as a primary quality, but as
a consequence of motion, and I hope that my Dynamics
will show in what this consists, as the understanding of
my hypothesis will also serve to remove several diffi-
culties which' still engage the attention of philosophers.
In fact, I believe I can intelligibly answer all the doubts
to which the late M. Bcrnier1* has specially devoted a

11 mentales, i. e. thinkable.

12 The reference is probably to the views of Foucher, who denied
that the essence of matter is extension, holding that all our ideas
(including those of external objects) are merely modifications of
ourselves and that, in order to represent an object, an idea must
be like it. See Foucher de Careil, Lettres et Opuscules inedits de Leibniz,
Introduction.

13 Hartsoeker's theory was that the ultimate elements of things
are perfectly hard atoms in a perfect fluid, the atoms combined
forming tangible bodies, while the fluid transmits light, &c.

14 Fran9ois Bernier (d. 1688) was more famous as a traveller

336 THIRD EXPLANATION

book ; and those who will think out what I have
formerly published will perhaps find that they already
have the means of making this answer.

than as a philosopher. After travelling in Syria and Egypt, he
went to India (where he was physician to Aurungzebe), and
afterwards to Cashmir. In Paris he was nicknamed ' the Mogul.'
He assisted Boileau in preparing the Mock Decree, given in the hall
of Parnassus, in favour of the Masters of Arts, Physicians, and Professors of
the University of Stagira, in the land of chimeras, for the support of the
doctrine of Aristotle, which by its ridicule killed the serious proposal
that the French Parliament should officially condemn the philo-
sophy of Descartes. Bernier's principal philosophical works were
Abrege de la philosophic de Gassendi (8 vols., 1678) and, by way of
supplement to this, Doutes de M. Bernier sur quelques-uns des principaux
chapitres de son abrege de la philosophic de Gassendi (7 vols., 1684). The
latter is probably the work to which Leibniz refers. There is
an English translation of Bernier's Travels in the Mogul Empire (new
ed., Constable, 1897).

ON THE ULTIMATE ORIGINATION
OF THINGS. 1697.

PREFATORY NOTE.

THIS paper, written in Latin, is dated by Leibniz, November
23> 1697. It may have been int'ended for the Ada Eruditorum ;
but it remained unpublished until 1840, when Erdmann in-
cluded it in his edition. Leibniz here explains the function
of the principle of sufficient reason in his philosophy, expand-
ing what he had already said in a paper written about 1685,
to which Erdmann give.s the title, De Scientia UniversaU seu
Calculo philosophico (see E. 83 b ; G. vii. 200). §§ 36-48 of the
Monadology may be regarded as a condensation of the main
argument of this Essay On the Ultimate Origination of Things.
In the latter part of the Essay we have a vindication of the
optimism of Leibniz (that this is the best of all possible
worlds), and some of the chief doctrines of the Theodicee are
given in outline.

The Ultimate Origination of Things is given by E. 147 sqq. ;
G. vii. 302 sqq.

BESIDES the world or the aggregate of finite things
there is a certain unity [unum] which is dominant, not
only as the soul is dominant in me or rather as the ego
itself is dominant in my body, but also in a much higher
sense1. For the dominant unity of the universe not
only rules the world but constructs or 2 fashions it. It
is higher than the world and, so 'to speak, extramuiidane,
and is thus the ultimate reason of things. For the

1 Of. Monadology, §§ 70 and 72, notes in and 115.

2 E. reads ' and.'

Z

33$ ON THE ULTIMATE

sufficient reason of existence cannot be found either in
any particular thing or in the whole aggregate and
series of things. Let us suppose that a book of the
elements of geometry existed from all eternity and that
in succession one copy of it was made from another, it
is evident that although we can account for the present
book by the book from which it was copied, nevertheless,
going back through as many books as we like, we could
never reach a complete reason for it, because we can
always ask why such books have at all times existed,
that is to say, why books at all, and why written in
this way. What is true of books is also true of the
different states of the world ; for, in spite of certain laws
of change, the succeeding state is, in some sort, a copy
of that which precedes it. Therefore, to whatever earlier
state you go back, you never find in it the complete
reason of things, that is to say, the reason why there
exists any world and why this world rather than some
other.

You may indeed suppose the world eternal ; but as
you suppose only a succession of states, in none of which
do you find the sufficient reason, and as even any number
of worlds does not in the least help you to account for
them, it is evident that the reason must be sought else-
where. For in eternal things, even though there be no
cause, there must be a reason 3 which, for permanent
things, is necessity itself or essence 4 ; but for the series
of changing things, if it be supposed that they succeed
one another from all eternity, this reason is, as we shall
presently see, the prevailing of inclinations 5 which con-

3 If a thing is eternal, it cannot have a cause in time ; but there
must still be some reason (other than a cause in time) for its
existence. Cf. Aristotle's airtov (which is wider than our 'cause')
and the German Grund.

4 By * permanent things' is meant things that are not contingent,
and these, in Leibniz's language, are i possible' things = ' necessary '
th ings = essences. Cf. Monadology, §§ 40 and 43, notes 64 and 67.

5 The sufficient reason of changing or contingent things is not
an absolute principle, whose opposite would be self-contradictory,

ORIGINATION OF THINGS 339

sist not in necessitating reasons, that is to say, reasons
of an absolute and metaphysical necessity, the opposite
of which involves a contradiction 6, but in inclining
reasons. From this it is manifest that even by sup-
posing the eternity of the world, we cannot escape the
ultimate extramundane reason of things, that is to say,
God7.

Accordingly the reasons of the world lie hid in some-
thing extramundane, different from the concatenation of
states or the series of things, the aggregate of which
constitutes the world. And thus we must go beyond
the physical or hypothetical necessity, according to which
the later things of the world are determined by the
earlier, to something which is of absolute or metaphysical
necessity8, of which a reason cannot be given. For the
present world is necessary physically or hypothetically,
but not absolutely or metaphysically. That is to say,
the nature of the world being such as it is, it follows
that things must happen in it just as they do. There-
fore, since the ultimate root of all must be in something
which has metaphysical necessity, and since the reason
of any existing thing is to be found only in an existing
thing, it follows that there must exist one Being which
has metaphysical necessity, one Being of whose essence

but a superiority of the good or desirable over the bad or un-
desirable in the things which come to pass. The balance or
preponderance of goodness inclines the will of God (without
absolutely necessitating it) to create these contingent things.

6 The word contradictionem seems to have been omitted per incuriam.
Neither E. nor G. gives it.

7 Even though the world be taken as eternal, its necessity is
not on that account absolute or compelling but merely 'inclining,'
and it therefore presupposes some one whose will is 'inclined,'
i e. God.

8 E. reads 'something which is absolute or metaphysical ne-
cessity.' Absolute or metaphysical necessity is a necessity that
is independent of actual things, in contrast with hypothetical
(conditional, relative) or physical necessity, which is the necessity
arising out of the .natures of actual things, the necessity which
a system of ' compossible ' things imposes on its members. Cf.
Introduction, Part ii. p. 67.

Z 2

340 ON THE ULTIMATE

it is to exist9; and thus there must exist something
different from that plurality of beings, the world, which
as we admitted and showed, has no metaphysical neces-
sity10.

But to explain more distinctly how from eternal or
essential or metaphysical truths there arise temporal,
contingent or physical truths, we must first observe that,
from the very fact that there exists something rather
than nothing,-/ it follows that in possible things, or in
possibility or essence itself, there is a certain need of
existence or, so to speak, a claim to exist, in a word,
that essence of itself tends to existence ^ From this it
further follows that all possible things, that is, things
expressing essence or possible reality, with equal right
tend to existence12 in proportion to the quantity of
essence or reality, or in proportion to the degree of per-
fection which belongs to them. For perfection is nothing
but quantity of essence 13.

Hence it is most evident that out of the infinite
possible combinations and series of possible things there
exists that one through which the greatest amount of
essence or possibility is brought into existence. Indeed,
there is always in things a principle of determination
according to maximum and minimum, so that, for instance,
the maximum effect is produced with the minimum out-
lay14. And the time, the place, or, in a word, the

9 Cf. Spinoza's distinction between Substance as id quod in se est
and Mode as id quod in alio est. Ethics, Part i. deff. 3 and 5. See
Monadology, §§36 sqq.

10 For Kant's criticism of the cosmological proof of the existence
of God, see Critique of Pure Reason, Transcendental Dialectic, bk. ii. ch. 2,
§ 2. Fourth Antinomy.

" Cf. Monadology, § 40, note 64.

12 Both E. and G. read essentiam, which is manifestly a slip for
existentiam. E. corrects the error in his Errata.

13 Cf. Monadology, §§41 and 54.

H Outlay or cost is in itself loss or limitation. But if there is to
be a world at all, there must be loss or limitation, for if the
elements of the world were not in different degrees limited, there
would be no variety. All would be one ' splendidly null ' perfec-
tion. Yet the world is the best possible world in the sense that it

ORIGINATION OF THINGS 341

receptivity or capacity of the world 15 may here be con-
sidered as the outlay or ground on which the world is
to be built as fittingly [guam commodissime] as possible,
while the variety of forms corresponds to the fitness
[commoditas] of the building and to the number and
elegance of its rooms. The whole matter may be likened
to certain games in which all the spaces on a board are
to be filled up according to definite rules, so that, unless
you make use of some ingenious contrivance, you find
yourself in the end kept out of some refractory spaces
and compelled to leave empty more spaces than you
intended and some which you might otherwise have
filled. Yet there is a definite method by which the
most complete filling up of the spaces may most easily
be accomplished. So if we have to draw a triangle, no
other determining condition being given, it will be an
equilateral triangle ; and if a line is to be drawn from
one point to another, no further condition being assigned,
the easiest or shortest way will be chosen. So if once
it is given that being is superior to not-being (that is to
say, that there is a reason why something should exist
rather than nothing 16), or that possibility must pass into
actuality, it follows that, though nothing further is
determined, there must exist as much as is possible con-
sidering the capacity of time and space (that is, of the
possible order of existing 17), just as tiles are put together

contains the greatest balance of perfection over limitation or of
good over evil, i. e. the maximum of advantage at the minimum
of cost. In this sense the 'principle of the best,' to which Leibniz
constantly refers, is a 'principle of determination according to
maximum and minimum.' That the cost should be minimum
might be taken as a way of stating the ' law of parsimony.'

15 That is, the natural or essential limits within which the
actual world may express an ideal possibility, which has no limits.
This limiting 'receptivity or capacity' (which is to the world what
the body is to the individual Monad) might be regarded as the
passivity or matter of the world, in contrast with its activity or
form.

16 Cf. Principles of Nature and of Grace, § 7.

17 i. e. not merely the order which we discover among actual
things, but the order which is a condition of possible things

342 ON THE ULTIMATE

in such a way that as many as possible may be contained
in a given area.

Thus it is wonderfully made known to us how in the
very origination of things a certain Divine mathematics 1S
or metaphysical mechanics is employed and the greatest
quantity is brought into existence [lit. the determination
of the greatest quantity takes place]. So among all
angles the determined [fixed] angle in geometry is the
right angle 19, and so also liquids put into heterogeneous
media take the form of greatest capacity, that of a sphere.
But best of all is the illustration we get in ordinary
mechanics, where, when several heavy bodies act against
one another, the resultant motion is that which produces
the greatest fall on the whole20. For as all possible
things by an equal right tend to exist in proportion to
their reality, so all weights by an equal right tend to
fall in proportion to their gravity ; and as in the case of
the latter there is produced a motion which involves the
greatest possible fall of the heavy bodies, so in the case of
the former there is produced a world in which the greatest
number of possible things comes into existence.
/ And thus we have physical necessity coming from
metaphysical necessity ; for although the world is not
metaphysically necessary, so that its opposite involves
a contradiction or logical absurdity, it is nevertheless
physically necessary or so determined that its opposite
involves imperfection or moral absurdity. And as possi-
bility is the principle of essence, so perfection or degree

coming into existence. Only compossible essences can give rise
to co-existing phenomena, and time and space are the order of
co-existence of these phenomena. See Introduction, Part iii. p. 102.
is < \\nhen God calculates and employs thought, the world is
made.' De connexione inter res et verba (1677) (E. 77 a ; G. vii. 191).
The phrase was written by Leibniz on the margin of the MS. and
may accordingly be of later date.

19 The right angle is always 90° ; but an acute or an obtuse angle
is variable in size. The right angle is thus l fixed ' or ' determined, '
and the right angle is the greatest angle at which one line can
meet another.

20 The suggestion is of some such arrangement as we have in
a system of pulleys.

ORIGINATION OF THINGS 343

of essence (through which more things are compossible
the greater it is) is the principle of existence. Whence
at the same time it is manifest how the Author of the
world is free, although He does all things determinately,
for He acts from a principle of wisdom or perfection.
Indifference springs from ignorance, and the wiser a
man is the more is he determined towards that which is
most perfect 21.

~T3ul, you will* say, however beautiful may seem this
comparison of a certain metaphysical determining me-
chanism with the physical mechanism of heavy bodies,
it nevertheless fails in this respect that heavy bodies
really exist and act, but possibilities or essences anterior
to existence or apart from it are imaginary or fictitious
and therefore no reason22 of existence is to be sought in
them. I reply that neither these essences nor what are
called eternal truths regarding these essences are ficti-
tious, but that they exist in a certain region (if I may so
call it) of ideas, that is to say, in God Himself, the source
of all essence and of the existence of other things. That
this is not a mere gratuitous assertion of mine is shown
by the existence of the actual series of things. For since
the reason of the series is not to be found in itself, as has
been shown above, but is to be sought in metaphysical
necessities or eternal truths, and since existing things
can come only from existing things, as we have already
remarked, eternal truths must have existence in some
absolutely or 23 metaphysically necessary subject, that is,
in God, through whom these things which would other-
wise be imaginary are (to use a barbarous but expressive
word) realized 24. ^

And indeed we actually find that all things in the

21 Cf. Introduction, Part iii. p. 145.

22 Or ' ground.' 23 E. reads ' and.'

24 That is to say, God gives them a certain reality or existence in
His understanding, as distinct from existence in the actual world, which
belongs to contingent things. Cf. Monadology, §§ 43, 44, 46 and
47, note 75.

344 ON THE ULTIMATE

/ world take place in accordance with the laws, not only
geometrical but also metaphysical, of eternal truths, that
is, not only in accordance with material necessities but
also in accordance with formal reasons25. And this is
not only true in general as regards the reason (which we
have just explained) -why a world exists rather than not,
and why it exists thus rather than otherwise (a reason
which is to be found only in the tendency of possible
things to exist) ; but also when we come down to par-
ticular things we see that metaphysical laws of cause,
power, activity, are present in a wonderful way through-
out the whole of nature, and that they are even superior
to the purely geometrical laws of matter, as to my great
astonishment I found when I was explaining the laws
of motion, so that, as I have elsewhere more fully ex-
plained 26, I was ultimately compelled to give up the law
of the geometrical composition of forces [conatus] which
I had maintained in my youth when I had more belief
in the material view.

/ Accordingly we have the ultimate reason of the reality
both of essences and of existences in one Being who is
necessarily greater, higher, and older [anterius] than the
world itself, since through Him not only the existing
things which the world contains but also possible things
have reality. But this ultimate reason can be found
only in one source on account of the inter-connexion of
all these things27. But it is manifest that from this
source existing things continually come forth [promanare],
that they are being and have been produced by it, since
it does not appear why one state of the world rather
than another, the state of yesterday rather than that of
to-day, should flow from it28. It is also manifest how

25 E. reads 'necessities' instead of 'reasons/

26 See Appendix I, p. 351.

27 That is to say, the actual system of things is one and therefore
its source is one. Cf. Monadology, § 39.

28 The reference is not quite clear. Janet translates 'from the
world itself.' Kirchmann translates 'from this source.' On Janet's

ORIGINATION OF THINGS 345

God acts not only physically but also freely, how not
only the efficient but also the final cause of things is in
Him, and how He manifests not only His greatness and
power in the mechanism of the world as already con-
structed, but also His wisdom and goodness in the
constructing of it 29.

And lest any one should think that we are here con-
founding moral perfection or goodness with metaphysical
perfection or greatness and, allowing the latter, should
deny the former, it is to be observed that it follows from
what has been said not only that the world is most
perfect physically, or, if you prefer it, metaphysically,
that is to say, that that series of things has come into
existence in which the greatest amount of reality is
actually manifested, but also that the world is most
perfect morally because genuine moral perfection is phy-
sical 30 perfection in minds [mentes] themselves. Where-
fore the world is not only the most admirable mechanism,
but it is also, in so far as it is made up of minds [mentes],
the best commonwealth, through which there is be-
stowed upon minds the greatest possible happiness or
joy, in which their physical perfection consists31.

interpretation, the passage would mean that all the states of the
world must come from God, in whose nature is to be found the
sufficient reason of all and of each, and not from the world itself,
which cannot supply the sufficient reason of any. On Kirchmann's
interpretation, the meaning would be that each state of the world
comes from God by a ' continual creation,' because there is no reason
why God should create one state rather than another. Both inter-
pretations are possible ; but Janet's seems the more natural.

29 Cf. Monadology, §§ 47, 48, 55.

so i Physical ' here means ' natural ' or ' according to the specific
nature (Averts] of the thing ' in contrast with ' metaphysical ' in the
sense of ' absolute, independent of the specific nature of the thing.'
Thus (cf. supra} l the world is most perfect physically ' means that
its individual members or elements are as perfect as the nature of
each allows, while ' the world is most perfect metaphysically ' means
that the world as a whole is the most perfect possible. So also
' genuine moral perfection is physical perfection in minds them-
selves ' means that the specific natural perfection of mind is moral
perfection.

31 Cf. Monadology, §§86 sqq. 'Felicity is to persons what per-
fection is to beings.' Paper without a title (1686) (G. iv. 462).

346 ON THE ULTIMATE

But, you will say, we find that the opposite of this
takes place in the world, for veiy often the best people
suffer the worst things, and those who are innocent, both
animals and men, are afflicted and put to death even
with torture ; and indeed the world, especially if we
consider the government of the human race, seems rather
a confused chaos than anything directed by a supreme
wisdom. So, I confess, it seems at a first glance, but
when we look at it more closely the opposite conclusion
manifestly follows a priori from those very considerations
which have been adduced, the conclusion, namely, that
the highest possible perfection of all things, and therefore
of all minds, is brought about. —

And indeed, as the lawyers say, it is not proper to
judge unless we have examined the whole law. We
know a very small part of eternity which is immeasure-
able in its extent ; for what a little thing is the record
of a few thousand years, which history transmits to us !
Nevertheless, from so slight an experience we rashly
judge regarding the immeasureable and eternal, like men
who, having been born and brought up in prison or,
perhaps, in the subterranean salt-mines of the Sarma-
tians32, should think that there is no oth^r light in the

" The reference is probably to some of the salt-mines in or near
the Carpathians, which are the richest in Europe. The most
famous salt-mines in the world are at Wielicza, near Cracow in
Galicia (which in Leibniz's time was still part of the kingdom of
Poland). They have been worked for about 600 years, and many
of the workers live permanently underground, there being streets
and houses and, in short, something like a village in the lower
levels. In Jeremy Collier's Dictionary, published towards the end
of the seventeenth century, the famous salt-mines are said to be
those of Eperies, in northern Hungary, on the other side of the
Carpathians from Cracow. Sarmatia is a very vague word. Ac-
cording to Ptolemy it included all the eastern European plain from
the Vistula and the Dniester to the Volga. In any case it included
the district of the salt-mines referred to. Leibniz elsewhere seems
to identify Sarmatian with Slavonic speech. (Nouveaux Essais, iii.
2, § i ; E. 299 b ; G. v. 259, 260.) In English verse, Sarmatia is
often used as synonymous with Poland, e. g. ' Sarmatia fell, un-
wept, without a crime ' (Campbell, Pkasures of Hope, Part i. line 376 ;
see also 1. 407).

ORIGINATION OF THINGS 347

world than that of the feeble lamp which hardly suffices
to direct their steps. If you look at a very beautiful
picture, having covered up the whole of it except a very
small part, what will it present to your sight, however
thoroughly you examine it (nay, so much the more, the
more closely you inspect it), but a confused mass of
colours laid on without selection and without art ? Yet
if you remove the covering and look at the whole picture
from the right point of view, you will see that what
appeared to have been carelessly daubed on the canvas
was really done by the painter with very great art33.
The experience of the eyes in painting corresponds to
that of the ears in music. Eminent composers very
often mingle discords with harmonies so as to stimulate
and, as it were, to prick the hearer, who becomes anxious
as to what is going to happen, and is so much the more
pleased when presently all is restored to order ; just as
we take pleasure in small dangers or risks of mishap,
merely from the consciousness of our power or our luck
or from a desire to make a display of them ; or, again, as
we delight in the show of danger that is connected with
performances on the tight-rope or sword-dancing (sauts
perilleux)3*, and we ourselves in jest half let go a little
boy, as if about to throw him from us, like the ape which
carried Christiern, King of Denmark35, while still an
infant in swaddling-clothes, to the top of the roof, and
then, as in jest, relieved the anxiety of every one by
bringing him safely back to his cradle. On the same
principle sweet things become insipid if we eat nothing
else ; sharp, tart, and even bitter things must be com-
bined with them, so as to stimulate the taste. He

33 A most interesting variant of this illustration occurs in
Bosanquet's Essentials of Logic, pp. 55 sqq.

34 Leibniz gives the French phrase to explain his Latin.

35 Probably Christiern or Christian V (1646-1699), the first
hereditary (not elected) King of Denmark, who was reigning at
the time when Leibniz wrote. In the text he is called Christiernus,
Christiern or Kristiern being the Danish form of the name.

3-j 8 OX THE ULTIMATE

who has not tasted bitter things does not deserve sweet
things and, indeed, will not appreciate them. This
is the very law of enjoyment, that pleasure does not
have an even tenor, for this begets loathing and makes
us dull, not happy36.

But as to our saying that a part may be disturbed
without destroying harmony in the whole, this must not
be understood as meaning that no account is taken of the
parts or that it is enough for the world as a whole to be
perfect, although it may be that the human race is
wretched, and that there is in the universe no regard
for justice and no care for us, as is the opinion of some
whose judgment regarding the totality of things is
not quite just. For it is to be observed that, as in
a thoroughly well-constituted commonwealth care is
taken, as far as may be, for the good of individuals,
so the universe will not be sufficiently perfect unless
the interests of individuals are attended to, while the
universal harmony is preserved37. And for this no

36 'To have a thousand well-bound Virgils in your library, always
to sing airs from the opera of Cadmus and Hermioiie, to break all
your porcelain that you might have nothing but cups of gold, to
have diamonds alone for buttons, to eat nothing but partridges,
to drink only Hungarian or Shiras wine — would you call that
reason?' Theodicee, § 124 (E. 539 b ; G. vi. 179). Cf. Principles of
Nature and of Grace, § 18 ; also Bacon, De Augmenlis, iii. i.

37 Cf. Theodicee, § 118 (E. 535 a ; G. vi. 169): 'No substance is
absolutely contemptible or precious in the sight of God. ... It
is certain that God gives more importance to a man than to
a lion ; yet I do not know if we can be certain that God prefers
one man to the whole species of lions in all respects. But even if
it were so, it would not follow that the interest of a certain number
of men should prevail in face of a general disorder, extending to an
infinite number of created things. This opinion would be a relic
of the old maxim, now quite out of repute,, that everything happens
solely on man's account.' Cf. Meditation sur la notion commune de la
justice (Mollat, p. 63) : 'There are people who think that we are of
too little consequence, in the sight of an infinite God, for Him to
have any care for us : we are supposed to be in relation to God
what the worms, which we crush without thinking about it, are in
relation to us. But this is to suppose that God is like a man and
cannot think of everything. Just because God is infinite, He does
things without labour by a kind of consequence of His will,- as it is
a consequence of my will and that of my friend that we are in

ORIGINATION OF THINGS 349

better standard could be set up than the very law of
justice which declares that each should participate in the
perfection of the universe and in a happiness of his own
in proportion to his own virtue and to the degree in which
his will has regard to the common good ; and by this is
fulfilled that which we call charity and the love of God,
in which alone, in the opinion of wise theologians, consists
the force and power even of the Christian religion 38. Nor
ought it to appear wonderful that so great a place should
be given to minds in the universe, since they most closely
resemble the image of the Supreme Author ; they are
related to Him, not (like other things) as machines to
their constructor, but as citizens to their prince ; they
are to last as long as the universe itself, and in a manner
they express and concentrate the whole in themselves, so
that it may be said that minds are whole parts [paries

totalesY9-

But as to the special question of the afflictions of good
men, it is to be held as certain that these afflictions have
as their result the greater good of those who are afflicted,
and this is true not only theologically but also naturally
[physice], as the grain cast into the earth suffers before it
bears fruit. And in general it may be said that afflictions
are for the time evil but in the end good, since they are
short ways to greater perfection. So in physics, liquids
which ferment slowly take also a longer time to purify,

agreement, no new action being required to produce our agree-
ment, beyond the resolve which each of us has made. Now if the
human race and even the smallest thing were not well governed,
the universe itself would not be well governed, for the whole
consists in its parts/

i8 Of. Pope, Essay on Man, Fourth Epistle, lines 327 sqq. Nature,
says Pope, connects

'Man's greatest virtue with his greatest bliss.

Self-love thus push'd to social, to divine,

Gives thee to make thy neighbour's blessing thine.

Happier as kinder, in whate'er degree
And height of bliss but height of charity.
39 See Introduction, Part ii. p. 31.

350 ULTIMATE ORIGINATION OF THINGS

while those which undergo a greater agitation throw off
certain of their ingredients with greater force, and are
thus more quickly rectified. And this is what you might
call going back in order that you may put more force
into your leap forward (qu'on recede pour mieux sauter™}.
Wherefore these things are to be regarded not only as
agreeable and comforting, but also as most true. And
in general I think there is nothing more true than
happiness, and nothing more happy and pleasant than
truth.

Further, to realize in its completeness the universal
beauty and perfection of the works of God, we must
recognize a certain perpetual and very free progress of
the whole universe, such that it is always going forward
to greater improvement [cuttus]. So even now a great
part of our earth has received cultivation [culturd] and
will receive it more and more. And although it is true
that sometimes certain parts of it grow wild again, or
again suffer destruction or degeneration, yet this is to be
understood in the way in which affliction was explained
above, that is to say, that this very destruction and
degeneration leads to some greater end, so that somehow
we profit by the loss itself41.

And to the possible objection that, if this were so, the
world ought long ago to have become a paradise, there
is a ready answer. Although many substances have

40 Cf. Principles of Nature and of Grace, § 12, note 51.

41 Cf. Lettre a la Princesse Sophie (1706) (G. vii. 568) : 'And as there
is reason to think that the universe itself develops from more to
more and that all tends to some end, since all comes from an
Author whose wisdom is perfect, we may similarly believe that
souls, which last as long as the universe, go also from better to
better, at least naturally [physiquement] and that their perfections
go on increasing, although most often this takes place imperceptibly
and sometimes after great circuits backward.' See also Lettre a
Bourguet (1716) (G. iii. 589) : 'Although the universe has always
been equally perfect ' [i. e. each momentary state of the universe
equally perfect with every other] ' it will never be supremely
perfect ; for it always changes and gains new perfections, though
it loses old ones.'

APPENDIX I 351

already attained a great perfection, yet on account of
the infinite divisibility of the continuous, there always
remain in the abyss of things slumbering parts which
have yet to be awakened, to grow in size and worth,
and, in a word, to advance to a more perfect state [ad
meliorem cultum\. And hence no end of progress is ever
reached.

APPENDIX I.

THE GROWTH OF LEIBNIZ^ THEORIES REGARDING FORCE
AND MOTION.

IN the second of two dialogues, entitled Phoranomus sen de
Potentia et Legibus Naturae (1689), Leibniz gives an account of
the progress of his views regarding dynamics and physics.
What follows is a portion of this account, combined with
part of a similar statement in the Specimen Dynamicum.
' When first I escaped from the prickly thorn-brakes of the
schools into the more pleasant fields of later philosophy, I was
greatly taken with that fascinating ease of understanding, in
which I saw a lucid imagination comprehending all the things
which formerly were wrapped in dark notions And after long
and careful deliberation I at length rejected the " forms " and
" qualities " of material things, and reduced all things to purely
mathematical principles ; but since I was not yet versed in
geometry, I was convinced that a continuum consists of points
and that a very slow motion is broken by little bits of rest, and
I was inclined to other doctrines of this kind, which commend
themselves to those who seek to comprehend all things with
the imagination and who do not notice the infinite which is
everywhere latent in things. But although, when I became
a geometrician, I put off these opinions, there yet remained for
a while atoms and the void, as relics of a state of mind that
was in revolt against the idea of the infinite ; for although
I granted that every continuum can in thought be divided
ad infinitum, yet I did not really accept the view that in things
there are innumerable parts which follow from motion in the
plenum. At last, not only was I freed from this scruple, but
also I began to recognize something deeper in bodies, which

352 APPENDIX I

could not be comprehended by the imagination. . . . This
ought not to seem wonderful, for it is the nature of foundations
to be humble, but if they are securely laid, great masses arise
upon them. Accordingly, when I as yet acknowledged the
jurisdiction of imagination alone in regard to material things,
I was of opinion that any natural inertia in bodies was
unintelligible, and that a body at rest in vacuo or in a free
space must receive the velocity of another, however small that
other might be ; and that this does not actually happen in our
experience I attributed to the system established by the wisdom
of the Supreme Author of things, in which all things are ruled
by the most just laws. Nor indeed did I doubt that the origin
of the system might be rationally thought out on mechanical
principles from those very laws of natural bodies, which explain
occurrences by the composition of motions, such as I expounded
regarding several cases in a treatise which I published when
a young man.' Phoranomus, see Arch. f. Gesch. d. Phil. i. 577.
'When I was a young man and, at that time, following
Democritus and his adherents in this matter, Gassendi and
Descartes, I regarded the nature of body as consisting in mere
inert mass, I issued a treatise with the title Hypothesis Physica,
in which I expounded a theory of motion both abstract (inde-
pendent of the system of things) and concrete (as it appears
in the system of things), which I see has pleased many
distinguished men better than its moderate worth deserved.
In this treatise I maintained that, supposing my view of the
nature of body to be right, every impinging body gives its
impulse [conatus] to the body on which it impinges or which
is directly in its way, as such. For when the impact takes
place, the body impinged upon endeavours to move forward
and thus to go away, and (since, as I then thought, body is
indifferent to motion or rest) this endeavour [effort, conatus]
must have its full effect in the body impinged upon, unless it
is hindered by an opposite effort, and even if it is so hindered,
since these different efforts must be compounded together.
Accordingly it was manifest that no cause can be given why
the impinging body should not achieve the effect towards
which it tends or why the body impinged upon should not
receive the whole impulse [conatus] of the impinging body, and
therefore the motion of the body impinged upon is compounded
of its own original impulse and the new or foreign impulse it
has received. Whence I further showed that if in body there

APPENDIX I 353

were recognized only mathematical notions, magnitude, figure,
place, and their changes or their tendency [conatus] to change
at the very moment of impact, and no account were taken of
metaphysical notions, namely, of moving power [potentia] in
the form, and of inertia (or resistance to motion) in the matter
[of the body], and if it were thus necessary that the result of
the impact should be determined by a purely geometrical
composition of forces [conatus], as we have explained: then
it ought to follow that the impulse of the impinging body,
however small that body may be, is communicated to the whole
of the body impinged upon, however large it may be, and thus
the very largest body at rest is moved away by an impinging
body, however small, without any retarding of the latter, since
matter, thus understood, is not repugnant but rather indifferent
to motion. Hence it would not be more difficult to move ^
a large body at rest than a small one, and therefore there >w
would be action without reaction, and no estimate of power )
could be made, since anything might be accomplished by /
anything. . . . But afterwards, having considered the whole /
matter more profoundly, I saw in what the systematic explana- x. .
tion of things ' [i. e. the explanation of things as they actually ^
are] ' should consist, and I observed that my former hypothesis
regarding the nature of body was not complete, and that this
as well as other arguments proved that body must be regarded
as having, in addition to magnitude and impenetrability,
something from which arises the consideration of forces [vires],
the metaphysical laws of which, when combined with the laws
of extension, give rise to those very laws of motion which I had
called systematic. . . .' Specimen Dynamicum, &c. (1695) (G.
Math. vi. 240). ' I am of opinion that the mechanical principles
and reasons of the laws of motion do themselves arise not from
the necessity of matter, but from some higher principle than
imagination, and one independent of mathematics. . . . Besides
I began to have considerable doubts as to the nature of motion.
For when formerly I regarded space as an immovable real
place, possessing extension alone, I had been able to define
absolute motion as change of this real space. But gradually
I began to doubt whether there is in nature such an entity
as is called space ;> whence it followed that a doubt might
arise about absolute motion. Certainly Aristotle had said
that place is notl>:ng but the surface of what surrounds us

A a

354 APPENDIX I

[superficies ambientis]1, and Descartes, following him, had defined
motion (that is, change of place) as change of neighbourhood
\mutatio mciniae]. Whence it seemed to follow that that which
is real and absolute in motion consists not in what is purely
'mathematical, such as change of neighbourhood or situation,
but in motive force [potentia matrix] itself; and if there is
none of this, then there is no absolute and real motion. . . .
Accordingly I found no other 'Ariadne thread to lead me out
of this labyrinth than the calculation of forces [potentiae],
assuming this metaphysical principle, "That the total effect
is always equal to its complete cause" \Quod effectus integer sit
semper aequalis causae suae plenae]. When I discovered that
this agrees perfectly with experience and satisfies all doubts,
I was more confirmed in my opinion that the causes of things
are not, so to speak, senseless [surdus] and purely mathematical,
like the concourse of atoms or the blind force of nature, but
proceed from an intelligence which employs metaphysical
reasons.' Phoranomus, see Arch. f. Gesch. d. Phil. i. 577. In the
first of these dialogues (Phoranomus, &c.) Leibniz says: 'As in
geometiy and numbers, through the principle of the equality
of the whole to all its parts, geometry is brought within the
ecope of an analytical calculus, so in mechanics, through the
principle of the equality of the eifect to all its causes or of
the cause to all its effects, we obtain certain equations, as it
were, and a kind of algebraic mechanics.' tloc. cit. p. 576. Cf.
Introduction to this book, Part iii. p. 107 note.

1 Phys. A. 4. 212* 20.

NEW ESSAYS ON THE HUMAN1 UNDER-
STANDING. 1704.

BY THE AUTHOR OF THE SYSTEM OF PRE-
ESTABLISHED HARMONY.

PREFATORY NOTE.

THE New Essays contain the fullest statement of Leibniz's
appreciation and criticism of Locke. Leibniz became ac-
quainted with the main outline of Locke's Essay, before it was
actually published in English, by means of an abstract of the
book, prepared by Locke, translated into French and published
in Le Clerc's Bibliofheque Universelle (1688), vol. 8, pp. 49 sqq.
When in 1690 the Essay itself was published Leibniz read it,
making notes as he went, and his criticisms were expressed in
various short papers, some of which were transmitted to Locke
through Thomas Burnet of Kemnay. Locke, however, seems
rather to have disparaged Leibniz's criticisms and he did not
count them worthy of a reply. Meanwhile Locke's Essay
passed through several editions, and in 1700 Coste's French
translation of it was published. This enabled Leibniz, whose
knowledge of English was somewhat imperfect, to make a
thorough study of the Essay, and after writing some papers on
special parts of it, he set himself to the task of preparing the
elaborate exposition and criticism of the Essay which was after-
wards published as the New Essays. The book was written
somewhat hurriedly and discontinuously, during scraps of

1 G., with over-accuracy, omits ' human,' which Leibniz cannot
deliberately have intended to omit, for he includes it in the titles
of the first three books of the New Essays.

A a 2

35^ NEW ESSAYS

leisure time. Accordingly Leibniz, in view of publication,
submitted his work to Hugony and Barbeyrac (the great jurist),
who revised a considerable portion of it, including the Intro-
duction, and made numerous changes in its expression.
Meanwhile a new edition of Coste's translation, revised and
corrected by Locke himself, was promised, and Leibniz was
strongly advised by Coste to delay publication until after he
had seen this new edition. Locke died in the end of 1 704, and
Leibniz, understanding that he had made considerable changes
in his .opinions, felt that it was now of little use to publish his
own criticism.

Accordingly the New Essays remained in manuscript until
1765, when they were published by Raspe. He printed the text
in the form which it had finally assumed after the correction
and revision of Hugony, Barbeyrac and Leibniz himself.
Erclmann (E. 194 sqq.) follows this text. Gerhardt (G. v. 39
sqq.), however, has thought it better to reconstruct the original
text, by going behind the corrections, on the ground that,
while these corrections often improve the French style of the
original, they do not always so well express Leibniz's thought.
Boutroux, approving the course taken by Gerhardt, has in
various points corrected the text made by that editor. My
translation is made from Boutroux's text. Such variations as
involve a change in translation are mentioned in foot-notes.

In the Introduction to the New Essays (which was written
later than the rest of the book), Leibniz summarizes the main
points regarding which he differs from Locke, while he
characteristically suggests that, after all, the differences
between his view and that of Locke are not altogether in-
surmountable. After some prefatory sentences, the Intro-
duction deals in the first place (a) with the question whether
(as Locke held) the mind is tabula rasa or whether (as Leibniz
thought) there are innate ideas, necessary truths, including
the question whether or not all our knowledge comes from the
senses (pp. 357-367). (V) This leads naturally to the question
whether (as Locke seems to say) there is nothing in our mind
of which we are not actually conscious or whether (as Leibniz
maintains) we have unconscious perceptions (pp. 367-385).
Leibniz here connects his psychology with his metaphysics by
showing how the petites perceptions throw light upon the pre-
established harmony, the law of continuity, the identity of

NEW ESSAYS 357

indiscernibles and the indestructibility of souls, as well as
their inseparability from bodies, (c) The next question con-
sidered is that of atoms and the void (in which Locke believes) as
against a plenum (Leibniz's view) (pp. 385 sqq.). (d) References
to the criticism of Locke by Stillingfleet lead to a consideration
of the question whether matter can think, Locke maintaining
the possibility of this, while Stillingfleet and Leibniz deny it
(PP- 39° sqq.-)' This gives occasion to Leibniz to draw a
distinction between .the physical or real genus of a thing
and its logical or ideal genus (p. 394), and in the remainder
of the Introduction he applies this distinction, maintaining
that as matter and soul are heterogeneous (i.e. not of the
same physical or real genus), thinking, which is a mode of
soul, cannot be a mode of matter, except by miracle, and that
accordingly, if Locke's contention were true, we should have
to adopt a philosophy of unintelligible qualities or faculties,
which would be even worse than the Scholastic theories of
' occult ' qualities or faculties, so justly derided by later
thinkers.

INTRODUCTION.

As the Essay on the Understanding 2, by an illustrious
Englishman, is one of the best and most highly esteemed
works of the present time, I have resolved to make some
remarks upon it, because, having for a long time given
considerable attention to the same subject and to most of
the matters with which the essay deals, I have thought
that this would be a good occasion for publishing some
of my opinions under the title of New Essays on the
Understanding, in the hope that my thoughts will obtain
a favourable3 reception through appearing in such good
company. I have hoped also to be able to profit by the
work of another, not only in the way of lessening my
own work (as in fact it is less trouble to follow the
thread of a good author than to work on entirely un-
trodden ground) 4, but also in the way of adding some-

2 E. reads 'human understanding.'

3 E. reads ' more favourable.'

4 E. omits the clause in brackets.

358 NEW ESSAYS

thing to what he has given us, which is always easier
than making an independent beginning5. For I think
I have removed some difficulties which he left entirely
alone. Thus his reputation is helpful to me ; and besides,
being disposed to do justice and very far from wishing
to lessen the esteem in which his work is held, I would
increase his reputation, if my approval have any weight 6.
It is true that I often differ from him in opinion ; but,
far from 7 denying the worth of famous writers, we bear
witness to it by making known in what respect and for
what reasons we differ from their opinion, when we
think it necessary to prevent their authority from pre-
vailing against reason on some important points 8 ; and
besides, in replying to such excellent men, we make
it easier for the truth to be accepted, and it is to be
supposed that it is principally for truth that they are
working.

In fact, although the author of the Essay says a thousand
fine things of which I cordially approve, our systems
greatly differ. His has more relation to Aristotle and
mine to Plato 9, although in many things both of us have

5 E. omits 'always' and adds (after 'beginning'), 'and working
on entirely untrodden ground.'

6 E. omits from ' For I think ' to ' any weight.'

7 E. reads 'denying on that account the worth of this famous
writer, I do him justice,' &c.

8 E. omits the remainder of the sentence, from this point.

9 The main principles of Leibniz's philosophy are really much
more akin to the philosophy of Aristotle than to the doctrines
which are peculiar to Plato. But, as regards Aristotle, Leibniz
is here thinking of that side of his philosophy which led the
Scholastics to attribute to him the saying, NihU est in intelledu quod
non prius fuerit in sensu. (Cf. Duns Scotus, Super Universalibus Porphyrii,
Question 3 : Itta propositio Aristotelis, nihil est in intelledu quin prius

fuerit in sensu. . . .) This phrase does not occur in any of Aristotle's
writings ; but it serves as a fair enough analysis of several passages
in the Posterior Analytics, in which firi(TTrjfj.T) is traced to aiaOijais,
though other passages supplement this by bringing in the work of
vovs. (See especially Anal. Post. ii. 19, and Eth. vi. 3, § 3.) The
view that the soul is a tabula rasa is suggested by the passage :

NEW ESSAYS 359

departed from the doctrine of these two ancient writers.
He is more popular, and I for my part am sometimes
compelled to be a little more acroamatic^ and abstract,
which is not of advantage to me, especially when a living
language is used. But I think that by introducing two
speakers, one of whom expounds opinions taken from
this author's Essay, while the other adds my observations,
I show the relation between us in a way that will be
more satisfactory to the reader than if I had put down
mere remarks, the reading of which would have been
constantly interrupted by the necessity of turning to his
book in order to understand mine. Nevertheless it will
be well also to compare our writings sometimes, and not
to judge of his opinions except from his own work,
although I have usually retained his expressions. It is
true that owing to the limitations involved in following
the thread of another person's argument and making
remarks upon it, I have been unable even to think of
achieving the graceful turns of which dialogue is sus-
ceptible ; but I hope that the matter will make up for
the defects of the style.

8vva.fj.ei TTWS fffTi ra vorjTO. 6 vovs, a\\' fVT(\f)^eiq. ovSev, irplf av vorj. 8(t
8' OVTQJS (aOTTCp kv Ypa/^uaTe/oj <£ ftrjOev vTrdpxd fVTf\€^ia yfypa/j.fj,evov
(De Anima, iii. 4. 429** 30). Cf. note 12, infra. In regard to Plato,
on the other handj Leibniz is probably thinking mainly of the
Platonic theory of reminiscence, according to which our knowledge
of realities, in so far as we can attain to it, is a recollection or
restoration of knowledge possessed by the soul in a previous state,
so that necessary and eternal truths are, in a sense, innate in us.
On the whole matter cf. Nolen, Quid Leibnizius Aristoteli debuerit, and
Trendelenburg, Hist. Beitrage, vol. ii.

10 i. e. esoteric. See Aulus G-ellius, Nodes Atticae, xx. 5 (quoted
by Eitter and Preller, Hist. Phil. Graec. § 298), where a distinction is
drawn between the exoteric and the ' acroatic ' writings of Aristotle.
Leibniz himself defines the word : ' The acroamatic way of philoso-
phizing is that in which all things are demonstrated, the exoteric
is that in which certain things are said without demonstra-
tion, and yet are confirmed by the consistency they have with
various other things and by probable [topicae] reasons (or even
reasons that might demonstrate, but are put forward only aa

360 NEW ESSAYS

The differences between us have regard to subjects u
of some importance. There is the question whether the
soul, in itself, is entirely empty, like a writing- tablet on
which nothing has yet been written (tabula rasa), (which
is the opinion of Aristotle 12 and of the author of the
Essay), and whether everything that is inscribed upon it
comes solely from the senses and experience ; or whether
the soul originally contains the principles13 of several
notions and doctrines, which are merely roused on certain
occasions by external objects, as I hold along with Plato
and even with the Schoolmen, and with all those who
interpret in this sense the passage of St. Paul (Eomans,
ii. 15), in which he shows that the law of God is written
in men's hearts. The Stoics called these principles H
15, that is, fundamental assumptions or what

probable), and are illustrated by instances and similar cases.' De
stilo philosophico Nisolii (1670) (E. 63 a ; G. iv. 146).

11 E. reads ' objects.'

12 Cf. note 9. Aristotle's meaning, however, is very different
from that of Locke. 6 vovs is not the ' soul,' but reason as opposed
to sense. And there is a vovs diraOrjs. The context of the passage in
which vovs is compared to the writing-tablet shows that Aristotle
merely meant to protest against the view that reason has certain
complete l ready-made ' ideas, apart from all sense- experience. But
this is quite consistent with holding that there are in reason
potential or virtual forms or ideas. Even the clean writing-tablet
is at least a writing-tablet and not a sheet of water on which
nothing can be written. Cf. De Anima, iii. 4. 429* 27 : KOL ev 5r)
ol \eyovT€S rr\v ^i/x^i/ fivai TOTTOV fiSuv, Tr\r]v on ovre o\rj a\\' rj voijriKr],
ovTf Ij/Te\«x€"? oAAa owdfi€i TO, 6?8?7. Cf. Analytica Post. ii. 19, 99b
20 sqq.

13 apxai, grounds or sources.

14 E. reads ' common notions ' after ' principles.'

15 The original has prolepses. The Stoic irp6\r}\f>is, however, was
not an anticipation prior to, or presupposed by, all experience, but
the common image resulting from a series of sense-impressions,
which leads us to expect other similar impressions. The distin-
guishing characteristic of the npo\Tj^fis is that they arise tyvtriKtas
(naturally), and are not deliberately constructed by us. Thus
Diogenes Laertius, vii. 54 : can 8' 77 TrpoA.^? (vvoia <f>vffiKt) ruv
Ka0u\ov. Cf. Placita, iv. ii, quoted by Hitter and Preller, Hist. Phil.
Graec. § 393, in which the Stoics are represented as holding a view

NEW ESSAYS 361

we take for granted beforehand. Mathematicians call
them common notions (KOLVOL ewowu)16. Modern philo-
sophers give them other excellent names ; and, in
particular, Julius Scaliger17 named them semina aeter-
nitatis item zopyra18, as much as to say, living fires,
flashes of light [traits lumineux] 19, hidden within us but
appearing at the instance of the senses, like the sparks
which come from the steel when it strikes the flint.
And not without reason it is thought that these flashes
[eclats] indicate something divine and eternal, which
appears above all in necessary truths. Hence there
arises another question, whether all truths are dependent
on experience, that is, on induction and instances ; or
whether there are some which have yet another founda-
tion. For if some events can be foreseen before we have
made any trial of them, it is manifest that we contribute

much more akin to that of Locke than to that of Leibniz : ot
(paffiv orav fevvrjOf) 6 dvOpcairos, *x6£ T° fftfuoviicbv pepos TTJS
wffTTfp xapTyv cvfpyov fh airoypcHprjv' els TOVTO fj.iav tKaarrjv TUV evvoiwv
fv<nroypa(f)€Ta.i. But the peculiarity of the Stoic Monism makes it
possible to regard this as less inconsistent with Leibniz's view than
at first sight it appears to be. Cf. Kendall's Marcus Aurelius Anto-
ninus, Introduction, pp. Ixxvi-lxxviii ; and Bonhoffer, Epictet und
die Stoa, pp. 187 sqq.

16 Euclid calls axioms KOIVCU cvvoiat.

17 Julius Caesar Scaliger (1484-1558), one of the great scholars of
the Renaissance. Among his chief works (besides many translations
from Greek into Latin) were a treatise on Latin grammar, De causis
linguae Latinae, and a book in opposition to the views of Cardan,
Exotericae Exercitationes de Subtilitate ad Hieronymum Cardanum.

18 'Seeds of the eternal and kindling sparks/ The reference
is to Poetice, Lib. iii. cap. n. (sth ed., 1617, p. 211) : <Sunt in nobis
insita zopyra quaedam, id est, semina aeternitatis/ For similar
expressions cf. Poetice, Lib. iii. cap. i and 20 ; Poemata, Pars Altera
(I574)? PP- 19 and l6°; and Ad Arnoldum Ferronum Atticum Oratio
(Epistolae et Orationes, p. 427). Zopyra is the Greek ffarvpa, ' lights
used for kindling fires.' In the Laws, bk. iii. 677 B, Plato speaks of
the survivors of the Flood as ev reopvfpats TTOV fffjiiKpa

ytvovs.

19 Trait de lumiere is used in French for an illuminating thought,
and probably Leibniz's phrase is intended to suggest this.

362 NEW ESSAYS

to them something of our own 20. The senses, although
they are necessary for all our actual acquiring of know-
ledge, are by no means sufficient to give us the whole of
our knowledge, since the senses never give anything but
instances21, that is to say particular or individual truths22.
Now all the instances which confirm a general truth,
however numerous they may be, are not sufficient to
establish the universal necessity of this same truth ; for
it does not at all follow that what has happened will 2S
happen in the same way. For example, the Greeks, the
Romans, and all the other peoples of the earth, as it was
known to the ancients24, always observed that before
twenty-four hours have passed, day changes into night

20 E. reads ' on our part.'

21 i. e. special cases.

22 In a Lettre touchant ce qui est independant des Sens et de la Matiere
written to Queen Sophia Charlotte in 1702 (during the time when
he was working at the New Essays'), Leibniz says : ' We use our
external senses as a blind man uses his stick (after the simile of an
ancient writer), and they make known to us their particular objects,
which are colours, sounds, odours, tastes, and touch-qualities. But
they do not make known to us what these sense -qualities are,
nor in what they consist. ... It may be said that sense-qualities are
in fact occult qualities, and that there must be other more manifest
qualities, which can make them explicable. And far from its being
true that we understand things of sense alone, these are the very
things we understand least. And although they are familiar to
us, we do not on that account comprehend them better, as a pilot
does not understand better than other people the nature of the
magnetic needle which turns to the north, although he has it
always before his eyes in the compass, and on that account has
almost ceased to wonder at it. ... Nevertheless I admit that, in
our present state, the external senses are necessary for our thinking,
and that, if we had none of them, we should not think. But what
is necessary for anything is not on that account the essence of the
thing. Air is necessary to us for life ; but our life is something
else than air. The senses furnish us with matter for reasoning,
and we never have thoughts so abstract that something of sense is
not mingled with them ; but reasoning requires in addition some-
thing other than that which is of sense.' (G. vi. 499, 500, 506.)

33 E. adds ' always.'

24 E. has merely l and all other peoples.'

NEW ESSAYS 363

and night into day. But they would have been wrong
if they had thought that the same rule is observed
everywhere else25, for since that time, the opposite has
been experienced 26 by people on a visit to Nova Zembla.
And he would still be wrong who should think that, in
our regions at least, it is a necessary and eternal truth
that shall endure for ever 27, since we must hold that the
earth and the sun itself do not exist necessarily, and that
perhaps there will come a time when this beautiful star
with its whole system will no longer exist, at least in its
present form 28. Whence it seems that necessary truths,
such as we find in pure mathematics and especially in
arithmetic and geometry, must have principles whose
proof does not depend upon instances nor, consequently,
upon the witness of the senses, although without the
senses it would never have come into our heads to think
of them. This is a point which should be carefully noted,
and it is one which Euclid so well understood that he
often proves by reason that which is evident enough
through experience and through sense-images'29. Logic
also, along with metaphysics and ethics [la morale], of
which the one forms natural theology30 and the other
natural jurisprudence, are full of such truths ; and con-
sequently their demonstration 31 can come only from the

25 E. omits < else/ . 26 E. reads « seen/

37 E. omits ' that shall endure for ever/

28 Cf. Monadology, § 28.

29 Cf. the letter to Queen Sophia Charlotte, quoted above : < The
senses can indeed in a way make known to us that which is, but
they cannot make known that which ought to be or which cannot
be otherwise. . . . The senses and inductions never yield us truth
perfectly universal nor that which is absolutely necessary, but only
that which is and that which occurs in particular instances.'
(G. vi. 504, 505.)

so i True metaphysics is hardly different from true logic, that is
to say, from the art of discovery in general ; for in fact metaphysics
is natural theology, and the same God, who is the source of all good
things, is also the principle of all parts of knowledge.' Lettre a la
Princesse Sophie (undated) (G. iv. 292).

31 i.e. the certainty of logic, metaphysics and ethics as sciences.

364 NEW ESSAYS

inner principles which are called innate. It is true we
must not imagine that we can read these eternal laws of
reason in the soul as in an open book32, as the edict
of the praetor may be read on his album 3S without trouble
or investigation ; but it is enough that we can discover
these laws in ourselves by means of attention, for which
opportunities are furnished by the senses ; and the
success of experiments serves also as a confirmation of
reason, somewhat as in arithmetic l proofs ' are useful in
helping us to avoid errors of calculation when the process
is a long one. In this also lies the difference between
human knowledge and that of the lower animals. The
lower animals are purely empirical and direct them-
selves by particular instances alone ; for, so far as we can
judge, they never succeed in forming necessary proposi-
tions ; while men, on the other hand, have the capacity
for demonstrative science. It is also on this account that
the power of making concatenations [of ideas] which the
lower animals possess is something inferior to the reason
which is in men 34. The concatenations [of ideas] made by
the lower animals are simply like those of mere empirics,
who maintain that what has sometimes happened will
happen again in a case which resembles the former in
characteristics which strike them, although 85 they are
incapable of judging whether or not the same reasons
hold good in both cases. That is why it is so simple
a matter for men to entrap animals, and so easy for
mere empirics to make mistakes. From this making of
mistakes even persons who have become skilful through
age and experience are not exempt, when they trust too
much to their past experience, as some have done in civil
and military affairs ; because enough consideration is
not given to the fact that the world changes and that

32 a livre ouvert, lit. = ad aperturam libri.

33 i. e. the tablets with 'notices/ posted up in a public place, so
that he who runs may read.

34 Cf. Monadology, §§ 26-29. S5 E. adds ' for all that.'

NEW ESSAYS 365

men become more skilful by finding countless new con-
trivances, while on the other hand the stags or the hares
of our time do not become36 more full of shifts than
those of former times. The concatenations [of ideas] in
the lower animals are only a shadow of reasoning, that is
to say they are only connexions37 of imagination and
passings 7 from one image to another, because in new
circumstances which seem to resemble others which have
occurred before we 38 expect anew what we 38 at other
times found along with them, as if things were actually
connected together because their images are connected in
memory. It is true that reason also leads us to expect,
as a rule, that there will occur in the future what is in
harmony with a long experience of the past, but this is,
nevertheless, not a necessary and infallible truth ; and
our forecast may fail when we least expect it, because
the reasons which have hitherto justified it no longer
operate 89. And on this account the wisest people do not
trust altogether to experience, but try, so far as possible,
to get some hold of the reason of what happens, in order
to decide when exceptions must be made. For reason
is alone capable of laying down trustworthy rules and

36 E. reads ' are not.'

37 E. reads ' a connexion' and l a passing.'
88 E. reads < they.'

39 Cf. Lettre a laEeine Sophie Charlotte (1702) : ' For instance, though
we may have observed a thousand times that iron, when it is put
by itself on the surface of water, goes to the bottom, we have no
assurance that it must always be so. And without referring to the
miracle of the prophet Elisha who made iron to swim, we know
that we can make an iron pot so hollow that it floats, and that it
can even carry a considerable load, as do boats made of copper and
tin. And even abstract sciences, like geometry, afford instances in
which that which usually happens no longer happens. For
instance, we usually find that two lines which continually approach
one another ultimately meet, and many people will be ready to
take oath that this can never fail to happen. Nevertheless geo-
metry makes known to us unusual lines (called, on that account,
Asymptotes) which, if prolonged to infinity, continually approach one
another and yet never meet.' (G. vi. 505.)

366 NEW ESSAYS

of supplying what is lacking in those which were not
trustworthy, by stating the exceptions to them, and in
short of finding sure connexions in the force of necessary
consequences ; and this often enables us to foresee the
event without having to experience the sense-connexions
of images, to which the animals are confined, so that
that which shows that the sources [principes] of necessary
truths are within us also distinguishes man from the
lower animals.

Perhaps our able author may not entirely diifer from
me in opinion. For after having devoted the whole of
his first book to the rejection of innate knowledge
[lumieres\ understood in a certain sense, he nevertheless
admits, at the beginning of the second book and in those
which follow, that the ideas which do not originate in
sensation come from reflexion. Now reflexion is nothing
but an attention to that which is in us, and the senses
do not give us what we already bring with us. That
being so, can it be denied that there is much that is
innate in our mind [esprit], since we are, so to speak,
innate to ourselves, and since in ourselves there are
being, unity, substance, duration, change, activity [action^
perception, pleasure and a thousand other objects of our
intellectual ideas 40 ? And as these objects are immediate
objects of our understanding and are always present41
(although they cannot always be consciously perceived
[aperpus] because of our distractions and wants), why
should it be surprising that we say that these ideas,
along with all that depends on them, are innate in us ?
Accordingly I have taken as illustration a block of veined

40 As distinguished from ideas or images of sense. Cf. Monadology,
§ 30, and Principles of Nature and of Grace, § 5 ; also Petit discours de
Metaphysique (1686) (G-. iv. 452) : 'Those expressions which are in
our soul, whether they are conceived or not, may be called ideas, but
those which are conceived or formed may be said to be notions,
conceptus.'

41 E. reads ' these objects are immediate and always present to
our understanding/

NEW ESSAYS 367

marble, rather than a block of perfectly uniform marble
or than empty tablets, that is to say, what is called by
philosophers tabula rasa. For if the soul were like these
empty tablets, truths would be in us as the figure of
Hercules is in a block of marble, when the block of marble
is indifferently capable of receiving this figure or any
other. But if there were in the stone veins, which
should mark out the figure of Hercules rather than other
figures, the stone would be more determined towards
this figure, and Hercules would somehow be, as it were,
innate in it, although labour would be needed to uncover
the veins and to clear them by polishing and thus
removing what prevents them from being fully seen.,;
It is thus that ideas and truths are innate in us, as
natural inclinations, dispositions, habits or powers [vir-
tualites] 42, and not as activities [actions'], although these
powers [virtualites] are always accompanied by some
activities [actions], often imperceptible, which correspond
to them.

Our able author seems to maintain that there is in us
nothing virtual, and even nothing of which we are not
always actually conscious 43. But this cannot be understood
in a strict sense ; otherwise his opinion would be too para-
doxical, since, for instance 44, we are not always conscious

42 Of. Monadology, §§ 40, 43 and 54, with the notes. By a virtualite
Leibniz means something between a mere potency or capacity
and a fully-developed activity or actual idea. Thus necessary and
eternal truths are not innate in the soul in a fully-developed form,
nor, on the other hand, does the soul merely have a capacity for
receiving or acquiring them, but they are innate in germ, as im-
perfectly perceived ideas with a tendency to become perfectly
perceived. See Introduction, Part iii. pp. 125 sqq. and 130.

43 Cf. Locke's Essay, bk. i. ch. i, § 5. This position is an imme-
diate result of Cartesian principles. See Introduction, Part iii.
p. 126. Cf. Geulincx, Metaphysica Vera, Part i. (Opera, Land's ed.,
vol. ii. p. 150) : ' It is impossible that he who does not know how
a thing is done should do it. If you do not know how a thing is
done you do not do it.'

** E. reads 'since, although we are not, &c. . . . we often
bring, &c.'

368 NEW ESSAYS

of acquired habits and of the things stored in our memory,
and, indeed, they do not always come to our aid when
we require them, although we often bring them back
easily into our mind on some slight occasion which recalls
them to us, as we need only the beginning of a song in
order to remember it45. Our author also limits his
thesis in other places, saying that there is in us nothing
of which we have not at least been conscious [aper$us\
formerly. But in addition to the fact that nobody can,
through reason alone, be quite certain how far our past
apperceptions have extended, for we may have forgotten
them, especially in light of the Platonic doctrine of
reminiscence, which, though a myth46, contains, in part
at least47, nothing incompatible with bare reason— in
addition, I say, to this fact, why must everything be
acquired by us through apperception of external things,
and why should it be impossible to unearth anything in

45 E. reads ' to make us remember the rest of it/

46 Leibniz's objection to the Platonic doctrine is that it implies
a complete (or clear and distinct) knowledge of the ' ideas ' in
a previous state. He accepts the Platonic doctrine in so far as it
implies that knowledge of the eternally true comes to the soul not
through external sense, but by development from its own inner
being. Cf. Nouveaux Essais, bk. i. ch. i, § 5 (E. 209 a ; Gr. v. 75 : l It
was the opinion of the Platonists that all our ideas [connaissances~\
were reminiscences, and that thus the truths which the soul brings
with it at a man's birth, and which are called innate, must be
remains of a former definite knowledge. But this opinion has no
foundation. And we may readily believe that the soul must have
already had innate ideas [connaissances] in its preceding state (if it
did pre-exist), however far back that state might be, just as it has
them now ; accordingly they must in turn have come from another
preceding state, in which they would ultimately be innate, or at
least created along with it ; or else we should have to go ad infinitum
and regard souls as eternal, in which case these ideas [connaissances]
would in fact be innate, because they would never have had a
beginning in the soul ; and if any one maintains that each prior
state has received from another, prior to itself, something which it
has not transmitted to those which follow, the answer is that it is
manifest that certain evident truths must have belonged to all
these states.'

47 E. omits ' in part at least.'

NEW ESSAYS 369

ourselves? Is our soul, then, so empty that, beyond48
images borrowed from outside, it is nothing? That, I
am sure, is not a view which our judicious author can
approve. And where shall we find tablets which have
not some variety in themselves? For there is never49
such a thing as a perfectly unbroken [uni] and uniform
surface. Why, then, should not we also be able to
provide ourselves with some sort50 of thought out of
our own inner being, when we deliberately try to
penetrate its depths 51 T Thus I am led to believe that
his opinion on this point is not fundamentally different
from mine, or rather from the common opinion, inas-
much as he recognizes two sources of our knowledge, the
senses and reflexion 5£

I do not know that it will be so easy to reconcile him
with us and with the Cartesians, when he maintains
that the mind does not always think, and especially that
it is without perception when we sleep without dreaming ;
and he holds that, since bodies can exist without motion,
souls might also quite well exist without thinking53.
But here I reply in a way somewhat different from that
which is usual ; for I maintain that, naturally P4, a sub-

48 E. reads ' without.'

49 In E. the sentence is interrogative : ' Is there ever,' &c.

50 E. reads ' object.'

51 Leibniz is here applying his principle of the ' identity of
indiscernibles,' viz. that no two things are absolutely identical,
which implies that no real thing is an absolute unity, exclusive of
all difference or variety, but that everything has some essential
characteristic or internal quality. See Monadology, § 9.

M If the mind is really tabula rasa, what are those ' internal
operations ' or ' actings of our own minds,' which Locke regards as
the objects of reflexion? Leibniz suggests that Locke may not
really mean all that he seems to mean by the tabula rasa, and that,
accordingly, Locke is fundamentally at one with him in admitting
at least innate ' dispositions.'

53 Essay, bk. ii. ch. i, § 9 (Eraser's ed., vol. i. p. 127). See Intro-
duction, Part iii. p. 129.

51 i.e. 'in the ordinary course of things,' 'otherwise than by
miracle.'

Bb

370 NEW ESSAYS

stance cannot exist without activity [action], and indeed
that there never is a body without motion. Experience
is already in my favour as regards this, and to be per-
suaded of it one has only to refer to the book of the
illustrious Mr. Boyle55 against an absolute rest. But
I think that reason also supports it, and this is one of the
proofs which I use to overthrow the theory of atoms 56.

Besides there are countless indications which lead us
to think that there is at every moment an infinity of
perceptions within us, but without apperception and
without reflexion ; that is to say, changes in the soul
itself of which we are not conscious [s'apercevoir], because
the impressions are either too small and too numerous
or too closely combined [trop unies], so that each is not
distinctive enough by itself, but nevertheless in com-
bination with others each has its effect and makes itself
felt, at least confusedly, in the whole. Thus it is that,
through being accustomed to it, we take no notice of the
motion of a mill or a waterfall when we have for some
tune lived quite near them. Not that this motion does
not continually affect our organs, nor that something
does not pass into the soul, which responds to it because
of the harmony of the soul and the body, but these
impressions which are in the soul and in the body,

55 Robert Boyle (b. Lismore, 1627, d. London, 1691), the famous
chemist and physicist, who (almost contemporaneously with
Mariotte) discovered the law of the pressure of gases, which is
called the Boyle-Mariotte law. He maintained that there is no
such thing as absolute rest, in the book here referred to, under the
title Of Absolute Rest in Bodies. [Boyle's Works (London, 1744), vol. i.
p. 281.] It was also published in Latin in his Opera Varia (Geneva,
1680). Leibniz had some intercourse with Boyle during his stay
in London in 1673. See Introduction, Part i. p. 7.

5(5 As rest is infinitely small motion, everything moves. Conse-
quently the essence of body cannot be absolutely unmoved
extension, but must be force, which is the source of motion. But
a force is a real unity, absolutely indivisible, while the atom is only
physically indivisible, it being ideally divisible. Hence physical
atoms are not the elements of things. Cf. New System, § u.

NEW ESSAYS 371

having lost the attractions of novelty, are not strong
enough to attract our attention and our memory, busied 5T
with more engrossing objects. For58 all attention re-
quires memory, and often fi9 when we are not, so to
speak, admonished 50 and warned to take notice of some
of our present perceptions, we let them pass without
reflexion and even without observing them ; but if some
one directs our attention to them immediately after-
wards 60, and for instance bids us notice some sound that
has just been heard, we remember it, and we are con-
scious that we had some feeling of it at the time. Thus
there were perceptions of which we were not immediately
conscious [s'apercevoir], apperception arising in this
case only from our attention being directed to them
after 61 some interval, however small. And for an even
better understanding of {;he petites perceptions which we
cannot individually distinguish in the crowd, I am wont
to employ the illustration of the moaning or sound of the
sea, which we notice when we are on the shore. In
order to hear this sound as we do, we must hear the
parts of which the whole sound is made up, that is to
say the sounds 62 which come from each wave, although
each of these little sounds makes itself known only in the
confused combination of all the sounds taken together,
that is to say, in the moaning of the sea63, and no one
of the sounds would be observed if the wave which
makes it were alone. For we must be affected a little
by the motion of this wave, and we must have some
perception of each of these sounds, however little they
may be ; otherwise we should not have the perception
of a hundred thousand waves, for a hundred thousand

57 E. reads i which are busied only.' 58 E. omits 'for.'

59 E. omits * often ' and ' admonished and.*

60 E. omits ' afterwards.'

61 E. reads * in this case of our attention being directed to them
only after,' &c.

6a E. reads ' sound.'

43 E. omits ' that is to say, in the moaning of the sea.'
B b 2

372 NEW ESSAYS

nothings cannot make something. We never sleep so
profoundly as not to have some feeble and confused
feeling, and we should never be wakened by the greatest
noise in the world if we had not some perception of its
beginning which is small, just as we should never break
a cord by the greatest effort 64 in the world, if it were
not strained and stretched a little by less efforts, though
the small extension they produce is not apparent 6\
" These petites perceptions have thus through their conse-
quences66 an influence greater than people think. It is
they that form this something I know not what, these
tastes, these images of sense-qualities, clear in combination
but confused in the parts67, these impressions which

6* G. reads ' effect.'

65 Cf. Montaigne, Essais, bk. ii. ch. 14 : 'If we suppose a piece
of twine equally strong throughout, it is utterly impossible that it
should ever break. For in what part of it is the breaking to begin,
the flaw to appear? And for it to break in every part at once is
against all nature.' See Introduction, Part iii. p. 144 note.

66 E. omits 'through their consequences.'

67 Sense-qualities, according to Leibniz, are each clear as a whole,
that is to say, each can %e perfectly distinguished from others.
But they are not also distinct ; that is to say, we cannot perfectly
analyze their elements. Such an analysis is possible ; but we cannot
perform it, for it would involve an infinite process. Each sense-
quality ' contains infinity,' for it "has connexions with everything
else in the universe. Cf. Lettre a la Heine Sophie Charlotte (1702) :
'We know by what kind of refraction blue and yellow are made,
and that these two colours when mixed make green. But we
cannot yet understand, for all that, how our perception of green
results from our perceptions of the two colours which compose it,
nor how our perceptions of these colours arise from their causes. We
have not even nominal definitions of such qualities so as to explain
the terms for them. ... If I were to say to some one : You know that
green means a colour consisting of blue and yellow mixed, he would
not make use of this definition as a means of recognizing green
when he came upon it. But this is the function of nominal
definitions. For the blue and the yellow which are in the green
are not distinguishable or recognizable^ and it is only by chance, so
to speak, that we have found this by observing that this mixture
always makes green. Thus the only way to enable a man to
recognize green in future is to show it to him at present ; but this

NEW ESSAYS 373

surrounding bodies make upon us, who contain infinity 68,
this connexion which each being has with all the rest
of the universe. It may even be said that in conse-
quence of these petites perceptions the present is big with c9
the future and laden with the past, that there is a conspi-
ration of all things (cn^Trvota 7rai/ra, as Hippocrates said 70),
and that in the least of substances eyes as penetrating
as those of God might, read the whole succession of the
things of the universe,

Quae sint, quae fuerint, quae mox futura trahantur 71.

These unconscious [insensible] perceptions also indicate
and constitute the identity of the individual, who is
characterized by the traces or expressions72 of his pre-
vious states which these unconscious perceptions preserve,
as they connect his previous states with his present state ;
and these unconscious perceptions73 may be known by

is not necessary in the case of more distinct notions, which can be
made known to people by description, although we do not have
them at hand. . . . For this reason we are wont to say that the
notions of sense-qualities are clear, for they enable us to recognize the
qualities ; but that these notions are not distinct, because we cannot
discriminate nor unfold what they contain Within them. What
they contain is an I know not what, of which we are conscious but of
which we can give no account/ (Passages combined from G. vi.
492, 493, 5oo.)

es E. reads ' and which contain infinity.'

69 E, reads < full of.'

70 See Monadology, note 97.

71 ' What things are, what things have been, and what future
things may soon be brought forth.' Virgil, Georgics, iv. 393. Virgil
ascribes this knowledge to Proteus. Leibniz misquotes futura for
ventura : futura would not scan.

72 E. omits l or expressions.'

73 Leibniz merely says 'and they,' so that the reference is
doubtful. He may mean 'the traces of previous states.' What
is meant is simply that as the unconscious perceptions are the
development of previous states of perception and at the same time
contain, in a germinal or confused way, all future states of percep-
tion, they give continuity to the individual possessing them, i. e.
they constitute his identity. Contrast Locke's view, Essay, bk. ii.
ch. 27. Cf. Monadolog^J, note 114.

374 NEW ESSAYS

a higher mind [esprit], although the individual himself
may not be conscious of them, that is to say, though he
may no longer have a definite recollection of them. But
they [these perceptions] furnish also the means of re-
covering this recollection, when it is needed, through
periodic developments which may some day occur 74. That
is why death, owing to these perceptions 75, can only be
a sleep, and cannot even last as a sleep, for in animals
perceptions merely cease to be distinct [distingue] enough76,
and are reduced to a state of confusion, in which con-
sciousness [aperception] is suspended, but which cannot
last for ever77, not to speak here of man who must have
great privileges in this regard in order to keep his
personality 78.

Further, the unconscious [insensible] perceptions ex-
plain79 that wonderful pre-established harmony of body
and soul, and indeed of all Monads or simple substances,
which takes the place of the untenable theory of the
influence of one upon another, and which, in the opinion

74 What is meant is that, as perceptions are not isolated but
linked together, they do not each independently rise and fall in
distinctness by a kind of chance, but as one group or system of
perceptions falls out of consciousness another rises into conscious-
ness, so that there is a kind of periodicity in our perceptions, with
troughs and crests as in wave-motion. Thus the recollection of any
former perception means that the system or group of which it is
a member has passed from the crest of consciousness to the trough
of sub-consciousness and so back to the crest again. Cf. Considerations
sur Za Doctrine d'un Esprit Universel Unique (1702) (E. 181 a; G. vi.
535) : ' The organs ' [of the animal] ' are merely " enveloped " and
reduced to a small size, but the order of nature requires that some
day all shall re-develop and return to an observable condition, and
that in these vicissitudes there be a certain well-ordered progress,
which serves to mature things and to bring them to perfection.'
For a development of this idea cf. James's Psychology, vol. i. ch. g.

75 E. omits ' owing to these perceptions.'

76 i. e. distinct enough to produce consciousness.

77 The remainder of this sentence is omitted by E.

7d Cf. Principles of Nature and of Grace, §12, note 51 ; Monadology, § 82,
note 130. See also Introduction, Part iii. p. 116.

79 E. reads ' by the unconscious perceptions I explain.'

NEW ESSAYS 375

of the author of the most excellent of Dictionaries 80,
exalts the greatness of the Divine perfections beyond
what has ever been conceived. After this I should add
little, if I were to say that81 it is these petites per-
ceptions which determine us on many occasions without
our thinking it, and which deceive people by the appear-
ance of an indifference of equilibrium, as if, for instance,
we were completely 82 indifferent whether to turn to the
right or to the left b3. It is also unnecessary for me to
point out here, as I have done in the book itself, that
they cause that uneasiness which I show to consist in
something which differs from pain only as the small
from the great, and which nevertheless often constitutes
our desire and even our pleasure, giving to it a kind of
stimulating relish 84. It is also due to these unconscious
[insensible] parts of our conscious [sensible] perceptions
that there is a relation between these perceptions of
colour, heat, and other sensible qualities, and the motions
in bodies which correspond to them ; while the Carte-
sians, along with our author, in spite of all his pene-
tration, regard the perceptions we have of these qualities
as arbitrary, that is to say, as if God had given them to
the soul according to His good pleasure, without regard
to any essential relation between the perceptions and
their objects ; an opinion which surprises me, and w^ich
seems to me not very worthy of the wisdom of the
Author of things, who does nothing without harmony
and without reason 85.

80 Pierre Bayle. See Monadology, § 16, notes 28 and 29. The
reference is to the article Rorarius in Bayle's Dictionary, where he
says (note L, i) : ' It ' [the system of pre-established harmony]
' exalts above all that can be conceived the power and intelligence
of Divine art.' Bayle, however, makes this remark by way of
objection to the system.

8L E. reads ' after this I ought also to add that.'

82 E. omits ' completely/

83 Cf. Introduction, Part iii. p. 141.
8* Cf. Introduction, Part iii. p. 140.

85 See Descartes, Principia, Part iv. §§ 196-198 and 204. Descartes

376 NEW ESSAYS

In a word, unconscious [insensible] perceptions are of as
great use in pneumatics i6 as imperceptible [insensible] S1
corpuscles are in physics ; and it is as unreasonable to
reject the one as the other on the ground that they are
beyond the reach of our senses *8. Nothing takes place
all at once, and . it is one of my great maxims, one
among the most completely verified of maxims, that nature
never makes leaps ; which I called the Jaw of continuity £9
when I spoke of it in the first 90 Nouvelks de la EepuUique
des Lettres 91 ; and the use of this law in physics is very
considerable : it is to the effect that we always pass from

held that 'colour, heat,' &c., as we perceive them, are not to be
attributed to external bodies, the qualities of which are all forms
of motion. There is on his view no absolute reason why one kind
of motion should produce in us the sensation of colour and another
the sensation of heat. Leibniz, on the other hand, regards motions
as themselves perceptions of a very low degree of distinctness, and
the unconscious perceptions which in combination give rise" to our
conscious sensation form a connecting link between the motions of
bodies and our corresponding sense-perception of their qualities.

86 A name for the philosophy of mind or spirit, derived from the
New Testament use of trvfvfjLa. In Scholastic times it included
natural theology and the doctrines regarding angels and demons,
as well as 'psychology.' In the seventeenth century it was used
in the more limited sense by Alsted in his Encyklopadie (1630),
a work which, according to Diderot, Leibniz thought of re-
modelling, with the assistance of other scholars ((Euvres de Diderot,
ed. Assezat, vol. xv. p. 440). Cf. G. vii. 67. The terms Pneumaticks
and Pneumatology (in the sense of philosophy of the mind) were
used in the Scottish Universities in the end of the seventeenth
and beginning of the eighteenth centuries. The word Pneumatics
has now ceased to have any connexion with the philosophy of
mind and is used to describe the branch of hydrodynamics which
is concerned with gases.

87 E. omits ' imperceptible [insensible'].'

88 The reference is probably to the views of Descartes. See
Principia, Part iv. § 201.

89 Cf. Introduction, Part ii. p. 37 ; Part iii. p. 83.

90 E. reads ' when I spoke of it elsewhere in the Nouvelles,' &c.

91 This was Bayle's magazine, and Leibniz formulated his law for
the first time in the letter to Bayle (1687) to which reference is
here made. (See G. iii. 51 ; E. 104.) For a translation of this see
Introduction, Part iii. p. 83 note.

NEW ESSAYS 377

small to great, and vice versa, through that which is
intermediate in degrees as in parts 9J ; and that a motion
never immediately arises from rest nor is immediately
reduced to rest, but comes or goes through a smaller
motion, just as we never completely traverse any line or
length without having traversed a smaller line, although
hitherto those who have laid down the laws of motion
have not observed this law, and have thought that a body
can in a moment receive a motion contrary to that which
it had immediately before93. And all this leads us to
think that noticeable perceptions also91 come by degrees
from those which are too small to be noticed. To think
otherwise is to know little of the illimitable fineness
[subtilite] of things, which always and everywhere contains
[cnveloppe] an actual infinity 95.

I have also noticed that, in virtue of imperceptible
[insensible] variations, two individual things cannot be
perfectly alike, and that they must always differ more
than numero yV This makes an end of ' the empty tablets
of the soul,' 'a soul without thought,' 'a substance with-
out activity' [action], 'the void in space,' 'atoms,' and

92 i. e. in degree as in quantity.

93 Cf. Introduction, Part iii. pp. 87 sqq.
91 E. omits ' also.'

95 See Monadology, § 65, note 107.

96 Cf. Introduction, Part ii. pp. 36 sqq. Also Monadology, § 9, note
15, and Nouveanx Essais, bk. ii. ch. 27,. § i (E. 277 b ; G. v. 213) :
' Besides the difference of time and place, there must always be an
internal principle ^£ distinction, and although there are several things
of the same kind, it is nevertheless true that none of them are
ever perfectly alike. Thus although time and place (that is to say,
external relation) enable us to distinguish things, which we do not
readily distinguish by themselves, the things are none the less
distinguishable in themselves. The exact determination of identity
and diversity is not a matter of time and place, although it is true
that the diversity of things is accompanied by that of time and
place ; because they ' [i. e. time and place] ' bring with them
different impressions about the thing. Not to mention the fact
that it is rather by means of the things that we must distinguish
one place or time from another, for in themselves they are perfectly
alike, but of course they are not substances or complete realities/

378 NEW ESSAYS

even particles not actually divided in matter, l absolute
rest/ ' complete uniformity in one part of time, place or
matter,' ' perfect globes of the second element, arising
from original perfect cubes97,' and a thousand other
fictions of philosophers, which come from their incom-
plete notions and which the nature of things does not
admit of, and which are made passable by our ignorance
and the slight attention we give to the imperceptible
[insensible], but which cannot be made tolerable unless in
the limited sense of abstractions of the mind, which
protests that it does not deny what it sets aside and
thinks ought not to come into any present consideration.
Otherwise, if we seriously meant this, namely that the
things of which we are not conscious [s'apercevotr] are
neither in the soul nor in the body, we should err in
philosophy as is done in statecraft [politique], when no
account is taken of TO fUKpov 98, imperceptible [insensible]

97 The reference is to the vortex hypothesis of Descartes. Ac-
cording to Descartes, as body is ultimately extension in three
dimensions, the original division of it (as the result of motion
imparted by God) would result in perfectly cubical parts. This
original motion Descartes supposes to have been such as to make
the parts revolve on their own axes and also in groups round
different centres. As a result of this (matter being a plenum] the
angles of the cubes are rubbed down, and the detrition proceeds at
an ever-increasing rate, because the smaller the body, the larger
(in proportion to its bulk) is the surface it exposes to the rubbing
of other bodies. Accordingly there are three primary elements of
the visible world, (i) the detritus, which includes the sun and the
fixed stars, (2) the remains of the original cubes in the form of
exceedingly minute globules, of which element the sky consists,
and (3) some parts of matter which have been less easy to move
than the globules of the second element and consequently have
not been rubbed down so quickly ; such as the earth, the planets
and comets. In short, the first element consists of luminous
bodies, the second of transparent bodies and the third of opaque
bodies. See Descartes, Principia, Part iii. §§46 sqq. In a letter to
Nicaise (1692) Leibniz speaks about the * useless chatter regarding
little bodies and the first, second or third element, which are of as
little value as the occult qualities ' (G. ii. 534).

98 A«f ... TO fJitKpbv <pv\arT€iv (Aristotle, Politics, \. 8, § 2, i3O7b 32).

NEW ESSAYS 379

progressions ; but on the other hand an abstraction is
not an error, provided we know that what we ignore
is actually there. So mathematicians make use of
abstractions when they speak of the perfect lines which
they ask us to consider, the uniform motions and other
regular effects, although matter (that is to say, the inter-
mingling of the effects of the surrounding infinite19)
always makes some exception. We proceed thus in
order to discriminate conditions [considerations] from one
another and in order to reduce effects to their grounds
[raisons], as far as possible, and to foresee some of their
consequences : for the more we are careful to neglect
none of the conditions which we can control, the more
does practice correspond to theory100. But it belongs
only to the supreme reason, which nothing escapes, to
comprehend distinctly all the infinite and to see101 all
grounds [raisons] and all consequences. All that we can
do as regards infinities is to recognize them confusedly,
and to know at least distinctly that they are there ;
otherwise 102 we have a very poor idea of the beauty and
greatness of the universe, and also we cannot have a
sound physics, which explains the nature of bodies IOS
in general, and still less a sound pneumatics104, which
includes the knowledge of God, of souls, and of simple
substances in general.

This knowledge of unconscious [insensible] perceptions
serves also to explain why and how no two souls, human

The chapter deals with maxims for avoiding revolutions. § 3 refers
to the fallacy of the spendthrift : l Each expense is little, there-
fore the whole is little.' Cf. Politics, v. 4, § i, I303b 18 : yivovrai fji(v
ovv al aracrcis ov Trepl jjuKpuv d\\' etc piKptav.

99 E. reads ' the infinite which surrounds us.'

100 That is to say, the more do actual occurrences correspond to
our explanation of them.

101 E. omits ' and to see.'

102 * Otherwise ' = ' but if we entirely ignore the infinities in
things.'

103 E. reads ' things.'

104 See note 86.

3^0 NEW ESSAYS

or other, of one and the same kind 10\ ever come perfectly
alike from the hands of the Creator, and each has always
from the first a reference to the point of view it will have
in the universe 103. But this indeed follows already from
what I observed regarding two individuals, namely, that
their difference is always more than a numerical one. There
is also another important point, as to which I must differ,
not only from the opinions of our author, but also from
those of the majority of modern writers. I believe, with
the majority of the ancients, that all superhuman spirits
[genies], all souls, all created simple substances are always
combined 107 with a body, and that there never are souls
entirely separated [from body] 108. I have a priori reasons
for this, but it will also be found that the doctrine is of
advantage in this respect, that it solves all the philo-
sophical difficulties about the state of souls 109, about their
perpetual preservation, about their immortality and about
their working ; for the difference between one state of
the soul arid another never is and never has been any-
thing but a difference between the more and the less
conscious [sensible], the more and the less perfect, or vice
versa, and thus the past or the future state of the soul
is as explicable as its present state110. The slightest
reflexion makes it sufficiently evident that this is in
accordance with reason, and that a leap from one state to
another infinitely different state could not be natural.
I am surprised that the philosophic schools have without
reason given up natural explanation m, and have deliber-
ately plunged themselves into very great difficulties and

103 E. reads ' no two human souls or two things of one and the
same kind/

106 Cf. Monadology, §§51 sqq.

1J7 E. omits ' combined,' reading ' sont toujours a un corps.'

108 God alone is actus purus, without body. Cf. Introduction,
Part iii. pp. 108 sqq., and Monadology, § 72, note 115.

log This probably means questions as to what has been the state
of souls in the past and what will be their state in the future.

110 See Introduction, Part iii. pp. 113 sqq.

m E. reads 'nature.'

NEW ESSAYS 381

given occasion for the apparent triumphs of freethinkers
[esprits forts] n2, all of whose arguments fall at once
through this explanation of things, according to which
there is no more difficulty in conceiving the preservation
of souls (or rather, as I think, of the animal), than there
is in the change of the caterpillar into the butterfly, and
in the preservation of thought during sleep, to which
Jesus Christ has divinely likened death113. But then
I have already said that no sleep can last for ever ; and
it will last for the shortest time or almost not at all in
the case of rational souls, which are destined always to
preserve the personal character [personnage] which has
been given them in the City of God, and consequently
to retain memory ; and this is so, in order that they may
be more susceptible of punishments and rewards. And
I add further that no derangement of its visible organs
is capable of reducing things to complete confusion in
an animal, or of destroying all its organs and depriving

112 Cf. Monadology, § 14, note 25. See also Considerations sur la
Doctrine d'un Esprit Universel Unique (1702) (G-. vi. 532; E. 179 b):
' What has also, in my opinion, contributed greatly towards
making men of intellect believe in the doctrine of a single uni-
versal spirit is this, that ordinary philosophers have set forth
a doctrino about souls separate [from bodies] and about the
functions of the soul being independent of the body and its organs,
which doctrine they could not sufficiently justify. They were
perfectly right in wishing to maintain the immortality of the soul
as in conformity with the Divine perfections and with a genuine
morality, but seeing that by death those organs in animals which
we observe are deranged and ultimately corrupted, they thought
it necessary -to have recourse to separated souls, that is to say, to
the opinion that the soul continues to exist without anybody and
none the less retains its thoughts and functions. And in order to
give a better proof of this they tried to show that the soul has
already in this life thoughts which are abstract and independent
of ideas of matter. Now those who rejected this separated con-
dition and independence [of the soul] as contrary to experience
and to reason were so much the more led to believe in the
extinction of the individual soul and the preservation of the
universal spirit alone.'
113 St. John xi. ver. n.

382 NEW ESSAYS

the soul of the whole of its organic body and of the
ineffaceable remains of all its former impressions 114.
But the ease with which people have given up the
ancient doctrine that the angels have ethereal [subtils^
bodies connected with them (which has been confounded
with the corporeality of the angels themselves), the in-
troduction of supposed unembodied [separes] intelligences
among created things (to which Aristotle's theory of
intelligences that make the skies revolve has greatly con-
tributed)115, and finally the ill-considered opinion people

114 Cf. Monadology, §§ 72-77 ; New System, §§7 and 8.

115 According to Aristotle the heavens are moved by the -npurov
KIVOVV or prime mover, i. e. by God, who (as Leibniz also admits) is
actus purus. But this is an eternal (aidiov} motion, and Aristotle
describes the heavens as <ro//*a TI 0€iov (De Caelo, ii. 3, 286* n).
Accordingly the heavens are not moved by ' intelligences.' On the
other hand, Aristotle represents the planets as having motions of
their own, different from that of the fixed stars or the sphere of
the heavens in general. These planetary motions are attributed
to an activity (trpa£is') similar to that which exists in animals and
plants (De Caelo, ii. 12, 292** i). But even so, Aristotle cannot be
regarded as meaning that the planets are moved by ' separate'
intelligences. It seems likely that Leibniz was thinking of the
views of Thomas Aquinas, who says : ' A heavenly body is moved
by some intellectual substance ' (Contra Gentes, iii. 23, i) ; and
also : ' Heavenly bodies are moved by the substances which move
them through apprehension : not however a sense-apprehension
.... and therefore an intellectual one.' At the end of the chapter
quoted, he says : ' For our present purpose it does not matter
whether a heavenly body is moved by an intellectual substance
conjoined with it as its soul, or by a separate substance : or
whether each of the heavenly bodies is moved by God or none
of them is immediately so moved, but all through the mediation of
created intellectual substances : or whether the first heavenly
body alone is immediately moved by God and the others by the
mediation of created substances — provided we hold that the motion
of the heavens is due to an intellectual substance.' There is here
a suggestion of the Neo-Platonic influences to which Thomas
Aquinas was necessarily subject. The theory mentioned by Leibniz
is stated also by Albertus Magnus, Metaphysica, Lib. xi. Tract. 2,
cap. 10 (Opera, ed. Jammy, 1651, vol. iii. p. 374 b\ and by J. C.
Scaliger, Comm. in Hippocratis lib. de Somniis (1539), p. 12. Cf. Leibniz's
Considerations sur la Doctrine d'un Esprit Universel Unique (E. 178 b ; G.

NEW ESSAYS 383

have held that we cannot believe in the preservation
of the souls of the lower animals without falling into
metempsychosis and making them go [promener] from
body to body, and the perplexity in which people have
been through not knowing what to do with them116,
have, in my opinion, led to the neglect of the natural
way of explaining the preservation of the soul. This
has done great injury to natural religion and has led
a good many to believe that our immortality is only
a miraculous grace of God ; and our celebrated author
also speaks of it with some doubt, as I shall mention
presently 117. But it were well if all those who are of
this opinion had spoken about it as wisely and as
sincerely as he ; for it is to be feared that a good many
people who speak of immortality through grace, do so
only to save appearances, and are at bottom nearly of
the same opinion as those Averroists118 and some erring

vi. 530) : ' It is true, the Peripatetic philosophers did not regard this
spirit as absolutely universal ; for besides the intelligences which,
according to them, animate the stars, they had an intelligence for
this lower world, and this intelligence performed the function
of active understanding in the souls of men.' See also Bayle's
Dictionary, vol. iv, article Ricius, note C.

116 E. omits from ' and making ' to < with them.'

117 Infra, pp. 389 sqq. See Locke, Essay, bk. iv. ch. 3, § 6 (Fraser's
ed., vol. ii. p. 195, with note), and bk. iv. ch. 4, § 15 (Fraser, vol. ii.
p. 240 note). Cf. also Locke's Reasonableness of Christianity (opening
paragraphs), where Locke seems to make the immortality of the
soul conditional on religious faith.

118 Averroes (or Ibn Roschd) was born at Cordova in 1126 and
died in 1198. Much of his philosophizing was concerned with the
relation between the vovs TTOIIJTIKOS (a phrase never actually used by
Aristotle) and the vovs iraOrjTifcos of Aristotle. (See De Anima, iii.
5, 430* 10 sqq.) Developing a suggestion of Aristotle, Averroes
regards the vovs TTOIIJTIKOS as one principle appearing in all men,
while the vovs iraOijTiKos is peculiar to the individual. The vovs
iroirjTiKos is ultimately identical with the Divine Spirit and is thus
immortal ; but there is no individual immortality, for the vovs
iraOrjTiKos is mortal. Cf. Leibniz's Considerations sur la Doctrine d'un
Esprit Universel Unique (1702) (E. 178 a ; Gr. vi. 529) : i Several people of
intellect have thought and do still think that there is only one spirit,

384

NEW ESSAYS

Quietists119, who imagine an absorption of the soul
and its reunion with the ocean of divinity, a notion

which is universal and which animates the whole universe and all
its parts, according to the structure of each and the organs it finds
in each, as the same blast of wind produces the various sounds
from different organ-pipes. And thus when the organs of an
animal are rightly arranged, this spirit appears in it as an in-
dividual soul, but when the organs are broken up, this individual
soul comes to nothing again or returns, so to speak, into the ocean
of bhe universal spirit. To many people Aristotle appears to have
had an opinion of this kind, which has been revived by Averroes,
a famous Arabian philosopher. He held that there is in us an
intellectus agens, or active understanding, and also an intelltctus paliens,
or passive understanding ; and that the former of these, coming
from outside of us, is eternal and universal for all, while the
passive understanding, which is peculiar to each, passes away at
the man's death. This doctrine was held by some of the Peri-
patetics, two or three centuries ago, such as Pomponatius,
Contarenus and others,'

119 See Considerations sur la Doctrine d'un Esprit Universel Unique
(E. 178 b ; G. vi. 530) : 'Apparently Molinos, and some other new
Quietists, among otliers a certain author called Joannes Angelus
Silesius, who wrote before Molinos, and some of whose works have
lately been reprinted, and even Weigelius before them, favoured
this opinion of the Sabbath or rest of souls in God. And for
this reason they held that the cessation of individual functions is
the highest state of perfection.' Miguel de Molinos was born at
Saragossa in 1627 and died (in the prison of the Inquisition) in
1697. His chief book was his Spiritual Guide, published in Spanish
and afterwards translated into many languages. Madame Guyon
and Fenelon were much influenced by his work. Valentine Weigel
w«s born at Hayn in Thuringia in 1533 and died in 1588. He was
a Protestant minister in a village near Dresden, and although only
one book of his was published in his lifetime, he left a large number
of works in manuscript, many of which are still unpublished. He
was a believer in the direct revelation of truth by the ' inward light,'
in answer to prayer. Leibniz elsewhere mentions him as ' a clever
man, who was indeed too clever,' and he says that Angelus was Hhe
author of certain rather pretty little bits of devotional verse, in
the form of epigrams.' Discours de la Conformite de la Foi avec la
Raison, § 9 (E. 482 b ; G. vi. 55). There has been much dispute as
to the identity of Angelus and little is known about him. His
best known poem is the CheruUnischer Wandersmann. See Vaughari,
Hours with the Mystics, bk. vii. ch. i ; and Schrader, Angelus Silcsius u.
seine Mystik. Leibniz distinguishes between the Quietist 'Sabbath'
and the 'beatific vision,' saying that the 'beatific vision of completely

NEW ESSAYS 385

which perhaps my system alone clearly shows to be ^o
impossible120.

We seem also to differ as regards matter in this, that
the author thinks there must be a void in it [matter] 121
for the sake of motion, because he believes that the
particles of matter are indivisible [roide]. And I admit
that if matter were composed of such parts, motion in
the plenum would be impossible, as if a room were filled
with a great many little pebbles, so that not even the
smallest place in it was empty. But this supposition
is not by any means granted, and indeed there does not
seem to be any reason for it ; although this able author
goes so far as to think that the rigidity or cohesion of its
particles constitutes the essence of the body. Space must
rather be conceived as full of an ultimately fluid matter,

happy souls is compatible with the functions of their glorified
bodies, which will still remain organic in their own way.' Esprit
Universel Unique (E. 182 a ; G. vi. 536).

120 For, according to Leibniz, no substance can be without an
activity of its own, and thus none can be lost in the ocean of the
one spirit. Against this idea that ' the universal spirit is like an
ocean composed of an infinity of drops, which are separated from
it when they animate some particular organic body, but are
reunited to their ocean after the destruction of the body's organs,'
Leibniz argues that ' as the ocean is a quantity of drops, God would
thus be an assemblage of all souls, somewhat in the same way as
a swarm of bees is an assemblage of these insects, but as the swarm
is not itself a genuine substance, it is clear that in this way the
universal spirit itself would not be a genuine being, and in place
of saying that it is the only spirit, we should have to say that in
itself it is nothing at all, and that in nature there is nothing but
individual souls of which it is the aggregate. ... If we hold that
the souls, when reunited to God, are without any functions of
their own, we fall into an opinion contrary to reason and to all
good philosophy, as if any being with a continued existence could
ever reach a state in which it is without function or impression.
For when one thing is combined with another it retains never-
theless its peculiar functions, which, when combined with the
functions of the others, produce the functions of the whole, other-
wise the whole would have no functions, if the parts had none.'
Esprit Universel Unique (E. 181 b ; G. vi. 535).

121 E. omits <init' [y].

c c

386 NEW ESSAYS

susceptible of all divisions and even subjected actually to
divisions and subdivisions ad infinitum™2 ; but neverthe-
less with this difference that it is divisible and divided
unequally in different places, because of the motions,
more or less tending to division, which are already in
the particular place. Consequently matter has every-
where some degree of rigidity as well as of fluidity, and
there is no body which is hard or fluid in the highest
degree, that is to say, there is no atom of invincible
hardness, and no quantity of matter [masse] completely
indifferent to division 123. Thus the order of nature and
especially the law of continuity make both124 equally
inadmissible.

I have also shown that cohesion, if not itself the effect
of impulse or motion, would cause a traction, strictly
speaking125. For if there were a fundamentally hard

122 Cf. Monaddogy, § 65.

123 Two extremes are both impossible : (i) the absolutely hard or
solid, (2) the absolutely soft or fluid. An absolutely hard piece of
matter would be one in which the force holding it together should
be so strong that no combination of other forces could overcome it.
An absolutely soft portion of matter would be one in which there is
no force of cohesion whatever, nothing to resist division, so that it
would be 'completely indifferent to division.' Hardness or solidity
is, according to the law of continuity, simply a low degree of
softness or fluidity.

m i.e. both a perfect atom and a perfect fluid. Cf. Third
Explanation of the New System, p. 335 with note. Also Nouveaux Essais.
bk. ii. ch. 4, § 4 : 'I am also of opinion that all bodies have some
degree of cohesion, as in the same way I hold that there are none
which have not some fluidity and of which the cohesion cannot be
overcome : and consequently in my opinion the atoms of Epicurus,
the hardness of which is supposed to be invincible, cannot exist
any more than the perfectly fluid minute [subtile'] matter of the
Cartesians.' (E. 229 b; G. v. 114.)

135 But, according to Leibniz, traction or attraction is unintelligible,
unless in the sense of a force or impulse which can be overcome by
counteracting forces. A * traction, strictly speaking.' would imply
that one part of matter is for ever bound (' thirled ') to another and
must therefore always be dragged along with it. Leibniz, however,
does admit that there is an apparent traction, even though there be
no visible contact between the parts which draw one another, as

NEW ESSAYS 387

body, for instance, one of the atoms of Epicurus, which
should have a part projecting in the form of a hook (as
we can imagine atoms of all kinds of shapes) 126, the hook
when impelled would draw with it the rest of the atom,
that is to say, the part which is not impelled and which
does not lie in the line of impulsion. Yet our able
author is himself opposed to these philosophical tractions,
such as were formerly attributed to nature's abhorrence
of a vacuum ; and he reduces them to impulses, maintain-
ing, with the moderns, that one part of matter acts
immediately upon another only by impelling it through
contact127. In this I think they are right, because
otherwise there would be nothing intelligible in the
operation.

Nevertheless I must not conceal the fact that I have
observed a kind of retraction regarding this matter on
the part of oun excellent author, whose unpretending
straightforwardness in this respect I cannot but praise,
as much as I have admired his penetrating genius on
other occasions. I refer to his reply to the second letter
of the late Bishop of Worcester128, printed in 1699,

in the case of the magnet and some electrical phenomena. But
in any such case, there is contact and 'impulse' between the bodies
concerned, although it may not appear so to our senses. Cf.
Nouveaux Essais, bk. ii. ch. 4, § 4 ; ch. 8, § u (E. 229 a, 231 b ; GK
v. 113, 118).

126 According to Democritus, atoms differ in * shape, arrangement
and position.' (Aristotle, Metaph. A. 4, 98sb 13.)

127 See Locke's Essay, bk. ii. ch. 8, § n (cf. Eraser's note, vol. i.
p. 171), and bk. ii. ch. 23, § 17 sqq.

128 Edward Stillingfleet, born at Cranbourne, Dorsetshire, 1635,
died at Westminster, 1699, having for ten years been Bishop of
Worcester. His chief work was the Origines Sacrae (1662). His
controversy with Locke originated in the anti-religious use to
which Toland (in his Christianity not Mysterious) turned some of
Locke's views. In 1696 Stillingfleet published A Discourse in
Vindication of the Doctrine of the Trinity with an answer to the late Socinian
objections, in which there appeared a criticism of Locke's ' way of
ideas.' To this Locke replied at great length and the controversy
continued until Stillingfleet's death. Cf. Eraser's ed. of Locke's

C C 2

388 NEW ESSAYS

p. 408, in which, by way of justifying the opinion he
had maintained against the learned prelate, namely that
matter might think, he says among other things : * It is
true, I say, " that bodies operate by impulse and nothing
else " (Essay, bk. ii. ch. 8, § 1 1). And so I thought when
I writ it, and can yet conceive no other way of their
operation. But I am since convinced by the judicious
Mr. Newton's incomparable book, that it is too bold a
presumption to limit God's power, in this point, by my
narrow conceptions. The gravitation of matter towards
matter, by ways inconceivable to me, is not only a demon-
stration that God can, if He pleases, put into bodies
powers and ways of operation above what can be devised
from our idea of body, or can be explained by what we
know of matter, but also an unquestionable and every-
where visible instance, that He has done so. And
therefore in the next edition of my book I shall take
care to have that passage rectified129.' I find that in the
French translation of this book, doubtless made from the
latest editions130, this section n reads thus: 'It is
evident, at least so far as we can conceive it, that bodies
act upon one another by impulse and not otherwise ; for
it is impossible for us to understand that a body can act
upon that which it does not touch, which is as much as
to imagine that it can act where it is not 1SV

Essay, vol. i. Prolegomena, p. xli ; Stillingfleet's Works (1710), vol. iii.
pp. 413 sqq. ; Locke's Works (1823), vol. iv.

129 See Fraser's ed. of Locke's Essay, vol. i. p. 171 note. Also
Locke's Works (10 vol. ed., 1823), vol. iv. p. 467.

130 See Prefatory Note. The italics are by Leibniz. The Eng-
lish edition has merely : ' The next thing to be considered is, how
bodies produce ideas in us ; and that is manifestly by impulse, the
only way which we can conceive bodies to operate in.'

31 Of course the Newtonian theory does not necessarily imply
that a body can act where it is not. « The whole is greater than the part:
how exceedingly true ! Nature abhors a vacuum : how exceedingly
false and calumnious ! Again, Nothing can act but where it is : with
all my heart ; only, WHERE is it ? ' Carlyle, Sartor Resartus, bk. i.
ch. 8 (Library ed., vol. i. p. 52). Cf. Newton, Principia, def. 8, and
Scholium Generale ; also Stallo, Concepts of Modern Physics, ch. 5.

NEW ESSAYS 389

I cannot but praise the modest piety of our celebrated
author, who recognizes that God can do beyond what we
can understand, and that thus there may be inconceivable
mysteries in the articles of faith ; but I would rather
that we were not compelled to have recourse to miracle
in the ordinary course of nature and to admit absolutely
inexplicable powers and operations. Otherwise too great
a licence will be given to bad philosophers on the strength
of what God can do ; and if we admit those centripetal
powers [vertus] 182 or those immediate attractions from a dis-
tance, without its being possible to make them intelligible,

13-' In Nouveaux Essais, bk.ii. ch. 8, § n, he calls them vires centripetae
(E. 231 b ; G. v. 1 18). Cf. Antibarbarus Physicuspro Philosophia reali contra
ren&cationes qualitatum scholasticarum et intelligentiarum chimaericarum
(G. vii. 342) : ' And all who are not content to recognize with us
qualities which are so far occult, that is, which are unknown, have
supposed qualities which are perpetually occult, d/J/Ji/Toi, inexplic-
able, which not even the highest spirit [genius] could thoroughly
know and make intelligible. Such are they who, led on by the
success of the observation that the large bodies of the world exert
among themselves and upon their own perceptible parts the
attraction of this system, suppose that every body is attracted by
every other through the very force of matter ; whether, as it were,
like feels like and delights in it even from afar, or whether God by
a perpetual miracle secures that they shall strive towards one
another, as if they had feeling. However that may be, these people
neither can reduce attraction to impulse or to explicable reasons (as
Plato did in the Timaeus) nor do they wish they could. ... It is
surprising that even now, in the great light of this age, there are
some who hope to persuade the world of a doctrine so opposed to
reason. John Locke, in the first edition of his Essay on the Under-
standing, declared rightly, and in accordance with the mechanical
physics established by his illustrious countrymen, Hobbes, Boyle,
and their numerous followers, that no body is moved except by the
impulse of a body coming into contact with it. But afterwards
(obeying, I think, the authority of his friends rather than his own
judgment) he withdrew this opinion, and held that there may lie
hid in the essence of matter I know not what extraordinary things
[mirabilia] ; which is just as if one were to think that there are
occult qualities in number, time, space and motion, taken by them-
selves, that is to say. as if one were to seek a knot in a bulrush '
[a difficulty where there is none], ' or to try deliberately to make
clear things obscure.'

39° NEW ESSAYS

I see nothing to hinder our Scholastics from saying that
everything happens merely through their * faculties/ and
from maintaining their 'intentional species/ which go
from objects to us and find it possible to enter even into
our souls 133. If that is so,

Omnia jam fient, fieri quae posse negabam 13*,

so that it seems to me that our author, judicious as he is,
goes here a little too much from one extreme to the other.
He raises difficulties about the operations of souls when
the question is merely whether that which is not per-
ceptible \sensible] is to be admitted ; and here we have
him giving to bodies that which is not even intelligible,
attributing to them powers and activities which surpass
all that a created spirit can, in my opinion, do or under-
stand, for he attributes to them attraction, and that at
great distances without any limit to the sphere of its
activity ; and he does this in order to support an opinion
which seems to me135 no less inexplicable, namely, the
possibility that within the order of nature matter may
think.

The question which he discusses with the distinguished
prelate who had attacked him is whether matter can think ;
and, as it is an important point, even for the present
work, I cannot avoid entering into it a little and exam-
ining their controversy 136. I will state the substance of

133 See Monadology, § 7, note 10.

131 ' All the things will presently happen, which I said could not
happen.' Ovid, Tristia, bk. i. el. 8, ver. 7. The whole passage is :—
Omnia naturae praepostera legibus ibunt,
Parsque suum mundi nulla tenebit iter :
Omnia jam fient, fieri quae posse negabam,
Et nihil est, de quo non sit habenda fides.

[All things by the laws of nature will go topsy-turvy, and no part
of the world will hold on its own way ; all the things will presently
happen which I said could not happen, and there is nothing we may
not believe.]

135 E. reads ' which is ' instead of ' which seems to me.'

136 That Leibniz was deeply interested in the controversy appears
from his letters to Thomas Burnet of Kemnay (G. iii. 151 sqq.), in

NEW ESSAYS 39!

the controversy on this subject, and will take the liberty
of saying what I think about it. The late Bishop
of Worcester, fearing (in my opinion without much
ground) that our author's doctrine of ideas was liable
to some abuses prejudicial to the Christian faith, set
himself to examine certain parts of it in his Vindication
of the Doctrine of the Trinity ; and having done justice to
this excellent author, in recognizing that he thinks the
existence of the mind [esprit] as certain as that of the
body, although the one of these substances is as little
known as the other, he asks (pp. 241 sqq.)137 how re-
flexion can assure us of the existence of the mind [espn£]
if God can give to matter the faculty of thinking, accord-
ing to the opinion of our author (bk. iv. ch. 3), since
thus the way of ideas, which should enable us to dis-
criminate l38 what may be proper to the soul and what
to the body, would become useless, while yet it was said
in the second book of the Essay on the Understanding
(ch. 23, §§ 15, 27, 28), that the operations of the soul
furnish us with the idea of the mind [esprit], and that
the understanding along with the will makes this idea
as intelligible to us as the nature of body is made intelli-
gible to us by solidity and impulse. This is how our
author replies in his first letter (p. 65)139: 'I think
I have proved that there is a spiritual substance in us,

which he frequently refers to it and likens it to his own controversy
with Arnauld. He has ' no doubt that Locke will come well out of
it. He [Locke] has too much judgment to give an advantage to
messieurs les ecdesiasliques, who are the natural directors of the
peoples and whose formularies must be followed as much as
possible.' (Gr. iii. 216.) Leibniz also wrote two accounts of the
controversy, with comments of his own. (G. iii. 223 sqq.) See
also Foucher de Careil, Lettres et Opuscules inedits de Leibniz, Introduc-
tion, pp. Ixii-lxxxiii.

137 Stillingfleet's Works (1710), vol. iii. p. 505.

138 E. reads i investigate ' [discuter] instead of discerner.

139 Locke's Works (ed. 1823), vol. iv. pp. 32 sqq. ; Bonn's ed.,
vol. ii. p. 387 ; Eraser's ed. of the Essay, vol. ii. p. 193 note. Here,
and in other passages quoted, I give the words of the author — not
re-translating from Leibniz.

392 NEW ESSAYS

for we experiment in ourselves thinking. The idea of
this action or mode of thinking is inconsistent with the
idea of self-subsistence, and therefore has a necessary con-
nexion with a support or subject of inhesion : the idea
of that support is what we call substance. . . . For the
general idea of substance being the same everytvhere 14°, the
modification of thinking, or the power of thinking joined
to it, makes it a spirit, without considering what other
modification it has, as whether it has the modification of
solidity or no. As on the other side, substance that has
the modification of solidity is matter, whether it has
the modification of thinking or no. And therefore if
your lordship means by a spiritual an immaterial sub-
stance, I grant I have not proved, nor upon my prin-
ciples can it be proved (your lordship meaning, as I think
you do, demonstratively proved) that there is an imma-
terial substance in us that thinks. Though I presume,
from what I have said about the supposition of a system
of matter thinking (bk. iv. ch. 10, § 16) (which there de-
monstrates that God is fmmaterial), it will prove in the
highest degree probable that the thinking substance in
us is immaterial. . . . Yet I have shown ' (adds the author,
p. 68) U1 ' that all the great ends of religion and morality
are secured barely by the immortality of the soul, without
a necessary supposition that the soul is immaterial.'

The learned Bishop in his reply to this letter, in order
to show that our author was of another opinion when
he wrote the second book of the Essay, quotes from it
(p. 5i)142 the passage (taken from the same book, ch. 23,
§ 1 5), in which it is said that l by the simple ideas we
have taken from our own minds 143 we are able to frame

140 Leibniz's italics. l41 Ed. 1823, vol. iv. p. 34.

142 Stillingfleet's Works, vol. iii. p. 534.

143 Leibniz's translation has ' from the operations of our mind.'
I give the words as they are in Stillingfleet, who condenses Locke's
sentence, which is as follows : ' By the simple ideas we have taken

\ iprfrom those operations of our own minds, which we experiment
.daily in ourselves, as thinking, understanding, willing, knowing.

NEW ESSAYS 393

the complex idea of a spirit. And thus by putting
together the ideas of thinking, perceiving, liberty and
power of moving themselves 144, we have as clear a per-
ception and notion of immaterial substances as well as
material 145.' He also quotes other passages to show that
our author opposed spirit [esprit] to body, and says
(p. 54) 146 that the ends of religion and morality are best
secured by proving that the soul is immortal by its
nature, that is to say that it is immaterial. He also
quotes (p. 7o)147 this passage that 'all the ideas we have
of particular distinct sorts of substances are nothing but
several combinations of simple ideas,' and that thus our
author thought that the idea of thinking and of willing
presupposes another substance, different from that which
is presupposed by solidity and impulse, and that thus
(§ i7)148 he indicates that these ideas constitute body as
opposed to spirit [esprit].

The Bishop of Worcester might have added that from
the fact that the general idea of substance is in body and
in spirit, it does not follow that their differences are

and power of beginning motion, &c., co-existing in some substance,
we are able to frame the complex idea of an immaterial spirit.'

144 Leibniz reads ' our body' instead of ' themselves.'

145 Leibniz reads ' as of material.' Stillingfleet here again
shortens Locke's statement, though he gives a more exact quotation
of it on p. 540. Locke wrote : ' And thus by putting together the
ideas of thinking, perceiving, liberty, and power of moving them-
selves and other things, we have as clear a perception and notion
of immaterial substances as we have of material. For putting
together the ideas of thinking and willing, or the power of moving
or quieting corporeal motion, joined to substance, of which we have
no distinct idea, we have the idea of an immaterial spirit ; and by
putting together the ideas of coherent solid parts, and a power of
being moved, joined with substance, of which likewise we have no
positive idea, we have the idea of matter.'

146 Stillingneet's Works, vol. iii. p. 535 : ' I am of opinion that
the great ends of religion and morality are best secured by the
proofs of the immortality of the soul from its nature and properties,
and which I think prove it immaterial.'

147 Stillingfleet, iii. 539 ; Locke's Essay, ii. 23, § 6.

148 Essay, ii. 23, § 17 ; Stillingfleet, iii. 540.

394 NEW ESSAYS

modifications of one and the same thing, as our author
said in the passage I have quoted from his first letter 149.
We must certainly distinguish between modifications
and attributes. The faculty of having perception and
that of acting, extension, and solidity are attributes or
perpetual and principal predicates ; but thinking, impetus
[impetuosity], figures and motions are modifications of
these attributes 15°. Further, we ought to distinguish be-
tween physical (or rather_real) genus and logical or ideal
serins. Things which are of the same physical genus,
or which are homogeneous, are of the same matter, so to
speak, and can often be changed one into another by
changing their modification, like circles and squares.
But two heterogeneous things may have a common logical
genus, and then their differences are not mere accidental
modifications of one and the same subject [swje£] m, or
one and the same matter, metaphysical or physical. Thus
time and space are very heterogeneous things, and it would
be a mistake to suppose I know not what real common
ground [sujet], having nothing but continuous quantity
in general, from the modifications of which time and
space arise. Nevertheless their common logical genus is
continuous quantity 152. Some one will perhaps ridicule
this distinction153 of the philosophers between two genera,
the one merely logical, the other real154, and between
two matters, the one physical (that of bodies), the other
merely metaphysical or general, as if one were to say
that two parts of space have the same matter, or that
two hours also have each the same matter as the other.
Yet these distinctions are distinctions not only of terms
but of things themselves, and they appear to be most

ia Supra, p. 392.

150 Cf. Introduction, Part ii. p. 34 ; Part iii. p. 127 ; Monadology,
§§14 sqq.

151 Qr < ground.' 152 E. gives this sentence ; G. omits it.
153 E. reads ' these distinctions.'

184 E. reads ' also real.'

NEW ESSAYS 395

pertinent here, where confusion between them has pro-
duced a false conclusion155. These two genera have a
common notion, and the notion of the real genus is
common to the two matters, so that their filiation will
be as follows156: —

^Merely logical, its variations consisting of mere differ-
ences.

real, the differences of
which are modifica-
tions, that is to say,
matter157

metaphysical merely, in which
there is homogeneity,

physical, in which there is a
solid homogeneous mass.

I have not seen the second letter of our author to the
Bishop ; and the answer which the prelate makes to it
hardly touches the point about the thinking of matter.
But our authors reply to this second answer returns to
that point. ' God ' (he says, nearly in these words,
P- 397)158> 'superadds to the essence of matter what
qualities and perfections He pleases : to some parts mere
motion, but to plants vegetation, and to animals feeling
[sentiment]. Those who agree with me so far exclaim

155 rpne pOin£ gjniply is that, no real thing can have two or more
conflicting attributes, though it may at different times have modifica-
tions which in themselves are conflicting. Nevertheless attributes
which, in a real thing, would be impossible because conflicting,
may abstractly or 'ideally' be comprehended under the same
concept or in the same class, on the ground that there is an
essential (not merely accidental) community between them. They
are thus species of a logical genus. Modifications, on the other
hand, are more or less accidental variations of some real thing,
which is the bond of union between them. They are thus species
of a real genus. Ultimately, perhaps, the modifications may^Eum
out to be species of a logical genus (it is probable that they are so in
the mind of God) ; but, for us, an infinite analysis would be needed
to show this."-~

156 TMS ' filiation ' as a whole is, of course, an arrangement of
logical genera and species.

187 * Matter ' here is equivalent to ' real genus/

158 wof-fa (e(L 1823), vol. iv. p. 460 ; Bonn's ed., vol. ii. p. 390.
In translating this passage I have used Locke's words as much as
possible.

S96 NEW ESSAYS

against me when I go a step further and say, God may
give to matter thought, reason and volition, as if that
were to destroy the essence of matter. But to make
good this assertion they say that thought and reason are
not included in the essence of matter ; which proves
nothing, for motion and life are just as little included in
it. They also urge that we cannot conceive how matter
can think ; but our conception is not the measure of God's
omnipotency 15V He afterwards takes as an instance
the attraction of matter, on p. 991CO, but especially on
p. 408 161, where he speaks of the gravitation of matter
towards matter, attributed to Mr. Newton (in words
which I have quoted above), declaring that we can never
conceive the * how ' of it. This is practically to go back
toj>ccult qualities 162, nay more, to inexplicable qualities.
He adds (p. 401) 163 that nothing is more calculated to
favour scepticism than to deny what one does not under-
stand, and (p. 402 )163 that we do not conceive how even
the soul thinks. He thinks (p. 403 )J68 that as the two
substances, material and immaterial, can be conceived
in their bare essence without any activity, it is in the
power of God to give to the one or the other the power
of thinking. And he endeavours to take advantage of
the admission of his opponent, who attributed sense
[sentiment] to the lower animals, but did not attribute
to them any immaterial substance l6*. He maintains that
liberty and self-consciousness [la consciosite] (p. 408 )It6,
and the power of making abstractions (p. 40p)16& can

159 Cf. Essay, Eraser's ed., vol. ii. p. 240 note.

160 All the. texts give '99,' which seems to be a slip for '399.'
Works (ed. 1823), iv. 463 sqq. ; Bohn's ed., ii. 392 sqq.

161 Works (ed. 1823), iv. 467 ; Bohn's ed., ii. 395.

162 The qualitates occultae of the Scholastics. See Introduction,
Part iv. p. 156.

163 Works (ed. 1823), iv. 463; Bohn's ed., ii. 392. Cf. Essay,
Eraser's ed., vol. ii. p. 194 note.

16* Works, iv. 466 ; Bohn's ed., ii. 394.
165 Works, iv. 468 ; Bohn's ed., ii. 395.

OF THK

I UNIVERSITY
NEW ESSAYS \397

be given to matter, not as matter, but as enriched by a
Divine power. Finally he quotes (p. 434) l66 the observa-
tion of a traveller so considerable 167 and judicious as
M. de la Loubere 16S that the Pagans of the east recognize
the immortality of the soul without being able to com-
prehend its immateriality.

Regarding all this I will observe, before coming to
the statement of my own view, that it is certain that
matter is as little capable of producing feeling [sentiment]
mechanically, as it is of producing reason169, as our
author admits ; and that I most certainly recognize that
it is not allowable to deny what one does not understand,
but I add that we have a right to deny (at least in the
order of nature) that which is absolutely neither intel-
ligible nor explicable. I maintain also that substances^
(material or immaterial) cannot be conceived in their]
bare essence without any activity, that activity is of the
essence of substance in general ; and that the conceptions^
of created beings are not the measure of the power of

lee Works, iv. 485 ; Bohn's ed., ii. 406.

167 Locke's word.

168 Simon de la Loubere, born at Toulouse in 1642, died in 1729.
In 1687 Louis XIV entrusted him with a mission to Siam for the
purpose of establishing diplomatic and commercial relations between
that country and France. As the result of a three months' resi-
dence in Siam he published two volumes DuRoyaume deSiam (1691 ;
Eng. trans. 1693), in which he gives an elaborate account of the
Siamese people, their history, customs, and institutions. The book
still ranks as an authority on its subject. Locke's quotation is
taken from vol. i. ch. 19, § 4.

169 Cf. Nouveaux Essais, bk. iv. ch. 3, § 6 (E. 346 b ; Q-. v. 360) :
1 The primary powers constitute the substances themselves ; and the
derivative powers, or if you like, the faculties, are merely modes [faqons
d'etre], which must be derived from substances, and they are not
derived from matter in so far as it is merely mechanical, that is to
say, in so far as by abstraction we take account only of the incomplete
being of materia prima, or that which is entirely passive. And in
this I think you will agree with me, sir, that it is not in the power
of a mere mechanism to produce perception, sensation, reason.'
Cf. Locke, Essay, bk. iv. ch. 10, § TO (Eraser, vol. ii. p. 313) ; also
Monadology, § 17.

398 NEW ESSAYS

God, but that their conceptivity, or ability [force] to
conceive, is the measure of the power of nature : for all
that is in accordance with the order of nature can be
conceived or understood by some created being170.
" Those who will think out my system will see that
I cannot wholly agree with either of these excellent
authors, whose controversy, however, is very instructive.
But, to explain myself distinctly, it is before all things to
be considered that the modifications which can naturally
or without miracle belong171 to a subject [sujet] must
arise from the limitations or variations of a real genus or
an original nature which is constant and absolute172.
For it is thus that among philosophers the modes of an
absolute being are distinguished from the being itself:
for instance, we know that size, figure and motion are
manifestly limitations and variations of the bodily nature.
For173 it is clear how an extension when limited gives
figures, and that the change which takes place in it is
nothing but motion. And whenever we find any quality
in a subject [sujei], we should believe that if we under-
stood the nature of the subject [sujei] and of the quality,
we should understand [concevoir] how the quality can be
a result of it174. Thus in the order of nature (setting

170 For Leibniz this would follow a priori from the essential unity
of nature, shown in the fact that each Monad (and therefore each
created being) contains within itself a representation of the whole
universe.

171 E. reads ' come ' [venir] for convener.

172 Things do have an ' absolute ' original essence of s6me kind.
They are not ultimate bare unities, equally capable of any kind of
modification.

173 E. omits ' for.' Cf. Spinoza's Letters, 50, § 4.

174 Cf. Lettre a Amauld (1686) (G. ii. 56) : < Always in every true
affirmative proposition, necessary or contingent, universal or
singular, the notion of the predicate is in some way comprehended
in that of the subject, praedicatum inest subjecto : otherwise I know not
what truth is. ... Tfiere musi always be some foundation for the con-
nexion of the terms in a proposition and this is to be found in their notions,
That is my great principle, to which I think all philosophers must
assent, and of which one of the corollaries is the common axiom,

NEW ESSAYS 399

aside miracles), God is not arbitrarily free to give to
substances one set of qualities or another indifferently ;
and He will never give them any but those which are
natural to them, that is to say, which can be derived
from their nature, as explicable modifications of it. Thus
we may hold that matter will not by nature have the
attraction mentioned above, and will not of itself go in
a curved line, because it is not possible to conceive how
that can happen, that is to say to explain it mechanically ;
while that which is according to nature [naturel] ought
to be capable of becoming distinctly conceivable, if we
were admitted into the secrets of things. This distinc-
tion, between that which is natural and explicable and
that which is inexplicable and miraculous, removes all
difficulties, and to reject it would be to maintain some-
thing worse than occult qualities and accordingly to
renounce philosophy and reason, and to provide refuges
for ignorance 175 and idleness by a confused [sourd] system
which allows, not only that there are qualities we do not
understand (of which there are only too many), but also
that there are qualities which the greatest mind [esprit],
even if God were to give it the widest possible grasp,
could not comprehend, that is to say, qualities which
would either be miraculous or without rhyme or reason ;
and that God should usually perform miracles would
certainly be without rhyme or reason. Accordingly this
lazy 176 hypothesis would equally destroy our philosophy,

that nothing happens without a reason, which can always be given
why the thing took place so rather than otherwise.' This, of
course, is radically opposed to the view of Locke.

178 Asiles de Vignorance. Cf. Spinoza, Ethics, Part i. Appendix: —
Donee ad Dei voluntatem, hoc est, ignorantiae asylum confugeris (Bruder's
ed., i. 220).

ne rpne French isfaineante. Leibniz is probably thinking of the
fallacy of dp-yds ^0705 or Ignava Ratio, to which he frequently refers
in the Theodicee (cf. E. 470 b ; G. vi. 30). The fallacy is that
which counsels doing nothing, because things are fated one way or
another, whatever we do. Leibniz means that the hypothesis of

400 NEW ESSAYS

which seeks reasons, and the Divine wisdom which
furnishes them.,

Now as to thinking it is certain, and our author
more than once allows it, that it cannot be a modification
of matter that is intelligible or can be comprehended
and explained by matter 177 : that is to say, a feeling or
thinking being is not a mechanical thing, like a watch
or a mill, so that one might conceive sizes, figures and
motions, the mechanical combination of which could pro-
duce something thinking and even feeling in a quantity
of matter in which there was nothing of this kind —
which thinking and feeling would also come to an end in
the same way when the mechanism falls into disorder 178.
Accordingly it is not a natural thing for matter to feel
and to think, and this can take place in it only in two
ways, 'one of which is, that God should unite with it a
substance to which it is natural to think, and the other
is, that God should miraculously impart thinking to it.
In this matter, then, I am entirely of the opinion of the
Cartesians, except that I extend it even to the lower
animals, and hold that they have feeling [sentiment], and
that their souls are immaterial (properly speaking) and
no more perishable than are atoms according to Demo-
critus or Gassendi 179 ; while the Cartesians, who are
without reason perplexed regarding the souls of the
lower animals, not knowing what to make of them
if there is conservation of them (because it has not
occurred to them that there is conservation of the animal
itself in a minute form), have been compelled to deny
even feeling [sentiment] to the lower animals, contrary
to all appearance and to the judgment of mankind180.

which he is speaking is a ' lazy ' one, because acceptance of it
would imply that it is futile to investigate the * secrets of things.'

177 E. omits from l or can be ' to ' matter.'

178 Cf. Monadology, § 17.

179 Cf. New System, § 4.

180 See Monadology, § 14.

NEW ESSAYS 401

But if some one should say that at any rate God can add
the faculty of thinking to a mechanism prepared for it,
I would answer that, if this took place and God added
this faculty to matter, without at the same time putting
into matter a substance which should be the subject in
which this same faculty (as I conceive it) is inherent
(that is to say, without .adding to matter an immaterial
soul), matter must needs have been miraculously exalted
so as to receive a power of which it is not naturally
capable : as some Scholastics declare that God exalts fire
so as to give it the power directly to burn spirits separated
from matter181, which would be entirely miraculous182.
And it is enough that we cannot maintain that matter
thinks, unless there is attributed to it an imperishable
soul or rather a miracle, and that thus the immortality
of our souls follows from that which is natural183: since
we cannot maintain that they are extinguished, unless
it be by a miracle, consisting either in the exaltation of
matter or in the annihilation of the soul. For we know,
of course, that the power of God could make our souls
mortal, although they may be quite immaterial (or im-
mortal by nature), since He can annihilate them t84.

181 E. reads 'bodies.'

182 Of. Nouveaux Essais, bk. iv. ch. 3, § 6 (E. 347 a ; G. v. 360 :
' To suppose that God acts otherwise and gives to things accidents,
which are not modes [fapons d'etre] or modifications derived from
substances, is to have recourse to miracles and to what the Schools
called obediential power, through a kind of supernatural exaltation,
as when certain theologians hold that the fire of hell burns
"' separated " souls. In which case it may even be doubted whether
it would be the fire which would do it, and whether God would
not Himself produce the effect, acting in place of the fire.'
Cardinal Bellarmine (1542-1621) in his fie Purgatorio, bk. ii. chs. 10-
12, expounds a view of this kind, holding that the fire of purgatory
is material fire, but nevertheless miraculously burns souls. In this
opinion he openly follows Augustine (fie Civitate fiei, bk. xxi. ch. 10),
and a similar view is expressed by Thomas Aquinas (Summa Theol.
Suppl. P. iii. Q. 70, Art. 3, conclusion.

183 i. e. ' from their nature ' or ' from the order of nature.'

184 Cf. Monadology, § 6.

Dd

402 NEW ESSAYS

Now this truth of the immateriality of the soul is un-
doubtedly of importance. For it is infinitely more helpful
to religion and morality, especially at the present day
(when many people have very little regard for revelation
by itself and for miracles) 185, to show that souls are natur-
ally immortal and that it would be a miracle if they were
not. than to maintain that our souls would die in the
course of nature, and that it is in virtue of a miraculous
grace, founded on nothing but the promise of God, that
they do not die. Besides it has for some time been
generally known 18n that those who have tried to destroy
natural religion and to reduce all to revealed religion, as
if reason taught us nothing about it, have been counted
suspect, and not always without reason '87. But our
author is not of their number. He upholds the demon-
stration of the existence of God 188, and he attributes
probability in the highest degree to the immateriality of
the soul 189, which may accordingly be accounted a moral
certainty ; and consequently it seems to me that, having
as much candour as penetration, he could quite well agree
with the doctrine I have expounded, which is fundamental
in every rational philosophy; for190 otherwise I do not
see how we are to keep from falling back into fanatical
philosophy, such as the Mosaic philosophy of Fludd m, which

185 E. omits the passage in brackets.

186 E. reads ' it has for some time been the case.'

187 In his Discours de la Conformite de la Foi avec la Raison (1710).
Leibniz gives, at considerable length, an account of those who
insisted on the opposition between reason and revelation, in which
he traces the origin of this view to the Averroists. He approves of
the condemnation of this position by the fifth Lateran Council,
under Leo X, in 1512. (See E. 483 sqq. ; G. vi. 56 sqq.) Cf. Nouveaux
Essais, bk. iv. ch. 17, § 23 (E. 403 a; G. v. 477); also Bayle's
Dictionary, Appendix (vol. iv. p. 620, jjr"16 Eclaircissemenf).

188 See Essay, bk. iv. ch. 10, § 10 (Eraser, vol. ii. pp. 306 sqq.
with notes).

lf9 See Essay, bk. iv. ch. 3, § 6 (Eraser, vol. ii. p. 194).
193 E. omits < for.'

191 Robert Fludd (Eobertus de Fluctibus) was born at Milgate,
Kent, in 1574 (or 1571), and died at London in 1637. After

NEW ESSAYS 403

finds a ground for all phenomena by attributing them
directly and miraculously to God, or into the barbarous
philosophy, like that of certain philosophers and physicians
of the past, who 192 still showed traces of the barbarous-
ness of their time, and who nowadays are rightly con-
temned, who found a ground for phenomena [apparences]
by inventing for this purpose occult qualities or faculties,
which were pictured as being like little sprites or elves 19 ',

studying at Oxford he travelled abroad and made acquaintance
with the theosophical views of Paracelsus, which he sought to
make known in England through his Philosophia Mosaica (1638) and
his Hisloria Macro-et-Micro-Cosmi Mefaphysica, Physica et Technica (1617).
In these writings he tries to find a complete philosophy in the Old
Testament and more especially in the Pentateuch. His system, if
so it can be called, is a combination of Neo-Platonic doctrines with
those of the Kabbala, and one of his favourite ideas is that of the
analogy between the universe (macrocosm) and the human body
(microcosm). Leibniz is here referring to his theory that all things
flow directly from God, who continually produces the variations in
phenomena by condensation and rarefaction of matter. All things
are emanations from God and return into His absolute unity.
Gassendi and Kepler wrote against the views of Fludd.

j92 E. reads * which ' [philosophy].

193 Leibniz is probably referring to the 'elemental spirits' of
which Paracelsus (1493-1541) writes in his De Nymphis, Sylphis,
Pygmaeis et Salamandris. He attributes to the ' nymphs ' the pheno-
mena of water, to the i sylphs ' the phenomena of air, to the
'pygmies' the phenomena of earth, and to the 'salamanders'
the phenomena of fire. Fludd also adopted this view. Possibly
Leibniz may also be thinking of the elder Van Helmont (Johann
Baptista Van Helmont, 1577-1644), who was a follower of
Paracelsus. In the Epistola ad Thomasium (1669), § n (E. 52 b ;
G. i. 23), Leibniz speaks of Van Helmont along with Paracelsus
and others as representative of the stupid [stolidd] form of the
reformed philosophy, absolutely rejecting Aristotle. In the
same letter he refers to the ' occult philosophy of Agrippa '
(Heinrich Cornelius Agrippa von Nettesheim, 1486-1535% 'who
ascribes to everything an angel to bring it to birth' [quasi
obsletricatorem]. ' Thus,' adds Leibniz, * we return to as many little
gods \_deunculi~\ as there are substantial forms and we approach the
Gentile 7roAv0ei'cr/*os.' There may also here be a reference to the
spiritus familiaris of the Italian physician, philosopher and mathe-
matician, Girolamo Cardano (1501-1575). See his De Vita Propria,
ch. 47, Opera (1663), vol. i. p. 44. On the whole matter, cf. Leibniz s

D (! 2

404 NEW ESSAYS

capable of artlessly doing what is ir4 required, as if watches
were to indicate the time of day by a certain horodeictic
faculty without needing wheels, or as if mills were to
crush the grain by a tractive faculty without needing
anything resembling millstones 195. As to the difficulty
several peoples have had in conceiving an immaterial
substance, it will readily pass away (at any rate in great
part), if it be no longer maintained that there are sub-
stances separated from matter, as in fact I do not believe
that there are ever naturally 196 any such substances
among created things.

Antibarbarus Physicus, &c. (G. vii. 337N. See also Vaughan's Hours
with the Mystics, bk. viii. chs. 4 and 5, and the Dedication of Pope's
Rape of the Lock, where the * nymphs,' &c. are attributed to the
Rosicrucians. Milton speaks of

'Those demons that are found
In fire, air, flood or under ground.'

11 Penseroso, 1. 93.

194 E. reads 'all that is required.'

195 See Introduction, Part iv. pp. 156 sqq.

156 i. e. other than miraculously. Cf. Monadology, § 72.

PRINCIPLES OF NATURE AND OF
GRACE, FOUNDED ON REASON. 1714.

PREFATORY NOTE.

THE Principles of Nature and of Grace has much in common
with the Monadology ; and, indeed, it reads like a preliminary
study, out of which the Monadology has been elaborated. They
seeni to have been written about the same time ; and Gerhardt
holds, against the view of previous editors, that the Principles
of Nature and of Grace is the treatise which was written for
Prince Eugene. It has been shown by Gerhardt that when
Nicholas Remond wrote to Leibniz from Paris in 1714, asking
for a condensed statement of his philosophy, Leibniz sent
him a copy of the Principles of Nature and of Grace, with a
letter in course of which he says : ' I now send you a little
discourse on my philosophy, which I have written here for
Prince Eugene of Savoy. I hope that this little work will help
to make my ideas better understood, when taken in connexion
with what I have written in the Journals of Leipzig, Paris and
Holland. The Leipzig papers are on the whole in the language
of the Scholastics; the others are more in the style of the
Cartesians; and in this last writing I have endeavoured to
express myself in a way which can be understood by those who
are not yet thoroughly accustomed to either of the other styles.'
(Letter of Aug. 26, 1714, quoted by Gerhardt, vi. 485 ; E. p. xxvii
and p. 704 a.) Kirchmann suggests that probably Leibniz
wrote the Principles of Nature and of Grace for Prince Eugene,
and afterwards, thinking it insufficient, worked it up into the
Monadology, which he gave to the Prince. The Principles of
Nature and of Grace was first published in the French journal,
L' Europe Savante, in November, 1718.

There are three different MSS. of this work. The first of

406 PRINCIPLES OF NATURE AND GRACE

*

these, which is the shortest, is divided, not into paragraphs,
but into two chapters, the point of division being the end of
paragraph 6, where transition is made from 'Physics' to
' Metaphysics.' In the other two MSS. the paragraph division
appears, and the text from which the translation is made is
that of the last and most complete manuscript. In the
Principles of Nature and of Grace the arrangement of the
matter is much less clear and careful than it is in the Monad-
ology. But, following the lines of the division originally made
by Leibniz himself, we may say that paragraphs 1-6 inclusive
give an account of the created Monads in themselves and in
their relations to one another, so far as these can be considered
apart from God ; while the remaining paragraphs consider the
nature of God as ultimate reason of the universe, and the
consequences which follow from His perfection in power,
wisdom and goodness. Some of the most important points in
the Monadology are either passed over or very slightly treated
in the Principles of Nature and of Grace. For instance, in
the Principles of Nature and of Grace there is nothing to
correspond to the passage in the Monadology regarding the two
great principles of knowledge, and while the pre-established
harmony is mentioned, it is not dwelt upon. But the connexion
between the two writings, both in treatment and expression, is
so close that the annotations to the Principles of Nature and of
Grace may be comparatively brief.

The Principles of Nature and of Grace will be found in E.
714 sqq. ; G. vi. 598 sqq.

i. Substance is a being capable of action. It is simple
or compound. Simple substance is that which has no
parts. Compound substance 1 is the combination of simple
substances or Monads. Monas is a Greek word, which
means unity, or that which is one. Compounds or bodies
are pluralities [multitudes] ; and simple substances, lives,
souls, spirits, are unities. And everywhere there must
be simple substances, for without simple substances there

1 See Monadology, note 2. Strictly speaking 'compound sub-
stance,' according to Leibniz, is not ' substance ' at all. It is not
substantia but substantiatum. Failure to observe this distinction was
to some extent the source of Wolff's misinterpretation of Leibniz.

PRINCIPLES OF NATURE AND GRACE 407

8

would not be compounds ; and consequently all nature is
full of life2.

2. The Monads, having no parts, can neither be made
\formees] nor unmade. They can neither come into being
nor come to an end by natural means, and consequently
they last as long as the universe, which will be changed,
but which will not be destroyed. They can have no
shape [figure] ; otherwise they would have parts 3. Con-
sequently any one Monad in itself and at a particular
moment can be distinguished from any other only by
internal qualities and activities [actions] 4, which cannot
be other than apperceptions (that is to say, the represen-
tations of the compound, or of that which is outside 5, in
the simple) and its appetitions (that is to say, its tendencies
to pass from one perception to another), which are the
principles of change. For the simplicity of substance is
by no means inconsistent with the multiplicity of the
modifications which are to be found together in that
same simple substance, and these modifications must
consist in variety of relations to the things which are
outside6. It is as in the case of a centre or point, in

2 To say that matter is infinitely divisible is the same as saying
that there is compound substance everywhere ; for to be divisible
is to be compound. But compound substances are made up of
simple substances. Consequently there are simple substances or
living beings everywhere.

3 If they had shape, they would be extended or spatial. But
everything extended is divisible, and hence they would not be
simple but compound, having parts.

4 Thus we cannot perceive Monads by means of our senses.
What the senses give us is not the substance itself, but merely
a phenomenon bene fundatum. l Spirits, souls, and simple substances
or Monads in general cannot be known [comprehendi~] by the senses
and imagination, because they have no parts/ Epistola ad Bierlingium
(1711) (E. 678 a; G. vii. 501).

5 The compound, as compound, consists of partes extra partes ; but
as compound, it is merely phenomenal.

6 'The simplicity of a substance is by no means inconsistent
with its having within it several modes at one time. There are
successive perceptions ; but there are also simultaneous perceptions.
For when there is perception of a whole, there are at the same

408 PRINCIPLES OF NATURE AND GRACE

which, although it is perfectly simple, there is an infinite
number of angles formed by the lines which meet in it.

3. All nature is a plenum. There are simple substances
everywhere7, which are actually separated from one
another by activities of their own 8, and which continually
change their relations ; and each specially important
[distmguee] !1 simple substance or Monad, which forms the
centre of a compound substance (e. g. of an animal) and
the principle of its oneness, is surrounded by a mass
composed of an infinity of other Monads, which constitute
the particular body of this central Monad, and according
to the affections of its body10 the Monad represents, as in
a kind of centre, the things which are outside of it. This
body is organic, though it forms a kind of automaton or

time perceptions of the actual parts, and even each part has more
than one modification ; and there is perception at the same time
not only of each modification, but also of each part. These multi-
plied perceptions are different from one another, although our
attention cannot always distinguish them, and thus we have
confused perceptions, an infinity of which is contained in each
distinct perception, because of its relation to everything which is
outside. In short, that which is combination of parts in the out-
side world is represented in the Monad only by combination of its
modifications ; and without this simple beings could not be
internally distinguished from one another, and they would have
no relation whatever to external things ; and in short, as there
are everywhere only simple substances, of which compounds are
merely the aggregates, there would be no variation or diversity in
things, if there were no internal variation or diversity in simple
substances.' Lettre a Masson (1716) (G-. vL 628). Cf. Monadology,
notes 12 and 20.

7 E. omits partout, ' everywhere.'

8 The idea is that each Monad is separated from every other
inasmuch as it has spontaneity, i. e. an activity entirely its own ; for
if it had merely an activity like motion, which passes from one
thing to another indifferently, it would be united with all other
Monads in a continuum and would thus cease to be a real, indepen-
dent unit.

9 E. omits distinguee, reading ' each simple substance.'

10 Of course, this does not mean that the Monads constituting
the body are really affected by outside things. Leibniz is here using
popular language. .

PRINCIPLES OF NATURE AND GRACE 409

natural machine, which is a machine not only as a whole,
but also in the smallest parts of it that can come into
observation ". Since the world is a, plenum all things are
connected together and each body acts upon every other,
more or less, according to their distance, and each, through
reaction, is affected by every other. Hence it follows that
each Monad is a living mirror, or a mirror endowed with
inner activity v~, representative of the universe, according
to its point of view, and as subject to rule as is the
universe itself. /And the_ perceptions in the Monad are
produced one from another according to the laws of desires
[appetits] or of the final causes of good and evil, which con-
sist in observable perceptions, regular or irregular, as, on
the other hand, the changes of bodies and external pheno-
mena are produced one from another according to the
laws of efficient causes, that is to say, of motions 13. Thus
there is a perfect harmony between the perceptions of the
Monad and the motions of bodies, a harmony pre-estab-
lished from the beginning between the system of efficient
causes and that of final causes. And it is in this way
that soul and body are in agreement and are physically
united, while it is not possible for the one to change the
laws of the other u.

^4. Each Monad, with a particular body, forms a living
substance. Thus not only is there everywhere life,
accompanied with members or organs, but there is also

11 Cf. Monadology, § 64.

12 ' This " mirror " is a figurative expression ; but it is suitable
enough and it has already been employed by theologians and
philosophers, when they spoke of a mirror infinitely more perfect,
namely, the mirror of the Deity, which they made the object of the
beatific vision.' Lettre a Masson (1716) (G. vi. 626).

15 Ultimately, motions and desires (appetits) are different degrees
of the same thing, viz. appetition, or the passage from one con-
scious or unconscious perception to another. The unconscious
appetition is motion or efficient cause, not setting before itself an
end, while the conscious appetition or desire does set before itself
an end of good or evil, i. e. a final cause.

14 Cf. Monadology, §§78 sqq.

410 PRINCIPLES OF NATURE AND GRACE

an infinity of degrees in the Monads, one dominating
more or less over another. But when the Monad has
organs so arranged that they give prominence and sharp-
ness [du relief et du distingue] to the impressions they
receive, and consequently to the perceptions which repre-
sent these (as, for instance, when, by means of the form
of the eye's humours, the rays of light are concentrated
and act with more force), this may lead to feeling [senti-
ment] 15, that is to say, to a perception accompanied by
memory, in other words, a perception of which a certain
echo long remains, so as to make itself heard l6 on occa-
sion. Such a living being is called an animal, as its
Monad is called a soul. And when this soul is raised to
reason, it is something more sublime and is reckoned
among spirits [esprits], as will presently be explained. It
is true that animals are sometimes in the condition of
mere [simple] living beings and their souls in the condition
of mere Monads 17, namely when their perceptions are not
sufficiently sharp [distingue:] to be remembered, as happens
in a deep dreamless sleep or in a swoon. But perceptions
which have become completely confused are sure to be
developed again in animals 18, for reasons which I shall

15 The transition from the unconscious to the conscious per-
ception is not by any means made clear. Leibniz is, of course,
using ordinary language ; but it is difficult to see how he could
translate it into the terms of his system, unless he were to content
himself with saying that conscious Monads have less confused
perceptions than unconscious Monads and have bodies whose
organs are differently arranged. For, in Leibniz's view, the action
of any one Monad upon another is purely ideal ; and there is
nothing in the world but Monads. Cf. Monadology, § 25.

115 G. reads etendre, which might here be translated 'increase,' for
entendre [heard], which is E.'s reading. Entendre seems more natural.

17 i. e. unconscious living beings and unconscious Monads.

18 That is, perceptions (in animals) which have passed into the
complete confusion of unconsciousness are sure to pass into con-
sciousness again. Confusion in perceptions is the same thing as
envelopment or contraction. (Hence the petites perceptions are con-
fused.) On the other hand, clearness in perceptions is the same
thing as development or expansion. Cf. note 51 and New Essays,
Introduction, note 74.

PKINCIPLES OF NATURE AND GRACE 4! I

presently mention (§ 12). Thus it is well to make dis-
tinction between perception, which is the inner state of
the Monad representing outer things, and apperception,
which is consciousness or the reflective knowledge of this
inner state, and which is not given to all souls nor to the
same soul at all times. It is for lack of this distinction
that the Cartesians have made the mistake of ignoring
perceptions of which we are not conscious 19, as ordinary
people ignore imperceptible [insensible] bodies1'0. It is
this also that has led these same Cartesians to believe
that only minds [esprits] are Monads, that the lower
animals have no soul, and that still less are there other
principles of life 21 . And as they came into too great con-
flict with the common opinion of men in denying feeling
[sentiment] to the lower animals, so on the other hand
they conformed too much to the prejudices of the crowd
in confounding a prolonged unconsciousness, which comes
from a great confusion of perceptions, with absolute death,
in which all perception would cease. This has confirmed
the ill-founded opinion that some souls are destroyed, and
the bad ideas of some who call themselves free-thinkers
[esprits forts] and who have disputed the immortality of
our soul 22.

20 'As in body we hold that there is avrirvma and figure in
general, although we do not know what are the figures of im-
perceptible bodies ; so in the soul we hold that there is perception
and appetition, although we do not distinctly know the imper-
ceptible elements of the confused perceptions by which the im-
perceptible parts of bodies are expressed. . . . You ask whether
I believe that there are bodies which do not fall within sight.
Why should I not believe it ? I think ib impossible to doubt it.
Through microscopes we see animalculae otherwise imperceptible,
and the nerves of these animalculae, and other animalculae,
perhaps swimming in the fluid parts of these, cannot be seen.
The minuteness [subtiUtas] of nature goes ad infinitum.' Epistola ad
Bierlingium (1711) (E. 678 a ; G. vii. 501).

121 Leibniz probably means what elsewhere, following Scholastic
usage, he calls ' forms/ Cf. Introduction, Part iv. p. 156.

22 Cf. Monadology, § 13.

412 PRINCIPLES OF NATURE AND GRACE

5. There is a connexion among the perceptions of
animals which has some likeness to reason ; but it is
based only on the memory of facts or effects 23, and not
at all on the knowledge of causes. Thus a dog avoids
the stick with which it has been beaten, because memory
represents to it the pain which this stick has caused it.
And men, in so far as they are empirics, that is to say
in three-fourths of their actions, do not act otherwise
than the lower animals. For instance, we expect that
there will be daylight to-morrow because our experience
has always been so : it is only the astronomer who
rationally foresees it, and even his prediction will ulti-
mately fail when the cause of daylight, which is not
eternal, ceases24. But genuine reasoning depends upon
necessary or eternal truths, such as those of logic, of
number, of geometry, which produce an indubitable
connexion of ideas and infallible inferences. The animals
in which these inferences do not appear are called the
lower animals [betes] ; but those which know these neces-
sary truths are properly those which are called rational
animals, and their souls are called minds [esprits]. These
souls have the power to perform acts of reflexion and
to observe that which is called ego, substance25, soul,
mind [esprit], in a word, immaterial things and truths.
And this it is which makes science or demonstrative
knowledge possible to us*6.

6. Modern research has taught us, and reason confirms
it, that the living beings whose organs are known to
us27, that is to say, plants and animals, do not come

33 G. reads ou effects ; E. omits this.

24 Cf. Munadology, §§ 26-28.

'a E. reads ' Monad ' between ' substance' and ' soul'; G. omits it.

26 Cf. Monadology, § § 29 and 30. In the Matiadology God is added
as an object of the self-conscious soul.

37 All Monads have organic bodies, and the series of Monads and
of organisms extends continuously from the lowest of Monads with
the least perceptible of organisms up to the Monad of Monads, God.
At both ends of the scale there are beings whose organs are not
known to us.

PRINCIPLES OF NATURE AND GRACE 413

from putrefaction or chaos, as the ancients thought, but
from preformed seeds, and consequently from the trans-
formation of pre-existing living beings. In the seed of
large animals there are animalcules which by means of
conception obtain a new outward form, which they
make their own and which enables them to grow and
become larger so as to pass to a greater theatre and to
propagate the large animal28. It is true that the souls
of human spermatic animals are not rational, and that
they become so only when conception gives to these
animals human nature 29. And as in general animals are
not entirely born in conception or generation, no more do
they entirely perish in what we call death ; for it is
reasonable that what does not come into being by natural
means should not any more come to an end in the course
of nature. Thus, throwing off their mask or their tattered
covering, they merely return to a more minute theatre,
where they may nevertheless be as sensitive [sensible]
and as well ordered as in the larger theatre 30. And what
has just been said about the large animals applies also
to the generation and death31 of spermatic animals
themselves, that is to say, they are growths of other

28 Cf. Monadology, §§ 74, 75.

29 Cf. Monadology, § 82. It would be inconsistent with Leibniz's
general principles to suppose that a spermatic animal could have
a rational soul (otherwise than in germ, as all souls may be regarded
as potentially rational). For the rationality of a soul is merely
a very high degree of clearness and distinctness in its perceptions,
which again determines its rank as a dominant Monad. But
nothing else than its rank as a dominant Monad determines the
nature of the body it has. Consequently a rational soul must
always have a human body or a body of some higher kind, spiritual
or angelic, and the union of a spermatic animal's body with a
rational soul is impossible.

30 Cf. Monadology, §§73, 76, 77.

31 E. (manifestly by mistake) omits a clause following these
words. A translation of his text would be: 'The generation and
death of the smaller spermatic animals in comparison with which
they' [sc. the large animals] 'may be counted large,' &c. This
misses the point of the sentence.

414 PRINCIPLES OF NATURE AND GRACE

smaller spermatic animals, in comparison with which
they in turn may be counted large, for everything in
nature proceeds ad infiniium72. Thus not only souls but
also animals are ingenerable and imperishable : they are
only developed, enveloped, clothed, unclothed 33, trans-
formed. Souls never put off the whole of their body,
and do not pass from one body into another body which
is entirely new to them. Accordingly there is no metem-
psychosis, but there is metamorphosis. Animals change,
take on and put off, parts only3*. In nutrition this
takes place gradually and by little imperceptible [insensible]
portions, but continually ; and on the other hand, in con-
ception or in death, when much ; 5 is gained or lost all at
once, it takes place suddenly and in a way that can be
noticed [notablement],- but rarely.

7. Thus far we have spoken merely as pure physicists™ :
now we must rise to metaphysics, making use of the
great principle, usually little employed, which affirms that
nothing takes place urithout sufficient reason, that is to
say, that nothing happens without its being possible for

3a ' So, naturalists observe, a flea

Has smaller fleas that on him prey ;
And these have smaller still to bite 'em,
And so proceed ad infinitum.' — Swift, On Poetry.
The idea of ' infinities of infinity ' is a favourite one with Leibniz,
and it is closely connected with the notions underlying his diffe-
rential calculus. ' For instance, we must conceive (i) the diameter
of a small element in a grain of sand, (2) the diameter of the grain
of sand itself, (3) that of the globe of the earth, (4) the distance of
a fixed star from us, (5) the magnitude of the whole system of fixed
stars, as (i) a differential of the second degree, (2) a differential of the
first degree, (3) an ordinary assignable line, (4) an infinite line, (5)
an infinitely infinite line.' Lettre a M. d'Angicourt (1716), Dutens, iii.
500. Cf. Monadology, §§ 65-70.

33 Cf. 2 Corinthians, v. 4.

34 Cf. Monadology, §§ 71, 72, 77. Aristotle condemns the theory of
transmigration of souls in his De Anima, i. 3, 407b 13.

35 E. omits beaucoup ['much'] and reads, ' all is gained or lost at
once.'

36 i. e. students of nature.

PRINCIPLES OF NATURE AND GRACE 415

one who should know things sufficiently, to give a reason
which is sufficient to determine why things are so and I
not otherwise. This principle being laid down, the first
question we are entitled to put will be — Why does some-
tiling exist rather than nothing ? For l nothing ' is simpler
and easier37 than ' something.' Further, granting that
things must exist, we must be able to give a reason why
they should exist thus and not otherwise38. -

8. Now this sufficient reason of the existence of the
universe cannot be found .in the sequence of contingent
things, that is to say, of bodies and their representations
in souls : because, matter being in itself indifferent to
motion and to rest and to one or another particular motion,
we cannot find in it the reason of motion and still less
the reason- of one particular motion 39. And although the
motion which is at present in matter comes from the pre-
ceding motion, and that again from another preceding
motion, we are no farther forward, however far we go ;
for the same question always remains. Thus the suffi-
cient reason, which has no need of any other reason,
must needs be outside of this sequence of contingent
things and must be in a substance which is the cause
of this sequence, or which is a necessary being, bearing
in itself the reason of its own existence, otherwise we
should not yet have a sufficient reason with which we
could stop. And this ultimate reason of things is called
God 40.

37 i. e. more easily brought into existence. But if we can say
even this of ' nothing/ must not ' nothing ' be ' something ' ? How
can we say of that which is not at all, that it is ' simple ' and ' easy '
in comparison with other things ?

:'8 Cf. Monadology, § 32.

39 Motion (which, for Leibniz, is what we should now call an
abstraction) is regarded as passing from body to body and as having
no definite source in the phenomenal world. The point of view is
that which Descartes substituted for the Peripatetic theories, and
Leibniz's point is that, while Descartes's view is good so far as it
goes, it is insufficient and requires to be supplemented by a deeper
explanation.

40 Cf. Monadology, §§ 36-38, and Ultimate Origination of Things, p. 338.

416 PRINCIPLES OF NATURE AND GRACE

9. This primary simple substance must include emi-
nently 41 the perfections contained in the derivative sub-
stances which are its effects. Thus it will have power,
knowledge and will in perfection, that is to say, it will
have supreme [souveraine] omnipotence, omniscience and
goodness. And as justice, taken very42 generally, is
nothing but goodness in conformity with wisdom, there
must also be in God supreme justice^3. The reason
which has led to the existence of things through Him
makes them also depend upon Him for their continued
existence and working ; and they continually receive
from Him that which makes them have any perfection ;
but any imperfection that remains in them comes from
the essential and original limitation of the created
thing44.

41 i. e. in a higher degree. See Monadology, note 61.

42 E. omits fort [very].

*3 * There is a great difference between the way in which men
are just and the way in which God is just ; but it is merely
a difference in degree. For God is perfectly and entirely just, and
the justice of men is mingled with injustice, faults, and sins
because of the imperfection of human nature. The perfections of
Gcd are infinite and ours are limited. . . . Justice is nothing but
that which is in conformity with wisdom and goodness taken
together ; the end of goodness is the greatest good, but in order to
recognize this there is need of wisdom, which is nothing but the
knowledge of the good. In the same way, goodness is nothing but
the inclination to do good to all and to prevent evil, unless it be
necessary in order to secure a greater good or to prevent a greater
evil. Thus wisdom is in the understanding and goodness in the
will. And consequently justice is in both. Power is another
thing ; b\it if it comes into play, it makes the right become
actual and causes what ought to be really to exist, so far as the
nature of things allows. This is what God does in the world.'
Meditation sur la notion commune de la justice (Mollat, pp. 60, 62 \
Cf. On the Notions of Right and Justice (1693), p. 283.

** Cf. Monadology, § 42. This is a brief statement of the main
contention of the Theodicee, in so far as it endeavours to vindicate
the goodness of God in face of the evil in the world. God is the
source of the perfections of each Monad, because it is through His
choice of the best of all possible worlds that each Monad actually
exists and continues in existence. But every Monad has some

PRINCIPLES OF NATURE AND GRACE 417

10. It follows from the supreme perfection of God
that in producing the universe He has chosen the best
possible plan, in which there is the greatest variety
along with the greatest order ; ground, place, time being
as well arranged as possible 45 ; the greatest effect pro-
duced by the simplest ways ; the most power, know-
ledge, happiness and goodness in created things that the
universe allowed46. For as all possible things in the
understanding of God claim existence in proportion to
their perfections, the result of all these claims must be
the most perfect actual world that is possible. And
apart from this it would not be possible to give a reason
why things have gone thus rather than otherwise 4T.

IT. The supreme wisdom of God led Him to choose
specially the laws of motion which are most fitting and
which are most in conformity with abstract or meta-
physical reasons. There is conserved the same quantity
of total and absolute force, or of activity [action], also
the same quantity of relative force or of reaction, and
finally the same quantity of force of direction48. Further,

essential, inalienable imperfection ; otherwise it would be indis-
tinguishable from God. And God cannot change the essence of
any Monad, as it is in the 'region of ideas,' which is His under-
standing. He can merely create and support, or withhold His
creation and preservation.

45 Cf. Ultimate Origination of Things, pp. 340 sqq.

46 Cf. Monadology, §§ 55-58. *7 Cf. Monadology, §§53 and 54.

48 Every system or aggregate of bodies has a total absolute force,
i. e. a total force belonging to the system as a completely indepen-
dent system— a total force calculated on the supposition that there
are no other total forces in relation to it, which might increase or
diminish it. The whole matter of the universe is such a system,
and consequently its total absolute force remains always the
same. But total absolute force is always made up of two partial
forces, i. e. forces which belong to the parts of the aggregate or
system. These partial forces are (i) 'relative force* or 'force of
reaction,' which is the force involved in the mutual action and
reaction of the bodies constituting the system or aggregate, i. e. its
internal action, and (2) ' force of direction,' which is the force
involved in the external action of the system. Cf. Introduction,
Part iii. pp. 89 sqq. See also Explanation of the New System, note 30.

E 6

418 PRINCIPLES OF NATURE AND GRACE

action is always equal to reaction, and the whole effect
is always equivalent to its full cause. And it is remark-
able \_surprenant] that by the sole consideration of efficient
causes or of matter it was impossible to explain these
laws of motion which have been discovered in our time
and of which a part has been discovered by myself.
For I have found that we must have recourse to final
causes, and that these laws are dependent not upon the
principle of necessity, like the truths of logic, arithmetic,
and geometry, but upon the principle of fitness [con-
venance], that is to say, upon the choice of wisdom. And
this is one of the most effective and remarkable proofs
of the existence of God for those who can go deeply into
these things 49.

12. Again, it follows from the perfection of the Su-
preme Author not only that the order of the whole
universe is the most perfect that can be, but also that
each living mirror representing the universe according
to its point of view, that is to say, each Monad, each
substantial centre, must have its perceptions and its
desires [appetite] as thoroughly well-ordered as is com-
patible with all the rest. Whence it also follows that
souls, that is to say, the most dominant Monads, or
rather animals themselves50 cannot fail to awake again

49 The laws of actual 'concrete' motion cannot be deduced a priori
under the law of contradiction ; but a knowledge of them involves
a reference to experience. As a result of this reference to experience
we are compelled to conceive body, not as mere externality of parts,
indifferent to motion, but as something which always has a, force of
its own. Thus bodies are ultimately or really (as distinct from
phenomenally) independent forces (Monads), which differ from one
another endlessly but are yet in such harmony that they form
one perfectly regular system, the laws of which we can discover
and state. Such a system could never have come into existence
'of itself,' by a law of blind necessity, indifferent to good and evil,
like the principle of contradiction. An all-wise, all-powerful and
infinitely good God must have chosen this system as the best
among all possible systems. Cf. Monadology, § 51.

50 E. omits, themselves.'

PRINCIPLES OF NATURE AND GKACE 419

from the condition of stupor into which death or some
other accident may put them 51.

13. For all is regulated in things, once for all, with as
much order and mutual connexion as possible, since
supreme wisdom and goodness can act only with perfect
harmony. The present is big with the future, the future
might be read in the past, the distant is expressed in the
near. We might get to know the beauty of the universe
in each soul, if we could unfold all that is enfolded in
it and that is perceptibly developed only through time.

51 Conscious Monads may for a time fall into unconsciousness ;
but that they should remain permanently in that Condition would
be against the general order of things. For the tendency of all
created Monads is to advance to higher perceptions. In this
advance each Monad is essentially limited to some extent ; but
apart from this essential limitation, which is independent of the
will of God, no other permanent limitation is imposed. Thus, if
a Monad has once been conscious, it may be conscious again, for
manifestly it is not essentially limited to the unconscious state. And
it must some day be conscious again, for the wor]d is the best of all
possible worlds, not merely on the whole but as regards each of
its parts, which is equivalent to saying that the world is so con-
structed that each of the Monads constituting it shall rise to the
highest point of perfection (i. e. of perception and appetition) which
its essential limitations allow. Leibniz elsewhere speaks of the
world in terms which, with slight alteration, he would apply to
the individual soul. l You are right in saying that our globe ought
to have been a kind of Paradise, and I add that, if that is so, it
can quite well become one yet, and it may have drawn back in
order to make a better leap forward.' Lettre a Bourguet (1715) (E.
731 a ; G. iii. 578). Cf. Lettre touchant ce qui est independent des Sens
et de la Matiere (1702) (G. vi. 507) : 'Always when we penetrate
into the depths of any things, we find in them the most beautiful
order that could be desired, even beyond what we imagined, as all
those who have gone deeply into the sciences are aware ; and
accordingly we may hold that the same is the case as regards all
other things, and, that not only do immaterial substances always
continue to exist but their lives, their progress and their changes
also are regulated so as to attain a certain end, or rather to
approach it more and more, as asymptotes do. And although we
sometimes fall back, like lines which have bends in them, advance
none the less prevails in the end and gets the victory.' Cf, New
Essays, Introduction, note 74.

E e 2

420 PRINCIPLES OF NATURE AND GRACE

But as each distinct perception of the soul includes an
infinite number of confused perceptions, which involve
the whole universe, the soul itself knows the things of
which it has perception, only in so far as it has distinct
and heightened [or unveiled] 52 perceptions of them ; and
it has perfection in proportion to its distinct perceptions.
Each soul knows the infinite, knows all, but confusedly ;
as when I walk on the sea-shore and hear the great noise
the sea makes, I hear the particular sounds which come
from the particular waves and which make up the total
sound, but I do not discriminate them from one another.
Our confused perceptions are the result of the impressions
which the whole universe makes upon us. It is the same

xwith each Monad 53, God alone has a distinct knowledge
of all, for He is the source of all. It has been very well
said that as a centre He is everywhere, but His circum-
ference is nowhere 54, for everything is immediately pre-

\sent to Him without any distance from this centre.

1 4. As regards the rational soul or mind [I'esprit], there is
in it something more than in the Monads or even in mere
[simple] souls 5\ It is not only a mirror of the universe
of created beings, but also an image of the Deity. The
mind [I'esprit] has not merely a perception of the works
of God, but it is even capable of producing something
which resembles them, although in miniature. For, to
say nothing of the wonders of dreams, in which we

w E. reads relevees • G. reads revdees. Revelees (without the usual
accents) looks like a slip of the pen and relevees is elsewhere used
in a similar connexion. Cf. Monadology, § 25.

53 Cf. Monadology, §§ 60 and 61.

54 l The world is an infinite sphere, of which the centre is every-
where, the circumference nowhere.' Pascal, Pensees, i. (Ha vet's ed.,
p. i). Havet traces the phrase to Rabelais (bk. iii. ch. 13^ thence
to Gerson and Bonaventura, and ultimately to Vincent de Beauvais
(early in the thirteenth century) who attributes it to Empedocles.
It is not in any writing of Empedocles now known. See Havet's
Pascal, pp. 17 sqq.

55 ' The Monads ' here means bare or unconscious Monads, while
* mere souls ' means conscious souls, which are not self-conscious.

PRINCIPLES OF NATURE AND GRACE 421

invent without trouble (but also without willing it) 56
things which, in our waking hours, we should have to
think long in order to hit upon, our soul is architectonic
also in its voluntary activities and, discovering the
scientific principles in accordance with which God has
ordered things (pondere, mensura, numero, &c.) 57, it
imitates, in its own province and in the little world in
which it is allowed to act, what God does in the great
world 58.

15. It is for this reason that all spirits [esprits], whether
of men or of angels [genies], entering in virtue of reason
and of eternal truths into a kind of fellowship with God,
are members of the City of God, that is to say, of the
most perfect state, formed and governed by the greatest
and best of monarchs : in which there is no crime with-
out punishment, no good action without a proportionate
reward, and in short as much virtue and happiness as
is possible ; and thisj not by any interference with the
course of nature, as if what God prepares for souls were
to disturb the laws of bodies, but by the very order of
natural things, in virtue of the harmony pre-established
from all time between the realms of nature and of grace,
between God as Architect and God as Monarch, so that
nature itself59 leads to grace, and grace, by the use it makes
of nature, brings it to perfection 60.

1 6. Thus although reason cannot make known to us
the details of the great future (which are reserved for
revelation), we can be assured by this same reason that
things are made in a way which exceeds our desires.

56 E. reads sans en avoir meme la volonte, 'without even willing it.'
G. (from whom I translate) has mais aussi sans en avoir la volonte.

57 Sed omnia in mensura, et numero et pondere disposuistis. A quotation
(frequently used in Leibniz's time) from the Vulgate, Book of Wisdom,
ch. n, v. 21. * But by measure and number and weight Thou didst
order all things' (R. V. ch. u, v. 20). The phrase pondere, numero,
mensura occurs in the remains of Ulpian, Instit. bk. i, fragment iii.

58 Cf. Monadology, § 82.

59 E. omits * itself,'

60 Cf. Monadology, §§ 84-89.

422 PRINCIPLES OF NATURE AND GRACE

Further, as God is the most perfect and most happy and
consequently the most lovable of substances, and as
genuine pure love 61 consists in the state in which we find
pleasure in the perfections and the felicity of the beloved,
this love is sure to give us the greatest pleasure of which
we are capable, when God is its object.

17. And it is easy to love God as we ought, if we know
Him as I have just said 62. For although God cannot be
perceived by our external senses, He is none the less very
lovable and He gives very great pleasure. We see how
much pleasure honours give to men, although they do
not consist in anything that appeals to the external
senses. Martyrs and fanatics (though the emotion of the
latter is ill-governed) show how much influence mental
pleasure \le plaisir de I' esprit] can have : and, what is more,
even the pleasures of sense are really intellectual plea-
sures confusedly known63. Music charms us, although
its beauty consists only in the harmonies [convenances] of
numbers and in the counting (of which we are unconscious
but which nevertheless the soul does make) of the beats
or vibrations of sounding bodies, which beats or vibrations
come together at definite intervals. The pleasure which
sight finds in good proportions is of the same nature ;
and the pleasures caused by the other senses will be
found to amount to much the same thing, although we
may not be able to explain it so distinctly 64.

61 i. e. ' disinterested ' love. See Monadology, § 90, note 142.

82 ' God is love [c/wm'fos], which is known by love [amor] and is
loved in being known.' Nicholas of Cusa, Excitationes ex Sermonibus,
10, 188 b.

63 For sense is confused perception. Cf. Introduction, Part
iii. p. 125.

6* Leibniz does not mean, as some of his critics (e.g. Kirchmann)
seem to have thought, that the pleasure we have in music or in
painting is entirely a matter of the senses. What he wants to
show is that even the sense-element in artistic pleasure is really
of an intellectual kind, and this he does by showing that it
depends upon an unrecognized perception of proportion, measure
or rhythm. He elsewhere calls it * a hidden [occulte] arithmetic '
(G. iv. 551).

PRINCIPLES OF NATURE AND GRACE 423

1 8. It may even be said that from this time forth the
love of God enables us to enjoy a foretaste of future
felicity. And although this love is disinterested, it con-
stitutes by itself our greatest good and interest, even
though we may not seek these in it and though we may
consider only the pleasure it gives without regard to the
advantage it brings ; for it gives us perfect confidence in
the goodness of our Author and Master, which produces
real tranquillity of mind, not as in the case of the Stoics,
who forcibly school themselves to patience, but through
a present content which also assures to us a future happi-
ness65. And besides the present pleasure it aifords,
nothing can be of more advantage for the future than this
love of God, for it fulfils our expectations also and leads
us in the way of supreme happiness, because in virtue
of the perfect order that is established in the universe,

65 'There is as much difference between genuine morality
[morale'] and that of the Stoics and Epicureans, as there is between
joy and patience ; for their tranquillity was founded only upon
necessity, while ours should be founded upon the perfection and
the beauty of things, upon our own felicity.' The'odicee, § 254 ;
E. 580 b ; G. vi. 268. < What is called Fatum Stoicum was not so
black as it is painted. It did not keep men from looking after
their affairs; but it tended to give them tranquillity as regard;
events, through the consideration of their necessity, which makes
our anxieties and regrets useless. . . . The teachings of the Stoics
(and perhaps also of some famous philosophers of our own time),
being confined to this supposed necessity, can only secure a forced
patience ; instead of which our Lord inspires us with more sublime
thoughts and teaches us even the way to have content, when He
assures us that as God is perfectly good and wise and takes all
under His care, so as not even to neglect a hair of our heads
our confidence in Him ought to be complete ; so that we should
see, if we were able to comprehend it, that it is impossible even
to desire anything better (either absolutely or for ourselves) than
what He does. It is as if we were to say to men : " Do your duty
and be content with what comes of it, not only because you
cannot resist Divine providence or the nature of things (which
would be enough to make us tranquil, but not to make us content)
but also because you have to do with a good Master." And this
might be called Fatum Christianum' Theodicee, Preface, E. 470 b;
G. vi. 30.

424 PEINCIPLES OF NATURE AND GRACE

everything is done as well as possible both for the
general good and also for the greatest individual good of
those who believe in it and who are satisfied with the
Divine government. And this belief and satisfaction
must inevitably be the characteristic of those who have
learned to love the Source of all good 66. It is true that
supreme felicity (by whatever beatific vision, or knowledge
of God, it may be accompanied) can never be complete,
because God, being infinite, cannot be entirely known ' 7.
Thus our happiness will never consist (and it is right
that it should not consist) in complete enjoyment, which
would leave nothing more to be desired and would make
our mind [esprit] stupid ; but it must consist in a per-
petual progress to new pleasures and new perfections 6K.

66 ' We ought always to be content with the order of the past,
because it is in conformity with the absolute will of God, which
we know through what has come to pass ; but we must try to
make the future, so far as it depends upon us, in conformity with
the presumptive will of God or His commandments, to adorn our
Sparta and to labour at doing good, yet without vexing out-selves
when success does not come to us, in the firm belief that God will
be able to find the most fitting season in which to make changes
for the better. Those who are not content with the order of things
cannot flatter themselves that they love God as they ought.'

1 Lettre a Arnauld (1690) (G. ii. 136; E. io8a).

67 According to Leibniz's system, if a Monad were to know God
entirely, it would be God and would thus cease to be itself, which
is impossible. Yet Leibniz regards the relation of men to God as
so close that he calls them ' little gods, subject to the great God.'
Lettre a Arnauld (1687) (G. ii. 125). Cf. Nicholas of Cusa, Excitationes
ex Sermonibusj x. i88a: 'To be able always more and more to
understand (to conform oneself to the Creator) without end, is the
likeness of eternal wisdom.'

68 'Felicity is to persons what perfection is to beings.' Paper
without a title (1686) (G. iv. 462). Cf. Ultimate Origination of Things,
PP. 345, 348.

INDEX

Abstractions rightly used are not

errors, 379.

Achilles and the tortoise, 8 1 n.
Action motrice, 92.
Activity essential to substance,

90 n, 325, 397.
Adamson (R.) on Fichte, i8on,

Agrippa von Netteslieim, 403 n.

Albertus Magnus, 260 n, 302.

Algebra, its connexion with geo-
metry, 76 ; relation to other
sciences, 80.

Alphabet of human thoughts, 85.

Alsted, 376 n.

Angelus Silesius (Joannes), 384 n.

Animals, birth and death of, 115,
259, 413; indestructibility and
immortality of, 262, 306, 374;
resuscitation of, 224 n, 306 ; ac-
cording to Descartes, are mere
machines, 52 ; according to
Leibniz, not mere machines,
300 ; animals incomparably
greater than ours may exist,
U4n, Ii6n; organs of animals
in relation to perception, 231 ;
organic body of, 253 ; souls of,
400 ; nature of animal con-
sciousness, 232, 322, 364, 412.

Animal spirits, 314 n.

Anselm, 277.

avTiTviria, 35 n, 94 sqq.

Apperception, in Leibniz's sense,
34, 121 ; Locke's view, 367 sqq.;
distinction between appercep-
tion and perception, 126 sqq.,
411. See also Perception.

Appetition denned, 33, 35, 226,
407; degrees of, 51, 138; not

; a

suf-

necessarily conscious, 3

result of the principle o

ficient reason, 71.
Aquinas, 243 n ; on sensible

species, 2i9n; on antecedent

and consequent will of God,

270 n ; on souls of lower
.animals, 302 ; on the motions

of the planets, &c., 382 n; his

explanation of ' eminent,' 238 n.
Aristotle, 32, 155, 238 n, 255 n,

308, 358 n, 378 n ; in relation

to Leibniz, 229 n ; his ethics,

293 n ; his description of place,

353 ; on the tabula rasa, 360 n ;

on the motion of the skies,

382 n.

Arnauld and Leibniz, 6, 298 n.
Association of ideas, 232 n.
Astraea, 64 n.
Atomism, 23, 26, 31 ; Leibniz's

relation to, 29, 30, 159;

Atomism of Descartes and

Locke, 124.
Atoms, 223 n ; Leibniz's early

liking for atoms and the void,

32; his criticism of atoms, &c.,

2i8n, 310, 335, 370, 385 ;

metaphysical atoms, 33 n ;

atoms of substance = Monads,

33 n, 3«-
Attraction (immediate) from a

distance, 389.
Attributes to be distinguished

from modifications, 394.
Augustine, 207 ; Civitas Dei,

267 n.
Automata, 254, 264 n; Monads are

automata, 229 ; soul a spiritual

automaton, 315.

426 INDEX

Averroes, 383 n.

Axioms may require proof, 59.

Bacon, John, 260 n, 302, 303 n.

Bayle, Pierre, 226, 236 n, 375;
on pre-established harmony,
249 n ; on multiplicity in the
Monad, 272.

Beautiful, definition of, 286 n.

Becoming, principle of, 82.

Bellarmine (Cardinal), 401 n.

Benevolence, 285 n.

Bernier, Fra^ois, 335.

Birth of an organism, not absolute,
115 ; birth and death, 259, 413.

Body not a substance, 98 n ; the
mechanical cause of substance,
107 ; in flux like a river, 97,
114, 258, 262 n; without soul
unreal, in; is soul's point of
view, 112, 248 n; is momentary
mind, 230 n; each body affected
by all others, 113 n, 224 n, 251;
infinite division of bodies, 237 ;
reason for the existence of bodies,
324 n. See also Matter and Soul.

Boineburg, 4.

Bossuet and Leibniz, n ; and
Fdnelon, 269 n.

Boutroux, E., 234 n.

Boyle, Kobert, 7, 370.

Brahe, Tycho, 318 n.

Bruno, Giordano, 34, 57 n.

Buddeus, 38.

Buffon, 198.

Cabbalists, 155 n.

Calculating machines of Leibniz
and Pascal, 6.

Calculation, every paralogism an
error of, 85.

Calculus, discovery of the differen-
tial, 7 ; infinitesimal, 80 sqq. ;
logical, 84 sqq.

Campanella, 155.

Cardano, Girolamo, 155, 403 n.

Carlyle, Thomas, 388 n.

Carneades, 284.

Cartesians on the souls of the lower
animals, &c., 411 ; imperfection
of their view of perception, 224.
See also Descartes.

Cause, Leibniz's view of, 204 sqq. ;

First Cause, 137; cause and effect
an ideal relation, 106, 245 n ; effi-
cient and final causes, 107, io8n,
205, 238 n, 263, 268 n, 409,
418 ; Kant on final causes, 176 ;
Lotze's view, 193 ; the world a
system of final causes, 107.

Cavalieri, 76 n.

Cell-theory of physiology, 198,
257 n.

Centripetal powers, 389.

Charity, 284.

Choice of God among possible
universes, 66, 174.

Christianity in relation to natural
law and the law of nations, 295.

Christiern V of Denmark, 347.

Churches, projects for reconcilia-
tion of, 5, n, ii9n.

City of God, 267, 293, 316, 421.

Clarke and Leibniz on space and
time, 102 n, 104 n.

Cleanthes, 243 n.

Clocks illustration of pre-estab-
lished harmony, 45, 331 ;
Foucher's use of, 320 ; Geu-
lincx's use of, 43, 331 n.

Codex Juris Gentium Diploma-
ticus, 281.

Cogito ergo sww,Leibniz's criticism

of, 55-

Cohesion of matter, 386.

Compossibility, explanation of, 64 ;
is sufficient reason, 64 ; in rela-
tion to Kant's position, 1 74. See
also Possible.

Compounds not real substances,
96 n, 97, 109, 310, 330.

Conception and perception, views
of Kant and Leibniz, 171.

Concours ordinaire of God, 43.

Conduct, the end of, 146.

Consciousness not essential to
perception, 34; not dependent
on organic structure, 321.

Contingent truths, 57, 134, 243;
demand an infinite analysis, 6 1 ;
their final reason to be sought
in God, 63. See also Truths.

Continuity, law of, 37, 38, 83,
223n> 376; applied to motion
and thought, 130; an applica-
tion of sufficient reason, 71.

INDEX

427

Continuous and indivisible, pro-
blem of their reconciliation,
21 sqq.

Contradiction, principle of, 58 sqq.,
235 ; a principle of exclusion,
67 ; inadequacy of, 60 ; relation
to sufficient reason, 66, 187;
according to Leibniz and Kant,
172 sqq. ; according to Schopen-
hauer, 184 ; according to Leib-
niz and Lotze, ig6 ; its conse-
quences in Leibniz's philosophy,
68. See also Sufficient reason.

Con way, Countess of, 155.

Copernicus, 318 n.

Cordemoi, 43 n, 310 n.

Created beings pregnant with their
future states, 44 n, 231, 373,
419 ; imperfections of, 240, 250,
416. See Monads.

Creation, emanation and figura-
tion, 243 n.

Cyrus, story of, 290.

Death, meaning of, 115, 259, 413 ;
is a sleep, 374.

De Diaeta quoted, 308 n.

Democritus, 155, 219 n, 306, 307 n,
352.

Demonstration, 56 n.

Descartes, 43 n, 155, 243 n, 352 ;
Leibniz's dissatisfaction with
his philosophy, 8, 9 ; Leibniz's
criticisms of, 54 n ; Descartes's
view of matter, 86 ; in relation
to transubstantiation, 5 ; his
views of matter and mind re-
jected by Leibniz, 27, 128 sqq.;
his proofs of the existence of
God criticized by Leibniz, 275 ;
his views on the immortality of
the soul criticized by Leibniz,
225 n; Descartes and Leibniz
on secondary qualities, &c., 375,
376 n; on the seat of the soul,
314 n ; Descartes's theory of
knowledge, 122; his view of per-
ception, 224 ; clear and distinct
ideas, 48 ; self-consciousness,
52 ; principle of contradiction,
58 ; eternal truths, 242 n ;
possible things, 64 n ; thinking
and extended substance, 42 ;

animals, 52 ; animal spirits,
314 n ; analytical geometry, 77 ;
conservation of motion, 86 sqq.,
88 n, 264 n, 327 ; nature of
substance, 25 ; sensation, 52 ;
soul and body, 263, 311 ; inten-
tional species, 2 20 n ; on the
meaning of ' eminent ' and
' formal,' 238 n ; method of
doubt, 24 ; vortex hypothesis,
378 n ; Descartes's use of the
idea of cause, 160 ; of the idea
of God, 161 ; attitude towards
earlier thought, 152, 157 ; affec-
tation of ignorance, 152 n; rela-
tion to Gassendi, 303 n ; Locke,
I24n; Kegis,305 n; Spinoza, 24.

Desire, instinctive, 138.

Development and envelopment,

H5, 259, 307, 374 n, 4I.4-
Diderot in praise of Leibniz, 1 7.
Dillmann on Leibniz, is6n; on

vinculum substantiate, 119 n.
Du Bois-Reyrnond, 37 n, 93 n,

199 n.
Duns Scotus, 243 n, 358 n.

Eckhart, Leibniz's secretary, 16,

J7-

Eduction of forms, 260 n.
Egypt, Leibniz's project for the

conquest of, 5.
Empirical knowledge, 52, 233, 364,

365, 412-

Enlightenment, value of, 149.

Entelechies, 50, 159, 221 n, 229,
301 ; in matter, 94 n, 96 ; of
compound substances, no ; dis-
tinguished from souls, 230.

Entia mentalia and semi-men-
talia, 101.

Epicurus, 264^

Equity, 287.

Erdinann on Leibniz's view of
space and time, 101 ; on the
vinculum substantiate, 1 19 n.

Ernest, Landgraf of Hesse- Rhein-
fels, 298 n.

Essences or possibilities, 241 n ;
tend to existence, 247, 340, 342 ;
essence and existence, 66

Eternal and necessary truths, 57,
120, 233, 363; conditional, 60 n,

428

INDEX

206 ; not dependent on the will
of God, 57, 242 ; understanding
of God is the region of, 241, 343.
See also Truths.

Ethics of Leibniz, 137 sqq.

Eugene, Prince, 215, 405.

Euler's criticism of Leibniz, 255 n.

Evil, origin of, 240 n ; problem of,
346 sqq., 416 n ; leads to greater
good, 349 ; evil of individuals
not to be justified by good of
the whole, 348.

Explanation of the New System,

3J9-

Extension, elements of, 329 ; not
the essence of matter, 28, 94.

Fact and reason, propositions of,
206.

Facultas, 288.

Fatum Stoicum, 423 n.

Feeling an element in every per-
ception, 139.

Fenelon and ±Jossuet, 27on.

Fernel, 260 n.

Fichte, 252 n; on the spirituality
of the universe, 267 n ; influence
of Leibniz upon, 178 sqq. ;
Fichte's Ego and Leibuiz's
Monad, 180 ; Fichte and Kant,
178 sqq.

Fitness or choice of the best, 243 ;
degrees of perfection, 247.

Fludd, Robert, 402.

Fluid, perfect, does not exist, 335,
386.

Fontenelte, 309 n.

Force, notion of, 91, soon; conser-
vation of, 90 sqq., 327, 417 ; dis-
tinct from Scholastic potency,
91 n ; essential to matter, 94 ;
a form of appetition, 2 26 n ;
development of Leibniz's views
regarding, 351 ; distinction be-
tween absolute and directing
force, 328n; total and partial,
&c., 417.

Forces proportional to squares of

velocities, 92.

Forms, accidental, 157 ; substan-
tial, 108 n, H9n, 156 sqq.;
rejected at first by Leibniz, 3 ;
re-introduced by Leibniz, 159,

301 ; origin and duration of,
2 59 s<¥i' > forms in matter, 94 n ;
indivisible, 302.

Foucher, Simon, 319, 320 ; Leib-
niz's comments on his dispute
with Hartsoeker, 334 sqq.

Freedom, Leibniz's view of, 141 ;
degrees of, including necessity,
145 ; freedom and determina-
tion, 343 ; is spontaneity and
intelligence, 145 ; highest free-
dom accompanied by most per-
fect knowledge, 146.

Fulgurations of the Divinity, 243.

Galen, 314 n.

Gassendi, 303^ 319, 352.

Genus, distinction between phy-
sical or real and logical or ideal,
394 sqq.

Geometrical relations not merely
quantitative, 77.

Geometry, synthetic and analytic,
75 ; connexion with algebra,
76 ; analytical geometry of
Descartes, 77.

Geulincx, 312 n, 367 n ; use of the
clocks illustration, 43, 331 n.

God, idea of, in Descartes' s system,
161 ; according to Leibniz and
Descartes, 57 ; inconsistency of
Leibniz's account of, 175, i77>
proof of His existence, 242 ;
ontological proof, according to
Descartes, Spinoza and Leibniz,
2 74 s^.(l' > Cosmological proof,
239 n ; proof from pre-estab-
lished harmony, 202, 316, 418 ;
Kant on the proofs, 173; God
the ultimate sufficient reason of
things, 66, 238, 339, 415 ; the
source both of essences and
existences, 241, 343 ; the ulti-
mate reality, 136; His relation
to the world, 257 n, 344, 416 ;-
to other Monads, &c., 243 n,
266, 304; God not the only
Spirit, 385 n ; ' assistance ' of
God, 43 ; love of God, 148, 286,
422, 423 ; His perfection, 240 ;
His antecedent and consequent
will, 270, 424 n; His justice
compared with human justice,

INDEX

416 n ; His understanding the
region of eternal truths, 66,
24r> 343J His possibility un-
limited, 240 n; His power,
knowledge and will, 244 ; His
choice among possible universes,
66, 1 74 ; His centre everywhere,
circumference nowhere, 420 ;
without body, 259 ; vision of all
things in God, 53 n ; things not
modes of God, I37n; ethical
importance of the idea of God,

293.

Good and evil, relative terms, 146.
Green, T. H., on Leibniz and

Kant, 168 n, 172 n.
Grotius, 288, 293 n.
Guhrauer, 37.

Happiness, 287 n; is a perpetual
progress to new perfections, 424 ;
nothing more true than, 350.

Hartmann, E., 199.

Hartsoeker, 305 n ; Leibniz's com-
ments on his dispute with
Foucher, 334 sqq.

Hegel, 34 ; his solution of the
dualism in Leibniz, 186 sqq. ;
shows that contradiction pre-
supposes sufficient reason, 187 ;
view of self-consciousness, 189,
190 ; his ' notion ' and Leibniz's
Monad, 188.

Herbart, 2 20 n ; his ' reals ' and
Leibniz's Monads, 1 85 ; mathe-
matical methods in psychology,
186.

Herder, 198.

Hermetics, 155 n.

Hermolaus Barbarus, 245.

Hippocrates, 251, 260 n, 373 ; on
the indestructibility of animals,
308.

Hobbes, 264 n ; influence upon
Leibniz, 7 ; definition of space,
101.

Huygens, 332 n ; intercourse with
Leibniz, 6 ; pendulum experi-
ment, 45 n, 332.

Hypotheses, uses of, 325.

Ideas, views of Descartes and
Leibniz regarding clear and

429

distinct, 48 ; clearness and dis-
tinctness not the sole criteria of
truth, 55 sqq. ; innate ideas,
233 n> 36° sqq- ; illustrated by
block of veined marble, 131,
366 ; views of Descartes, Locke
and Leibniz regarding innate
ideas, 125; region of ideas in
understanding of God, 66, 241,
343 ; symbolizing of ideas, 85.

Identity, principle of, see Contra-
diction. Identity of the indi-
vidual, how constituted, 133 n,
373 ; not determined by time
and place, 377 n; physical and
moral identity, 258 n.

Ignava ratio, 399 n.

Immortality of the soul, 1 16, 225 n,
259 sqq., 316, 383, 401 sqq. ;
of the rational soul, 116, 307;
in relation to ethics, 292, 293 n.

Impenetrability, 94 sqq.

Impulse in matter and bodies, 387,
388.

Indeterminism, error of, 143.

Indifference of equilibrium, 375.

Indiscernibles, identity of, 36, 222,
369 n, 377; an application of
sufficient reason, 71.

Indivisible elements, how can they
form a continuum, 21 sqa.

Inertia of body, 95, 240.

Infinite, different meanings of,
255 n.

Infinitely little, 79.

Infinitesimals, 81 ; a virtual re-
cognition of the principle of
Becoming, 82.

Infinity, notion introduced into
geometry, 75 ; degrees of, 414 n.

Influxus physicus, 42, 46, 219 n,
333-

Justice, definition of, 148, 283 ;
universal, 287 sqq., 294; com-
mutative, 287 sqq.; distributive,
287 sqq.; contributive, 289 n;
Aristotle's sub-divisions of par-
ticular justice, 287 n ; arith-
metical and geometrical equality
in justice, 290 n ; Divine and
human justice differ only in
degree, 291 n, 416 n.

430

INDEX

Kant, relation to Leibniz, 168
sqq. ; his own view of his relation
to Leibniz, 208 sqq. ; Kant and
Leibniz on perception* and con-
ception, 171 ; Kant's thing-in-
itself in relation to Leibniz, 1 75 ;
Kant's misunderstanding of
Leibniz, 163 n ; he misunder-
stands Leibniz's view of space,
221 n; his criticism of Leibniz,
i6gn; Kant and Wolff, 168 ;
Kant received problem of space
in Wolffs form, 169 ; develop-
ment of Kant's view of space,
170 ; Kant on intensive quan-
tity, 22on; on the ontological
proof of the existence of God,
277, 173 ; on the relation of
God to the world, 177 ; on final
causes, £c., 176.

Kepler's introduction of the notion
of infinity into geometry, 75.

Ker of Kersland, 16.

Kirchmann, 259 n.

Knowledge, Leibniz's theory of,
121 sqq. ; how dependent on his
main principles, 133 sqq. ; know-
ledge at once innate and experi-
ential, 126.

Knutzen, 168.

Language, philosophical, 85 sqq.

Law, positive Divine, 296.

LEIBNIZ, boyhood, i ; early studies,
1,2; university life, 2 ; gradua-
tion theses, 3; connexion with
Boineburg, 4 ; residence in
Niirnberg, 4; secretary to a
society of Rosicrucians, 4; in
the service of the Archbishop of
Mainz, 4 ; residence at Frank-
fort, 4 ; projects of Church
re-union, 5, n; residence in
Paris, 5 ; visit to London, 7 ;
intercourse with Huygens, 6 ;
study of higher mathematics, 6 ;
invented a calculating machine,
6 ; reason for writing in French,
6 ; advocated use of German for
philosophical writing, 6 ; relation
to Hobbes, 7 ; intercourse with
Boyle, 7 ; discovery of the Dif-
ferential Calculus, 7 ; study and

translation of Plato, 9 ; ac-
quaintance with Tschirnhausen,
9 ; Newton and the Calculus, 8 ;
personal relations with Spinoza,
9, 10 ; librarian to the Duke of
Brunswick, 8 ; residence in
Hanover, 1 1 ; visit to Rome, 1 1 ;
first publication of his philoso-
phical system, 12 ; growth of
his system, 12 ; writing and
publication ofNouveaux Essais,
T3> 3555 of TModicee, 14; his
correspondence, 14 ; founding of
academies, 14, 15; intercourse
with Peter the Great, Charles VI,
and Prince Eugene, 1 5 ; suffers
from prejudices of George I, 15 ;
death and funeral, 16 ; personal
characteristics, 16, 17 ; principal
works and editions, 18 sqq.

LEIBNIZ, three chief conceptions of
. his metaphysic, 47, 48 ; logical
principles of his philosophy, 58
sqq. ; his view of self-conscious-
ness, 53, 120, 128, 133, 234 n;
his ethics, 137 sqq. ; psychology
of volition, 142 n ; logic, 206
sqq. ; theory of knowledge, 121
sqq. ; his mathematics inrelation
to his philosophy, 74 sqq. > anti-
cipation of transformation of
energy, 93 n ; optimism,66, 147 n,
248, 271, 345 sqq., 417, 424 ;
on the ontological proof of the
existence of God, 275 sqq. ; holds
that matter cannot think, 400 ;
interest in microscopy, 256 n ;
eclecticism, 154, 155 ; fore-
shadows the critical spirit, 154;
early rejection of substantial
forms, 3 ; his account of his
early philosophical views, 299
sqq. ; growth of his views re-
garding force and motion, 351 ;
misunderstood by his disciples,
163 ; accused of borrowing clocks
illustration from Geulincx, 43.

— relation to Plato and Aristotle,
358 n, 229 n ; to earlier thinking,
151 sqq., 158; dissatisfaction
with Descartes's philosophy, 8 ;
difference from Descartes re-
garding clear and distinct ideas,

INDEX

43T

48 n ; Leibniz and Descartes on
secondary qualities, &c., 375>
376 n ; criticism of Spinoza's
Ethics, 24 n ; Leibniz and
Spinoza on empirical knowledge,
70 ; relations to Newton, 8, 80 ;
correspondence with Clarke,
102 n, 104 n ; discussion with
Bayle on multiplicity in the
Monad, 272 ; Leibniz's account
of his relation to Locke, 357
sqq. ; criticisms of Locke, 13 ;
criticism of the tabula rasa,
122 n, 369 ; via media between
Descartes and Locke, 123; on
the controversy between Locke
and Stillingfleet, 398 sqq. ; re-
lation to Kant, 168 sqq., 208
sqq. ; Kant's discussion of
Leibniz's first principles, 208 ;
relation to Fichte, 178 sqq. ; to
Schopenhauer, 183 ; toHerbart,
184; to Hegel, 1 86 ; to Lotze,
190 sqq.

Lemoine on the vinculum sul)-
stantiale, 119 n.

Lessing, 198.

Leuwenhoek, 256 n, 260 n, 305 n.

Liberty of indifference does not
exist, 141 sqq.

Life everywhere in nature, 105,
109, 112, 256,309,409.

Limitation, necessity of, 340 n.

Limitations of created things, 240,
250, 416, 419 n.

Limits, mathematical points are,
28, 29.

Locke, 36 n ; his Essay, 355 sqq. ;
Leibniz's relation to and criti-
cism of, 13, 123, 357 sqq.;
Locke's theory of knowledge,
122 ; his view that mind may
exist without thought, opposed
by Leibniz, 129 ; his account of
' uneasiness,' 140 ; his account
of virtue criticised, 149 n ; on
the immortality of the soul,
383 n ; on the immateriality of
the soul, 402 ; holds that matter
may think, 392, 395 ; Locke and
Descartes, I24n; Locke and
Stillingfleet, 387 sqq.

Logic of Leibniz, 206 sqq. ;

Leibniz's early interest in logic,
2.

Lotze, H4n ; relation to Leibniz,
194 sqq.; criticism of Leib-
niz, 195 sqq. ; on innate ideas,
126 n; on mechanism, 192;
his monadology, 194 ; teleology,
193; relation to Herbart, 191 ;
on Hegel, 190, 192.

Loubere, Simon de la, 397.

Louis XIV, 5.

Love, disinterested as distinct
from selfish, 148, 269, 285 ;
Divine, 286, 423.

Machines of nature are machines
throughout, 254, 309 ; have an
infinity of organs, 309.

Mainz, Archbishop of, employs
Leibniz, 4.

Malebranche, 305 n, 312; inter-
course with Leibniz, 6 ; sense
in which Leibniz agrees with
him, 53 n; he might approve
the pre-established harmony,
44 n.

Malpighi, 39 n, 256 n, 260 n, 305 n.

Materia prima, 95 ; and materia
secunda, no; possessed by
every created Monad, 97.

Materia secunda, 96, 258 ; an
aggregation, 97, 300 ; a mere
phenomenon, 97 ; in flux like a
river, 97, 114, 258, 262 n ; dis-
tinct from substance, 96 n.

Mathematics in relation to Leib-
niz's philosophy, 74; Divine
mathematics, 342 ; mathematical
points, 311.

Matter, Leibniz's theory of, 93
sqq. ; not mere extension, 28,
94 ; a mere aggregate, 300 ; in-
finitely divided as well as infin-
itely divisible, 39, 237, 255, 335 ;
living throughout, 256; cohesion
of, 386 ; primary and secondary
qualities, loo ; inseparable from
mind, in, 128; can matter
think ? 390 sqq. ; miraculous
exaltation of matter, 401 ; Des-
cartes's view of matter, 86.

Mechanical philosophy, 158.

Mechanism, Divine and human,

432

INDEX

254, 309 ; can explain nothing
but mechanism, 228n; cannot
produce perception, 227, 397,
400.

Melissus, 259 n, 308.

Memory the sign of consciousness,
230 n; in animals, 232, 322, 364,
412.

Metamorphosis in compound sub-
stance, 114, 258,307, 414.

Metaphysical laws in nature, 344.

Metempsychosis inadmissible, 1 14,

258, 3°4, 4H-

Microscopy in Leibniz's time, 256 n.

Milton quoted, 404 n.

Mind always thinks, 129, 369 sqq. ;
likened to veined marble, 131,
366. See also Souls (rational).

Miracles of reason, nature full of,

254n-

Molinos, Miguel de, 384 n.

Monads, history of the term, 34 ;
account of, 30 sqq., 217 sqq., 406
sqq. ; the only real existences,
97 ; infinite in number, 37 ; an
infinite series, 37 ; compared to
ordinates of a curve, 37 n, 38 ;
their production, 243 ; creation
and annihilation, 219 ; ingener-
able and imperishable, 36, 115,
218, 302, 407 ; qualities of, 220 ;
must have both perception and
appetition, 33 ; have no parts,
2 1 7 sqq., 407 ; not in space, 2 2 1 n ;
not perceived by the senses,
407 n; spontaneity of, 35, 50,
274, 313 ; are incorporeal auto-
mata, 229, 315, 408 ; present of
each Monad big with its future,
44 n, 231, 373, 419; all its
ideas innate, 125 ; its self-iden-
tity not static but dynamic,
69 ; continually unfolding or
enfolding itself, 113; Monads
have no windows, 219 ; mutual
exclusiveness, 36, 219; each as
independent as if there existed
only God and itself, 313 ; meta-
physical atoms, atoms of sub-
stance, of nature, &c., 33 n, 218 ;
metaphysical points, 311 ; centres
1 or concentrations of the world,
70, 407 ; changes in Monads, 40

sqq., 222 sqq. ; correlativity of
their changes, 41 ; multiplicity in
the Monad, 224 n, 226, 272, 407;
Monads as living mirrors of the
universe, 36, 41, 253, 409 ;
variously represent or implicitly
contain the whole universe, 50,
248, 420 ; each represents most
distinctly its own body, 253 ;
elements in Monads, 245 ; each a
concrete unity of soul and body,
109 ; activity and passivity
of,' 105, 245, 246, 317 ; influence
one another ideally, 42, 45, 105,
246 ; their mutual agreement,
313 sqq. ; their interrelation not
to be realized by sense or ima-
gination, 46 ; differences among
Monads, 49, 55 ; degrees of per-
ception, 410 ; three grades of
created Monads, 50, 229 sqq.,
409 sqq. ; each higher grade has
characteristics of lower, 52 ; im-
perfections of Monads, 240, 250,
416 ; their progress towards per-
fection, 419 n ; dominant Monad,
109 sqq., 253 n, 257, 408 ;
Monads in relation to Fichte s
' Ego,' 1 80 ; to Herbart's ' reals,'
185; to Hegel's < notion,' 188.
See also Souls.

Monadology, time and circum-
stances of its composition, 215 ;
relation to Principles of Nature
and Grace, 215,405 ; analysis of,
216; Kant's discussion of, 209.

Monas Monadum, 57, 189.

Montaigne, 372 n ; on indeter-
minism, 144^

More, Henry, 155.

Motion, Leibniz's view of, 89 ;
development of Leibniz's views,
351 ; relativity of motion and
rest, 89 sqq. ; conservation of
direction, 93, 264, 32 7, 41 7; Des-
cartes's view of motion, 86 sqq. ;
he maintains its conservation,
87, 264 n ; that it is not merely
relative to rest, 88 ; and that its
direction is variable, 89 ; laws of
motion, according to Descartes
and Leibniz, 327, 328, 353, 417;
absolute and relative motion,

INDEX

433

317, 318 ; absurdity of swiftest

possible motion, 275.
Miiller, Johannes, 192, 198.
Miiller, Otto F., 163 n.

Natura naturans and natura
naturata, 162.

Nature and grace, realms of, 268,
421.

Necessary and eternal truths, 56,
120, 233, 363 ; necessary and
contingent truths, 134, 340 ;
their difference compared to that
of commensurable and incom-
mensurable numbers, 6 1 n.

Necessity, different kinds of, 339 ;
metaphysical and physical, 342 ;
metaphysical and moral, 67, 145,

247 n, 277; necessity an infin-
itely small degree of freedom,
145 ; necessity and fitness, 418.

New Essays, circumstances of
writing, &c., 13, 355.

New System, 297.

Newton on the relations between
geometrical figures, 82 ; on
attraction, &c., 388 ; view of
space, 1 02 n ; relation to Leib-
niz as regards the Infinitesimal
Calculus, 8, 80.

Nicholas of Cusa, 32 n, 34 n, 222 n,

248 n, 250 n, 255 n, 267 n, 424 n.

Nizolius, Leibniz's essay on, 6.

Nolen, L\, quoted, 65 n ; on Leib-
niz and Kant, 1 78 n.

Number, 329.

Occasionalism, 43, 46, 333; de-
scribed and criticised, 312 ;
Leibniz's criticism of, 44.

Occult qualities, 157, 389 n, 399,
403.

Optimism of Leibniz, 66, 248, 271,
345 i=qq., 417, 424; his moral
optimism, I47n.

Organic and inorganic, nature of
the distinction between, in ;
organic beings between man and
God, I2on.

Organism, conception of, 31, 253
sqq. ; pervades nature, 105, 109,
112, 256, 309, 409; organisms
always come from seeds, 260, 413.

Ovid, 390 n.

Paracelsus, 403 n.

Parmenides, 155 n, 259 n, 308.

Pascal, 420 n ; on mathematical
infinity, 77 n.

Perception, its nature according
to Leibniz, 33, 135 sqq., 2 24, 370,
407 ; equivalent to multiplicity
in unity, 35 ; not to be explained
by mechanism, 227, 397, 400;
degrees of perception, 51 n, 231,
410 ; not necessarily conscious,
34, 231, 370, 411; unconscious
is symbol of corresponding con-
scious perception, 47 ; confused,
clear, and distinct perception, 48,
49, 105 ; never without feeling,
139 ; perceptions always leave
traces, 133 n, 373; likened to
projection in perspective, 136;
periodicity in perceptions, 374 n ;
perceptioa-and apperception, 126
sqq., 411 ; petites perceptions,
131 sqq., 230, 370 sqq. ; percep-
tion and conception, views of
Kant and Leibniz, 171.

Perfection, meaning of, according
to Leibniz, 249, 340 ; continual
progress of the world in, 419 n.

Peripatetic philosophy, 156 sqq.

Pfleiderer, Edmund, 43.

Phenomena l>ene fundata, 98 sqq.,
118 ; compared to rainbow, 100 ;
their reality different from that
of substance, 99 n ; how distin-
guished from phenomena of
dreams, 99.

Philosophy, fanatical or barbarous,
402, 403.

Piety, 287 sqq., 291.

Place, meaning of, 203 ; according
to Aristotle, 353.

Plant-animals, 38.

Plato, 34 n, 155, 261 n; world of
ideas, 241 n ; doctrine of remi-
niscence, 131, 359 n; Leibniz's
view of, 368.

Pleasure and pain, 139 sqq.; to
some extent in every soul, 140 ;
pleasure instinctively sought by
every soul, 141, 146, 285; un-
broken pleasure begets loathing,

434

INDEX

348, 424 ; artistic pleasure is
intellectual, 422.

Plenum, conception of theworld as,
40, 251, 385,408. See Vacuum.

Pliny, 306, 307 n.

Plotinus, 155 n.

Plutarch, 252 n.

Pneumatics, 376.

Points, metaphysical, mathema-
tical and physical, 311; mathe-
matical points are limits, 28, 29.

Poiret, 57, 243.

Pope, 198, 257 n, 349 n.

Possible, definition of, 63 ; possible
and compossible, 64, 340 sqq.

Possible things. See Essences.

Praedicatum inest subjecto, 61 n,

398 n-

Pre-established harmony, 39 sqq.,
246» 263, 374 sqq-» 409, 421 ;
first mentioned by Leibniz, 326 ;
called a hypothesis of agree-
ments, 315 ; compared with
Scholastic and Occasionalist
theories, 42, 44, 333 ; explained
by a special instance, 200 ;
advantages of, 323 ; a proof of
the existence of God, 202, 316,
418 ; clocks and choirs illustra-
tions of, 45, 47, 331 ; might be
approved by Malebranche, 44 n ;
Kant's account of, 209 sqq.

Preformation, 260, 412 sqq.

Present big with the future and
laden with the past, 44 n, 231,

373, 41?-

Preservation is a continual crea-
tion, 44 n, 244 n.

Principles of Nature and of Grace
in relation to the Monadology,
215, 405 sqq.

Progression, conservation of the
quantity of, 328.

Propositions, categorical and hypo-
thetical, 206 ; import of, 207.

Pufiendorf, 293 n.

Pythagoras, 34 n ; Pythagorean
views, 155 n.

Qualities, intrinsic and extrinsic,
222 n; occult, 157, 389^ 399,
403. See Substance.

Quantity, intensive and extensive,

220n; 'negligible,' 79; Leib-
niz's sharp distinction between
quantity and quality, 221 n;
quantitative unity, 78. See Sub-
stance.

Rainbow simile for phenomenon
bene fundatum, 100.

Reason, meaning of, 120 ; reason
and imagination, 232, 365 ;
reason and fact, propositions of,
206 ; ultimate reason of things,
66, 238, 337, 339, 415. See Suf-
ficient Reason.

Reasoning, truths of, 57, 235.

Reflexion, acts of, 56, 234, 412 ;
ideas of, 366.

Re"gis, 305 n.

Relativity, how Leibniz tries to
avoid, 135 sqq.

Representation the essence of the
relation between whole and
part, 32. See Perception.

Resistance a passive force, 95.

Resuscitation of animals, 224 n,
306.

Rewards and punishments, 269,
304, 381, 421.

Riedel, 0., on Kant, 178 n.

Right, doctrine of, 282 ; precepts
of, 288 ; degrees of natural
Right, 287 sqq. ; voluntary
Right, 295.

Rorarius, 227.

Rosicrucians, Leibniz's connexion
with, 4.

Sarmatian salt-mines, 346.

Scaliger, Julius Caesar, 361.

Sceptics, 155.

Schelling on Leibniz, 1 79 n ; on
the relation between Leibniz
and Fichte, 182.

Schiller, 198 n, 268 n.

Scholasticism, Leibniz finds value
in, 156 ; Scholastic potency
distinct from force, 91 n, 123 n.

Schopenhauer in relation to Leib-
niz and Fichte, 183.

Schwann, 198.

Self -consciousness more than
merely self-consistent, 59 ; im-
plies consciousness of objects,

INDEX

435

135 ; Leibniz's view of, 53, 120,
128, 133, 234 n ; Descartes's
view of, 52 ; difference between
Descartes and Leibniz, 54 ;
Fichte's view, 181 ; Hegel's
view, 189, 190.

Self- consistency, if real, must
have grounds, 59.

Self-love the ground of all our
actions, 148 ; disinterested in
proportion as it is enlightened,
148 ; self-love and the love of
God, 423.

Semi-pleasures and semi-pains,
140.

Sensation is confused perception,
I25> 37 2 ; necessary to thought
but not the essence of it, 362 n ;
according to Descartes, is purely
physical and mechanical, 52.

Sense-experience not the source
of all truth, 134, 361 sqq. ; gives
only particular truths, 362 ;
views of Locke and Leibniz
regarding, 134.

Sense-qualities are occult qualities,
362 n ; clear but not distinct,
372 n.

Series, infinite, 78 sqq.

Sigwart, H. C. W., 45 n.

Sin and virtue, 269.

Sophia Charlotte,Queen of Prussia,

H, J5-

Souls, class of Monads called, 51,
410 ; distinguished from ente-
lechies, 230; indivisible, 302;
spontaneity of, 274, 313 ; infi-
nite complexity of, 252 ; each
has some perception of all things,
1 1 3 n ; souls and atoms, differ-
ence between the changes in,
223 n ; seat of the soul, 314,
315 n ; soul likened to an animal
musician, 273 ; the final cause
of substance, 107 ; souls all in-
stinctively seek pleasure, 141,
146; origin and duration of,
259 sqq. ; transcreation of, 1 1 7 n ;
traduction of, 260 n ; indestructi-
bility and immortality of, 1 1 6,
225n, 259 sqq., 316, 383, 401
sqq. ; souls cannot remain per-
manently unconscious, 230, 374,

419 ; utterly forget nothing.
252 n. See Monads.

Souls, rational, or spirits, 51, 233,
265, 413 ; creation of, 117, 265 ;
personal immortality of, 307 ;
like small divinities, 266, 304,
424 n; are partes totales, 349;
relation to God, 266, 293, 349,

420 ; to other souls and Monads,
1 16 sqq., 121, I72n, 266, 303,
410,412.

Soul and body, relations between,
42, 258, 262 sqq., 31 1 sqq., 323,
331 sqq., 408 ; Descartes's com-
plete separation between, 42,
263 ; mutual independence of,
334 n. ; souls never entirely sepa-
rate from bodies, 105, 225, 258,
380 ; souls act as if there were
no bodies, 264 ; how soul is con-
scious of body, 200 ; soul not
perfectly conscious of what
happens in body, 1 1 2 n.

Space, independent reality of,
contrary to principle of suf-
ficient reason, 102 sqq. ; empty
space an abstraction, 102 ; for-
mation of the idea of space,
202 sqq. ; Leibniz's theory of,
101 sqq. ; Kant on space, 169
sqq., 221 n ; Wolff's view,
1 68 sqq.

Species, sensible, 219.

Spermatozoa, 261.

Spinoza, 31, 106 n, 155 n, 219 n,
230 n, 239 n, 244 n, 399 n ;
view of substance, 22 ; use of
the idea of cause, 162 ; on
possible things, 64 n; his cona-
tus, 71 n ; Leibniz's criticism,
24 n, 276; correspondence and
intercourse with Leibniz, 9 ;
Spinoza and Leibniz on empi-
rical knowledge, 7° > relation
to Descartes, 24 ; Spinoza's
philosophy ruled by the prin-
ciple of contradiction, 58.

Spirit, universal, 239 n.

Spirits. See Souls, rational.

Stallo, 92 n, 93 n.

Stein, Ludwig, 34 n, 43 n.

Stillingfleet and Locke, 387 sqq. ;
on the question whether matter

f 2

436

INDEX

can think, 390 ; Stillingfleet
charges Locke with incon-
sistency, 392.

Stoics, 155 n, 243 n ; irpo\r)$is,
360 ; Stoic patience compared
with Christian, 423 n.

Substance, Leibniz's view of, 27;
development of Leibniz's view,
1 2 ; unit of, 30 ; unity of,
98 n ; cannot be without activity,
90 n, 325, 397; analogous to the
human soul, 159 ; all substances
potentially self-conscious, 128;
qualities of substances not arbi-
trarily given by God, 399 ; spon-
taneity of, 33, 200, 204, 313;
intar - relation of substances,
summary of Leibniz's view,
io6n; mutual action of sub-
stances, 317; extension not the
essence of material substance,
28, 94; Leibniz on Descartes's
theory' of material substance,
27 ; Descartes's account of sub-
stance, 25 ; Spinoza's theory, 22.

Substance, compound, 109 ; unity
of, 96, 118, 310, 330; a mere
aggregate, 310, 330 ; inter-
relations of compound sub-
stances, 251 ; classes of organic
compound substances, 120;
changes in, 113, 258,414; simple
and compound substance, no,
217, 330, 406.

Substance, simple, 27; variety in,
223. See Monads.

Sufficient reason, principle of,
61 n, 62, 235, 414 sqq.j out-
side the sequence of contingent
things, 238, 338,415 ; synonyms
for, 235 n; consequences in the
philosophy of Leibniz, 69 ; rela-
tion to principle of contradic-
tion, 66, 164, 187 ; Descartes and
Spinoza, 160, 163; Leibniz and
Kant on the relation between
contradiction and sufficient
reason, 172 sqq.; Schopenhauer,
184; Hegel, 187; Lotze, 196.

Swammerdam, 256 n, 305 n.

Swift quoted, 41 4 n.

Symbolizing of ideas, 85 ; of
thought, 137; of whole by part,

33 ; mutual symbolizing of
things, 251 n.

Symbols, thinking and reasoning
in, 147.

Tabula rasa, 124 n, 360 sqq.;
Leibniz's criticism of, 1 2 2 n, 369.

Tendency or impulse, lowest de-
gree of appetition, 138; tenden-
cies to action, 123 n ; tendencies
to motion in all things, 90.

Tetens, 1 39 n.

Th&odicte, 215, 216, 240 n, 337,
416 n ; writing and publication
of, 14.

Thomasius, Jacob, 3.

Thought, self-sufficiency of, 136.

Time, Leibniz's theory of, 101 ;
empty time an abstraction, 102 ;
its independent reality contrary
to principle of sufficient reason,
103.

Toland, John, 226n.

Toletus, 157.

Traction of matter inadmissible,
386.

Traduction of souls, 260 n.

Transmigration of souls. See
Metempsychosis.

Transubstantiation, 119; in rela-
tion to Cartesian and Leibnitian
views of substance, 5.

Trinity, doctrine of, 244 n.

Truth, two kinds of, 57, 134, 235
sqq. ; nothing more agreeable
than truth, 350.

Truths, analysis of, 236 sqq. ; of
fact, 57 ; truths of fact require
an infinite analysis, to obtain
sufficient reason, 61, 237; con-
tingent truths, 57, 134, 243;
relation between necessary and
contingent, 61 n, 134, 340 ;
necessary truths not dependent
on the senses, 363.

Tschirnhausen's account of Leib-
niz, 9.

Ulpian, 288 n, 421 n.
Unconsciousness, 230, 374, 411.
Uneasiness, Locke and Leibniz on,

140, 142 n, 375.
Unit of substance, 30; no real

INDEX

437

whole without real units, 32,
217, 300 sqq., 310, 406.

Unity, quantitative and geome-
trical, 78 ; mechanical and
organic, 321 ; dominant unity
of the universe, 337. See Sub-
stance.

Universe, continual progress of,
350, 419 n ; contains nothing
fallow, sterile or chaotic, 257 ;
infinite number of possible
universes, 65, u6n, 247.

Unum per accidens and unum per
se, 97 n, 98 n, 118.

d'Urfe, Honore", 65 n.

Vacuum, impossibility of, 72 n,

25711, 385, 4°8-
Van Helmont, F. Mercure, 34 n,

155-

Van Helmont, J. B., 403 n.

Vinculum substantiate, 118.

Virgil, 373 n.

Virtualite in Leibniz's sense,
367 n.

Virtue, definition of, 283 n.

Vis viva, 92.

Void. See Atoms and Vacuum.

Volition not absolutely necessi-
tated, 144 ; Leibniz's psycho-
logy of, 142 n.

Wallace, W., 18511.

Weigel, Erhard, 3.

Weigel, Valentine, 384 n.

Weisrnann, 198 n.

Whole and parts, problem of, 22 ;

dynamic relation between, 31 ;
relation of representation, 32 ;
their relation under the principle
of contradiction, 68 ; Descartes's
presupposition regarding, 26 ;
Atomist view, 26.

Will or self-conscious desire, 138 ;
frequently acts from a sufficient,
not necessitating, reason, 145 ;
willing to will, 142, 144 n. See
Freedom.

Windelband, 149.

Wisdom defined, 287.

Wolff, Christian, 'philosophy of,
164 sqq.; relation to Leib-
niz, 165 ; misunderstanding of
Leibniz, 46 n ; his point of view
Cartesian, 166, 167 ; combination
of Monad ology with Atomism,
166; optimism, 168; teleology,
167; view of space, 168 sqq.;
relation to Kant, 168.

Words like algebraic symbols. 147.

World entirely in each of its parts,
50 n ; receptivity of, 341 ; its
physical and moral perfection,
345 ; best of all possible worlds,
66,248,271,345,417; infinity of
worlds, 65, n6n, 247 ; infinity
of worlds of living beings in
each particle of matter, 256.

Xenophon, 290.

Zeller, 43 n.
°t

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