Discourse on metaphysics, correspondence with Arnauld and monadology, with an introduction by Paul Janet ... tr. by George R. Montgomery

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THE LEIBNIZ MONUMENT NEAR THE THOMAS-KIRCHE IN LEIPSIC.

LEIBNIZ

DISCOURSE ON METAPHYSICS

CORRESPONDENCE WITH ARNAULD

AND MONADOLOGY

WITH AN INTRODUCTION BY PAUL JANET,
MEMBER OF THE FRENCH INSTITUTE.

TRANSLATED BY

DR. GEORGE R. MONTGOMERY

INSTRUCTOR IN PHILOSOPHY IN VALE UNIVERSITY

CHICAGO
THE OPEN COURT PUBLISHING COMPANY

LONDON AGENTS

KKGAN PAUL, TRENCH, TRUBNER & Co., LTD.
1908

TRANSLATION COPYRIGHTED

BY

THE OPEN COURT PUBLISHING Co.
1902.

/•fog

EDITOR'S PREFACE.

The present volume of Leibniz's writings, which now takes
its place in the "Philosophical Classics" alongside the works of
Descartes, Berkeley, Hume, and Immanuel Kant, is made up
of three separate treatises: (i) The Discourse on Meta-
physics, (2) Leibniz's Correspondence with Arnauld, and
(2) The Monadology. Together they form a composite and
logical whole, and afford an excellent survey of Leibniz's
thought. The first two, the Metaphysics and the Corre-
spondence with Arnauld, have never before been translated
into English, while the translation of the Monadology is new.
The thanks of the public for this translation are due to Dr.
George R. Montgomery, instructor in philosophy in Yale
University, and for the suggestion of making the translation
to Dr. G. M. Duncan, professor of philosophy in Yale Univer-
sity. The clear and admirable resume of the history of
philosophy in Libniz's time and of his own system from the
pen of the late Paul Janet, Member of the French Institute,
was added at the suggestion of the editor. Thus with the
index, all the necessary material has been furnished in this
volume for a comprehension of the thought of one of the most
versatile geniuses the world has produced.

"What a marvellously gifted man Leibniz was!" admirably
remarks Dr. Duncan. ' 'The king of Prussia truly said of him,
'He represents in himself a whole Academy' ; and George I. of
England was quite justified in saying, 'I count myself happy
in possessing two kingdoms, in one of which I have the honor
of reckoning a Leibniz, and in the other a Newton, among my
subjects. ' A brilliant mathematician, contesting with Newton
the honor of discovering the Calculus; a gifted psychologist
and epistemologist, equalling and surpassing, in his New
Essays, Locke's famous Essay; a profound theologian, writing
the most famous book on Theodicy which has ever been printed ;
a learned historian, producing a history of the House of
Brunswick commended by Gibbon himself; a far-sighted
statesman and diplomatist, honored at several of the most
powerful courts of Europe; a great philosopher, founder of

IV EDITOR S PREFACE.

modern German speculative philosophy and worthy to be
named with Kant himself; and, withal, an eminent scientist,
'a man of science, in the modern sense, of the first rank,' as
Professor Huxley calls him, — these are a few of his claims to
consideration. ' '

And the same author remarks as to the value of the present
selection from his writings:

"The profound and quickening thought of this most com-
prehensive thinker since Aristotle was never presented by him
in a more simple and untechnical form than in his Discourse
on Metaphysics and the correspondence with Arnauld relating
thereto. These together with the Monadology, the last sys-
tematic presentation of his philosophy written by him a quarter
of a century later, are here, at a nominal price, made accessible
to the general reading public and to university students. If
one will read these letters between Leibniz and Arnauld, and
then the Discourse on Metaphysics, and finally the Monad-
ology— and that is the best order in which to read the book —
one will be introduced in the simplest and the best possible
way to Leibniz's philosophy. The Discourse on Metaphysics
is probably the best account of his philosophy which he ever
wrote. His views underwent but little modification between
the writing of the Discourse of Metaphysics and the writing
of the Monadology. The only important difference is in the
introduction in the latter of a more artificial terminology."

In the present volume, therefore, The Open Court Pub-
lishing Company hopes to have rendered a considerable service
to the philosophical public.

THOMAS J. McCORMACK.

LA SALLE, ILL.,
August 20, 1902.

CONTENTS.

PAGE

THE LEIBNIZ MONUMENT NEAR THE THOMAS-KIRCHE IN

LEIPZIG ; Frontispiece

INTRODUCTION BY PAUL JANET VII

DISCOURSE ON METAPHYSICS i

CORRESPONDENCE BETWEEN LEIBNIZ AND ARNAULD . . 65
MONADOLOGY 249

INTRODUCTION.

By PAUL JANET.

When Descartes, in the first half of the seventeenth century,
said that there are only two kinds of things or substances
in nature, namely, extended substances and thinking substances,
or bodies and spirits ; that, in bodies, everything is reducible to
extension with its modifications of form, divisibility, rest and
motion, while in the soul everything is reducible to thinking
with its various modes of pleasure, pain, affirmation, reason-
ing, will, etc. . . ; when he in fact reduced all nature to a
vast mechanism, outside of which there is nothing but the
soul which manifests to itself its existence and its independ-
ence through the consciousness of its thinking, he brought
about the most important revolution in modern philosophy. To
understand its significance however an account must be given
of the philosophical standpoint of the time.

In all the schools at that time the dominant theory was that
of the Peripatetics, altered by time and misunderstood, the
theory of substantial forms. It posited in each kind of sub-
stance a special entity which constituted the reality and the
specific difference of that substance independently of the rela-
tion of its parts. For example, according to a Peripatetic of the
time, "fire differs from water not only through the position of
its parts but through an entity which belongs to it quite dis-
tinct from the materials. When a body changes its condition,
there is no change in the parts, but one form is supplanted by
another."* Thus, when water becomes ice, the Peripatetics
claimed that a new form substituted itself in place of the pre-
ceding form to constitute a new body. Not only did they
admit primary or basal entities, or substantial forms to explain
the differences in substances, but for small changes also, and
for all the sensible qualities they had what were called acci-
dental forms: thus hardness, heat, light were beings quite
different from the bodies in which they were found.

*L- P. I/agrange, Les Principes de la Philosophie contre les Nouveaux
Philosophes. — See Bouillier's Histoire de la Philosophie Cariesienne, Vol.
I. Chap. 26.

VII

VIII INTRODUCTION.

To avoid the difficulties inherent in this theory, the School-
men were led to adopt infinite divisions among the substantial
forms. In this way the Jesuits of Coimbre admitted three kinds
of these forms: first, the being which does not receive its exist-
ence from a superior being and is not received into an inferior
subject, — this being is God ; second, the forces which receive
their being from elsewhere without being themselves received
into matter, — these are the forms which are entirely free from
any corporeal concretion ; third, the forms dependent in every
respect, which obtain their being from a superior cause and
are received into a subject, — these are the accidents and the
substantial forms which determine matter.

Other Schoolmen adopted divisions still more minute and
distinguished six classes of substantial forms, as follows: first,
the forms of primary matter or of the elements ; second, those
of inferior compounds, like stones ; third, those of higher com-
pounds, like drugs ; fourth those of living beings, like plants ;
fifth, those of sensible beings, like animals; sixth, above all
the rest, the reasoning (rationalis) substantial form which is
like the others in so far as it is the form of a body but which
does not derive from the body its special function of thinking.

Some have thought, perhaps, that Moliere, Nicole, Male-
branche and all those who in the seventeenth century ridiculed
the substantial forms, calumniated the Peripatetic Schoolmen
and gratuitously imputed absurdities to them. But they
should read the following explanation, given by Toletus, of
the production of fire: "The substantial form of fire," says
Toletus, "is an active principle by which fire with heat for an
instrument produces fire." Is not this explanation even more
absurd than the -virtus dormitivaf The author goes on to
raise an objection, that fire does not always come from fire.
To explain this he proceeds, "I reply that there is the great-
est difference between the accidental and the substantial forms.
The accidental forms have not only a repugnance but a
definite repugnance, as between white and black, while
between substantial forms there is a certain repugnance but it
is not definite, because the substantial form repels equally all
things. Therefore it follows that white which is an accidental
form results only from white and not from black, while fire
can result from all the substantial forms capable of producing it
in air, in water or in any other thing."

INTRODUCTION. IX

The theory of substantial or accidental forms did more than
to lead to nonsense like the above ; it introduced errors which
stood in the way of any clear investigation of real causes. For
example, since some bodies fell toward the earth while others
rose in the air, it was said that gravity was the substantial form
of the former and lightness of the latter. Thus heavy and
light bodies were distinguished as two classes of bodies having
properties essentially different, and they were kept from the
inquiry whether these apparently different phenomena did not
have an identical cause and could not be explained by the same
law. It was thus again that seeing water rise in an empty
tube, instead of inquiring under what more general fact this
phenomena could be subserved, they imagined a -virtue, an
occult quality, a hatred on the part of the vacuum, and this
not only concealed the ignorance under a word void of sense
but it made science impossible because a metaphor was taken
for an explanation.

So great had become the abuse of the substantial forms, the
occult qualities, the sympathetic virtues, etc., that it was a
true deliverance when Gassendi on the one hand and Descartes
on the other founded a new physics on the principle that there
is nothing in the body which is not contained in the mere
conception of bodies, namely extension. According to these
new philosopners all the phenomena of bodies are only modi-
fications of extension and should be explained by the proper-
ties inherent in extension, namely, form, position, and motion.
Upon this principle nothing happens in bodies of which the
understanding is not able to form a clear and distinct idea.
Modern physics seems to have partially confirmed this theory,
when it explains sound and light by movements (vibrations,
undulations, oscillations, etc.), either of air or of ether

It has often been said that the march of modern science has
been in the opposite direction from the Cartesian philosophy,
in that the latter conceives of matter as a dead and inert sub-
stance while the former represents it as animated by forces,
activities and energies of every kind. This it seems to me is
to confuse two wholly different points of view, that is the phys-
ical and the metaphysical points of view. The fact seems to
be that from the physical point of view, science has rather
followed the line of Descartes, reducing the number of occult
qualities and as far as possible explaining all the phenomena

X INTRODUCTION.

in terms of motion. In this way all the problems tend to
become problems of mechanics ; change of position, change of
form, change of motion — these are the principles to which our
physicists and our chemists have recourse whenever they can.
It is therefore wrong to say that the Cartesian line of
thought has completely failed and that modern science has
been moving away from it more and more. On the contrary
we are witnessing the daily extension of mechanicalism in the
science of our time. The question takes on a different phase
when it is asked whether mechanicalism is the final word of
nature, whether it is self-sufficient, in fact whether the princi-
ples of mechanicalism are themselves mechanical. This is a
wholly metaphysical question and does not at all affect positive
science ; for the phenomena will be explained in the same way
whether matter is thought of as inert, composed of little par-
ticles which are moved and combined by invisible hands, or
whether an interior activity and a sort of spontaneity is
attributed to them. For the physicist and for the chemist,
forces are only words representing unknown causes. For the
metaphysician they are real activities. It is metaphysics,
therefore, and not physics which is rising above mechanicalism.
It is in metaphysics that mechanicalism has found, not its
contradiction, but its completion through the doctrine of dyn-
amism. It is this latter direction that philosophy has mainly
taken since Descartes and in this the prime mover was
Leibniz.*

* We give here in a note the resume of Leibniz's life and the names of
his principal works. Leibniz (Gottfried Wilhelm) was born at Leipzig in
1646. He lost his father at the age of six years. From his very infancy he
gave evidence of remarkable ability. At fifteen years of age he was ad-
mitted to the higher branches of study (philosophy and mathematics) which
he pursued first at Leipzig and then at Jena. An intrigue not very well
understood prevented his obtaining his doctor's degree at Leipzig and he
obtained it from the small university of Altdorf near Nuremberg, where he
made the acquaintance of Baron von Boineburg, who became one of his
most intimate friends and who took him to Frankfort. Here he was named
as a councillor of the supreme court in the electorate of Mainz, and wrote
his first two works on j urisprudence. The Study of Law and The Reform of
the Corpus Juris. At Frankfort also were written his first literary and
philosophical works and notably his two treatises on motion: Abstract Mo-
tion, addressed to the Academy of Sciences at Paris, and Concrete Motion,
addressed to the Royal Society at London. He remained with the Elector
till the year 1672, when he began his journeys. He first went to Paris and
then to London, where he was made a member of the Royal Society. Re-
turning to Paris he remained till 1677, when he made a trip through Hol-
land, and finally took up his residence at Hanover, where he was appointed
director of the library. At Hanover he lived for ten years, leading a very

INTRODUCTION. XI

In order to understand Leibniz's system we must not forget a
point to which sufficient attention has not been paid, namely,
that Leibniz never gave up or rejected the mechanicalism of
Decartes. He always affirmed that everything in nature
could be explained mechanically ; that, in the explanation of
phenomena, recourse must never be had to occult causes ; so
far indeed did he press this position that he refused to admit
Newton's attraction of gravitation, suspecting it of being an
occult quality : while, however, Leibniz admitted with Descartes
the application of mechanicalism he differed from him in regard
to the basis of it and he is continually repeating that if every-
thing in nature is mechanical, geometrical and mathematical
the source of mechanicalism is in metaphysics.*

Descartes explained everything geometrically and mechani-

busy life. He contributed to the founding of the Ada Eruditorum, a sort of
journalof learning. From 168710 1691,31 the request ofhis patron, Duke
Ernst-Augustus, he was engaged in searching various archives in Ger-
many and Italy for the writing of the history of the house of Brunswick. To
him the Academy of Berlin, of which he was the first president, owes its
foundation. The last fifteen years of his life were given up principally to
philosophy. In this period must be placed the New Essays, the "Theodicy,
the Monadology, and also his correspondence with Clarke, which was
interrupted by his death— November 14, 1716. For fuller details, see
Guhrauer's learned and complete biography, 2 yols, Breslau, 1846. During
the life-time of Leibniz, aside from the articles in journals, only some five
of his writings were published, including his doctor's thesis, De Principle
Individui (1663), and the Theodicee (1710). After his death (1716) all his papers
were deposited in the library at Hanover, where they are to-day, a great
part of them (15,000 letters) still unpublished. In 1717-1719 appeared the
Correspondence with Locke; in 1720 a German translation of the Mon-
adology; in 1765 his Oeuvres Philosophiques, etc., includingthe New Essays on
the Human understanding; in 1768 Duten's edition of his works in six vol-
umes; in 1840 appeared Erdmann's edition of his works, including among
other unpublished writings the original French of the Monadology. The
Correspondence with Arnauld and the Treatise on Metaphysics were first
published by Grotefend in 1840. Gerhardt published Leibniz's math-
ematical works 1843 to 1863, and the Philosophical Works (seven volumes),
1875-1890. In 1900 Paul Janet, who had already published the Philosophical
Works (1866) in two volumes, brought out a second edition, revised and en-
larged. The first English translation of Leibniz's works was made by
Professor G. M. Duncan, who included in one volume all of the better
known shorter works (1890). This was followed in 1896 with a translation
of the New Essays by A. G. Langley. Latta's translation of some of the
shorter works, including the Monadology, has earned a well-merited reputa-
tion, and Russell's work on Leibniz's philosophy contains much that is
suggestive to a translator.

'Letter to Schulemburg (Dutens, T. Ill, p. 332): "The Cartesians rightly
felt that all particular phenomena of bodies are produced mechanically, but
they failed to see that the sources of mechanicalism in turn arise in some
other cause." Letter to Reniond de Montmort (Erdman, Opera Philo-
sophica,^. 702): "When I seek for the ultimate reasons of mechanicalism
and the laws of motion I am surprised to discover that they are not to be
found in mathematics and that we must turn to metaphysics." — See also:
De Natura Ipsa, 3; De Origine Radicali; Animadversiones in Cartesiunt
Guhrauer, p. 80), etc.

XII INTRODUCTION.

cally, that is by extension, form, and motion, just as Democritus
had done before ; but he did not go farther, finding in exten-
sion the very essence of corporeal substance. Leibniz's genius
showed itself when he pointed out that extension does not
suffice to explain phenomena and that it has need itself of an
explanation. Brought up in the scholastic and peripatetic
philosophy, he was naturally predisposed to accord more of
reality to the corporeal substance, and his own reflections soon
carried him much farther along the same line.

It is also worth noticing, as Guhrauer has said in his Life of
Leibniz, that it was a theological problem which put Leibniz
upon the track of reforming the conception of substance. The
question was rife as to the real presence in transubstantia-
tion. This problem seemed inexplicable upon the Cartesian
hypothesis, for if the essence of a body is its extension, it is a
contradiction that the same body can be found in several places
at the same time. Leibniz, writing to Arnauld in 1671, says
he thinks he has found the solution to this great problem, since
he has discovered ' 'that the essence of a body does not consist
in extension, that the corporeal substance, even taken by
itself, is not extension and is not subject to the conditions of
extension. This would have been evident if the real character
of substance had been discovered sooner."

Leaving aside this point, however, the following are the
different considerations which led Leibniz to admit non-
mechanical principles as above corporeal mechanicalism, and to
reduce the idea of the body to the idea of active indivisible sub-
stances, entelechies or monads, having innate within them-
selves the reason for all their determinations.

i. The first and principal reason which Leibniz brings up
against Descartes is that, "If all that there is in bodies is
extension and the position of the parts, then when two bodies
come into contact and move on together after the contact,
that one which was in motion will carry along the body at rest
without losing any of its velocity, and the difference in the sizes
of the bodies will effect no change," which is contrary to expe-
rience. A body in motion which comes in contact with one at
rest loses some of its velocity and its direction is modified,
which would not happen if the body were purely passive.
"Higher conceptions must therefore be added to extension,
namely, the conceptions of substance, action and force ; these

INTRODUCTION. XIII

latter carry the idea that that which suffers action, acts recipro-
cally and that that which acts is reacted upon." *

2. Extension cannot serve to give the reason for the
changes which take place in bodies, for extension with its
various modifications constitutes what is called in the school
terminology extrinsic characteristics, whence nothing can result
for the being itself ; whether a body be round or square does
not affect its interior condition, nor can any particular change
result for it. f Furthermore every philosophy which is exclu-
sively mechanical is obliged to deny change and to hold that
everything is changeless and that there are only modifications
of position or displacements in space or motion. Who does
not see, however, that motion itself is a change, and should
have its reason in the being which moves or which is moved,
for even passive motion must correspond to something in the
essence of the body moved? Besides if corporeal elements
differ from one another through form, why have they one form
rather than any other? Epicurus talks to us of round and
hooked atoms. Why is a certain atom round and another
hooked? Should not the reason be in the very substance of the
atom? Therefore form, position, motion and all the extrinsic
modifications of bodies should emanate from an internal
principle analogous to that which Aristotle calls nature or
entelechy. \

3. Extension cannot be substance. On the contrary it pre-
supposes substance. "Aside from extension there must be a
subject which is extended, that is, a substance to which con-
tinuity appertains. For extension signifies only a continued
repetition or multiplication of that which is expanded, a plu-
rality, a continuity or co-existence of parts and consequently it
does not suffice to explain the real nature of expanded or repeated
substance whose conception precedes that of repetition." §

4. Another reason given by Leibniz is that the conception of

* Letter, Whether the essence of bodies consists in extension, 1691 (Erd-
maim, Vol. 27, p. 112).

&uur>iiiui_c aiiuuiu. — ivClici LU .ni uduiu*

\Confessio Naturae Contra Artheista, 1668, Erdm., p. 45. Leibniz in
this little treatise proves: ist, that bodies and indeed atoms have not in
themselves the reason for their forms; 2d, that they have not the reason for
their motion: 3d, that they have not the reason for their coherence.

§ Extract from a letter (Erdmann, Vol. 28, p. 115): Examination of the
principles of Malebranche (Erdmanu, p. 692).

XIV INTRODUCTION.

substance necessarily implies the idea of unity. No one thinks
that two stones very far apart form a single substance. If now
we imagine them joined and soldered together, will this juxta-
position change the nature of things? Of course not; there
will always be two stones and not a single one. If now we
imagine them attached by an irresistible force, the 'impossibility
of separating them will not prevent the mind from distin-
guishing them and will not prevent their remaining two and
not one. In a word every compound is no more a single sub-
stance than is a pile of sand or a sack of wheat. We might
as well say that the employees of the India Company formed
a single substance.* It is evident therefore that a compound
is never a substance and in order to find the real substance we
must attain unity or the indivisible. To say that there are no
such unities is to say that matter has no elements, in other
words that it is not made up of substance but it is a pure phe-
nomenon like the rainbow. The conclusion is then either that
matter has no substantial reality or else it must be admitted
that it is reducible to simple and consequently unextended
elements, called monads,

5. Leibniz brings forward another argument in behalf of
his theory of monads. This is that the essence of every sub-
stance is in force, which fact is as true of the soul as of the body.
It can be proved a priori. Is it not evident that a being really
exists only in so far as it acts? A being absolutely passive
would be a pure nothing, and would involve a contradiction ;
or, by hypothesis, receiving everything from outside and hav-
ing nothing through itself, it would have no characteristic, no
attribute and hence would be a pure nothing. The mere fact
of existence, therefore, already supposes a certain force and a
certain energy.

Leibniz presses this thought of the activity of substances so
far that he even admits no degree of passivity. According to

* " If the parts which act together for a common purpose, more properly
compose a substance than do those which are in contact, then all the offi-
cials of the India Company would much better constitute a real substance
than would a pile of stones. What else, however, is a common purpose
rather than a resemblance or indeed an orderliness which our minds notice
in different things? If on the other hand the unity by contact be made the
basis, other difficulties arise. The parts of solid bodies are united perhaps
only by the pressure of surrounding bodies, while inthemselves and ifc their
substance there is no more union than in a heap of sand, arena sine calce.
Why do many rings when interlaced to form a chain compose a veritable
substance rather than when there are openings so that they can be taken
apart? . . . They are all fictions of the mind." (Letter to Arnauld;.

INTRODUCTION XV

him, no substance is, properly speaking, passive. Passion in
a substance is nothing else than an action considered bound
to another action in another substance. Every substance acts
only through itself and cannot act upon any other. The
monads have no windows through which to receive anything
from outside. They do not undergo any action and conse-
quently are never passive. All that takes place in them is the
spontaneous development of their own essence. All that there
is, is that the states of each one correspond to the states of all
the others. When we consider one of these states in one
monad as corresponding to a certain other state in another
monad, in such a way that the latter is the condition of the
former, the first state* is called a passion and the second an
action. There is, therefore, between all monad-substances a
pre-established harmony, in accordance with which each one
represents (or expresses, as Leibniz says) the whole universe.
But this is ever only the development of its own activity.

In restoring to created substances the activity which the
Cartesian school had too much sacrificed, Leibniz thought to
contribute to the clearer distinction between the created and
the Creator. He justly remarked that the more the activity of
the created things is diminished, the more necessary becomes
the intervention of God, in such a way that if all activity in
created things is suppressed, then we must say that it is God
who brings everything in them to pass and who is at the same
time their being and their action (operari et esse). What
difference, however, is there between this point of view and
that of Spinoza? Would we not thus make nature the life and
the development of the divine nature? In fact, by this hypothe-
sis, nature is reduced to a mass of modes of which God is the
substance. He, therefore, is all that there is of reality in bodies
as well as in spirits.

To these -five fundamental reasons given by Leibniz it will
perhaps be allowed us to add a few particular considerations.

Those who deny that the essence of bodies is only in
force, either admit the vacuum with the atomists, ancient and
modern, or else like the Cartesians they do not admit it. Let
us take up each of these positions separately.

For the atomists, disciples of Democritus and of Epicurus,
or of Gassendi, the universe is composed of two elements, the
vacuum and the plenum, on the one hand space and on the

XVI INTRODUCTION.

other hand bodies. The bodies are reducible to a certain
number of solid corpuscles, indivisible, with differing forms,
heavy and animated by an essential and spontaneous motion.
These are the atoms which by their coming together constitute
bodies.

Now it is evident that atoms in taking the place of other
atoms, successively occupy in empty space places that are
adequate to them, which have exactly the same extension and
the same forms as the respective atoms. If at the moment
when an atom is motionless in some place we imagine lines
drawn following its contours (as when an object is being traced
for transferring), is it not clear that if the atom were removed,
we should have preserved its effigy, or a sort of silhouette, its
geometric form upon a foundation of empty space? We should
obtain thus a portion of space, which I will call an empty
atom, in contrast with the full atom which was there before.

Now I ask the atomists to explain what distinguishes the
full atom from the empty one, what are the characteristics that
-may be found in one and not in the other. Is it the being
extended? No, for the empty atom is extended like the full
atom. Is it the having a form? No, for the empty atom has
a form as has the full atom and exactly the same form. Is
it the being indivisible? No, for it is still more difficult to
understand the divisibility of space than of the body. In a
word everything which depends on extension is the same in
the empty atom as in the full atom. But the empty atom is
not a body and contains nothing corporeal ; therefore extension
is not the essence of bodies and perhaps does not constitute a
part of this essence. May we say that it is the motion which
distinguishes the full atom from the empty atom? But before
beginning to move the atom must have already been some-
thing, because that which is nothing in itself can be neither at
rest, nor in motion. Motion, therefore, is a dependent and
subordinate phenomenon which already presupposes a defined
essence. If we examine carefully we will see that what really
distinguishes the full atom from the empty atom is its solidity
or weight. Neither solidity nor weight, however, are modifica-
tions of extension ; both come from force. It is accordingly,
force and not extension which constitutes the essence of the
body.

Turning now to those who, like the Cartesians, are unwill-

INTRODUCTION. XVII

ing to admit the "possibility of a vacuum and maintain that all
space is full, the demonstration is still more simple, for we may
ask in what filled space, taken in its entirety, differs from
empty space taken in its entirety. Both are infinite; both are
ideally divisible and both are really indivisible ; both are sus-
ceptible of modalities in form or of geometrically defined forms.
Perhaps it will be claimed that in full space the particles are
movable and can supplant one another; in this case we are
back in the preceding line of argument and we shall ask in
what these movable particles are distinguished from the
immovable particles of space among which they move. Thus
the Cartesians, like the atomists, will be obliged to recognize
that the plenum is distinguished from the vacuum only by
resistance, solidity, motion, activity, in a word, force.

To those who reproach the Leibnizian conception with
idealizing matter too much, it may be replied that matter
taken in itself is necessarily ideal and super-sensible. Of
course it cannot be said that a body is only an assembly of
subjective modifications. The Berkeleyan idealism is a super-
ficial idealism, which will not stand examination; for when I
shall have reduced the whole universe to a dream of my mind
and to an expansion of myself the question will still remain
whence comes this my dream and what are the causes which
have produced in me so complicated a hallucination; these
causes are outside of me and they go beyond me on every
side ; it. would therefore be very inappropriate for me to call them
myself, for the I is strictly that of which I have consciousness.
The Fichtean Ich, which by reaction against itself thus pro-
duces the nicht-ich is only a complicated and artificial circum-
locution for saying in a paradoxical form that there is a not-I.
At most, we can conjecture with the absolute idealism that
the I and the not-I are only two faces of one and the same
being, which involves them both in an infinite activity; but
we thus reach a position very far from the idealism of Berkeley.

To return to the idealism of Leibniz, I think it can be shown
a priori that matter taken in itself is something ideal and
super-sensible, at least to those who admit a divine intelligence.
For it will readily be granted that God does not know matter
by means of the senses ; for it is an axiom in metaphysics that
God has no senses and consequently cannot have sensations.
Thus: God can be neither warm nor cold; he cannot smell the

XVIII INTRODUCTION.

odor of flowers ; he cannot hear'sounds, he cannot see colors ;
he cannot feel electrical disturbances, etc. In a word, since he
is a pure intelligence he can conceive only the purely intelligi-
ble ; not that he is ignorant of any of the phenomena of nature,
only that he knows them in their intelligible reasons and not
through their sensible impressions, by means of which creatures
are aware of them. Sensibility supposes a subject with senses,
organs and nerves, that is, it is a relation between created
things. From God's point of view, therefore, matter is not
sensible; it is, as the Germans say, ubersinnlich. The con-
clusion is easy to draw, namely, that God, being absolute
intelligence, necessarily sees things as they are, and con-
versely the things in themselves are such as he sees them.
Matter is, accordingly, such in itself as God sees it, but he
sees it only in its ideal and intelligible essence ; whence we
see that matter is an intelligible something and not something
sensible.

To be sure we may not conclude from this point that the
essence of matter does not consist in extension, for it could be
maintained that extension is an object of pure intelligence
quite as well as force. But without taking up the difficulty
of disengaging extension from every sensible element, I wish
to establish only one thing, namely that Leibniz cannot [be
reproached with idealizing matter, since this must be done in
every system, at least in those which admit a divine logos and
a foreordaining reason.

One of the most widely spread objections against the
monadological system is the impossibilty of composing an
extended whole out of non-extended elements. This is Euler's
principal objection in one of his Letters to a German Princess
and he considered it absolutely definitive because the necessary
consequence of such a system would be to deny the reality of
extension and of space, and to launch out thus into all the
difficulties of the idealistic labyrinth. I think, however, that
Euler's objection is not at all insoluble, and that it is even
possible to separate the system of monads from the system of
the ideality of space. It can be shown that all the questions
relating to space can be adjourned or kept back without com-
promising the hypothesis of the monads.

For, let us suppose with the atomists, with Clarke and
Newton, the reality of space, vacuums, and atoms. It is no

INTRODUCTION. XIX

more difficult to conceive of monads in space than of atoms ; a
point of indivisible activity might be at a certain point of space
and a collection of the points of activity would constitute the
mass which we call a body. Now, even if we grant that these
points of activity are separated by space, yet when they were
taken together they might produce upon the senses the
impression of continuous space. Even in the case of what is
called a body, say a marble table, every one knows that there
are forces, that is to say, vacuums, between the parts. Since
these vacuums, however, escape our sense organs, the body
appears to us to be continuous, like the circle described by a
moving succession of luminous points. In fact the bodies
would be composed, as the Pythagoreans have already said, of
two elements; the intervals (Stcurri^iaTa) and the monads
(nbvadet) ; except that the Pythagorean monads were mere
geometric points, while for Leibniz they are active points,
radiating centers of activity, energies.

Regarding the difficulty of admitting into space forces non-
extended and consequently having no relation to space, I grant
that it is very serious. It cannot be raised, however, b/ those
who consider the soul as a non-extended force and as an indi-
vidual substance ; for they are obliged to recognize that it is
in space although in its essence it has no relation to space;
there is, therefore, for them no contradiction in holding that a
simple force is in space. If, on the other hand, it be denied
that the soul is in space, that it is in the body, and even
that it is in a certain part of the body, is it not clear that this
would be attributing to the soul a character which is true only
of God? To be sure, those who consider the soul as a divine
idea, an eternal form temporarily united to an individual,
might speak thus. Thus regarded, with the idealists or with
Spinoza, the soul is not in space. But if the soul is represented
as an individual and created substance, how can it be thought
of except as in space and in the body to which it is united?
Still more, therefore, in the case of monads will we be obliged
to admit that they may be in space and then, as we have seen,
the appearance of extension is explained without difficulty.

If, now, instead of admitting the reality of space we hold
with Leibniz or with Kant that it is ideal, the system of
monads offers no longer any serious difficulty, except from the
point of view of those who deny the plurality of individual

XX INTRODUCTION.

substances. In any case Euler's objection evidently loses its
force.

Another difficulty raised against the monadology is that it
effaces the distinction between the soul and the body. This
difficulty seems to me like the preceding one to be merely
apparent. Because in every hypothesis, the essential distinc-
tion between the body and the soul is that the body is a com-
posite, while the soul is simple. In order to prove that the
soul is not extended the proof is offered that it is not a com-
posite, while the body on the contrary is. Now in Leibniz's
hypothesis also, the body is only a composite, only an aggrega-
tion of simple elements. What difference does the nature of
the elements make in this case? It is the whole, it is the
aggregation which we contrast with the soul ; and in Leibniz's
hypothesis, quite as well as in that of Descartes, the body as
an aggregation is wholly incapable of thought.

Some one will reply: "granting all that, the elements are
nevertheless single and indivisible like the soul itself and they
are therefore of the same nature as the soul — they are souls
themselves. ' ' This last consequence is very incorrectly drawn,
however.

What is meant by the words : "of the same nature"? Does
it mean that the monads which compose the body are feeling,
thinking, willing beings? Leibniz never said such a thing.
What is the basis for affirming that the particles of my body
are thinking substances? Let us look at the semblance they
have to the soul. Doubtless they are like it single and indivisi-
ble substances. But what difficulty does it introduce to admit
that the soul and body have common attributes? The atoms,
for instance, have they not in common with the soul, existence,
indestructibility, self -identity? And does the argument of the
identity of the ego in contrast with the changing nature of
organized matter, cease to be valid, because the atom is quite
as self-identical as the soul? Indeed the indestructibility of
the atom is used as an analogy to establish the indestructi-
bility of the soul. If this common character does not prevent
their being distinguished, why should their being distinguished
be more difficult when they have in common a character essen-
tial to all substance, namely, the attribute of activity?

Furthermore, if the atoms of the substance, which constitutes
the universe, are indivisible units, the power of thinking is not

INTRODUCTION. XXI

inconsistent with their conception. They may be thinking
substances, and it cannot be denied that in this system a
monad may become, if God wishes it, a thinking soul. If on
the one hand it is not impossible, there is no way, on the other
hand, of proving that it may be so. Why may there not be
several orders of monads which are unable to pass from one
class to another? Why may there not be monads having
merely mechanical properties ; others of a higher order, con-
taining the principle of life, like plant souls ; still higher sen-
sitive souls; and finally free and intelligent souls endowed
with personality and immortality? Leibniz's system is no more
opposed than any other to these orders.

If, however, by a bolder hypothesis, the possibility of a
monad's passing from one order to another be admitted, there
would still be nothing here degrading to the true dignity of
man, for, after all it must be recognized that the human soul
in its first state is hardly anything more than a plant-soul
which lifts itself by degrees to the condition of a thinking soul.
Therefore there will be no contradiction in admitting that
every monad contains potentially a thinking soul. Should
such a hypothesis be repugnant, I still maintain that the mon-
adological system does not force one to it, since monadism
quite as well as the popular atomism can admit a scale of
substances essentially distinct from one another.

Another objection which the Leibnizian excites, and one
which Arnauld does not fail to raise in one of his letters, is
that the system of monads weakens the argument of a first
mover, since it implies that matter can be endowed with
active force and consequently with spontaneous motion.
Leibniz does not meet this objection in a convincing manner
and says merely that recourse must be had to God to explain
the co-ordination of movements. This, however, avoids the
point, for the co-ordination has no relation to the argument of
the first mover, only to that of the ordering and of the arrange-
ment which is a wholly different matter. We may, however,
remark that Leibniz, in order • to establish the reality of the
force in corporeal substance, much more frequently uses the
fact of resistance to motion, than that of the so-called spon-
taneous motion. For instance, one of his principal arguments
is that a moving body, when it comes in contact with another,
loses motion in proportion to the resistance which the other

XXII INTRODUCTION.

opposes to it, and this is what he calls inertia. It is evi-
dent, therefore that if a substance in repose reveals itself by
its resistance to motion, the argument of the first mover, far
from being weakened is, on the contrary, strengthened.

Besides this, even if a spontaneous disposition to movement,
be admitted in the elements of bodies, yet experience compels
us to recognize that this disposition passes over into action only
upon the excitation of an exterior action because we never see
a body put in motion except in the presence of another. The
actual indifference to movement and to repose, which at the
present time is called, in mechanics, inertia, must always be
admitted, whether we posit in the body a virtual disposition to
movement or whether, on the contrary, the body be considered
as absolutely passive ; in either case there must be a cause deter-
mining the motion ; it is not necessary that this first cause pro-
duce everything in the body moved, and that it should be in
some sort the total cause of the motion ; sufficient is it for it to be
the complementary cause as the Schoolmen used to say.

Furthermore inertia must not be confounded with absolute
inactivity. Leibniz showed admirably that an absolutely
passive substance would be a pure nothing; that a being is
active in proportion as it is in existence; in a word, that to
be and to act are one and the same thing. From the fact,
however, that a substance is essentially active, it does not nee.
essarily follow that it is endowed with spontaneous motion, for
th e latter is only a special mode of activity and is not the only
one. For example, resistance, or impenetrability, is a certain
kind of activity, but is not motion. They are mistaken, there-
fore, who think that the theory of active matter does away
with a first cause for motion, because even if motion be essential
to matter, we will still have to explain why no portion of mat-
ter is ever spontaneously in motion.

In short, according to Leibniz, every being is essentially
active. That which does not act does not exist ; quid non
agtt non existit. Now, whatever acts is force ; therefore, every-
thing is force or a compound of forces. The essence of matter
is not, as Descartes thought, inert extension, it is action, effort,
energy. Furthermore the body is a compound and the com*
pound presupposes a simple. The forces, therefore, which
compose the body are simple elements, unextended — incor-
poreal atoms. Thus the universe is a vast dynamism, a wise

INTRODUCTION. XXIII

system of individual forces, harmoniously related under the
direction of a primordial force, whose absolute activity permits
the existence outside of itself of the appropriate activities of
created things, which it directs without absorbing them. This
system, therefore, may be reduced to three principal points:
i, it makes the idea of force predominate over the idea of sub-
stance, or rather reduces substance to force; 2, it sees in exten-
sion only a mode of appearance of force and compares the
bodies of simple and unextended elements as more or less
analogous, except in their degree, to what is called the soul ;
3, it sees in the forces not only general agents or modes of
action of a universal agent, as have the scientists, but it sees
also individual principles, both substances and causes which are
inseparable from the material, or rather which constitute mat-
ter itself; Dynamism thus understood, is only universal
spiritualism.

In this introduction I have examined the different difficul-
ties which might be raised against the Leibnizian Monadology
from the point of view of the Cartesian spiritualism. They
have still to be examined from the point of view of those who
deny the plurality of substances, that is, from the Spinozistic
or pantheistic point of view. Here, however, come in a wholly
different class of ideas, which we cannot enter upon without
extending this introduction beyond measure. We will merely
say that the force of Leibniz's system is in the fact of individ-
uality, of which the advocates of the unity of substance have
never been able to give an explanation. It is true, we must
pass here from the objective to the subjective standpoint,
because it is in the consciousness that the individuality mani-
fests itself in the most striking manner, while in nature it is
more veiled. One's position, therefore, should be taken in the
region of the individual consciousness in order to combat
Spinozism. This point of view has been particularly devel-
oped in our day by Maine de Biran and by his school. We
have been content to mention it merely, not desiring to skim
over a problem which is connected with the knottiest points of
metaphysics and of the philosophy of religion.

METAPHYSICS.

METAPHYSICS.

I. Concerning the divine perfection and that God
does everything in the most desirable way.

The conception of God which is the most common
and the most full of meaning is expressed well
enough in the words: God is an absolutely perfect
being. The implications, however, of these words
fail to receive sufficient consideration. For in-
stance, there are many different kinds of perfection,
all of which God possesses, and each one of them
pertains to him in the highest degree.

We must also know what perfection is. One
thing which can surely be affirmed about it is that
those forms or natures which are not susceptible of
it to the highest degree, say the nature of numbers
or of figures, do not permit of perfection. This is
because the number which is the greatest of all (that
is, the sum of all the numbers), and likewise the
greatest of all figures, imply contradictions. The
greatest knowledge, however, and omnipotence
contain no impossibility. Consequently power and
knowledge do admit of perfection, and in so far as
they pertain to God they have no limits.

Whence it follows that God who possesses
supreme and infinite wisdom acts in the most per-
fect manner not only metaphysically, but also from
the moral standpoint. And with respect to our-

3

4 LEIBNIZ.

selves it can be said that the more we are
enlightened and informed in regard to the works
of God the more will we be disposed to find them
excellent and conforming entirely to that which we
might desire.

II. Against those who hold that there is in the
works of God no goodness, or that the principles of
goodness and beauty are arbitrary.

Therefore I am far removed from the opinion of
those who maintain that there are no principles of
goodness or perfection in the nature of things, or
in the ideas which God has about them, and who
say that the works of God are good only through
the formal reason that God has made them. If this
position were true, God, knowing that he is the
author of things, would not have to regard them
afterwards and find them good, as the Holy Scrip-
ture witnesses. Such anthropological expressions
are used only to let us know that excellence is
recognized in regarding the works themselves, even
if we do not consider their evident dependence on
their author. This is confirmed by the fact that it
is in reflecting upon the works that we are able to
discover the one who wrought. They must there-
fore bear in themselves his character. I confess
that the contrary opinion seems to me extremely
dangerous and closely approaches that of recent
innovators who hold that the beauty of the universe
and the goodness which we attribute to the works
of God are chimeras of human beings who think
of God in human terms. In saying, therefore, that
things are not good according to any standard of
goodness, but simply by the will of God, it seems

DISCOURSE ON METAPHYSICS. 5

to me that one destroys, without realizing it, all
the love of God and all his glory; for why praise
him for what he has done, if he would be equally
praiseworthy in doing the contrary? Where will
be his justice and his wisdom if he has only a cer-
tain despotic power, if arbitrary will takes the place
of reasonableness, and if in accord with the defini-
tion of tyrants, justice consists in that which is
pleasing to the most powerful? Besides it seems
that every act of willing supposes some reason for
the willing and this reason, of course, must precede
the act. This is why, accordingly, I find so strange
those expressions of certain philosophers who say
that the eternal truths of metaphysics and Geometry,
and consequently the principles of goodness, of
justice, and of perfection, are effects only of the will
of God. To me it seems that all these follow from
his understanding, which does not depend upon his
will any more than does his essence.

III. Against those who think that God might have
made things better than he has.

No more am I able to approve of the opinion of
certain modern writers who boldly maintain that
that which God has made is not perfect in the
highest degree, and that he might have done better.
It seems to me that the consequences of such an
opinion are wholly inconsistent with the glory of
God. Uti minus malum habet rationem boni, ita
minus bonum habet rationem mali. I think that one
acts imperfectly if he acts with less perfection
than he is capable of. To show that an architect
could have done better is to find fault with his
work. Furthermore this opinion is contrary to the

6 LEIBNIZ.

Holy Scriptures when they assure us of the good-
ness of God's work. For if comparative perfection
were sufficient, then in whatever way God had
accomplished his work, since there is an infinitude
of possible imperfections, it would always have
been good in comparison with the less perfect; but
a thing is little praiseworthy when it can be praised
only in this way.

I believe that a great many passages from the
divine writings and from the holy fathers will be
found favoring my position, while hardly any will
be found in favor of that of these modern thinkers.
Their opinion is, in my judgment, unknown to the
writers of antiquity and is a deduction based upon
the too slight acquaintaince which we have with
the general harmony of the universe and with the
hidden reasons for God's conduct. In our igno-
rance, therefore, we are tempted to decide auda-
ciously that many things might have been done
better.

These modern thinkers insist upon certain hardly
tenable subtleties, for they imagine that nothing is
so perfect that there might not have been something
more perfect. This is an error. They think,
indeed, that they are thus safeguarding the liberty
of God. As if it were not the highest liberty to
act in perfection according to the sovereign reason.
For to think that God acts in anything without hav-
ing any reason for his willing, even if we overlook
the fact that such action seems impossible, is an
opinion which conforms little to God's glory. For
example, let us suppose that God chooses between
A and B, and that he takes A without any reason
for preferring it to B. I say that this action on the

DISCOURSE ON METAPHYSICS. ^

part of God is at least not praiseworthy, for all
praise ought to be founded upon reason which ex
hypothesi is not present here. My opinion is that
God does nothing for which he does not deserve to
be glorified

IV. That love for God demands on our part complete
satisfaction with and acquiescence in that which he has
done.

The general knowledge of this great truth that
God acts always in the most perfect and most
desirable manner possible, is in my opinion the basis
of the love which we owe to God in all things; for
he who loves seeks his satisfaction in the felicity
or perfection of the object loved and in the perfec-
tion of his actions. Idem velle et idem nolle vera
amicitia est. I believe that it is difficult to love
God truly when one, having the power to change
his disposition, is not disposed to wish for that
which God desires. In fact those who are not
satisfied with what God does seem to me like dis-
satisfied subjects whose attitude is not very differ-
ent from that of rebels. I hold therefore, that on
these principles, to act conformably to the love of
God it is not sufficient to force oneself to be patient,
we must be really satisfied with all that comes to
us according to his will. I mean this acquiescence
in regard to the past; for as regards the future one
should not be a quietist with the arms folded,
open to ridicule, awaiting that which God will do;
according to the sophism which the ancients called
Ao'yov atpyov, the lazy reason. It is necessary to act
conformably to the presumptive will of God as
far as we are able to judge of it, trying with all our

8 LEIBNIZ.

might to contribute to the general welfare and par-
ticularly to the ornamentation and the perfection of
that which touches us, or of that which is nigh and
so to speak at our hand. For if the future shall
perhaps show that God has not wished our good
intention to have its way, it does not follow that
he has not wished us to act as we have; on the con-
trary, since he is the best of all masters, he ever
demands only the right intentions, and it is for him
to know the hour and the proper place to let good
designs succeed.

V. In what the principles of the divine perfection
consist, and that the simplicity of the means counter-
balances the richness of the effects.

It is sufficient therefore to have this confidence in
God, that he has done everything for the best and
that nothing will be able to injure those who love
him. To know in particular, however, the reasons
which have moved him to choose this order of the
universe, to permit sin, to dispense his salutary
grace in a certain manner, — this passes the capacity
of a finite mind, above all when such a mind has
not come into the joy of the vision of God. Yet it
is possible to make some general remarks touching
the course of providence in the government of
things. One is able to say, therefore, that he who
acts perfectly is like an excellent Geometer who
knows how to find the best construction for a prob-
•lem; like a good architect who utilizes his location
and the funds destined for the building in the
most advantageous manner, leaving nothing which
shocks or which does not display that beauty of

DISCOURSE ON METAPHYSICS. 9

which it is capable; like a good householder who
employs his property in such a way that there shall
be nothing uncultivated or sterile; like a clever
machinist who makes his production in the least
difficult way possible; and like an intelligent author
who encloses the most of reality in the least possi-
ble compass.

Of all beings those which are the most perfect and
occupy the least possible space, that is to say those
which interfere with one another the least, are the
spirits whose perfections are the virtues. That is
why we may not doubt that the felicity of the spirits
is the principal aim of God and that he puts this
purpose into execution, as far as the general har-
mony will permit. We will recur to this subject
again.

When the simplicity of God's way is spoken of,
reference is specially made to the means which he
employs, and on the other hand when the variety,
richness and abundance are referred to, the ends or
effects are had in mind. Thus one ought to be
proportioned to the other, just as the cost of a
building should balance the beauty and grandeur
which is expected. It is true that nothing costs
God anything, just as there is no cost for a philos-
opher who makes hypotheses in constructing his
imaginary world, because God has only to make
decrees in order that a real world come into being;
but in matters of wisdom the decrees or hypotheses
meet the expenditure in proportion as they are
more independent of one another. The reason
wishes to avoid multiplicity in hypotheses or prin-
ciples very much as the simplest system is preferred
in Astronomy.

10 LEIBNIZ.

VI. That God does nothing which is not orderly, and
that it is not even possible to conceive of events which
are not regular.

The activities or the acts of will of God are com-
monly divided into ordinary and extraordinary.
But it is well to bear in mind that God does nothing
out of order. Therefore, that which passes for
extraordinary is so only with regard to a particular
order established among the created things, for as
regards the universal order, everything conforms to
it. This is so true that not only does nothing occur
in this world which is absolutely irregular, but
it is even impossible to conceive of such an occur-
rence. Because, let us suppose for example that some
one jots down a quantity of points upon a sheet of
paper helter skelter, as do those who exercise the
ridiculous art of Geomancy; now I say that it is
possible to find a geometrical line whose concept
shall be uniform and constant, that is, in accordance
with a certain formula, and which line at the same
time shall pass through all of those points, and
in the same order in which the hand jotted them
down; also if a continuous line be traced, which is
now straight, now circular, and now of any other
description, it is possible to find a mental equiva-
lent, a formula or an equation common to all the
points of this line by virtue of which formula the
changes in the direction of the line must occur.
There is no instance of a face whose contour does
not form part of a geometric line and which can not
be traced entire by a certain mathematical motion.
But when the formula is very complex, that which
conforms to it passes for irregular. Thus we may

DISCOURSE ON METAPHYSICS. II

say that in whatever manner God might have
created the world, it would always have been regu-
lar and in a certain order. God, however, has
chosen the most perfect, that is to say the one
which is at the same time the simplest in hypotheses
and the richest in phenomena, as might be the case
with a geometric line, whose construction was easy,
but whose properties and effects were extremely
remarkable and of great significance. I use these
comparisons to picture a certain imperfect resem-
blance to the divine wisdom, and to point out that
which may at least raise our minds to conceive in
some sort what cannot otherwise be expressed. I
do not pretend at all to explain thus the great mys-
tery upon which depends the whole universe.

VII. That miracles conform to the regular order
although they go against the subordinate regulations;
concerning that which God desires or permits and con-
cerning general and particular intentions.

Now since nothing is done which is not orderly,
we may say that miracles are quite within the order
of natural operations. We use the term natural of
these operations because they conform to certain
subordinate regulations which we call the nature of
things. For it can be said that this nature is only
a custom of God's which he can change on the
occasion of a stronger reason than that which
moved him to use these regulations. As regards
general and particular intentions, according to the
way in which we understand the matter, it may be
said on the one hand that everything is in accor-
dance with his most general intention, or that which
best conforms to the most perfect order he has

12 LEIBNIZ.

chosen; on the other hand, however, it is also pos-
sible to say that he has particular intentions which
are exceptions to the subordinate regulations above
mentioned. Of God's laws, however, the most
universal, i. e., that which rules the whole course
of the universe, is without exceptions.

It is possible to say that God desires everything
which is an object of his particular intention.
When we consider the objects of his general inten-
tions, however, such as are the modes of activities
of created things and especially of the reasoning
creatures with whom God wishes to co-operate, we
must make a distinction; for if the action is good
in itself, we may say that God wishes it and at
times commands it, even though it does not take
place; but if it is bad in itself and becomes
good only by accident through the course of events
and especially after chastisement and satisfaction
have corrected its malignity and rewarded the ill
with interest in such a way that more perfection
results in the whole train of circumstances than
would have come if that ill had not occurred, — if
all this takes place we must say that God permits
the evil, and not that he desired it, although he has
co-operated by means of the laws of nature which
he has established. He knows how to produce the
greatest good from them.

VIII. In order to distinguish between the activities
of God and the activities of created things we must
explain the conception of an individual substance.

It is quite difficult to distinguish God's actions
from those of his creatures. Some think that God
does everything; others imagine that he only con-

DISCOURSE ON METAPHYSICS. 13

serves the force that he has given to created things.
How far can we say either of these opinions is right?
In the first place since activity and passivity per-
tain properly to individual substances (actiones sunt
suppositonini} it will be necessary to explain what
such a substance is. It is indeed true that when
several predicates are attributes of a single subject
and this subject is not an attribute of another, we
speak of it as an individual substance, but this is not
enough, and such an explanation is merely nom-
inal. We must therefore inquire what it is to be an
attribute in reality of a certain subject. Now it is
evident that every true predication has some basis
in the nature of things, and even when a proposition
is not identical, that is, when the predicate is not
expressly contained in the subject, it is still neces-
sary that it be virtually contained in it, and this is
what the philosophers call in-esse, saying thereby
that the predicate is in the subject. Thus the con-
tent of the subject must always include that of the
predicate in such a way that if one understands
perfectly the concept of the subject, he will know
that the predicate appertains to it also. This being
so, we are able to say that this is the nature of an
individual substance or of a complete being, namely,
to afford a conception so complete that the concept
shall be sufficient for the understanding of it and
for the deduction of all the predicates of which the
substance is or may become the subject. Thus the
quality of king, which belonged to Alexander the
Great, an abstraction from the subject, is not suffi-
ciently determined to constitute an individual, and
does not contain the other qualities of the same
subject, nor everything which the idea of this

14 LEIBNIZ.

prince includes. God, however, seeing the indi-
vidual concept, or haecceity, of Alexander, sees
there at the same time the basis and the reason of
all the predicates which can be truly uttered regard-
ing him; tor instance that he will conquer Darius
and Porus, even to the point of knowing a priori
(and not by experience) whether he died a natural
death or by poison, — facts which we can learn only
through history. When we carefully consider the
connection of things we see also the possibility of
saying that there was always in the soul of Alexan-
der marks of all that had happened to him and
evidences of all that would happen to him and
traces even of everything which occurs in the uni-
verse, although God alone could recognize them all.

IX. That every individual substance expresses the
whole universe in its own manner and that in its full
concept is included all its experiences together with all
the attendent circumstances and the whole sequence of
exterior events.

There follow from these considerations several
noticeable paradoxes; among others that it is not
true that two substances may be exactly alike and
differ only numerically, solo mimero, and that what St.
Thomas says on this point regarding angels and
intelligences (quod ibi omne individuum sit species
infimd) is true of all substances, provided that the
specific difference is understood as Geometers
understand it in the case of figures; again that
a substance will be able to commence only through
creation and perish only through annihilation; that
a substance cannot be divided into two nor can one
be made out of two, and that thus the number of

DISCOURSE ON METAPHYSICS. 15

substances neither augments nor diminishes through
natural means, although they are frequently trans-
formed. Furthermore every substance is like an
entire world and like a mirror of God, or indeed of
the whole world which it portrays, each one in its
own fashion; almost as the same city is variously
represented according to the various situations of
him who is regarding it. Thus the universe is mul-
tiplied in some sort as many times as there are sub-
stances, and the glory of God is multiplied in the
same way by as many wholly different representa-
tions of his works. It can indeed be said 'that every
substance bears in some sort the character of God's
infinite wisdom and omnipotence, and imitates him
as much as it is able to; for it expresses, although
confusedly, all that happens in the universe, past,
present 'and future, deriving thus a certain resem-
blance to an infinite perception or power of know-
ing. And since all other substances express this
particular substance and accommodate themselves to
it, we can say that it exerts its power upon all the
others in imitation of the omnipotence of the cre-
ator.

X. That the belief in substantial forms has a cer-
tain basis in fact, but that these forms effect no changes
in the phenomena and must not be employed for the
explanation of particular events.

It seems that the ancients, able men, who were
accustomed to profound meditations and taught the-
ology and philosophy tor several centuries and some
of whom recommend themselves to us on account of
their piety, had some knowledge of that which we
have just said and this is why they introduced and

l6 LEIBNIZ.

maintained the substantial forms so much decried
to-day. But they were not so far from the truth
nor so open to ridicule as the common run of our
new philosophers imagine. I grant that the con-
sideration of these forms is of no service in the
details of physics and ought not to be employed in
the explanation of particular phenomena. In regard
to this last point, the schoolmen were at fault, as
were also the physicians of times past who followed
their example, thinking they had given the reason
for the properties of a body in mentioning the forms
and qualities without going to the trouble of exam-
ining the manner of operation; dS if one should be
content to say that a clock had a certain amount
of clockness derived from its form, and should not
inquire in what that clockness consisted. This is
indeed enough for the man who buys it, provided
he surrenders the care of it to someone else. The
fact, however, that there was this misunderstanding
and misuse of the substantial forms should not bring
us to throw away something whose recognition is
so necessary in metaphysics. Since without these
we will not be able, I hold, to know the ultimate
principles nor to lift our minds to the knowledge
of the incorporeal natures and of the marvels of
God. Yet as the geometer does not need to
encumber his mind with the famous puzzle of the
composition of the continuum, and as no moralist,
and still less a jurist or a statesman has need to
trouble himself with the great difficulties which
arise in conciliating free will with the providential
activity of God, (since the geometer is able to make
all his demonstrations and the statesman can com-
plete all his deliberations without entering into

DISCOURSE ON METAPHYSICS. 17

these discussions which are so necessary and impor-
tant in Philosophy and Theology), so in the same
way the physicist can explain his experiments, now
using simpler experiments already made, now
employing geometrical and mechanical demonstra-
tions without any need of the general considerations
which belong to another sphere, and if he employs
the co-operation of God, or perhaps of some soul or
animating force, or something else of a similar
nature, he goes out of his path quite as much as that
man who, when facing an important practical ques-
tion would wish to enter into profound argumenta-
tions regarding the nature of destiny and of our
liberty; a fault which men quite frequently com-
mit without realizing it when they cumber their
minds with considerations regarding fate, and thus
they are even sometimes turned from a good reso-
lution or from some necessary provision.

XI. That the opinions of the theologians and of the
so-called scholastic philosophers are not to be wholly
despised.

I know that I am advancing a great paradox in
pretending to resuscitate in some sort the ancient
philosophy^ and to recall postliminio the substan-
tial forms almost banished from our modern thought.
But perhaps I will not be condemned lightly when
it is known that I have long meditated over the
modern philosophy and that I have devoted much
time to experiments in physics and to the demon-
strations of geometry and that I, too, for a long time
was persuaded of the baselessness of those "beings"
which, however, I was finally obliged to take up
again in spite of myself and as though by force.

l8 LEIBNIZ.

The many investigations which I carried on com-
pelled me to recognize that our moderns do not do
sufficient justice to Saint Thomas and to the other
great men of that period and that there is in the
theories of the scholastic philosophers and theo-
logians far more solidity than is imagined, provided
that these theories are employed a propos and in
their place. I am persuaded that if some careful
and meditative mind were to take the trouble to
clarify and direct their thoughts in the manner of
analytic geometers, he would find a great treasure
of very important truths, wholly demonstrable.

XII. That the conception of the extension of a body
is in a way imaginary and does not constitute the sub-
stance of the body.

But to resume the thread of our discussion, I
believe that he who will meditate upon the nature
of substance, as I have explained it above, will find
that the whole nature of bodies is not exhausted in
their extension, that is to say, in their size, figure
and motion, but that we must recognize something
which corresponds to soul, something which is com-
monly called substantial form, although these forms
effect no change in the phenomena, any more than
do the souls of beasts, that is if they have souls.
It is even possible to demonstrate that the ideas of
size, figure and motion are not so distinctive as is
imagined, and that they stand for something imag-
inary relative to our preceptions as do, although to
a greater extent, the ideas of color, heat, and the
other similar qualities in regard to which we may
doubt whether they are actually to be found in the
nature of the things outside of us. This is why

DISCOURSE ON METAPHYSICS. 19

these latter qualities are unable to constitute "sub-
stance" and if there is no other principle of identity
in bodies than that which has just been referred to
a body would not subsist more than for a moment.
The souls and the substance-forms of other bodies
are entirely different from intelligent souls which
alone know their actions, and not only do not perish
through natural means but indeed always retain the
knowledge of what they are; a fact which makes
them alone open to chastisement or recompense,
and makes them citizens of the republic of the uni-
verse whose monarch is God. Hence it follows that
all the other creatures should serve them, a point
which we shall discuss more amply later.

XIII. As the individual concept of each person
includes once for all everything which can ever happen
to him, in it can be seen, a priori the evidences or the
reasons for the reality of each event, and why one hap-
pened sooner than the other. But these events, how-
ever certain, are nevertheless contingent, being based
on the free choice of God and of his creatures. It is
true that their choices always have their reasons, but
they incline to the choices under no compulsion of
necessity.

But before going further it is necessary to meet a
difficulty which may arise regarding the principles
which we have set forth in the preceding. We have
said that the concept of an individual substance
includes once for all everything which can ever hap-
pen to it and that in considering this concept one will
be able to see everything which can truly be said
concerning the individual, just as we are able to
see in the nature of a circle all the properties which

20 LEIBNIZ.

can be derived from it. But does it not seem that
in this way the difference between contingent and
necessary truths will be destroyed, that there will
be no place for human liberty, and that an absolute
fatality will rule as well over all our actions as over
all the rest of the events of the world? To this I
reply that a. distinction must be made between that
which is certain and that which is necessary. Every
one grants that future contingencies are assured
since God foresees them, but we do not say just
because of that that they are necessary. But it will
be objected, that if any conclusion can be deduced
infallibly from some definition or concept, it is
necessary; and now since we have maintained that
everything which is to happen to anyone is already
virtually included in his nature or concept, as all
the properties are contained in the definition of
a circle, therefore, the difficulty still remains. In
order to meet the objection completely, I say
that the connection or sequence is of two kinds;
the one, absolutely necessary, whose contrary im-
plies contradiction, occurs in the eternal verities
like the truths of geometry; the other is necessary
only ex hypothesi, and so to speak by accident,
and in itself it is contingent since the contrary is
not implied. This latter sequence is not founded
upon ideas wholly pure and upon the pure under-
standing of God, but upon his free decrees and upon
the processes of the universe. Let us give an
example. Since Julius Caesar will become perpet-
ual Dictator and master of the Republic and will
overthrow the liberty of Rome, this action is con-
tained in his concept, for we have supposed that it
is the nature of such a perfect concept of a subject

DISCOURSE ON METAPHYSICS. 21

to involve everything, in fact so that the predicate
may be included in the subject ut possit inesse sub-
jecto. We may say that it is not in virtue of this
concept or idea that he is obliged to perform this
action, since it pertains to him only because God
knows everything. But it will be insisted in reply
that his nature or form responds to this concept,
and since God imposes upon him this personality,
he is compelled henceforth to live up to it. I
could reply by instancing the similar case of the
future contingencies which as yet have no reality
save in the understanding and will of God, and which,
because God has given them in advance this form,
must needs correspond to it. But I prefer to over-
come a difficulty rather than to excuse it by instanc-
ing other difficulties, and what I am about to say
will serve to clear up the one as well as the other.
It is here that must be applied the distinction in
the kind of relation, and I say that that which hap-
pens conformably to these decrees is assured, but
that it is not therefore necessary, and if anyone did
the contrary, he would do nothing impossible in
itself, although it is impossible ex hypothesi that that
other happen. For if anyone were capable of carry-
ing out a complete demonstration by virtue of which
he could prove this connection of the subject, which
is Caesar, with the predicate, .which is his successful
enterprise, he would bring us to see in fact that the
future dictatorship of Caesar had its -basis in his
concept or nature, so that one would see there a
reason why he resolved to cross the Rubicon rather
than to stop, and why he gained instead of losing
the day at Pharsalus, and that it was reasonable and
by consequence assured that this would occur, but

22 LEIBNIZ.

one would not prove that it was necessary in itself,
nor that the contrary implied a contradiction,
almost in the same way in which it is reasonable and
assured that God will always do what is best
although that which is le'ss perfect is not thereby
implied. For it would be found that this demon-
stration of this predicate as belonging to Caesar is
not as absolute as are those of numbers or of geom-
etry, but that this predicate supposes a sequence of
things which God has shown by his free will. This
sequence is based on the first free decree of God
which was to do always that which is the most
perfect and upon the decree which God made fol-
lowing the first one, regarding human nature, which
is that men should always do, although freely, that
which appears to be the best. Now every truth
which is founded upon this kind of decree is con-
tingent, although certain, for the decrees of God do
not change the possibilities of things and, as 1 have
already said, although God assuredly chooses the
best, this does not prevent that which is less per-
fect from .being possible in itelf. Although it will
never happen, it is not its impossibility but its
imperfection which causes him to reject it. Now
nothing is necessitated whose opposite is possible.
One will then be in a position to satisfy these kinds
of difficulties, however great they may appear (and
in fact they have not been less vexing to all other
thinkers who have ever treated this matter), pro-
vided that he considers well that all contingent
propositions have reasons why they are thus, rather
than otherwise, or indeed (what is the same thing)
that they have proof a priori of their truth, which
render them certain and show that the connection

DISCOURSE ON METAPHYSICS. 23

of the subject and predicate in these propositions
has its basis in the nature of the one and of the
other, but he must further remember that such con-
tingent propositions have not the demonstrations
of necessity, since their reasons are founded only on
the principle' of contingency or of the existence of
things, that is to say, upon that which is, or which
appears to be the best among several things equally
possible. Necessary truths, on the other hand, are
founded upon the principle of contradiction, and
upon the possibility or impossibility of the essences
themselves, without regard here to the free will of
God or of creatures.

XIV. God produces different substances according to
the different views which he has of the world, and by
the intervention of God, the appropriate nature of each
substance brings it about that what happens to one
corresponds to what happens to all the others, without,
however, their acting upon one another directly.

After having seen, to a certain extent, in what the
nature of substances consists, we must try to explain
the dependence they have upon one another and
their actions and passions. Now it is first of all
very evident that created substances depend upon
God who preserves them and can produce them
continually by a kind of emanation just as we pro-
duce our thoughts, for when God turns, so to say,
on all sides and in all fashions, the general system
of phenomena which he finds it good to produce for
the sake of manifesting his glory, and when he
regards all the aspects of the world in all possible
manners, since there is no relation which escapes

24 LEIBNIZ.

his omniscience, the result of each view of the uni-
verse as seen from a different position is a sub-
stance which expresses the universe conformably
to this view, provided God sees fit to render his
thought effective and to produce the substance,
and since God's vision is always true, our per-
ceptions are always true and that which deceives
us are our judgments, which are of us. Now we
have said before, and it follows from what we
have just said that each substance is a world by
itself, independent of everything else excepting
God; therefore, all our phenomena that is all things
which are ever able to happen to us, are only con-
sequences of our being. Now as the phenomena
maintain a certain order conformably to our nature,
or so to speak to the world which is in us (from
whence it follows that we can, for the regulation of
our conduct, make useful observations which are
justified by the outcome of the future phenomena)
and as we are thus able often to judge the future by
the past without deceiving ourselves, we have suffi-
cient grounds for saying that these phenomena are
true and we will not be put to the task of inquiring
whether they are outside of us, and whether others
perceive them also.

Nevertheless it is most true that the perceptions
and expressions of all substances intercorrespond,
so that each one following independently certain
reasons or laws which he has noticed meets others
which are doing the same, as when several have
agreed to meet together in a certain place on a set
day, they are able to carry out the plan if they wish.
Now although all express the same phenomena,
this does not bring it about that their expressions

DISCOURSE ON METAPHYSICS. 25

are exactly alike. It is sufficient if they are pro-
portional. As when several spectators think they
see the same thing and are agreed about it, although
each one sees or speaks according to the measure
of his vision. It is God alone, (from whom all
individuals emanate continually, and who sees the
universe not only as they see it, but besides in a
very different way from them) who is the cause of
this correspondence in their phenomena and who
brings it about that that which is particular to one,
is also common to all, otherwise there would be no
relation. In a way, then, we might properly say,
although it seems strange, that a particular sub-
stance never acts upon another particular substance
nor is it acted upon by it. That which happens to
each one is only the consequence of its complete
idea or concept, since this idea already includes all
the predicates and expresses the whole universe.
In fact nothing can happen to us except thoughts
and perceptions, and all our thoughts and percep-
tions are but the consequence, contingent it is true,
of our precedent thoughts and perceptions, in such
a way that were I able to consider directly all that
happens or appears to me at the present time, I
should be able to see all that will happen to me or
that will ever appear to me. This future will not
fail me, and will surely appear to me even if all
that which is outside of me were destroyed, save
only that God and myself were left.

Since, however, we ordinarily attribute to other
things an action upon us which brings us to per-
ceive things in a certain manner, it is necessary to
consider the basis of this judgment and to inquire
what there is of truth in it.

26 LEIBNIZ.

XV. The action of one finite substance upon another
consists only in the increase in the degrees of the
expression of the first combined with a decrease in that
of the second, in so far as God has in advance fashioned
them so that they shall act in accord.

Without entering into a long discussion it is suffi-
cient for reconciling the language of metaphysics
with that of practical life to remark that we pref-
erably attribute to ourselves, and with reason, the
phenomena which we express the most perfectly,
and that we attribute to other substances those
phenomena which each one expresses the best.
Thus a substance, which is of an infinite extension
in so far as it expresses all, becomes limited in pro-
portion to its more or less perfect manner of expres-
sion. It is thus then that we may conceive of
substances as interfering with and limiting one
another, and hence we are able to say that in this
sense they act upon one another, and that they, so
to speak, accommodate themselves to one another.
For it can happen that a single change which aug-
ments the expression of the one may diminish that
of the other. Now the virtue of a particular sub-
stance is to express well the glory of God, and the
better it expresses it, the less is it limited. Every-
thing when it expresses its virtue or power, that is
to say, when it acts, changes to better, and expands
just in so far as it acts. When therefore a change
occurs by which several substances are affected (in
fact every change affects them all) I think we may
say that those substances, which by this change
pass immediately to a greater degree of perfection,
or to a more perfect expression, exert power and

DISCOURSE ON METAPHYSICS. 27

act, while those which pass to a lesser degree dis-
close their weakness and suffer. I also hold that
every activity of a substances which has perception
implies some pleasure, and every passion some pain,
except that it may very well happen that a present
advantage will be eventually destroyed by a greater
evil, whence it comes that one may sin in acting or
exerting his power and in finding pleasure.

XVI. The extraordinary intervention of God is not
excluded in that which our particular essences express,
because their expression includes everything. Such
intervention, however, goes beyond the power of our
natural being or of our distinct expression, because
these are finite, and follow certain subordinate regula-
tions.

There remains for us at present- only to explain
how it is possible that God has influence at times
upon men or upon other substances by an extraor-
dinary or miraculous intervention, since it seems
that nothing is able to happen which is extraor-
dinary or supernatural in as much as all the events
which occur to the other substances are only the
consequences of their natures. We must recall
what was said above in regard to the miracles in
the universe. These always conform to the univer-
sal law of the general order, although they may con-
travene the subordinate regulations, and since every
person or substance is like a little world which
expresses the great world, we can say that this
extraordinary action of God upon this substance
is nevertheless miraculous, although it is comprised
in the general order of the universe in so far as it

28 LEIBNIZ.

is expressed by the individual essence or concept
of this substance. This is why, if we understand
in our natures all that they express, nothing is sup-
ernatural in them, because they reach out to every-
thing, an effect always expressing its cause, and
God being the veritable cause of the substances.
But as that which our natures express the most per-
fectly pertains to them in a particular manner, that
being their special power, and since they are limited,
as I have just explained, many things there are
which surpass the powers of our natures and even
of all limited natures As a consequence, to speak
more clearly, I say that the miracles and the extraor-
dinary interventions of God have this peculiarity
that they cannot be foreseen by any created mind
however enlightened. This is because the distinct
comprehension of the fundamental order surpasses
them all, while on the other hand, that which is
called natural depends upon less fundamental reg-
ulations which the creatures are able to understand.
In order then that my words may be as irreprehen-
sible as the meaning I am trying to convey, it will
be well to associate certain words with certain sig-
nifications. We may call that which includes every-
thing that we express and which expresses our
union with God himself, nothing going beyond it,
our essence. But that which is limited in us may be
designated as our nature or our power and in accor-
dance with this terminology that which goes
beyond the natures of all created substances is
supernatural.

DISCOURSE ON METAPHYSICS. 29

XVII. An example of a subordinate regulation in
the law of nature which demonstrates that God always
preserves the same amount of force but not the same
quantity of motion : — against the Cartesians and many
others.

I have frequently spoken of subordinate regula-
tions, or of the laws of nature, and it seems that
it will be well to give an example. Our new
philosophers are unanimous in employing that
famous law that God always preserves the same
amount of motion in the universe. In fact it is a
very plausible law, and in times past I held it for
indubitable. But since then I have learned in what
its fault consists. Monsieur Descartes and many
other clever mathematicians have thought that the
quantity of motion, that is to say the velocity mul-
tiplied by the mass* of the moving body, is exactly
equivalent to the moving force, or to speak in
mathematical terms that the force varies as the
velocity multiplied by the mass. Now it is rea-
sonable that the same force is always preserved in
the universe. So also, looking to phenomena, it
will be readily seen that a mechanical perpetual
motion is impossible, because the force in such a
machine, being always diminished a little by fric-

*This term is employed here for the sake of clearness.
Leibniz did not possess the concept "mass," which was
enunciated by Newton in the same year in which the present
treatise was written, 1686. Leibniz uses the terms "body,"
"magnitude of body, " etc. The technical expression "mass"
occurs once only in the writings of Leibniz (in a treatise pub-
lished in 1695), and was there doubtless borrowed from Newton.
For the history of the controversy concerning the Cartesian and
Leibnizian measure of force, see Mach's Science of Mechanics,
Chicago, 1893, pp. 272 et seq. — Trans.

30 LEIBNIZ.

tion and so ultimately destined to be entirely spent,
would necessarily have to recoup its losses, and con-
sequently would keep on increasing of itself without
any new impulsion from without; and we see further-
more that the force of a body is diminished only
in proportion as it gives up force, either to a con-
tiguous body or to its own parts, in so far as they
have a separate movement. The mathematicians to
whom I have referred think that what can be said of
force can be said of the quantity of motion. In
order, however, to show the difference I make two
suppositions: in the first place, that a body falling
from a certain height acquires a force enabling it to
remount to the same height, provided that its direc-
tion is turned that way, or provided that there are
no hindrances. For instance, a pendulum will rise
exactly to the height from which it has fallen, pro-
vided the resistance of the air and of certain other

small particles do not di-
minish a little its acquired
force.

I suppose in the second
place that it will take as
much force to lift a body
A weighing one pound
to the height CD, four
feet, as to raise a body B
weighing four pounds to
the height EF, one foot.
These two suppositions are granted by our new
philosophers. It is therefore manifest that the
body A falling from the height CD acquires exactly
as much force as the body B falling from the height
EF, for the body B at F, having by the first suppo-

(f\
( }

DISCOURSE ON METAPHYSICS. 31

sition sufficient force to return to E, has therefore
the force to carry a body of four pounds to the dis-
tance of one foot, EF. And likewise the body
A at D, having the force to return to C, has also
the force required to carry a body weighing one
pound, its own weight, back to C, a distance of four
feet. Now by the second supposition the force
of these two bodies is equal. Let us now see if the
quantity of motion is the same in each case. It is
here that we will be surprised to find a very great
difference, for it has been proved by Galileo that
the velocity acquired by the fall CD is double the
velocity acquired by the fall EF, although the
height is four times as great. Multiplying, there-
fore, the body A, whose mass is I, by its velocity,
which is 2, the product or the quantity of move-
ment will be 2, and on the other hand, if we multi-
ply the body B, whose mass is 4, by its velocity,
which is i, the product or quantity of motion will
be 4. Hence the quantity of the motion of the
body A at the point D is half the quantity of motion
of the body B at the point F, yet their forces are
equal, and there is therefore a great difference
between the quantity of motion and the force. This
is what we set out to show. We can see therefore
how the force ought to be estimated by the quantity
of the effect which it is able to produce, for exam-
ple by the height to which a body of certain weight
can be raised. This is a very different thing from
the velocity which can be imparted to it, and in
order to impart to it double the velocity we must
have double the force. Nothing is simpler than
this proof and Monsieur Descartes has fallen into
error here, only because he trusted too much to his

32 LEIBNIZ.

thoughts even when they had not been ripened by
reflection. But it astonishes me that his disciples
have not noticed this error, and I am afraid that
they are beginning to imitate little by little certain
Peripatetics whom they ridicule, and that they are
accustoming themselves to consult rather the books
of their master, than reason or nature.

XVIII. The distinction between force and the quan-
tity of motion is, among other reasons, important as
showing that we must have recourse to metaphysical
considerations in addition to discussions of extension if
we wish to explain the phenomena of matter.

This consideration of the force, distinguished
from the quantity of motion is of importance, not
only in physics and mechanics for rinding the real
laws of nature and the principles of motion, and
even for correcting many practical errors which
have crept into the writings of certain able mathe-
maticians, but also in metaphysics it is of impor-
tance for the better understanding of principles.
Because motion, if we regard only its exact and
formal meaning, that is, change of place, is not
something entirely real, and when several bodies
change their places reciprocally, it is not possible
to determine by considering the bodies alone to
which among them movement or repose is to be
attributed, as I could demonstrate geometrically,
if I wished to stop for it now. But the force, or
the proximate cause of these changes is something
more real, and there are sufficient grounds for
attributing it to one body rather than to another, and
it is only through this latter investigation that we
can determine to which one the movement must

DISCOURSE ON METAPHYSICS. 33

appertain. Now this force is something different
from size, from form or from motion, and it can be
seen from this consideration that the whole mean-
ing of a body is not exhausted in its extension
together with its modifications as our moderns per-
suade themselves. We are therefore obliged to
restore certain beings or forms which they have ban-
ished. It appears more and more clear that although
all the particular phenomena of nature can be
explained mathematically or mechanically by those
who understand them, yet nevertheless, the general
principles of corporeal nature and even of mechan-
ics are metaphysical rather than geometric, and
belong rather to certain indivisible forms or natures
as the causes of the appearances, than to the cor-
poreal mass or to extension. This reflection is
able to reconcile the mechanical philosophy of the
moderns with the circumspection of those intelli-
gent and well-meaning persons who, with a certain
justice, fear that we are becoming too far removed
from immaterial beings and that we are thus preju-
dicing piety.

XIX. The utility of final causes in Physics.

As I do not wish to judge people in ill part I
bring no accusation against our new philosophers
who pretend to banish final causes from physics, but
I am nevertheless obliged to avow that the conse-
quences of such a banishment appear to me danger-
ous, especially when joined to that position which
I refuted at the beginning of this treatise. That
position seemed to go the length of discarding final
causes entirely as though God proposed no end and
no good in his activity, or as if good were not to be

34 LEIBNIZ.

the object of his will. I hold on the contrary that
it is just in this that the principle of all existences
and of the laws of nature must be sought, hence
God always proposes the best and most perfect. I
am quite willing to grant that we are liable to err
when we wish to determine the purposes or councils
of God, but this is the case only when we try to
limit them to some particular design, thinking that
he has had in view only a single thing, while in
fact he regards everything at once. As for instance,
if we think that God has made the world only for
us, it is a great blunder, although it may be quite
true that he has made it entirely for us, and that
there is nothing in the universe which does not
touch us and which does not accommodate itself to
the regard which he has for us according to the
principle laid down above. Therefore when we
see some good effect or some perfection which hap-
pens or which follows from the works of God we are
able to say assuredly that God has purposed it, for
he does nothing by chance, and is not like us who
sometimes fail to do well. Therefore, far from
being able to fall into error in this respect as do the
extreme statesmen who postulate too much foresight
in the designs of Princes, or as do commentators
who seek for too much erudition in their authors, it
will be impossible to attribute too much reflection
to God's infinite wisdom, and there is no matter in
which error is less to be feared provided we confine
ourselves to affirmations and provided we avoid
negative statements which limit the designs of God.
All those who see the admirable structure of ani-
mals find themselves led to recognize the wisdom
of the author of things and I advise those who have

DISCOURSE ON METAPHYSICS. 35

any sentiment of piety and indeed of true philos-
ophy to hold aloof from the expressions of certain
pretentious minds who instead of saying that eyes
were made for seeing, say that we see because we
find ourselves having eyes. When one seriously
holds such opinions which hand everything over to
material necessity or to a kind of chance (although
either alternative ought to appear ridiculous to
those who understand what we have explained
above) it is difficult to recognize an intelligent
author of nature. The effect should correspond to
its cause and indeed it is best known through the
recognition of its cause, so that it is reasonable to
introduce a sovereign intelligence ordering things,
and in place of making use of the wisdom of this sov-
ereign being, to employ only the properties of matter
to explain phenomena. As 'if in order to account
for the capture of an important place by a prince,
the historian should say it was because the particles
of powder in the cannon having been touched by a
spark of fire expanded with a rapidity capable of
pushing a hard solid body against the walls of the
place, while the little particles which composed the
brass of the cannon were so well interlaced that
they did not separate under this impact, — as if he
should account for it in this way instead of making
us see how the foresight of the conqueror brought
him to choose the time and the proper means and
how his ability surmounted all obstacles.

XX. A noteworthy disquisition in Plato's Phaedo
against the philosophers who were too materialistic.

This reminds me of a fine disquisition by Socrates
in Plato's Phaedo, which agrees perfectly with my

36 LEIBNIZ.

opinion on this subject and seems to have been
uttered expressly for our too materialistic philos-
ophers. This agreement has led me to a desire to
translate it although it is a little long. Perhaps
this example will give some of us an incentive to
share in many of the other beautiful and well bal-
anced thoughts which are found in the writings of
this famous author.*

XXI, If the mechanical laws depended upon Geome-
try alone without metaphysical influences, the phenom-
ena would be very different from what they are.

Now since the wisdom of God has always been
recognized in the detail of the mechanical struc-
tures of certain particular bodies, it should also be
shown in the general economy of the world and in
the constitution of the laws of nature. This is so
true that even in the laws of motion in general, the
plans of this wisdom have been noticed. For if
bodies were only extended masses, and motion were
only a change of place, and if everything ought to
be and could be deduced by geometric necessity
from these two definitions alone, it would follow, as
I have shown elsewhere, that the smallest body on
contact with a very large one at rest would impart
to it its own velocity, yet without losing any of the
velocity that it had. A quantity of other rules
wholly contrary to the formation of a system would
also have to be admitted. But the decree of the
divine wisdom in preserving always the same force
and the same total direction has provided for a

* There is a gap here in the MS., intended for the passage
from Plato, the translation of which Leibniz did not supply. —
Trans.

DISCOURSE ON METAPHYSICS. 37

system. I find indeed that many of the effects of
nature can be accounted for in a twofold way, that
is to say by a consideration of efficient causes, and
again independently by a consideration of final
causes. An example of the latter is God's decree
to always carry out his plan by the easiest and most
determined way. I have shown this elsewhere in
accounting for the catoptric and dioptric laws, and
I will speak more at length about it in what follows.

XXII. Reconciliation of the two methods of explana-
tion, the one using final causes, and the other efficient
causes, thus satisfying both those who explain nature
mechanically and those who have recourse to incorpo-
real natures.

It is worth while to make the preceding remark
in order to reconcile those who hope to explain
mechanically the formation of the first tissue of an
animal and all the interrelation of the parts, with
those who account for the same structure by refer-
ring to final causes. Both explanations are good;
both are useful not only for the admiring of the
work of a great artificer, but also for the discovery of
useful facts in physics and medicine. And writers
who take these diverse routes should not speak ill
of each other. For I see that those who attempt to
explain beauty by the divine anatomy ridicule those
who .imagine that the apparently fortuitous flow of
certain liquids has been able to produce such a
beautiful variety and that they regard them as over-
bold and irreverent. These others on the contrary
treat the former as simple and superstitious, and
compare them to those ancients who regarded the
physicists as impious when they maintained that

38 LEIBNIZ.

not Jupiter thundered but some material which is
found in the clouds. The best plan would be to
join the two ways of thinking. To use a practical
comparison, we recognize and praise the ability of
a workman not only when we show what designs he
had in making the parts of his machine, but also
when we explain the instruments which he employed
in making each part, above all if these instruments
are simple and ingeniously contrived. God is also
a workman able enough to produce a machine still
a thousand times more ingenious than is our body,
by employing only certain quite simple liquids pur-
posely composed in such a way that ordinary laws
of nature alone are required to develop them so as
to produce such a marvellous effect. But it is also
true that this development would not take place if
God were not the author of nature. Yet I find that
the method of efficient causes, which goes much
deeper and is in a measure more immediate and a
priori, is also more difficult when we come to details,
and I think that our philosophers are still very
frequently far removed from making the most of
this method. The method of final causes, however,
is easier and can be frequently employed to find out
important and useful truths which we should have
to seek for a long time, if we were confined to that
other more physical method of which anatomy is
able to furnish many examples. It seems to me
that Snellius, who was the first discoverer of the laws
of refraction would have waited a long time before
finding them if he had wished to seek out first how
light was formed. But he apparently followed that
method which the ancients employed for Catoptrics,
that is, the method of final causes. Because, while

DISCOURSE ON METAPHYSICS. 39

seeking for the easiest way in which to conduct a
ray of light from one given point to another given
point by reflection from a given plane (supposing
that that was the design of nature) they discovered
the equality of the angles of incidence and reflec-
tion, as can be seen from a little treatise by Helio-
dorus of Larissa and also elsewhere. This principle
Mons. Snellius, I believe, and afterwards independ-
ently of him, M. Fermat, applied most ingeniously
to refraction. For since the rays while in the same
media always maintain the same proportion of sines,
which in turn corresponds to the resistance of the
media, it appears that they follow the easiest way,
or at least that way which is the most determinate
for passing from a given point in one medium to a
given point in another medium. That demonstra-
tion of this same theorem which M. Descartes has
given, using efficient causes, is much less satisfac-
tory. At least we have grounds to think that he
would never have found the principle by that means
if he had not learned in Holland of the discovery
of Snellius.

XXIII. Returning to immaterial substances we ex-
plain how God acts upon the understanding of spirits
and ask whether one always keeps the idea of what he
thinks about.

I have thought it well to insist a little upon final
causes, upon incorporeal natures and upon an
intelligent cause with respect to bodies so as to
show the use of these conceptions in physics and in
mathematics. This for two reasons, first to purge
from mechanical philosophy the impiety that is
imputed to it, second, to elevate to nobler lines of

40 LEIBNIZ.

thought the thinking of our philosophers who
incline to materialistic considerations alone. Now,
however, it will be well to return from corporeal
substances to the consideration of immaterial
natures and particularly of spirits, and to speak of
the methods which God uses to enlighten them and
to act upon them. Although we must not forget
that there are here at the same time certain laws of
nature in regard to which I can speak more amply
elsewhere. It will be enough for now to touch
upon ideas and to inquire if we see everything in
God and how God is our light. First of all it will
be in place to remark that the wrong use of ideas
occasions many errors. For when one reasons in
regard to anything, he imagines that he has an idea
of it and this is the foundation upon which certain
philosophers, ancient and modern, have constructed
a demonstration of God that is extremely imperfect.
It must be, they say, that I have an idea of God, or
of a perfect being, since I think of him and we can-
not think without having ideas; now the idea of
this being includes all perfections and since exist-
ence is one of these perfections, it follows that he
exists. But I reply, inasmuch as we often think
of impossible chimeras, for example of the highest
degree of swiftness, of the greatest number, of the
meeting of the conchoid with its base or determinant,
such reasoning is not sufficient. It is therefore in
this sense that we can say that there are true and
false ideas according as the thing which is in ques-
tion is possible or not. And it is when he is assured
of the possibility of a thing, that one can boast of
having an idea of it. Therefore, the aforesaid argu-
ment proves that God exists, if he is possible. This

DISCOURSE ON METAPHYSICS. 41

is in fact an excellent privilege of the divine nature,
to have need only of a possibility or an essence in
order to actually exist, and it is just this which is
called ens a se.

XXIV. What clear and obscure, distinct and con-
fused, adequate and inadequate, intuitive and assumed
knowledge is, and the definition of nominal, real, causal
and essential.

In order to understand better the nature of ideas it
is necessary to touch somewhat upon the various
kinds of knowledge. When I am able to recognize a
thing among others, without being able to say in what
its differences or characteristics consist, the knowl-
edge is confused. Sometimes indeed we may know
clearly, that is without being in the slightest doubt,
that a poem or a picture is well or badly done
because there is in it an "I know not what" which
satisfies or shocks us. Such knowledge is not yet
distinct. It is when I am able to explain the pecu-
liarities which a thing has, that the knowledge is
called distinct. Such is the knowledge of an
assayer who discerns the true gold from the false by
means of certain proofs or marks which make up
the definition of gold. But distinct knowledge has
degrees, because ordinarily the conceptions which
enter into the definitions will themselves have need
of definition, and are only known confusedly.
When at length everything which enters into a
definition or into distinct knowledge is known dis-
tinctly, even back to the primitive conception, I
call that knowledge adequate. When my mind
understands at once and distinctly all the primitive
ingredients of a conception, then we have intuitive

42 LEIBNIZ.

knowledge. This is extremely rare as most human
knowledge is only confused or indeed assumed. It
is well also to distinguish nominal from real defini-
tion. I call a definition nominal when there is
doubt whether an exact conception of it is pos-
sible; as for instance, when I say that an endless
screw is a line in three dimensional space whose
parts are congruent or fall one upon another.
Now although this is one of the reciprocal proper-
ties of an endless- screw, he who did not know from
elsewhere what an endless screw was could doubt if
such a line were possible, because the other lines
whose ends are congruent (there are only two: the
circumference of a circle and the straight line) are
plane figures, that is to say they can be described
in piano. This instancfe enables us to see that any
reciprocal property can serve as a nominal defini-
tion, but when the property brings us to see the
possibility of a thing it makes the definition real,
and as long as one has only a nominal definition he
cannot be sure of the consequences which he draws,
because if it conceals a contradiction or an impos-
sibility he would be able to draw the opposite con-
clusions. That is why truths do not depend upon
names and are not arbitrary, as some of our new
philosophers think. There is also a considerable
difference among real definitions, for when the pos-
sibility proves itself only by experience, as in the
definition of quicksilver, whose possibility we know
because such a body, which is both an extremely
heavy fluid and quite volatile, actually exists, the
definition is merely real and nothing more. If,
however, the proof of the possibility is a priori, the
definition is not cmly real but also causal as for

DISCOURSE ON METAPHYSICS. 43

instance when it contains the possible generation of
a thing. Finally when the definition, without
assuming anything which requires a proof a priori
of its possibility, carries the analysis clear to the
primitive conception, the definition is perfect or
essential.

XXV. In what cases knowledge is added to mere con-
templation of the idea.

Now it is manifest that we have no idea of a con-
ception when it is impossible. And in case the knowl-
edge, where we have the idea of it, is only assumed,
we do not visualize it because such a conception is
known only in like manner as conceptions internally
impossible. And if it be in fact possible, it is not
by this kind of knowledge that we learn its possi-
bility. For instance, when I am thinking of a
thousand or of a chiliagpn, I frequently do it with-
out contemplating the idea. Even if I say a thou-
sand is ten times a hundred, I frequently do not
trouble to think what ten and a hundred are,
because I assume that I know, and I do not con-
sider it necessary to stop just at present to conceive
of them. Therefore it may well happen, as it in
fact does happen often enough, that I am mistaken
in regard to a conception which I assume that I
understand, although it is an impossible truth or at
least is incompatible with others with which I join
it, and whether I am mistaken or not, this way of
assuming our knowledge remains the same. It is,
then, only when our knowledge is clear in regard to
confused conceptions, and when it is intuitive in
regard to those which are distinct, that we see its
entire idea.

44 LEIBNIZ.

XXVI. Ideas are all stored up within us. Plato's
doctrine of reminiscence.

In order to see clearly what an idea is, we must
guard ourselves against a misunderstanding. Many
regard the idea as the form or the differentiation of
our thinking, and according to this opinion we have
the idea in our mind, in so far as we are thinking
of it, and each separate time that we think of it
anew we have another idea although similar to the
preceding one. Some, however, take the idea as
the immediate object of thought, or as a permanent
form which remains even when we are no longer
contemplating it. As a matter of fact our soul has
the power of representing to itself any form or
nature whenever the occasion comes for thinking
about it, and I think that this activity of bur soul
is, so far as it expresses some nature, form or
essence, properly the idea of the thing. This is in
us, and is always in us, whether we are thinking of
it or no. (Our soul expresses God and the uni-
verse and all essences as well as all existences.)
This position is in accord with my principles that
naturally nothing enters into our minds from outside.

It is a bad habit we have of thinking as though
our minds receive certain messengers, as it were, or
as if they had doors or windows. We have in our
minds all those forms for all periods of time
because the mind at every moment expresses all its
future thoughts and already thinks confusedly of
all that of which it will ever think distinctly.
Nothing can be taught us of which we have not
already in our minds the idea. This idea is as it
were the material out of which the thought will form
itself. This is what Plato has excellently brought

DISCOURSE ON METAPHYSICS. 45

out in his doctrine of reminiscence, a doctrine
which contains a great deal of truth, provided that
it is properly understood and purged of the error of
pre-existence, and provided that one does not con-
ceive of the soul as having already known and
thought at some other time what it learns and
thinks now. Plato has also confirmed his position
by a beautiful experiment. He introduces a small
boy, whom he leads by short steps, to extremely
difficult truths of geometry bearing on incommen-
surables, all this without teaching the boy anything,
merely drawing out replies by a well arranged se-
ries of questions. This shows that the soul virtually
knows those things, and needs only to be reminded
(animadverted) to recognize the truths. Conse-
quently it possesses at least the idea upon which
those truths depend. We may say even that it
already possesses those truths, if we consider them
as the relations of the ideas.

XXVII. In what respect our souls can be compared
to blank tablets and how conceptions are derived from
the senses.

Aristotle preferred to compare our souls to blank
tablets prepared for writing, and he maintained that
nothing is in the understanding which does not
come through the senses. This position is in
accord with the popular conceptions as Aristotle's
positions usually are. Plato thinks more pro-
foundly. Such tenets or practicologies are never-
theless allowable in ordinary use somewhat in the
same way as those who accept the Copernican
theory still continue to speak of the rising and set-
ting of the sun. I find indeed that these usages can

46 LEIBNIZ.

be given a real meaning containing no error, quite
in the same way as I have already pointed out that
we may truly say particular substances act upon one
another. In this same sense we may say that
knowledge is received from without through the
medium of the senses because certain exterior things
contain or express more particularly the causes
which determine us to certain thoughts. Because
in the ordinary uses of life we attribute to the soul
only that which belongs to it most manifestly and
particularly, and there is no advantage in going
further. When, however, we are dealing with the
exactness of metaphysical truths, it is important to
recognize the powers and independence of the soul
which extend infinitely further than is commonly
supposed. In order, therefore, to avoid misunder-
standings it would be well to choose separate terms
for the two. These expressions which are in the
soul whether one is conceiving of them or not may
be called ideas, while those which one conceives of
or constructs may be called conceptions, conceptus.
But whatever terms are used, it is always false to
say that all our conceptions come from the so-called
external senses, because those conceptions which
I have of myself and of my thoughts, and con-
sequently of being, of substance, of action, of
identity, and of many others came from an inner
experience.

XXVIII. The only immediate object of our percep-
tions which exists outside of us is God, and in him alone
is our light.

In the strictly metaphysical sense no external
cause acts upon us excepting God alone, and he is

DISCOURSE ON METAPHYSICS. 47

in immediate relation with us only by virtue of our
continual dependence upon him. Whence it fol-
lows that there is absolutely no other external
object which comes into contact with our souls and
directly excites perceptions in us. We have in our
souls ideas of everything, only because of the con-
tinual action of God upon us, that is to say, because
every effect expresses its cause and therefore the
essences of our souls are certain expressions, imita-
tions or images of the divine essence, divine thought
and divine will, including all the ideas which are
there contained. We may say, therefore, that God
is for us the only immediate external object, and
that we see things through him. For example,
when we see the sun or the stars, it is God who gives
to us and preserves in us the ideas and whenever
our senses are affected according to his own laws
in a certain manner, it is he, who by his continual
concurrence, determines our thinking. God is the
sun and the light of souls, lumen illuminans omnem
hominem venientem in hunc mundum, although this
is not the current conception. I think I have
already remarked that during the scholastic period
many believed God to be the light of the soul,
intellectus agens animce rationalis, following in this
the Holy Scriptures and the fathers who were always
more Platonic than Aristotelian in their mode of
thinking. The Averroists misused this conception,
but others, among whom were several mystic theo-
logians, and William of Saint Amour, also I think,
understood this conception in a manner which
assured the dignity of God and was able to raise the
soul to a knowledge of its welfare.

48 LEIBNIZ.

XXIX. Tet we think directly by means of our own
ideas and not through God's.

Nevertheless I cannot approve of the position of
certain able philosophers who seem to hold that
our ideas themselves are in God and not at all in
us. I think that in taking this position they have
neither sufficiently considered the nature of sub-
stance, which we have just explained, nor the entire
extension and independence of the soul which
includes all that happens to it, and expresses God,
and with him all possible and actual beings in the
same way that an effect expresses its cause. It is
indeed inconceivable that the soul should think
using the ideas of something else. The soul when
it thinks of anything must be affected effectively in
a certain manner, and it must needs have in itself
in advance not only the passive capacity of being
thus affected, a capacity already wholly determined,
but it must have besides an active power by virtue
of which it has always had in its nature the marks
of the future production of this thought, and the
disposition to produce it at its proper time. All of
this shows that the soul already includes the idea
which is comprised in any particular thought.

XXX. How God inclines our souls without necessitat-
ing them; that there are no grounds for complaint; that
we must not ask why Judas sinned because this free act
is contained in his concept, the only question being why
Judas the sinner is admitted to existence, preferably to
other possible persons; concerning the original imperfec-
tion or limitation before the fall and concerning the
different degrees of grace.

Regarding the action of God upon the human

DISCOURSE ON METAPHYSICS. 49

will there are many quite different considerations
which it would take too long to investigate here.
Nevertheless the following is what can be said in
general. God in co-operating with ordinary actions
only follows the laws which he has established,
that is to say, he continually preserves and pro-
duces our being so that the ideas come to us spon-
taneously or with freedom in that order which the
concept of our individual substance carries with
itself. In this concept they can be foreseen for all
eternity. Furthermore, by virtue of the decree
which God has made that the will shall always seek
the apparent good in certain particular respects (in
regard to which this apparent good always has in
it something of reality expressing or imitating
God's will), he, without at all necessitating our
choice, determines it by that which appears most
desirable. For absolutely speaking, our will as
contrasted with necessity, is in a state of indiffer-
ence, being able to act otherwise, or wholly to sus-
pend its action, either alternative being and remain-
ing possible. It therefore devolves upon the soul
to be on guard against appearances, by means of a
firm will, to reflect and to refuse to act or decide in
certain circumstances, except after mature delibera-
tion. It is, however, true and has been assured
from all eternity that certain souls will not employ
their power upon certain occasions.

But who could do more than God has done, and
can such a soul complain of anything except itself?
All these complaints after the deed are unjust, inas-
much as they would have been unjust before the
deed. Would this soul a little before committing
the sin have had the right to complain of God as

50 LEIBNIZ.

though he had determined the sin. Since the deter-
minations of God in these matters cannot be fore-
seen, how would the soul know that it was pre-
ordained to sin unless it had already committed the
sin? It is merely a question of wishing to or not
wishing to, and God could not have set an easier or
juster condition. Therefore all judges without
asking the reasons which have disposed a man to
have an evil will, consider only how far this will is
wrong. But, you object, perhaps it is ordained
from all eternity that I will sin. Find your own
answer. Perhaps it has not been. Now then,
without asking for what you are unable to know and
in regard to which you can have no light, act accord-
ing to your duty and your knowledge. But, some
one will object; whence comes it then that this
man will assuredly do this sin? The reply is easy.
It is that otherwise he would not be a man. For
God foresees from all time that there will be a
certain Judas, and in the concept or idea of him
which God has, is contained this future free act.
The only question, therefore, which remains is why
this certain Judas, the betrayer who is possible only
because of the idea of God, actually exists. To
this question, however, we can expect no answer
here on earth excepting to say in general that it is
because God has found it good that he should exist
notwithstanding that sin which he foresaw. This
evil will be more than overbalanced. God will
derive a greater good from it, and it will finally
turn out that this series of events in which is
included the existence of this sinner, is the most
perfect among all the possible series of events. An
explanation in every case of the admirable econ-

DISCOURSE ON METAPHYSICS. $1

omy of this choice cannot be given while we are
sojourners on earth. It is enough to know the
excellence without understanding it. It is here
that must be recognized altitudinem divitiarum, the
unfathomable depth of the divine wisdom, without
hesitating at a detail which involves an infinite
number of considerations. It is clear, however,
that God is not the cause of ill. For no,t only
after the loss of innocence by men, has original sin
possessed the soul, but even before that there was
an original limitation or imperfection in the very
nature of all creatures, which rendered them open
to sin and able to fall. There is, therefore, no more
difficulty in the supralapsarian view than there is in
the other views of sin. To this also, it seems to
me can be reduced the opinion of Saint Augustine
and of other authors: that the root of evil is in the
negativity, that is to say, in the lack or limitation
of creatures which God graciously remedies by what-
ever degree of perfection it pleases him to give.
This grace of God, whether ordinary or .extraordi-
nary has its degrees and its measures. It is always
efficacious in itself to produce a certain proportion-
ate effect and furthermore it is always sufficient not
only to keep one from sin but even to effect his
salvation, provided that the man co-operates with
that which is in him. It has not always, however,
sufficient power to overcome the inclination, for, if
it did, it would no longer be limited in any way,
and this superiority to limitations is reserved to
that unique grace which is absolutely efficacious.
This grace is always victorious whether through
its own self or through the congruity of circum-
stances.

52 LEIBNIZ.

XXXI. Concerning the motives of election ; concern-
ing faith foreseen and the absolute decree and that
it all reduces to the question why God has chosen and
resolved to admit to existence just such a possible per-
son, whose concept includes just such a sequence of free
acts and of free gifts of grace. This at once puts an end
to all difficulties.

Finally, the grace of God is wholly unprejudiced
and creatures have no claim upon it. Just as it is
not sufficient in accounting for God's choice in his
dispensations of grace to refer to his absolute or
conditional prevision of men's future actions, so it
is also wrong to imagine his decrees as absolute
with no reasonable motive. As concerns foreseen
faith and good works, it is very true that God has
elected none but those whose faith and charity he
foresees, quos se fide donaturum praescivit. The
same question, however, arises again as to why God
gives to some rather than to others the grace of
faith or of good works. As concerns God's ability
to foresee not only the faith and good deeds, but
also their material and predisposition, or that which
a man on his part contributes to them (since there
are as truly diversities on the part of men as on
the part of grace, and a man although he needs to
be aroused to good and needs to become converted,
yet acts in accordance with his temperament), — as
regards his ability to foresee there are many who
say that God, knowing what a particular man will
do without grace, that is without his extraordinary
assistance, or knowing at least what will be the
human contribution, resolves to give grace to those
whose natural dispositions are the best, or at any rate
are the least imperfect and evil. But if this were the

DISCOURSE ON METAPHYSICS. 53

case then the natural dispositions in so far as they
were good would be like gifts of grace, since God
would have given advantages to some over others;
and therefore, since he would well know that the
natural advantages which he had given would serve
as motives for his grace or for his extraordinary
assistance, would not everything be reduced to his
mercy? I think, therefore, that since we do not
know how much and in what way God regards
natural dispositions in the dispensations of his grace,
it would be safest and most exact to say, in accord-
ance with our principles and as I have already
remarked, that there must needs be among possible
beings the person Peter or John whose concept or
idea contains all that particular sequence of ordi-
nary and extraordinary manifestations of grace
together with the rest of the accompanying events
and circumstances, and that it has pleased God to
choose him among an infinite number of persons
equally possible for actual existence. When we
have said this there seems nothing left to ask, and
all difficulties vanish. For in regard to that great
and ultimate question why it has pleased God to
choose him among so great a number of possible
persons, it is surely unreasonable to demand more
than the general reasons which we have given.
The reasons in detail surpass our ken. Therefore,
instead of postulating an absolute decree, which
being without reason would be unreasonable, and
instead of postulating reasons which do not succeed
in solving the difficulties and in turn have need
themselves of reasons, it will be best to say with
St. Paul that there are for God's choice certain
great reasons of wisdom and congruity which he

54 LEIBNIZ.

follows, which reasons, however, are unknown to
mortals and are founded upon the general order,
whose goal is the greatest perfection of the world.
This is what is meant when the motives of God's
glory and of the manifestation of his justice are
spoken of, as well as when men speak of his mercy,
and his perfection in general; that immense vastness
of wealth, in fine, with which the soul of the same
St. Paul was to thrilled.

XXXII. Usefulness of these principles in matters of

piety and of religion.
.or

* W- In addition it seems that the thoughts which we

c^ "\ have just explained and particularly the great prin-
ciple of the perfection of God's operations and the
concept of substance which includes all its changes
with all its accompanying circumstances, far from
injuring, serve rather to confirm religion, serve to
dissipate great difficulties, to inflame souls with a
divine love and to raise the mind to a knowledge
of incorporeal substances much more than the
present-day hypotheses. For it appears' clearly
that all other substances depend upon God just as
our thoughts emanate from our own substances;
that God is all in all and that he is intimately united
to all created things, in proportion however to their
perfection; that it is he alone who determines them
from without by his influence, and if to act is to
determine directly, it may be said in metaphysical
language that God alone acts upon me and he alone
causes me to do good or ill, other substances con-
tributing only because of his determinations;
because God, who takes all things into considera-

DISCOURSE ON METAPHYSICS. 55

tion, distributes his bounties and compels created
beings to accommodate themselves to one another.
Thus God alone constitutes the relation or commu-
nication between substances. It is through him that
the phenomena of the one meet and accord with the
phenomena of the others, so that there may be a
reality in our perceptions. In common parlance,
however, an action is attributed to particular causes
in the sense that I have explained above because it
is not necessary to make continual mention of the
universal cause when speaking of particular cases.
It can be seen also that every substance has a per-
fect spontaneity (which becomes liberty with intel-
ligent substances). Everything which happens to it
is a consequence of its idea or its being and noth-
ing determines it except God only. It is for this
reason that a person of exalted mind and revered
saintliness may say that the soul ought often to
think as if there were only God and itself in the
world. Nothing can make us hold to immortality
more firmly than this independence and vastness of
the soul which protects it completely against exte-
rior things, since it alone constitutes our universe
and together with God is sufficient. for itself. It is
as impossible for it to perish save through annihila-
tion as it is impossible for the universe to destroy
itself, the universe whose animate and perpetual
expression it is. Furthermore, the changes in this
extended mass which is called our body cannot pos-
sibly affect the soul nor can the dissipation of the
body destroy that which is indivisible.

LEIBNIZ.

XXXIII. Explanation of the relation between the
soul and the body, a matter which has been regarded as
inexplicable or else as miraculous; concerning the origin
of confused perceptions.

We can also see the explanation of that great
mystery "the union of the soul and the body," that
is to say how it comes about that the passions and
actions of the one are accompanied by the actions
and passions or else the appropriate phenomena of
the other. For it is not possible to conceive how
one can have an influence upon the other and it is
unreasonable to have recourse at once to the extraor-
dinary intervention of the universal cause in an
ordinary and particular case. The following, how-
ever, is the true explanation. We have said that
everything which happens to a soul or to any sub-
stance is a consequence of its concept; hence the
idea itself or the essence of the soul brings it about
that all of its appearances or perceptions should be
born out of its nature and precisely in such a way
that they correspond of themselves to that which
happens in the universe at large, but more partic-
ularly and more perfectly to that which happens in
the body associated with it, because it is in a partic-
ular way and only for a certain time according to
the relation of other bodies to its own body that the
soul expresses the state of the universe. This last
fact enables us to see how our body belongs to us,
without, however, being attached to our essence.
I believe that those who are careful thinkers will
decide favorably for our principles because of this
single reason, viz., that they are able to see in what
consists the relation between the soul and the body,
a parallelism which appears inexplicable in any

DISCOURSE ON METAPHYSICS. 57

other way. We can also see that the perceptions of
our senses even when they are clear must necessarily
contain certain confused elements, for as all the
bodies in the universe are in sympathy, ours receives
the impressions of all the others, and while our
senses respond to everything, our soul cannot pay
attention to every particular. That is why our con-
fused sensations are the result of a variety of per-
ceptions This variety is infinite. It is almost like
the confused murmuring which is heard by those
who approach the shore of a sea. It comes from
the continual beatings of innumerable waves. If
now, out of many perceptions which do not at all
fit together to make one, no particular one percep-
tion surpasses the others, and if they make impres-
sions about equally strong or equally capable of
holding the attention of the soul, they can be per-
ceived only confusedly.

XXXIV. Concerning the difference between spirits
and other substances, souls or substantial forms; that the
immortality which men desire includes memory.

Supposing that the bodies which constitute a
unum per se, as human bodies, are substances, and
have substantial forms, and supposing that animals
have souls, we are obliged to grant that these souls
and these substantial forms cannot entirely perish,
any more than can the atoms or the ultimate ele-
ments of matter, according to the position of other
philosophers; for no substance perishes, although
it may become very different. Such substances
also express the whole universe, although more
imperfectly than do spirits. The principle differ-

58 LEIBNIZ.

ence, however, is that they do not know that they
are, nor what they are. Consequently, not being
able to reason, they are unable to discover necessary
and universal truths. It is also because they do not
reflect regarding themselves that they have no
moral qualities, whence it follows that undergoing
a thousand transformations, as we see a caterpillar
change into a butterfly, the result from a moral or
practical standpoint is the same as if we said that
they perished in each case, and we can indeed say
it from the physical standpoint in the same way
that we say bodies perish in their dissolution. But
the intelligent soul, knowing that it is and having
the ability to say that word "I" so full of meaning,
not only continues and exists, metaphysically far
more certainly than do the others, but it remains
the same from the moral standpoint, and constitutes
the same personality, for it is its memory or knowl-
edge of this ego which renders it open to punish-
ment and reward. Also the immortality which is
required in morals and in religion does not consist
merely in this perpetual existence, which pertains
to all substances, for if in addition there were no
remembrance of what -one had been, immortality
would not be at all desirable. Suppose that some
individual could suddenly become King of China
on condition, however, of forgetting what he had
been, as though being born again, would it not
amount to the same practically, or as far as the
effects could be perceived, as if the individual were
annihilated, and a king of China were the same
instant created in his place? The individual would
have no reason to desire this.

DISCOURSE ON METAPHYSICS. 59

XXXV. The excellence of spirits; that God considers
them preferable to other creatures; that the spirits ex-
press God rather than the world, while other simple
substances express the world rather than God.

In order, however, to prove by natural reasons
that God will preserve forever not only our sub-
stance, but also our personality, that is to say the
recollection and knowledge of what we are (although
the distinct knowledge is sometimes suspended
during sleep and in swoons) it is necessary to join
to metaphysics moral considerations. God must be
considered not only as the principle and the cause
of all substances and of all existing things, but also
as the chief of all persons or intelligent substances,
as the absolute monarch of the most perfect city or
republic, such as is constituted by all the spirits
together in the universe, God being the most com-
plete of all spirits at the same time that he is great-
est of all beings. For assuredly the spirits are the
most perfect of substances and best express the
divinity. Since all the nature, purpose, virtue and
function of substances is, as has been sufficiently
explained, to express God and the universe, there
is no room for doubting that those substances which
give the expression, knowing what they are doing
and which are able to understand the great truths
about God and the universe, do express God and the
universe incomparably better than do those natures
which are either brutish and incapable of recogniz-
ing truths, or are wholly destitute of sensation and
knowledge. The difference between intelligent
substances and those which are not intelligent is
quite as great as between a mirror and one who sees.
As God is himself the greatest and wisest of spirits

60 LEIBNIZ.

it is easy to understand that the spirits with which
he can, so to speak, enter into conversation and
even into social relations by communicating to
them in particular ways his feelings and his will so
that they are able to know and love their benefac-
tor, must be much nearer to him than the rest of
created things which may be regarded as the instru-
ments of spirits. In the same way we see that all
wise persons consider far more the condition of a
man than of anything else however precious it may
be; and it seems that the greatest satisfaction which
a soul, satisfied in other respects, can have is to see
itself loved by others. However, with respect to
God there is this difference that his glory and our
worship can add nothing to his satisfaction, the
recognition of creatures being nothing but a conse-
quence of his sovereign and perfect felicity and
being far from contributing to it or from causing
it even in part. Nevertheless, that which is reason-
able in finite spirits is found eminently in him and
as we praise a king who prefers to preserve the life
of a man before that of the most precious and rare
of his animals, we should not doubt that the most
enlightened and most just of all monarchs has the
same preference.

XXXVI. God is the monarch of the most perfect re*
public composed of all the spirits, and the happiness of
this city of God is his principal purpose.

Spirits are of all substances the most capable of
perfection and their perfections are different in this
that they interfere with one another the least, or
rather they aid one another the most, for only the
most virtuous can be the most perfect friends.

DISCOURSE ON METAPHYSICS. 6l

Hence it follows that God who in all things has the
greatest perfection will have the greatest care for
spirits and will give not only to all of them in
general, but even to each one in particular the
highest perfection which the universal harmony will
permit. We can even say that it is because he is a.
spirit that God is the originator of existences, for
if he had lacked the power of will to choose what
is best, there would have been no reason why one
possible being should exist rather than any other.
Therefore God's being a spirit himself dominates
all the consideration which he may have toward
created things. Spirits alone are made in his
image, being as it were of his blood or as children
in the family, since they alone are able to serve
him of free will, and to act consciously imitating
the divine nature. A single spirit is worth a whole
world, because it not only expresses the whole
world, but it also knows it and governs itself as
does God. In this way we may say that though
every substance expresses the whole universe, yet
the other substances express the world rather than
God, while spirits express God rather than the
world. This nature of spirits, so noble that it
enables them to approach divinity as much as is
possible for created things, has as a result that God
derives infinitely more glory from them than from
the other beings, or rather the other beings furnish
to spirits the material for glorifying him. This
moral quality of God which constitutes him Lord
and Monarch of spirits influences him so to speak
personally and in a unique way. It is through this
that he humanizes himself, that he is willing to
suffer anthropologies, and that he enters into social

6a LEIBNIZ.

relations with us and this consideration is so dear
to him that the happy and prosperous condition of
his empire which consists in the greatest possible
felicity of its inhabitants, becomes supreme among
his laws. Happiness is to persons what perfection
is to beings. And if the dominant principle in the
existence of the physical world is the decree to
give it the greatest possible perfection, the primary
purpose in the moral world or in the city of God
which constitutes the noblest part of the universe
ought to be to extend the greatest happiness pos-
sible. We must not therefore doubt that God has
so ordained everything that spirits not only shall
live forever, because this is unavoidable, but that
they shall also preserve forever their moral
quality, so that his city may never lose a person,
quite in the same way that the world never loses a
substance. Consequently they will always be con-
scious of their being, otherwise they would be open
to neither reward nor punishment, a condition
which is the essence of a republic, and above all of
the most perfect republic where nothing can be
neglected. In fine, God being at the same time
the most just and the most debonnaire of monarchs,
and requiring only a good will on the part of men,
provided that it be sincere and intentional, his sub-
jects cannot desire a better condition. To render them
perfectly happy he desires only that they love him.

XXXVII. Jesus Christ has revealed to men the mys-
tery and the admirable laws of the kingdom of heaven,
and the greatness of the supreme happiness which God
has prepared for those who love him.

The ancient philosophers knew very little of these

DISCOURSE ON METAPHYSICS. 63

important truths. Jesus Christ alone has expressed
them divinely well, and in a way so clear and sim-
ple that the dullest minds have understood them.
His gospel has entirely changed the face of human
affairs. It has brought us to know the kingdom of
heaven, or that perfect republic of spirits which
deserves to be called the city of God. He it is who
has discovered to us its wonderful laws. He alone
has made us see how much God loves us and with
what care everything that concerns us has been
provided for; how God, inasmuch as he cares for
the sparrows, will not neglect reasoning beings, who
are infinitely more dear to him; how all the hairs of
our heads are numbered; how heaven and earth may
pass away but the word of God and that which
belongs to the means of our salvation will not pass
away; how God has more regard for the least one
among intelligent souls than for the whole machin-
ery of the world; how we ought not to fear those
who are able to destroy the body but are unable to
destroy the soul, since God alone can render the soul
happy or unhappy; and how the souls of the right-
eous are protected by his hand against all the
upheavals of the universe, since God alone is able
to act upon them; how none of our acts -are forgot-
ten; how everything is to be accounted for; even
careless words and even a spoonful of water which
is well used; in fact how everything must result in
the greatest welfare of the good, for then shall the
righteous become like suns and neither our sense
nor our minds have ever tasted of anything
approaching the joys which God has laid up for
those that love him.

CORRESPONDENCE

RELATING TO THE METAPHYSICS.

CORRESPONDENCE RELATING TO
THE METAPHYSICS.

I.

Leibniz to Count Ernst von Hessen-Rheinfels,

i/i i Feb., 1686.

. . . Being at a place lately for several days with
nothing to do, I wrote out a short discourse on
Metaphysics on which I should be very glad to have
the opinion of Mons. Arnaud.* For the questions
in regard to grace, in regard to the relations of God
with created beings, in regard to the nature of mir-
acles, the cause of sin, the origin of evil, the
immortality of the soul, ideas, etc., are discussed in
a way which seems to offer new points of. approach
fitted to clear up some great difficulties. I enclose
herewith a summary of the articles which it con-
tains, as I have not had time to make a clean copy
of the whole.

I therefore beg Your Serene Highness to send him
this summary, requesting him to look it over and
give his judgment upon it. For, as he excels
equally in Theology and in Philosophy, in erudition
and in power of thought, I know of no one who is
better fitted to give an opinion upon it. I am very
desirous to have a critic as careful, as enlightened
and as open to reason as is Monsieur Arnaud, being
myself also a person the most disposed in the world
to submit to reasoning.

* Leibniz always used the form Arnaud. — Trans.

6?

68 CORRESPONDENCE.

Perhaps Mons. Arnaud will not find this outline
wholly unworthy of his consideration, especially
since he has been somewhat occupied in the exam-
ination of these matters. If he finds obscurities I
will explain myself sincerely and frankly, and if he
finds me worthy indeed of his instruction I shall try
to behave in such a way that he shall find no cause
for being dissatisfied on that point. I beg Your
Serene Highness to enclose this with the summary
which I am sending and to forward them both to
Mons. Arnaud.

SUMMARY OF THE DISCOURSE ON META-
PHYSICS

1. Concerning the divine perfection and that God
does everything in the most desirable way.

2. Against those who hold that there is in the
works of God no goodness, or that the principles of
goodness and beauty are arbitrary.

3. Against those who think that God might have
made things better than he has.

4. That love for God demands on our part com-
plete satisfaction with and acquiescence in that
which he has done.

5. In what the principles of the perfection of the
divine conduct consist and that the simplicity of
the means counterbalances the richness of the
effects.

6. That God does nothing which is not orderly
and that it is not even possible to conceive of
events which are not regular.

7. That miracles conform to the general order
although they go against the subordinate regula-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 69

tions; concerning that which God desires or permits
and concerning general and particular intentions.

8. In order to distinguish between the activities
of God and the activities of created things, we must
explain the conception of an individual substance.

9. That every individual substance expresses the
whole universe in its own manner, and that in its full
concept is included all its experiences together
with all the attendant circumstances and the whole
sequence of exterior events.

10. That the belief in substantial forms has a cer-
tain basis, in fact but that these forms effect no
changes in the phenomena and must not be employed
for the explanation of particular events.

11. That the opinions of the theologians and of
the so-called scholastic philosophers are not to be
wholly despised.

12. That the conception of the extension of a
body is in a way imaginary and does not constitute
the substance of the body.

13. As the individual concept of each person
includes once for all everything which can ever
happen to him, in it can be seen a priori the evi-
dences or the reasons for the reality of each event
and why one happened sooner than the other. But
these events, however certain, are nevertheless
contingent being based on the free choice of God
and of his creatures. It is true that their choices
always have their reasons but they incline to the
choices under no compulsion of necessity.

14. God produces different substances according
to the different views which he has of the world
and by the intervention of God the appropriate
nature of each substance brings it about that what

7O CORRESPONDENCE.

happens to one corresponds to what happens to all
the others without, however, their acting upon one
another directly.

15. The action of one finite substance upon
another consists only in the increase in the degree
of the expression of the first combined with a
decrease in that of the second, in so far as God has
in advance fashioned them so that they should
accord.

16. The extraordinary intervention of God is not
excluded in that which our particular essences
express because this expression includes every-
thing. Such intervention however goes beyond the
power of our natural being or of our distinct
expression because these are finite and follow cer-
tain subordinate regulations.

17. An example of a subordinate regulation in the
law of nature which demonstrates that God always
preserves the same amount of force but not the
same quantity of motion; against the Cartesians
and many others.

18. The distinction between force and the quantity
of motion is, among other reasons, important as
showing that we must have recourse to metaphysical
considerations in addition [to discussions of exten-
sion, if we wish to explain the phenomena of matter.

19. The utility of final causes in physics.

20. A noteworthy disquisition by Socrates in
Plato's Phaedo against the philosophers who were
too materialistic.

21. If the mechanical laws depended upon geom-
etry alone without metaphysical influences, the phe-
nomena would be very different from what they are.

22. Reconciliation of the two methods of expla-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 71

nation, the one using final causes and the other effi-
cient causes, thus satisfying both those who explain
nature mechanicariy and also those who have
recourse to incorporeal natures.

23. Returning to immaterial substances we explain
how God acts upon the understanding of spirits, and
ask whether one always keeps the idea of what he
thinks about.

24. What clear and obscure, distinct and con-
fused, adequate and inadequate, intuitive and
assumed knowledge is, and the definition of nom-
inal, real, causal and essential.

25. In what cases knowledge is added to mere
contemplation of the idea.

26. Ideas are all stored up within us. Plato's
doctrine of reminiscence.

27. In what respect our souls can be compared to
blank tablets and how conceptions are derived from
the senses.

28. The only immediate object of our perceptions
which exists outside of us is God and in him alone
is our light.

29. Yet we think directly by means of our own
ideas and not through God's.

30. How God inclines our souls without necessi-
tating them; that there are no grounds for com-
plaint; that we must not ask why Judas sinned
because this free act is contained in his concept,
the only question being why Judas the sinner is
admitted to existence, preferably to other possible
persons; concerning the original imperfection or
limitation before the fall and concerning the differ-
ent degrees of grace.

31. The motives for election, faith foreseen, par-

72 CORRESPONDENCE.

tial knowledge, the absolute decree and that the
whole inquiry is reduced to the question why God
has chosen and resolved to admit to existence such
a possible person whose concept involves such a
sequence of gifts of grace and of free acts. This at
once overcomes all the difficulties.

32. Applicability of these principles in matters of
piety and of religion.

33. Explanation of the inter-relation of soul and
body which has been usually considered inexplica-
ble and miraculous; also concerning the origin of
confused perceptions.

34. The difference between spirits and other sub-
stances, souls or substantial forms, and that the
immortality which people wish for includes remem-
brance.

35. Excellence of spirits; that God considers
them preferably to the other created things; that
spirits express God rather than the world while
other simple substances express rather the world
than God.

36. God is the monarch of the most perfect repub-
lic which is composed of all the spirits, and the
felicity of this city of God is his principal purpose.

37. Jesus Christ has disclosed to men the mystery
and the admirable laws of the Kingdom of Heaven
and the greatness of the supreme happiness which
God has prepared for those who love him.

II

Arnauld to Count Ernst von Hessen-Rheinfels.

March 13, 1686.

I have received, Monseigneur, the metaphysical
thoughts which Your Highness sent me from Mr.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 73

Leibniz as a witness of his affection and his esteem
for which I am very grateful to him. But I
have been so busy ever since that only within the
last three days have I been able to read his mis-
sive.

And at the present time I have such a bad cold
that all that I can do now is to tell Your Highness
in a couple of words that I find in his thoughts so
many things which frightened me and which if I
am not mistaken almost all men would find so star-
tling that I cannot see any utility in a treatise which
would be evidently rejected by everybody.

I will instance for example what is said in Article
13: That the individual concept of every person
involves once for all everything which will ever
happen to him, etc. If this is so, God was free to
create or not to create Adam, but supposing he
decided to create him, all that has since happened
to the human race or which will ever happen to it
has occurred and will occur by a necessity more
than fatal. For the individual concept of Adam
involved that he would have so many children and
the individual concepts of these children involved
all that they would do and all the children that
they would have; and so on. God has therefore no
more liberty in regard to all that, provided he
wished to create Adam, than he was free to create
a nature incapable of thought, supposing that he
wished to create me. I am not in a position to
speak of this at greater length, but Mr. Leibniz
will understand my meaning and it is possible that
he will find no difficulties in the consequence which
I have drawn. If he finds none, however, he has
reason to fear that he will be alone in his position,

74 CORRESPONDENCE.

and were I wrong in this last statement I should be
still sorrier.

I cannot refrain from expressing to Your High-
ness my sorrow at his attachment to those opinions,
which he has indeed felt could hardly be permitted
in the Catholic Church. The Catholic Church would
prohibit his entertaining them, and it is apparently
this attachment that has prevented his entering the
fold, notwithstanding the fact that Your Highness,
if I remember rightly, brought him to recognize that
there was no reasonable doubt as to its being the
true church.* Would it not be better for him to
leave those metaphysical speculations which can
be of utility neither to himself nor to others, in
order to apply himself seriously to the most im-
portant matter he can ever undertake, namely,
to assure his salvation, by entering into the
Church from which new sects can form only by
rendering themselves schismatic? I read yesterday
by chance one of Saint Augustine's letters in which
he answers various questions that were put forward
by a Pagan who showed a desire to become a Chris-
tian but who always postponed doing so. He says,
at the end, what may be applied to our friend
"There are numberless problems which are not to
be solved before one has faith and will not be solved
in life without faith."

Ill
Leibniz to Count Ernst von Hessen-Rheinfels.

April 12, 1686.
I do not know what to say to M. A.'s letter, and

* Leibniz remarks on the margin of Arnauld's letter: "I have
never endorsed this sentiment." Interesting as indicating
Leibniz's attitude toward Catholicism. — Editor.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 75

I never should have thought that a person whose
reputation is so great and so real and from whom
we have such excellent Reflections on Morals and
Logic would be so precipitate in his judgments.
After this instance I am not surprised that some
are angry at him. Nevertheless I think it well to
be patient at times under the ill humor of one whose
merit is extraordinary, provided his acts have no
serious results and I believe that a judicious reply
may dissipate a prejudice ill-founded. I anticipate
this justice in M. A.

Whatever reason, however, I may have for com-
plaint, I desire to suppress all reflections which are
not essential to the matter in hand and which
might serve to increase the ill-feeling, but I hope
he will use the same moderation, in case he has the
graciousness to act as my instructor. I am only
able to assure him that he is quite mistaken in cer-
tain of his conjectures, because people of good sense
have judged otherwise regarding my positions, and
that notwithstanding their encouragement I have
not been over quick in publishing anything upon
abstract subjects which are to the taste of few peo-
ple, inasmuch as the public even has as yet heard
almost nothing in regard to certain more plausible
discoveries which I made several years ago.

I have written down these Meditations only in
order to profit for my own sake by the criticisms of
more able thinkers and in order to receive confi-
dence or correction in the investigation of these
most important truths. It is true that some per-
sons of intelligence have found my opinions accept-
able, but I should be the first to warn them if I thought
there were the slightest evil effects from them.

76 CORRESPONDENCE.

This declaration is sincere, and this will not be
the first time that I have profited by the instruc-
tion of enlightened persons. This is why I shall
assuredly be under great obligations to M. A. in
case I merit his having the goodness to deliver me
from the errors which he thinks dangerous and of
which, I declare it in good faith, I am unable to
see the evil. But I hope that he will use modera-
tion, and that he will do me justice, because men
deserve at least that no wrong be done to them
through precipitate judgments.

He chooses one of my theses to show that it is
dangerous. But either I am incapable for the
present of understanding the difficulty or else there
is none in it. This has enabled me to recover from
my surprise and has made me think that M.
Arnaud's remarks are the result of misconceptions.
I will try therefore to deflect him from that strange
opinion, which he conceived a little too hurriedly.

I said in the I3th article of my summary that the
individual concept of each person involved once
for all, all that would ever happen to him. From that
he draws this conclusion that all that happens to
any person and even to the whole human race must
occur by a necessity more than fatal, as though
concepts and previsions rendered things necessary
and as though a free act could not be included in
the concept or perfect view which God has of the
person who performs it. And he adds that per-
haps I will not find difficulties in the conclusion
which he draws. Yet I have expressly protested in
that same article that I do not admit such a conclu-
sion. It must be then either that he doubts my
sincerity for which I have given him no grounds or

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 77

else he has not sufficiently examined that which he
controverts. I do not complain as much as it
appears I have a right to, because I remember that
he was writing at a time when an indisposition did
not permit him the liberty of his whole mind, as the
letter itself witnesses. And I desire to have him
know how much regard I have for him.

He says: "If this is true (that is to say that the
individual concept of each person involves once
for all all that will ever happen to him), God has
not been free to create everything that has since
happened to the human race, and all that will hap-
pen to it for all eternity must occur through a
necessity more than fatalistic." (There is some fault
in the copy but I have felt able to amend it as
above.) "For the individual concept, Adam, has
involved that he should have so many children
and the individual concept of each one of these
children has involved everything that they would
do and all the children that they would have, and
so on. There is therefore no more liberty in God
regarding all that, supposing that he wished to
create Adam, than there is to create a nature
incapable of thought, supposing that he wished to
create me."

To these last words ought properly to have been
added the proof of the consequence but it is quite
evident that they confuse necessitatem ex hypothesi
with absolute necessity. A distinction has always
been made between God's freedom to act absolutely
and his obligation to act in virtue of certain resolu-
tions already made. He hardly understands the
case who does not take the whole into considera-
tion. It is little consonant with God's dignity to

78 CORRESPONDENCE.

conceive of him (with the pretext of assuring his
freedom) like certain Socinians, as a human being
who forms his resolutions according to circum-
stances. These maintain that he would be no
longer free to create what he found good if his first
resolutions in regard to Adam or other men already
involved a relationship to that which concerned
their posterity. Yet all agree that God has regu-
lated from all eternity the whole course of the
universe without this fact diminishing his freedom
in any respect. It is clear also that these objec-
tors separate the will-acts of God one from another
while his acts are in fact inter-related. For we
must not think of the intention of God to create
a certain man Adam as detached from all the other
intentions which he has in regard to the children
of Adam and of all the human race, as though God
first made the decree to create Adam without any
relation to his posterity. This, in my opinion,
does away with his freedom in creating Adam's
posterity as seems best to him, and is a very strange
sort of reasoning. We must rather think that God,
choosing not an indeterminate Adam but a par-
ticular Adam, whose perfect representation is found
among the possible beings in the Ideas of God and
who is accompanied by certain individual circum-
stances and among other predicates possesses also
that of having in time a certain posterity, — God, I
say, in choosing him, has already had in mind his
posterity and chooses them both at the same time.
I am unable to understand how there is any evil
in this opinion. If God should act in any other
way he would not act as God. I will give an illus-
tration. A wise prince in choosing a general whose

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS 79

intimates he knows, chooses at the same time cer-
tain colonels and captains whom he well knows this
general will recommend and whom he will not wish
to refuse to him for certain prudential reasons.
This fact, however, does not at all destroy the
absolute power of the prince nor his freedom. The
same applies to God even more certainly.

Therefore to reason rightly we must think of God
as having a certain more general and more compre-
hensive intention which has regard to the whole
order of the universe because the universe is a whole
which God sees through and through with a single
glance. This more general intention embraces
virtually the other intentions touching what tran-
spires in this universe and among these is also that
of creating a particular Adam who is related to the
line of his posterity which God has already chosen
as such and we may even say that these particular
intentions differ from the general intention only in
a single respect, that is to say, as the situation of
a city regarded from a particular point of view has
its particular geometrical plan. These various
intentions all express the whole universe in the
same way that each situation expresses the city.
In fact the wiser a man is, the less detached inten-
tions does he have, and again the more views and
intentions that one has the less comprehensive and
inter-related they are.

Each particular intention involves a relation to
all the others, so that they may be concerted together
in the best way possible. Far from finding in this
anything repellent, I think that the contrary view
destroys the perfection of God. In my opinion
one must be hard to please or else prejudiced when

8o CORRESPONDENCE.

he finds opinions so innocent or rather so reason-
able, worthy of exaggerations so strange as those
which were sent to Your Highness.

If what I said be thought over a little it will be
found to be evident ex terminis: for by the indi-
vidual concept, Adam, I mean of course a perfect
representation of a particular Adam who has certain
individual characteristics and is thus distinguished
from an infinity of possible persons very similar to
him yet for all that different from him (as ellipses
always differ from the circle, however closely they
may approach it). God has preferred him to these
others because it has pleased God to choose pre-
cisely such an arrangement of the universe, and
everything which is a consequence of this resolu-
tion is necessary only by a hypothetical necessity
and by no means destroys the freedom of God nor
that of the created spirits. There is a possible
Adam whose posterity is of a certain sort, and an
infinity of other possible Adams whose posterity
would be otherwise; now is it not true that these
possible Adams (if we may speak of them thus)
differ among themselves and that God has chosen
only one who is precisely ours? There are so many
reasons which prove the impossibility, not to say
the absurdity and even the impiety of the contrary
view, that I believe all men are really of the same
opinion when they think over a little what they are
saying. Perhaps M. A. also, if he had not been
prejudiced against me as he was at first, would not
have found my propositions so strange and would
not have deduced from them the consequences
which he did.

I sincerely think I have met M. Arnaud's objec-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 8l

tion and I am glad to see that the point which he
has selected as the most startling, is in my opinion
so little so. I do not know, however, whether I
will have the pleasure of bringing M. Arnaud to
acknowledge it also. Among the thousand advan-
tages of great intellectual ability there is this little
defect, that those who are possessed of this great
intellectual ability, having the right to trust to their
opinions, are not easily changed. As for myself,
who am not of this stamp, I glory in acknowledging
that I have been taught, and I should even find pleas-
ure in being taught, provided I could say it sincerely
and without flattery.

In addition I wish M. Arnaud to know that I
make no pretentions to the glory of being an inno-
vator, as he seems to have understood my opinions.
On the contrary I usually find that the most ancient
and the most generally accepted opinions are the
best. I think that one cannot be accused of being
an innovator when he produces only certain new
truths without overturning well established beliefs.
This is what the Geometers are doing and all those
who are moving forward. I do not know if it will be
easy to indicate authorized opinions to which mine
are opposed. That is why what M. Arnaud says
concerning the church has nothing to do with these
meditations of mine, and I hope that he does not
wish to hold and that he will not be able to prove
them to contain anything that can be considered as
heretical in any church whatever. Yet if the Church
to which he belongs is so prompt to censure, such
a proceeding should serve as a notice to be on one's
guard. As soon as a person might wish to express,
some view which would have the slightest bearing

82 CORRESPONDENCE.

upon Religion and which might go a little beyond
what is taught to children, he would be in danger of
getting into difficulties or at least of having some
church father as a sponsor, which is saying the
same things in terminis. Yet even that would not
be perhaps sufficient for complete safety, above all,
when one has no means of support.

If Your Serene Highness were not a Prince whose
intelligence is as great as is his moderation, I should
have been on my guard in speaking of these things.
To whom, however, do they relate better than to
you, and since you have had the goodness to act as
intermediary in this discussion, can we without
imprudence have recourse to any other arbitrator?
In so far as the concern is not so much regarding
the truth of certain propositions as regarding their
consequences and their being tolerated, I do not
believe that you will approve so much vehemence
over so small a matter. It is quite possible, how-
ever, that M. A. spoke in those severe terms only
because he believed that I would admit the conse-
quence which he had reason to find so terrifying and
that he will change his language after my explana-
tion. To this, his own sense of justice will con-
tribute as much as the authority of Your Highness.
I am, with devotion, etc.

IV
Leibniz to Count Ernst von Hessen-Rheinfels.

April 12, 1686.

I have received M. Arnaud's verdict and I think
jt well to disabuse his mind by the enclosed reply
in the form of a letter to Your Highness. But I

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 83

confess that I have had much difficulty in suppress-
ing a desire as much to laugh as to express pity,
inasmuch as the good man seems really to have lost
a part of his mind and seems not to have been able
to keep from crying out against everything as do
those seized with melancholy to whom everything
which they see or think of appears black. I have
shown a good deal of moderation toward him but I
have not avoided letting him quietly know that he
is wrong. If he has the kindness to rescue me
from the errors which he attributes to me and which
he thinks to have seen in my writings, I wish that
he would suppress the personal reflections and the
severe expressions, which I have feigned not to
notice out of the respect which I have for Your
Serene Highness and also because of the respect
which I have for the merits of the good man.

Yet I am surprised at the difference which there
is between our pretended Santons and those persons
of the world who pretend to no such position and have
much more the effect. Your Serene Highness is a
Sovereign Prince and still you have shown to me a
moderation which I wonder at, while M. Arnaud is
a famous theologian whose meditations on religious
subjects ought to have rendered him mild and char-
itable, yet what he says seems often haughty, rough
and full of severity. I am not surprised now that
he has so easily fallen out with Father Malebranche
and others who used to be his fast friends. Father
Malebranche has published writings which M.
Arnaud treated extravagantly almost as he has done
in my case. The world has not always been of his
opinions. He must take care, however, not to
excite his bilious temper. It will deprive us of

84 CORRESPONDENCE.

all the pleasure and all the satisfaction which 1
had anticipated in a mild and reasonable debate.

1 believe he received my paper when he was in an
ill humor and finding himself put to trouble by it,
he wanted to revenge himself by a rebuff. I know
that if Your Serene Highness had the leisure to con-
sider the objection which he brought forward, you
could not refrain from laughing at seeing the slight
cause he had for making such tragic exclamations;
quite as one would laugh on hearing an orator who
should say every few minutes, "O coelum, O terra,
O maria Neptuni."

I am glad that there is nothing more repellent, or
more difficult in my thoughts than what he objects
to. For according to him if what I say is true
(namely that the individual concept or considera-
tion of Adam, involves all that will happen to him
and to his posterity), it follows that God will have
no liberty any longer with respect to the human
race. He imagines therefore that God is like a
human being who forms his resolves in accordance
with circumstances, while on the contrary, God,
foreseeing and having regulated all things from all
eternity, has chosen from the first the entire sequence
and inter-relation of the universe and consequently
not simply an Adam but such an Adam in regard to
whom he foresaw that he would do such and such
things and would have such and such children, with-
out, however, this prevision of God's, though
ordained from all time, interfering at all with his
freedom. On this point all theologians, excepting
some Socinians who think of God as a human being,
are agreed. And I am surprised that the desire to
find something repellent in my thoughts, prejudice

LEIBNIZ. ARNAULD. HKSSEN-RHEINFELS. 85

against which had engendered in his mind a con-
fused and ill-directed idea, has led this learned man
to speak against his own knowledge and convic-
tions. For I am not so unfair as to imitate him
and to impute to him the dangerous doctrine of
those Socinians which destroys the sovereign per-
fection of God, although he seems almost to incline
to that doctrine in the heat of debate.

Every man who acts wisely considers all the cir-
cumstances and bearings of the resolve which he
makes, and this in accordance with the measure of
his abilities. And God, who sees every thing per-
fectly and with a single glance, can he have failed
to make his plans in conformity with everything
which he saw? And can he have chosen a particular
Adam without considering and having in mind all
that has relations to him? Consequently it is ridic-
ulous to say that this free resolve on God's part
deprives him of his liberty. Otherwise in order to
be free one must need be ever undecided. Such
are the thoughts which are repellent to Mr. Arnaud.
We will see if through their consequences he will
be able to derive something worse from them. Yet
the most important reflection which I have made
in the enclosed is that he himself some time ago
expressly wrote to Your Serene Highness that no
trouble was given to a man who was in their church
or who wished to be in it, for his philosophical
opinions and here is he now, forgetting this modera-
tion, and losing control of himself over a trifle. It
is therefore dangerous to consort with such people
and Your Serene Highness sees how many precau-
tions one should take. This was one of the very
reasons why I communicated the summary to M.

86 CORRESPONDENCE.

Arnaud, viz., to probe a little and to see what his
behaviour would be. But tange monies et fumiga-
bunt As soon as one swings away the least amount
from the positions of certain professors they burst
forth into explosions and thunders.

I am very positive that the world will not be of
his opinion but it is always well to be on one's
guard. Perhaps, however, Your Highness will
have a chance to let him know that to act in such
a way, is to rebuke people unnecessarily, so that
henceforth he may use a little more moderation.
If I am not mistaken Your Highness had a corre-
spondence with him about the methods of restraint
and I should like to learn the results of it.

I may add that milord has now gone to Rome and
apparently will not return to Germany so soon as
was thought. One of these days I am going to
Wolfenbiitel and will do my best to recover Your
Highness's book. It is said that M. Varillas has
written a History of Modern Heresies.

Mastrich's letter which Your Highness commun-
icated to me regarding the conversions of Sedan
seems quite reasonable. M. Maimburg, they say,
reports that St. Gregory the Great also approved of
this principle, namely that one should not trouble
himself even if the conversion of Heretics was
feigned, provided that thus their children were
really gained over. But it is not permitted to kill
some persons in order to gain others, although
Charlemagne used almost exactly this method
against the Saxons, forcing them to accept Religion
with the sword at their throats. We have now here
a Monsieur Leti who has brought us his History of
Geneva in five volumes dedicated to the House of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 87

Brunswick. I do not know what relationship he
finds between the two. He says quite good things
at times and is a good conversationalist.

I am, etc.

V
Leibniz to Count Ernst von Hessen-Rheinfels.

5/15 April, 1686.

Your Serene Highness will have received the let-
ter which I sent by the preceding post, to which I
joined, in the form of a letter to Your Highness, a
communication of which a copy could be sent to
M. A. I have since thought it would be better to
change those words toward the end, beginning
"Nevertheless, if the church in which he is be so
prompt to censure, such a procedure ought to serve
as a notice," etc., as far as the words, "above all,
when one has no means of support," lest M. A.
may take the opportunity from them to enter
into controversial disputes as if the church
were being attacked, which is not at all the inten-
tion.

In the copy could be put in their place, "least of
all in the communion to which M. A. belongs,
where the Council of Trent as well as the Popes
have been very wisely satisfied with censuring
opinions in which there are points manifestly
against the faith and against the customs. They
have not gone into the philosophic consequences.
If it were necessary to listen to these, then in mat-
ters of censure Thomists would pass for Calvinists
according to the Jesuits, and the Jesuits would be
classed as Semipelagians according to the Thomists.

88 CORRESPONDENCE.

Both would destroy freedom according to Durandus
and Father Louys de Dole, and in general every
absurdity would pass for atheism because it could be
shown to destroy the nature of God."

VI

Arnauld to Leibniz.

May 13, 1686.

I thought that I ought to address myself to you
personally to ask pardon for having given you cause
to become angry against me, in that I employed too
severe terms when I indicated what I thought of one
of your positions. But I protest before God that
the fault which I committed was not at all the result
of prejudice against you, for I have never had cause
to have of you other than a most favorable opin-
ion save in the matter of Religion, in which you
found yourself fixed through your birth; neither was
I in an ill humor when I wrote the letter which has
wounded you, nothing being further from my char-
acter than the evil disposition which it pleases many
people to attribute to me; neither by a too great
attachment to my own opinions was I shocked in see-
ing you hold contrary opinions, for I can assure you
that I have meditated so little on these kinds of
subjects that I am able to say that my opinions are
not at all fully made up.

I beg you, sir, to believe nothing like that about
me but to be convinced that what caused my indis-
cretion was simply that, having been accustomed to
write off-hand to His Highness because he is so
good as to readily excuse all my faults, I imagined
that I could tell him frankly what I was unable to
approve of in one of your opinions because I was

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 89

very sure it would not pass muster and if I had
misunderstood your meaning you would be able to
correct me without its going any further.

But I hope, sir, that the Prince will be willing to
make peace for me and I may engage him in this
by using the words which Saint Augustine used on
a similar occasion. He had written very harshly
against those who thought that God could be seen
with the physical eyes, and a Bishop in Africa who
held this opinion, having seen this letter which was
not at all addressed to him, was seriously offended
by it. This necessitated Saint Augustine's employ-
ing a common friend to appease the Prelate and I
beg you to imagine that I am saying to the Prince
for your ears what Saint Augustine wrote to this
friend, to be said to the Bishop: Dum essem in
admonendo sollicitus, in corripiendo nimius atque
improvidus fui. Hoc non defendo sed reprehendo: hoc
non excuse, sed accuso. Ignoscatur, peto ; recordetur
nostrum dilectionem pristinem et obliviscatur offensionem
novam. Faciat certe quod me non fecisse succensuit:
habeat lenitatem in dandi venia, quam non habui in ilia
epistola conscribenda.

I was in doubt whether I ought not to stop here
without going again into the question which was
the occasion for our falling out, lest there might
again escape me some word which could wound
you. But I fear, however, that that would be not
to have a sufficiently good opinion of your fairness.
I will tell you, therefore, in a few words the diffi-
culties which I still have with this proposition:
"The individual concept of each person involves,
once for all, all that will ever happen to him."

It seems to me to follow from this that the indi-

90 CORRESPONDENCE.

vidual concept of Adam has involved that he would
have so many children and the individual concept
of each one of these children involves all that they
will do and all the children which they will have
and so on. Whence I thought that we could infer
that God was free, in so far as the creating or not
creating of Adam, but supposing that he had wished
to create him, all that has since happened to the
human race has come and must come by a fatalistic
necessity or I thought at least that there was no
more freedom in God regarding all that, supposing
that he had wished to create Adam, than there was
not to create a being capable of thinking, suppos-
ing he had wished to create me.

It does not appear to me, Monsieur, that, in
speaking thus, I have confused necessitate™, ex
hypothesi and absolute necessity, for I was all the
time speaking only against the necessity ex
hypothesi; what I find strange is, that all human
events should be quite as necessary by a necessity ex
hypothesi after this first supposition that God
wished to create Adam, as it is necessary by the
same necessity for there to be in the world a nature
capable of thinking simply because he has wished
to create me.

You say in this connection various things about
God which do not seem to me sufficient to solve my
difficulty.

1. "That a distinction has always been made
between what God is free to do absolutely and what
he is obliged to do by virtue of certain resolutions
already made." This position is valid,

2. "That it is little consonant with the dignity
of God to conceive of him (under the pretext of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 9!

safeguarding his freedom) in the way that the
Socinians do, as a man who forms his resolutions
according to the circumstances." Such an opinion
is very foolish, I grant you.

3. "That the purposes of God, which are all inter-
related must not be isolated. Therefore, the purpose
of God to create a particular Adam must not be
looked at detached from all the others which he has
regarding the children of Adam and of the whole
human race." To this also I agree, but I cannot
yet see how these can serve to solve my difficulty.

For i. I confess, in good faith, not to have under-
stood that, by the individual concept of each person
(for example of Adam), which you say involves,
once for all, all that will ever happen to him, you
meant this person in so far as he is in the divine
understanding instead of simply what he is in himself.
For it seems to me that it is not customary to con-
sider the specific concept of a sphere in relation to
that which is its representation in the divine under-
standing but in relation to what it is in itself. I
thought it was thus with the individual concept of
~ach person or of everything.

2. It is enough, however, for me to know what you
intend, so that I can conform to it, and inquire if
that overcomes all the difficulty which I mentioned
above. It does not seem to me that it does.

I agree that the knowledge which God had of
Adam when he resolved to create him involved
what happened to him and what has happened, or
will happen, to his posterity; and therefore if we
understand in this sense the individual concept,
Adam, what you say about it is very true.

I grant also that the purpose which he had in

92 CORRESPONDENCE.

creating Adam was not detached from that which
he had regarding what would happen to him and in
regard to all his posterity.

But it seems to me, that after all this there still
remains the question (and this is where my diffi-
culty lies) whether the relationship between those
objects (I mean Adam on the one hand and what
will happen to him and to his posterity on the
other), is such through itself, independently of all
the free decrees of God; or, whether it has been
dependent. That is to say, whether it is only in
consequence of the free decrees by which God has
foreordained all that will happen to Adam and to
his posterity that God has known all that will happen
to Adam and to his posterity; or whether there is,
independent of these decrees, between Adam on
the one hand, and what has happened and will hap-
pen to him and his posterity on the other, an intrin-
sic and necessary connection. Unless you mean the
latter I do not see how it can be true when you say,
"that the individual concept of each person involves
once for all, all that which will ever happen to him,"
even if we understand this concept in its relation to
God.

It seems, moreover, that it is this latter which
you do not accept. For I believe you to suppose
that, according to our way of conceiving, possible
things are possible before any free decree of God,
whence it follows that what is involved in the con-
cept of possible things is involved independently of
all God's free decrees. Now you say "that God
has found among possible things a possible Adam,
accompanied by certain individual circumstances,
who, among other predicates, possesses also that of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 93

having in time a certain posterity." There is,
therefore, according to you a connection intrinsic,
so to speak, and independent of all the free decrees of
God; a connection between this possible Adam and
all the separate persons of his posterity and not the
persons alone, but in general all that must happen
to them. It is this, Monsieur, I speak plainly, that
is incomprehensible to me. For your meaning
seems to be that the possible Adam whom God has
chosen preferably to other possible Adams, had a
connection with the very same posterity as the
created Adam. In either case it is, as far as I can
judge, the same Adam considered now as possible
and now as created. If this is your meaning then
here is my difficulty.

How many men there are who have come into the
world only through the perfectly free decrees of
God, such as Isaac, Samson, Samuel and many
others! Now the fact that God has known them
conjointly with Adam is not owing to their having
been involved independently of the decrees of God
in the individual concept of the possible Adam. It
is, therefore, not true that all the individual person-
ages of the posterity of Adam have been involved in
the individual concept of the possible Adam since
they would then have been thus involved inde-
pendently of God's decress.

The same can be said of an infinite number of
human events which have occurred by the express
and particular commands of God, for instance, the
Jewish and Christian Religions, and, above all, the
Incarnation of the Word of God. I do not see how
it can be said that all these are involved in the
individual concept of the possible Adam. What-

94 CORRESPONDENCE.

ever is considered as possible must have all that is
conceived of under this idea of possibility independ-
ently of the Divine decrees.

Moreover, Monsieur, I do not see how, in taking
Adam as an example of a unitary nature, several
possible Adams can be thought of. It is as though
I should conceive of several possible me's; a thing
which is certainly inconceivable. For I am not
able to think of myself without considering myself
as a unitary nature, a nature so completely distin-
guished from every other existent or possible being
that I am as little able to conceive of several me's
as to think of a circle all of whose diameters are not
equal. The reason is that these various me's are
different, one from the other, else there would not
be several of them. There would have to be, there-
fore, one of these me's which would not be me, an
evident contradiction.

Permit me, therefore, Monsieur, to transfer to this
me what you say concerning Adam and you may
judge for yourself if it will hold. Among possible
beings God has found in his ideas several
me's, of which one has for its predicates, to have
several children and to be a physician, and another
to live a life of celibacy and to be a Theologian.
God, having decided to create the latter, or the
present me, includes in its individual concept the
living a life of celibacy and the being a Theologian
while the former would have involved in its indi-
vidual concept being married and being a physician.
Is it not clear that there would be no sense in such
statements, because, since my present me is neces-
sarily of a certain individual nature, which is the
same thing as having a certain individual concept,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 95

it will be as impossible to conceive of contradictory
predicates in the individual concept me, as to con-
ceive of a me different from me? Therefore we
must conclude, it seems to me, that since it is
impossible for me not to always remain myself
whether I marry or whether I live a life of celibacy,
the individual concept of my me has involved
neither the one nor the other of those two states.
Just as we might say that this block of marble is the
same whether it be in repose or in a state of move-
ment and therefore neither movement nor repose
are involved in its individual concept. This is why
Monsieur, it seems to me, that I ought to regard as
involved in my individual concept only what is of
such a nature that I would no longer be myself if it
were not in me, while, on the other hand, every-
thing which is of such a nature that it might either
happen to me or not happen to me without my
ceasing to be myself, should not be considered as
involved in my individual concept; (although, by
the ordinance of God's providence, which never
changes the nature of things, it could never happen
that that should be in me). This is my thought,
which, 1 believe, conforms wholly to what has always
been held by all the philospohers in the world.

That which confirms me in this position is the
difficulty I experience in believing it to be good
philosophy, to seek in God's way of knowing things,
what we ought to think out, either from their specific
concepts or from their individual concepts. The
divine understanding is the measure of the truth of
things, quoad se, (as far as they are concerned,) but
it does not appear to me that, inasmuch as we are in
this life, it can be the measure for us, quoad nos.

9<5 CORRESPONDENCE.

For what do we know at present of God's knowl-
edge? We know that he knows all things and that
he knows them all by a single and very simple act,
which is his essence. When I say that we know it
I mean that we are sure that this must be so. But
do we understand it? And ought we not to recog-
nize that however sure we may be that it is so, it is
impossible for us to conceive how it can be?
Further, are we able to conceive that, although the
knowledge of God is his very essence, wholly neces-
sary and immutable, he has, nevertheless, knowledge
of an infinity of things which he might not have had
because these things might not have been? It is
the same in the case of his will which is also his
very essence where there is nothing except what is
necessary; and still he wills and has willed, from all
eternity, things which he would have been able not
to will. I find therefore a great deal of uncertainty
in the manner in which we usually represent to our-
selves that God acts. We imagine that before pur-
posing to create the world he looked over an
infinity of possible things, some of which he chose
and rejected the others — many possible Adams,
each one with a great sequence of persons and
events between whom there was an intrinsic con-
nection. And we think that the connection of all
these other things with the one of the possible
Adams is exactly like that which we know has been
between the created Adam and all his posterity.
This makes us think that it was that one of all the
possible Adams which God chose and that he did
not at all wish any of the others. Without however
stopping over that which I have already said,
namely, that taking Adam for an example of a

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 97

unitary nature it is as little possible to conceive of
several Adams as to conceive of several me's, I
acknowledge in good faith that I have no idea of
substances purely possible, that is to say, which
God will never create. I am inclined to think that
these are chimeras which we construct and that
whatever we call possible substances, pure possi-
bilities are nothing else than the omnipotence of
God who, being a pure act, does not allow of there
being a possibility in him. Possibilities, however,
may be conceived of in the natures which he has
created, for, not being of the same essence through-
out, they are necessarily composites of power and
action. I can therefore think of them as possi-
bilities. I can also do the same with an infinity of
modifications which are within the power of these
created natures, such as are the thoughts of intelli-
gent beings, and the forms of extended substance.
But I am very much mistaken if there is any one
who will venture to say that he has an idea of a
possible substance as pure possibility. As for
myself, I am convinced that, although there is so
much talk of these substances which are pure possi-
bilities, they are, nevertheless, always conceived of
only under the idea of some one of those which God
has actually created. We seem to me, therefore,
able to say that outside of the things which God has
created, or must create, there is no mere negative
possibility but only an active and infinite power.

However that may be, all that I wish to conclude
from this obscurity and from the difficulty of know-
ing the way that things are in the knowledge of
God and of knowing what is the nature of the con- •
nection which they have among themselves and

98 CORRESPONDENCE.

whether it is intrinsic or, so to speak, extrinsic-
all that I wish to conclude, I say, from this, is that
it is not through God, who with respect to us,
dwells in inaccessible light, that we should try to
find the true concepts either specific or individual of
the things we know; but it is in the ideas about
them which we find in ourselves.

Now I find in myself the concept of an individual
nature since I find there the concept me. I have, there-
fore, only to consult it in order to know what is
involved in this individual concept, just as I have
only to consult the specific concept of a sphere to
know what is involved there. Now I have no other
rule in this respect except to consider whether the
properties are of such a character that a sphere would
no longer be a sphere if it did not have them; such,
for instance, as having all the points of its circum-
ference equally distant from the center. Or to con-
sider whether the properties do not affect its being
a sphere, as for instance, having a diameter of only
one foot while another sphere might have ten,
another a hundred. I judge by this that the former
is involved in the specific concept of a sphere
while the latter, which was the having a greater or
smaller diameter, is not at all involved in it.

The same principle I apply to the individual con-
cept me. I am certain, that, inasmuch as I think, I
am myself. But I am able to think that I will
make a certain journey or that I will not, being
perfectly assured that neither the one nor the
other will prevent me from being myself. I main-
tain very decidedly that neither the one nor the
other is involved in the individual concept me.
"God however has foreseen," it will be said,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 99

"that you will make this journey." Granted. "It
is therefore indubitable that you will make it."
I grant that also. But does that alter anything
in the certitude which I have that whether I make
it or do not make it I shall always be myself? I
must, therefore, conclude that neither the one nor
the other enters into my me, that is to say, into my
individual concept. It is here it seems to me that
we must remain without having recourse to God's
knowledge, in order to find out what the individual
concept of each thing involves.

This, Monsieur, is what has come into my mind
regarding the proposition which troubled me and
regarding the explanation which you have given.
I do not know if I have wholly grasped your
thought but such has been at least my intention.
The subject is so abstract that a mistake is very
easy. I should, however, be very sorry if you had
of me as poor an opinion as those who represent me
as a hot-headed writer who refutes others only in
calumniating them and in purposely misrepresenting
their opinions. This is most assuredly not my
character. At times I may express my thoughts
too frankly. At times also I may fail to grasp the
thoughts of others (for I certainly do not consider
myself infallible, and such one would have to be in
order never to be mistaken), but even if this should
be through self-confidence, never would it be that I
misstated them purposely; for I find nothing to be
so low as the using of chicanery and artifice in
differences which may arise regarding matters of
doctrine. This even if it should be with persons
whom we have no reason otherwise to love, and
still more if the difference is between friends. I

100 CORRESPONDENCE.

believe, Monsieur, that you wish indeed that I
place you in this latter class. I can not doubt that
you do me the honor to love me. You have given
me too many marks of it. And, in my behalf, I
protest that the very fault for which I beg you once
more to pardon me, was only the result of the
affection which God has given me for you and of a
zeal for your salvation, a zeal which has been by no
means moderate. I am, etc.,

VII

Arnauld to Count Ernst von Hessen-Rheinfels.

May 13, 1686.

I am very sorry, Monseigneur, to have given to
Mr. Leibniz cause to become so angry at me. If I
had foreseen it, I should have been on my guard
against saying so frankly what I thought of one of
his metaphysical propositions. But I ought to have
foreseen it and I did wrong in employing such
severe terms, not against him personally but against
his position. Therefore, I have felt myself com-
pelled to beg his pardon for it and I have done it
very sincerely in the letter which I have written him
and am sending open to Your Highness. It is also
from my heart that I pray you to make peace for
me and to reconcile me with a former friend of
whom I should be very sorry to have made an
enemy by my imprudence.

I shall be very glad, however, if the matter rests
there and if I shall not be obliged to tell him what
I think of his positions, because I am so over-
whelmed with so many other occupations that I
should have difficulty in convincing him and these

LEIBNIZ. ARNAULD. HESSEN-RHKINFELS. IOI

abstract subjects require a great deal of application
which I can not devote to them on account of the
time which it consumes.

I do not know but that I have forgotten to send
you an addition to the Apology for the Catholics.
I fear lest I may have, because Your Highness has
not mentioned it to me. I am accordingly sending
it to you to-day with two Memoirs. The Bishop
of Namur, whom the Internuncio has appointed
judge, has had difficulty in deciding to accept this
post, so great is the fear of the Jesuits. But if their
power is so great that justice can not be obtained
against them in this world, they have reason to fear
that God will punish them with so much the more
severity in the next. It is a terrible history and
a long one, that of this Canon, whose wickedness
apparently would be unpunished if he had not ren-
dered himself odious by his conspiracies and his
cabals.

This Lutheran minister of whom Your Highness
speaks must have good qualities, but it is some-
thing incomprehensible and marking an extremely
blind prejudice that he can regard Luther as a man
destined by God for the Reformation of the Chris-
tian religion. He must have a very low idea of true
piety to find it in a man like him, imprudent in his
speech and so gluttonous in his manner of living. I
am not surprised at what this minister has said to
you against those who are called Jansenists, since
Luther at first put forward extreme propositions
against the co-operation of grace and against the
freedom of will so far as to give to one of his
books the title De servo arbitrio, Necessitated Will.
Melancthon, some time after, mitigated these propo-

102 CORRESPONDENCE.

sitions a great deal and since then the Lutherans
have gone over to the opposite extreme so that the
Arminians have nothing stronger to oppose to the
Gummarists than the doctrines of the Lutheran
Church. There is no cause then for astonishment
that the Lutherans of to-day, who occupy the same
positions as the Arminians, are opposed to the dis-
ciples of Saint Augustine. For the Arminians are
more sincere than are the Jesuits. They grant that
Saint Augustine is opposed to them in the opinions
which they have in common with the Jesuits but
they do not think themselves obliged to follow him.

What Father Jobert is requiring from new con-
verts gives grounds for hope that those who are con-
verts only in name may return, little by little,
provided that instruction is given them, that they
are edified by good examples, and that the curacies
are filled with good men. But it woud be spoiling
everything to take from them the vernacular trans-
lations of what is said at Mass. It is only such
leniency that can cure them from the aversion that
has been given to them regarding it. Yet we have
not yet been informed of what has been the outcome
of the storm aroused against the Annte Chrttienne,
about which I wrote to Your Highness some time
ago.

A gentleman named Mr. Cicati, who is in charge
of the Academy at Brussels and who says he is well-
known by Your Highness because he had the honor
to teach the Princes, Your sons, to ride on horse-
back, is acquainted with a German, a very honest
man, who knows French very well and is a good
lawyer, even having had a charge as councillor, and
who has already been employed to take charge of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 103

young Seigneurs. Mr. Cicati thinks that he would
be a very available man for Your grandsons, above
all, when they make their journey in France and
that meanwhile he could render other services to
Your Highness. I thought it couldn't do any harm
to give you this information. It binds you to
nothing and may be of service to you if you think
it best to have somebody with the young Princes—
someone who shall leave them neither day nor night.
Not knowing the characteristics of Mr. Leibniz, I
beg Your Highness to have the above forwarded
along with the letter which I have written him.

VIII

Remarks upon Mr. Arnaud' s letter in regard to my
statement that the individual concept of each per-
son involves, once for all, all that will ever hap-
pen to him:

May, 1686.

"I thought," says Mr. Arnaud, "that we might
infer that God was free either to create or not to
create Adam, but supposing that he wished to create
him, all that has since happened to the human race
was, or all which will happen is by a fatalistic
necessity, or we might infer at least that there was
no more liberty in God, supposing that he once
wished to create Adam, than there was of not
creating a nature capable of thought in case he
wished to create me." I replied at first that a
distinction must be made between absolute and
hypothetical necessity. To this Mr. Arnaud replies
here that he is speaking only of necessity ex
hypothesi. After this declaration the argumenta-
tion takes a different phase. The words "fatal

104 CORRESPONDENCE.

necessity" which he used and which are ordinarily
understood as an absolute necessity obliged me to
make this distinction, which, however, is now
uncalled for, inasmuch as M. Arnaud does not insist
upon the fatalistic necessity. He uses alternative
phrases; "by a fatalistic necessity or at least, etc."

It would be useless to dispute in regard to the
word. In regard to the matter, however, M. Arnaud
still finds it strange for me to maintain "that all
human events occur by necessity ex hypothesi after
this single presupposition that God wished to create
Adam." To which I have two replies to give. The
one is, that my supposition is not merely that God
wished to create an Adam whose concept was vague
and incomplete but that God wished to create a par-
ticular Adam sufficiently determined as an indi-
vidual. This complete individual concept, in my
opinion, involves the relation to the whole sequence
of things — a position which ought to appear so much
the more reasonable, because M. Arnaud grants here
the inter-connection among the resolutions of God,
that is to say, that God, having resolved to create a
certain Adam, takes into consideration all the reso-
lutions which he will form concerning the whole
sequence of the universe; almost in the same way that
a wise man who forms a resolution in regard to one
part of his plan, has the whole plan in view and will
make resolutions better in proportion as he is able
to plan for all the parts at the same time.

The other reply is that the sequence, in virtue of
which events follow from the hypothesis, is indeed
always certain, but that it is not always necessary
by a metaphysical necessity, as is that instance
which is found in M. Arnaud's example: that God,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 105

resolving to create me, could not avoid creating a
nature capable of thought. The sequence is often
only physical and presupposes certain free decrees
of God, as, for instance, do consequences which
depend on the laws of motion or which depend upon
the following principle of morality — namely, that
every mind will pursue that which appears to it the
best. It is true that when the supposition of the
decrees which produce the consequence is added to
the first supposition which constituted the antece-
dent, namely, God's resolution to create Adam — it
is true, I say, that if all these suppositions or reso-
lutions are regarded as a single antecedent, then the
consequence follows.

As I have already touched upon these two replies
somewhat in my letter sent to the Count, M. Arnaud
brings forward answers to them here which must be
considered. He acknowledges in good faith that he
understood my opinion as if all the events happen-
ing to an individual were deducible from his indi-
vidual concept in the same manner and with the
same necessity as the properties of the sphere may
be deduced from its specific concept or definition,
and as though I had considered the concept of the
individual in itself, without regard to the manner in
which it is present in the understanding or will of
God. "For," he says, "it seems to me that it is
not customary to consider the specific concept of a
sphere in relation to its representation in the divine
understanding but in relation to what it is in itself,
and I thought that it was thus with the individual
concept of each person."

But, he adds, that now, since he knows what my
thought is, it is enough for him to conform to it in

106 CORRESPONDENCE.

inquiring if it overcomes all the difficulties. Of
this, he is still doubtful.

I see that M. Arnaud has not remembered, or at
least, has not adhered, to the position of the
Cartesians who maintain that God, by his will, estab-
lishes the eternal truths such as are those regarding
the properties of the sphere. But, as I share their
opinion no more than does M. Arnaud, I will simply
say why I believe that we must philosophize differ-
ently in the case of an individual substance from our
way of philosophizing in the case of a specific con-
cept of the sphere. It is because the concept of
space relations involves only eternal or necessary
truths but the concept of an individual involves sub
ratione possibilitatis that which is in fact or which
has relation to the existence of things and to time,
and consequently it depends upon certain free
decrees of God considered as possible. Because
the truths of fact or of existence depend upon the
decrees of God. Furthermore, the concept of the
sphere in general is incomplete or abstract, that is
to say we consider only the essence of the sphere in
general or theoretically without regard to the par-
ticular circumstances, and consequently the concept
does not involve that which is required for the
existence of a certain sphere. The concept of the
sphere which Archimedes had put upon his tomb is
complete and should involve all that pertains to the
subject of this thing. That is why in individual or
practical considerations, where singulars are dealt
with, in addition to the form of the sphere there
enters the material of which it is made, the time,
the place, and the other circumstances which, by a
continual network, would finally involve the whole

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 107

sequence of the universe, provided we were able to
follow out all that these concepts involve. For the
concept of this bit of matter out of which this
sphere is made, involves all the changes which it
has undergone and which it will some day undergo.

In my opinion each individual substance always
contains the traces of what has ever happened to it
and marks of that which will ever happen to it.
What I have just said, however, may suffice to
justify my line of thought.

Now, M. Arnaud declares that in taking the indi-
vidual concept of a person in relation to the knowl-
edge which God had of it when he resolved to create
it, what I have said regarding this concept is very
true, and he grants also that the will to create Adam
was not at all detached from God's will in regard to
whatever has happened both to him and to his pos-
terity. He now asks if the connection between
Adam and the events occurring to his posterity is
dependent or independent of the free decrees of
God. "That is to say," as he explains, "whether it
is only in consequence of the free decrees by which
God has ordained all that will happen to Adam and
to his posterity that God has known what will hap-
pen to them, or whether, independently of these
decrees there is between Adam and the events
aforesaid, an intrinsic and necessary connection."

He does not doubt that I would take the second
alternative and, in fact, I am unable to take the first
in the manner in which he has just explained it.
But there seems to me to be a mean position. He
proves that I ought to choose the latter because I
consider the individual concept of Adam as possible
when I maintain that among an infinity of possible

108 CORRESPONDENCE.

concepts God has selected a certain Adam, while
the possible concepts in themselves do not at all
depend upon the free decrees of God.

But here I must needs explain myself a little
better. I say, therefore, that the connection
between Adam and human events is not indepen-
dent of all the free decrees of God, but also, that it
does not depend upon them in such a way that each
event could happen or be foreseen only because of
a particular primitive decree made about it. I
think that there are only a few primitive free
decrees regulating the sequence of things which
could be called the laws of the universe and which,
being joined to the free decree to create Adam,
bring about the consequences. In very much the
same way as but few hypotheses are called for to
explain phenomenon. I will make this clearer in
what follows.

As regards the objection that possibles are inde-
pendent of the decrees of God I grant it of actual
decrees (although the Cartesians do not at all agree
to this), but I maintain that the possible individual
concepts involve certain possible free decrees; for
example, if this world was only possible, the indi-
vidual concept of a particular body in this world
would involve certain movements as possible, it
would also involve the laws of motion, which are the
free decrees of God; but these, also, only as possi-
bilities. Because, as there are an infinity of pos-
sible worlds, there are also an infinity of laws,
certain ones appropriate to one; others, to another,
and each possible individual of any world involves
in its concept the laws of its world.

The same can be said of miracles, or of the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 109

extraordinary operations of God. These are a part
of the general order and conform to the principal
purposes of God and consequently, are involved in
the concept of this universe, which is a result of
these designs. Just as the idea of a building results
from the purposes or plans of him who undertakes
it, so the idea or concept of this world is a result of
the designs of God considered as possible. For
everything should be explained by its cause and of
the universe the cause is found in the purposes of
God. Now, each individual substance, in my opin-
ion, expresses the whole universe, according to a
certain aspect and consequently it also expresses
the so-called miracles. All this ought to be under-
stood in regard to the general order, in regard to the
plans of God, in regard to the sequences of this uni-
verse, in regard to the individual substance and in
regard to miracles, whether they are taken in the
actual condition or whether they are considered sub
ratione possibilitatis. For another possible world
would have all such orderings, according to its own
manner, although the plans of ours were preferred.

It can be seen also from what I have just said con-
cerning the plans of God and concerning the prim-
itive laws, that this universe has a certain primary
or primitive concept, from which the particular
events are only the consequences — with the excep-
tion of liberty and contingencies, whose certitude,
however, is not affected, because the certitude of
events is based in part upon free acts. Now every
individual substance of this universe expresses in its
concept the universe into which it has entered. Not
only the supposition that God has resolved to create
this Adam but also any other individual substance

IIO CORRESPONDENCE.

that may be, involves the resolves for all the rest,
because this is the nature of an individual sub-
stance, namely, to have so complete a concept that
from it may be deduced all that can be attributed to
it, and even the whole universe, because of the
inter-connection between things; nevertheless, to
speak more strictly, it must be said that it is not so
much because God has resolved to create this Adam
that he made all his other resolutions, but because
the resolution which he made in regard to Adam,
as also that which he made in regard to other par-
ticular things, are consequences of the resolve which
he made in regard to the whole universe and to the
principal designs which determine its primary con-
cept; these resolves have established this general
and unchangeable order to which everything con-
forms without even excepting the miracles which
are doubtless conformable to the principal designs of
God, although the particular regulations which are
called the laws of Nature are not always observed.

I have said that the supposition from which all
human events can be deduced is not simply that of
the creation of an undetermined Adam but the crea-
tion of a particular Adam, determined to all the cir-
cumstances, chosen out of an infinity of possible
Adams. This has given M. Arnaud opportunity to
object, not without reason, that it is as little pos-
sible to conceive several Adams, understanding
Adam as a particular nature, as to conceive of
several me's. I agree, but yet, in speaking of
several Adams, I do not take Adam for a deter-
mined individual. I must, therefore, explain.
This is what I meant. When we consider in Adam
a part of his predicates, for example, that he was the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. Ill

first man, put into a garden of enjoyment, and that,
from his side, God took a woman, and, if we con-
sider similar things, conceived sub ratione generali-
tatis (that is to say, without mentioning Eve or
Paradise, or the other circumstances which consti-
tute his individuality), and if we call the person to
whom these predicates are attributed Adam, all this
does not suffice to determine the individual, for
there might be an infinity of Adams, that is to say,
of possible persons to whom these would apply who
would, nevertheless, differ among themselves. Far
from disagreeing with M. Arnaud, in what he says
against the plurality of the same individual, I
would myself, employ the idea to make it clearer
that the nature of an individual should be complete
and determined. I am quite convinced in regard to
what St. Thomas has taught about intelligences,
and what I hold to be a general truth, namely,
that it is not possible for two individuals to exist
wholly alike, that is, differing solo numero. We
must, therefore, not conceive of a vague Adam or
of a person to whom certain attributes of Adam
appertain when we try to determine him, if we
would hold that all human events follow from the
one presupposition, but we must attribute to him a
concept so complete that all which can be attributed
to him may be derived from his. Now, there is no
ground for doubting that God can form such a con-
cept or, rather, that he finds it already formed in
the region of possibilities, that is to say, in his
understanding.

It follows, also, that if he had had other circum-
stances, this would not have been our Adam, but
another, because nothing prevents us from saying

112 CORRESPONDENC E.

that this would be another. He is, therefore,
another. It indeed appears to us that this block of
marble brought from Genoa would be wholly the
same if it had been left there, because our senses
cause us to judge only superficially, but in reality,
because of the inter-connection of things, the uni-
verse, with all its parts, would be wholly different
and would have been wholly different from the very
commencement if the least thing in it happened
otherwise than it has. It is not because of their
inter-connection that events are necessary, but it is
because they are certain after the choice which God
made of this possible universe whose concept con-
tains this sequence of things. I hope that what I
am about say will enable M. Arnaud himself to
agree to this.

Let a certain straight line, ABC, represent a
certain time, and let there be a certain individual
substance, for example, myself, which lasts or
exists during this period. Let us take then, first,
the me which exists during the time A B, and
again the me which exists during the time B C.
Now, since people suppose that it is the same indi-
vidual substance which perdures, or that it is the
me which exists in the time A B while at Paris
and which continues to exist in the time B C
while in Germany, it must needs be that there
should be some reason why we can veritably say
that I perdure, or, to say, that the me which
was at Paris is now in Germany, for, if there
were no reason, it would be quite right to say that
it was another. To be sure, my inner experience
convinces me a posteriori of this identity but there
must be also some reason a priori. It is not pos-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 113

sible to find any other reason, excepting that my
attributes of the preceding time and state, as well
as the attributes of the succeeding time and state
are predicates of the same subject; insunt eidem
subjecto. Now, what is it to say that the predicate
is in the subject if not that the concept of the
predicate is found in some sort involved in the con-
cept of the subject? Since from the very time that
I began to exist it could be said of me truly that
this or that would happen to me, we must grant that
these predicates were principles involved in the sub-
ject or in my complete concept, which constitutes
the so-called me, and which is the basis of the inter-
connection of all my different states. These, God
has known perfectly from all eternity. After this I
think that all doubts ought to disappear, for when I
say that the individual concept of Adam involves
all that will ever happen to him I mean nothing else
than what the philosophers understand when they
say that the predicate is contained in the subject of
true propositions. It is true that the consequences
of so clear a teaching are paradoxical, but it is the
fault of the philosophers who have not sufficiently
followed out perfectly clear notions.

Now I think that M. Arnaud, discerning and fair
as he is, will not find my proposition so strange and,
although he may not be able to approve of it
entirely, yet I almost flatter myself with having his
approbation. I agree with what he judiciously has
added, in regard to the care that must be employed
in having recourse to knowledge of divine things for
the determination of what we should decide con-
cerning the concepts of mundane things. But rf
properly understood, what I have just said must be

114 CORRESPONDENCE.

said even when we speak of God only as much as is
necessary. For, even if we should not say that
God, in considering Adam, whom he resolved to
create, saw all the events which will happen to him,
it is enough that we can always prove that he had a
complete concept of this Adam which involved
these events. Because all the predicates of Adam,
either depend upon the other predicates of the same
Adam, or they do not. Putting one side those
which depend upon others, we have only to gather
together all the primitive predicates in order to form
a concept of Adam sufficiently complete to deduce
whatever will happen to him in so far as a reason is
needed. It is evident that God can discover, and
indeed effectively conceive such a concept sufficient
to assign a reason to all the phenomena pertaining
to Adam; but not less clear is it, however, that this
concept is possible in itself. Truly, we must not
submerge ourselves more than necessary, when we
investigate, in divine knowledge and will, because
of the great difficulties which there are there.
Nevertheless, we may explain what we have derived
for our question from such a source without enter-
ing into those difficulties which M. Arnaud men-
tions; for instance, the difficulty of understanding
how the simplicity of God is reconcilable with cer-
tain things which we are obliged to distinguish from
it. It is also very difficult to explain perfectly how
God has knowledge which he was able not to have,
that is, the knowledge of prevision, for, if future
contingencies did not exist, God would have no
vision of them. It is true that he might have sim-
ple knowledge of future contingencies which would
become prevision when joined to his will so that the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 11$

difficulty above would be reduced to the difficulties
present in conceiving of the will of God. That is
to say, the question how God is free to will. This,
without doubt, passes our ken, but it is not essen-
tial to understand it in order to solve our question.
In regard to the manner in which we conceive
that God acts when he chooses the best among
several possibilities, M. Arnaud has reason to find
some obscurity. He seems, nevertheless, to recog-
nize that I am inclined to think that there are an
infinity of possible first men, each one with a great
sequence of personages and events, and that God
chose among them the one which pleased him,
together with his sequence. This is not, therefore,
so strange as it appears at first. It is true, M.
Arnaud says he is inclined to think that substances
which are purely possible are only chimeras. In
regard to this, I do not wish to dispute, but I hope
that, nevertheless, he will grant m'e as much as I
have need of. I agree that there is no other reality
in pure possibilities than what they have in the
divine understanding, and we see, therefore, that M.
Arnaud will be obliged himself to have recourse
to the divine knowledge in order to explain them,
while he seems above to have wished that they
might be sought in "themselves. When I grant
further what M. Arnaud is' convinced of and what I
do not deny, that we conceive nothing as possible
excepting through the ideas which are actually
found in the things which God has created, this
does not at all injure my position, for, in speaking
of possibilities, I am content if true propositions
may be formed concerning them. For example, if
there were no perfect square in the world, we should,

Il6 CORRESPONDENCE.

nevertheless, see that no contradiction was implied
in the idea. If we wish to reject absolutely the
pure possibles, contingencies will be destroyed,
because if nothing is possible except what God has
actually created then what God has actually created
would be necessary in case he resolved to create
anything.

Finally, I agree that in order to determine the
concept of an individual substance it is good to con-
sult the concept which I have of myself, just as the
specific concept of the sphere must be consulted in
order to determine its properties. Nevertheless,
there is a great difference in the two cases for the
concept of myself and of any other individual sub-
stance, is infinitely more extended and more diffi-
cult to understand than is a specific concept like
that of a sphere which is only incomplete. It is
not sufficient that I feel myself as a substance which
thinks; 1 must also distinctly conceive whatever dis-
tinguishes me from all other spirits. But of this I
have only a confused experience.

Therefore, although it is easy to determine that
the number of feet in the diameter is not involved
in the concept of the sphere in general, it is not so
easy to decide if the journey which I intend to make
is involved in my concept; otherwise, it would be as
easy for us to become prophets as to be Geometers.
I am uncertain whether I will make the journey but
I am not uncertain that, whether I make it or no, I
will always be myself. Such human previsions are
not the same as distinct notions or distinct knowl-
edge. They appear to us undetermined because the
evidences or marks which are found in our sub-
stance are not recognizable by us. Very much as

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 117

those who regard sensations merely, ridicule one
who says that the slightest movement is communi-
cated as far as matter extends, because experience
alone could not demonstrate this to them. When,
however, they consider the nature of motion and
matter they are convinced of it. It is the same here
when the confused experience, which one has of his
individual concept in particular, is consulted. He
does not take care to notice this inter-connection of
events, but, when he considers general and distinct
notions which enter into them, he finds the connec-
tion. In fact, when I consult the conception which
I have of all true propositions, I find that every
necessary or contingent predicate, every past, pres-
ent, or future, predicate, is involved in the concept
of the subject, and I ask no more.

I think, indeed, that this will open to us a means
of reconciliation. For, I think, that M. Arnaud
disliked to grant this proposition, only because he
understood the connection which I held to, both as
intrinsic and necessary at the same time, while I
hold it indeed as intrinsic but not at all as neces-
sary. I have now sufficiently explained that it is
founded upon free decrees and free acts. I mean
no other connection between the subject and the
predicate than that which there is in the most con-
tingent of true propositions. That is to say, I mean
that there is always something to be conceived of in
the subject which serves to give the reason why this
predicate or event pertains to it or why a certain
thing has happened to it rather than not.

These reasons of contingent truths, however,
bring about results without necessitation. It is
therefore true that I am able not to make this

Il8 CORRESPONDENCE.

journey, but it is certain that I will make it. This
predicate or event is not connected certainly with
my other predicates conceived of incompletely or
sub ratione generalitatis ; but it is certainly con-
nected with a complete individual concept because
I presuppose that this concept is constructed
expressly in such a way that from it may be deduced
all that happens to me. This concept is found doubt-
less a parte rei and is properly a concept of myself
which I find under different conditions, since it is
this concept alone that can include them all.

I have so much deference for M. Arnaud and such
a good opinion of his judgment, that I easily give
up my opinions or at least my expressions as soon
as I see that he finds something objectionable in
them. It is for this reason that I have carefully fol-
lowed the difficulties which he put forward and now,
after I have attempted to meet them in good faith,
it seems to me that I am still not far from those
very positions.

The proposition which we are discussing is of
great importance and should be firmly established,
since from it follows that every soul is a world by
itself, independent of everything excepting God; that
it is not only immortal, and, so to speak, permanent,
but that it bears in its substance traces of everything
that happens to it. From it can be deduced also in
what the inter-activities of substances consist and
particularly the union of soul and body. This
inter-activity is not brought about according to the
usual hypothesis of the physical influence of one
substance upon another because every present state
of a substance comes to it spontaneously and is only
a sequence of its preceding state. No more is the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 1 19

inter-activity accounted for by the hypothesis of
occasional causes as though God intervened differ-
ently for ordinary events than when he preserved
every substance in its course; and as though God
whenever something happened in the body aroused
thoughts in the soul which would thus change the
course that the soul would itself have taken with-
out this intervention. The inter-activity is in
accordance with the hypothesis of concomitants
which, to me, appears demonstrative. That is to
say, each substance expresses the whole sequence of
the universe according 'to the view or relation that
is appropriate to it. Whence it follows that sub-
stances agree perfectly and when we say that one
acts upon another, we mean that the distinct expres-
sion of the one which is acted upon diminishes, but
of the one which acts, augments, conformably to
the sequence of thoughts which its concept involves.
For, although each substance expresses everything,
we are justified in attributing to it ordinarily only
the expressions which are most evident in its partic-
ular relation.

Finally, I think after this, that the propositions
contained in the abstract sent to M. Arnaud will
appear not only more intelligible but, perhaps, bet-
ter founded and more important than might have
been thought at first.

IX
Leibniz to Arnauld.

Hanover, July 14, 1686.
Monsieur:

As I have great deference for your judgment, I
was glad to see that you moderated your censure

120 CORRESPONDENCE.

after having seen my explanation of that proposi-
tion which I thought important and which appeared
strange to you: "That the individual concept of
each person involves once for all, all that will ever
happen to him." From this at first you drew this
consequence, namely, that from the single supposi-
tion that God resolved to create Adam, all the rest
of the human events which happened to Adam and
to his posterity would have followed by a fatalistic
necessity, without God's having the freedom to
make a change any more than he would have been
able not to create a creature capable of thought
after having resolved to create me.

To which I replied, that the designs of God re-
garding all this universe being inter-related conform-
ably to his sovereign wisdom, he made no resolve
in respect to Adam without taking into considera-
tion everything which had any connection with him.
It was therefore not because of the resolve made in
respect to Adam but because of the resolution made
at the same time in regard to all the rest (to which
the former involves a perfect relationship), that
God formed the determination in regard to all
human events. In this it seems to me that there was
no fatalistic necessity and nothing contrary to the
liberty of God any more than there is in this gener-
ally accepted hypothetical necessity which God is
under of carrying out what he has resolved upon.

You accept, M., in your reply, this inter-relation
of the divine resolves which I put forward and you
even have the sincerity to acknowledge that at first
you understood my proposition wholly in a differ-
ent sense, "Because it is not customary for exam-
ple" (these are your words), "to consider the specific

LIIBNIZ. ARNAULD. HESSEN-RHEINFELS. 121

concept of a sphere in relation to its representation
in the Divine understanding but in relation to that
which it is itself." And you thought "that it was
thus also with respect to the individual concept of
each person."

On my part, I thought that complete and com-
prehensible concepts are represented in the divine
understanding as they are in themselves but now
that you know what my thought is, you say it is
sufficient to conform to it and to inquire if it
removes the difficulty. It seems then that you
realize that my position as explained in this way,
to mean complete and comprehensive concepts
such as they are in the divine understanding, is not
only innocent but is, indeed, right, for here are your
words, "I agree that the knowledge which God had
of Adam when he resolved to create him involved
everything that has happened to him and all that
has happened and will happen to his posterity, and
therefore, taking the individual concept of Adam in
this sense, what you say is very certain." We will
go on to see very soon in what the difficulty which
you still find consists. Yet I will say one word in
regard to the cause for the difference which there
is here between concepts of space and those of indi-
vidual substances, rather in relation to the divine
will than in relation to the simple understand-
ing. This difference is because the most abstract
specific concepts embrace only necessary or eter-
nal truths which do not depend upon the decrees
of God (whatever the Cartesians may say about this
'whom it seems you have not followed at this point),
but the concepts of individual substances which are
complete, and sufficient to identify entirely their

122 CORRESPONDENCE.

subjects and which involve consequently truths that
are contingent or of fact, namely, individual circum-
stances of time, of space, etc. — such substances, I say,
should also involve in their concept taken as pos-
sible, the free decrees or will of God, likewise taken
as possible, because these free decrees are the prin-
cipal sources for existences or facts while essences
are in the divine understanding before his will is
taken into consideration.

This will suffice to make clearer all the rest and to
meet the difficulties which still seem to remain in
my explanation. For you continue in this way:
"But it seems that after that the question still
remains, and here is my difficulty, whether the con-
nection between these objects, I mean Adam and
human events, is such, of itself, independently of
all the free decrees of God or if it is dependent upon
them. That is to say, whether God knows what
will happen to Adam and his posterity only because
of the free decrees by which God has ordained all
that will happen to them, or if there is, independ-
ently of these decrees, between Adam on the one
hand and that which has happened to him and will
happen to him and to his posterity on the other, an
intrinsic and necessary connection." It seems to
you that I will take the latter alternative because I
have said, "That God has found among the possi-
bilities an Adam accompanied by certain individual
circumstances and who, among other predicates, has
also this one of having in time a certain pos-
terity." Now you suppose that I agree that the
possibilities are possible before all the free decrees
of God; supposing, therefore, this explanation of
my position according to the latter alternative, you

LEIBNIZ. ARNAULD. HISSEN-RHEINFELS. 123

think that it has insurmountable difficulties. For
there are, as you say with good reason, "an infinity
of human events that happen by the expressly par-
ticular ordinances of God. Among others, the Jew-
ish and Christian religions and, above all, the Incar-
nation of the divine word. And I do not know how
one could say that all this (which has happened by
the free decrees of God), could be involved in the
individual concept of the possible Adam. What-
ever is considered as possible ought to have every-
thing that could be conceived as being under this
concept, independently of the divine decrees."

I wish to state your difficulty exactly, Monsieur,
and this is the way in which I hope to satisfy it
entirely to your own taste. For it must needs be
that it can be resolved, since we cannot deny that
there is truly a certain concept of Adam accom-
panied by all its predicates and conceived as pos-
sible, which God knew before resolving to create
him, as you have just admitted. I think, therefore,
that the dilemma of the alternative explanation
which you have proposed may have a mean, and
the connection which I conceive of between Adam
and human events is intrinsic but it is not neces-
sarily independent of the free decrees of God
because the free decrees of God taken as possible
enter into the concept of the possible Adam, and
when these same decrees become actual they are
the cause of the actual Adam. I agree with you,
in opposition to the Cartesians, that the possibles
are possible before all the actual decrees of God, but
the decrees themselves, must be regarded also as
possibles. For the possibilities of the individual or
of contingent truths involve in their concept the

1 24 CORRESPONDENCE.

possibility of their causes, that is to say, the free
decrees of God in which they are different from
generic possibilities or from eternal truths. These
latter depend solely upon the understanding of God
without presupposing any will, as I have explained
it above.

This might be enough, but in order to make
myself better understood, I will add that 1 think
there were an infinity of possible ways of creating
the world according to the different plans which
God might have formed and that each possible
world depends upon certain principal plans or
designs of God that are his own; that is to say,
upon certain primary free decrees conceived sub
ratione possibilitatis^ or upon certain laws of the
general order of this possible universe with which
they agree and whose concept they determine. At
the same time they determine the concepts of all
individual substances which ought to enter into this
same universe. Everything, therefore, is in order
even including miracles, although these latter are
contrary to certain subordinate regulations or laws
of nature. Thus, all human events cannot fail to
happen as they have actually happened, supposing
that the choice of Adam was made. But this is so,
not so much because of the concept of the indi-
vidual Adam, although this concept involves them,
but because of the purposes of God, which also
enter into this individual concept of Adam and
determine the concept of the whole universe. These
purposes determine, consequently, as well the con-
cept of Adam as the concepts of all the other indi-
vidual substances of this universe, because each
individual substance expresses the whole universe,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 125

of which it is a part according to a certain relation,
through the connection which there is between all
things, and this connection is owing to the connec-
tion of the resolutions or plans of God.

I find that you bring forward another objection,
Monsieur, which does not depend upon the conse-
quences, apparently contradicting freedom, as was
the objection which I just met, but which depends
upon the matter itself and upon the idea which we
have of an individual substance. Because, since I
have the idea of an individual substance, that is to
say of myself, it seems to you that we must seek
what is meant by an individual concept in this idea
and not in the way in which God conceives of indi-
viduals; and just as I have only to consult the
specific concept of the sphere in order to decide if
the number of feet in the diameter is not determined
by this concept, in the same way you say I find
clearly in the individual concept which I have of
myself that I will be myself, in either case whether
I make or do not make the journey which I intend.

In order to make my reply clear, I agree that the
connection of events, although it is certain, is not
necessary, and that I am at liberty either to make
or not to make the journey, for, although it is
involved in my concept that I will make it, it is also
involved that I will make it freely. And there is
nothing in me of all that can be conceived sub
ratione generalitatis, whether of essence or of
specific or incomplete concepts from which it can be
deduced that 1 will make it necessarily. While, on
the other hand, from the fact that I am a man, the
conclusion can be drawn that I am capable of think-
ing, and consequently, if I do not make this journey,

126 CORRESPONDENCE.

this will be against no eternal or necessary truth.
Still, since it is certain that I will make it there
must be indeed some connection between the me
which is the subject, and the carrying out of the
journey, which is the predicate. The concept of
the predicate is always in the subject of a true propo-
sition. There is, therefore, an omission, if I do
make it, which will destroy my individual or com-
plete concept, or which would destroy what God
conceives or conceived in regard to me even before
resolving to create me. For this concept involves,
sub ratione possibilitatis, the existences or the truths
of fact or the decrees of God upon which the facts
depend.

I agree, also, that in order to determine the con-
cept of an individual substance it is good to consult
that which I have of myself, as we must consult a
specific concept of a sphere in order to determine
its properties. Nevertheless, there is between the
two cases a great difference, for the concept of
myself in particular and of any other individual
substance is infinitely more extensive and more
difficult to understand than is a specific concept,
such as a sphere, which is only incomplete and does
not involve all the practically necessary circum-
stances to get at a particular sphere. It is not
enough in order to understand what the me is that I
am sensible of a subject which thinks, I must also
conceive distinctly of all that which distinguishes
me from other possible spirits and of this latter I
have only a confused experience. Therefore, it is
easy to determine that the number of feet in the
diameter is not involved in the notion of the sphere
in general, it is not so easy to determine certainly,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 127

although we can decide quite probably whether the
voyage which I intend to make is involved in my
concept; were it not so it would be as easy to be a
prophet as to be a geometer. Nevertheless as
experience is unable to make me recognize a great
number of insensible things in the body in regard
to which the general consideration of the nature of
bodies and of movements might convince me; in
the same way, although experience cannot make me
feel all that is involved in my concept, I am able to
recognize in general that everything which pertains
to me is involved in it through the general con-
sideration of an individual concept.

Surely since God can form and does actually form
this complete concept which involves whatever is
sufficient to give a reason for all the phenomena
that happen to me, the concept is therefore pos-
sible. And this is the true complete concept of
that which I call the me. It is in virtue of this con-
cept that all my predicates pertain to me as to their
subject. We are, therefore, able to prove it with-
out mentioning God, except in so far as it is neces-
sary to indicate my dependence. This truth is
expressed more forcefully in deriving the concept
which is being examined from the divine cognizance
as its source. I grant that there are many things in
the divine knowledge which we are unable to com-
preherid but it does not seem to me that we must
needs go into them to solve our question. Besides,
if, in the life of any person, and even in the whole
universe anything went differently from what it
has, nothing could prevent us from saying that it
was another person or another possible universe
which God had chosen. It would then be indeed

128 CORRESPONDENCE.

another Individual. There must then be some
reason a priori independent of my existence why we
may truly say that it was I who was at Paris and
that it is still I and not another who am now in
Germany and consequently it must be that the con-
cept of myself unites or includes different condi-
tions. Otherwise it could be said that it is not the
same individual although it appears to be the same
and in fact certain philosophers who have not
understood sufficiently the nature of substance
and of individual beings or of beings per se
have thought that nothing remained actually the
same. It is for this, among other reasons, that I
have come to the conclusion that bodies would
not be substances if they had only extension in
them.

I think, Monsieur, that I have sufficiently met
the difficulties regarding the principal proposition,
but, as you have made in addition some important
remarks in regard to certain incidental expressions,
which I used, I will attempt to explain them also.
I said that the presupposition from which all human
events could be deduced, was not that of the crea-
tion of an undetermined Adam but of the creation
of a certain Adam determined in all circumstances,
selected out of an infinity of possible Adams. In
regard to this you make two important remarks, the
one against the plurality of Adams and the other
against the reality of substances which are merely
possible. In regard to the first point, you say with
good reason that it is as little possible to think of
several possible Adams, taking Adam for a partic-
ular nature, as to conceive of several me's. I agree,
but in speaking of several Adams I do not take

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 129

Adam for a determined individual but for a certain
person conceived sub ratione generalitatis under the
circumstances which appear to us to determine
Adam as an individual but which do not actually
determine him sufficiently. As if we should mean
by Adam the first man, whom God set in a garden
of pleasure whence he went out because of sin, and
from whose side God fashioned a woman. All this
would not sufficiently determine him and there
might have been several Adams separately possible
or several individuals to whom all that would apply.
This is true, whatever finite number of predicates
incapable of determining all the rest might be taken,
but that which determines a certain Adam ought to
involve absolutely all his predicates. And it is this
complete concept which determines the particular
individual. Besides, I am so far removed from a
pluralistic conception of the same individual that I
agree heartily with what St. Thomas has already
taught with regard to intelligences and which I
hold to be very general, namely, that it is not pos-
sible for two individuals to exist entirely alike or
differing solo numero.

As regards the reality of substances merely pos-
sible, that is to say, which God will never create,
you say, Monsieur, that you are very much inclined
to believe that they are chimeras. To which I
make no objection, if you mean, as I think, that they
have no other reality than what comes to them in
the divine understanding and in the active power of
God. Nevertheless, you see by this, Monsieur, that
we are obliged to have recourse to the divine knowl-
edge and divine power in order to explain them
well. I find very well founded that which you say

130 CORRESPONDENCE.

afterwards, "That we never conceive of any sub-
stance merely as possible except under the idea of
a particular one (or through the ideas understood in
a particular one) of those which God has created."
You say also, "We imagine that, before creating
the world, God looked over an infinity of possible
things out of which he chose certain ones and
rejected the others, certain possible Adams (first
men), each with a great sequence of personages with
whom he has an intrinsic connection; and we sup-
pose that the connection of all these other things
with one of these possible Adams (first men) is
wholly similar to that which the actually created
Adam had with all his posterity. This makes us
think that it is this one of all the possible Adams
which God has chosen and that he did not wish any
of the others." In this you seem to recognize that
those ideas, which I acknowledge to be mine (pro-
vided that the plurality of Adams and their possi-
bilities is understood according to the explanation
which I have given and that all this is understood
according to our manner of conceiving any order in
the thoughts or the operations which we attribute to
God), enter naturally enough into the mind when
we think a little about this matter, and indeed can-
not be avoided; and perhaps they have been displeas-
ing to you, only because you supposed that it was
impossible to reconcile the intrinsic connection
which there would be, with the free decrees of God.
All that is actual can be conceived as possible and
if the actual Adam will have in time a certain pos-
terity we cannot deny this same predicate to this
Adam conceived as possible, inasmuch as you grant
that God sees in him all these predicates when

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 131

he determines to create him. They therefore per-
tain to him. And I do not see how what you say
regarding the reality of possibles could be contrary
to it. In order to call anything possible it is enough
that we are able to form a notion of it when it is
only in the divine understanding, which is, so to
speak, the region of possible realities. Thus, in
speaking of possibles, I am satisfied if veritable
propositions can be formed concerning them. Just
as we might judge, for example, that a perfect
square does not imply contradiction, although there
has never been a perfect square in the world, and if
one tried to reject absolutely these pure possibles
he would destroy contingency and liberty. • For if
there was nothing possible except what God has
actually created, whatever God created would be
necessary and God, desiring to create anything
would be able to create that alone without having
any freedom of choice.

All this makes me hope (after the explanations
which I have given and for which I have always
added reasons so that you might see that these were
not evasions contrived to elude your objections),
that at the end your thoughts will not be so far
removed from mine as they appeared to be at first.
You approve the inter-connection of God's resolu-
tions; you recognize that my principal proposition
is certain in the sense which 1 have given to it in
my reply; you have doubted only whether I made
the connection independent of the free decrees of
God, and this with good reason you found hard to
understand. But I have shown that the connection
does depend in my opinion upon the decree and
that it is not necessary, although it is intrinsic.

I3« CORRESPONDENCE.

You have insisted upon the difficulties which there
would be in saying, "If I do not make the journey,
which I am about to make, I will not be myself," and
I have explained how one might either say it or not.
Finally, I have given a decisive reason which, in my
opinion, takes the place of a demonstration; this
is, that always in every affirmative proposition
whether veritable, necessary or contingent, univer-
sal or singular, the concept of the predicate is com-
prised in some sort in that of the subject. Either
the predicate is in the subject or else I do not know
what truth is.

Now, I do not ask for any. more connection here
than what is found a parte rei between the terms of
a true proposition, and it is only in this sense that I
say that the concept of an individual substance
involves all of its changes and all its relations, even
those which are commonly called extrinsic (that is
to say, which pertain to it only by virtue of the gen-
eral inter-connection of things, and in so far as it
expresses the whole universe in its own way),
since "there must always be some foundation for
the connection of the terms of a proposition and
this is found in their concepts." This is my funda-
mental principle, which I think all philosophers
ought to agree to, and one of whose corollaries is
that commonly accepted axiom: that nothing hap-
pens without a reason which can be given why the
thing turned out so rather than otherwise. This
reason, however, often produces its effects without
necessitation. A perfect indifference is a chimer-
ical or incomplete supposition. It has seemed that
from the principle above mentioned I draw surpris-
ing consequences but the surprise is only because

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 133

people are not sufficiently in the habit of following
out perfectly evident lines of thought.

The proposition which was the occasion of all this
discussion is very important and should be clearly
established, for from it follows that every indi-
vidual substance expresses the whole universe
according to its way and under a certain aspect, or,
so to speak, according to the point of view from
which it is regarded; and that a succeeding condi-
tion is a consequence, whether free or contingent, of
its preceding state as though only God and itself
were in the world. Thus every individual substance
or complete being is, as it were, a world apart, inde-
pendent of everything else excepting God. There
is no argument so cogent not only in demonstrating,
the indestructibility of the soul, but also in showing
that it always preserves in its nature traces of all
its preceding states with a practical remembrance
which ca.n always be aroused, since it has the con-
sciousness of or knows in itself what each one calls
his me. This renders it open to moral qualities, to
chastisement and to recompense even after this life,
for immortality without remembrance would be of
no value. This independence however does not
prevent the inter-activity of substances among them-
selves, for, as all created substances are a continual
production of the same sovereign Being according to
the same designs and express the same universe or the
same phenomena, they agree with one another
exactly; and this enables us to say that one acts
upon another because the one expresses more dis-
tinctly than the other the cause or reason for the
changes, — somewhat as we attribute motion rather
to a ship than to the whole sea; and this with

134 CORRESPONDENCE.

reason, although, if we should speak abstractly,
another hypothesis of motion could be maintained,
that is to say, the motion in itself and abstracted
from the cause could be considered as something
relative. It is thus, it seems to me, that the inter-
activities of created substances among themselves
must be understood, and not as though there were a
real physical influence or dependence. The latter
idea can never be distinctly conceived of. This is
why, when the question of the union of the soul and
the body, or of action and of passion of one spirit
with regard to another created thing, comes into
question, many have felt obliged to grant that their
immediate influence one upon another is inconceiv-
able. Nevertheless, the hypothesis of occasional
causes is not satisfactory, it seems to me, to a philos-
opher, because it introduces a sort of continuous
miracle as though God at every moment was changing
the laws of bodies on the occasions when minds had
thoughts, or was changing the regular course of the
thinking of the soul by exciting in it other thoughts
on the occasion of a bodily movement; and in general
as though God was interfering otherwise for the ordi-
nary events of life than in preserving each substance
in its course and in the laws established for it.
Only the hypothesis of the concomitance or the
agreement of substances among themselves there-
fore is able to explain these things in a manner
wholly conceivable and worthy of God. And as this
hypothesis alone is demonstrative and inevitable in
my opinion, according to the proposition which we
have just established, it seems also that it agrees
better with the freedom of reasonable creatures than
the hypothesis of impressions or of occasional

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 135

causes. God created the soul from the very start in
such a manner that for the ordinary events it has no
need of these interventions, and whatever happens
to the soul comes from its own being, without any
necessity, on its part, of accommodation in the
sequence of events to the body, any more than there
is of the body's accommodating itself to the soul.
Each one follows its laws, the one acts freely, the
other without choice, and they accord with one
another in the same phenomena. The soul is never-
theless the form of its body, because it expresses
the phenomena of all other bodies according to their
relation to its own.

It may be surprising, perhaps, that I deny the
action of one corporeal substance upon another,
when this seems so evident, but, besides the fact that
others have already done this, we must also con-
sider that it is rather a play of the imagination than
a distinct conception. If the body is a substance
and not a mere phenomenon, like a rainbow, nor a
being, brought together by accident or by accumula-
tion, like a pile of stones, its essence cannot consist
in extension and we must necessarily conceive of
something which is called substantial form and
which corresponds in some sort to the soul. I have
been convinced of this, as it were, in spite of myself,
after having held a very different opinion before.
But, however much I may approve of the School-
men in this general and, so to speak, meta-
physical accounting for the basis of bodies, I also
hold to the corpuscular theory as it is used in the
explanation of particular phenomena, and for these
latter nothing is gained by applying the terms, forms
and qualities. Nature must always be explained

136 CORRESPONDENCE.

mathematically and mechanically, provided it be
kept in mind that the principles or the laws of
rhechanics and of force do not depend upon mathe-
matical extension alone but have certain meta-
physical causes.

After all this I think that now the propositions
contained in the abstract which was sent to you will
appear not only more intelligible but perhaps ten-
able and more important than might have been
thought at first,

X

Leibniz to Arnauld.

Hanover, July 14, 1686.
Monsieur:

I have always had so much esteem for your well-
known ability that even when I thought myself ill-
treated by your criticism I made the firm resolve to
say nothing but what would express great deference
toward you; and now you have had the generosity
of making me a restitution with interest, or, rather,
with liberality — a kindness which I shall cherish
deeply, because it brings the satisfaction of think-
ing that you are well disposed toward me. When I
was obliged to speak a little strongly, in order to
defend myself from positions which you thought I
held, it was because I disapproved of them extremely
and because I thought so much of your approbation,
that I was the more sensitive when I saw you imput-
ing them to me. I hope that I have been able as
well to justify the truth of my opinions as their
harmlessness. This, however, is not absolutely
necessary and since error by itself can do injury

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 137

neither to piety nor to friendship I shall not defend
myself with the same force; and if in the enclosed
paper I have made a reply to your gracious letter
where you have pointed out very clearly and in a
very instructive manner in what respect my reply
has not yet satisfied you, it is not because I pretend
that you will take the time to examine again my
reasons, for it is easy to see that you have more
important business and these abstract questions
require leisure. But I have made the reply so that
at least you maybe able to do so in case, on account
of the unexpected consequences which can be
derived from these abstract notions, you may wish
to divert yourself some day. I would desire this
extremely for my own profit and for the clearing up
of certain important truths contained in my abstract,
whose acceptance on your part or at least the
acknowledgement of whose harmlessness, would be
of great consequence to me. I would wish it, I say,
if I had not learned long since to prefer the public
benefit, which is interested in a wholly different
manner in the way in which your time is expended,
to my own particular advantage, which, however,
would not be by any means small. I have already
experienced this advantage from your letter and I
know well enough that there is hardly any one in
the world who can penetrate more ably into the
heart of the matter and who will be able to shed
more light upon so clouded a subject. It is with
difficulty that I speak of the manner in which you
have been willing to do me justice, M., when I asked
only that you be gracious to me. I am covered with
confusion and I say these words only to indicate to
you how sensible I am of this generosity which is

138 CORRESPONDENCE.

very instructive to me; this all the more because it
is unusual and more than unusual in a mind of the
first rank Such a mind, reputation usually puts on
guard, not only against the criticism of others but
also against its own. It is rather I who must ask
your pardon, and, as it appears that you have granted
me it in advance, I will do my best to acknowledge
this goodness, to merit its effects, and to preserve
for myself always the honor of your friendship,
which should be esteemed as so much the more
precious because it leads you to act in accord with
such Christian and such noble sentiments.

I am not able to let this occasion pass without
speaking to you in regard to certain of my medita-
tions since 1 had the honor of seeing you. Among
other things I have made quite a number of investi-
gations into jurisprudence and it seems to me that
something permanent and useful might be estab-
lished, quite as much for the sake of having ascer-
tained laws, of which there is a great lack in Germany
and perhaps also in France, as also for the establish-
ment of short and good forms of procedure. For
this purpose it is not sufficient to be strict with
regard to the terms or the established days and
other conditions, as is the case with the laws com-
piled under the code of Louis; for to suffer a good
cause to be lost because of formalities, is in juris-
prudence a remedy comparable to that of a sur-
geon who is continually cutting off arms and legs
They say that the King is having work done for
the reform of chicanery, and I think that some-
thing of importance might be done along this line.

I have also been interested in the subject of
mines, because of those which we have in our coun-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 139

try; and I have frequently visited them by command
of the Prince. I think I have made several dis-
coveries in regard to the formation, not so much of
the metals as of those forms in which the metals are
found and of certain bodies among which they lie.
For example, I have shown the manner of the for-
mation of slate.

Besides this I have gathered together memoirs
and titles concerning the history of Brunswick, and
recently I read a document regarding the boundaries
of the Hildesheim bishopric of the canonized Em-
peror Henry II., where I was surprised to find these
words, "for the safety of his royal wife and child."
This seemed to me to be quite contrary to the
accepted opinion which would have us believe that
he maintained a state of virginity toward his wife,
St. Cunigunde.

Besides this I have diverted myself frequently
with abstract thoughts in metaphysics and geometry.
I have discovered a new method of tangents, which
I have had printed in the Journal of Leipsic. You
know, that Hudde and later De Sluse developed this
matter quite far, but there were two things lacking.
The one was that when the unknown term or
indeterminate was expressed in fractions and irra-
tionals, these had to be eliminated in order to use
their methods, which made the calculation assume
an extent and an elaborateness very awkward and
often unmanageable; while my method is not encum-
bered at all with fractions or irrationals. This is
why the English have made so much of it. The
other fault of the method of tangents is that it does
not apply to the lines which Descartes calls mechan-
ical and which I prefer to call transcendental; while

140 CORRESPONDENCE.

my method applies to them just the same, and I can
calculate the tangent of the cycloid or of any other
line. I claim also to give in general the means
of reducing these lines to calculation, and I hold
that they must be received into geometry, whatever
M. Descartes may say. My reason is that there
are analytical problems which are of no degree or
whose degree is required; e.g., to cut an angle in the
incommensurable ratio of one straight line to another
straight line. This problem is neither in plane geom-
metry nor in solid nor in super-solid geometry, it is,
nevertheless, a problem, and for this reason I call it
transcendental. Such is also this problem: Solve
the following equation: 2^ + 2 = 30, where the un-
known term x is found also in the exponent and
the degree also of an equation is required. It is
easy to find here that x is equal to 3 for 3* + 3 or
27 + 3 makes 30. But it is not always so easy to
solve it, above all when the exponent is not a
rational number; and we must have recourse to lines
or loci which are appropriate to the purpose and
which therefore must be admitted into geometry.
Now I show that the lines which Descartes would
exclude from geometry depend upon equations
which transcend algebraic degrees but are yet not
beyond analysis, nor geometry. I therefore call the
lines, which M. Descartes accepts, algebraic because
they are of a certain degree in an algebraic equation.
The others I call transcendental. These I reduce to
calculations, and their construction I show either
through points or through motion; and, if I might
venture to say, I claim to advance analysis thereby
ultra Herculis columnas.

Regarding the subject of metaphysics I claim to

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 141

advance by geometrical demonstrations, positing
only two primary truths; to wit, in the first place,
the principle of contradiction, (for if two contradic-
tories could be true at the same time all reasoning
would be useless); and secondly, the principle that
nothing is without reason, or that every truth has
its proof a priori, drawn from the meaning of the
terms, although we have not always the power to
attain this analysis. I reduce all mechanics to a
single metaphysical proposition and I have several
important propositions in geometric form regarding
causes and effects, and the same regarding simili-
tude by my definition of which I easily demonstrate
several truths which Euclid proves in a roundabout
way.

In addition I cannot approve the custom of those
who have recourse to their ideas, when they are at
the end of their proofs, and who abuse the principle
that every clear and distinct conception is good.
For I hold that we must possess the criteria of dis-
tinct knowledge And seeing that we often think
without ideas, employing in place of the ideas in
question, characters whose signification we wrongly
suppose ourselves to know, and thus form impos-
sible chimeras, therefore I hold that the criterion
of a true idea is that its possibility can be proved,
whether a priori in conceiving its cause or reason,
or a posteriori when experience enables us to know
that it is actually found in nature. This is why I
consider definitions to be real when it is known that
the defined is possible; otherwise they are only
nominal and cannot be trusted; for if by chance the
thing defined implies contradictions, two contradic-
tories can be deduced from the same definition. It

142 CORRESPONDENCE.

is for this reason that you had good cause to insist
against Father Malebranche that a distinction must
be made between true and false ideas, and that too
much confidence must not be placed in the imagina-
tion under the pretext of a clear and distinct intel-
lection.

I know no one who is better able than yourself to
examine this class of thoughts, particularly those
whose consequences lead into theology; few
people having the necessary penetration and the
broad enlightenment which is called for; and few
people having that fairness which you have now dis-
played toward me. I therefore pray God to
lengthen your life and not to deprive us too soon of
an ally whose like will not be easily found again.
I am yours, sincerely, Monsieur,

XI

Arnauld to Leibniz.

Sept. 28, 1686.

I thought, M., that I might make use of the lib-
erty which you gave me to take my time in reply-
ing to your kindness; and therefore I have put it
off, until I had completed a work which I had com-
menced. I have been a gainer in doing you justice,
for there was never anything more honorable or
more gracious than the manner in which you
received my excuses. So much was not called for
to make me resolve to acknowledge in good faith
that I am satisfied with the manner in which you
have explained what was startling to me at first,
regarding the concept of the individual nature.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 143

For no man of honor should have any difficulty in
accepting a truth as soon as it is made known to
him. I have been above all struck by this argu-
ment, that in every affirmative true proposition,
necessary or contingent, universal or singular, the
concept of the attributes is comprised in some way
in that of the subject. Predicatum inest subjecto.

There remains for me only the difficulty in regard
to the possibility of things and in regard to this way
of conceiving of God as though he had chosen the
universe, which he created, out of an infinity of other
possible universes which he saw at the same time
and which he did not choose to create. But as this
has nothing to do properly with the concept of the
individual nature, and as I should have to meditate
at too great length in order to make clear what I
think about it or rather what I find to object to in
the thoughts of others, because they do not seem to
me to do justice to God's power, you will permit me
to pass over this subject.

I would prefer to ask you to clear up two thfngs
which I find in your last letter. They seem to me
important, but I do not understand them very
well.

The first is as to what you mean by "the hypoth-
esis of the concomitance and of the agreement of
substances among themselves." You claim that by
this means, that which happens in the union of the
soul and the body and in the action or the passion
of a mind with respect to any other created thing,
can be explained. I cannot understand what you
say in explaining this thought, which, according to
you, agrees neither with those who think that the
soul acts physically upon the body and the body

144 CORRESPONDENCE.

upon the soul, nor with those who think that God
alone is the physical cause of these effects, and that
the soul and the body are only the occasional
causes. You say, "God created the soul in such a
way that for the ordinary events it has no need of
these changes, and that which happens to the soul
arises from its own being without its having to
agree with the body in what results, any more than
the body does with the soul. Each one follows its
laws. The one acting with freedom and the other
without choice, they fit in together, one with
another, in the same phenomenon." Examples
will enable you to make your thought clearer: some
one wounds my arm. With regard to my body, this
is only a bodily motion but my soul at once has a
feeling of pain which it would not have if this had
not happened to my arm. The question is, what is
the cause of this pain? You deny that my body has
acted upon my soul, and that God, on the occasion
of this which happened to my arm, immediately
produced in my soul the feeling of pain. It must
be, therefore, that you think that it is the soul
which has formed this feeling in itself and this must
be what you mean when you say that, "What hap-
pens in the soul on the occasioning of the body
arises from its own being." St. Augustine was of
this opinion because he thought that bodily pain
was nothing else than the grief which the soul had
when its body was ill-affected. But what reply can
be made to those who object that the soul must
therefore have known that its body was ill-affected
before it could become sorrowful, while in fact it
seems to be the pain which informs the soul that
the body is injured.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 145

Let us take another example where the body has
some movement on the occasioning of the soul. If
I wish to take off my hat, I lift my arm to my head
This movement of my arm upward is not at all in
line with the ordinary laws of motion. What then
is its cause? It is because the spirits, having
entered into certain nerves, have stimulated them.
But these spirits have not been through their
own power determined to enter into these nerves.
They had not given to themselves the movements
which cause them to enter into these nerves. What
has given it to them then? Is it God, who has done
it on the occasion of my wishing to lift my arm?
This is what the partisans of occasional causes say.
It seems that you do not approve of their position.
It must, therefore, be our soul itself, but this again
it seems that you will not grant, for this would be to
act physically upon the body; and you appear to
deny that a substance can act physically upon
another.

The second thing upon which .1 should like to be
enlightened is your statement, "In order that the
body or matter should not be a simple phenomenon,
like a rainbow, nor a being brought together by acci-
dent or by an accumulation, like a pile of stones, it
must not consist merely in extension, and there
must needs be something which is called the sub-
stantial form and which corresponds in some sort
to what is called the soul." There are a good many
things to ask upon this point.

ist. Our body and our soul are two substances
really distinct. Now, if we put into the body a
substantial form aside from this extension, we can-
not imagine how there should be two distinct

146 CORRESPONDENCE.

substances, we cannot see therefore that this sub-
stantial form has any relation to what we call our
soul.

2nd. This substantial form of the body must be
either extended and divisible or not-extended and
indivisible. If we should say the latter, it would
seem to be as indestructible as is our soul; and if we
should say the former, it would seem that nothing
would be gained toward making the body a nnum
per se, any more than if it consisted only in exten-
sion. For it is the divisibility of extension into
an infinity of parts which presents the difficulty of
conceiving it as a unit. This substantial form there-
fore would not remedy this difficulty at all so long
as it also is divisible like extension itself.

3rd. Is it the substantial form of a block of mar-
ble which makes it one? If this is so, what becomes
of that substantial form when it ceases to become
one, after it has been cut in two? Is it annihilated,
or does it become two? The first is inconceivable,
if this substantial form is not a mere manner of
being, but is a substance; and it cannot be said that
it is a manner of being or a mode, because then the
substance, of which this form would be the mode,
would be an extension. This apparently is not your
thought. And if this substantial form should be-
come two instead of one, why would not the same
be said of the extended alone without this substan-
tial form?

4th. Do you give to extension a general sub-
stantial form such as has been admitted by certain
Schoolmen who have called it formam corporeitatis?
Or do you wish that there should be as many differ-
ent substantial forms as there are different bodies

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 147

and are these different in kind when the bodies are
different in kind?

5th. In what do you put the unity which is
attributed to the earth, to the sun, or to the moon,
when we say that there is only one earth which we
inhabit, one sun which lightens us, only one moon
which turns about the earth in so many days? Do
you think that this earth, for example, made up of
so many heterogeneous parts must necessarily have
a substantial form which is appropriate to it and
which gives to it this unity? It does not seem that
you believe this. I should say the same thing of a
tree, of a horse, and still further I would instance
mixtures; for example, milk is composed of the
serum, of the cream, and of the portion which hard-
ens. Are there here three substantial forms, or is
there only one?

6th. Finally, it will be said that it is not worthy
of a philosopher to admit entities of which there are
no clear distinct ideas; and there are no such clear
and distinct ideas of these substantial forms. And
furthermore even, you do not let them be proved by
their effects, since you acknowledge that it is by a
corpuscular philosophy that all the particular
phenomenon of nature should be explained, and that
there is no advantage in bringing up these forms.

7th. The Cartesians in order to find unity in
bodies have denied that matter was divisible to
infinity and they have held that indivisible atoms
must be accepted; but I think that you do not share
their opinion.

I have examined your little brochure and I find it
very subtle, but take care lest the Cartesians should
reply that it brings nothing up against their position,

148 CORRESPONDENCE.

because you p'osit something which they think false
— namely, that a stone, in descending, gives to its
own self this greater velocity which it acquires as it
descends. They will say that this acceleration
comes from the corpuscles, which, in rising, cause
everything that they find in their way to descend
and impart to them a part of the motion which they
had; and therefore there is no cause for surprise if
the body B, four times the weight of A, has more
motion when it has fallen one foot than the body A
when it has fallen four feet, because the corpuscles
which have pressed upon B have communicated to
it a motion proportioned to its mass and those which
have pressed upon A, in proportion to its mass. I
do not assure you that this reply will be valid, but I
think at least that you ought to see if there be
anything in it. I shall be very glad to know what
the Cartesians have said to your brochure.

I do not know whether you have examined what
M. Descartes says in his letters in regard to the gen-
eral principle of mechanics. It seems to me that
when he wishes to show why the same force can lift
by means of a machine twice or four times as much
as what it can lift without a machine, he declares
that he has not taken into consideration the velocity.
My recollection about it, however, is very, confused,
for I have gone into those things only from time to
time and at odd moments, and it is more than
twenty years since I have seen any of those books.

I do not wish you, M., to turn away from any of
your occupations however important, in order to
reply to the two objections which I have brought
forward. You may do as you please about them and
at your leisure.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 149

I should like very much to know if you have not
given the finishing touches to the two machines
which you invented while at Paris. The one in
the province of arithmetic seemed to be much more
perfect than that of M. Pascal, and the other was
an absolutely correct watch.

I am yours devotedly,

XII

Count Ernst von Hessen-Rheinfels to Leibniz.

Rheinfels, 21/31, Oct., 1686.
Monsieur:

I enclose herewith a letter from M. Arnauld,
which, by some carelessness of mine, has been here
over two weeks. On account of occupation in
other business 1 have not read it, and besides such
matters are too remote and speculative for me. I
send you also four other writings that you may be
interested in, and remain,

Yours very affectionately,

E.

XIII

Draft of the letter of Nov. 28-Dec. 8 to Arnauld.

The hypothesis of concomitance is a consequence
of the conception which I have of substance, for, in
my opinion, the individual concept of a substance
involves all that will ever happen to it, and it is in
this that complete beings differ from those which
are not complete. Now, since the soul is an indi-
vidual substance it must be that its concept, idea,

150 CORRESPONDENCE.

essence or nature involves all that will happen to it,
and God, who sees it perfectly, sees there what it
will do or endure forever and all the thoughts which
it will have. Therefore, since our ideas are only
the consequences of the nature of the soul and are
born in it by virtue of its concept, it is useless to ask
regarding the influence of another particular sub-
stance upon it. This aside from the fact that this
influence would be absolutely inexplicable. It is
true that certain thoughts come to us when there are
certain bodily movements and that certain bodily
movements take place when we have certain
thoughts, but this is because each substance ex-
presses the whole universe in its fashion and this
expression of the universe which brings about a
movement in the body is perhaps a pain in regard
to the soul. It is customary to attribute the action
to that substance whose expression is more distinct
and which is called the cause, just as when a body is
swimming in water there are an infinity of move-
ments of the particles of water in such a way that
the place which the body leaves may always be filled
up in the shortest way. This is why we say that
this body is the cause of the motion, because by its
means we can explain clearly what happens. But if
we examine the physics and the reality of the motion,
it is quite as easy to suppose that the body is in
repose and that all the rest is in motion conform-
ably to this hypothesis, since every movement in
itself is only relative, that is to say, is a change
of position which cannot be assigned to any one
thing with mathematical precision; but the change is
attributed to that body by means of which the whole
is most clearly explained. In fact, if we take all

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 151

phenomena, great or small, there is only one single
hypothesis which serves to explain everything
clearly. We can therefore say, that, although this
body is not an efficient physical cause of these
effects, its idea is at least, so to speak, the final cause
of them, or, if you prefer, a model cause* of them in
the understanding of God; because, if we wish to
ask what reality there is in motion we may imagine
that God desires expressly to produce all the
changes of position in the universe exactly the
same as that ship was producing them while going
through the water. Is it not true that it happens
exactly in the same way, for it is not possible to
assign any real difference? If we speak with meta-
physical precision there is no more reason for say-
ing that the ship presses upon the water in order to
make that large number of circular movements
because of which the water takes the place of the
ship, than to say that the water itself exerts pressure
to make all these circles and that it therefore causes
the ship to move conformably. Unless we say, how-
ever, that God expressly desired to produce such a
great number of movements so well fitted together,
we do not give any real cause for it, and as it is not
reasonable to have recourse to divine activity for
explaining a particular detail, we have recourse to
the ship, notwithstanding the fact that, in the last
analysis, the agreement of all the phenomena of
different substances comes about only because they
are productions of the same cause, that is to say,
of God. Therefore, each individual substance ex-
presses the resolves which God made in regard to
the whole universe. It is therefore for the same

*Cause e.vemplaire in the original.

152 CORRESPONDENCE.

reason that pain is attributed to changes in the
body, because thus we reach something distinct and
this is enough for us to produce the phenomena or
to prevent them. In order not to advance anything
that is unnecessary, however, I say that we only
think, and also that we produce only thoughts, and
that the phenomena are only thoughts. As, how-
ever, all our thoughts are not effective and do not
serve to produce for us others of a certain nature,
and since it is impossible for us to work out the
mystery of the universal connection between
phenomena, we must pay attention by means of
experience to those which have produced thoughts
before, and this is the way the senses do and this is
what is called external action, outside of us.

The hypothesis of the concomitance or of the
agreement of substances among themselves, follows
from what I have said regarding each individual
substance: that it involves, forever, all the acci-
dents that will happen to it and that it expresses
the whole universe in its manner. Thus whatever
is expressed in the body by a movement .or by a
change of position, is perhaps expressed in the soul
by a sense of pain. • Since pains are only thoughts,
we must not be surprised if they are the conse-
quences of a substance whose nature it is to think.
If it happens constantly that certain thoughts are
joined to certain movements, this is because God
has created from the very start all substances in
such away that in the sequence, all their phenomena
shall correspond without any need for a mutual
physical influence. This latter does not even
appear explicable. Perhaps M. Descartes would
rather have accepted this concomitance than the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 153

hypothesis of occasional causes, for so far as I
know, he has never expressed himself upon the
matter. I am pleasantly surprised, M., that St.
Augustine, as you say, already held some such view,
when he maintained that pain is nothing else than
the grief which the soul has when its body is ill dis-
posed. This great man surely thought far into
things. The soul, however, feels that its body is ill
disposed, not through an influence of the body upon
the soul, nor by a particular intervention of God who
carries the information, but because it is the nature
of the soul to express whatever happens in the
body, having been created from the start in such a
way that the sequence of its thoughts will agree
with the sequence of the movements. The same can
be said of the motion of my hand upward. It will
be asked what it is that influences the spirits to enter
into the nerves of a certain material; 1 reply that it
is as much the impressions made by the objects, in
virtue of the ordinary laws of motion, as it is the dis-
position of the spirits or even of the nerves. By
the general inter-agreement of things, however, all
these dispositions happen only when there is at the
same time in the soul the will to which we have
been accustomed to attribute the operation. Thus,
the souls change nothing in the ordering of the
body nor do the bodies effect changes in the order-
ing of the souls (and it is for this reason that forms
should not be employed to explain the phenomena of
nature). One soul changes nothing in the sequence
of thought of another soul, and in general one par-
ticular substance has no physical influence upon
another; such influence would besides be useless
since each substance is a complete being which

154 CORRESPONDENCE.

suffices of itself to determine by virtue of its own
nature all that must happen to it. Nevertheless,
one has good reason to say that my will is the cause
of this movement of my arm and that an interrup-
tion in the continuity of the matter of my body is the
cause of the pain, for the one expresses distinctly
what the other expresses more confusedly and the
action should be attributed to the substance whose
expression is most distinct. The same can be said
practically where phenomena are produced. If it is
not a physical cause, we can say that it is a final
cause or better a model cause, that is to say, that the
idea in the understanding of God has contributed to
God's resolve in regard to this particularity, when
the determination regarding the universal sequence
of things was being made.

The second difficulty is incomparably greater
regarding the substantial forms and the souls of
bodies, and I grant that I am not myself satisfied in
regard to it. First of all, we must maintain that
the bodies are substances and not merely true
phenomena like the rainbow, but, on the other hand,
even if this were granted, it might be inferred, I
think, that the corporeal substance consists neither
in extension nor in divisibility for it will be granted
that two bodies distant from each other, for exam-
ple, two triangles are' not really one substance; sup-
pose now that they come together to compose a
square, does the mere contact make them one sub-
stance? I do not think so. Now, every extended
mass may be considered as a composite of two or of
a thousand others, and the only extension there is, is
that by contact. Consequently, we shall never find
a body of which we can say that it is really one

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 155

substance; it will always be an aggregate of several.
Or rather, it will not be a real being, because the
component parts are subject to the same difficulty,
and we should never reach a real being, for the
beings which result from an aggregation have only
as much reality as there is in their ingredients.
Whence it follows that the substance of a body, if it
has one, must be indivisible; whether we call it
soul or form makes no difference to me.

The general conception of individual substance,
which seems to appeal to you, M., evidences the
same thing, that extension is an attribute which can
never constitute a complete being; no action can
ever be derived from extension, and no change. It
merely expresses a present state. Never does it
express the future or the past state as the concep-
tion of a substance should. When two triangles are
joined, we cannot decide how this union is made,
for this might happen in several ways, and what-
ever can have several causes is never a complete
being.

Nevertheless, I acknowledge that it is very diffi-
cult to answer several question which you have put,
I think we must say that if bodies or substantial
forms, for example, if the beasts have souls, then
these souls are indivisible. This is also the opin-
ion of St. Thomas. Are these souls therefore inde-
structible? I think they are, unless it is possible
that in accordance with the opinion of M. Leeuwen-
hoeck every birth of an animal is only the transfor-
mation of an animal already alive. There is
ground, moreover, for thinking that death is also
another transformation. The soul of man, how-
ever, is something more divine. It is not only

156 CORRESPONDENCE.

indestructible but it always knows itself and con-
tinues to exist with self-consciousness. Regarding
its origin, it can be said that God produced it only
when this animated body, which was in the seed,
determined itself to assume human form. This brute
soul, which formerly animated this body before
the transformation, is annihilated when the reasoning
soul takes its place; or if God changes the one into
the other by giving to the former a new perfection
by means of an extraordinary intervention, this is a
particular in regard to which I have not sufficient
light.

I do not know whether the body, when the soul or
substantial part is put aside, can be called a sub-
stance. It might very well be a machine, an aggre-
gation of several substances, of such sort that if I
were asked what I should say regarding the forma
cadaveris or regarding a block of marble, I should
say that they might perhaps be units by aggre-
gation, like a pile of stones, but that they are not
substances. The same may be said of the sun, of
the earth, of machines; and with the exception of
man, there is no body, of which I can be sure that it
is a substance rather than an aggregate of several
substances or perhaps a phenomenon. It seems to
me, however, certain, that if there are corporeal sub-
stances, man is not the only one, and it appears
probable that beasts have souls although they lack
consciousness.

Finally, although I grant that the consideration of
forms or souls is useless in special physics, it is,
nevertheless, important in metaphysics. Just as
geometers pay no attention to the composition of
the continuum, and physicists do not ask whether

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. I$7

one ball pushes another or whether it is God who
does this.

It would be unworthy of a philosopher to admit
these souls or forms without reason, but without
them it is not possible to understand how bodies
are substances.

XIV

Leibniz to Arnauld.

Hanover, Nov. 28-Dec. 8, 1686.
Monsieur:

As I have found something very extraordinary in
the franknes^ and in the sincerity with which you
accepted certain arguments which I employed, I
cannot avoid recognizing it and wondering at it. 1
was quite confident that the argument, based upon
the general nature of propositions, would make
some impression upon your mind, but I confess at
the same time that there are few people able to
enjoy truths so abstract whose cogency, perhaps, no
one else would have been able to see so easily. I
should like to be instructed by your meditations
regarding the possibilities of things. They would
certainly be profound and important, inasmuch as
they would have to deal with those possibilities in a
manner that might be worthy of God. But this will
be at your convenience. As regards the two diffi-
culties which you have found in my letter, the one
regarding the hypothesis of the concomitance or of
the agreement of substances among themselves, the
other regarding the nature of the forms of corporeal
substances, I grant that the difficulties are consider-
able, and if I were able to meet them entirely I

158 CORRESPONDENCE.

should think myself able to decipher the greatest
secrets of universal nature. But est aliquid prodire
tenus.

As regards the first I find that you have yourself
sufficiently explained the obscurity that you found
in my statement concerning the hypothesis of con-
comitance, for, when the soul has a feeling of pain
at the same time that the arm is injured, I think it
is as you say, M., that the soul forms for itself this
pain, which is a natural consequence of its condition
or of its concept. And it is surprising that St.
Augustine, as you have remarked, seems to have
recognized the same thing, when he said that the
pain which the soul has in these accidents is noth-
ing else than a grief which accompanies the ill con-
dition of the body. In fact, this great man has
very stable and profound thoughts. But it will be
asked, how does the soul know this ill condition of
the body? I reply that it is not by any impression
or action of the body upon the soul but because the
nature of every substance carries a general expres-
sion of the whole universe and because the nature
of the soul bears more particularly a distincter
expression of that which happens immediately to
its body. This is why it is natural for it to notice
and to recognize the accidents of its body by its own
accidents. The same is true with regard to the
body when it accommodates itself to the thoughts
of the soul, and when I wish to raise my arm it is
exactly at the very moment when everything is
ready in the body for this effect; in such a way that
the body moves in virtue of its own laws; while it
happens, by the wonderful though unfailing agree-
ment of things among themselves, that these laws

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 159

work together exactly at the moment that the will is
so inclined. God had regard to this in advance when
he formed his resolve in regard to this sequence of
all the things in the universe. All of this is only
the consequence of the concept of an individual
substance, which involves all its phenomena in such
a way that nothing can happen to its substance that
does not come from its own being, conformably,
however, to that which happens to another, although
the one may act freely and the other without
choice. This agreement is one of the best proofs
that can be given of the necessity of a substance
which shall be the sovereign cause of everything.

I should like to be able to explain as clearly and
decisively the other question with regard to the
substantial forms. The first difficulty which you
point out, M., is that our souls and our bodies are
two substances really distinct; therefore, it seems
that one is not the substantial form of the other. I
reply that in my opinion our body by itself, leaving
out of question the soul, the physical body, can be
called one substance only by a misuse of terms,
just as a machine or a pile of stones might be
called one although they are beings only by accu-
mulation. The regular or irregular arrangement
does not constitute a substantial unity. Aside from
this, the last Lateran council declares that the soul is
veritably the substantial form of our body.

Regarding the second difficulty I agree that the
substantial form of our body is indivisible and this
seems also to be the opinion of St. Thomas. I
agree, also, that every substantial form, or, indeed,
every substance is indestructible and also ingener-
able, which latter was also the opinion of Albertus

l6o CORRESPONDENCE.

Magnus and among the ancients of the author of the
book called De diaeta, usually attributed to Hippoc-
rates. They can come into being therefore only
by an act of creation. I am a good deal inclined to
believe that all the births of unreasoning animals,
which do not deserve a new act of creation, are only
transformations of another animal already living,
but at times invisible. Consider for example, the
changes which happen to a silk-worm and other like
creatures, where nature has disclosed its secrets in
certain instances while it conceals them in others.
Thus, brute souls would have all been created from
the very beginning of the world, in accordance with
that fertility of seeds mentioned in Genesis, but the
reasoning soul is created only at the time of the
formation of its body, being entirely different from
the others souls which we know because it is cap-
able of reflection and imitates on a small scale the
divine nature.

Thirdly, I think that a block of marble is, per-
haps, only a mass of stones and thus cannot be
taken as a single substance but as an assembly of
many. For, supposing there are two stones, (for
example, the diamond of the Grand Duke and that
of the Great Mogul), the same collective name
could be put for both of them, and we could say that
it is a pair of diamonds, although they are very far
apart; but, we should not say that these two dia-
monds compose one substance. Matters of greater or
less in this case would make no difference. They
might be brought nearer together, even to touch-
ing. Yet they would not be substantially one, and
if, after they had touched they were joined together
by some other body, constructed to prevent their

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. l6l

separation — for instance, if they were set in the
same ring — all this would make only what is called
a unity by accident, for it is as by accident that
they are subjected to the same motion. I hold,
therefore, that a block of marble is no more a
thoroughly single substance than would be the
water in a pond with all the fish included, even
when all the water and all the fish were frozen; or
any more than a flock of sheep, even when the sheep
were tied together so that they could only walk in step
and so that one could not be touched without pro-
ducing a cry from all. There is as much difference
between a substance and such a being, as there is
between a man and a community — say a people, an
army, a society or college, which are moral beings,
yet they have an imaginary something and depend
upon the fiction of our minds. Substantial unity
calls for a thoroughly indivisible being, naturally
indestructible since its concept involves all that
must happen to it. This characteristic cannot be
found either in forms or in motions, both of which
involve something imaginary as I could demon-
strate. It can be found, however, in a soul or a
substantial form, such as is the one called the me.
These latter are the only thoroughly real beings as
the ancients recognized and, above all, Plato, who
showed very clearly that matter alone does not
suffice for forming a substance. Now, the me
above mentioned or whatever corresponds to it, in
each individual substance can neither be made nor
destroyed by the bringing together or the separa-
tion of the parts. Such juxtapositions are wholly
apart from the constitution of a substance. I can-
not tell exactly whether there are other true cor-

l6« CORRESPONDENCE.

poreal substances beside those which have life.
But souls serve to give us a certain knowledge of
others at least by analogy.

All this can contribute to clear up the fourth dif-
ficulty, for, without bothering with what the School-
men have called formam corporeitatis, I assign sub-
stantial forms to all corporeal substances that are
more than mechanically united.

But fifthly, if I am asked in particular what I
should say of the sun, the earth, the moon, of the
trees, and of similar bodies, and even of the beasts,
I am not able to say surely whether they are ani-
mated, or at least whether they are substances, or
whether they are merely machines or aggregations
of several substances, but I am able to say that if
there are no corporeal substances such as I claim, it
follows that bodies are only true phenomena like
the rainbow. For a continuum is not only divis-
ible to infinity, but every particle of matter is
actually divided into other parts as different among
themselves as were the two diamonds above men-
tioned. And since this could always be continued,
we should never reach anything of which we could
say, here is really a being, unless there were
found animated machines whose soul or sub-
stantial form constituted the substantial unity inde-
pendently of the external union of contact. And if
there are no substantial forms, it follows that with
the exception of men there is nothing substantial in
the visible world.

Sixthly, since the conception of an individual
substance in general, which I have given, is as clear
as is the conception of truth, the conception of cor-
poreal substance will be clear also, and consequently

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 163

that of substantial forms. If, however, this should
not be so, we should be obliged to admit a good
many things whose knowledge is not so clear and
distinct. I hold that the conception of extension
is much less clear and distinct; witness the remark-
able difficulties found in the composition of the con-
tinuum. And it can, indeed, be said that there is no
definite and precise form in the body because of the
actual subdivision of the parts. With infinite sub-
division the body would be doubtless imaginary and
a mere appearance, if there was only the material and
its modifications. Nevertheless, it is useless to make
mention of the unity, the concept, or the substantial
forms of bodies when it is a question of explaining
the particular phenomena of nature, just as it is use-
less for Geometers to examine the difficulties of the
continuum when they are at work in solving some
problem. These things are nevertheless important
and worthy of consideration in their place; all the
phenomena of the body can be explained mechanic-
ally or by the corpuscular philosophy in accor-
dance with certain assumed mechanical principles
without troubling oneself as to whether there are
souls or not. In the ultimate analysis of the prin-
ciples of physics and mechanics, however, it is found
that these assumed principles cannot be explained
solely by the modifications of extension, and the
very nature of force calls for something else.

Finally, in the seventh place I remember that M.
Cordemoy, in his treatise on the distinction between
the body and the soul, in order to save the substan-
tial unity in the body, feels himself obliged to
assume atoms or indivisible extended bodies, so as
to have something permanent to constitute a simple

164 CORRESPONDENCE.

being; but you rightly concluded, M., that I did not
share this opinion. It appears that M. Cordemoy
made an approach to the truth, but he did not yet
see in what the true notion of a substance consisted
and this latter is the key for most important knowl-
edge. The atom, which consists of only an imagined
mass with an infinite duration, an idea which I hold
conforms no more to the divine wisdom than does
a vacuum, cannot contain in itself all its past
and future states and much less those of the whole
universe.

I come to your observations upon my objection to
the Cartesian principle regarding the quantity of
motion, and I grant, M., that the acceleration of a
body comes from the impulse of some invisible fluid
and that it is like a ship which the wind causes to
go at first very slowly and then faster; my demon-
stration, however, is independent of any hypothesis.
Without troubling myself at present as to how the
body has acquired the velocity which it has, I
accept it such as it is, and I say that a body weigh-
ing one pound, which has a velocity of two degrees,
has twice as much force as a body weighing two
pounds which has a velocity of one degree, because
it can raise the same weight twice as high. I hold
that in distributing the motion between bodies
which come into contact, regard must be had, not
to the quantity of motion, as is the case in the
Cartesian principle, but to the quantity of the force;
otherwise, we should obtain perpetual motion in
mechanics. For example, suppose that in a square
LM a body A goes along the diagonal lA 2A to
strike two equal bodies B and C at the same
moment in such a way that at the moment of con-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS.

tact the three centers of these three spheres are
found in an isosceles right triangle, the whole being
in a horizontal plane. Suppose now that the body
A remains at rest after the contact in the place 2A,
and imparts all its force to the bodies B and C. In
this case B would go from iB to 26, having the
velocity and direction 1626, and C from iC to 2C,
with the velocity and direction iCzC. That is to
say, if A takes one
second of time to pass
with uniform motion
from lA to 2A before
contact, then in one
second after contact B
will pass to 26, and C
to 2C. The question
is, what is the length
of 1626 or i C 2 C,
which represent the
velocity. I say that
it will be equal to AL or AM sides of the square
LM, for the bodies, being supposed equal, the
forces would be only as the height from which the
body would have to descend in order to acquire
these velocities, that is to say, as the squares of the
velocities. Now, the squares of 1626 and iCaC
taken together are equal to the square iA2A.
Hence, there is as much force after as before the
contact. But we see that the quantity of motion
has been augmented; for, since the bodies are equal,
the quantity of motion can be estimated by their
velocities. Now, before the contact this was the
velocity iA2A but after the contact it is the
velocity iB2B plus the velocity iC2C; 1626 plus

l66 CORRESPONDENCE.

lC2C, however, is greater than lA2A; it must needs
be, therefore, that, according to M. Descartes, in
order to maintain the same amount of motion the
body B would go from iB only to /3, or from iC
only to K, in such a way that iB/3 or iGc shall each be
equal to half I A2A. In this way, however, there will
be as much force lost as the two squares of iB/3 and of
iGc, taken together are less than the square iA2A.

And, on the other hand, I will show that by
another means force can be gained through the con-
tact. For, since according to M. Descartes, the
body A with the velocity and direction iA2A gives
by hypothesis to the bodies at rest B and C
velocities and directions iB/3 and iC/c so that it may
come to rest in their place, reciprocally if these
bodies should return and come in contact with the
body A resting at 2A with the velocities and direc-
tions fiiB and KiC and should come to rest after the
contact, they would make A move with the velocity
and direction 2AiA. In this way, however, per-
petual motion would be inevitably attained for, sup-
posing that the body B, weighing one pound with
the velocity ftiB could rise to the height of one foot,
and C the same, there would be before the shock a
force capable of lifting two pounds to the height of
one foot, or one pound the height of two feet, but,
after the contact of iB and iC with 2A the body A
weighing one pound and having a double velocity
(that is to say, the velocity of 2AiA, double the
velocity of /?iB or of KiC), could lift one pound to
the height of four feet, for the height to which the
bodies can rise by virtue of their velocities is as the
squares of their velocities. If, therefore, double the
force can be gained, perpetual motion is completely

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 167

discovered, or it is possible that force should be
gained or lost, and principles are not well-based
when such consequences can be derived from
them.

I found in Descartes' letters what you mentioned
to me — namely, that he had tried to avoid the con-
sideration of velocities in formulating the reasons
for moving forces and had taken into account only
the heights. If he had remembered this when he
wrote his principles of physics perhaps he would
have avoided the errors into which he has fallen
with respect to the laws of nature, but he happens to
have avoided the consideration of velocity there
where he might have retained it, and to have retained
it in the case where it could produce errors. For,
with regard to the power which I call dead (as when
a body makes its first effort to descend before it has
acquired any impetus from the continuance of the
motion), and with regard to the case when two
bodies are in equilibrium (for then, the first efforts
which the one exercises on the other are always
dead), it happens that the velocities are as the dis-
tances; when, however, we consider the absolute
force of bodies which have a certain impetuosity
(and this is necessary for establishing the laws of
motion), the calculation should be made from the
cause or from the effect, that is to say, according to
the height to which it can rise by virtue of this
velocity, or according to the height from which it
must descend in order to acquire this velocity. If
we should attempt to employ the velocity, we should
gain or lose a great deal of force without any reason
for it. In place of the height we might suppose a
spring or any other cause or effect, and the result

l68 CORRESPONDENCE.

would always be the same; viz., proportional to the
squares of the velocities.

I find in The News of the Republic of Letters for
the month of September, of this year, that someone
named Abbe D. C., of Paris, whom I do not know,
has replied to my objection. The trouble is that he
seems not sufficiently to have thought over the
difficulty. While pretending to contradict me
vehemently he grants me more than I wish and he
limits the Cartesian principle to the single case of
isochronous powers as he calls them, as in the five
usual forms of machinery, and this is entirely
against Descartes' intention. Besides this, he
thinks that the reason why in the case which I pro-
posed one of the bodies has quite as much force as
the other although it has a smaller quantity of
motion, is the result of this body's having fallen for
a longer period since it has come from a greater
height. If this made any difference, the Cartesian
principle which he wishes to defend would be ruined
by that very fact. This reason, however, is not
valid, for the two bodies can descend from those
different heights in the same time, according to the
inclination which is given to the planes along which
they must descend; and my objection would still be
entirely valid. I hope, therefore, that my objec-
tion maybe examined by a Cartesian who shall be a
Geometer and well versed in these matters.

Finally, M., as I honor you infinitely and am very
much interested in whatever concerns you I will be
delighted to learn from time to time of the state of
your health and of the works which you have in
hand; whose value I am proud to be able to recog-
nize. I am, with a passionate zeal,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 169

XV

Leibniz to Count Ernst von Hessen-Rheinfels.

[Taken from my letter of November, 1686.]

I take the liberty, Monseigneur, to beg your Serene
Highness to have the enclosed sent to M. Arnaud,
and, as it treats of matters far from the external
senses and dependent upon pure intellection, which
are not agreeable to and most frequently are looked
down upon by persons who are, nevertheless, active
and successful in the affairs of the world, I will say
here something in favor of these meditations; not
because I am so fatuous as to wish your Serene High-
ness to amuse himself with them (this would be as
unreasonable as to wish that the general of an army
should apply himself to algebra, however important
this science may be to any one who is concerned
with mathematics), but so that your Serene High-
ness may better estimate the purpose and the use of
such thoughts that might appear unworthy of taking
up a man's time; especially since all a man's
moments ought to be so precious to him. As these
matters are usually treated by the Schoolmen, they
are only disputations and distinctions and plays
upon words; but there are veins of gold among these
barren rocks. I think in fact that thought is the
principal and perpetual function of the soul. We
shall always think, but we shall not always live here;
this is why whatever renders us more capable of
thinking about most perfect objects and in the most
perfect way is what naturally contributes to our per-
fection. Nevertheless, the present state of our life
compels us to a great number of confused thoughts

170 CORRESPONDENCE.

which do not add to our perfection, such is the
knowledge of customs, of genealogies, of languages,
and even all historical knowledge of facts, whether
civil or natural; these are useful for us in 'avoiding
dangers and in taking care of the bodies and of the
men whom we have around us, but they do not
enlighten the mind. The knowledge of routes is
useful to a traveller while he is on his journey, but
whatever has a greater relation to the duties that lie
before him in patria is more important for him.
Now we are destined to live some day a spiritual
life, where substances separated from matter will
occupy us much more than do the bodies.

Here are a few examples taken from the arts, which
will enable us to distinguish between that which
enlightens the mind and that which only leads it
along as a blind man might be led. If a workman
knows by experience or by hearsay that when the
diameter is seven feet the circumference of the
circle is a little less than twenty-two feet, or if a gun-
ner knows by hearsay, or because he has frequently
measured it, that bodies are thrown the farthest at
an angle of 45 degrees, the knowledge is confused
and is that of an artisan; it does very well for earn-
ing a living and for performing services to others,
but the knowledge which enlightens the mind is that
which is distinct, or which gives the causes or rea-
sons involved, as when Archimedes gave the demon-
stration for the first rule and Galileo for the second.
In a word, it is only knowledge of the reasons in
themselves or of the necessary eternal truths, above
all of those which are the most comprehensive and
which have the most relation to the sovereign being,
that are able to make us more perfect. This knowl-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 17 1

edge alone is good in itself; all the rest is mercenary,
and should be learned only when necessary and to
serve the needs of this life, and so that this life may
be in a better position to contribute afterwards to
the perfection of the mind when one's subsistence
has been provided for. But the intemperance of
men, and what is called the care de pane lucrando,
and often also vanity, lead us to forget the lord for
the valet and the end for the means. This, accord-
ing to the poet is "to lose the reasons for living
while trying to live." Very much as a miser pre-
fers gold to his health, while gold is only for pro-
curing the commodities of life. Now, since that
which perfects the mind (leaving aside the light of
grace), is the demonstrative knowledge of the great-
est truths through their causes or reasons, it must be
granted that metaphysics or natural theology which
treats of immaterial substances and particularly of
God and of the soul, is the most important of all.
One cannot go very far in this without inquiring
into the true conception of substance, which I, in
my preceding letter to M. Arnaud explained in
such a manner that he himself who is so exact and
who was at first repelled by it, accepted it.

Finally, these meditations furnish surprising con-
sequences which are, nevertheless, of wonderful use
in freeing men from doubts regarding the relation of
God to created things, his fore-knowledge and fore-
ordination and the union of the soul with the body,
the origin of evil and other things of this nature. I
say nothing here of the great applications that these
principles have in the humanities, but at least I am
able to say that nothing lifts our minds more to the
knowledge and to the love of God, however much

172 CORRESPONDENCE.

nature may help us in this. I confess that all these
speculations are of no service without grace and
that God gives grace to people who have never
dreamed of these meditations, but God wishes also
that we should not omit anything on our part and
that each one of us according to his vocation and
according to the time, should make use of the per-
fections which God has given to human nature.
And since he has created us only that we may know
and love him, we cannot work enough toward this
nor can we make a better use of our time and of our
energy except when we are occupied elsewhere for
the public and for the welfare of others.

XVI

Arnauld to Leibniz.

March 4th, 1687.

It has been a long time, M., since I received your
letter, but I have been so busy since then that I have
not been able to reply to it earlier.

I do not understand very well what you mean by
this "distincter expression which our soul bears of
that which is now happening to its body," and
how it comes about that when someone pricks my
finger my soul knows of this pricking before it feels
the pain of it. This very "distincter expression,"
etc., ought to let it know therefore an infinity of
other things which happen in my body which, never-
theless, it does not know, for instance all that goes
on in the process of digestion and of nutrition.

As for your saying that although my arm raises
itself when I wish to raise it, it is not because my
soul causes this movement in my arm but it is

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 173

because "when I wish to raise it it is exactly at the
very moment when everything is ready in the body
for this very effect, in such a way that the body
moves itself by virtue of its own laws, although it
happens through the wonderful but unfailing agree-
ment of things among themselves that these laws
conspire together at the very same moment that the
will makes its resolution. For God had regard
to this in advance when he resolved upon this
sequence of all the things in the universe." It
seems to me that this is to say the same thing in
other terms that those say who maintain that my
will is the occasional cause for the movement of my
arm and that God is its real cause; for they do not
claim that God does this at the moment by a new
act of will each time that I wish to raise my arm,
but by a single act of the eternal will by which he
has chosen to do everything which he has foreseen
that it will be necessary to do, in order that the uni-
verse might be such as he has decided it ought to be.
Does not what you say come to this very thing,
namely that the cause of the movement of my arm
when I wish to lift it is "the wonderful but unfailing
agreement of things among themselves which results
because God had them in mind in advance when he
resolved upon this sequence of all the things in the
universe"? For this forethought of God has not
been able to bring about any event without a real
cause. We must, therefore, find the real cause of
this movement of my arm. You do not wish it to
be my will. I do not think, either, that you believe
a body can move itself or any other body as a real
or efficient cause. There remains therefore only this
"forethought of God," which can be the real and

174 CORRESPONDENCE.

efficient cause of the movement of my arm. Now
you, yourself, called this forethought of God his
resolve; and resolve and will are the same thing.
Therefore, according to you, every time that I wish
to raise my arm, it is the will of God which is the
real and efficient cause of this movement.

In regard to the second difficulty, I now under-
stand your position to be very different from what I
thought, for I supposed that you would reason thus:
the body should be the true substance; now there
can be no true substances which have no true unity
nor can there be any true unity which has not a sub-
stantial form; therefore the essence of a body can-
not be its extension, but every body besides its
extension should have a substantial form. To this
I have replied that a divisible substantial form, such
as almost all those who hold to substantial forms
understand them, could not give to a body any unity
that it did not have without this substantial form.

You agree, but you claim that every substantial
form is indivisible, indestructible and ingenerable,
being produced only by a real creation; whence it
follows:

ist. That every body which can be divided so that
each part will remain of the same nature as the
whole, such as metals, stones, wood, air, water and
the other fluid bodies, have no substantial form.

2nd. That the plants have none, either, since a
part of a tree, whether placed in the ground or
grafted to another tree, remains a tree of the same
sort that it was before.

3rd. That only animals have substantial forms,
and that therefore in your opinion only animals are
true substances.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 175

4th. And since, as you say, you are not very sure
whether brutes have souls or substantial forms, it
follows that with the exception of man there is
nothing substantial in the visible world, because you
claim that substantial unity requires a complete
being, indivisible, and through natural means inde-
structible. This can be found only in a soul or a
substantial form like that which I call the Me.

All of this means that every body whose parts are
only mechanically united is not a substance but
only a machine or an aggregate of several sub-
stances.

I will begin with this last. And I will say
frankly that it is only a dispute regarding a word.
For St. Augustine did not hesitate to recognize that
bodies have no real unity; because a unit should be
indivisible and no body is indivisible. There is,
therefore, no true unity excepting in Spirit, any
more than there is a true Me outside of them.
Now, what is your conclusion from that? "That
there is nothing substantial in those bodies which
have no soul or substantial form." In order that
this conclusion may be valid we must first of all
define substance and substantial in these terms, "I
call substance and substantial that which has a true
unity." But since this definition has not yet been
received there is no philosopher who has not
as much right to say, "I call substance that
which is not modality or manner of being," and
he could therefore maintain that it is untrue to
say that there is nothing substantial in a block of
marble, "because this block of marble is by no
means a manner of being of another substance, and
all that can be said of it is that it is not a single

176 CORRESPONDENCE.

substance but several substances joined together
mechanically." This philosopher would say "this
is what seems to me paradoxical: that there should
be nothing substantial in that which seems to be
made up of several substances." He could add
that he understood still less what you meant by the
words "bodies would be without doubt something
imaginary and only of appearance if they were com-
posed only of matter and its modifications." For
you postulate only matter and its modifications in
everything that has no soul or no substantial, inde-
structible, indivisible and ingenerable form and it
is only in the case of animals that you admit this
class of forms. You will therefore be obliged to say
that all the rest of nature is something imaginary
and merely an appearance, and for a still stronger
reason you would have to say the same thing of all
the works of men.

I cannot agree to these latter propositions, but I
see no objection to thinking that in every corporeal
nature there is only a machine and an aggregate of
substances, because of no one of its parts could one
say strictly that it is a single substance. This
serves merely to make evident what is worth while
noticing, as St. Augustine has done, that the
substance which thinks, or a spiritual substance,
is through this fact much more excellent than
extended or corporeal substance. The spiritual
substance alone has a true unity and a true ego,
while the corporeal substance does not have them.
It follows from this, that this fact, that the body has
no true unity when its essence is extension, cannot
be put forward to prove that extension is not of the
essence of the body; for, perhaps, the essence of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 177

the body has no true unity, as you grant in the case
of all those which are not united to a soul or to a
substantial form.

I do not know, M., what inclined you to believe
that brutes have these souls or substantial forms,
which, according to you, must be indivisible, inde-
structible and ingenerable. It is not because you
consider it necessary to explain their actions, for
you say expressly "that all the phenomena can be
explained mechanically or by the corpuscular
philosophy in accordance with certain postulated
mechanical principles, without going into the ques-
tion whether there are souls or not." It is also not
because the bodies of brutes need to have a true
unity and because they are not mere machines or
aggregations of substances; if plants are merely the
latter what necessity is there that brutes should be
anything else? Further, it is not clear how this
opinion can be easily maintained, if we consider
these souls as indivisible and indestructible. What
would be said of a worm, of which, when cut in two,
both parts move off as before? If a house where a
hundred thousand silk-worms were being kept should
catch fire and burn up, what would become of
those one hundred thousand indestructible souls?
Would they exist apart from all matter like our
souls? In the same way, what became of the souls
of those millions of frogs which Moses caused to
die when he stopped the plague? And of that
innumerable number of quails which the Israelites
killed in the desert or of all the animals which
perished in the flood? There are also other embar-
rassing questions in regard to the condition of these
souls in each brute at the moment that they are con-

178 CORRESPONDENCE

ceived. Is it that they are in seminibus ? Are they
there indivisible and indestructible? Quid ergo fit,
cum irrita cadunt sine ullis conceptions semina ? Quid
cum bruta mascula ad foeminas non accedunt toto vitae
suae tempore ? It will suffice to have indicated these
difficulties.

There still remains the discussion of the unity
which a reasoning soul has. It is agreed that it has
a true and a perfect unity, a true Me, and that it
communicates in some sort this unity and this
Me to that composite whole of the soul and body
which is called the man; for, although this whole is
not indestructible because it perishes when the soul
is separated from the body, it is indivisible in this
sense, that half a man cannot be conceived of. In
considering the body apart, however, in the same
way that our soul does not communicate to it its
indestructibility, we cannot see, properly speaking,
that it communicates either its true unity or its
indivisibility. Even though it be united to our
soul, nevertheless, its parts are truly united among
themselves only mechanically, and thus there is not
a single bodily substance, but an aggregation of
many corporeal substances. Not less true is it that
it is quite as divisible as all the other bodies in
nature. The divisibility, however, is inconsistent
with unity, therefore it has no true unity. But you
say, it acquires the unity through the soul, that is to
say, because it belongs to a soul which is a true
unit; this, however, is not an intrinsic unity in the
body, but is like that of different provinces which
are governed by a single king and thus constitute
one kingdom.

Although, however, it is true that there is no real

LEIBNIZ. ARNAULD. HESSEN-RHKINFELS. 179

unity except in intelligent natures, each of which
can say the word Me^ there are, nevertheless, differ-
ent degrees in this inexact unity which belongs to
bodies; for although there are no bodies which are
not made up of several substances there is, never-
theless, reason for attributing more unity to those
whose parts work together for a similar purpose like
a house or a watch than to those whose parts are only
in contact one with another like a pile of stones or
a bag of coins and only these latter can properly be
called an accidental aggregation. Almost all natural
bodies, which we call one, like a piece of gold, a
star, a planet, are of the first kind; but there are
none which appear to be more so than the organized
bodies, that is, the animals and plants; though there
is no reason to assign souls to them on this account
(and I think also that you assigned none to plants).
For why should not a horse or an orange be consid-
ered each one as a complete and whole work quite
as well as a church or a watch ? What is essential in
order that a thing may be called one (that is, this
oneness which applies to bodies, but which is very
different from that that applies to spiritual natures)
when the parts are united among themselves only
mechanically as are the parts of the machine? Is
it not the greatest perfection that they can have,
that they are machines so wonderful that only an
all-powerful God could have constructed them?
Our body, considered by itself, is therefore one in
this sense. The relationship, which an intelligent
nature, united to it and governing it, has with it,
may, perhaps, add some unity, but it is not that kind
of unity which pertains to spiritual natures.

I confess, M., that my ideas on the laws of motion

l8o CORRESPONDENCE.

are not clear and distinct enough to enable me to
pass judgment upon the difficulty which you have
brought up against the Cartesians. The one who
replied to you is the Abbe Catelan who has a good
mind and is a good geometer; since I left Paris I
have not had much intercourse with the philoso-
phers of that country. Inasmuch, however, as you
have decided to reply to this Abbe, and as he will
perhaps wish to defend his position, it is to be
hoped that these discussions will so clear up the
difficulty that it will be possible to know which side
to take.

I thank you very much for the desire you show to
know how I am. I am thankful to say that I am
very well for my age, only I had a very bad cold at
the beginning of the winter. I am very glad that
you are thinking of completing your arithmetical
machine. It would be a pity if so fine an invention
were lost. I desire greatly, however, that the inten-
tion in regard to which you wrote a word to the
Prince, who has so much affection for you, may not
remain without its effects, for there is nothing
towards which a wise man should work with more
care and with less of delay than towards what has
to do with his salvation. I am, Monsieur,
Your very humble and obedient servant.

A. ARNAULD.
XVII
Leibniz to Arnauld.

Gottingen, April 30, 1687.
Monsieur:

Since I regard your letters as personal benefactions
to me and as sincere marks of your liberality, I

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. l8l

have no right to ask for them and consequently
your reply is never too late. However agreeable
and useful they may be to me, I take into con-
sideration what you owe to the public weal and
thus suppress my desires. Your criticisms are
always instructive and I will take the liberty to go
through them in order.

I do not think that there is any difficulty in my
saying that "the soul expresses more distinctly,
other things being equal, that which pertains to its
own body"; since it expresses the whole universe
in a certain sense according to the special relation
of other bodies to itself, it is not able to express all
things equally, otherwise there would be no distinc-
tion between souls, but it does not follow from this
that the soul should perceive perfectly whatever
goes on in the parts of its body, since there are
degrees of relationship between these parts them-
selves and these parts are no more equally expressed
than are external things. The greater distance of
the latter is made up for by the smallness or by
some other hindrance in the internal parts. Thales
saw the stars though he did not see the ditch which
was at his feet.

The nerves and membranes are for us the parts
which are more sensitive than the others and it is, per-
haps, only through them that we perceive what seems
to happen to the others, because the movements of
the nerves, or of the liquids in them, imitate the
impressions better and confuse them less, and the
most distinct expressions of the soul correspond to
the most distinct impressions of the body. Meta-
physically speaking, it is not the nerves which act
upon the soul, but the one represents the state of the

1 82 CORRESPONDENCE.

other through the spontaneous relation; it must also
be remembered that too many things take place
within our bodies to be all separately perceived; we
feel only a certain result, to which we are accus-
tomed, and we are not able to distinguish the ele-
ments that are involved, because of their multitude.
Just as when we hear from afar the sound of the sea,
we do not distinguish what each wave does, although
each wave has its effect upon our ears. When
a striking change happens in our body, we notice it
at once and more clearly than the changes outside,
which are not accompanied by any special change
in our organs.

I do not say that the soul knows the pricking
before it has the sense of pain, except as it knows
or expresses confusedly all things in accordance
with the principles already established. This expres-
sion, however, although obscure and confused,
which the soul has in advance of the future, is the
real cause of that which happens to it and of the
clearer conception which it will have later when
the obscurity shall have worked out. The future
state is only a consequence of the preceding.

I said that God created the universe in such a way
that the soul and the body, each acting according to
its laws, agree in their phenomena. You think, M.,
that this coincides with the hypothesis of occasional
causes. Were this so I should not be sorry, and I
am always glad to find those who hold my positions.
I see, however, the reason for your thinking this.
You are of the opinion that I would not say a body can
move itself, and, the soul not being the real cause
either of the motion of the arm or of the body, there-
fore the cause must be God. My opinion, how-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 183

ever, is different. I hold that whatever reality there
is in the state which is called motion, may issue
quite as well from the bodily substance as the
thought and will proceed from the spirit. Every-
thing happens to each substance in consequence of
the first state which God gave to it in creating it,
and putting aside extraordinary interventions the
ordinary agreement consists only in the conserva-
tion of the substance itself conformably to its pre-
ceding state and to the changes which it carries in
itself. Nevertheless, we have the right to say that
one body pushes another; that is to say, that one
body never begins to have a certain tendency except-
ing when another which touches it loses proportion-
ately, according to the constant laws which we observe
in phenomena; and since movements are rather real
phenomena than beings, a movement as a phenom-
enon is in my mind the immediate consequence or
effect of another phenomenon, and the same is true
in the minds of others The condition of one sub-
stance, however, is not the immediate consequence
of the condition of another particular substance.

I dare not maintain that plants have no souls, nor
life, nor any substantial form; since, although one
part of a tree planted or grafted can produce a tree
of the same kind, it is possible that there is in it a
seminal part which already contains a new plant, as
it is likely there are living animalcula although
very small in the seed of animals which can be
transformed into a similar animal; I do not there-
fore dare to maintain that animals alone are living
and endowed with substantial forms. Perhaps there
is an infinity of degrees in the forms of corporeal
substances.

184 CORRESPONDENCE.

You say, M., that "those who hold to the hypoth-
esis of occasional causes, saying that my will is
the occasional cause, while God is the real cause of
the movement of my arm, do not claim that God
does this at the moment by a new volition, which
he has each time I wish to lift my arm, but through
that single act of eternal will, by which he resolved
to do everything which he foresaw would be neces-
sary for him to do." To this I reply that we can
say with the same reasoning, that miracles also are
not the result of a new act of will on God's part,
being conformable to a general plan; and I have
already stated, in what precedes, that every act of
will on God's part involves all the others, but with a
certain order of priority; if I properly understand
the position of the authors of occasional causes, they
introduce a miracle which is not less miraculous
for being continual, for it seems to me that infre-
quency does not constitute the conception of mir-
acle. It will be said that God acts in that, only
according to a general rule and consequently with-
out miracle, but I do not grant this consequence and
I think that God could make general rules with
regard to the miracles themselves. For instance,
if God resolved to give his grace immediately, or to
perform some other action of this nature every time
that a certain condition came about, this action
would, nevertheless, be a miracle although quite in
the ordinary. I confess that the authors of occas-
ional causes can give another definition of the term,
but it seems that according to usage a miracle
differs internally and substantially from that which
results from ordinary activity, and its distinctiveness
does not depend upon its unusualness; properly

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 185

speaking, God performs a miracle when he does any-
thing which surpasses the powers which he has given
to created things and which he maintains in them; for
example, if God should make a body, which was
put in circular motion by means of a sling, to go on
freely in a circular line even when it was released
from the attachment, this, when it was neither
pushed nor retained by anything, would be a mir-
acle, for, according to the laws of Nature the body
should travel along the line of the tangent: if, more-
over, God should decide that such should always be
the case, he would perform a natural miracle, for
this movement could not be explained by anything
more simple. In the same way, we should have to
say in accordance with the current conception, that
if the continuation of the motion were beyond the
power of bodies, the continuation of the motion
would be a true miracle; while my position is that
the corporeal substance has the power to continue
its changes according to the laws which God has
put into its nature and which he maintains there.

To make myself better understood I will add that
the activities of the mind change nothing at all in
the nature of the body, nor the body in that of
the mind; and I will also add that neither does God
change anything on the occasion of their action
except when he performs a miracle. In my opin-
ion, things are so concerted together that the mind
never desires anything efficaciously excepting when
the body is ready to accomplish it in virtue of its own
laws and forces; while, according to the authors
of occasional causes, God changes the laws of the
body on the occasion of the action of the soul and, vice
versa. That is the essential difference between our

l86 CORRESPONDENCE.

positions. Therefore, we should not ask how the soul
can give any motion or new determination to the
animal spirits, since it never does anything of the
kind, for there is no interaction between spirit and
body, and there is nothing which can determine
what degree of velocity a mind will give to a body,
nor what degree of velocity God may be minded to
give to the body on the occasion of the mind's action
according to a certain law. The same difficulty is
found with regard to the hypothesis of occasional
causes which there is in the hypothesis of a real
influence of the soul upon the body and vice versa;
because we can see no relation or basis for such a
rule. If one were to say, as M. Descartes seems to,
that the soul, or God on the occasion of its acting,
changes merely the direction or determination of the
motion and not the force which is in bodies, (since
it does not seem probable to him that God would
interrupt at each moment on the occasion of the
willing of spirits, this general law of nature,
namely, that the same force should perdure), I
would reply that it will be quite difficult to explain
what connection there can be between the thoughts
of the soul and the sides or the angles of direc-
tion of bodies, and furthermore that there is in
nature another general law which M. Descartes has
not perceived but which is, nevertheless, important
— namely, that the sum total of the determinations
or directions must always perdure. For I find that
if any straight line be drawn, for example, from
east to west, through a given point, and if all the direc-
tions of all the bodies in the world in so far as they
advance toward or move away in lines parallel to
this line be calculated, the difference between the

LEIBNIZ. ARNAULD. HESSKN-RHEINFELS. 187

sums of the quantities of all the easterly direc-
tions and of all the westerly directions will ever be
found the same, whether certain particular bodies
which might alone be supposed to have relations
among themselves, be regarded or whether the
whole universe be regarded. In this latter case
the difference is always zero. Everything is per-
fectly balanced and the easterly and westerly direc-
tions in the universe are exactly equal. If God
wished to do anything against this principle it
would be a miracle.

It is therefore much more reasonable and more
worthy of God to suppose that he has created the
machinery of the world in such a fashion from the
very start, that without doing violence at every
moment to the two great laws of nature, that of
force and that of direction, but rather by following
them exactly, (except in the case of miracles,) it so
comes about that the internal springs of bodies are
ready to act of themselves, as they should, at the
very moment when the soul has a conforming
desire or thought. The soul, in turn, has had this
desire or thought only conformably to preceding
states of the body and thus the union of the soul
with the machinery of the body and with the parts
which compose it, and the action of the one upon
the other consists only in this concomitance, which
betokens the wonderful wisdom of the Creator much
more than any other hypothesis. It cannot be
denied that this at least is possible, and that God is
a sufficiently great workman to be able to carry it
out; therefore, it can easily be decided that this
hypothesis is the most probable, being the simplest
and most intelligible and at once avoiding all diffi-

1 88 CORRESPONDENCE.

culties; for example, the difficulties involved in
criminal actions, where it seems much more reason-
able to let God intervene only through the conserva-
tion of the created forces.

To employ a comparison, I will say in regard to
this concomitance, which I hold to be true, that it
is like several bands of musicians or choirs separ-
ately taking up their parts and placed in such a way
that they neither see nor hear one another, though
they nevertheless, agree perfectly in following their
notes, each one his own, in such a way that he who
hears the whole finds in it a wonderful harmony
much more surprising than if there were a connec-
tion between the performers. It is quite possible
also that a person who is close by one of two such
choirs could judge from the one what the other
was doing, and would form such a habit (particularly
if we supposed that he was able to hear his own choir
without seeing it and to see the other without hear-
ing it), that his imagination would come to his aid
and he would no longer think of the choir where he
was, but of the other, and he would take his own for
an echo of the other, attributing to his own only
certain interludes, in which certain rules of sym-
phony by which he understood the other did not
appear, or else attributing to his own certain move-
ments which he caused to be made from his side,
according to certain plans that he thought were
imitated by the other because of the inter-relation-
ship which he found in the kind of melody, not
knowing at all that those who were in the other
choir were doing also something which corresponded
according to their own plans.

Nevertheless, I do not at all disapprove of the

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 189

statement that minds are in some sort the occasional
and even real causes of certain movements in the
body, for, with regard to the divine resolves, what-
ever God has foreseen and pre-established with
regard to minds, has been an occasion for his thus
regulating the body from the very start, so that
they might fit in together, each following the laws
and forces that he has given them; and as the state
of one is an unfailing consequence of the other, al-
though frequently contingent and even free, we can
say that God has established a real connection in
virtue of this general conception of substances, which
brings it about that they express one another per-
fectly. This connection, however, is not immediate,
being founded only upon what God has given them
in creating them.

If my opinion, that substances require a true unity,
is founded only upon a definition which I have
made up contrary to the common usage, this would
be a mere question of words; but besides the fact
that most philosophers have understood this term
in nearly the same way, namely, that "a distinction
should be made between unity through itself and
unity through accident, between substantial form and
accidental form, between an imperfect and a perfect
compound, between natural and artificial," I take
still higher ground and, leaving the question of
terminology, I believe that where there are only
beings by aggregation, there are not even real beings,
because every being by aggregation pre-supposes
beings endowed with true unity, because it ob-
tains its reality only from the reality of the ele-
ments of which it is composed, so that it will have
no reality at all if every being of which it is com-

IpO CORRESPONDENCE.

posed is again a being by aggregation; or else we
must seek some other foundation for its reality,
seeing that by this method it can never be reached,
even by searching forever. I grant, M., that in all
corporeal nature there exist only machines (some of
which are alive), but I do not grant that there exist
only aggregations of substances, and if there do exist
aggregations of substances it must be that there are
also real substances of which all these aggregations
are the product; we therefore come necessarily
to the mathematical points out of which certain
writers have constructed extension, or to the atoms
of Epicurus and of M. Cordemoy — things which
you reject quite as much as I do; or else we must
acknowledge that no reality is to be found in bodies.
The other alternative is to say that there are certain
substances which have a real unity. I have already
said in another letter that the composite of the dia-
monds of the Grand Duke and of the Great Mogul
could be called a pair of diamonds, but this would
only be a being of the reason, and if they were
brought together they would become a being of
the imagination or perception, that is to say,
a phenomenon, because contact, common move-
ment and even agreement in design, do not effect
a substantial unity. It is true that sometimes there
is more and sometimes less basis for supposing
that several things constitute one, according as the
things have more or less connection, but this is only a
means to abbreviate our thinking and to represent
the phenomenon.

It seems also that what constitutes the essence of a
being by aggregation consists solely in the mode
of the being of its component elements. For exam-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 191

pie, what constitutes the essence of an army? It is
simply the mode of being of the men who compose
it. This mode of being presupposes, accordingly a
substance of which the essence is not a mode of being
of a substance. Every machine therefore presup-
poses some substance in the parts out of which it is
made, and there is no plurality without true unities;
in short, I consider as an axiom this identical propo-
sition, which receives two meanings only through a
change in accent; namely, that what is not truly a
being is not truly a being. It has always been
thought that one and being are reciprocal terms.
Being is very different from beings, but the plural
presupposes the singular; and there where there is
no being, are there still less several beings. What
can be clearer? I thought, therefore, that I should
be permitted to distinguish beings by aggrega-
tion from substances, since these beings have their
unity only in our minds, and our minds repose
upon the relations or the modes of real substances.
If a machine is a substance, a circle of men who are
holding hands would be one also, so an army, and
in fact, any gathering together of substances. I do
not say that there is nothing substantial or nothing
but appearance in things which have not a true unity,
for I acknowledge that they have as much of reality
or substantiality as there is of true unity in that
which enters into their composition.

You object, M., that it might be of the essence
of bodies to have no true unity. But it will be then
the essence of bodies to be phenomena deprived
of all reality as would be an orderly dream, for
phenomena, like the rainbow or like a pile of stones,
will be wholly imaginary if they are not com-

I9« CORRESPONDENCE.

posed of beings which have a true unity. You
say that you do not see why I admit substantial
forms or rather corporeal substances endowed with
a true unity. It is because I can conceive of no
reality without a true unity, and in my opinion the
concept of the singular substance involves conse-
quences incompatible with its being a mere aggre-
gation. I can conceive of properties in the sub-
stance which cannot be explained by extension, by
form and by motion, quite apart from the fact that
there is no exact and definite form in bodies because
of the actual subdivision of the continuum to infin-
ity, and that their motion in so far as it is only a
modification of extension and a change of place,
involves something imaginary so that we cannot
determine to which object, among those that change,
it belongs, unless we have recourse to the force that
is the cause of the motion and that inheres in the
corporeal substance. I confess that there is no need
of mentioning these substances and qualities in
explaining particular phenomena, but no more is
there need of inquiring about the intervention of
God, the composition of the continuum, the plenum,
and a thousand other things. The particular events
of nature I confess can be explained mechanically,
but only after having recognized or presupposed the
principles of mechanics. These can be established
a priori only through metaphysical speculations.
The difficulties involved in the composition of the
continuum will never be resolved so long as exten-
sion is considered as constituting the substance of
the bodies, and we shall find ourselves entangled
in our own chimeras.

I think furthermore that to attempt to limit true

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 193

unity or substance to man alone is as shortsighted
in metaphysics as it was in the realm of physics
to desire to enclose the world in a sphere. And
since true substances are so many expressions of the
whole universe taken in a certain sense and so many
reduplications of the divine work, it is in conformity
with the grandeur and the beauty of the works of
God, (seeing that these substances do not clash with
one another,) to create in this universe as many of
them as is possible and as superior reasons permit.
The wholly bare supposition of extension destroys
this wonderful variety, since mass, by itself (if we
were able to conceive of it), is as much inferior to
a substance which is perceptive and which rep-
resents the whole universe according to its point
of view and according to the impressions or rather
relations that its body receives mediately or im-
mediately from all others, as a dead body is below
an animal or as a machine is inferior to a man.
It is, indeed, through the idea of substance that
the evidences of the future are formed in advance
and that the traces of the past are preserved
forever in everything, and that cause and effect
are exactly equivalent even to the slightest circum-
stance, although each effect depends upon an infinity
of causes and every cause has an infinity of effects.
It would not be possible to obtain this state of
things, if the essence of the body consisted only in
a certain form, motion or modification of extension,
which was predetermined. Furthermore, there is
nothing of the kind in nature; taken strictly, every
thing is indefinite with regard to extension, and
whatever we attribute to bodies are only phenom-
ena and abstractions: this enables us to see how

194 CORRESPONDENCE.

easy it is to fall into error if reflections so necessary
for recognizing the true principles and for having a
valid idea of the universe are not made. It seems
to me that as much prejudice is displayed in refus-
ing to accept so reasonable an idea as this, as there
would be in not recognizing the grandeur of the
world, the subdivision to infinity and the mechani-
cal explanations of nature. It is as great an error
to conceive of extension as a primitive concept
without looking into the real concept of substance
and of action, as it was formerly to be contented
with considering substantial forms as a whole with-
out entering into details as to the modifications of
extension.

The great number of souls (to which, however, I
do not necessarily attribute in every case pain and
pleasure), should not trouble us any more than do
the great number of the atoms put forward by Gas-
sendi, which are quite as indestructible as the soul.
On the contrary it is one of the perfections of
nature to have so many of them, since a soul or
indeed a living substance is infinitely more perfect
than an atom, which is without variety or subdivis-
ion. Every living thing contains a world of diver-
sity in a real unity. Our experience is in favor of
this great number of living things; we find that there
is a prodigious quantity of them in a drop of water
tinctured with powder and with one blow millions
of them can be killed so that neither the frogs of
the Egyptians nor the quails of the Israelites of
which you spoke, M., at all approach the number.
Now, if these animals have souls, the same must be
said of their souls which can probably be said of the
animals themselves; namely, that they have been

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 195

living from the very creation of the world and that
they will live to its end, and that birth being appar-
ently only a change consisting in growth, so death
is only a change or diminution which causes this
animal to re-enter into the engulfing of a world of
minute creatures, where perceptions are very lim-
ited until the command comes calling them to return
to the theater of action. The ancients made the
mistake of introducing the transmigration of souls,
in place of the transformation of the same animal
which always preserves the same soul. They put
metempsychoses in place of metaschematismi.
Spirits, however, are not subjected to these revolu-
tions, or rather these revolutions of bodies must
serve the divine economy for the sake of spirits.
God creates them when it is time and he detaches
them from the body, at least from the material
body by death; since they must always preserve
•their moral qualities and their memory in order to
be perpetual citizens of that universal republic,
absolutely perfect, whose monarch is God. This
republic can never lose any of its members and its
laws are superior to those of the body. I grant that
bodies by themselves without the soul have only a
unity of aggregation, but the reality which inheres
in them comes from the parts which compose them
and which retain their substantial unity through the
living bodies that are included in them without num-
ber.

Nevertheless, although it is possible that a soul
have a body made up of animated parts or of separ-
ate souls, the soul or the form of the whole is not,
therefore, composed of souls or forms of parts. In
regard to an insect which is cut in two, it is not

196 CORRESPONDENCE.

necessary that the two parts shall remain animated,
although there may be some movement in them, at
least the soul of the whole insect will remain only
on one side and as in the formation and in the
growth of the insect the soul has already been in a
certain part alive from the very start, it will remain
also after the destruction of the insect, still alive in
. a certain part, which will always be as small as is nec-
essary to serve as an asylum from the action of him
who is tearing or destroying the body of this insect.
We need not, however, imagine with the Jews that
there is a little bone of irrefrangible hardness where
the soul preserves itself.

I agree that there are degrees of accidental unity,
that a regulated society has more unity than a con-
fused mob and that an organized body or indeed a
machine has more unity than a society. That is,
it is more appropriate to conceive of them as a sin-
gle thing because there is more relation between
the component elements. All these unities, how-
ever, receive their name only through thoughts and
through appearances like colors and other phenom-
ena that are, nevertheless, called real. The fact that
a pile of stones or a block of marble can be touched
does not prove its substantial reality any more suc-
cessfully than the visibility of a rainbow proves
its reality; and as nothing is so solid that it has not
a certain degree of fluidity, perhaps the block of
marble itself is only a mass of an infinite number
of living bodies like a lake full of fish, although
such animals in a body can be ordinarily distin-
guished by the eye only when the body is partially
decayed. We may say of these compounds and of
similar things what Democritus said very well of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 197

them, namely esse opinione, lege, vofup. Plato had
the same opinion in regard to all that is purely
material. Our mind sees or conceives of certain
true substances which have certain modes. These
modes involve relations to other substances when-
ever the mind finds occasion to join them in thought
and to make one name stand for the whole assem-
bly of these things, which name shall serve as
a means of reasoning; but we must not make the
mistake of thinking that they are substances or
veritably real beings. This, position can be held
only by those who go no farther than appearances,
or else by those who consider as realities all the
abstractions of the mind and who conceive number,
time, place, motion, form and sensible quality as
so many beings by themselves. I, on the contrary,
hold that philosophy cannot be restored in a better
way nor better reduced to precision than by recog-
nizing substances or complete beings endowed with
a true unity in which different states succeed. All
the rest are to be considered only as phenomena,
abstractions or relations.

Nothing will ever be found fitted to constitute a
true substance out of several beings by means of
aggregation; for example, if the parts which fit
together for a common design are more appropriate
to constitute a true substance than those which are
in contact, all the officials of the India Company in
Holland would constitute a real substance better
than would a pile of stones. But such a common
design — what is it but a resemblance, or rather an
arrangement of actions and passions, which our
mind sees in different things? If this unity by con-
tact should be preferred as the most reasonable

198

CORRESPONDENCE.

hypothesis, other difficulties would be found: the
parts of solid bodies are perhaps united only by the
pressure of surrounding bodies and by their own
pressure, and in their substance they may have no
more union than a pile of sand arena sine calce,
Why will many rings linked together to constitute
a chain compose more of a true substance than if
they had openings by means of which they could
be separated? It is possible that the links of a chain
should not touch one another and should not even
be interlinked and yet, nevertheless, unless they
were taken in a certain particular way they could
not be separated, as in the accompanying figure.

Would it be said in such a case that the substance
of this compound is, as it were, in suspense, and
depends upon the future cleverness of him who
wishes to separate them? These are all fictions of
the mind, and so far as we do not discern what is
truly a complete being, or indeed, a substance, we
shall have no resting place, and through this distinc-
tion of substances alone is there a means of estab-
lishing stable and real principles.

In conclusion, nothing should be considered cer-
tain without a basis. It is therefore for those who
speak of beings and substances without a real unity
to prove that there is more reality than that which
has just been spoken of; and I am awaiting that

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 199

concept of a substance or of a being which can
include all those things and in accordance with
which, parts and perhaps even dreams may some
day pretend to reality: at least I hope that precise
limits will be given to the citizenship rights which
are being granted to beings formed by aggregation.

I have treated this subject at length so that you
might understand not only my positions but also the
reasons which have compelled me to assume them.
I submit them to your judgment whose fairness and
exactness I know. I send also an article in The
News of the Republic of Letters which you may
find will serve as a reply to the Abbe Catelan. I
consider him an able man after what you have said,
but what he has written against M. Huygens and
against me, makes it clear that he goes a little too
fast. We shall see what he will do now. I am
delighted to learn of the good condition of your
health ; I desire its continuation with all the zeal
and all the passion which makes me, M., etc.

P. S. — I reserve for another time certain subjects
which you have touched upon in your letter.

XVIII

Leibniz to Count Ernst von Hessen-Rheinfels.

April 30, 1687.

Monseigneur:

I hope that your Serene Highness will receive the
book which was delayed so long; I looked for it
myself at Wolfenbuttel in order that you might have
it again since you were laying the blame on me.
I have taken the liberty to add a letter and some

200 CORRESPONDENCE.

documents for M. Arnaud. I have some hope that
when he shall have read them, his penetration and
his sincerity will, perhaps, enable him to approve
entirely of that which at the beginning seemed
strange to him, because since he has modified his
position after having seen my first explanation, per-
haps he will come to approbation after having seen
this last one which, in my opinion, clearly does
away with all the difficulties that he said still
troubled him. However that may be, I shall be
content if he decides, at least, that these opinions,
even though they may be very false, entail nothing
directly contrary to the definitions of the Church
and that consequently they are tolerable even in a
Roman Catholic. For your Serene Highness
knows, better than 1 can tell, that there are toler-
able errors, and that there are even errors whose
consequences are believed to destroy the articles of
faith, and yet, nevertheless, neither these errors
nor those who hold them are condemned because
the consequences are not approved of. For exam-
ple, the Thomists hold that the hypothesis of the
Molinists destroys the perfection of God; while, on
the other hand, the Molinists think that the predeter-
mination of the former destroys the freedom of
man; nevertheless, since the Church has not yet
come to any conclusion upon the matter, neither the
former nor the latter can be considered as heretics
nor their opinions as heresies. I think the same
can be said of my proposition, and for many reasons
I should like to know if M. Arnaud does not him-
self now acknowledge their harmlessness. He is
very busy and his time is too valuable for me to
pretend that he should employ it in discussing a

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 2OI

matter regarding the truth or falsehood of an opin-
ion; but it is easy for him to decide upon its tolera-
bility, since it is merely a question of knowing
whether they are contrary to certain definitions of
the Church.

XIX

Leibniz to A rnauld.

August ist, 1687.

I have learned with much pleasure that his Serene
Highness, Count Ernst, has seen and found you in
good health. I hope with all my heart that I shall
have such news frequently, and that the body will
feel as little the effects of age as has the mind, whose
energy still manifests itself. I have myself appre-
ciated this energy, and I confess that I know no one
from whom I look for a judgment upon my medita-
tions more stable, more penetrating, and also more
sincere than from you.

I do not wish to trouble you, but the material of
the later letters being of an importance second
only to that of religion and having great affinities
with it, I confess that I should like to be able to
enjoy once more your enlightenment and at least
to learn your opinion in regard to my last explana-
tions ; for if you find in them an appearance of
reason, I shall be confirmed, but if you find anything
to say against them I shall advance more cautiously
and shall be obliged to examine some day the whole
subject anew.

In place of M. Catelan it was the Rev. Father Male-
branche who replied a short time ago in The News

202 CORRESPONDENCE.

of the Republic of Letters to the objection which I
had put forward. He seems to realize that cer-
tain of the laws of nature or principles of motion
which he advanced would be difficult to maintain ;
but he thought this was because he had based them
on the assumption of absolute hardness which is
not found in nature, while I think that if absolute
hardness could be found in nature these laws would
still be untenable. It is a defect in the reasoning
of Descartes and his followers not to have consid-
ered that everything that is said of motion, of ine-
quality, and of elasticity, should also be true if
things are supposed to be infinitely small. In this
case motion (infinitely small) becomes rest, inequal-
ity (infinitely small) becomes equality , and elasticity
(infinitely prompt) is nothing else than extreme hard-
ness; somewhat as everything which geometers
demonstrate regarding an ellipse proves true of a
parabola, when conceived as an ellipse with its second
focus infinitely distant. It is a remarkable thing to
see that almost all Descartes' laws of motion conflict
with this principle, which I hold to be quite as infal-
lible in physics as it is in geometry, because the
author of things acts as a perfect geometer. If I
make any reply to Father Malebranche it will be
principally in order to point out the above men-
tioned principle, which is x>f great utility and which
has not as yet been generally considered, so far as
I know.

But I am detaining you too long and this matter
is not worthy of your attention, I am, etc.,

LEIBNIZ. ARNAULD. HESSEN-RHEINFKLS. 203

XX

Arnauld to Leibniz.

August 28th, 1687.

I must begin by making excuses for replying so
late to your letter of April 3d. Since then I have
had various illnesses and various occupations and
beside it is a little hard for me to apply myself to
such abstract things; 1 therefore ask for your con-
sideration if I give rather briefly my opinion about
the new points in your last letter.

1. I have no clear idea what you mean by the
word express when you say that "our soul expresses
more distinctly, other things being equal, that which
pertains to its own body, since it expresses even all
the universe in a certain sense." For if by this
expression you mean a certain thought or a certain
knowledge, I cannot agree that my soul has more
thought and knowledge regarding the movement of
the lymph in the lymphatic ducts than regarding
the movement of the satellites of Saturn; if what
you call expression is neither thought nor knowl-
edge, I do not know what it is. Therefore it cannot
be of service in solving the difficulty which I raised;
namely, how my soul can have a feeling of pain
when I am pricked during my sleep; since for this
it would have to know that some one were pricking
me, while in fact it obtains this knowledge only by
the pain which it feels.

2. In regard to the following reasoning in the
philosophy of occasional causes: "my hand moves
as soon as I wish it; now it is not my soul which is
the real cause of this motion, neither is it the body,
therefore it is God"; you say that this supposes that

204 CORRESPONDENCE.

a body cannot move itself. Your thought, how-
ever, is that it can, and you hold that whatever there
is of reality, in the state which is called motion,
proceeds quite as much from the corporeal sub-
stance itself, as the thought and the will proceeds
from the mind.

This is what seems to me very hard to understand,
that a body which has no motion can give itself
motion. And if this is admitted, one of the proofs for
the being of God is destroyed; namely, the neces-
sity for a first mover.

Moreover, if a body could give motion to itself,
it would not result in my hand's moving itself every
time that I wished it; for, being without knowledge,
how would it know when I wished it to move
itself.

3. I have more to say in regard to the indivisible
and indestructible substantial forms which you think
should be admitted in the case of all animals and
perhaps even in the case of plants, because other-
wise matter (which you consider as neither com-
posed of atoms nor of mathematical points, but to
be divisible to infinity) would not be a unutn perse
but only an aggregotum per accidens.

(i). I replied to you that perhaps it is an essential
of matter, which is the most imperfect of all beings,
not to have any true and proper unity, just as St.
Augustine thought, that is, to be plura entia and
not properly unum ens; and that this is no more
incomprehensible than is the infinite divisibility of
matter, which you admit.

But you replied that this cannot be so, because
there can be no plura entia where there is no unum
ens.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 205

But how can you employ this argument, which M.
Cordemoy perhaps might have thought true, but
which, according to you, must be necessarily false,
since, excepting animated beings, which do not
form one hundred thousand thousandth part, all the
rest must, in your opinion, be without substantial
forms, merely plura entia and not properly unum
ens? It is, therefore, not impossible that there
should be plura entia even where there is properly
no unum ens.

(2). I do not see that your substantial forms can
remedy this difficulty, for the attribute of the ens which
is called unum, taken as you take it, strictly meta-
physically, must be essential and intrinsic to what
is called the unum ens. Therefore, if a particle of
matter is not a unum ens but plura entia, I do not
see how a substantial form, which being really dis-
tinguished from it, could only give it an extrinsic
property — how this substantial form could make it
cease being a plura entia and should make it a unum
ens by an intrinsic property. I understand easily that
this would give us a reason for calling it unum ens,
if we did not take the word unum in this meta-
physical strictness. Substantial forms, however, are
not called for in order to be able to give the name
one to an infinity of inanimate bodies, because, is it
not correct usage to say that the sun is one, that the
earth which we inhabit is one, etc? It is not evident,
therefore, that there is any necessity for admitting
these substantial forms in order to give to bodies a
true unity, which they would not otherwise have.

(3). You admit these substantial forms only in
animate bodies.* Now there are no animate bodies

* Leibniz's note: "I do not remember having said that."

2O6 CORRESPONDENCE.

which are not organized, nor are there any organized
bodies which are not plura entia; therefore your
substantial forms, far from preventing bodies to
which they are joined from being plura entia, must
themselves become plura entia in order that they may
be joined.

(4). I have no clear idea of these substantial forms
or souls as applied to brutes. It must be that you
regard them as substances, since you call them sub-
stantial, and since you say that only substances are
truly real beings, among which you include above all
these substantial forms. Now I know only two sorts
of substances, bodies and minds, and it is for those
who claim that there are others to show me them,
according to the maxim with which you conclude
your letter, "that nothing should be considered certain
without a basis. ' ' Suppose therefore that these sub-
stantial forms are either bodily or mental; if they
are bodily they must be extended and consequently
divisible and divisible to infinity; hence it follows
that they are not a unum ens but plura. entia\ just as
are the physical bodies which they animate; they
are not therefore able to impart a true unity. If,
however, the subtantial forms are mental, their
essence will be to think, for this is what I under-
stand by the word mind. It is hard for me to under-
stand how an oyster thinks or a worm thinks; and
since you say in your last letter that you are not sure
but that plants have a soul, have a life or a sub-
stantial form, it must be you are not sure that plants
do not think, because their substantial forms, if they
have any, not being corporeal because they are not
extended, must be mental, that is to say, a sub-
stance which thinks.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 207

(5). The indestructibility of these substantial
forms or souls in brutes appears to me still more
untenable. I asked you what became of the souls
of these brutes when they died or when they were
killed, just as when worms were burned what became
of their souls. You reply "that they remain for
each worm in a small part of the body that remains
alive. This will always be as small as is necessary
to serve as a shelter from the action of the fire which
tears to pieces or which destroys the bodies of these
worms." This brings you to say that "the ancients
were mistaken in introducing the transmigration of
souls in place of the transformation of the same ani-
mal which always preserves the same soul." Noth-
ing can be imagined more subtle for meeting the
difficulty that I raised, but you will have to be on
your guard, M., against what I am about to say;
when a silk moth casts its eggs each one of these
eggs in your opinion has the soul of a silk worm,
whence it happens that five or six months later little
silk worms hatch out. Now, if a hundred of these
silk worms had been burned there would be, in your
opinion, a hundred souls of silk worms in so many
little particles of the ashes; but on the one hand I
do not know any one whom you can persuade that
each silk worm after having been burned remains
the same animal preserving the same soul joined
now to a speck of ashes which was formerly a little
portion of its own body; and, on the other hand, if
this were so, why is no silk worm born out of these
specks of ashes as they are born out of the eggs?

(6). This difficulty appears greater in the case of
animals, where it is known certainly that they can-
not be born except through the alliance of two

208 CORRESPONDENCE,

sexes; I ask, for example, what became of the soul
of the ram which Abraham offered in place of Isaac
and which he burned? You will not say that it passed
into the foetus of another ram, for this would be the
metempsychosis which you condemn; but you reply
that it remained in a particle of the body of this ram
reduced to ashes and that therefore it is only the
transformation of the same animal which has always
preserved the same soul. This could be said with
some appearance of truth in your hypothesis of the
substantial forms of a caterpillar which becomes a
butterfly, because the butterfly is an organized body
quite as much as is the caterpillar, and therefore it
is an animal which can be considered the same as
the caterpillar because it preserves many of the
parts of the caterpillar without any change, and the
other parts have changed only the forms. But this
part of the ram, reduced to ashes, in which the soul
of the ram has taken refuge, not -being organized,
cannot be taken for an animal, and therefore the
soul of the ram which is joined to it, does not com-
pose an animal, much less a ram, such as the soul of
a ram should. What will then become of the soul of
this ram in this cinder? For it cannot separate
itself away, to go elsewhere, since this would be a
transmigration of the soul, that you have con-
demned. The same is the case with an infinity of
other souls which would never form animals because
of being joined to particles of matter not organ-
ized, but which invisible could become organized
according to laws established in nature. What an
infinity of monstrous things would be this infinity
of souls joined to bodies which cannot become ani-
mated!

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 209

Not long since I saw what Abbe Catelan replied
to your answer in The News of the Republic of Let-
ters for the month of June. What he said there
seemed very clear to me, perhaps however, he did
not entirely understand your thought; therefore,
I am awaiting the reply which you will make to him.
I am, Monsieur,

Your very humble and very obedient servant,

A. A.

XXI

A. Arnauld to Count Ernst von Hessen-Rheinfels.

August 3 ist, 1687.

Here, M., is the reply to the last letter which M.
Leibniz sent through your Serene Highness in April
last. I was not able to apply myself to it sooner in
order to reply to it. I beg you to send it on to him
because I do not know his traits. If you will look
it through you will see that there are a good many
very strange opinions in regard to physics and some
which appear to be hardly tenable, but I have tried
to tell him my opinion regarding them in a way
which should not wound him; it would be better
were he to quit, for a time at least, these kinds of
speculations, in order to apply himself to the most
important business that he can have, which is the
choice of the true religion in accordance with what
he wrote to your Highness a few years ago. There
is cause for fear that death may overtake him before
he has taken a step so important for his salvation.
M. Nicole's book against Seigneur Jurieu's new
ecclesiastical system has just been printed. We are
expecting it from Paris in five or six days. I will

210 CORRESPONDENCE.

send you a copy by the Cologne stage together
with certain other books which you will like to see.

XXII

Count Ernst von Hessen-Rhemfels to Leibniz.
My dear M. Leibniz:

There is reason for saying what M. Arnauld has
said; for even if there were thousands among the
Protestants who did not know their right hand from
their left, who, in comparison with the savants,
would be reputed as unthinking brutes, and who
adhered only materially to heresy, certainly this
cannot be said of you who have so much enlighten-
ment, and with respect to whom, if there had never
been any other but myself, as much as possible has
been done to make you come forth from the Schis-
matics and to represent to you whatever there was
to be represented. To mention merely one out of a
thousand points; do you believe that Christ would
have so constituted his Church that what one thought
white another might think black, and that he would
have constituted the ecclesiastical ministry in such
a contradictory fashion that we should be in debate
about it with the Protestants, we thinking one thing
and you thinking another? For example, we hold
that your ministers are laymen and are usurpers in
the ministry. I do not know what you may think
of ours who are so opposed to yours on this point.
O, my dear M. Leibniz, do not lose thus the time
of grace and hodie si vocem Domini auderitis, nolite
obdurare corda vestra. Christ and Belial can no more
agree together than do the Catholics and Protest-
ants, and I know nothing which promises your sal-
vation unless you become a Catholic.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 211

XXIII

Leibniz to Arnauld.

October 6, 1687.

As I always hold in high esteem your criticism
when you have seen the point at issue, I will try this
time so to write that the positions which I hold as
important and almost as certain, may appear to you,
if not certain, at least as entertainable; for it does not
seem to me at all difficult to answer the doubts which
you still have, and which, in my opinion, result only
because a person, however able he may be, when he
has his mind made up and is otherwise diverted,
has difficulty at first in entering into a new line of
thought upon an abstract subject, where neither
figures nor models nor illustrations can assist him.

I have said that the soul naturally expresses the
whole universe in a particular sense and according
to the relation which other bodies have to its own;
consequently, as it expresses most directly that
which belongs to the parts of its own bodies, it
ought, in virtue of the laws of relationship which are
essential to it, to express in particular certain
unusual changes of its own body; for instance, that
which happens when it feels pain. To this you
reply that you have no clear idea of what I mean by
the word express; that, if I mean by it a thought,
you will not agree that the soul has any more
thought and cognizance of the movement of the
lymph in the lymphatic ducts than of the move-
ments of the satellites of Saturn. If I mean, how-
ever, something else, you say you do not know what
it is, and, consequently (supposing that I were not
able to explain it distinctly), this word would be

212 CORRESPONDENCE.

of no service in letting us know how the soul can
become aware of the feeling of pain, since it would
needs be, you say, that it already knew that I was
being pricked instead of obtaining this knowledge
only by the pain which it felt.

In reply to this I will explain this word which
you think is obscure, and I will apply it to the diffi-
culty which you have raised. One thing expresses
another, in my use of the term, when there is a con-
stant and regulated relation between what can be
said of the one and of the other. It is thus that a
projection in perspective expresses a structure.
Expression is common to all forms, and is a class
of which ordinary perception, animal feeling and
intellectual knowledge are species. In ordinary
perception and in feeling it is enough that what is
divisible and material and what is found common to
several beings should be expressed or represented in
a single indivisible being, or in the substance which
is endowed with a true unity. We cannot at all
doubt the possibility of such a representation of
several things in a single one, since our own souls
furnish us examples; this representation, however,
is accompanied by consciousness in a rational soul
and becomes then what is called thought.

Now, such expression is found everywhere, because
all substances sympathize with one another and
receive some proportional change corresponding to
the slightest motion which occurs in the whole uni-
verse. These changes, however, may be more or
less noticeable, as other bodies have more or less
relation with ours. I think that M. Descartes would
have agreed with this himself, for he would doubt-
less grant that because of the continuity and divis-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 113

ibility of all matter the slightest movement would
have its effect upon neighboring bodies and conse-
quently from body to body to infinity, but in dimin-
ishing proportion. Thus, our bodies ought to be
affected in some sort by the changes of all others.
Now, to all the movements of our bodies certain
perceptions or thoughts of our soul, more or less con-
fused, correspond; therefore, the soul also will have
some thought of all the movements of the universe,
and in my opinion every other soul or substance will
have some perception or expression of them. It is
tfue that we do not distinctly perceive all the move-
ments in our body, as for example the movement of
the lymph, but to use an example which I have already
employed, it is somewhat in the same way that I
must have some perception of the motion of every
wave upon the shore so that I may perceive what
results from the whole; that is to say, that great
sound which is heard near the sea. In the same way
we feel also some indistinct result from all the
movements which go on within us, but, being accus-
tomed to this internal motion, we perceive it clearly
and noticeably only when there is a considerable
change, as at the beginning of an illness. It is to
be desired that physicians should apply themselves
to distinguish more exactly these kinds of confused
feeling which we have within our bodies. Now,
since we perceive other bodies only by the relation
which they have to our own, I had reason for saying
that the soul expresses better what belongs to its
own body and knows the satellites of Jupiter and of
Saturn only in accordance with a motion which is
produced within the eye. In all this I think the
Cartesians would argee with me, excepting that I sup-

314 CORRESPONDENCE.

pose that there are around us other souls beside our
own to which I attribute a lower expression or percep-
tion than thought. For the Cartesians deny feelings to
animals and do not admit any substantial forms out-
side of men. This does not at all affect our question
here regarding the cause of pain. We have now to
ask how the soul perceives the movements of its
body, since there seems to be no way of explaining
by what means the action of an extended mass may be
transmitted to an indivisible being. Most Cartesians
confess that they can give no reason for this union;
the authors of the hypothesis of occasional causes
think that it is a nodus vindice dignus, cut Deus ex
machina intervenire debeat, a knot worthy of such
an extricator that God must intervene to solve it.
For my part, I explain it in a natural way. From
the concept of substance or of complete being in gen-
eral, where the present state is always a natural
consequence of the preceding state, it follows that
the nature of every singular substance and conse-
quently of every singular soul is to express the uni-
verse. From the start it was created in such a way
that in virtue of the laws of its own nature it is
obliged to agree with whatever takes place in bodies,
and particularly in its own. There is no cause for
astonishment therefore, that it is of the nature of
the soul to represent to itself a pricking sensation
when its body is pricked: in order to explain this
matter let us put on opposite sides:

State of the body at the State of the soul at mo-
moment A. ment A.

State of the body at the State of the soul at the

succeeding moment B (prick- moment B (pain),
ing).

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 215

Just as the state of the body at the moment B
follows the state of the body at the moment A, »in
the same way the state B of the soul is a conse-
quence of the preceding state A of the same soul,
according to the concept of substance in general.
Now, the states of the soul are naturally and essen-
tially expressions of the corresponding states of the
world, and particularly of the bodies which belong
to them; therefore, since the pricking constitutes
a part of the condition of the body at the moment
B, the representation or expression of the pricking,
which is the pain, will also form a part of the state
of the soul at moment B; because, as one motion fol-
lows from another motion, so one representation in
a substance, whose nature it is to be representative,
follows from another repesentation. Accordingly the
soul must needs perceive the pricking when the
laws of correspondency require it to express more
distinctly some extraordinary change in the parts of
its body. It is true that the soul does not always
distinctly perceive the causes of the pricking and of
its future pain, when they are still concealed in the
representation of the state A, as when one is asleep
or for some other reason does not see the pin
approaching. This is, however, because, at such a
time, the motion of the pin makes too little impres-
sion and although we are already affected in some
sort by all the motions and representations in our
soul, and though we have thus in us the representa-
tion or expression of the causes of the pricking, and
consequently the cause of the representation of the
same pricking, that is to say, the cause of the pain,
we are yet not able to separate them out from all the
other thoughts and movements excepting when they

2l6 CORRESPONDENCE.

become quite considerable. Our soul notices only
more special phenomena, which are distinguishable
from others, never thinking distinctly of any one
when the thought is about them all equally. ,

In accordance with this, I do not see that the
slightest shade of difficulty can be found in this
position, unless it be denied that God can create sub-
stances which are made from the start in such a way
that by virtue of their own natures they agree in the
series of events with the phenomena of all the
others. Now, there are no plausible grounds for
denying this possibility. Mathematicians represent
the movements of the heavens by means of machines,
(as when

Jura poli rerumgue fidem legesque deorum
Cuncta Syracusius transtulit arte senex,

a thing which we can do much better to-day than
Archimedes could in his time), and why cannot God,
who infinitely surpasses these mathematicians, create
from the very start representative substances in such
a way that they shall express by their own laws, in
accordance with the natural changes of their
thoughts or representations, whatever is to happen to
all bodies. This appears to me not only easy to
conceive, but also worthy of God and of the beauty
of the universe, and in a way a necessary conception,
since all substances must have a harmony and union
among themselves, and all must express in them-
selves the same universe and the universal cause,
which is the will of their Creator, and the decrees or
laws which He has so established that they fit
together in the best possible way. Furthermore, this
mutual correspondence of different substances which

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 217

are not able, if we speak with metaphysical strict-
ness, to act one upon another, and which, neverthe-
less, agree as though one were acting upon the
other, is one of the strongest proofs for the exist-
ence of God or of a common cause which each
effect must always express according to its point of
view and its capacity. Otherwise the phenomena of
different minds would not agree and there would be
as many systems as substances; or rather, it would
be a pure chance if they at times agreed. All the
conceptions which we have of time and of space are
based upon this agreement. But I should never fin-
ish, were I to explain exhaustively all that is con-
nected with our subject; however, I prefer to be
prolix rather than not to express myself sufficiently.
To go on to your other objections, I now think
that you will see, M., what I mean, when I say that
a corporeal substance gives to itself its own motion,
or, rather, whatever there is of reality in the motion
at each moment, that is, the derivative force, of
which it is a consequence; for, every preceding state
of a substance is a consequence of its preceding state.
It is true that a body which has no motion cannot
give itself motion; but I hold that there are no such
bodies. (Also, strictly speaking,bodies are not pushed
by others when there is a contact, but it is by their
own motion or by the internal spring, which again is
a motion of the internal parts. Every corporeal
mass, large or small, has already in it all the force
that it will ever acquire, the contact with other
bodies gives it only the determination, or, better, this
determination takes place only at the time that the
contact does). You will say that God can reduce a
body to a state of perfect repose; I reply, however,

2 1 8 CORRESPONDENCE.

that God can also reduce it to nothing, and that this
body, deprived of action and of passion, need not
be considered a substance; at least, it is enough if I
say that when God ever reduces a certain body to
perfect repose, something that can happen only by a
miracle, he would require a new miracle in order to
restore any motion to it. You see that my opinion
confirms rather than destroys the proof of a prime
mover: a reason must always be given for the com-
mencement of the motion and for the laws and the
agreement of the motions among themselves, and
this can never be done without having recourse to
God. Furthermore, my hand does not move because
I wish it for it would be in vain, unless I had a
miraculous faith, for me to wish the mountain to
move, and in the case of my hand I should not be
able to wish its moving with success unless it were
exactly at that moment that the muscles of my hand
made the necessary contraction for this effect; so
much the more must what I suffer agree with the
changes of my body. The one always accompanies
the other in virtue of the correspondence which I
established above; each one, however, has its cause
immediately in itself.

I come to the point regarding the forms or the
souls which I consider to be indivisible and inde-
structible. I am not the first one to hold this opin-
ion. Parmenides, of whom Plato speaks with
respect, as well as Melissus, held that there was
neither generation nor corruption except in appear-
ance. Aristotle takes the same position in Book 3,
De ccelo, chapter 2, and the author of De di&ta,
Book I., which is attributed to Hippocrates, says
expressly that an animal cannot be born wholly as a

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 219

new animal nor entirely destroyed. Albertus
Magnus and John Bacon seem to have thought that
the substantial forms were already concealed in mat-
ter from all time; Fernel has them descend from
heaven, to say nothing of those who derive them
from the soul of the world. These have all seen a
part of the truth, but they have not developed it.
Most of them believed in the transmigration and
others in the traduction of souls, instead of think-
ing of the transmigration and transformation of an
animal already formed. Others, not being able to
explain the origin of the forms, have said that they
begin by a true creation. Such a creation in time I
admit only in the case of reasoning souls, and hold
that all the forms which do not think were created
at the same time tha/ the world was. But they
believe that this creation takes place all the time
whenever the smallest worm is born. Philoponus,
an ancient commentator upon Aristotle, in his book
against Proclus, and Gabriel Biel seem to have been
of this opinion. I think that St. Thomas considered
the souls of beasts as indivisible. Our Cartesians go
much further when they say that every soul and
every true substantial form must be indestructible
and ingenerable. This is why they refused souls to
beasts, although M. Descartes, in a letter to M.
Morus, says that he is not certain that they have no
souls. Since no special objection is made to those
who speak of perduring atoms, why is it found
strange when the same is said of souls to which
indivisibility should belong by their very nature,
especially because, if we combine the position of the
Cartesians regarding the substance and the soul,
with the prevailing opinion regarding the souls of

230 CORRESPONDENCE.

beasts, the indestructibility necessarily follows. It
will be difficult to overcome this opinion which has
been always and everywhere received and which has
been broadcast, namely, that beasts have feelings.
Now, if we grant that they have souls, what I hold
regarding the indestructibility , of the souls is not
only necessary according to the Cartesians but it is
important again in ethics and in religion, in order
to controvert a dangerous tenet toward which
several personages of intelligence are inclined and
which the Italian philosophers, who are disciples of
Averroes, have disseminated; namely, that when an
animal dies the particular souls return to the soul of
the world. This is in contradiction to my demon-
stration of the nature of the individual substance
and cannot be conceived of distinctly, since every
individual substance must always subsist apart when
once it has commenced its being; that is why the
truths which I advance are so important. Those who
recognize that the beasts have souls should approve
of them, the others at least should not find them
strange.

To come, however, to your objections regarding
this indestructibility:

i. I have held that we must admit in bodies some-
thing which may be truly a single being, since mat-
ter or extended mass in itself can never be more
than plura entia, as St. Augustine, following Plato,
has very truly observed. Now, I infer that there
are not several beings where there is not even one
which may be truly a being, and I hold that every
multitude presupposes unity; to this you make
various replies, but without touching the argument
itself, which is unassailable; you use only arguments

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 221

ad hominem and from inconveniences which would
arise, and you try to show that what I say does not
solve the difficulty. First of all, you are aston-
ished, M., how I am able to make use of this reason,
which would be apparent to M. Cordemoy who con-
stitutes everything out of atoms, but which, from my
position, as you think, would be necessarily false,
since, leaving aside animated bodies that do not con-
stitute the hundred thousand thousandth part of the
universe, all the others would necessarily have to
be plura entia and the difficulty would thus come up
again. From this I see, M.,that I did not explain
myself sufficiently to enable you to grasp my
hypothesis, for, aside from the fact that I do not
remember having said that there are no substantial
forms excepting souls, I am far from saying that
animated bodies constitute only a small proportion
of the bodies in the world; for, I think rather that
everything is full of animated bodies, and in my
opinion there are incomparably more souls than M.
Cordemoy has atoms. His atoms are finite in
number, while I hold that the number of souls, or at
least of forms, is wholly infinite, and that mat-
ter being divisible without end, no portion can be
obtained so small that there are not in it animated
bodies, or at least such as are endowed with a prim-
itive entelechy, and (if you will permit me to use
the word life so generally), with the vital principle \
that is to say, with corporeal substances, of all of
which it may be said in general that they are alive.
2. As regards this other difficulty which you made,
M., namely that the soul joined to matter does not
make the latter truly one, since the matter is not
really one in itself, and since the soul, as you think,

322 CORRESPONDENCE.

gives it only an extrinsic character I reply that
it is the animated substance to which this matter
belongs that is really a being, and the matter which
is understood as the mass in itself is only a pure
phenomenon or appearance, as well-founded, how-
ever, as is space and time. It has not even those
precise and determined qualities which can enable
it to pass as a determined being, as I have already
indicated in what precedes, because figure itself,
which is the essence of a limited extended mass, is
never, strictly speaking, perfectly determined in the
state of nature because of the actually infinite
division of the parts of matter: there is never a
globe without inequalities, never a straight line
without an intermingling of curves, never a curve
of a certain finite nature without an intermixture
of some other, and this is as true in small portions
as in large, so that far from the figure being a con-
stitutive element in the body, it is not a quality
at all real and determined outside of the thought.
Never can an exact surface be assigned to any
body as could be done if there were atoms; I
can say the same thing of size and of motion,
namely, that these qualities or predicates are phe-
nomena like colors and sounds, and although they
involve a more distinct knowledge they cannot
hold up under a final analysis. Consequently
extended mass, when considered without ente-
lechies, that is, as consisting only in those qualities
of size and motion, is not a corporeal substance
but a wholly pure phenomenon like the rainbow.
It has been also recognized by philosophers that it
is the substantial form which gives a definite being
to matter, and those who do not pay attention to

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 223

that point will never get out of the labyrinth of the
composition of the continuum if they once enter:
only indivisible substances and their different states
are absolutely real. This Parminedes and Plato and
many other ancients have indeed seen.

However, I grant that the word one can be
applied to a gathering together of inanimate bodies
although no substantial form unites them, just as I
am able to say there is one rainbow, there is one
herd. But this is a unity, phenomenal or of
thought, which is not sufficient for the reality back
of the phenomenon. [If we take as the matter of
the corporeal substance, not its formless mass but a
secondary matter which is the manifold of sub-
stances whose mass constitutes the whole body, it
can be said that these substances are parts of this
matter; just as those which enter into our body
make a part of it. It is the same with other cor-
poreal substances as it is with our body, which is
the matter and the soul, which is the form of our
substance; and I find no more difficulty in this
respect than is found in the case of man, in regard to
whom all are agreed upon this point. The diffi-
culties which come up in these subjects are due,
among other reasons, to the fact that we have not
ordinarily a sufficiently distinct conception of the
whole and of the parts, because essentially the part
is nothing else than an immediate requisite for the
whole and is, in a way, homogeneous with it; there-
fore, the parts can constitute a whole, whether there
is a real unity or not. It is true that the whole,
which has a real unity, may continue as the same
individual in the strictest sense even when it loses
or gains parts as our experience shows us. In these

224 CORRESPONDENCE.

cases the parts are immediate requisites only pro
tempore but if, however, we understand by the term
matter something which will always be essential to
the same substance we might, in the sense of certain
of the Schoolmen, understand by this the primitive
passive power of a substance and, in this sense, the
matter would be neither extended nor divisible
although it would be the principle of divisibility or
of that which stands for divisibility in the substance.
However, I do not wish to argue regarding the use
of terms.]

3. You object that I admit substantial forms only
in the case of animated bodies — a position which I do
not, however, remember to have taken. Now, you
continue: all organized bodies being plura entia the
forms or souls by no means suffice to constitute a
being, but rather there must be several beings so
that the body can be animated. I reply that sup-
posing there is a soul or entelechy in beasts or in
other corporeal substances, we must reason in regard
to them as we all reason regarding man, who is a
being endowed with a real unity; his soul gives him
this unity although the mass of his body is divided
into organs, ducts, humors, spirits, and that the
parts are doubtless full of an infinity of other cor-
poreal substances endowed with their own entele-
chies. As this third objection agrees in substance
with the preceding the former solution will suffice.

4. You think that it is without a basis, when souls
are attributed to animals, and you think that if they
had souls there would be a mind, that is to say, a
substance which thinks since we know only bodies
and spirits and have no idea of any other substance;
now, that an oyster thinks or a worm thinks,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 225

it is difficult to believe. This objection applies
equally to all those who are not Cartesians.
Besides the fact, however, that that cannot be
entirely unreasonable, which the whole human race
has always accepted, namely that animals have feel-
ings, I think I have shown that every substance is
indivisible, and that consequently every cor-
poreal substance must have a soul or at least an
entelechy which has an analogy with the soul,
because otherwise the body would be only a phe-
nomenon.

To hold that every substance which is not divisible
(that is to say, in my opinion, every substance in
general), is a mind and must think, appears to me
incomparably more rash and more destitute of basis
than the conservation of forms. We know only
five senses and a certain number of metals, should
we conclude that there are none other in the world?
It seems more evident that nature, which loves
variety, has produced other forms than those which
think. If I am able to prove that there are no other
figures of the second degree than those found in
conic sections it is because I have a distinct idea of
those lines, which enables me to reach an exact
division; as, however, we have no distinct idea of
thought and are not able to demonstrate that the
concept of an indivisible substance coincides with
that of a substance which thinks, we have no cause
for being certain about it. I agree that the idea
which we have of thought is clear but everything
which is clear is not distinct. As Father Malebranche
has already noticed, it is only by internal feeling
that we recognize thought, we can recognize by feel-
ing only the things which we have experienced, and

226 CORRESPONDENCE.

as we have not experienced the functions of other
forms we must not be astonished if we have no clear
idea of them; for, we ought not to have such ideas
even if it were granted that there are these forms.
It is a mistake to try to employ confused ideas, how-
ever clear they may be, to prove that something
cannot be; and when I pay attention to distinct ideas
it seems that we can conceive that phenomena which
vary or which come from several beings, can be
expressed or represented in a single indivisible being,
and this is sufficient to constitute a perception with-
out any necessity of adding thought or reflection
to this representation. I would wish to be able
to explain the differences or the degrees of the
other immaterial expressions which are without
thought, so that we might distinguish corporeal or
living substances from animals, as far as they can
be distinguished. I have not, however, meditated
enough about the above, nor sufficiently examined
the things in nature in older to pass judgment upon
the forms as compared with their organs and activ-
ities. M. Malpighi, well versed in important
analogies of anatomy, is very much inclined to
think that plants can be embraced under the same
class with animals and that they are imperfect ani-
mals.

5. There remains for me only to satisfy the diffi-
culties which you have raised, M., against the inde-
structibility of the substantial forms; and, first of all,
I am surprised that you find this point strange and
untenable, because, according to your own position,
all those who assign to animals a soul and feeling
ought to maintain this indestructibility. These sup-
posed difficulties are only prejudices of the mind,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 227

which may detain common thinkers but which have
no influence upon minds capable of meditation. I
think it will be easy to satisfy you in regard to
them. Those who perceive that there is an
infinity of small animals in the least drop of water,
as the experiments of M. Leewenhoeck have shown,
and who do not find it strange that matter should be
entirely filled with animated substances, will not
find it strange either that there should be some-
thing animated in the ashes themselves, and that fire
can transform an animal and reduce it, without, how-
ever, entirely destroying it. That which can be said
of one caterpillar or silk-worm could be said of one
hundred or one thousand, but it does not follow that
we should see the silk worm re-born from the ashes.
Perhaps such is not the order of nature. I know
that many assure us that the generative powers
remain in ashes in such a way that plants can be
produced from them but I do not wish to employ
doubtful experiments. Whether these small organ-
ized bodies produced by a kind of contraction from
larger bodies that have become destroyed, are, as it
seems wholly out of the series of generation, or
whether they can come back again to the theater of
action in due time, is something which I am unable to
determine. These are secrets of nature where men
must acknowledge their ignorance.

6. It is only apparently and as a result of the
imagination that the difficulty seems greater with
regard to the larger animals which are born only by
the union of two sexes. This is apparently not less
necessary with the smallest insects. I have recently
learned that M. Leewenhoeck holds opinions quite
like mine, in that he maintains that the largest ani-

228 CORRESPONDENCE.

mals are born by a kind of transformation. I do
not dare either to approve or to reject the details of
his opinion, but I hold it as true in general, and M.
Swammerdam, another great investigator and
anatomist, says that he also has leanings toward
that opinion. Now, the opinions of these men are
far more important in such matters than those of
many others. True it is, I do not see that they
have carried out their opinions so far as to say that
corruption, and death itself, is also a transformation
with respect to the living beings which are destitute
of a reasonable soul, as I hold; but I think that if
they were informed of my position they would not
find it absurd, for there is nothing so natural as to
think that that which does not begin does not perish
either, and when it is acknowledged that all births
are only growths or developments of an animal
already formed, it is easy to be persuaded that decay
or death is nothing else than the diminution or the
decrease of an animal, which, nevertheless, continnes
to exist and to be living and organized. It is true
that it is not as easy to render this position accept-
able through special experiments as it is with
respect to generation, but the reason for this is evi-
dent; it is because generation advances from phys-
ical matter, little by little, so that we have time to
see it, but death goes backward too much by a
spring and at once returns to particles too small for
us, because death occurs usually in too violent a
manner for us to be able to follow out the details of
this retrogression. Sleep, however, which is an
image of death, and ecstacies, and the condition of
the silk worm in its cocoon, which might pass for a
death, also the resuscitation of flies quite drowned,

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 229

through the means of a certain dry powder that may
be sprinkled upon them (these flies remaining
wholly dead if they are left without any assistance),
and, furthermore, the state of swallows, which
hibernate in the reeds, where they are found appar-
ently dead, and the experiences of men who die
from cold, from drowning or from strangulation,
whom it is possible to bring to life again (in regard
to which not long since a careful thinker in Germany
wrote a treatise where, after having given instances
known to himself personally, he exhorts those who
have to do with such persons, to make more efforts
than are usually made to revive them, and he
describes the proper method) — all these things serve
to confirm my position that these different states
differ only in degree, and if we have not the means
of bringing about the resuscitation after other kinds
of death, it is because we do not know what must
be done, or, even if we should know what must be
done, our hands and our instruments and our
remedies would not be successful, above all, when
the dissolution goes at once into too minute par-
ticles. We must not, therefore, hold to the notions
which common people may have regarding death or
life, when there are both analogies and, what is
better, weighty arguments to prove the contrary,
for, I think, I have sufficiently shown that there
must be entelechies if there are corporeal substances,
and if these entelechies or souls are acknowl-
edged, their ingenerability and indestructibility
must be recognized. After this, it is incomparably
more reasonable to think of the transformation of
animated bodies than to conceive of the passage of
souls from one body to another, which latter opin-

33° CORRESPONDENCE.

ion, though very ancient, seems to be merely a form
of transformation not well understood. To say that
the souls of animals remain without a body or that
they remain concealed in a body which is not organ-
ized, appears less natural than my position. Whether
the animal resulting from the diminution of the body
of the ram which Abraham sacrificed in place of Isaac
should be called a ram is only a question of names,
very much as would be the question whether a moth
should be called a silkworm; the difficulty which
you have found, M., in regard to the ram reduced
to ashes comes only because I did not sufficiently
explain myself. You suppose that no organized
body remains in the ashes and therefore you have a
right to say that it would be a monstrous thing, this
infinity of souls without organized bodies; while my
position is that in the state of nature there are no
souls without animated bodies and no animated
bodies without organs Neither ashes nor any other
mass appears to me incapable of containing organ-
ized bodies.

With regard to spirits, that is to say, substances
which think and which are able to recognize God
and to discover eternal truths, I hold that God gov-
erns them according to laws different from those
with which he governs the rest of substances; for,
while all the forms of substances express the whole
universe, it can be said that animal substances
express the world rather than God, while spirits
express God rather than the world. God governs
animal substances according to the material laws of
force and of the transfer of motion, but spirits,
according to spiritual laws of justice, of which the
others are incapable. It is for this reason that ani-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 231

mal substances can be called material, because the
economy which God observes with regard to them
is that of a worker or of a machinist, but with regard
to spirits God performs the functions of a Prince or
of a Legislator, which is infinitely higher; with
regard to material substances, God is only what he
is with regard to everything, namely, the universal
author of beings. He assumes, however, another
aspect with regard to spirits who conceive of him as
endowed with will and with moral qualities;
because he is, himself, a spirit and, like one among
us, to the point of entering with us into a social
relation, where he is the head. It is this universal
society or republic of spirits under this sovereign
monarch which is the noblest part of the universe,
composed of so many little gods under this one
great God; for, it can be said that created spirits
differ from God only in degree, only as the finite
differs from the infinite, and it can be truly said that
the whole universe has been made only to con-
tribute to the beautifying and to the happiness of
this city of God. This is why everything is so con-
structed that the laws of force or the purely material
laws work together in the whole universe to carry
out the laws of justice or of love, so that nothing
will be able to injure the souls that are in the hands,
of God, and so that everything should result for
the greatest good of those who love him; this is
why, furthermore, it must be that spirits keep their
personalities and their moral qualities so that the
city of God shall lose no member and they must in
particular preserve some sort of memory or con-
sciousness or the power to know what they are, upon
which depends all their morality, penalties and

23» CORRESPONDENCE.

chastisements. Consequently, they must be exempt
from those transformations of the universe which
would render them unrecognizable to themselves
and, morally speaking, would make another person
of them. For animal substances, however, it is
enough if they remain as the same individual in the
metaphysical sense, while they are subjected to all
imaginable changes because they are without con-
science or reflection.

As far as the particulars of this condition of the
human soul after death are concerned and in what
way it is exempted from the transformation of things,
revelation alone can give us particular instruction;
the jurisdiction of the reason does not extend so far.
Perhaps an objection may be made to my position
when I say that God has given souls to all natural
machines which are capable of them, because the
souls do not interfere with one another and do not
occupy any position; and that it is possible to
assign to them as much perfection as they are able
to have, since God has made everything in the most
perfect possible manner; "there is no more a
vacuum of forms than of bodies." It might be said
that, by the same reasoning, God should give reason-
ing souls or souls capable of reflection to all ani-
mated substances. But I reply that laws superior to
the laws of material nature are opposed to this, that
is to say, the laws of justice, because the order of
the universe would not permit justice to be observed
toward all, and it would have to be, therefore, that
at least no injustice should be done them; that is
why they have been made incapable of reflection or
consciousness, and consequently, not susceptible of
happiness and unhappiness.

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 233

Finally, to recapitulate my position in a few
words, I maintain that every substance involves in its
present state all its past and future states and even
expresses the whole universe according to its point
of view, since nothing is so far from anything else
that there is no relation between them. This
expression would be particularly complete, however,
with regard to the relations to the parts of its own
body, which it expresses more immediately. Conse-
quently, nothing happens to the substance except
out of its own being and in virtue of its own laws,
provided that we add the concurrence of God. It
perceives other things because it expresses them
naturally, having from the start been created in such
a way that it can do this in a series of events, accom-
modating itself as called for, and it is in this agree-
ment imposed from the beginning that consists what
is called the action of one substance upon another.
With regard to corporeal substances, I hold that
mass, when we mean by this what is divisible, is a
pure phenomenon; that every substance has a true
unity in the strictness of metaphysics; that it is
indivisible, ingenerable, and incorruptible; that all
matter must be full of animated or, at least, living
substances; that generation and corruption are only
transformations from the little to the great, and vice
versa; that there is no particle of matter in which is
not found a world with an infinity of creatures
organized as well as brought together; and, above
all, that the works of God are infinitely greater,
more beautiful, and better ordered than is commonly
thought, and that mechanism, or organization, that
is to say, order, is essential to them even in their
smallest parts. Therefore, no hypothesis can enable

234 CORRESPONDENCE.

us better to recognize the wisdom of God than mine:
according to which there are everywhere substances
indicating God's perfection, and there are just so
many differing reflections of the beauty of the uni-
verse, where nothing remains empty, sterile, unculti-
vated and without perception. It must also be held as
indubitable that the laws of motion and the changes
of bodies serve the laws of justice and of control,
which are without doubt observed the best way pos-
sible in the government of spirits; that is to say, of
the intelligent souls which enter into social relations
with God and, together with him, constitute a kind
of perfect city of which he is the monarch.

I think now, M., that I have omitted none of all
the difficulties which you spoke of, or at least indi-
cated, and also of those which I have thought you
might still have. It is true that this has increased
the size of this letter but it would have been more
difficult to put my meaning in less words, and had
I attempted it, obscurity might have been involved.
I think that you will now find my positions as well
articulated among themselves as with the accepted
opinions. I do not at all overthrow established
opinions, but I explain them and I carry them out
further. If you might have the leisure some day to
look over again what we finally established regard-
ing the concept of an individual substance, you will
perhaps find, that in granting me this premise it
will be necessary to grant all the rest. I have
attempted, however, to write this letter in such a
way that it shall explain and defend itself. It is
quite possible, indeed, to separate the questions.
Those who are unwilling to recognize souls in ani-
mals and substantial forms elsewhere, may, neverthe-

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 235

less, approve of the way in which I have explained
the union of the mind and the body, and all that I
have said regarding true substance. It will be for
them to save as they can, without such forms and
without a true unity, whether by points or by atoms,
as seems best to them, the reality of matter and of
corporeal substances, or else to leave this undecided;
since investigation can be cut off wherever one
thinks best. We must not, however, stop half way
when we desire to have true ideas of the universe
and of the perfection of God's works, which are able
to furnish us most weighty arguments with respect
to God and with respect to our souls.

It is very remarkable how Catelan has so entirely
missed my meaning, as you suspected he had; he
advances three propositions and says that I find con-
tradictions in them, while, in fact, I find none there,
and employ these very propositions to prove the
absurdity of the Cartesian principle. This is the
result of dealing with men who take up things only
superficially. If it can happen in a question of
mathematics what should we not expect in meta-
physics and in ethics. It is for this reason that I
consider myself fortunate in having found in you a
critic as exact as he is fair. I wish you long life, as
well for the interests of the public as for my own.
I am, etc.

Part of a letter sent at the same time to Arnauld.

Here is the reply to your last objection, it has
become a little long because I wish to explain
myself explicitly and to leave none of your doubts
untouched. Several times I inserted your own
words which contributed toward increasing its size.

236 CORRESPONDENCE.

As I took all those positions a long time ago and
have foreseen, if I might dare to say, most of the
objections, they cost me hardly any meditation, and
all I needed to do was to pour out my thoughts
upon paper and to re-read them afterwards. I say
this, M., so that you may not think me too deeply
engrossed in such matters at the expense of other
necessary business; you drew me on to go so far,
when you made objections and questions which I
wished to satisfy, as much in order to profit by your
enlightenment as to make you recognize my wish to
disguise nothing.

At the present time I am very busy with a history
of the noble house of Brunswick. I have looked
over several archives this summer and I am to make
a journey in Southern Germany to seek certain docu-
ments; this does not prevent my desiring to learn
your opinion regarding my explanations when
your leisure will permit it and also regarding
my reply to Catelan which I send herewith; I do
this because it is short and, in my opinion, demon-
strative, provided that it is read with the least
attention. If Catelan does not do better than
hitherto, I cannot expect any enlightenment from
him on this subject. I wish you might be able to
give a moment of serious attention to it, and you
would, perhaps, be surprised to see that something
which is so easy to overthrow has been accepted as
an incontrovertible principle because it is clear that
the velocities which bodies acquire in descending
are as the square roots of the heights from which
they have fallen: now, if we leave out of question
external resistances a body can return exactly to the
height from which it has descended, therefore

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 237

Another draft of the above.

1 herewith send you my reply to Catelan which
will, perhaps, be inserted in The News of the
Republic of Letters; we are at the beginning again,
and I made a mistake in replying to his first answer.
I should simply have said that he did not touch my
objection, and should have indicated these points to
which a reply was necessary, as I have now done —
I have added in my reply a mechanical problem,
which can be solved by geometry, but a good deal of
skill must be used and I will see if M. Catelan will
dare tackle it. It seems to me that he is not very
able, and I am surprised to see that among so many
Cartesians there are so few who imitate Descartes in
trying to advance further.

XXIV

Leibniz to Count Ernst von Hessen-Rheinfels.

I beg your Highness to ask M Arnauld as well as
yourself if there is really so great an evil in saying
that everything (whether a species or whether an
individual or person), has a certain perfect concept
which involves all that can be truly said regarding
it, and, according to this concept, God, who con-
ceives of everything perfectly, conceives of the said
thing? And to ask further if M. A. thinks in
good faith that a man who holds such a position
could not be accepted into the Catholic church, even
when he sincerely rejects the supposed fatalistic
consequence; and Your Highness may ask how that
agrees with what M. A. formerly wrote, namely,
that no trouble was made for a man in the Church on

238 CORRESPONDENCE.

account of these kinds of opinions, and if it is not to
repulse men by a useless and untimely strictness, to
condemn so easily all kinds of opinions which have
nothing to do with the faith?

Can it be denied that everything, whether genus,
species or individual has a complete concept accord-
ing to which God conceives of it (he who conceives
of everything perfectly), a concept which involves
or embraces all that can be said of the thing? And
can it be denied that God is able to have such an
individual conception of Adam or of Alexander that
it shall embrace all the attributes, affections, acci-
dents and, in general, all the predicates of this sub-
ject? And finally since St. Thomas could maintain
that every separate intelligence differed in kind
from every other, what evil will there be in saying
the same of every person and in conceiving indi-
viduals as final species, provided that the species
shall not be understood physically but metaphys-
ically or mathematically; for, in physics when a
thing engenders something similar to it, they are
said to be of the same kind, but in metaphysics or
in geometry we say that things differ in kind when
they have any difference in the concept which
suffices to describe them, so that two ellipses in
one of which the major and minor axes are in the
ratio of two to one and in the other in the ratio of
three to one, differ in kind. Two ellipses which
differ only in magnitude or proportionately, and
where, in their description, there is no difference
of ratio in the axes, have no specific difference or
difference in kind, for it must be remembered that
complete beings cannot differ merely because of
differences in size.

LEIBNIZ. ARNAULIX HESSEN-RHEINFELS. 239

XXV
Leibniz to Arnauld.

January 14, 1688.
Monsieur:

Perhaps you will have seen in The News of the
Republic of Letters for the month of September
what I replied to M. 1'Abbe C. It is a remarkable
thing to see how many people reply, not to what
has been said, but to what they have imagined.
This is what M. 1'Abbe has done up to the pres-
ent. For this reason it was necessary to break off
abruptly, and bring him back to the first objection.
I have only taken the opportunity of this argumen-
tation to put forward a very curious geometrico-
mechanical problem which I have just solved. It
is to find what I call an isochronous curve, in which
a body shall descend uniformly and approach equal
distances to the horizon in equal times, notwith-
standing the acceleration it undergoes. This latter
I offset by continually changing the inclination. I
did this in order to bring out something useful and to
show M. 1'Abbe that the ordinary analysis of the
Cartesians is too limited for difficult problems. I
succeeded partly in this, for M. Hugens* gave a solu-
tion of the problem in the News for October. I
knew well enough that M. Hugens could do it, and
therefore I didn't expect that he would take the
trouble, or, at least, that he would publish his solu-
tion and set M. 1'Abbe free: since, however, M.
Hugens' solution is in part enigmatical, apparently
to see if I can do it also, I have sent him the
rest of it. Now we will see what M. 1 Abbe will

* So spelled by Leibniz.— EdL

240 CORRESPONDENCE.

say about it. ' It is true that if the nature of the line
which M. Hugens has published is known, the rest can
be obtained by ordinary analysis, but without that
the thing is difficult, for the converse of the rule of
tangents, to find the line, having given the property
of the tangents, to which this proposed problem
reduces itself, is a problem which M. Descartes him-
self has confessed in one of his letters not to have
mastered. For, usually, what I call transcendentals
result, which have no degree; and when the problem
reduces itself to curves of a certain degree, as it
happens in this case, an ordinary analyst will have
difficulty in recognizing it.

I wish, with all my heart, that you might have
leisure to think over for half an hour my objection
to the Cartesians, which M. 1'Abbe tries to meet.
Your enlightenment and your sincerity assure me
that we should come to the point and that you
would recognize in good faith what was the real dis-
cussion. The discussion is not long, and the matter
is of importance, not only for mechanics, but also in
the realm of metaphysics, because movement in
itself separated from force is something merely
relative and its subject cannot be determined; force,
however, being something real and absolute, and its
calculations, as I clearly show, different from that of
motion, we must not be surprised if nature preserves
the same quantity of force but not the same quantity
of motion. It follows that there is in nature some-
thing besides extension and motion, unless ajl
force or energy be denied to things, which would
be to change them from substances into modes, as
Spinoza does, who holgls that God alone is a sub-
stance and that all qther things are modifications of

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 241

him. Spinoza is full of confused reveries and his
pretended demonstrations de Deo have only an
apparent truth. However, I hold that one created
substance, in metaphysical strictness, does not act
upon another, that is to say, with a real influence;
furthermore, it is impossible to explain distinctly
in what this influence consists unless we refer it to
God, whose operation is a continual creation, and
the source of this influence is the essential depend-
ence of created things. If we wish to speak as
ordinary men do, who say that one substance acts
upon another, we must give some other conception
to what is called action. It would take too long to
develop this point and I refer to my last letter, which
is prolix enough.

I do not know whether the Rev. Father Male-
branche has replied to my answer given in one of
the summer months of last year, where I advanced
another general principle useful in mechanics as in
geometry, which clearly overthrew all the laws of
motion that Descartes put forward as well as those
of Malebranche himself, together with what he said
in The News to defend them.

Some day, if I find leisure I hope to write out my
meditations upon the general characteristic or
method of universal calculus, which should be of
service in the other sciences as well as in mathe-
matics. I have already made some successful
attempts. I have definitions, axioms, and very
remarkable theorems and problems in regard to
coincidence, determination (or de unico), similitude,
relation in general, power or cause, and substance,
and everywhere I advance with symbols in a precise
and strict manner as in algebra. I have made some

242 CORRESPONDENCE.

applications of it in jurisprudence, and it can be
truly said that there are no authors whose style
approaches nearer that of the geometers than the
style of the jurists in the Digests. But you will ask
how is calculation to be applied to conjectural mat-
ters. I reply that it is in the way that Pascal,
Hugens, and others, have given demonstrations of
possible chances, Because the most probable and
the most certain can always be determined in so far
as it is possible to know anything ex datis.

I do not however wish to take more of your time,
and perhaps I have already taken too much. I
should not dare to do it so frequently, if the matters
upon which I desire to have your criticisms were not
important. I pray God to prolong your life a long
time, so that we may always profit by your enlighten-
ment. I am, with zeal, etc.

XXVI
Leibniz to Arnauld.

Venice, March 23, 1690.

I am now on the point of returning home after a
long journey, undertaken under the orders of my
Prince for the purpose of historical investigations.
And I have found diplomas, certificates and indubi-
table proofs sufficient to establish the common origin
of the noble Houses of Brunswick and Este, which
Justel, du Cange and others had strong grounds for
calling in question, because there were contradic-
tions and errors on the part of the historians of Este
in this respect, together with a complete confusion
in dates and personages.

At present I am thinking of returning to my old

LEIBNIZ. ARNAULD. HESSKN-RHEINFELS. 243

life and of taking up my former occupations again.
I wrote to you two years ago, a little before my
departure, and I take the same liberty again, for the
purpose of asking after your health and to let you
know how constantly the thought of your well-
known merits are in my mind. When I was at
Rome, I saw the denunciation of a new letter which
is attributed to you or to your friends. Since then
I have seen a letter of the Rev. Father Mabillon's to
one of my friends in which he says that the Rev.
Father Tellier's apology for the missionaries against
the practical morality of the Jesuits had given to
many persons favorable impressions of these Fathers,
but he had heard that you had replied to it, and that
it was said you had with geometrical logic com-
pletely overthrown the reasoning of this Father.
All this has led me to think that you are still in a
condition to render service to the public, and I pray
God that it may be so for a long time yet. It is
true that I have a personal interest in this, but it is a
praiseworthy interest since I am given a means of
being instructed, whether in common with all the
others, who will read your works, or in particular
when your criticisms shall instruct me, provided the
little leisure which you have may still permit me to
hope for this advantage at times.

As this journey has served in part to release my
mind from routine business, I have had the satisfac-
tion of conversing with several able men on matters
of learning and science, and I have communicated
to some of them my own views, which you are
acquainted with, in order to profit by the doubts and
difficulties which they raised, and there were some
of these men who, not satisfied with the current

244 CORRESPONDENCE.

doctrines, found an unusual satisfaction in certain
of my positions. This has led me to put them down
in writing so that they may be communicated more
easily, and some day, perhaps, 1 will have a few
copies printed without my name, merely to circulate
them among my friends in order to obtain their
criticisms. I should like you to be able to examine
them first and therefore I have made the following
abstract:

A body is an aggregation of substances, and is
not a substance, properly speaking. Consequently,
in all bodies must be found indivisible substances
which cannot be generated and are not corruptible,
having something which corresponds to souls.

All these substances have been always and will
always be united to organic bodies diversely trans-
formable.

Each of these substances contains in its nature the
law of the continuous progression of its own work-
ings and all that has happened to it and all that will
happen to it.

Excepting the dependence upon God, all these
activities come from its own nature.

Each substance expresses the whole universe,
some substances, however, more distinctly than
others, each one especially distinctly with regard
to certain things and according to its own point of
view.

The union of the soul with the body and even the
action of one substance upon another consists only
in the perfect mutual accord, expressly established
by the ordinance of the first creation, by virtue of
which each substance following its own laws falls in
with what the others require, and thus the activities

LEIBNIZ. ARNAULD. HKSSEN-RHEINFELS. 245

of the one follow or accompany the activities or
changes of the other.

Intellects, or souls which are capable of reflection
and of knowing the eternal truths and God, have
many privileges that exempt them from the trans-
formations of bodies.

In regard to them moral laws must be added to
physical laws.

It is for them principally that every thing has been
made.

They, taken together, constitute the Republic of
the Universe, with God as the monarch.

There is perfect justice and order observed in
this city of God, and there is no evil action without
its chastisement, nor any good action without its
proportionate reward.

The better things are understood, the more
are they found beautiful and conformable to the
desires which a wise man might form.

We must always be content with the ordering of
the past because it has absolutely conformed to the
will of God, which can be known by the events, but
we must try to make the future, in so far as it
depends upon us, conform to the presumptive will
of God or to his commandments, to beautify our
Sparta and to labor in well-doing, without, however,
being cast down when unsuccessful, in the firm
belief that God will know how to find the most fit-
ting times for changes to the better.

Those who are not content with the ordering of
things cannot boast of loving God properly.

Justice is nothing else than love felt by the
wise.

Charity is universal benevolence whose fulfillment

246 CORRESPONDENCE.

the wise carry out conformably to the dictates of
reason so as to obtain the greatest good.

Wisdom is the science of happiness or of the
means of attaining the lasting contentment which
consists in the continual achievement of a greater
perfection or at least in variations of the same degree
of perfection.

In regard to the subject of physics: the nature of
force must be understood as wholly different from
motion, which is something more relative. Force
must be measured by the quantity of effect: there is
an absolute force, a directive force and a respective
force.

Each of these forces is conserved in the same
quantity in the universe, or in each machine which
has no communication with others, and the two lat-
ter forces taken together compose the former or the
absolute force. The same amount of motion, how-
ever, is not conserved, for I can show that if it were,
perpetual motion would be possible, and that an
effect would be greater than its cause.

Some time ago I published in the Acts of
Leipsic an essay in the domain of physics for the
purpose of finding the physical causes of the astral
motions. I assume as basal that every motion of a
solid in a fluid, where the motion is in a curved line
or the velocity is constantly changing, is derived from
the motion of the fluid itself. Whence I draw the
conclusion that the heavenly bodies have deferent
but fluid orbs, which we may call with Descartes
and with the ancients, vortexes. I think there are
neither vacuums nor atoms, for these are things far
removed from the perfection of God's works, and
that every motion is propagated from one body to

LEIBNIZ. ARNAULD. HESSEN-RHEINFELS. 247

all other bodies, although more feebly as the dis-
tances are greater. Supposing that all the great
globes in the universe have something analogous to
magneti?m, I think that in addition to a certain tend-
ency which causes them to maintain the parallel-
ism of their axes, they have a kind of attraction
whence arises something comparable to gravity.
We can picture this by imagining rays of some
material substance which is trying to move away
from a center and consequently pushes others which
have not this tendency toward the center. We may
compare these rays of attraction with those of light,
and by the same law which holds in illumination we
shall find that the attraction is inversely as the
square of the distance.

These things agree wonderfully with the phe-
nomena. Kepler found that in general the areas of
the orbits of the planets described by radii drawn
from the sun to the orbits are in proportion to the
times of the revolutions around the sun, and I have
demonstrated an important general proposition,
namely, that all those bodies which revolve in
harmonic motion (that is to say, so move that their
distances from the center are in arithmetical pro-
gression, while their velocities are in harmonic
progression or inversely as the distances), and
moreover, if these bodies have a paracentric
motion (that is to say, are heavy or light as
regards the same center, whatever law this attrac-
tion or repulsion may obey) — all such bodies
describe areas which vary necessarily as the times,
just as Kepler observed in the case of the
planets. I conclude that the deferent fluid orbs
of the planets revolve harmonically, and I give an a

248 CORRESPONDENCE.

priori reason for this. Now, empirically observing
that in fact this motion is elliptical, I find that the
law of paracentric motions, which when combined
with the harmonic revolutions describe ellipses,
ought to be such that the attraction is inversely
as the squares of the distances, that is, exactly the
same as what we found above to be true a priori by
the laws of radiation. From this I then deduce
special characteristics and the whole was broached
in my publication in the Acts of Leipsic some time
ago.

I will say nothing of my calculus of increments or
differences, by which I determine the tangents with-
out eliminating irrationals and fractions even when
unknown quantities are involved in them and by
which I subject quadratics and transcendental prob-
lems to analysis. Neither will I speak of an entirely
new analysis confined to Geometry and differing
entirely from Algebra, and even less of certain other
subjects which I have not yet had the time to
develop. I should have liked to be able to explain
them all to you in a few words, so as to have upon
them your opinion, which would be of infinite serv-
ice to me, had you as much leisure as I have defer-
ence for your criticism. Your time, however, is too
precious, and my letter is already quite long.
Therefore I bring it to an end here, and am
sincerely, etc.

THE MONADOLOGY.

THE MONADOLOGY.

1. The Monad, of which we will speak here, is
nothing else than a simple substance, which goes to
make up composites; by simple, we mean without
parts.

2. There must be simple substances because there
are composites; for a composite is nothing else than
a collection or aggregatum of simple substances.

3. Now, where there are no constituent parts
there is possible neither extension, nor form, nor
divisibility. These Monads are the true Atoms of
nature, and, in fact, the Elements of things.

4. Their dissolution, therefore, is not to be feared
and there is no way conceivable by which a simple
substance can perish through natural means.

5. For the same reason there is no way conceiv-
able by which a simple substance might, through
natural means, come into existence, since it can
not be formed by composition.

6. We may say then, that the existence of Monads
can begin or end only all at once, that is to say, the
Monad can begin only through creation and end
only through annihilation. Composites, however,
begin or end gradually

7. There is also no way of explaining how a
Monad can be altered or changed in its inner being
by any other created thing, since there is no possi-
bility of transposition within it, nor can we conceive

251

252 LEIBNIZ.

of any internal movement which can be produced,
directed, increased or diminished there within the
substance, such as can take place in the case of
composites where a change can occur among the
parts. The Monads have no windows through
which anything may come in or go out. The
Attributes are not liable to detach themselves and
make an excursion outside the substance, as could
sensible species of the Schoolmen. In the same
way neither substance nor attribute can enter from
without into a Monad.

8. Still Monads must needs have some qualities,
otherwise they would not even be existences. And
if simple substances did not differ at all in their
'qualities, there would be no means of perceiving
any change in things. Whatever is in a composite
can come into it only through its simple elements
and the Monads, if they were without qualities, since
they do not differ at all in quantity, would be
indistinguishable one from another. For instance,
if we imagine a plenum or completely filled space,
where each part receives only the equivalent of its
own previous motion, one state of things would not
be distinguishable from another.

9. Each Monad, indeed, must be different from
every other. For there are never in nature two
beings which are exactly alike, and in which it is
not possible to find a difference either internal or
based on an intrinsic property.

10. I assume it as admitted that every created
being, and consequently the created Monad, is sub-
ject to change, and indeed that this change is con-
tinuous in each.

11. It follows from what has just been said, that

MONADOLOGY. 253

the natural changes of the Monad come from an
internal principle, because an external cause can
have no influence upon its inner being.

12. Now besides this principle of change there
must also be in the Monad a manifoldness which
changes. This manifoldness constitutes, so to
speak, the specific nature and the variety of the
simple substances.

13. This manifoldness must involve a multiplicity
in the unity or in that which is simple. For since
every natural change takes place by degrees, there
must be something which changes and something
which remains unchanged, and consequently there
must be in the simple substance a plurality of con-
ditions and relations, even though it has no parts.

14. The passing condition which involves and
represents a multiplicity in the unity, or in the
simple substance, is nothing else than what is called
Perception. This should be carefully distinguished
from Apperception or Consciousness, as will appear
in what follows. In this matter the Cartesians have
fallen into a serious error, in that they treat as non-
existent those perceptions of which we are not con-
scious. It is this also which has led them to believe
that spirits alone are Monads and that there are no
souls of animals or other Entelechies, and it has led
them to make the common confusion between a
protracted period of unconsciousness and actual
death. They have thus adopted the Scholastic
error that souls can exist entirely separated from
bodies, and have even confirmed ill-balanced minds
in the belief that souls are mortal.

15. The action of the internal principle which
brings about the change or the passing from one

254 LEIBNIZ.

perception to another may be called Appetition.
It is true that the desire (I'appetit) is not always
able to attain to the whole of the perception which
it strives for, but it always attains a portion of it
and reaches new perceptions.

16. We, ourselves, experience a multiplicity in a
simple substance, when we find that the most trifling
thought of which we are conscious involves a variety
in the object. Therefore all those who acknowl-
edge that the soul is a simple substance ought to
grant this multiplicity in the Monad, and Monsieur
Bayle should have found no difficulty in it, as he has
done in his Dictionary, article "Rorarius."

17. It must be confessed, however, that Percep-
tion, and that which depends upon it, are inex-
plicable by mechanical causes, that is to say, by
figures and motions. Supposing that there were a
machine whose structure produced thought, sensa-
tion, and perception, we could conceive of it as
increased in size with the same proportions until
one was able to enter into its interior, as he would
into a mill. Now, on going into it he would find
only pieces working upon one another, but never
would he find anything to explain Perception. It
is accordingly in the simple substance, and not in
the composite nor in a machine that the Perception
is to be sought. Furthermore, there is nothing
besides perceptions and their changes to be found in
the simple substance. And it is in these alone that
all the internal activities of the simple substance
can consist.

18. All simple substances or created Monads may
be called Entelechies, because they have in them-
selves a certain perfection («x«w<ri TO «vr«Xes). There

MONADOLOGV. 255

is in them a sufficiency (avrop«ia) which makes them
the source of their internal activities, and renders
them, so to speak, incorporeal Automatons.

19. If we wish to designate as soul everything
which has perceptions and desires in the general
sense that I have just expJained, all simple sub-
stances or created Monads could be called souls.
But since feeling is something more than a mere
perception I think that the general name of
Monad or Entelechy should suffice for simple sub-
stances which have only perception, while we may
reserve the term Soul for those whose perception is
more distinct and is accompanied by memory.

20. We experience in ourselves a state where we
remember nothing and where we have no distinct
perception, as in periods of fainting, or when we are
overcome by a profound, dreamless sleep. In such
a state the soul does not sensibly differ at all from a
simple Monad. As this state, however, is not per-
manent and the soul can recover from it, the soul is
something more.

21. Nevertheless it does not follow at all that the
simple substance is in such a state without percep-
tion. This is so because of the reasons given above;
for it cannot perish, nor on the other hand would it
exist without some affection and the affection is
nothing else than its perception. When, however,
there are a great number of weak perceptions where
nothing stands out distinctively, we are stunned; as
when one turns around and around in the same direc-
tion, a dizziness comes on, which makes him swoon
and makes him able to distinguish nothing. Among
animals, death can occasion this state for quite a
period.

256 LEIBNIZ.

22. Every present state of a simple substance is a
natural consequence of its preceding state, in such
a way that its present is big with its future.

23. Therefore, since on awakening after a period
of unconsciousness we become conscious of our per-
ceptions, we must, without having been conscious of
them, have had perceptions immediately before; for
one perception can come in a natural way only from
another perception, just as a motion can come in a
natural way only from a motion.

24. It is evident from this that if we were to have
nothing distinctive, or so to speak prominent, and
of a higher flavor in our perceptions, we should be
in a continual state of stupor. This is the condition
of Monads which are wholly bare.

25. We see that nature has given to animals
heightened perceptions, having provided them with
organs which collect numerous rays of light or numer-
ous waves of air and thus make them more effective in
their combination. Something similar to this takes
place in the case of smell, in that of taste and of
touch, and perhaps in many other senses which are
unknown to us. I shall have occasion very soon to
explain how that which occurs in the soul represents
that which goes on in the sense-organs.

26. The memory furnishes a sort of consecutive-
ness which imitates reason but is to be distinguished
from it. We see that animals when they have the
perception of something which they notice and of
which they have had a similar previous perception,
are led by the representation of their memory to
expect that which was associated in the preceding
perception, and they come to have feelings like those
which they had before. For instance, if a stick be

MONADOLOGY. 257

shown to a dog, he remembers the pain which it has
caused him and he whines or runs away.

27. The vividness of the picture, which comes to
him or moves him, is derived either from the magni-
tude or from the number of the previous perceptions.
For, oftentimes, a strong impression brings about, all

'at once, the same effect as a long-continued habit or
as a great many re-iterated, moderate perceptions.

28. Men act in like manner as animals, in so far
as the sequence of their perceptions is determined
only by the law of memory, resembling the empir-
ical physicians who practice simply, without any
theory, and we are empiricists in three-fourths of our
actions. For instance, when we expect that there
will be day-light to-morrow, we do so empirically,
because it has always happened so up to the present
time. It is only the astronomer who uses his reason
in making such an affirmation.

29. But the knowledge of eternal and necessary
truths is that which distinguishes us from mere
animals and gives us reason and the sciences, thus
raising us to a knowledge of ourselves and of God.
This is what is called in us the Rational Soul or the
Mind.

30. It is also through the knowledge of necessary
truths and through abstractions from them that we
come to perform Reflective Acts, which cause us to
think of what is called the I, and to decide that this
or that is within us. It is thus, that in thinking
upon ourselves we think of being, of substance, of
the simple and composite, of a material thing and
of God himself, conceiving that what is limited in
us is in him without limits. These Reflective Acts
furnish the principal objects of our reasonings.

258 LEIBNIZ.

31. Our reasoning is based upon two great prin-
+ ciples: first, that of Contradiction, by means of

which we decide that to be false which involves
contradiction and that to be true which contradicts
or is opposed to the false.

32. And second, the principle of Sufficient
Reason, in virtue of which we believe that no fact
can be real or existing and no statement true unless
it has a sufficient reason why it should be thus and
not otherwise. Most frequently, however, these
reasons cannot be known by us.

33. There are also two kinds of Truths: those of
"' Reasoning and those of Fact. The Truths of

Reasoning are necessary, and their opposite is
impossible. Those of Fact, however, are con-
tingent, and their opposite is possible. When a
truth is necessary, the reason can be found by
analysis in resolving it into simpler ideas and into
simpler truths until we reach those which are pri-
mary.

34. It te thus that with mathematicians the Spec-
ulative Theorems and the practical Canons are
reduced by analysis to Definitions, Axioms, and
Postulates.

35. There are finally simple ideas of which no
definition can be given. There are also the Axioms
and Postulates or, in a word, the primary principles
which cannot be proved and, indeed, have no need
of proof. These are identical propositions whose
opposites involve express contradictions.

36. But there must be also a sufficient reason for
contingent truths or truths of fact; that is to say,
for the sequence of the things which extend
throughout the universe of created beings, where

MONADOLOGY. 259

the analysis into more particular reasons can be
continued into greater detail without limit because
of the immense variety of the things in nature and
because of the infinite division of bodies. There is
an infinity of figures and of movements, present and
past, which enter into the efficient cause of my
present writing, and in its final cause there are an
infinity of slight tendencies and dispositions of my
soul, present and past.

37. And as all this detaiPagain involves other and
more detailed contingencies, each of which again
has need of a similar analysis in order to find its
explanation, no real advance has been made.
Therefore, the sufficient or ultimate reason must
needs be outside of the sequence or series of these
details of contingencies, however infinite they may
be.

38. It is thus that the ultimate reason for things
must be a necessary substance, in which the detail
of the changes shall be present merely potentially,
as in the fountain-head, and this substance we call
God.

39. Now, since this substance is a sufficient reason
for all the above mentioned details, which are linked
together throughout, there is but one God, and this
God is sufficient.

40. We may hold that the supreme substance,
which is unique, universal and necessary with noth-
ing independent outside of it, which is further a pure
sequence of possible being, must be incapable of
limitation and must contain as much reality as pos-
sible.

41. Whence it follows that God is absolutely per-
fect, perfection being understood as the magnitude

260 LEIBNIZ.

of positive reality in the strict sense, when the
limitations or the bounds of those things which have
them are removed. There where there are no
limits, that is to say, in God, perfection is abso-
lutely infinite.

42. It follows also that created things derive their
perfections through the influence of God, but their
imperfections come from their own natures, which
cannot exist without limits. It is in this latter
that they are distinguished from God. An example
of this original imperfection of created things is to
be found in the natural inertia of bodies.

43. It is true, furthermore, that in God is found
not only the source of existences, but also that of
essences, in so far as they are real. In other words,
he is the source of whatever there is real in the pos-
sible. This is because the Understanding of God is
in the region of eternal truths or of the ideas upon
which they depend, and because without him there
would be nothing real in the possibilities of things,
and not only would nothing be existent, nothing
would be even possible.

44. For it must needs be that if there is a reality
in essences or in possibilities or indeed in the eternal
truths, this reality is based upon something existent
and actual, and, consequently, in the existence of
the necessary Being in whom essence includes exist-
ence or in whom possibility is sufficient to produce
actuality.

45. Therefore God alone (or the Necessary Being)
has this prerogative that if he be possible he must
necessarily exist, and, as nothing is able to prevent
the possibility of that which involves no bounds, no
negation, and consequently, no contradiction, this

MONADOLOGY. 261

alone is sufficient to establish a priori his existence.
We have, therefore, proved his existence through
the reality of eternal truths. But a little while ago
we also proved it a posteriori, because contingent
beings exist, which can have their ultimate and
sufficient reason only in the necessary being which,
in turn, has the reason for existence in itself.

46. Yet we must not think that the eternal truths
being dependent upon God are therefore arbitrary
and depend upon his will, as Descartes seems to have
held, and after him Monsieur Poiret. This is the
case only with contingent truths which depend upon
fitness or the choice of the greatest good; necessary
truths on the other hand depend solely upon his
understanding and are the inner objects of it.

47. God alone is the ultimate unity or the orig-
inal simple substance, of which all created or deriva-
tive Monads are the products, and arise, so to speak,
through the continual outflashings of the divinity
from moment to moment, limited by the receptivity
of the creature to whom limitation is an essential.

48. In God are present: Power, which is the
source of everything; Knowledge, which contains
the details of the ideas; and, finally, Will, which
produces or effects changes in accordance with the
principle of the greatest good. To these correspond
in the created Monad, the subject or the basis of the
faculty of perception and the faculty of appetition.
In God these attributes are absolutely infinite or
perfect, while in the created Monads or in the
entelechies (perfectihabies, as Hermolaus Barbarus
translates this word), they are imitations approach-
ing him in proportion to their perfection.

49. A created thing is said to act outwardly in

262 LEIBNIZ.

so far as it has perfection, and to suffer from another
in so far as it is imperfect. Thus action is attributed
to the Monad in so far as it has distinct perceptions,
and passion or passivity is attributed in so far as
it has confused perceptions.

50. One created thing is more perfect than
another when we find in the first that which gives
an a priori reason for what occurs in the second
This is why we say that one acts upon the other.

51. In the case of simple substances, the influence
which one Monad has upon another is only ideal.
It can have its effect only through the mediation of
God, in so far as in the Ideas of God each Monad
can rightly demand that God, in regulating the
others from the beginning of things, should have
regarded it also. For, since one created Monad
cannot have a physical influence upon ( the inner
being of another, it is only through this primal
regulation that one can have dependence upon
another.

52. It is thus that among created things action
and passion are reciprocal. For God, in comparing
two simple substances, finds in each one reasons
obliging him to adapt the other to it; and conse-
quently that which is active in certain respects is
passive from another point of view, — active in so far
as that which we distinctly know in it serves to give
a reason for that which occurs in another, and
passive in so far as the reason for what transpires in
it is found in that which is distinctly known in
another.

53. Now as there are an infinity of possible uni-
verses in the Ideas of God, and but one of them can
exist, there must be a sufficient reason for the

MONADOLOGY. 263

choice of God which determines him to select one
rather than another.

54. And this reason is to be found only in the fit-
ness or in the degree of perfection which these
worlds possess, each possible thing having the right
to claim existence in oroportion to the perfection
which it involves.

55. This is the cause for the existence of the
greatest good; namely, that the wisdom of God
permits him to know it, his goodness causes him to
choose it and his power enables him to produce it.

56. Now, this interconnection, relationship, or
this adaptation of all things to each particular one,
and of each one to all the rest, brings it about that
every simple substance has relations which express
all the others and that it is consequently a perpetual
living mirror of the universe.

57. And as the same city regarded from different
sides appears entirely different, and is, as it were,
multiplied perspectively, so, because of the infinite
number of simple substances, there are a similar
infinite number of universes which are, nevertheless,
only the aspects of a single one, as seen from the
special point of view of each Monad.

58. Through this means has been obtained the
greatest possible variety, together with the greatest
order that may be; that is to say, through this means
has been obtained the greatest possible perfection.

59. This hypothesis, moreover, which I venture
to call demonstrated, is the only one which fittingly
gives proper prominence to the greatness of God.
Monsieur Bayle recognized this when in his Dic-
tionary (article "Rorarius"), he raised objections to
it; indeed, he was inclined to believe that I attrib-

264 LEIBNIZ.

uted too much to God, and more than should be
attributed. But he was unable to bring forward
any reason why this universal harmony, which
causes every substance to express exactly all others,
through the relation which it has with them, is
impossible.

60. Besides, in what has just been said, can be
seen the a priori reasons why things cannot be
otherwise than they are. It is because God, in
ordering the whole, has had regard to every part
and in particular to each Monad whose nature it is
to represent. Therefore, nothing can limit it to
represent merely a part of the things. It is never-
theless true, that this representation is, as regards
the details of the whole universe, only a confused
representation, and is distinct only as regards a
small part of them, that is to say, as regards those
things which are nearest or most in relation to
each Monad. If the representation were distinct as
to the details of the entire universe, each Monad
would be a Deity. It is not in the object repre-
sented that the Monads are limited, but in the modi-
fications of their knowledge of the object. In a
confused way they reach out to infinity or to the
whole, but are limited and differentiated in the
degree of their distinct perceptions.

61. In this respect composites are like simple
substances. For all space is filled up; therefore,
all matter is connected; and in a plenum or filled
space every movement has an effect upon bodies in
proportion to their distance, so that not only is
every body affected by those which are in contact
with it, and responds in some way to whatever
happens to them, but also by means of them the

MONADOLOGV. 265

body responds to those bodies adjoining them, and
their intercommunication can be continued to any
distance at will. Consequently every body responds
to all that happens in the universe, so that he who
saw all, could read in each one what is happening
everywhere, and even what has happened and what
will happen. He can discover in the present what
is distant both as regards space and as regards
time; O-U/U-TTVOIO. iravra, as Hippocrates said. A soul
can, however, read in itself only what is there rep-
resented distinctly. It cannot all at once open up
all its folds, because they extend to infinity.

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 constitutes the entelechy. And as the body
expresses all the universe through the interconnec-
tion of all matter in the plenum, the soul also rep-
resents the whole universe in representing this body,
which belongs to it in a particular way.

63. The body belonging to a Monad, which is its
entelechy or soul, constitutes together with the
entelechy what may be called a living being, and
with a soul what is called an animal. Now, this
body of a living being or of an animal is always
organic, because every Monad is a mirror of the
universe according to its own fashion, and, since the
universe is regulated with perfect order, there must
needs be order also in the representative, that is to
say, in the perceptions of the soul and consequently
in the body through which the universe is repre-
sented in the soul.

64. Therefore, every organic body of a living
being is a kind of divine machine, or natural autom-

266 LEIBNIZ.

aton, infinitely surpassing all artificial automatons.
Because a machine constructed by man's skill is
not a machine in each of its parts; for instance, the
teeth of a brass wheel have parts or bits which to us
are not artificial products and contain nothing in
themselves to show the use to which the wheel was
destined in the machine. The machines of nature,
however, that is to say, living bodies, are still
machines in their smallest parts ad infinitum. Such
is the difference between nature and art, that is to
say, between Divine art and ours.

65. The author of nature has been able to employ
this divine and infinitely marvellous artifice, because
each portion of matter is not only, as the ancients
recognized, infinitely divisible, but also because it
is really divided without end, every part into other
parts, each one of which has its own proper motion.
Otherwise it would be impossible for each portion
of matter to express all the universe.

66. Whence we see that there is a world of created
things, of living beings, of animals, of entelechies,
of souls, in the minutest particle of matter.

67. Every portion of matter may be conceived as
like a garden full of plants, and like a pond full of
fish. But every branch of a plant, every member of
an animal, and every drop of the fluids within it, is
also such a garden or such a pond.

68. And although the ground and the air which
lies between the plants of the garden, and the water
which is between the fish in the pond, are not them-
selves plant or fish, yet they nevertheless contain
these, usually so small, however, as to be impercep-
tible to us.

69. There is, therefore, nothing uncultivated, or

MONADOLOGY. 267

sterile or dead in the universe, no chaos, no con-
fusion, save in appearance; somewhat as a pond
would appear at a distance when we could see in it
a confused movement, and so to speak, a swarming
of the fish, without, however, discerning the fish
themselves.

70. It is evident, then, that every living body has a
dominating entelechy, which in animals is the soul.
The parts, however, of this living body are full of
other living beings, plants and animals, which, in
turn, have each one its entelechy or dominating
soul.

71. This does not mean, as some who have mis-
understood my thought have imagined, that each
soul has a quantity or portion of matter appropriated
to it or attached to itself for ever, and that it conse-
quently owns other inferior living beings destined
to serve it always; because all bodies are in a state
of perpetual flux like rivers, and the parts are con-
tinually entering in and passing out.

72. The soul, therefore, changes its body only
gradually and by degrees, so that it is never
deprived all at once of all its organs. There is
frequently a metamorphosis in animals, but never
metempsychosis or a transmigration of souls. Neither
are there souls wholly separate from bodies, nor bodi-
less spirits. God alone is without body.

73. This is also why there is never absolute gener-
ation or perfect death in the strict sense, consisting
in the separation of the soul from the body. That
which we call generation is development and
growth, and that which we call death is envelop-
ment and diminution.

74. Philosophers have been much perplexed in

268 LEIBNIZ,

t

accounting for the origin of forms, entelechies, or
souls. To-day, however, when it has been learned
through careful investigations made in plant, insect,
and animal life, that the organic bodies of nature
are never the product of chaos or putrefaction, but
always come from seeds in which there was without
doubt some preformation, it has been decided that
not only is the organic body already present before
conception, but also that a soul, in a word, the ani-
mal itself, is also in this body; and it has been
decided that, by means of conception the animal is
disposed for a great transformation, so as to become
an animal of another species. We can see cases
somewhat similar outside of generation when grubs
become flies and caterpillars become butterflies.

75. These little animals, some of which, by con-
ception, become large animals, may be called sper-
matic. Those among them which remain in their
species, that is to say, the greater part, are born,
multiply, and are destroyed, like the larger animals.
There are only a few chosen ones which come out
upon a greater stage.

76. This, however, is only half the truth. I
believe, therefore, that if the animal never actually
commences in nature, no more does it by natural
means come to an end. Not only is there no gener-
ation, but also there is no entire destruction or abso-
lute death. These reasonings, carried on a
posteriori, and drawn from experience, accord
perfectly with the principles which I have above
deduced a priori.

77. Therefore, we may say, that not only the soul
(the mirror of an indestructible universe) is inde-
structible, but also the animal itself is, although its

MONADOLOGY. 269

mechanism is frequently destroyed in parts and
although it puts off and takes on organic coatings.

78. These principles have furnished me the means
of explaining on natural grounds the union, or,
rather the conformity between the soul and the
organic body. The soul follows its own laws, and
the body has its laws. They are fitted to each other
in virtue of the pre-established harmony between all
substances, since they are all representations of one
and the same universe.

79. Souls act in accordance with the laws of final
causes through their desires, purposes and means.
Bodies act in accordance with the laws of efficient
causes or of motion. The two realms, that of
efficient causes and that of final causes, are in har-
mony, each with the other.

80. Descartes saw that souls cannot at all impart
force to bodies, because there is always the same
quantity of force in matter. Yet, he thought that
the soul could change the direction of bodies. This
was, however, because at that . time the law of
nature, which affirms also the conservation of the
same total direction in the motion of matter, was
not known. If he had known that law, he would
have fallen upon my system of Pre-established Har-
mony.

81. According to this system bodies act as if (to
suppose the impossible) there were no souls at all,
and souls act as if there were no bodies, and yet both
body and soul act as if the one were influencing the
other.

82. Although I find that essentially the same
thing is true of all living things and animals, which
we have just said, namely, that animals and souls

370 LEIBNIZ.

begin from the very commencement of the world
and that they come to an end no more than does the
world, there is, as far as minds or rational souls are
concerned nevertheless, this thing peculiar, that their
little spermatic progenitors, as long as they remain
such, have only ordinary or sensuous souls, but those
of them which are, so to speak, elevated, attain by
actual conception to human nature, and their sen-
suous souls are raised to the rank of reason and to
the prerogative of minds.

83. Among the differences that there are between
ordinary souls and spirits, some of which I have
already instanced, there is also this that, while souls
in general are living mirrors or images of the uni-
verse of created things, minds are also images of the
Deity himself or of the author of nature. They
are capable of knowing the system of the universe,
and to imitate it somewhat by means of architec-
tonic patterns, each mind being like a small divinity
in its sphere.

84. Therefore, spirits are able to enter into a sort
of social relationship with God, and with respect to
them he is not only what an inventor is to his
machine (as is his relation to the other created
things), but he is also what a prince is to his sub-
jects, and even what a father is to his children.

85. Whence it is easy to conclude that the
totality of all the spirits must compose the city of
God, that is to say, the most perfect state that is
possible under the most perfect monarch.

86. This city of God, this truly universal mon-
archy, is a moral world within the natural world. It
is what is noblest and most divine among the works
of God. And in it consists in reality the glory of

MONADOLOGY. 271

God, because he would have no glory were not his
greatness and goodness known and wondered at by
spirits. It is also in relation to this divine city that
God properly has goodness. His wisdom and his
power are shown everywhere.

87. As we established above that there is a perfect
harmony between the two natural realms of efficient
and final causes, it will be in place here to point out
another harmony which appears between the phys-
ical realm of nature and the moral realm of grace,
that is to say, between God, considered as the
architect of the mechanism of the world and God
considered as the Monarch of the divine city of
spirits.

88. This harmony brings it about that things
progress of themselves toward grace along natural
lines, and that this earth, for example, must be
destroyed and restored by natural means at those
times when the proper government of spirits
demands it, for chastisement in the one case and
for a reward in the other.

89. We can say also that God, the Architect, satis-
fies in all respects God the Law-Giver, that there-
fore sins will bring their own penalty with them
through the order of nature, and because of the very
mechanical structure of things. And in the same
way the good actions will attain their rewards in
mechanical ways through their relation to bodies,
although this cannot, and ought not, always to take
place without delay.

90. Finally, under this perfect government, there
will be no good action unrewarded and no evil
action unpunished; everything should turn out for
the well-being of the good; that is to say, of those

272 LEIBNIZ.

who are not disaffected in this great state, who,
after having done their duty, trust in Providence
and who love and imitate, as is meet, the Author of
all Good, delighting in the contemplation of his
perfections according to the nature of that genuine,
pure love which finds pleasure in the happiness of
those who are loved. It is for this reason that wise
and virtuous persons work in behalf of everything
which seems conformable to the presumptive or
antecedent will, and are, nevertheless, content with
what God actually brings to pass through his secret,
consequent and determining will, recognizing that
if we were able to understand sufficiently well the
order of the universe, we should find that it goes
beyond all the desires of the wisest of us, and that
it is impossible to have it better than it is, not only
for all in general, but also for each one of us in par-
ticular, provided that we cleave as we should to the
Author of all. For he is not only the Architect and
the efficient cause of our being, but he is also our
Lord and the Final Cause, who ought to be the
whole goal of our will, and who, alone, can make
our happiness.

INDEX.

Abraham, 208, 230.

Action and passion, 262.

Activity and passivity, 13 et seq.

Acts, reflective, 257.

Adam, concept of, 73 et seq., go et
seq., 108 et seq., 120 et seq., 238.

Aggregation, 197.

Agreement. See Concomitance and
Freest abliihed Harmony,

Albertus Magnus, 159, 219.

Alexander the Great, 13, 238.

Analysis, 140.

Animals, souls of, 224, 265 ; transfor-
mation of, 207 et seq., 268.

Apperception, 253.

Appetition, 254.

Archimedes, 107, 170, 216.

Aristotle, xi, 45.

Arnauld, x, et seq., xix ; letters to
Count Ernst von Hessen-Rheinfels,
72-74,100-103,209-210; to Leibnitz,
88-100, 142-149, 172-180, 203-209 ;
Leibnitz to, 119-136, 136-142, 149-
157, 157-168, 180-199, 201-203, 211-
237, 239-242, 242-248.

Atoms, xiv et seq,, 221, 251 et seq.

Attributes, 252.

Automatons, 255, 265.

Averroes, 220.

Axioms, 258.

Bacon, John, 219.

Bayle, 254, 263.

Beauty, principles of, 4 et seq.

Being, a, 17, 191.

Berkeley, xv.

Biel, Gabriel, 219.

Body, xviii et seq., 145 et seq., 244;

and soul, relation between the, 56;

153, 159. 171, 244-
Boineburg, viii.

Bouillier, v.

Brunswick, history of, 139, 236, 242.

Caesar, Julius, concept of, 20 et seq.

Calculating machine, 149.

Calculus of increments, 248

Calculus, universal, 241.

Canons, practical, 258.

Catelan, Abbe, 168, 180, 199, 201, 209,
235 et seq., 239 et seq.

Catholic Church, 74, 200, 210.

Causal, definition of, 41 et seq.

Causes, model, 151 ; efficient, 37, 173;
occasional, 173, 182 et seq., 203, 214;
final, 33 et seq., 272 ; metaphysical
136.

Characteristic, general, 241.

Charity, 245.

Charlemagne, 86.

Christ, Jesus, 62 et seq., 72.

Cicati, 102, 103.

City of God, 60.

Clarke, ix.

Composites, 251 et seq., 264.

Concept, individual, 89, 95 et seq.,
103 et seq.

Conceptions, 45 et seq.

Concomitance or the agreement of
substances, 134, 149 et seq., 152 et
seq., 187. See Prelstablished Har-
mony.

Consciousness, 253.

Contingent truths, 117.

Continuum, 156, 162.

Contradiction, principle of, 141.

Contradictions, 258.

Cordemoy, 163, 190, 205, 221.

Corporeal substance, 163.

Correspondency, laws of, 215. (See
Preestablished Harmony.}

Created thing, 261.

274

INDEX.

Darius, 14.

Death, 155.

Definition, 42 et seq., 258.

Democritus, x, xiii, 196.

Descartes, his philosophy, v et seq.,

29, 31, 139 et seq., 148, 152, 167 et

seq., 186, 202, 212, 219, 237, 240 et

seq., 261, 269.
De Sluse, 139.
Diamonds of the Grand Duke and

the Great Mogul, 190.
Du Cange, 242.
Duke Ernst-Augustus, ix.
Duncan, G. M., ix.
Durandus, 88.
Duton, ix.

Efficient causes, 37, 173.
Ego, xviii, 58, 179.
Election, 52.
Emperor Henry II., 139.
Entelechies, 253, 254, 266.
Epicurus, xi, xiii, 190.
Equations, 140.
Erdmann, ix.

Essences, particular, their expres-
sion includes everything, 27 et seq.
Essential, definition of, 41 et seq.
Este, House of, 242.
Euclid, 141.
Euler, xvi, xviii.

Express, the word, 203, 211 et seq.
Extension, x, 18, 155, 192.

Fact, 258.

Faith, 52.

Fermat, 39.

Fichte, xv.

Final causes, 33 et seq.

Force, God always preserves the

same amount of, 29 et seq.
Force, measure of, 29 et seq., 148 et

seq., 164 et seq., 246.

Form, 192.

, 15 et seq., 146

, .

Forms, substantial, v, 15
et seq., 174, 204.

Galileo, 31, 170.
Gassendi, vii, xiii.
Geomancy, 10.
Geometry, 36, 140.

Gerhardt, ix.

God, xv et seq.; conception of, 3 et
seq.; substances like a mirror of,
15 ; produces different correspond-
ing substances, 23 et seq.; always
preserves the same amount of
force, 29 et seq. ; acts upon spirits,
39; only immediate object of our
perceptions, 46 et seq.; action of,
upon the human will, 48 et seq.;
grace of, 51 et seq.; all substances
depend upon, 54 ; spirits express,
59; city of, 60, 270; his love, 62; his
freedom, 77 et seq.; his knowledge,
96; resolutions of, inter-connection
among the, 104 et seq., 131 ; free
decrees of, 122, 131 ; his perfection,
234 ; absolutely perfect, 259 ; the
Necessary Being, 260; the Final
Cause, 272.

Goodness, principles of, 4 et seq.

Grace of God, 51 et seq.

Grotefend, ix.

Guhrauer, ix, x.

Harmonic motion, 247.

Heliodorus of Larissa, 39.

Hermolaus Barbarus, 261.

Hessen-Rheinfels, Leibnitz to Count
Ernst von, 67-72, 74-82, 82-88, 169-
172, 199-201, 237-238; Arnauld to
Count Ernst von, 72-74, 100-103, 209
-210; to Leibnitz, Count Ernst von,
149, 210-211.

Hippocrates, 265.

Hudde, 139.

Huygens, 199, 239 et seq.

Idea, contemplation of the, 43 et seq.
Ideas, we think by means of, 48.
Immortality, 55, 57.
Increments, calculus of, 248.
Individual concept, 19, 89, 95 et seq.,

103 et seq., 149 et seq.
Individual substance, concept of our,

49, 149, 163.
Individual substance expresses the

whole universe, every, 133 et seq.
Isaac, 93, 230.
Isochronous curve, 239.

INDEX.

275

Janet, Paul, ix.
Jesuits, 87.

Jesus Christ, 62 et seq., 72.
Jobert, Father, 102.
Judas, 48 et seq.
Jurieu, 209.

Jurisprudence, 138, 242.
Justel, 242.
Justice, 245.

Kant, xvii.

Kepler, 247.

Knowledge, 170, 261 ; clear and ob-
-scure, distinct and confused, ade-
quate and inadequate, intuitive and
assumed, 41 et seq.

Lagrange, L. P., v.

Langley, ix.

I.atta, ix.

Leeuwenhoeck, 155, 227.

Leibnitz, his philosophy, Janet on,
v-xxi ; letters to Count Ernst von
Hessen-Rheinfels, 67-72, 74-82, 82-
88, 169-172, 199-201, 237-238; Ar-
nanld to, 88-100, 142-149, 172-180,
203-209 ; his remarks upon a letter
of Arnauld, 103-119; to Arnauld,
119-136, 136-142, 149-157, 157-168,
180-199, 201-203, 211-237, 239-242,
242-248 ; Count Ernst von Hessen-
Rheinfels to, 149, 210-211.

Louys de Dole, Father, 88.

Luther, 101.

Machine, 156, 177, 191 ; divine, 265.
Maim burg, 86.
Maine de Biran, zxi.
Malebranche, vi, xi, 83, 142, 201 et

seq., 241.
Malpighi, 226.
Mass, 29.

Materialistic philosophers, 36.
Matter, 214 ; extension of, 32 et seq.;

phenomena of, 32 et seq.
Me, the (See Ego).
Mechanicalism, viii, 136.
Mechanics, 141.
Mciancthon, loi.
Melissus, 218.
Memory, 57, 256.

Metaphysical causes, 136.

Metaphysics, summary of the dis-
course on, 68.

Mind, 257.

Miracles, n, 184.

Moliere, vi.

Monadology, 251-272.

Monads, x, xii et seq., 251 etseq.

Morus, 219.

Moses, 177.

Motion, xiv, 192; quantity of, 29 et
seq., 164 et seq.; laws of, 167, 202,
236; perpetual, 167; harmonic, 247;
planetary, laws of, 247.

Nainur, Bishop of, 10.

Necessary truths, 23, 170, 257.

Nerves, 181.

Newton, xvi.

Nicole, vi, 209.

Nominal, definition of, 41 et seq.

Occasional causes, 153, 173, 182 et

seq., 203, 214.
Order, 10 et seq.

Parmenides, 218, 223.
Pascal, 148, 242.
Passion, action and, 262.
Passivity and activity, 13 et seq.
Perception, 253, 254.
Perfection, divine, 3 et seq.
Perpetual motion, 166.
Phcfdo, 35.
Philoponus, 219.
Philosophers, materialistic, 36.
Planetary motion, laws of, 247.
Plato, 35 et seq., 44 et seq., 70 et seq.,

161, 218, 220, 223; his doctrine of

reminiscence, 44.
Plenum, 264.
Poiret, 261.
Porus, 14.
Postulates, 258.
Power, 261.

Predicate, subject and, 126.
Predication, 13.
Pre-established, harmony, xiii, 32 et

seq., 134 et seq., 143 et seq., 149 et

seq., 157 et seq , 172 et seq., 185,

187, 215, 263, 269 et seq.

276

INDEX.

Preformation, 268.

Problems, transcendental, 139 et seq.,

248.
Proclus, 219.

Qualities, occult, vii.
Quantity of directions, 187.

Rational soul, 257.

Real, definition of, 41 et seq.

Reasoning, 258.

Reason, principle of sufficient, 258.

Reflective acts, 257.

Refraction, laws of, 38.

Regulations, subordinate, n.

Reminiscence, Plato's doctrine of, 44.

RfSmond de Montmort, ix.

Republic of the Universe, 245.

Republic, universal, 195.

Roman Catholic Church, 200.

Saint Augustine, 51, 74, 89, 102, 144,
153. 158, 175 et seq., 220.

St. Cunigunde, 139.

St. Gregory the Great, 86.

St. Paul, 53 et seq.

St. Thomas, 14, 18, in, 129, 155, 159,
238.

Samson, 93.

> aniuel, 93.

Scholastic philosophers, 17.

Schulemburg, ix.

Sin, 51.

Snellius, 38, 39.

Socinians, 84 et seq.

Socrates, 35, 70.

Soul, xviii et seq., 55, 145 et seq., 149,
267 ; union of, with the body, 56,
153. 159. 171. 2441 rational, 257; ani-
mal, 265 ; the mirror of an inde-
structible universe, 268 ; compared
to blank tablets, 45 et seq.; indivis-
ible and indestructible, 155; have
brutes — ? 175 et seq.; great number
of, 194 ; transmigration of, 207 et
seq.

Speculative theorems, 258.

Sphere, concept of the, 116.

Spinoza, xiii, xvii, 241.

Spirits, 270; and other substances,
difference between, 57; and souls

or substantial forms, difference be-
tween, 57 ; excellence of, 59 ; ex-
press God, 59 ; how God acts upon,
39-

Spiritual substance, 176.

Subject and predicate, 126.

Substance, individual, 12 et seq., 49,
112, 124, 162 ; like a mirror of God,
15 ; action of one upon another, 26
et seq.; corporeal, 163; spiritual,
176 ; each expresses the whole uni-
verse, 233 et seq., 263.

Substances, x et seq., 244 ; nature of,
23etseq.; immaterial, 39; possible,
129 et seq. ; concomitance and agree-
ment of, 134 et seq., 143 et seq., 157;
simple, 251.

Substantial form, 174.

Sufficient reason, principle of, 258.

Swammerdam, 228.

Tangents, 248 ; method of, 139; rule

of, 240.

Theologians, 17.
Theorems, speculative, 258.
Things, adaptation of all, 263.
Thomists, 87.
Thought, 169.
Toletus, vi.
Transcendental problems, 139 et seq.,

248.

Transcendentals, 240.
Transformation, 160, 219, 228.
Transmigration, 160, 219, 228.
Truths, necessary, 257, 260 et seq;

two kinds of, 258; eternal, 260 et

seq.; contingent, 261.

Unity, substantial, 175, 189, igi et

seq., 204, 220 et seq.
Universe, Republic of the, 245.
Universes, infinity of possible, 262.

Vacuum, xv et seq.
Varillasi 86.
Virtus dorntitiva, vi.
Vortexes, 246.

Will, 261 ; action of God upon the

human, 48 et seq.
Wisdom, 246.

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