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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 


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. 


August 20, 1902. 




LEIPZIG ; Frontispiece 






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. 



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." 


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 


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 

* 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 


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. 


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 


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). 


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;. 


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 


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 

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 

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


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 


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 

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 


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 


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

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, 

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 


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 


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 


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 

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. 



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- 



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 


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 


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 

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 


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 

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 


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 


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 

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. 


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 


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 


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- 


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 


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 


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- 

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 


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 


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 

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. 


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 


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 

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 


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 


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 


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 


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 


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 


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. 


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 


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- 

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 


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 


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 

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. 


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 

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- 

( } 


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 


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 


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 


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 


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 


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. 


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 


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 


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 


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 


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 


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 


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 

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. 


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 


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 


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 

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 


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. 


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 


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 


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- 


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- 


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 


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 


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. 

* 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- 


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. 


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 


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- 


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. 


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 


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. 


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 


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 


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. 





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. 



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. 


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 

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- 


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 


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 

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- 


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- 


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- 

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. 


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 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- 

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, 


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." 

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. 


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. 


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 


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 


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 


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 


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- 


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 


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. 

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 


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 


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 


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. 


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 


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. 

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- 

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. 


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." 


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 


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- 


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 

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 


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 


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 

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 


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- 


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, 


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. 


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 


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 


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, 


"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 


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., 


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 


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 

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- 


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 

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 


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. 


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 


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, 


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 


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 


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 


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 


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 


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 


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 

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 


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- 


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 


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 


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, 


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 

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 


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 


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 


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. 

Leibniz to Arnauld. 

Hanover, July 14, 1686. 

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


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 


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 


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 


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 


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, 


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, 


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 

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, 


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 


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 

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 


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 


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 


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. 


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 


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 


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 


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 


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, 


Leibniz to Arnauld. 

Hanover, July 14, 1686. 

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 


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 


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- 


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 


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 


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 

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 


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- 

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, 


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. 


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 

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 


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. 


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 

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 


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

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 


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, 


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. 


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, 


Count Ernst von Hessen-Rheinfels to Leibniz. 

Rheinfels, 21/31, Oct., 1686. 

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, 



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, 


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 


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. 


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 


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 


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 


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 

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 


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 

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 

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 


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. 


Leibniz to Arnauld. 

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

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 


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

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 


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 


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 


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- 


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 


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 


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 

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- 


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 


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 


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 

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 


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 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 


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- 


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 


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. 


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 


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 


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 

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. 


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- 

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 


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 


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- 


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 

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 


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 


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. 

Leibniz to Arnauld. 

Gottingen, April 30, 1687. 

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


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 


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- 


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 


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 


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 


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 


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- 


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 


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- 


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- 


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- 


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 


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 


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 

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 


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- 

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 


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 


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 



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 


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. 


Leibniz to Count Ernst von Hessen-Rheinfels. 

April 30, 1687. 


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 


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 


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. 


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 


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., 



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 


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 

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 


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." 


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. 


(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 


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- 


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. 


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 


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


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 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 


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- 


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- 


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), 


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 


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 


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, 


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 


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 


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 

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 


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, 


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 


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 


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, 


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- 

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 


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- 

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, 


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- 


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, 


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- 


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- 


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 


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. 


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 


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- 


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. 


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 


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. 


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 


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 to Arnauld. 

January 14, 1688. 

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 


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 


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 


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. 

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 


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 


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 

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- 

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 

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 


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 

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 

Charity is universal benevolence whose fulfillment 


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 

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 


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 


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 

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. 



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 

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 



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 


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 


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 (xw<ri TO vrXes). There 


is in them a sufficiency (avropia) 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 


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 


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 

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. 


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- 

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

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 


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 

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 

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- 

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


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 

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 


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 


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 

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 

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 


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- 


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 

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 


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- 


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 


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 

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 

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 



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 


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- 

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 

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 


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 


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 

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 


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. 


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 

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- 

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. 



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. 



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. 



Preformation, 268. 

Problems, transcendental, 139 et seq., 

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, 

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 

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, 

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., 


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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