## 1. Life




Leibniz was born in Leipzig on July 1, 1646, two years prior to the
end of the Thirty Years War, which had ravaged central Europe. His
family was Lutheran and belonged to the educated elite on both sides:
his father, Friedrich Leibniz, was a jurist and professor of Moral
Philosophy at the University of Leipzig, and his mother, Catharina
Schmuck, the daughter of a professor of Law. Leibniz's father
died in 1652, and his subsequent education was directed by his mother,
uncle, and according to his own reports, himself. He was given access
to his father's extensive library at a young age and proceeded to
pore over its contents, particularly the volumes of ancient history and
the Church Fathers.




In 1661 Leibniz began his formal university education at the
University of Leipzig. As the "modern" philosophy of
Descartes, Galileo, Gassendi, Hobbes and others had not made a great
impact by this time in the German-speaking lands, Leibniz's
philosophical education was chiefly Scholastic in its nature, though
he was also exposed to elements of Renaissance humanism. While in
Leipzig, Leibniz met Jacob Thomasius, who would have an important
influence on Leibniz and who supervised Leibniz's first philosophical
treatise *On the Principle of Individuation* (*De principio
individui*). It was Thomasius more than anyone else perhaps who
instilled in Leibniz a great respect for ancient and medieval
philosophy. Indeed, one of the leitmotifs of Leibniz's philosophical
career is his desire to reconcile the modern philosophy with the
philosophy of Aristotle, Plato, the Scholastics and the Renaissance
humanist tradition. After receiving his baccalaureate from Leipzig, he
continued his studies at the University of Altdorf. While there
Leibniz published in 1666 the remarkably original *Dissertation on
the Art of Combinations* (*Dissertatio de arte
combinatoria*), a work that sketched a plan for a "universal
characteristic" and logical calculus, a subject that would
occupy him for much of the rest of his life. Although Leibniz was
offered a position on the faculty of Law upon the completion of his
Doctorate of Law in 1667, he had a different future in mind.




In that year, Leibniz met Baron Johann Christian von Boineburg,
a Protestant convert to Catholicism, who was able to secure a position
for Leibniz with the Elector of Mainz. While in the court of the
Elector, Leibniz composed a series of works in philosophical theology,
the *Catholic Demonstrations*, which are another manifestation
of Leibniz's lifelong irenicism: in this case, in their attempt
to provide a basis and justification for the reconciliation of
Protestantism and Catholicism. Leibniz also turned his mind to natural
philosophy, having finally been able to study some of the works of the
moderns; the result was a two-part treatise in 1671, the *New
Physical Hypothesis* (*Hypothesis physica nova*). The first
part, the *Theory of Abstract Motion* (*Theoria motus
abstracti*), was dedicated to the Academie des Sciences de
Paris, and the second part, the *Theory of Concrete Motion*
(*Theoria motus concreti*), was dedicated to the Royal Society
in London. These works, however, were not likely to impress their
audiences, for, given his circumstances, Leibniz could not but produce
amateurish works in the field.




This changed, however, in 1672, when Leibniz was given the single
most important opportunity of his life: the Elector of Mainz sent him
on a diplomatic mission to Paris, the center of learning and science at
the time. Leibniz was able to stay in Paris for four years (with a
brief trip to London in 1673), during which time he met many of the
 major figures of the intellectual world, among them 
 Antoine Arnauld,
 Nicholas Malebranche, 
 and,
 most important, the Dutch mathematician and physicist, 
 Christiaan Huygens. 
 It was he, "the great Huygenius" (as John Locke would
call him in the Dedicatory Epistle to his *Essay Concerning Human
Understanding*), who took Leibniz under his wing and tutored him
in the developments in philosophy, physics, and mathematics. Not only
was Leibniz able to converse with some of the greatest minds of the
seventeenth century while in Paris, he was also given access to the
unpublished manuscripts of Descartes and Pascal. And, according to
Leibniz, it was while reading the mathematical manuscripts of Pascal
that he began to conceive what would eventually become his
differential calculus and his work on infinite series. In this time,
Leibniz also designed a calculating machine able to perform addition,
subtraction, multiplication, and division (see the Other Internet
Resources for a picture). And his trip to London in 1673 was meant in
part to present his designs to the Royal Society.




While Leibniz was living the life of the mind in Paris, his employer
died, and Leibniz was thus forced to look for another position. He
eventually found one as the librarian for Duke Johann Friedrich of
Brunswick, who ruled in Hanover. On the way to Hanover, Leibniz stopped
in Amsterdam to meet with Spinoza between November 18 and
21, 1676, three months before the latter's death;
according to Leibniz's own notes, they spoke of Spinoza's
yet-to-be-published *Ethics*, Cartesian physics, and
Leibniz's improved version of the ontological argument (see
below). Although Leibniz would travel to Italy for a time in the late
1680s in order to conduct historical research for the House of Hanover
and make many shorter trips (including to Vienna), the rest of his life
was essentially spent in Hanover and its environs, working in different
capacities for the court, first, for Johann Friedrich until his death
in 1680, then for Johann Friedrich's brother, Ernst August (from
1680 to 1698), and finally for the latter's son, Georg Ludwig,
who in 1714 would become George I of England. Leibniz's relations
with Ernst August and Georg Ludwig were not as amicable as his
relations with his original employer, but he was close to Sophie, the
wife of Ernst August and youngest sister of Princess Elisabeth of
Bohemia, with whom Descartes had an important philosophical
correspondence. (Sophie was also the daughter of Elizabeth Stuart, and
it is for this reason that her son became King of England.)




While Leibniz may have felt physically isolated from the
intellectual scene of Europe, he did manage to stay connected through a
vast network of correspondents. (Leibniz exchanged letters with over
1100 different people in the course of his life.) Despite the great
demands placed on Leibniz as librarian, then historian, and Privy
Councillor at the court of Hanover, he was able to complete work that,
in its breadth, depth, and sheer quantity, is staggering.




Leibniz's final years were bleak. He was engaged in a
vituperative debate with Newton and his followers over the priority of
the discovery of the calculus, even being accused of stealing
Newton's ideas. (Most historians of mathematics now claim that
Newton and Leibniz developed their ideas independently: Newton
developing the ideas first with Leibniz the first to publish.) And at
the court he was mocked for his wig and old-fashioned clothing (think
1670s Paris!). When Georg became George, the acrimony surrounding
Leibniz in England was so great that Leibniz was asked to remain in
Hanover rather than follow his employer to London. Leibniz died
November 14, 1716.


### 1.1 Chronology of Major Writings




|  |  |
| --- | --- |
| 1684 | *Meditations on Knowledge, Truth, and Ideas* |
| 1686 | *Discourse on Metaphysics* |
| 1686f | Correspondence with Arnauld |
| 1689 | *Primary Truths* |
| 1695 | *New System* |
| 1695 | *Specimen Dynamicum* |
| 1697 | *On the Ultimate Origination of Things* |
| 1698 | *On Nature Itself* |
| 1699f | Correspondence with De Volder |
| 1704 | *New Essays on Human Understanding* |
| 1706f | Correspondence with Des Bosses |
| 1710 | *Theodicy* |
| 1714 | *Monadology* |
| 1714 | *Principles of Nature and Grace* |
| 1715f | Correspondence with Clarke |


## 2. Overview of Leibniz's Philosophy




Unlike most of the great philosophers of the period, Leibniz did not
write a *magnum opus*; there is no single work that can be said
to contain the core of his thought. While he did produce two books, the
*Theodicy* (1710) and the *New Essays Concerning Human
Understanding* (finished in 1704 but not published until 1765), the
student of Leibniz's thought must piece together Leibniz's
philosophy from his myriad writings: essays published in scholarly
journals and in more popular journals; unpublished works left abandoned
by their author; and his many letters. Moreover, many of
Leibniz's writings have not yet been published. The authoritative
scholarly version of Leibniz's works, the Akademie edition, has
thus far only published his philosophical writings from 1663 to 1690;
in other words, only *half* of his writing life has been
covered. And the mere act of dating pieces often depends upon careful
analysis of the paper Leibniz wrote on and watermarks and so on.
(Hence, for example, the important short work, *Primary Truths*,
which, because of its content, was often thought to date to 1686 (as in
AG), has recently been redated by the Akademie editors to 1689 because
of a watermark.) Piecing together Leibniz's philosophy into a
systematic whole is made more difficult because Leibniz seems to have
changed or at least refined his views on a number of issues over the
course of his career and because he was always very aware (some might
say too aware) of the audience for any of his writings.




As stated above, Leibniz's intellectual training was squarely
in the tradition of Scholasticism and Renaissance humanism; his
background, then, was of Aristotelianism, Platonism, and orthodox
Christianity. Yet, as he became more familiar with the modern
philosophy of the seventeenth century, he came to see many of its
virtues. Although there is some reason to be skeptical of the details,
the spirit of the self-portrait Leibniz paints to Nicolas Remond in
1714 can be a helpful guide for approaching his work. He writes:



> 
> 
> ...I have tried to uncover and unite the truth buried and
> scattered under the opinions of all the different philosophical sects,
> and I believe I have added something of my own which takes a few steps
> forward. The circumstances under which my studies proceeded from my
> earliest youth have given me some facility in this. I discovered
> Aristotle as a lad, and even the Scholastics did not repel me; even now
> I do not regret this. But then Plato too, and Plotinus, gave me some
> satisfaction, not to mention other ancient thinkers whom I consulted
> later. After finishing the trivial schools, I fell upon the moderns,
> and I recall walking in a grove on the outskirts of Leipzig called the
> Rosental, at the age of fifteen, and deliberating whether to preserve
> substantial forms or not. Mechanism finally prevailed and led me to
> apply myself to mathematics.... But when I looked for the ultimate
> reasons for mechanism, and even for the laws of motion, I was greatly
> surprised to see that they could not be found in mathematics but that I
> should have to return to metaphysics. This led me back to entelechies,
> and from the material to the formal, and at last brought me to
> understand, after many corrections and forward steps in my thinking,
> that monads or simple substances are the only true substances and that
> material things are only phenomena, though well founded and well
> connected. Of this, Plato, and even the later Academics and the
> skeptics too, had caught some glimpses... I flatter myself to have
> penetrated into the harmony of these different realms and to have seen
> that both sides are right provided that they do not clash with each
> other; that everything in nature happens mechanically and at the same
> time metaphysically but that the source of mechanics is metaphysics. (G
> III 606/L 654-55)




Again, there is some reason to doubt whether Leibniz was really
fifteen when he made his philosophical perambulations and whether and
to what extent he had actually read any of the moderns. Nevertheless,
this self-portrait does express something that one sees in
Leibniz's writings: the weaving together of varying strands of
ancient and modern philosophy in a remarkably creative and
sophisticated manner.




The letter to Remond makes clear that Leibniz had reservations about
certain aspects of the modern philosophy, qualms that arose from and
led him back to this eclectic mix of Aristotle and Christian Platonism.
It is probably most helpful, then, to see Leibniz's philosophy as
a reaction to two sets of modern opponents: on the one hand, Descartes
and his followers; on the other hand, Hobbes and Spinoza.




Leibniz's critique of Descartes and his followers was focused
principally on the Cartesian account of body or corporeal substance.
According to Descartes, the essence of body is extension; that is, a
corporeal substance is simply a geometric object made concrete, an
object that has size and shape and is in motion. This view, indeed, is
the cornerstone of the new mechanical philosophy to which Leibniz was
originally attracted. Nevertheless, Leibniz came to see two distinct
problems with this view. First, in claiming that the essence of body is
extension, Descartes is endorsing the view that matter is infinitely
divisible. But if matter is infinitely divisible, then one can never
arrive at the simple unities that must exist at some ontological ground
level. Second, if matter is simply extension, then there is in its
nature no source of activity. If this is so, Leibniz thought, then the
bodily objects of the world cannot count as substances.




Hobbes and Spinoza, despite their own differences, advanced, or were
read as advancing, a number of objectionable and deeply troubling
theses which Leibniz (and most of his contemporaries) saw as an
enormous threat: materialism, atheism, and necessitarianism. It is
Leibniz's response to Hobbesian and Spinozistic necessitarianism
that is perhaps of greatest interest, for he sought to develop an
account of action and contingency that would preserve divine and human
freedom. As will be shown, central to Leibniz's philosophy was
the view that God freely chose the best world from an infinite number
of possible worlds and that a person could be said to act freely when
the contrary of that action does not imply a contradiction. (This topic
will be addressed principally in the article on Leibniz's Modal
Metaphysics.)


## 3. Some Fundamental Principles of Leibniz's Philosophy




Leibniz asserts in the *Monadology* SSSS31-32,
"Our reasonings are based on *two great principles, that of
contradiction...* [and] *that of sufficient
reason*" (G II 612/AG 217). To these two great principles
could be added four more: *the Principle of the Best*, *the
Predicate-in-Notion Principle*, *the Principle of the Identity
of Indiscernibles*, and *the Principle of Continuity*. The
relation among these principles is more complicated than one might
expect. Leibniz sometimes suggests that the Principle of the Best and
the Predicate-in-Notion Principle can be said to ground his "two
great principles"; at other times, however, all four principles
seem to work together in a system of circular implication. And while
the Principle of the Identity of Indiscernibles is often presented in
contemporary discussions in analytic metaphysics as a stand-alone axiom,
Leibniz tells us that it follows from the two great principles.
Finally, the Principle or Law of Continuity is actually a principle
that Leibniz takes from his work in mathematics and applies to the
infinite hierarchy of monads in the world and to the quality of their
perceptions; it appears to derive only tenuous support from the
Principle of Sufficient Reason.


### 3.1 The Principle of the Best




Leibniz presented a number of arguments for the existence of God,
which represent great contributions to philosophical theology and
which will be discussed below. But one of the most basic principles of
his system is that God always acts for the best. While this is
generally treated as an axiom, the opening of the *Discourse on
Metaphysics* does present something of an argument for it:
"God is an absolutely perfect being"; "power and
knowledge are perfections, and, insofar as they belong to God, they do
not have limits"; "Whence it follows that God, possessing
supreme and infinite wisdom, acts in the most perfect manner, not only
metaphysically, but also morally speaking..." (AG 35) This
might not appear a surprising claim from a theist, but it is not
obvious that God must always act for the best or even create the best
world. (See Adams 1972) And Leibniz sometimes implicitly, sometimes
explicitly, appeals to this principle in his metaphysics, most notably
when he is also employing the Principle of Sufficient Reason. Indeed,
when it comes to the creation of the world, the "sufficient
reason" for God's choice of this world is that this world is the
"best" of all possible worlds; in other words, in this
case the Principle of Sufficient Reason is essentially the Principle
of the Best. 


### 3.2 Predicate-in-Notion Principle (PIN)




Leibniz has a very distinctive notion of truth, one which underlies
much of his metaphysics. But this notion of truth goes back to
Aristotle's *Organon* (cf. *Posterior Analytics* I.4),
as Leibniz himself says, and it is also present in Arnauld and
Nicole's *Logic, or the Art of Thinking* (Book IV, Chapter 6).
As Leibniz puts it in a letter to Arnauld, "in every true
affirmative proposition, whether necessary or contingent, universal or
particular, the notion of the predicate is in some way included in
that of the subject. *Praedicatum inest subjecto;* otherwise I
do not know what truth is" (G II 56/L 337). As he tells us in
the *Primary Truths* and the *Discourse on Metaphysics*,
many things follow from the Predicate-in-Notion Principle (PIN),
including what he believes to be the correct analysis of necessity and
contingency.


### 3.3 Principle of Contradiction (PC)




Leibniz also follows Aristotle (cf. *Metaphysics* IV.3), in
placing great emphasis on the Principle of Identity or the Principle of
Contradiction (PC). PC states simply that "a proposition cannot
be true and false at the same time, and that therefore 
*A* is *A* and cannot be not *A*" 
(G VI 355/AG 321). According to Leibniz, the
primary truths of his metaphysical system are identities, but, in a
striking move, he combines PC with PIN and asserts in *Primary
Truths* that "all remaining truths are reduced to primary
truths with the help of definitions, that is, through the resolution of
notions" (A VI iv 1644/AG 31). Furthermore, the combination of PC
and PIN will mean that, since in any true proposition the predicate is
contained explicitly or implicitly within the subject, this is so for
*all* affirmative truths, whether they be universal or
particular, necessary or contingent. Leibniz will use this seemingly
innocuous principle to draw profoundly strong metaphysical conclusions
about the nature of substance and modality.


### 3.4 Principle of Sufficient Reason (PSR)




The Principle of Sufficient Reason (PSR) in its classic form is
simply that *nothing is without a reason* (*nihil est sine
ratione*) or *there is no effect without a cause*. As
Leibniz remarks, this principle "must be considered one of the
greatest and most fruitful of all human knowledge, for upon it is built
a great part of metaphysics, physics, and moral science" (G VII
301/L 227). In the *Principles of Nature and Grace*, Leibniz
suggests that the claim that nothing takes place without a sufficient
reason means that nothing happens in such a way that it is impossible
for someone with enough information to give a reason why it is so and
not otherwise. In the *Monadology* and elsewhere, however,
Leibniz frankly admits that "most of the time these reasons
cannot be known to us" (G VI 612/AG 217). While the idea that
every event must have a cause and that there is a reason why everything
is so and not otherwise again might not seem novel, it is the
connection that Leibniz sees between this principle and his other
metaphysical principles that is noteworthy. According to Leibniz, PSR
must actually follow from PIN, for if there were a truth that had no
reason, then there would be a proposition whose subject did not contain
the predicate, which is a violation of Leibniz's conception of
truth.


### 3.5 Principle of the Identity of Indiscernibles (PII)




PC and PSR may seem innocent enough, but Leibniz's other
well-known principle, the Principle of the Identity of Indiscernibles
(PII), is more controversial. (See also the entry on 
identity of indiscernibles.) 
In one of Leibniz's typical
formulations, PII states that "it is not true that two substances
can resemble each other completely and differ only in number [*solo
numero*]" (A VI, iv, 1541/AG 42). In other words, if two things
share all properties, they are identical, or 
([?]*F*)(*F**x* -
*F**y*) - *x* = *y*. 
What is particularly important to note,
however, is that Leibniz is adamant that certain kinds of properties
are *excluded* from the list of properties that could count as
difference-making properties, chief among these *spatio-temporal
properties*. This is what Leibniz means (in part) when he asserts that there
can be no purely extrinsic (i.e., relational) determinations.
Therefore, it is not the case that there could be two chunks of matter
that are qualitatively identical but existing in different locations.
In Leibniz's view, any such extrinsic difference must be founded
on an intrinsic difference. As he puts it in the 
*New Essays*,



> 
> 
> although time and place (i.e., the relations to what lies outside) do
> distinguish for us things which we could not easily tell apart by
> reference to themselves alone, things are nevertheless distinguishable
> in themselves. Thus, although diversity in things is accompanied by
> diversity of time or place, time and place do not constitute the core
> of identity and diversity, because they [sc. different times and
> places] impress different states upon the thing. To which it can be
> added that it is by means of things that we must distinguish one time
> or place from another, rather than *vice versa*. (A VI vi 230/RB
> 230)




There is also the related, though uncontroversial, *Principle of the Indiscernibility of
Identicals:* if two things are identical, then they share all
properties, or *x* = *y* -
([?]*F*)(*F**x*
- *F**y*). The combination of these two principles
is sometimes called "Leibniz's Law": two things are
identical if and only if they share all properties, or
*x* = *y* - 
([?]*F*)(*F**x*
- *F**y*). (Sometimes, unfortunately, only the Principle of
the Indiscernibility of Identicals is so called.)




It is also interesting to note that in his *Primary Truths*
and Correspondence with Clarke, Leibniz presents PII not as a bedrock
axiom of his system but as a *consequence* of PC and PSR.
Briefly, one way to sketch the argument is this:



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | Suppose there were two indiscernible individuals,
> *a* and *b*, in our
> world, *W*. |
> | (2) | If this were the case, then there must
> also be a possible world, *W*\*, in which *a*
> and *b* are "switched." |
> | (3) | But if this were the case, then God could
> have had no reason for choosing *W* over
> *W*\*. |
> | (4) | But God must have a reason for acting as
> he does. (PSR) |
> | (5) | Therefore, our original supposition must
> be false. There are *not* two indiscernible individuals in our
> world. (PII) |
> 
> 
> 




Now, it was said above that Leibniz excludes purely extrinsic
denominations (or relational properties) from the kinds of properties
that are constitutive of an individual. To allow purely extrinsic
denominations would be to accept the possibility that that two things
could be discernible in terms of their relational properties while
being identical in terms of their intrinsic properties, for their
relational properties would not follow from their intrinsic properties.
(Again, if relational properties were allowed to factor into the nature
of an individual, then PII would be relatively weak. Of course two
things that exist in different spatio-temporal locations are distinct,
and that is what Leibniz admits in the passage from the *New
Essays* above.) But if we follow Leibniz in excluding such
relational properties as difference-making properties and reflect on
the above argument, then we see that worlds are distinguished in terms
of intrinsic properties of individuals and that this difference has a
bearing on the relative greatness or perfection of a world. Again, let
*a* and *b* be
indiscernible but occupying mirror positions in
*W* and *W*\*. How could
we ever say that *W* was more worthy of
God's choice than *W*\*? We could not.
There must be a reason why *a* is *here*
and *b* is *there*, and this reason has
to do with the intrinsic properties of *a* and
*b*. In other words, even the relational
properties must be somehow derivative of the intrinsic properties of
substances.




As we shall see, Leibniz employs this principle in a range of
arguments: against the mind as a *tabula rasa*, against atomism,
against Newtonian absolute space, and so on. (For more on this subject,
 consult the entry on 
 identity of indiscernibles.)


### 3.6 Principle of Continuity




According to Leibniz, there are "two famous labyrinths where
our reason very often goes astray" (G VI 29/H 53). The first
concerns human freedom, the latter the composition of the continuum.
Leibniz, however, thought that he had found the way out of each
labyrinth, and his solution to the problem of the continuum is related
ultimately to a maxim or law that he
employs not only in his mathematical writings but also in his
metaphysics. As he puts it in the Preface to the *New Essays*,
"Nothing takes place suddenly, and it is one of my great and best
confirmed maxims that *nature never makes leaps*" (A VI
vi 56/RB 56). More exactly, Leibniz believes that this law or principle
implies that any change passes through some intermediate change and
that there is an actual infinity in things. The Principle of Continuity
will be employed to show that no motion can arise from a state of
complete rest and that "noticeable perceptions arise by degrees
from ones which are too minute to be noticed" (ibid.).


## 4. Metaphysics: A Primer on Substance



> 
> 
> I consider the notion of substance to be one of the keys to
> the true philosophy. (G III 245/AG 286)




For Leibniz, the fundamental questions of metaphysics were reducible
to questions of ontology: What is there? What are the most basic
components of reality? What grounds what? In a certain sense, his answer remained constant
throughout his life: everything is composed of or reducible to
*simple substances*; everything is grounded in simple
substances. While Leibniz appears to have given slightly different
accounts of the precise nature of these simple substances over the
course of his career, there are many features that remained constant
in his mature philosophy: Leibniz always believed that a substance had
a "complete individual concept" and that it was
essentially an active unity endowed with perception and appetition.


### 4.1 The Logical Conception of Substance




In SS8 of the *Discourse on Metaphysics*, Leibniz gives
one of his most important accounts of the nature of individual
substance. There he claims that the Aristotelian idea that a substance
is that which is the subject of predication and which cannot be
predicated of something else is insufficient for a true analysis of the
nature of substance. He next appeals to the PC and the PIN: in every
true predication, the concept of the predicate is contained in the
concept of the subject. "Since this is so," Leibniz claims,
"we can say that the nature of an individual substance or of a
complete being is to have a notion so complete that it is sufficient to
contain and to allow us to deduce from it all the predicates of the
subject to which this notion is attributed" (A VI iv 1540/AG 41).
In other words, *x* is a substance if and only
if *x* has a *complete individual
concept* (CIC), that is, a concept that contains within it
all predicates of *x* past,
present, and future. The CIC, then, serves to individuate substances;
it is able to pick out its bearer from an infinity of other finite
created substances. Leibniz gives as an example Alexander the Great. The
concept of Alexander contains being a King, being a student of
Aristotle, conquering Darius and Porus, and so on. Now, "God,
seeing Alexander's individual notion or haecceity, sees in it at the
same time the basis and reason for all the predicates which can be said
truly of him" (A VI iv 1540-41/AG 41). Leibniz's invocation
of the Scotist notion of a *haecceity* is intriguing. What
Leibniz is telling us is that Alexander's *thisness* is
determined by the sum of his qualitative properties. Moreover, we can
see a metaphysical aspect to this logical conception of substance: the
complete individual concept of a substance is the notion or
*essence* of the substance as it known by the divine
understanding.




Leibniz concludes this section with his celebrated *doctrine
of marks and traces*: "when we consider
carefully the connection of things, we can say that from all time in
Alexander's soul there are vestiges of everything that has
happened to him and marks of everything that will happen to him and
even traces of everything that happens in the universe, even though God
alone could recognize them all" (A VI iv 1541/AG 41). The
doctrine of marks and traces, therefore, claims that, because the CIC
contains all predicates true of a substance past, present, and future,
the entire history of the universe can be read (if only by God) in the
essence of any individual substance.




The consequences that Leibniz draws from the logical conception of
substance and the doctrine of marks and traces are remarkable. In the
following section (SS9) of the *Discourse on Metaphysics*,
we are told they include the following:



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | No two substances can resemble each other
> completely and be distinct. (PII) |
> | (2) | A substance can only begin in creation and end
> in annihilation. |
> | (3) | A substance is not divisible. |
> | (4) | One substance cannot be constructed from
> two. |
> | (5) | The number of substances does not naturally
> increase and decrease. |
> | (6) | Every substance is like a complete world and
> like a mirror of God or of the whole universe, which each expresses in
> its own way. |
> 
> 
> 




Unfortunately, Leibniz's reasons for drawing these
consequences are not in all cases obvious. Why should PII follow from
the complete individual concept account of substance? If we consider
the CIC as that which allows us to pick out and individuate any
individual substance from an infinity of substances, then we realize
that, if the individual concepts of two substances,
*a* and *b*, do not
allow us (or God) to distinguish the one from the other, then their
individual concepts are not *complete*. That is, there must
always be a reason, found within the complete individual concept of
substances and issuing from the free decree of God, that
*a* is discernible from
*b*. And this fact points to another important
fact about the interpretation suggested above: it is not only the case
that each substance has a complete individual concept-the
essence of the substance as it exists in the divine mind-but
for every essence or complete individual concept there is one and only
one substance in a world. (The argument here is essentially that which
was given above in the section describing the relation between PSR and
PII; namely, what reason could God have had for instantiating two
substances with identical CICs?) Further, why should it be the case
that substances can only arise naturally in God's creation of the
world and end in his annihilation? If one takes quite literally
Leibniz's claim that the CIC contains within it all predicates
true of the substance past, present, and future, then one might be able
to say that this must include truths extending back to the creation and
forward either infinitely or to the end of time. This argument might be
somewhat weak in itself, but it certainly would seem to follow from
Leibniz's logical notion of substance *and* one of the
other consequences, namely, that each substance is a mirror of the
*entire* universe. If this is the case, then a substance,
insofar as it is a mirror of the entire universe, must have within its
complete individual concept predicates that extend back to creation and
forward in time. At first glance, it is also not readily apparent
merely from the CIC and doctrine of marks and traces why a substance
cannot be constructed from two substances or be divided into two new
substances. Let substance *x* have within its
complete individual concept predicates *g, h, i...* which
are true of it past, present and future. Suppose
*x* were to be divided into
*xa* and
*xb*. One might imagine that
both new substances would have all of
*x*'s pre-division predicates in common
and unique predicates thereafter. But the relevant part of
Leibniz's logical notion of substance is that the CIC is
sufficiently rich to allow us (or God) to deduce from it all predicates
past, present and future. Leibniz's implicit suggestion is that
the pre-division predicates would not allow the logical deduction of
branching or divided substances. If *g, h, i,...* imply
*la, ma, na*,
they cannot also imply *lb, mb,
nb*. A similar argument works against the
possibility of the fusion of two substances. Further, if we already
grant PII, then it should be clear that the substance having within its
CIC predicates *g, h, i, ... la,
ma, na*, and the substance having
within its CIC predicates *g, h, i, ... lb,
mb, nb* are numerically distinct
substances and not simply one substance in its pre-division phase that
has multiplied. Since substances can only naturally arise during
God's creation of the world and since substances cannot undergo
fusion or fission, it is obvious that the number of substances must
remain constant. Finally, if it is the case that it is of the nature of
a substance to have a notion so complete that one can deduce from it
all its predicates past, present, and future and if substances exist
from the creation of the world, then it would seem (relatively) natural
to conclude that each substance contains within it a kind of story of
the entire universe from its own particular perspective. While more
will be said below, what Leibniz is suggesting here is a set of
doctrines that he will develop in greater detail: the
*worlds apart* doctrine, the
*mirroring (or expression) thesis*, and the
doctrine of *universal harmony*.



Another notable consequence of the logical conception of substance is
the *denial of the causal interaction* of finite
substances. This is clearest in *Primary Truths* (C 521/L
269/AG 33), where a very similar argument concerning the nature of
substance is given. Not only is it the case, Leibniz claims, that
genuine physical influx - the transfer of some property within
one substance to a second substance - is inexplicable, but more
important the logical conception of substance shows us that
the *reasons* for any property that a substance may have are
already contained within its CIC. In other words, every state of a
substance is explained, grounded, or caused by its own notion or
CIC. (Of course, the ground or reason for the existence or actuality
of any particular substance is to be found in God and his free choice
of worlds. A more detailed account of Leibniz's views on causation is
available in the entry
 Leibniz on Causation.) 
As we shall see below, the denial of the causal interaction of
substances forms an essential premise of Leibniz's argument for
pre-established harmony.


### 4.2 Unity




If a finite substance is to have a CIC, as Leibniz claims in SS8
of the *Discourse on Metaphysics*, what is its ontological
status? That is, what kind of thing could have such a CIC or such a
nature? Leibniz's answer to this question brings to the fore
another paradigm of substancehood: unity. While it is the nature of an
individual substance to *have* a CIC, only a genuine unity can
qualify as a substance. Leibniz expresses his position in a letter to
Arnauld in a very clear and forceful manner: "To put it briefly,
I hold this identical proposition, differentiated only by the emphasis,
to be an axiom, namely, *that what is not truly
**one*** *being is not truly one
**being*** *either.*" (G II 97/AG 86)
In the period of the *Discourse on Metaphysics* and
Correspondence with Arnauld, Leibniz appeals to certain Scholastic
notions, chief among them, the notion of a substantial form. In later
years, the Scholastic way of speaking fades away, but the fundamental
idea remains the same: there must be something that guarantees or makes
possible the unity of a substance, and this is the substantial form or
the soul. The point Leibniz wants to make is that only a soul or a
substantial form is the kind of thing that can be said to have or
underlie a complete individual concept, for only a soul or substantial
form is by its nature an imperishable *unity*. Leibniz makes
this point very clear in another letter to Arnauld: "A
substantial unity requires a thoroughly indivisible and naturally
indestructible being, since its notion includes everything that will
happen to it, something which can be found neither in shape nor in
motion (both of which involve something imaginary, as I could
demonstrate), but which can be found in a soul or substantial form, on
the model of what is called *me*" (G II 76/AG 79). Thus,
unity is the hallmark of a genuine substance, but equally important is
Leibniz's paradigm case of a substance: the *self*. This
thought underlies much of Leibniz's reflections on the nature of
substance and has important consequences. For, following not only
Descartes but also the entire Augustinian tradition, the
"I" is essentially immaterial, a mind or a soul. Similarly,
he writes in *Primary Truths*, "Something lacking
extension is required for the substance of bodies, otherwise there
would be no source [*principium*] for the reality of phenomena
or for true unity... But since atoms are excluded, what remains is
something lacking extension, analogous to the soul, which they once
called form or species" (A VI iv 1648/AG 34). (Material atoms, as
advocated by Democritus in the classical period and by Gassendi and
others in the seventeenth century, are excluded, Leibniz thinks,
because they violate PII; that is, two purely material atoms would seem
to be qualitatively identical and yet distinct, which is impossible if
one accepts PC, PSR, and the derivation of PII.)




Leibniz is not as clear as one would like him to be, for at this
point in his career it is possible to read him as seeing that something
is a substance so long as it *has* a soul or a substantial form,
whereas later in his career it seems more clearly to be the case that
the only substances *are* souls or soul-like entities, the
monads. In other words, Leibniz can be interpreted as advocating, at
least in this period, a kind of Aristotelian hylomorphism, in which
substances are composites of matter and form. This has been the subject
of debate in the field, but this entry cannot adjudicate the
matter. (For more on this dispute, see Look 2010.)




Nevertheless, in declaring that a substance is necessarily
indivisible, Leibniz renders it impossible for a *body*, or
matter alone, to be a substance. Thus, Cartesian *corporeal
substance*, the essence of which is simply extension, cannot exist
as substance. Put differently, Leibniz's argument is that nothing that
is divisible is a substance; a Cartesian chunk of matter is divisible;
therefore, a Cartesian chunk of matter is not a substance. This
points to the first part of Leibniz's critique of the Cartesianism
mentioned above: namely, that according to Leibniz, Cartesian matter
fails to have the unity required of a genuine substance. Indeed, in
the Correspondence with Arnauld, Leibniz considers the case of a human
body deprived of a soul and says the body, or cadaver, would not be a
substance at all but merely an aggregate of substances. Moreover,
anything lacking a substantial form or soul is not a substance, that
is, if a thing is not truly "animated", then it is only a
true phenomenon. (G II 77/AG 80) It should be noted how strong
Leibniz's claim is: he is arguing that Cartesian corporeal substances
or any such chunks of matter are not real beings - at least not
as real as simple substances. Aggregates of simple substances,
therefore, have a different ontological status from simple
substances.




The distinction between simple substances and aggregates becomes an
important one in Leibniz's philosophy. To Arnauld, he writes the
following: "I hold that philosophy cannot be better reestablished
and reduced to something precise, than by recognizing only substances
or complete beings endowed with a true unity, together with the
different states that succeed one another; everything else is only
phenomena, abstractions, or relations" (G II 101/AG 89). If this
is the case, then aggregates of simple substances are merely phenomena
and fail to have the reality of the underlying simples. Further, the
bodies of natural philosophy, the bodies of the world we observe around
us, would seem to be in some sense *mere phenomena.* 




While some scholars of Leibniz's thought have suggested this, it does
not get at the full story of Leibniz's metaphysical system. The
distinction that Leibniz draws is one between a real unity and a
phenomenal unity, or as he also puts it, between a *unum per
se* and a *unum per aggregationem*. Leibniz's favorite
comparison in the case of the latter is to a rainbow: bodies, for
example, fail to have intrinsic unity, but we do represent them as
being single and unified objects much as we represent a rainbow as
being one thing when it is in fact merely the result of the refraction
of light through innumerable water droplets. But just as the rainbow
results from the presence of genuine unities, the water droplets (to
continue the metaphor, even if this is not true when speaking with
Leibniz in metaphysical rigor), so do the bodies of the natural world
result from the genuine simple substances. Put differently, the
simple substances *ground* the phenomena of bodies in the
world. This relation between the phenomena and the underlying simple
substances is what Leibniz means when he talks about
"well-founded phenomena" [*phenomena bene
fundata*]. But insofar as the bodies of the natural world are
well-founded phenomena - that is, insofar as they are grounded
in the simple substances - they are not simply phenomena as in
Berkeley's philosophy. (This view is also not uncontroversial. To
compare Leibniz with Berkeley, see the entry on
 Berkeley.) 


### 4.3 Activity




The second part of Leibniz's critique of the Cartesian
doctrine of corporeal substance relates to the notion of activity.
According to Leibniz, substances are not only essentially unities, but
also active. As he says in the opening line of the *Principles of
Nature and Grace*: "A *Substance* is a being capable
of action" (G VI 598/AG 207). But Cartesian corporeal substance,
insofar as its essence is extension, cannot be itself a source of
activity. (G IV 510/AG 161) There are at least two strands to
Leibniz's argument on this point. First, Leibniz holds that this
is so because he adheres to the classical and Scholastic idea that
*actions pertain to supposita*; that is, only something that can
be the subject of predication can be active, and only true unities can
be genuine subjects of predication (and not mere phenomena). Put
differently, Cartesian extended stuff cannot, insofar as it is
infinitely divisible, constitute a *suppositum*, or subject of
predication. But, second, Leibniz believes that something is active if
and only if the *source* of its activity can arise within
itself, that is, if and only if its activity arises spontaneously from
within itself. This is another reason, then, that individual substances
will be understood as mind-like, for Leibniz believes that only minds
or mind-like things can originate and alter their modifications.




In saying that substances are essentially active, Leibniz means that
they are endowed with *forces*. More precisely, according to
Leibniz, "the very substance of things consists in a force for
acting and being acted upon," (G IV 508/AG 159) that is, each
simple substance is endowed with what Leibniz calls primitive active
and passive powers. The idea here again sounds Aristotelian: a
substance has a certain essentially active component, the soul or
substantial form or first entelechy, and a passive component, primary
matter. In Leibniz's mature account, the primitive active force
is "an inherent law, impressed by divine decree," that is,
it is the law of unfolding or the law of the series of the simple
substance. As he puts it in a letter to De Volder, "I think that
it is obvious that primitive forces can be nothing but the internal
strivings [*tendentia*] of simple substances, strivings by means
of which they pass from perception to perception in accordance with a
certain law of their nature, and at the same time harmonize with one
another, representing the same phenomena of the universe in different
ways, something that must necessarily arise from a common cause"
(G II 275/AG 181). Since simple substances are minds, their
modifications are representations or perceptions, and the activity of
the simple substance will relate to the change or succession of its
perceptions. One way to think of this is that each substance has a
unique series of perceptions programmed by God to play in harmony with
all other substances, and the internal tendency of a substance to move
from perception to perception is its active force, or what Leibniz also
calls appetite or appetition.


### 4.4 Pre-established Harmony




While separate entries detail Leibniz's account of causation
and his account of the mind, it will still be useful to provide a short
exegesis of Leibniz's celebrated solution to the mind-body
problem which Leibniz had inherited from Descartes and his followers.
The problem, briefly, is this: if mind is essentially thought (and
nothing else), and body is essentially extension, then how can mind and
body interact or form a unity as we know from experience they must? Or
how do thinking substance and extended substance unite in the substance
of a human being? Leibniz answers this question by, first, denying the
possibility of the causal interaction of finite substances. In this
way, Leibniz undermines Cartesian dualism because it takes as a premise
the idea that mind-body interaction is to be explained by the influence
of the one on the other via the pineal gland. (See the Sixth
*Meditation*: AT VII 86-87/CSM II 59-60) But Leibniz also saw
pre-established harmony as an account of the mind-body relation that
avoided the difficulties inherent in Occasionalist theories of the mind
and the interaction of substances. In one of Leibniz's best-known
metaphors, he asks his readers to imagine the mind and body as two
pendula hanging from a beam. Whence comes their agreement? One could
imagine that the motion of the one is communicated through the wooden
beam to the other, thus causing them eventually to swing harmoniously
(the theory of influx). Or one could imagine that God intervenes and
moves the pendula, guaranteeing their synchronicity (the theory of
occasionalism). Or, Leibniz says, one could imagine that God, the
supreme artificer, created the world (and the pendula) so perfectly
that, by their own natures, they would swing in perfect harmony.
Naturally, it is this last thesis that Leibniz endorses and asks his
readers to endorse as well. (See, for example, the Postscript of a
Letter to Basnage de Beauval (G IV 498-500/AG 147-49).)




More precisely, Leibniz argues that God created the world so
perfectly that each substance acts according to its own law of
unfolding and is at the same time in perfect harmony with all others
substances; further, that the mind has a distinct point of view of the
world by virtue of its being the center of some mass (body), and that
the law of unfolding of the mind is in accord with the laws of the
corporeal machine. He puts this most succinctly in his 1695 essay,
*A New System of Nature*, in which he effectively presents a
five-step argument for *pre-established harmony*:



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | "[T]here is no real influence of one created
> substance on another." (G IV 483/AG 143) |
> | (2) | "God originally created the soul (and any
> other real unity) in such a way that everything must arise for it from
> its own depths [*fonds*], through perfect *spontaneity*
> relative to itself, and yet with a perfect *conformity* relative
> to external things." (G IV 484/AG 143) |
> | (3) | "This is what makes every substance
> represent the whole universe exactly and in its own way, from a
> certain point of view, and makes the perceptions or expressions of
> external things occur in the soul at a given time, in virtue of its
> own laws, as if in a world apart, and as if there existed only God and
> itself." (G IV 484/AG 143) |
> | (4) | "[T]he organized mass, in which the point of
> view of the soul lies, being expressed more closely by the soul, is in
> turn ready to act by itself, following the laws of the corporeal
> machine, at the moment when the soul wills it to act, without
> disturbing the laws of the other - the spirits and blood then
> having exactly the motions that they need to respond to the passions
> and perceptions of the soul." (G IV 484/AG 144) |
> | (5) | "It is this mutual relation, regulated in
> advance in each substance of the universe, which produces what we call
> their *communication*, and which alone brings about *the
> union of soul and body*." (G IV 484-85/AG 144) |
> 
> 
> 




Now, when Leibniz speaks in metaphysical rigor, he denies the
underlying premise of Cartesian dualism: body is *not* a
substance; so there can be no question of how it qua substance
interacts with or is related to the mind, or thinking substance.
Nevertheless, Leibniz was able to express his view for the vulgar
- that is, for those expecting a Cartesian metaphysics - by
saying that the mind and body can be said to form a union and interact
insofar as the mind follows its laws, the body follows its laws, and
they are in perfect harmony. The body and soul are not united to each
other in the sense that Descartes had suggested, but the perceptions
and appetitions of the soul will arise spontaneously from
its own stores and will correspond to the actions of the body as well
as to the events of the world. In other words, while the perceptions
and appetitions of the mind or soul will be independent of the body, they
will nevertheless correspond precisely to the actions of the particular
body to which it is attached and be in perfect conformity with all the
other substances of the world.




On Leibniz's view, to individual substances there belong only
perceptions and appetitions, and these perceptions and appetitions can
be understood to form a series within the individual substance. In
other words, every individual substance can be thought to have a set
of perceptions and appetitions such that one could say that, at any
given time, a particular substance was experiencing such-and-such a
perception and such-and-such an appetition. Indeed, Leibniz's view is
that a given substance, *x*, has, within its individual
concept, information of the following sort: *x* at
time *t*1 will have perception1 and/or
appetition1; *x* at *t*2 will have
perception2 and/or appetition2; and so on. (In
fact, the position is more complex; for, as will be shown in a
subsequent section, the mind has at any moment an infinity of
*petites perceptions* within it, perceptions of everything that
is occurring in the universe, but the human mind at least will be truly
aware of one thing at a time. For example, the reader of this article
could be said to have a temporally-ordered series of perceptions
- with *t*1 corresponding to the first sentence,
*t*2 the second sentence, etc. - and also
"background noise" of which the reader is not directly
aware - for example, the sound of an ambulance's siren
gradually approaching and retreating from *t*1 to
*t*3.) Moreover, the series of perceptions and appetitions are
generated from within the individual substance itself. That is, Leibniz
speaks as if perceptions and appetitions follow naturally from prior
perceptions and appetitions - and it is in this respect, after all,
that a finite individual substance is causally independent from all
other finite created substances.




The crucial idea is that the body will follow its own laws, the mind
its own laws, and there will be no true influence between the two. The
mind and body thus seem to constitute, as it were, worlds apart, as
indeed Leibniz claims later when he explains the world in terms of
monads, and these worlds apart are, according to Leibniz, unified
solely by virtue of the correspondence of their actions and
perceptions. Further, to these separate realms there will apply two
distinct means of explaining the events of the world: we may explain
things according to the final causes of the mind or according to the
efficient causes of the body or of bodies in general. Thus, not only do
the mind and body each seem to follow a different set of laws, but the
world, according to Leibniz, can be described in terms of either set of
laws.


### 4.5 Efficient and Final Causes and the Kingdoms of Nature and Grace




Leibniz's account of the pre-established harmony of mind and
body is part of a more general position in his metaphysics: the
existence of parallel modes of explanation. As we saw above, Leibniz
believes that the mind will act according to its laws and the body
according to its laws and the two will be in harmony. But Leibniz also
believes that the mind or soul operates for particular ends and that
therefore its actions are explicable in terms of *final causes*,
whereas the actions of the body, purely instances of matter in motion
according to the claims of the mechanical philosophy, are to be
explained in terms of *efficient causes.* As he puts it in the
*Monadology* SSSS79 and 81,



> 
> 
> Souls act according to the laws of final causes, through
> appetitions, ends, and means. Bodies act according to the laws of
> efficient causes or of motions. And these two kingdoms, that of
> efficient causes and that of final causes, are in harmony with each
> other.




According to this system, bodies act as if there were no souls
(though this is impossible); and souls act as if there were no bodies;
and both act as if each influenced the other. (G VI 620-21/AG 223)





In the realm of natural philosophy, Leibniz will say clearly that
"all corporeal phenomena can be derived from efficient and
mechanical causes," though there are final causes (or
"higher reasons") that underlie them. (See *Specimen
Dynamicum*: GM VI 242/AG 126) But Leibniz pushes the parallelism
even further:



> 
> 
> In general, we must hold that everything in the world can be
> explained in two ways: through the *kingdom of power*, that is,
> through *efficient causes*, and through the *kingdom of
> wisdom*, that is, through *final causes*, through God,
> governing bodies for his glory, like an architect, governing them as
> machines that follow the *laws of size* or *mathematics*,
> governing them, indeed, for the use of souls, and through God governing
> for his glory souls capable of wisdom, governing them as his fellow
> citizens, members with him of a certain society, governing them like a
> prince, indeed like a father, through *laws of goodness* or
> *moral laws*. (GM VI 243/AG 126) 




Though Leibniz speaks here of the kingdoms of power and wisdom, the
two-tiered explanatory approach - the phenomena of the natural
world explained through efficient causes and the actions of the mind
explained through final causes - leads to the distinction between
what he more commonly calls the kingdom of nature and the kingdom of
grace. (See *Monadology* SS87) Thus, on Leibniz's
view, we can understand the world as if designed by God, the perfect
engineer or architect, and we can also understand the world as if
ordered and guided by God, the supreme monarch, who is concerned solely
with the happiness of his subjects.


## 5. Metaphysics: Leibnizian Idealism


### 5.1 Monads and the World of Phenomena




Thus far we have seen that Leibniz rejected the Cartesian account of
matter, according to which matter, the essence of which is extension,
could be considered a substance. Leibniz held instead that only beings
endowed with true unity and capable of action can count as substances.
The ultimate expression of Leibniz's view comes in his celebrated
theory of monads, in which the only beings that will count as genuine
substances and hence be considered real are mind-like simple substances
endowed with perception and appetite. What was said above concerning
the unity and activity of simple substance should suffice to explain
Leibniz's reasons for holding such a position. Now a fuller
version of Leibniz's idealism must be presented.




According to Leibniz, if the only genuinely real beings are
mind-like simple substances, then bodies, motion, and everything else
must result from or be derivative of those simple substances and their
perceptual states. In a typical statement of his idealism, Leibniz
says, "I don't really eliminate body, but reduce
[*revoco*] it to what it is. For I show that corporeal mass
[*massa*], which is thought to have something over and above
simple substances, is not a substance, but a phenomenon resulting from
simple substances, which alone have unity and absolute reality"
(G II 275/AG 181). Yet, this position, denying the reality of bodies and
asserting that monads are the grounds of all corporeal phenomena, as
well as its metaphysical corollaries has shocked many. Bertrand
Russell, for example, famously remarked in the Preface to his book on
Leibniz that he felt that "the *Monadology* was a kind of
fantastic fairy tale, coherent perhaps, but wholly arbitrary."
And, in perhaps the wittiest and most biting rhetorical question asked
of Leibniz, Voltaire gibes, "Can you really believe that a drop
of urine is an infinity of monads, and that each of these has ideas,
however obscure, of the universe as a whole?" (*Oeuvres
completes*, Vol. 22, p. 434) Well, if you are Leibniz, you
can. But how so?


### 5.2 Panorganicism and Idealism




When Leibniz argues that bodies are the results of monads and that
matter itself is a phenomenon, he has something very specific in
mind. First, in Leibniz's system there is a special kind of order
in the natural world corresponding to a hierarchy of monads. Consider
first a well-known comment that Leibniz makes to De Volder, introducing
a five-fold ontological scheme: "I distinguish: (1) the primitive
entelechy or soul; (2) the matter, namely, the primary matter or
primitive passive power; (3) the monad made up of these two things; (4)
the mass [massa] or secondary matter, or the organic machine in which
innumerable subordinate monads come together; and (5) the animal, that
is, the corporeal substance, which the dominating monad makes into one
machine" (G II 252/AG 177). One of the points Leibniz is making
here is that in an animal there is a dominant monad that bears a
special relation to all the monads subordinate to it that make the
"organic machine" of that animal. But, ultimately, the
picture is even more complex than this, for each of the subordinate
monads can be considered as having an organic machine attached to it,
and this relation continues on to the infinitely small. Thus, for
example, Leibniz writes in the *Monadology* SS70,
"Thus we see that each living body has a dominant entelechy,
which in the animal is the soul; but the limbs of this living body are
full of other living beings, plants, animals, each of which also has
its entelechy, or its dominant soul" (G VI 619/AG 222).
Similarly, in a letter to Bierling, he writes, "Any mass contains
innumerable monads, for although any one organic body in nature has its
corresponding [dominant] monad, it nevertheless contains in its parts
other monads endowed in the same way with organic bodies subservient to
the primary one; and the whole of nature is nothing else, for it is
necessary that every aggregate result from simple substances as if from
elements" (G VII 502). In other words, each monad will have an
organic body which is in turn composed of other monads, each of which
likewise has an organic body. Similarly, any seemingly inanimate chunk
of matter - a stone or, yes, a drop of urine - will be the
result of an infinity of monads and their organic bodies, which are
nothing more than more monads and their organic bodies. This view is
associated with a *panorganicist* strand of Leibniz's
thought. And it is for this reason that Leibniz will claim that
"all of nature is full of life" (*Principles of Nature
and Grace* SS1: G VI 598/AG 207) and that "there are
infinite degrees of life in the monads" (*Principles of
Nature and Grace* SS4: G VI 599/AG 208).




Second, there is what can best be described as a genuinely idealist
strand of Leibniz's thought. That is, if idealism is the thesis that
the only things that truly exist are minds and their ideas, then
Leibniz clearly espouses this doctrine. Here the operative idea is
that bodies, and in particular the bodies associated with particular
minds, are intentional objects - though they result from or are
grounded in monads. This is what Leibniz is getting at in the
following passage from another letter to De Volder: "considering
the matter carefully, we must say that there is nothing in things but
simple substances, and in them, perception and appetition. Moreover,
matter and motion are not substances or things as much as they are the
phenomena of perceivers, the reality of which is situated in the
harmony of the perceivers with themselves (at different times) and
with other perceivers" (G II 270/AG 181). Thus, the only real
things are simple substances; the bodies that we perceive in motion
around us are phenomena and not themselves substances, though they are
grounded ultimately in simple substances or monads. Furthermore, the
bodies of the natural world ought be considered intentional objects in
that they are objects about which we have certain beliefs. This is
what Leibniz means in saying that they have reality insofar as there
is a harmony between perceivers or between the same perceivers'
beliefs or perceptions at different times. In other words, one's body
or even a stone is real because it is an object of perception that
fits into an account of the world that is both coherent from the point
of view of the single perceiver and in harmony with the perceptions of
other minds.


### 5.3 Perspective and Divine Emanation




Still Leibniz's version of idealism tends to produce confusion
precisely because of these two strands: the commitment to the
"embodiment" of monads along with the rejection of the
reality of bodies; the view that monads are not spatial but have a
point of view. Leibniz's point, however, is that, while monads
are not extended, they do have a situation insofar as they bear an
ordered relation to other bodies through the body in which they are
present or through the body to which they represent themselves as being
attached. (G II 253/AG 178) In other words, in the Leibnizian
monadology, simple substances are mind-like entities that do not,
strictly speaking, exist in space but that represent the universe from
a unique perspective.




Leibniz's conception of such a perspectival universe has,
however, a distinctively Platonist origin. Again, each mind-like simple
substance represents itself as having a body and a position relative to
other bodies, but in doing so each simple substance offers a
perspective on the world for the divine mind. This idea comes out very
clearly in the *Discourse on Metaphysics* SS14, where
Leibniz writes the following:



> 
> 
> Now, first of all, it is very evident that created substances depend
> upon God, who preserves them and who even produces them continually by
> a kind of emanation, just as we produce our thoughts. For God, so to
> speak, turns on all sides and in all ways the general system of
> phenomena which he finds it good to produce in order to manifest his
> glory, and he views all the faces of the world in all ways possible,
> since there is no relation that escapes his omniscience. The result of
> each view of the universe, as seen from a certain position, is a
> substance which expresses the universe in conformity with this view,
> should God see fit to render his thought actual and to produce this
> substance. (A VI iv 1549-50/AG 46-47)




This is a striking passage. Leibniz is telling us that each finite
substance is the result of a different perspective that God can take of
the universe and that each created substance is an emanation of God.
The argument here can be expressed in several different ways. First,
since God *could* occupy any and all points of view of the
universe, there must be a simple substance to represent the world from
that perspective. (And since the simple substance must have
representations of its unique perspective, it must be a mind-like
substance, a monad, capable of having perceptions.) Second, and
stronger, God's omniscience entails knowledge of the world from
every perspective simultaneously, and the infinite perspectives of the
world originating from God's nature simply *are*
monads.


### 5.4 Monadic Hierarchies




If the only things that truly exist are mind-like entities, monads,
then the differences between them must be explicable in terms of mental
features. Now, it was stated above that a central feature of
Leibniz's account of substance was his claim that substances are
endowed with active and passive forces. In his mature metaphysics,
Leibniz expresses this view somewhat differently by saying that a
substance is active insofar as it has distinct perceptions and passive
insofar as it has confused perceptions. Thus, for example, in SS49
of the *Monadology*, Leibniz writes that, "we attribute
*action* to a monad insofar as it has distinct perceptions, and
*passion*, insofar as it has confused perceptions" (G VI
615/AG 219). But, as we learn later in the same work, "Monads all
go confusedly to infinity, to the whole; but they are limited and
differentiated by the degrees of their distinct perceptions" (G
VI 617/AG 221). The fundamental idea here is two-fold: first, activity
and passivity are features of the relative clarity and distinctness of
the representations of the monad, and, second, insofar as the organic
bodies of a particular monad are themselves constituted by monads, they
- the monads of the organic body - will have confused
perceptions. This chain goes down to the infinitely small, with monads
having only very confused and inexact perceptions of the world.




Since there is a hierarchy among monads within any animal, from the
soul of a person down to the infinitely small monad, the relation of
domination and subordination among monads is a crucial feature of both
Leibniz's idealism and his panorganicism. But the hierarchy of
substances is not simply one of containment, in which one monad has an
organic body which is the result of other monads, each of which has an
organic body, and so on. In the case of animals (brutes and human
beings), the hierarchy of monads is also related to the
*control* of the "machine of nature" (as Leibniz had
put it in a letter to De Volder considered above). What is it then that
explains the relation of dominant and subordinate monads? As Leibniz
tells Des Bosses, domination and subordination consists of degrees of
perfection. Since monads are to be differentiated in terms of their
perceptions, one natural reading would simply be that suggested in the
paragraph above: monad *x* is dominant over
monad *y* when *x* has
clearer perceptions than *y*. But, if we follow
the description of the appearance of causal interaction that we find in
the *Monadology* (SSSS49-51), we can get a slightly more
sophisticated picture. Monad *x* is dominant
over monad *y* when *x*
contains within it reasons for the actions of
*y*. This is why the mind of an animal can be
said to direct the actions of its body, and why, for example, there
will be a hierarchy of functionality within any one animal. Thus,
one's mind has clearer perceptions than those contained in the
monads of its organic body, but it contains the reasons for everything
that happens in one's body; one's liver contains the
reasons for what happens in its cells; a cell contains the reasons for
what happens in its mitochondria; and, according to Leibniz, this
relation continues infinitely on down.


## 6. Epistemology




Leibniz's reflections on epistemological matters do not rival
his reflections on logic, metaphysics, divine justice, and natural
philosophy in terms of quantity. Nevertheless, he did think deeply
about the possibility and nature of human knowledge, and his main
doctrines will be presented here.


### 6.1 "Meditations on Knowledge, Truth, and Ideas"




In 1684, Leibniz published a short treatise with the above title. It
was his first mature publication and one to which he often referred
in the course of his philosophical career. In it, Leibniz sets out a series of
distinctions for human knowledge or cognition (*cognitio*):
knowledge is either obscure or clear; clear knowledge is either
confused or distinct; distinct knowledge is either inadequate or
adequate; and adequate knowledge is either symbolic or intuitive. Now,
according to Leibniz, clear knowledge means being able to recognize
something that is represented to us, for example, a rose; and knowledge
is both clear and distinct when one can enumerate marks sufficient to
distinguish a rose from other things. When one can give such an
enumeration, one possesses a distinct notion or concept and is thus able to give a
*nominal definition* of the thing. Further, if all the marks
that form part of a distinct notion are themselves distinctly known,
then the cognition is adequate. And, finally, if a notion is complex
and we are able to consider all its component notions simultaneously,
then our knowledge of it is intuitive. Ultimately, Leibniz holds that
human beings have intuitive knowledge only of primary notions and
propositions, whereas God, of course, has intuitive knowledge of all
things.




Leibniz believes his distinctions also serve to show the difference
between true and false ideas. "An idea is true," he writes,
"when its notion is possible and false when it includes a
contradiction" (A VI iv 589/AG 26). Now, possibility can be
established *a priori* and *a posteriori*. On the one
hand, we can know *a priori* that something is possible if we
can resolve it into its component notions which are themselves possible
and if we know that there is no incompatibility among those component
notions. On the other hand, we know *a posteriori* that
something is possible merely through experience, for the actual
existence of a thing is proof of its possibility.


### 6.2 Truths of Reason and Truths of Fact




While Leibniz's Principle of Contradiction and Principle of Sufficient
Reason were discussed above, it was not mentioned that these two
principles are employed in the service of Leibniz's distinction
between *truths of reasoning* and *truths of fact*, that
is, between *necessary truths* and *contingent truths*.
Leibniz's account of modality is treated elsewhere, but a
short account of this distinction is here required. In the case of a
truth of reasoning, its reason or explanation can be discovered by
analysis of the notions or concepts, "resolving it into simpler ideas and
simpler truths until we reach the primitives" (G VI 612/AG 217).
Ultimately, all truths of reasoning will be resolvable into primitives
or identities, and the Principle of Contradiction is thereby
operative. In the case of a truth of fact, on the other hand, its
reason cannot be discovered through a *finite* process of
analysis or resolution of notions. However, there must be a reason
that some particular fact is so and not otherwise (PSR), and,
according to Leibniz, this reason is found outside the series of
contingent things. (See below.)


### 6.3 Innate Ideas




Leibniz is often put in the camp of rationalists and opposed to the
empiricists (for example, Locke, Berkeley, and Hume). While there are
good grounds to be unhappy with this standard textbook distinction,
Leibniz does fit the bill in two important respects: he is a
rationalist insofar as he holds to the Principle of Sufficient Reason,
and he is a rationalist insofar as he accepts innate ideas and denies
that the mind is at birth a *tabula rasa* or blank slate. In
terms of Leibniz's classical allegiances, it is interesting to see
that in the realm of metaphysics, he often couched his philosophy in
Aristotelian (and Scholastic) terms but that in the realm of
epistemology, he was a fairly open Platonist - at least in terms
of the existence of innate ideas. Indeed, in the opening passages of
his *New Essays on Human Understanding*, his book-length
commentary on Locke's *Essay Concerning Human Understanding*,
Leibniz explicitly aligns himself with Plato on the fundamental
question of the origin of ideas. (A VI vi 48/RB 48)




Leibniz has several straightforwardly *metaphysical*
reasons for denying that the mind could be a *tabula rasa*.
First, and most obvious, since there can be no genuine causal
interaction among substances, then there could be no way that all our
ideas could come from experience; indeed, no ideas could, strictly
speaking, come from experience. (Leibniz will, however, adopt a more
liberal understanding of sense experience, so that this is not mooted
*tout court*.) But, second, and rarely remarked upon, Leibniz
believes that the view that our minds are blank slates at birth violates
the Principle of the Identity of Indiscernibles. In short, PII works
against qualitatively identical physical atoms and against
qualitatively identical (because blank) souls. Further, in one
telling passage, he shows us the metaphysical underpinnings of the
empiricist view that he finds so objectionable. He writes,
"Experience is necessary, I admit, if the soul is to be given
such and such thoughts, and if it is to take heed of the ideas that are
within us. But how could experience and the senses provide the ideas?
Does the soul have windows? Is it similar to writing-tablets, or like
wax? Clearly, those who take this view of the soul are treating it as
fundamentally corporeal" (A VI vi 110/RB 110). Locke famously
entertained the possibility of "thinking matter", and
Leibniz found such a thesis abhorrent. Throughout his career, Leibniz
expresses no doubt that the human mind or soul is essentially
immaterial, and Locke's skepticism about the nature of substance
is fundamentally at odds with Leibniz's most deeply held
philosophical commitments. But, of course, the consequence of this is
that Leibniz seeks to undermine Locke's position with respect to
the origin and nature of ideas. That the mind, according to Leibniz,
*must* be essentially immaterial has been shown above in the
section on metaphysics. But Leibniz does have a particular argument for
the mind's immateriality or against its mechanism that concerns
the nature of thought and ideas. This is his famous metaphor of a mill,
which comes forth both in the *New Essays* and the
*Monadology*. According to Leibniz, perceptions cannot be
explained in mechanical or materialistic terms. Even if one were to
create a machine to which one attributes thought and the presence of
perceptions, inspection of the interior of this machine would not show
the *experience* of thoughts or perceptions, only the motions of
various parts.




But even when Leibniz accepts the common way of speaking - that
is, as if the senses are causally responsible for some ideas - he
has arguments against the empiricist claim that the senses are the
origin of *all* ideas. According to Leibniz, while the
empiricist position can explain the source of contingent truths, it
cannot adequately explain the origin and character of necessary truths.
For the senses could never arrive at the universality of any necessary
truth; they can, at best, provide us with the means of making a
relatively strong induction. Rather, it is the understanding itself,
Leibniz claims, which is the source of such truths and which guarantees
their very necessity. While we are not aware of all our ideas at any
time - a fact demonstrated by the function and role of memory
- certain ideas or truths are in our minds as dispositions or
tendencies. This is what is meant by an innate idea or an innate truth.
Indeed, Leibniz believes that the mind has a "special
affinity" for necessary truths. On this subject, Leibniz uses a
distinctive metaphor: a piece of marble has veins that indicate or are
disposed to indicate shapes that a skillful sculptor can discover and exploit.
Similarly, there is a "disposition, an aptitude, a preformation,
which determines our soul and brings it about that [necessary truths]
are derivable from it" (A VI vi 80/RB 80). 


### 6.4 Apperception, Memory, and Reason




The hierarchy of monads mentioned above has a corollary in
Leibniz's epistemology. Monads are more or less perfect depending
upon the clarity of their perceptions, and a monad is dominant over
another when the one contains reasons for what happens in the other.
But some monads can also rise to the level of *souls* when, for
example, they experience *sensations*, that is, when their
perceptions are very distinct and accompanied by memory. This is a
position occupied by animals. Furthermore, some souls are sometimes
also in a position to engage in *apperception*, that is, to
reflect on their inner states or perceptions. As Leibniz tells us in
the *Principles of Nature and Grace*, "it is good to
distinguish between *perception*, which is the internal state of
the monad representing external things, and *apperception*,
which is *consciousness*, or the reflective knowledge of this
internal state, something not given to all souls, nor at all times to a
given soul" (G VI 600/AG 208). The point that Leibniz wants to
make is clearly an anti-Cartesian one: it is not the case that animals
lack souls and are mere machines. There is a continuum here from God,
angels, and human beings through animals to stones and the dull monads
which underlie the muck and grime of the world; and this continuum is
not solely to be understood in terms of the comparative clarity of the
mind's perceptions but also in terms of the kinds of mental
activity possible for a particular being. Indeed, according to Leibniz,
animals operate not as mere automata as they do in the Cartesian
philosophy, but rather have fairly sophisticated mental faculties. Even
a dog, for example, is capable, by virtue of its memory, of having a
perception of a prior perception: "[t]hat is why a dog runs away
from the stick with which he was beaten, because his memory represents
to him the pain which the stick caused him" (G VI 600/AG 208).
While this resembles reasoning, it is not the kind of reasoning that
human beings are capable of; for the mental processes of the dog are
"only founded in the memory of *facts* or effects, and not
at all in the knowledge of *causes*" (ibid.). At the same
time, Leibniz is quick to add that the mental activity of the dog is
the *same* as the mental activity of human beings in three
fourths of their actions, for most of us most of the time are not
actually reasoning from causes to effects. And yet we are different
from the beasts, Leibniz believes. Some creatures are capable of
knowing the necessary and eternal truths of logic and mathematics and
*a priori* truths (from cause to effect), and they "are
properly called *rational animals*, and their souls are called
*minds.*" (G VI 601/AG 209) As Leibniz says, "These
souls are capable of performing reflective acts, and capable of
considering what is called "I", substance, soul, mind
- in brief, immaterial things and immaterial truths. And that is
what makes us capable of the sciences of demonstrative
knowledge" (ibid.). Thus, what makes human beings (and higher
minds) special is the capacity, via apperception, to formulate a
conception of the *self*. Indeed, as we see in this passage,
Leibniz suggests that rationality itself follows from the capacity for
reflection: we begin with a conception of the self; we move from this
point to thinking of being, of substance, of God; and we become aware
as well of eternal and necessary truths. Rationality, however, is
really only the ability to form "indubitable connection[s] of
ideas" and to follow them to their "infallible
consequences" (ibid.). In other words, animals and most human
beings most of the time are purely empiricists; a rational person,
however, is one who can engage in genuine *a priori* reasoning,
moving from knowledge of a true cause via deduction to necessary
effects.


### 6.5 *Petites Perceptions*




One of the fundamental theses of Leibniz's philosophy is that
each substance expresses the entire universe. In order to incorporate
this thesis into his general epistemology and philosophy of mind,
Leibniz develops his account of "*petites
perceptions*" or "minute perceptions" mentioned
briefly in the section on pre-established harmony. As he puts it in the
Preface to the *New Essays*, "at every moment there is in
us an infinity of perceptions, unaccompanied by awareness or
reflection; that is, of alterations in the soul itself, of which we are
unaware because these impressions are either too minute and too
numerous, or else too unvarying, so that they are not sufficiently
distinctive on their own" (A VI vi 53/RB 53). In other words,
everything that takes place in the universe really is expressed by each
finite mind, but the infinite perceptions present in the mind -
from the butterfly's flight in the Amazonian jungle to the
penguin's waddling in Antarctica - are usually too minute
or too indistinct to outweigh, for example, the appearance of this
computer screen or the feeling of hunger. Indeed, this infinity of
perceptions is likened by Leibniz to the roar of the sea. "To
hear this noise as we do," Leibniz says, "we must hear the
parts which make up this whole, that is the noise of each wave,
although each of these little noises makes itself known only when
combined confusedly with all the others, and would not be noticed if
the wave which made it were by itself" (A VI vi 54/RB 54). The
infinity of *petites perceptions* is, then, simply epistemological white
noise.




For Leibniz, the simplicity and unity of the mind still allows for the
multiplicity of perceptions and appetitions. The multiplicity, however,
should not only be interpreted as *diachronous* but also
*synchronous*; that is, the mind despite its simplicity and
unity has within it *at any time* an infinity of different
*petites perceptions*. A human being, in a waking state, is
conscious of particular perceptions, but never all. And here we see
that Leibniz's doctrine is important, insofar as it offers a
contrast to the Cartesian theory of the mind. According to Leibniz, the
mind is *always* active, for there are always perceptions
present to it, even if those perceptions are minute and do not rise to
such a level that we are cognizant of them. Thus, even in a deep and
dreamless sleep, the mind is active, and perceptions are in the mind.
Moreover, if Descartes really did advocate the perfect transparency of
the mind, then it should be clear that Leibniz allows for a subtler
picture of mental contents: there are many things in the mind that are
confused and minute and to which we do not always have complete
access.


### 6.6 The Extent of Human Knowledge




Leibniz, however, does not simply disagree with Locke about the
nature of the mind and the possibility of innate ideas. It is also
Leibniz's contention that human beings are capable of knowledge
in a way that Locke had clearly denied. As shown above, Leibniz is
convinced that our knowledge of necessary truths has a completely
different foundation from that for which Locke argues. Similarly,
Leibniz holds that we can have genuine knowledge of the real essences
of things, something called into question by Locke. After all, Locke
had argued that we ought to admit that "essence" is really
just a word that we use to describe "nominal essence," a
set of sortal concepts based upon sensible qualities; we ought not to
act as if "essence" means anything about the real or inner
constitution of a thing, for we will remain ignorant of that. Leibniz,
however, holds that we can know certain things not only about
individuals but also about their species and genera. In Book IV of the
*New Essays*, in which Philalethes - the Locke character
- gives his critique of the possibility of our certain knowledge
about substances *qua* natural kinds, Theophilus (Leibniz) says,
"[L]et me tell you that there are, for example, hundreds of
truths that we can be certain of concerning gold, i.e. that body whose
inner essence reveals itself through the greatest weight known here on
earth, or through the greatest ductility or by other marks. For we can
say that the body with the greatest known ductility is also the
heaviest of all known bodies" (A VI vi 400/RB 400). Earlier in
the *New Essays*, Leibniz had said that "essence is
fundamentally nothing but the possibility of the thing under
consideration" (A VI vi 293/RB 293) and "essences are
everlasting because they only concern possibilities" (A VI vi
296/RB 296). It would seem, then, that Leibniz has something like the
following in mind: experience informs us of a certain consistent set of
sensible properties in, for example, gold; that is, a certain set of
properties is *compossible*. And, more important, we ought to be
able to assert with certainty that if some object has the greatest
ductility, then it also has the greatest weight.


## 7. Philosophical Theology




Like most of his great contemporaries (Descartes, Spinoza,
Malebranche), Leibniz developed a number of arguments for the existence
of God. Two of these are presented in condensed versions in the
*Monadology* SSSS36-45, as *a priori* and *a
posteriori* arguments (or ontological and cosmological arguments,
to borrow Kant's terminology). But they have long histories in
Leibniz's thought. Yet, unlike Descartes and Spinoza at least,
Leibniz also expended great efforts in explaining and justifying
God's justice and benevolence in this world. In other words,
Leibniz was keen to answer the problem of evil. His work on this
subject led to his thesis, so roundly mocked in Voltaire's
*Candide*, that we live in the *best of all possible
worlds.*


### 7.1 The Existence of God


#### 7.1.1 The Ontological Argument




Leibniz made an important contribution to the history of the
ontological argument. His reflections on this form of argument go back
to the 1670s, and we know that he shared his thoughts on this matter
with Spinoza when Leibniz visited him on the way to Hanover. According
to Leibniz, the argument that Descartes gives implicitly in the Fifth
*Meditation* and explicitly in the First Set of Replies is
faulty. Descartes had argued that God is a being having all
perfections, existence is a perfection, therefore, God exists. (AT VII
118-19/CSM II 84-85) But, Leibniz thinks, one needs to show that it is
*possible* for such a being to exist, that is, that it is
possible for all perfections to co-exist in one being. If this is so,
then and only then an *ens perfectissimum* can be said to exist.
In his short essay *That a Most Perfect Being Exists*
(*Quod ens perfectissimum existit*) from 1676, Leibniz
argues just this. He defines a "perfection" as a
"simple quality which is positive and absolute, or, which
expresses without any limits whatever it does express" (A VI iii
578/SR 101). And with this definition in hand, Leibniz is then able to
claim that there can be no inconsistency among perfections, since a
perfection, in being simple and positive, is unanalyzable and incapable
of being enclosed by limits. That is, if A and B are perfections, then
the proposition "A and B are incompatible" cannot be
demonstrated because A and B are simples, nor can the proposition be
known per se. Therefore, it is possible that any and all perfections
are in fact compatible. And, therefore, Leibniz reasons, a subject of
all perfections, or an *ens perfectissimum*, is indeed
possible.




But this argument by itself is not sufficient to determine that God
necessarily exists. Leibniz must also show that existence is itself a
perfection, so that a being having all perfections, an *ens
perfectissimum*, may be said to exist. More exactly, Leibniz needs
to show that *necessary existence* belongs to the essence of
God. And this he does in another short piece from this period, writing
"Again, a necessary being is the same as a being from whose
essence existence follows. For a necessary being is one which
necessarily exists, such that for it not to exist would imply a
contradiction, and so would conflict with the concept or essence of
this being" (A VI iii 583/SR 107). In other words, if it is the
case that a necessary being is the *same* thing as a being whose
existence follows from its essence, then existence must in fact be one
of its essential properties. Leibniz continues in this short
reflection, "And so existence belongs to its concept or essence.
From this we have a splendid theorem, which is the pinnacle of modal
theory and by which one moves in a wonderful way from potentiality to
act: If a necessary being is possible, it follows that it exists
actually, or, that such a being is actually found in the
universe" (A VI iii 583/SR 107). The "pinnacle of Modal
Theory" that Leibniz mentions here is none other than one of the
notorious axioms of the modal logic **S5**:
*#*p* - #*p*. In short,
Leibniz's argument is the following:



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | God is a being having all perfections. (Definition) |
> | (2) | A perfection is a simple and absolute property. (Definition) |
> | (3) | Existence is a perfection. |
> | (4) | If existence is part of the essence of a thing, then
> it is a necessary being. |
> | (5) | If it is possible for a necessary being to exist,
> then a necessary being does exist. |
> | (6) | It is possible for a being to have all
> perfections. |
> | (7) | Therefore, a necessary being (God) does exist. |
> 
> 
> 




It should be noted that Leibniz's argument bears a certain
affinity with the ontological argument that Godel gives, insofar
as it also seeks to demonstrate the possibility of a being having all
simple, positive properties. (For Godel's argument, see the
 entry on 
 ontological arguments.)


#### 7.1.2 The Cosmological Argument




As we have seen, the Principle of Sufficient Reason is one of the
bedrock principles of all of Leibniz's philosophy. In the
*Monadology*, Leibniz appeals to PSR, saying that even in the
case of contingent truths or truths of fact there must be a sufficient
reason why they are so and not otherwise. (*Monadology*
SS36) But, since each particular truth of fact is contingent upon
some other (prior) truth of fact, the reason for the entire series of
truths must be located outside the series, and this ultimate reason is
what we call *God*. (*Monadology* SS37)




In the *Theodicy*, Leibniz fills out this argument with a
fascinating account of the nature of God. First, insofar as the first
cause of the entire series must have been able to survey all other
possible worlds, it has understanding. Second, insofar as it was able
to select one world among the infinity of possible worlds, it has a
will. Third, insofar as it was able to bring about this world, it has
power. (Leibniz adds here that "power relates to *being*,
wisdom or understanding to *truth*, and will to
*good.*") Fourth, insofar as the first cause relates to
all possibles, its understanding, will and power are infinite. And,
fifth, insofar as everything is connected together, there is no reason
to suppose more than one God. Thus, Leibniz is able to
*demonstrate* the uniqueness of God, his omniscience,
omnipotence, and benevolence from the twin assumptions of the
contingency of the world and the Principle of Sufficient Reason.
(*Theodicy* SS7: G VI 106-07/H 127-28)
Naturally, if one were deny the existence of possible worlds in the
sense conceived by Leibniz or deny PSR (by, say, admitting
"brute facts"), then one would hardly be moved by this
kind of argument.


### 7.2 Optimism




Leibniz's account of the nature of possible worlds is dealt
with in a separate entry. Here the following simple question will be
addressed: How can this world be the best of all possible worlds? After
all, as Voltaire brought out so clearly in *Candide*, it
certainly seems that this world, in which one finds no short supply of
natural and moral horrors, is far from perfect - indeed, it seems
pretty lousy. Certainly only a fool could believe that it is the best
world possible. But, Leibniz speaks on behalf of the fool, with an
argument that has essentially the following structure:



> 
> 
> 
> |  |  |
> | --- | --- |
> | (1) | God is omnipotent *and* omniscient
> *and* benevolent *and* the free creator of the world. (Definition) |
> | (2) | Things could have been otherwise-i.e., there are other
> possible worlds. (Premise) |
> | (3) | Suppose this world is *not* the best of
> all possible worlds. (I.e., "The world could be
> better.") |
> | (4) | If this world is not the best of all possible
> worlds, then at least one of the following must be the case:
> 
>  * God was not powerful enough to bring about a better world;
> or
> * God did not know how this world would develop after his creation
> of it (i.e. God lacked foreknowledge); or
> * God did not wish this world to be the best; or
> * God did not create the world; or
> * there were no other possible worlds from which God could
> choose.
>  |
> | (5) | But, any one or more of the disjuncts of (4) contradicts
> (1) or (2). |
> | (6) | Therefore, this world is the best of all
> possible worlds. |
> 
> 
> 




In other words, Leibniz seems to argue that, if one is to hold the
traditional theistic conception of God *and* believe that one
can meaningfully assert that the world could have been other than it
is, then one must hold that *this* world is the best possible.
Naturally, this argument is simply the Christian retort to the
Epicurean argument against theism.




But what are the criteria by which one can say that this world is
the *best*? It should be clear that Leibniz nowhere says that
this argument implies that everything has to be wonderful. Indeed,
Leibniz is squarely in the tradition of all Christian apologists going
back to Augustine, arguing that we cannot have knowledge of the whole
of the world and that even if a piece of the mosaic that is
discoverable to us is ugly the whole may indeed have great beauty.
Still, Leibniz does offer at least two considerations relevant to the
determination of the happiness and perfection of the world. He tells us
in the *Discourse on Metaphysics*, first, that
"...the happiness of minds is the principal aim of
God..." (A VI iv 1537/AG 38) and, second, that "God
has chosen the most perfect world, that is, the one which is at the
same time the simplest in hypotheses and the richest in
phenomena" (A VI iv 1538/AG 39). So, is this world of genocide
and natural disaster better than a world containing only one
multifoliate rose? Yes, because the former is a world in which an
infinity of minds perceive and reflect on the diversity of phenomena
caused by a modest number of simple laws. To the more difficult
question whether there is a better world with perhaps a little less
genocide and natural disaster Leibniz can only respond that, if so, God
would have brought it into actuality. And this, of course, is to say
that there really is no better possible world.