Leibniz: Metaphysics

leibnizThe German rationalist philosopher, Gottfried Wilhelm Leibniz
(1646-1716), is one of the great renaissance men of Western thought.
He has made significant contributions in several fields spanning the
intellectual landscape, including mathematics, physics, logic, ethics,
theology, and philosophy. Unlike many of his contemporaries of the
modern period, Leibniz does not have a canonical work that stands as
his single, comprehensive piece of philosophy. Instead, in order to
understand Leibniz's entire philosophical system, one must piece it
together from his various essays, books, and correspondences. As a
result, there are several ways to explicate Leibniz's philosophy. This
article begins with his theory of truth, according to which the nature
of truth consists in the connection or inclusion of a predicate in a
subject.

Together with several apparently self-evident principles (such as the
principle of sufficient reason, the law of contradiction, and the
identity of indiscernibles), Leibniz uses his predicate-in-subject
theory of truth to develop a remarkable philosophical system that
provides an intricate and thorough account of reality. Ultimately,
Leibniz's universe contains only God and non-composite, immaterial,
soul-like entities called "monads." Strictly speaking, space, time,
causation, material objects, among other things, are all illusions (at
least as normally conceived). However, these illusions are
well-founded on and explained by the true nature of the universe at
its fundamental level. For example, Leibniz argues that things seem to
cause one another because God ordained a pre-established harmony among
everything in the universe. Furthermore, as consequences of his
metaphysic, Leibniz proposes solutions to several deep philosophical
problems, such as the problem of free will, the problem of evil, and
the nature of space and time. One thus finds Leibniz developing
intriguing arguments for several philosophical positions–including
theism, compatibilism, and idealism.

This article is predominately concerned with this broad view of
Leibniz's philosophical system and does not deal with Leibniz's work
on, for example, aesthetics, political philosophy, or (except
incidentally) physics. Leibniz's "mature metaphysical career" spanned
over thirty years. During this period, it would be surprising if some
of his basic ideas did not change, but, remarkably, the broad outline
of his philosophy does remain constant.

1. Life

Gottfried Wilhelm Leibniz was born in Leipzig, Germany, on July 1,
1646. He was the son of a professor of moral philosophy. After
university study in Leipzig and elsewhere, it would have been natural
for him to go into academia. Instead, he began a life of professional
service to noblemen, primarily the dukes of Hanover (Georg Ludwig
became George I of England in 1714, two years before Leibniz's death).
His professional duties were various, such as official historian and
legal advisor. Above all, he was required to travel widely, meeting
many of the foremost intellectuals in Europe–of particularly formative
importance were the astronomer, mathematician, and physicist Huygens,
and the philosopher Spinoza.

Leibniz was one of the great polymaths of the modern world. Moreover,
a list of his significant contributions is almost as long as the list
of his activities. As an engineer, he worked on calculating machines,
clocks, and even mining machinery. As a librarian, he more or less
invented the modern idea of cataloguing. As a mathematician, he not
only produced ground-breaking work in what is now called topology, but
came up with the calculus independently of (though a few years later
than) Newton, and his notation has become the standard. In logic, he
worked on binary systems, among numerous other areas. As a physicist,
he made advances in mechanics, specifically the theory of momentum. He
also made contributions to linguistics, history, aesthetics, and
political theory.

Leibniz's curiosity and genius ranged widely, but one of the most
constant of his concerns was to bring about reconciliation by
emphasizing the truths on each side of even the most seemingly
contradictory positions. Throughout his life, he hoped that his work
on philosophy, as well as his work as a diplomat, would form the basis
of a theology capable of reuniting the Church, which had been divided
since the Reformation in the 16th Century. Similarly, he was willing
to engage with, and borrow ideas from, the materialists as well as the
Cartesians, the Aristotelians as well as the most modern scientists.
It is quite ironic, then, that he was a partial cause of a dispute
between British and Continental mathematicians concerning who was
first to develop the calculus (and who might have plagiarized who), a
dispute which slowed the advance of mathematics in Europe for over a
century.

However, the great variety of Leibniz's work meant that he completed
few of his ambitious projects. For present purposes, this means above
all that Leibniz's rich and complex philosophy has to be gathered
primarily from a large set of quite short manuscripts, many
fragmentary and unpublished, as well has his various correspondences.
(The last section of this entry–Editions of Leibniz–provides
bibliographical details of several editions of Leibniz's work.) As a
result, a major controversy in Leibniz scholarship is the question of
where to begin. Insofar as Leibniz is a logician, it is tempting to
begin with his conception of truth (and, indeed, this will be the
starting point of this article). But insofar as Leibniz is a
metaphysician, it is equally tempting to begin with his account of the
nature of reality, in particular his notion of substance as monads.
Less common, but perhaps equally likely, starting points might reside
in Leibniz the mathematician, the theologian, or the physicist. These
controversies, however, already contain a lesson: to an important
degree it doesn't matter. So integrated were his various philosophical
interests–so tightly laced together into a system–that one ought to be
able to begin anywhere and reconstruct the whole. Or at least Leibniz
evidently thought so, since often he uses an idea from one part of his
philosophy to concisely prove something in an apparently quite distant
philosophical region. However, due to this systematic nature of his
philosophy, in which every idea seems to rely upon others, engaging
Leibniz's ideas often proves to be challenging.
2. The Idea of Truth

According to Leibniz, a conception of truth has important consequences
for a conception of reality and how it is to be understood at its most
profound level. Intuitively, a proposition is true when its content is
adequate to the situation in the world to which it refers. For
example, "the sky is gray" is true if and only if the thing out there
in the world called "the sky" is actually the color called "gray" at
the time the proposition is stated. This, however, raises issues about
the relationship of language to the world and what "adequacy" consists
in.

Leibniz claims that one can bypass problems with the intuitive notion
of truth, at least for the moment. Truth, according to Leibniz, is
simply a proposition in which the predicate is contained in the
subject. The predicate is what is asserted; the subject is what the
assertion is about. All true propositions, then, can be expressed by
the following general form: "subject is predicate." This is not, by
any means, an idea unique to Leibniz. What is unique, however, is the
single-mindedness with which he pursues the consequences of such an
idea of truth. (See, for example, "Correspondence with Arnauld," 14
July 1686.)

This notion of truth seems straight-forward enough for what are
commonly called analytic propositions, such as "Blue is a color,"
which has more to do with the definition of blue than it does with the
world. The notion of color is part of the notion of blue. Similarly,
in the basic logical truth "A is A," the predicate is not just
contained in the subject, it is the subject. But, Leibniz states that
this "being contained" is implicitly or virtually the case with other
truths (see "Primary Truths" and "The Nature of Truth"). Take, for
example, the statement "Peter is ill." Intuitively, this proposition
is true only if it refers to a real world in which Peter is, in fact,
ill. Leibniz, however, analyzes this as follows: if one knew
everything there is to know about Peter, that is, if one had a
complete concept of Peter, one would also know (among many other
things) that he is ill at the moment. Therefore, the statement "Peter
is ill" is true not primarilybecause of some reference to the world,
but in the first instance because someone has the concept of Peter,
which is the subject of the proposition, and that concept contains (as
a predicate) his being ill. Of course, it may be the case that one
happens to know that Peter was ill because one refers to the world
(perhaps sees him cough repeatedly). But the fact that one finds out
about Peter in this way does not make the statement that "Peter is
ill" true and thus a piece of knowledge because of that reference. One
must distinguish the concept of truth from pragmatic or methodological
issues of how one happens to find out about that truth, or what one
can do with the truth. The latter, according to Leibniz, are
completely irrelevant to the question "What is truth?" in itself.

Leibniz also claims that a statement is true for all time–that is,
whenever the statement is made. So, for example, the statement "Peter
is ill (on January 1st, 1999)" was true in the year 1998 (even though
no one knew it yet) as well as in the year 2000 (even though everyone
may have forgotten about the illness by then). It was also true a
million years ago, and will be true a million years from now, although
it is very unlikely that anyone will actually know this truth at those
times.

Leibniz's own example is of Julius Caesar. He writes:

For if some person were capable of completing the whole
demonstration by means of which he could prove this connection of the
subject (which is Caesar) with the predicate (which is his successful
enterprise [winning the battle of Pharsalus, etc.]), he would then
show that the future dictatorship of Caesar had its foundation in his
notion or nature, that a reason can be found there why he resolved to
cross the Rubicon rather than stop, and why he won rather than lost
the day at Pharsalus… (Discourse on Metaphysics, §13).

However, there are several ideas Leibniz introduces in this passage
that require further investigation. What is meant by "completing the
whole demonstration," by something having a "foundation," or by "a
reason can be found?"
3. Sufficient Reason

As previously stated, for any proposition, truth is defined by Leibniz
in the same way: the predicate is contained in the subject. It only
takes a little thought to realize that for any one subject (like Peter
or Caesar), the number of predicates which are true of it will be
infinite (or at least very large), for they must include every last
thing Peter or Caesar did or will do, as well as everything that did
or will ever happen to them. But now it is natural to ask: Why do all
these predicates come together in the one subject? It could be that
the predicates are a quite arbitrary or random collection– although
Leibniz does not believe this, and it is certainly not intuitive.
Rather, one predicate or set of predicates explains another. For
example, Peter's coming into contact with a virus explains his
illness. Or, Caesar's ambition and boldness explains why he decided to
cross the Rubicon. So, many (at least) of the predicates that are true
of a subject "hang together" as a network of explanations.

Leibniz goes further still by claiming that for every predicate that
is true of a subject, there must be a set of other true predicates
which constitute a sufficient reason for its being true. This he calls
the principle of sufficient reason–that there must be a sufficient
reason for why things are as they are and not otherwise. This is why
he uses words like "foundation" and "reason" in the quotation above.
Unless this were true, Leibniz argues, the universe would not make any
sense, and science and philosophy both would be impossible (see, for
example, New Essays on Human Understanding, preface, p. 66). Moreover,
it would be impossible to account for a basic notion like identity
unless there was a sufficient reason why Caesar, for example, with his
particular properties at a given time, is identical with the Caesar
who existed a week prior with such different properties (see "Remarks
on Arnauld's Letter," May 1686).

The principle of sufficient reason also accounts for why Leibniz uses
the phrase "completing the whole demonstration" in the above quote. If
the complete concept of the subject (that is, all of its true
predicates) together constitutes a complete network of explanation,
then these explanations can be followed forward and backward, so to
speak, at least in principle. That is, working forward, one
coulddeduce that Caesar will cross the Rubicon from a all the
predicates that have been true of him; or, working backward, one can
deduce from all those predicates true of Caesar at his death the
reasons why he won the battle of Pharsalus. The "whole demonstration,"
then, is the revelation of the logical structure of the network of
explanations that make Caesar who he is.

However, this is clearly not something the average person can do.
Human minds are not subtle and capacious enough for a task which may
be infinite. Still, in a more limited way, one can certainly talk
about personalities, characters, and causes or reasons for things. The
quotation from Leibniz given above continues:

… [he who completed the whole demonstration would then show] that
it was rational and therefore definite that this would happen, but not
that it is necessary in itself, or that the contrary implies a
contradiction (Discourse on Metaphysics, §13).

These qualifications are quite important for Leibniz. It was often
suggested by Leibniz's contemporaries (and is still being suggested)
that his idea of the sufficient reason of all the predicates of a
subject meant that everything true of a subject is necessarily true.
This might entail that Caesar did not choose to cross the Rubicon, but
that he was acting in a determined manner, like a machine. In other
words, Leibniz seems to be denying any sort of free will. The free
will problem will be discussed in more detail below, but for the
moment, a few observations can be made.

First, Leibniz claims that Caesar's crossing of the Rubicon is not
necessary in the sense that "A is A" is necessary. Because while "A is
not A" is a contradiction, Caesar's deciding not to cross the Rubicon
does not imply a contradiction. To be sure, history would have been
different–even Caesar would have been different–but there is no
contradiction in that strong sense. Caesar's properties are not
logically necessary.

Second, any truth about Caesar–indeed, the whole complete concept of
Caesar–is not "necessary in itself." Caesar is Caesar, but nothing
about Caesar in himself proves that Caesar has to be. By contrast, "A
is A" doesn't need any other explanation for its truth. So, while
every property of Caesar is explained by some other property of
Caesar, no property explains why it is true that Caesar existed.
Caesar is not anecessary being.

What the precise details are of Leibniz's account of free will remain
a strenuously debated issue in Leibniz scholarship (especially what
the exact nature is of these distinctions, whether he is justified in
making them, and even if justified whether they yield the results he
claims in the area of free will). More detail will be added to this
account below, but the existence of this debate should be kept in mind
throughout.
4. Substance, Briefly

At this point, it is useful to turn from a conception of truth to a
conception of substance. Leibniz's philosophy of substance will be
explicated in more detail in section 8 (Substance as Monad). For the
moment, simply observe that for humans (though not for God), complete
concepts are always concepts of existing substances–that is, of really
existing things. Leibniz writes:

Now it is obvious that all true predication has some foundation in
the nature of things, and when a proposition is not identical, that is
to say when the predicate is not expressly included in the subject, it
must be virtually included in it.[...] This being so, 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 include, and to
allow the deduction of, all the predicates of the subject to which
that notion is attributed (Discourse on Metaphysics, §8, emphasis
added).

To be the individual substance, Caesar, then, is to be such as to have
a notion which includes everything that can truthfully be predicated
of the subject Caesar. Thus, one might say that, for Leibniz, a
substanceis a complete concept made real, and a complete concept is a
real substance expressed or "perceived" in thought. Moreover, just as
for any one predicate, the complete concept contains other predicates
which explain that predicate, for any given property of a substance,
the complete individual substance will itself be the explanation for
that property. Caesar chose to cross the Rubicon for many complex
reasons, but they all boil down to this: that was the kind of
individual Caesar was.

Leibniz has much more to say about substance, but he claims that it
all follows from this insight. However, the exact relationship Leibniz
intended between the logical idea of a complete concept and the
metaphysical idea of a substance is still debated in Leibniz
scholarship.
5. Necessary Being

The complete concept of Caesar, according to Leibniz, cannot explain
itself in its entirety. Expressed ontologically, this means that
Caesar himself provides no explanation of why Caesar should have
existed at all–Caesar is a contingent being. "Contingent" here simply
means something that could have been otherwise; in the case of Caesar
as a being, then, it means something that could have not existed at
all. The principle of sufficient reason must not only apply to each
predicate in the complete concept of a subject, but also it must apply
to the concept itself in its entirety as the concept of an existing
thing. Thus, there must be a sufficient reason for why this particular
substance, Caesar, exists, rather than some other substance, or
nothing at all.

What, then, sufficiently explains a contingent being such as Caesar?
Possibly other substances, such as his parents, and they in turn are
explained by still others? But the entire course of the universe, the
total aggregate of substances across space and time, are one and all
contingent. There are other possible things, to be sure; but there are
also other possible universes that could have existed but did not. The
totality of contingent things themselves do not sufficiently explain
themselves. Here again, the principle of sufficient reason applies.
There must be, Leibniz insists, something beyond the totality of
contingent things which explains them, something which is itself
necessary and therefore requires no explanation other than itself.
(Note, however, that this does not assume an origin or beginning in
any sense. Even if time stretched infinitely into the past, there
would still be no explanation for the total course of things.)

suffrea

God, according to Leibniz, is the necessary being which constitutes
the sufficient explanation of the totality of contingent things–why
the universe is this way rather than any other. Thus far, God's
necessity is the only thing mentioned about such a being (there is not
much religious or theological about this initially bare metaphysical
concept). God as a being may be necessary, but if the contingent
universe were simply a random or arbitrary act of God, then God would
not constitute the required explanation of all things. In other words,
God must not only be necessary, but also the source of the
intelligibility of all things. It must be possible, therefore, to
inquire into the reasons God had for authorizing or allowing this,
rather than any other, universe to be the one that actually exists.
And if God is to be the explanation of the intelligibility of the
universe, then God must have access to that intelligibility, such that
God could be said to know what it is that is being allowed to
exist–that is, God must have the ability to grasp complete concepts,
and to see at once the "whole demonstration" discussed above. God so
far is therefore (i) a necessary being, (ii) the explanation of the
universe, and (iii) the infinite intelligence.

Here Leibniz famously brings in the notion of perfection (see, for
example, "A Specimen of Discoveries"). One has to try to imagine God,
outside of time, contemplating the infinite universe that "he" is
going to, not create, but allow to be actual and sustain in existence.
In the mind of God are an infinite number of infinitely complex and
complete concepts, all considered as possibly existent substances,
none having any particular "right" to exist. There is just one
constraint on this decision: it must not violate the other basic
principle of Leibniz's, the law of non-contradiction (also known as
"the law of contradiction"). In other words, each substance may
individually be possible, but they must all be possible together–the
universe forming a vast, consistent, non-contradictory system. For
example, God could not create a universe in which there are both more
sheep than cows and more cows than sheep. God could choose a universe
in which there is the greatest possible quantity of pizza, or in which
everything is purple, and so on. However, according to Leibniz, God
chooses the universe that is the most perfect. This principle of
perfection is not surprising since it is most consummate with the idea
of God as an infinite being; to choose any other less perfect universe
would be to choose a lesser universe. Thus, according to Leibniz, the
actual world is the best of all possible worlds. (This claim, and its
apparent implications, were very effectively and famously satirized by
Voltaire in his Candide. Note also that Leibniz is often taken as an
ancestor of modern possible worlds semantics; however, it is
undeniable that at least the context and purpose of Leibniz's notion
of a possible universe was quite different.) Leibniz explores the
theological consequences of this at, for example, the end of Discourse
on Metaphysics. (There may be a difficult theological implication
here: must God be thought of as constrained, first by the concept of
perfection, and then by the systemic nature of his creation? Leibniz
attempts, for example, in the "Correspondence with Arnauld" to escape
this conclusion.)

To try to understand further this notion of perfection, Leibniz
explores several concepts in various writings: notions of the best,
the beautiful, the simply compossible, greatest variety or the
greatest quantity of essence. The last of these is the explanation he
continually comes back to: perfection simply means the greatest
quantity of essence, which is to say the greatest richness and variety
in each substance, compatible with the least number of basic laws, so
as to exhibit an intelligible order that is "distinctly thinkable" in
the variety (see "A Resume of Metaphysics;" there is a relationship to
the Medieval, and particularly Augustine, notion of plenitude).
Leibniz seems to understand this principle as simply self-evident. It
certainly seems to be a big jump to the aesthetic, moral, and wise God
from the ontological conception of God deduced above. However, Leibniz
may have a point in arguing that it would be absurd in some sense for
an infinite being to choose anything other than an infinitely rich and
thus perfect universe. He also finds this aesthetic observed
throughout nature: natural forms tend towards a maximum of variety
compatible with orderliness. Nevertheless, contemporary philosophers
generally find Leibniz's conclusion here to not strictly follow from
the previous considerations.

For Leibniz, this forms a proof for the existence of God (see
Monadology §§37-39 and "A Specimen of Discoveries"). In fact, it is a
version of the third of the cosmological arguments given by St. Thomas
Aquinas, and subject to many of the same difficulties. One might, for
example, object in a Kantian vein that the concept of explanation,
rightly demanded of all individual contingent beings, is applied
beyond its proper sphere in demanding an explanation of the totality
of contingent beings. But Leibniz might well counter that this
objection assumes a whole theory of the "proper spheres" of concepts.
6. Problems of Freedom, Sin, and Evil
a. Freedom and Sin

Leibniz's conception of God, however, may seem to cause more problems
than it solves. For example, if the complete concept of any being,
such as a human being, is known for all time, and was chosen by God
for existence, then is such a being free? It seems that what one means
by "freedom" is that the outcome is not predictable, as opposed to,
for example, the way in which the operation of a washing machine or
the addition of two numbers is predictable. Further, what must one
make of morality and sin? Why, for example, should God punish Adam and
Eve for sinning when they seemed to have no free choice, since God
knew in advance (predicted and, indeed, made it the case) that they
were going to sin?

While Leibniz's philosophical system demands a certain sense of
determinism about the universe, he does not want to deny the existence
of free will. Leibniz thus seeks to substantiate a form or
compatibilism(that is, a view which takes determinism to be compatible
with free will). In order to accomplish this, Leibniz distinguishes
between several ways in which things might be determined in advance.
Whatever is determined is clearly true. Truth, however, comes in
several varieties. (Much of the following is taken from the set of
distinctions Leibniz makes in "Necessary and Contingent Truths;"
Leibniz makes similar but rarely identical sets of distinctions in a
variety of texts.)

1. Truths of Essence
These come in two varieties:
1. Primary/original truth: the law of non-contradiction, for example.
2. Eternal, metaphysical, or geometrical truths: the laws of
arithmetic or geometry, for example, which Leibniz claims can be
reduced by a finite process of argumentation and substitution of
definitions to primary truth. These are valid in all possible
universes.
2. Truths of Existence, of Fact, or of Hypothesis
Here, arguably, Leibniz sees four varieties:
1. Absolutely universal truths: those truths definitive of
this universe as being the most perfect universe. Leibniz writes:
"Indeed, I think that in this series of things there are certain
propositions which are true with absolute universality, and which
cannot be violated even by a miracle" ("Necessary and Contingent
Truths").
2. Universal-physical truths: the laws of physics and other
such efficient causes, for example; truths which hold universally of
all substances in this, but not in all possible, universes, but which
also could, in principle, be violated by a miracle, in accordance with
overall divine providence.
3. Individual metaphysical truths: truths about the
properties of individual substances, where those properties follow
from the complete concept–and thus are apparent to God, but do not
follow any "subordinate universal laws." Deduction of such truths is
available to no being, no matter how perfect or perceptive, other than
God.
4. Hypothetical truths: only truths of essence can be
necessary, absolutely and strictly speaking. All other truths, such as
the actions of Caesar, are only "hypothetically" necessary–that is,
only on the hypothesis that a universe exists as it is, with beings
such as these in it (see Discourse on Metaphysics, §13 and
"Correspondence with Arnauld," April 12th, 1686).

A person's actions are, therefore, not necessary by definition
(regardless, at this point, of which type of "truth of existence" they
fall under). Thus, the concept of an individual "inclines without
necessitating" (seeDiscourse on Metaphysics, §30). Leibniz further
writes:

For speaking absolutely, our will is in a state of indifference,
in so far as indifference is opposed to necessity, and it has the
power to do otherwise, or to suspend its action altogether, both
alternatives being and remaining possible. [...] It is true, however,
and indeed it is certain from all eternity, that a particular soul
will not make use of this power on such and such an occasion. But
whose fault is that? Does it have anyone to blame but itself?
(Discourse on Metaphysics, §30, emphasis added)

By "indifference," Leibniz means a physical indifference–that is to
say, there is no universal-physical truth, as defined above, which
governs human action. For Leibniz, this means that human action is
further freed: the will has the power to suspend its action with
respect to the physical sequence of efficient causes, but also even
with respect to what would otherwise be seen as a decisive final
cause. Leibniz states: "For they [free or intelligent substances] are
not bound by any certain subordinate laws of the universe, but act as
it were by a private miracle" ("Necessary and Contingent Truths").

Minds, then, are different from mechanical causes. (As it will be
shown below, Leibniz goes against the trend of 17th and 18th century
thought by reintroducing the Aristotelian and Scholastic notion of a
final cause and, indeed, substantial forms.) Although Leibniz
occasionally uses the analogy of a machine to describe the soul, the
kinds of forces and causes operative in the former are simply
inapplicable to the latter. Thus, if by individual free choice one
means an individual action that cannot be known in advance by even an
infinitely subtle application of the laws of physics, chemistry, or
biology, then humans have free choice in that sense as well.

Leibniz also offers the following additional arguments for his
particular conception of human free will:

(i) Freedom as "unpredictability" might be taken to mean freedom as an
act uncaused. But this makes no sense, for free choice is not
randomness. Caesar's free act, for example, has a cause–namely,
Caesar. Why should one complain when the individual concept of Caesar
intrinsically determines what Caesar does? Isn't Caesar free if he is
the source of his action, and not anyone or anything else?

(ii) A necessary ignorance of the future is practically, perhaps even
logically, equivalent to freedom. Again, grasping the full explanation
of any predicate that lies in the complete concept is an infinite
task. To help illustrate the distinction between contingent and
necessary truths, Leibniz makes a famous analogy with the
incommensurability of any whole number or fraction with a "surd" (for
example, the square root of two, the value of which cannot be
represented numerically by any finite series of numbers.) For finite
human minds, that incommensurability is a positive fact, just like
contingency–no matter that for God neither calculation is impossible,
or even more difficult. Thus contingent truths can in principle be
known from all time, but necessarily not by a human being (see, for
example, "On Freedom"). Leibniz writes: "Instead of wondering about
what you cannot know and what can tell you nothing, act according to
your duty, which you do know" (Discourse on Metaphysics, §30). (It
should be pointed out that this is somewhat more than an analogy,
since it is closely related to the kinds of problems infinitesimal
calculus was designed to deal with–and Leibniz takes the possibility
of a calculus as having real metaphysical implications.)

(iii) A famous scholastic debate concerned the so-called "Sloth
Syllogism." If everything is fated, the argument goes, then whatever
action one "does" will or will not happen whether or not one wills it,
therefore one need not will anything at all. One can just be a sloth,
and let the universe happen. Leibniz thinks this is absurd–indeed,
immoral. The will of an individual matters. If John Doe is the kind of
person who is a sloth, then (everything else being the same) the
course of his life will indeed be quite different than if he is the
kind of person (like Caesar) who takes events by the scruff of the
neck.

(iv) What many philosophers mean by "contingent" is that an individual
predicate "could have been different," and everything else the same.
For Leibniz, this is impossible. To change one predicate means to
alter the whole complete concept, the substance, and with it the whole
universe. Leibniz thus claims that philosophers of a more radical
sense of freedom do not take seriously the extent to which the
universe is an integrated network of explanations, and that this in
turn has implications for the idea of contingency (see the discussion
of Adam in Leibniz's letter to Landgraf Ernst von Hessen-Rheinfels,
April 12, 1686). Thus, contingent events, even one's free acts, must
be part of the perfection of the universe. Although, that does not
mean that all contingent events are so in the same way.

According to Leibniz, any remaining objections to this idea of free
will only result from a metaphysically incoherent idea of what freedom
means. There is no question that Leibniz introduced a spirited and
powerful position into the age-old philosophical debate concerning
free will. Which position is "metaphysically incoherent," however,
remains under debate. (For more on the philosophical debate of free
will, see the "Free Will" entry.)
b. Problem of Evil

Leibniz's approach to the classic problem of evil is similar. The
problem of evil, for Leibniz, can be put in the following way: If God
is supremely good, and the creator (or author) of the best possible
universe, then why is there so much pain and sin in the world? Leibniz
claims that this apparent paradox is not a real problem. Leibniz
coined the term "theodicy" to refer to an attempt to reconcile God's
supremely benevolent and all-good nature with the evil in the world.
Thus, Leibniz's Theodicy is largely a proposed solution to the problem
of evil. However, his thoughts on the issue are to be found spread
over many texts. (For more on the problem of evil, see the entries
"The Evidential Problem of Evil" and "The Logical Problem of Evil.")

Here, very briefly, are three of Leibniz's main replies to the problem of evil:

(i) Human minds are only only aware of a small fraction of the
universe. To judge it full of misery on this small fraction is
presumptuous. Just as the true design–or, indeed, any design–of a
painting is not visible from viewing a small corner of it, so the
proper order of the universe exceeds one's ability to judge it.

(ii) The best possible universe does not mean no evil, but that less
overall evil is impossible.

(iii) Similarly to the previous argument, and in the best
Neo-Platonist tradition, Leibniz claims that evil and sin are
negations of positive reality. All created beings are limitations and
imperfect; therefore evil and sin are necessary for created beings
(see Discourse on Metaphysics, §30).
7. Space, Time, and Indiscernibles
a. Against the Absolute Theory

Between 1715 and 1716, at the request of Caroline, Princess of Wales,
a series of long letters passed between Leibniz and the English
physicist, theologian, and friend of Newton, Samuel Clarke. It is
generally assumed that Newton had a hand in Clarke's end of the
correspondence. They were published in Germany and in England soon
after the correspondence ceased and became one of the most widely read
philosophical books of the 18th Century. Leibniz and Clarke had
several topics of debate: the nature of God's interaction with the
created world, the nature of miracles, vacua, gravity, and the nature
of space and time. Although Leibniz had written about space and time
previously, this correspondence is unique for its sustained and
detailed account of this aspect of his philosophy. It is also worth
pointing out that Leibniz (and after him Kant) continues a long
tradition of philosophizing about space and time from the point of
view of space, as if the two were always in a strict analogy. It is
only rarely that Leibniz deals in any interesting way with time on its
own (we shall return to this in section 10).

Newton, and after him Clarke, argued that space and time must be
absolute (that is, fixed background constants) and in some sense
really existent substances in their own right (at least, this was
Leibniz's reading of Newton). The key argument is often called the
"bucket argument." When an object moves, there must be some way of
deciding upon a frame of reference for that motion. With linear
motion, the frame does not matter (as far as the mathematics are
concerned, it does not matter if the boat is moving away from the
shore, or the shore is moving away from the boat); even linear
acceleration (changing velocity but not direction) can be accounted
for from various frames of reference. However, acceleration in a curve
(to take Newton's example, water forced by the sides of a bucket to
swirl in a circle, and thus to rise up the sides of the bucket), could
only have one frame of reference. For the water rising against the
sides of the bucket can be understood if the water is moving within a
stationary universe, but makes no sense if the water is stationary and
the universe is spinning. Such curved acceleration requires the
postulation of absolute space which makes possible fixed and unique
frames of reference. (Similar problems made Einstein's General Theory
of Relativity so much more mathematically complicated than the Special
Theory.)

Leibniz, however, has a completely different understanding of space
and time. First of all, Leibniz finds the idea that space and time
might be substances or substance-like absurd (see, for example,
"Correspondence with Clarke," Leibniz's Fourth Paper, §8ff). In short,
an empty space would be a substance with no properties; it will be a
substance that even God cannot modify or destroy.

But Leibniz's most famous arguments for his theory of space and time
stem from the principle of sufficient reason (the principle that
everything which happens has, at least in principle, an explanation of
why it happened as it did and not otherwise). From this principle,
together with the law of non-contradiction, Leibniz believes that
there follows a third: the principle of the identity of
indiscernibles, which states that any entities which are indiscernible
with respect to their properties are identical. Leibniz is fond of
using leaves as an example. Two leaves often look absolutely
identical. But, Leibniz argues, if "two" things are alike in every
respect, then they are the same object, and not two things at all. So,
it must be the case that no two leaves are ever exactly alike.

Leibniz's support for the principles of the identity of indiscernibles
primarily derives from his commitment to the principle of sufficient
reason in the following way. If any objects are in every way the same,
but actually distinct, then there would be no sufficient reason (that
is, no possible explanation) for why the first is where (and when) it
is, and the second is where (and when) it is, and not the other way
around. If, then, one posits the possible existence of two identical
things (things that differ in number only–that is, one can count them,
but that is all), then one also posits the existence of an absurd
universe, one in which the principle of sufficient reason is not
universally true. Leibniz often expresses this in terms of God: if two
things were identical, there would be no sufficient reason for God to
choose to put one in the first place and the other in the second
place. (Note that Leibniz's argument relates to a scholastic debate
centered on the notion of "Buridan's Ass.")

Similar considerations apply to Newtonian absolute space. Leibniz's
argument against the Newton-Clarke position can be understood here as
two related reductio ad absurdum arguments. The first concerns the
violation of the principle of the identity of indiscernibles. Suppose
that space is absolute. Since every region of space would be
indiscernible from any other and spatial relations would be construed
as extrinsic, it would be possible for two substances to be
indiscernible yet distinct in virtue of being in different locations.
But this is absurd, Leibniz argues, because it violates the principle
of the identity of indiscernibles. Therefore, space must not be
absolute (see "Correspondence with Clarke," Leibniz's Third Paper).
The second reductio concerns the violation of the principle of
sufficient reason. Suppose that space is absolute. Leibniz argues that
there would then be no sufficient reason for why the whole universe
was created here instead of two meters to the left (because no region
of space is discernible from any other). Thus, absolute space is
absurd, because it violates the principle of sufficient reason (see
"Correspondence with Clarke," Leibniz's Fourth Paper). (Analogous
problems are thought to result from a conception of absolute time.)

space
b. The Relational Theory

That is the negative portion of Leibniz's argument. But what does all
this say about space? For Leibniz, the location of an object is not a
property of an independent space, but a property of the located object
itself (and also of every other object relative to it). This means
that an object here can indeed be different from an object located
elsewhere simply by virtue of its different location, because that
location is a real property of it. That is, space and time are
internal or intrinsic features of the complete concepts of things, not
extrinsic. Let us return to the two identical leaves. All of their
properties are the same, except that they are in different locations.
But that fact alone makes them completely different substances. To
swap them would not just involve moving things in an indifferent
space, but would involve changing the things themselves. That is, if
the leaf were located elsewhere, it would be a different leaf. A
change of location is a change in the object itself, since spatial
properties are intrinsic (similarly with location in time).

Leibniz's view has two major implications. First, there is no absolute
location in either space or time; location is always the situation of
an object or event relative to other objects and events. Second, space
and time are not in themselves real (that is, not substances). Space
and time are, rather, ideal. Space and time are just metaphysically
illegitimate ways of perceiving certain virtual relations between
substances. They are phenomena or, strictly speaking, illusions
(although they are illusions that are well-founded upon the internal
properties of substances). Thus, illusion and science are fully
compatible. For God, who can grasp all at once complete concepts,
there is not only no space but also no temptation of an illusion of
space. Leibniz uses the analogy of the experience of a building as
opposed to its blueprint, its overall design (see, for example,
"Correspondence with Arnauld" 12 April 1686 and Monadology §57). It is
sometimes convenient to think of space and time as something "out
there," over and above the entities and their relations to each other,
but this convenience must not be confused with reality. Space is
nothing but the order of co-existent objects; time nothing but the
order of successive events. This is usually called a relational theory
of space and time. (For more information, see §6 on relative vs.
absolute theories of time of the "Time" entry).

Space and time, according to Leibniz, are thus the hypostatizations of
ideal relations, which are real insofar as they symbolize real
differences in substances, but illusions to the extent that (i) space
or time are taken as a thing in itself, or (ii) spatial/temporal
relations are taken to be irreducibly exterior to substances, or (iii)
extension or duration are taken to be a real or even fundamental
property of substances. Take the analogy of a virtual reality computer
program. What one sees on the screen (or in a specially designed
virtual reality headset) is the illusion of space and time. Within the
computer's memory are just numbers (and ultimately mere binary
information) linked together. These numbers describe in an essentially
non-spatial and temporal way a virtual space and time, within which
things can "exist," "move" and "do things." For example, in the
computer's memory might be stored the number seven, corresponding to a
bird. This, in turn, is linked to four further numbers representing
three dimensions of space and one of time–that is, the bird's
position. Suppose further the computer contains also the number one,
corresponding to the viewer and again linked to four further numbers
for the viewer's position, plus another three giving the direction in
which the viewer's virtual eyes are looking. The bird appears in the
viewer's headset, then, when the fourth number associated with the
bird is the same as the viewer's fourth number (they are together in
time), and when the first three numbers of the bird (its position in
virtual space) are in a certain algebraic relation to the number
representing the viewer's position and point of view. Space and time
are reduced to non-spatial and non-temporal numbers. For Leibniz, God
in this analogy apprehends these numbers as numbers, rather than
through their translation into space and time.
c. Objections and Replies

This, however, raises a serious logical problem for Leibniz. Recall
Leibniz's theory of truth as the containedness of a predicate in a
subject. This seemed acceptable, perhaps, for propositions such as
"Caesar crossed the Rubicon" or "Peter is ill." But what about "This
leaf is to the left of that leaf?" The latter proposition involves not
one subject, but three (the two leaves, and whatever is occupying the
point-of-view from which the one is "to the left"). Leibniz has to
argue that all relational predicates are in fact reducible to internal
properties of each of the three substances. This includes time, as
well as relations such as "the sister of" or "is angry at." But can
all relations be so reduced, at least without radically deforming
their sense? Modern logicians often see this as the major flaw in
Leibniz's logic and, by extension, in his metaphysics.

Furthermore, Leibniz must provide a response to the Newtonian bucket
argument. Indeed, Leibniz thinks that one simply needs to provide a
rule for the reduction of relations. For linear motion the virtual
relation is reducible to either or both the object and the universe
around it. For non-linear motion, one must posit a rule such that the
relation is not symmetrically reducible to either of the subjects
(bucket, or universe around it). Rather, non-linear motion is assigned
only when, and precisely to the extent that, the one subject shows the
effects of the motion. That is, the motion is a property of the water,
if the water shows the effects (see "Correspondence with Clarke,"
Leibniz's Fifth Paper, §53). Perhaps it seems strange that the laws of
nature should be different for linear as opposed to non-linear motion.
It sounds like anarbitrary new law of nature, but Leibniz might
respond that it is no more arbitrary that any other law of nature;
people have just become used to the illusion of space and time as
extrinsic relations of entities that they are not used to thinking in
these terms.
8. Substance as Monad

We are now, finally, ready to get a picture of what Leibniz thinks the
universe is really like. It is a strange, and strangely compelling,
place. Around the end of the Seventeenth Century, Leibniz famously
began to use the word "monad" as his name for substance. "Monad" means
that which is one, has no parts and is therefore indivisible. These
are the fundamental existing things, according to Leibniz. His theory
of monads is meant to be a superior alternative to the theory of atoms
that was becoming popular in natural philosophy at the time. Leibniz
has many reasons for distinguishing monads from atoms. The easiest to
understand is perhaps that while atoms are meant to be the smallest
unit of extension out of which all larger extended things are built,
monads are non-extended (recall that space is an illusion on Leibniz's
view).
a. Monads and Complete Concepts

We must begin to understand what a monad is by beginning from the idea
of a complete concept. As previously stated, a substance (that is,
monad) is that reality which the complete concept represents.
Acomplete concept contains within itself all the predicates of the
subject of which it is the concept, and these predicates are related
by sufficient reasons into a vast single network of explanation. So,
relatedly, the monad must not only exhibit properties, but contain
within itself "virtually" or "potentially" all the properties it will
exhibit in the future, as well as contain the "trace" of all the
properties it did exhibit in the past. In Leibniz's extraordinary
phrase, found frequently in his later work, the monad is "pregnant"
with the future and "laden" with the past (see, for example,
Monadology §22). All these properties are "folded up" within the
monad; they unfold when they have sufficient reason to do so (see, for
example,Monadology §61). Furthermore, the network of explanation is
indivisible; to divide it would either leave some predicates without a
sufficient reason or merely separate two substances that never
belonged together in the first place. Correspondingly, the monad is
one, simple and indivisible.

Just as in the analysis of space and time Leibniz argues that all
relational predicates are actually interior predicates of some
complete concept, so the monad's properties include all of its
relations to every other monad in the universe. A monad, then, is
self-sufficient. Having all these properties within itself, it doesn't
need to be actually related to or influenced by another other monad.
Leibniz writes:

So if I were capable of considering distinctly everything which is
happening or appearing to me now, I would be able to see in it
everything which will ever happen or appear to me for all time. And it
would not be prevented, and would still happen to me, even if
everything outside me were destroyed, so long as there remained only
God and me (Discourse on Metaphysics, §14).

Thus, just like space and time, cause and effect is a "well-founded"
illusion. According to Leibniz, causation is to be account for by
saying that one thing, A, causes another, B, when the virtual relation
between them is more clearly and simply expressed in A than in B. But
metaphysically, Leibniz argues, it makes no difference which way
around the relation is understood, because the relation itself is not
real. Leibniz writes:

Thus, in strict metaphysical precision, we have no more reason to
say that the ship pushes the water to produce this large number of
circles…than to say that the water is caused to produce all these
circles and that it causes the ship to move accordingly ("Draft letter
to Arnauld," 8 December 1686).

Leibniz goes on to insist that the first direction of explanation is
much simpler, since the second would involve leaping directly to the
action of God to explain the extraordinary action of so many
individual bits of water. But that simplicity is hardly the same as
truth.
b. Pre-established Harmony, Windowlessness, and Mirroring

So, instead of cause and effect being the basic agency of change,
Leibniz is offering a theory of pre-established harmony (sometimes
referred to as the hypothesis of concomitance) to understand the
apparently inter-related behavior of things. Consider the common
analogy of two clocks. The two clocks are on different sides of a room
and both keep good time (that is, they tell the same time). Now,
someone who didn't know how clocks work might suspect that one was the
master clock and it caused the other clock to always follow it. When
two things behave in corresponding ways, then it is often assumed
(without any real evidence) that there is causation occurring. But
another person who knew about clocks would explain that the two clocks
have no influence one on the other, but rather they have a common
cause (for example, in the last person to set and wind them). Since
then, they have been independently running in sync with one another,
not causing each other. On Leibniz's view, every monad is like a
clock, behaving independently of other monads. Nevertheless, every
monad is synchronized with one another by God, according to his vast
conception of the perfect universe. (We must be careful, however, not
to take this mechanical image of a clock too literally. Not all monads
are explicable in terms of physical, efficient causes.)

In accordance with his theory of pre-established harmony, Leibniz
argues that monads do not affect one another and that each monad
expresses the entire universe. He has rather unique and extraordinary
set of phrases for this; Leibniz states that every monad mirrors the
whole of the universe in that it expresses every other monad, but no
monad has a window through which it could actually receive or supply
causal influences (see Monadology, §7 & §56). Furthermore, since a
monad cannot be influenced, there is no way for a monad to be born or
destroyed (except by God through a miracle–defined as something
outside the natural course of events). All monads are thus eternal.
(It is fair to say that Leibniz's attempt to account for what happens
to "souls" before the birth of body, and after its death, lead him to
some colorful, but rather strained, speculations.)
9. Implications of Conceiving Substances as Monads

We will examine briefly four important implications of Leibniz's
account of substance: first, the distinction between metaphysical
truth and phenomenal description; second, the idea of little
perceptions; third, the infinitely composite nature of all body; and
fourth, innate ideas.
a. Levels of Reality

Leibniz posits a distinction between levels or "spheres" in his
account of reality ("Discourse on Metaphysics," §10). The primary,
most fundamental level of reality is the metaphysical level, which
includes only monads, their perceptions, and their appetitions (no
causality, no space, no time–at least as ordinarily understood–each
monad spontaneously unfolding according to the kind of thing that it
is). Thephenomenal or descriptive level involves what appears to be
happening from the finite, imperfect perspective of human minds
(things cause one another in space and time). Science's object is the
latter, which is an illusion, but in which nothing happens that is not
based upon what really happens in the metaphysical level (that is, the
illusion is "well-founded"). Therefore, the laws of physics are
perfectly correct, as a description. (Berkeley borrows this idea, see
especially his "De Motu," and Kant produces a highly original version
of it.) Indeed, Leibniz believes, following Descartes and many other
materialists, that all such laws are mechanical in nature, exclusively
involving the interaction of momenta and masses–hence his accusation
that Newton's idea of gravity is merely "occult." However, at the
metaphysical level, no account of reality could be less mechanical.
Not surprisingly, then, Leibniz's own contributions to physical
science were in the fields of the theory of momentum and engineering.

A serious error would arise only if one took the "objects" of science
(matter, motion, space, time, etc.) as if they were real in
themselves. Consider the following analogy: in monitoring a nation's
economy, it is sometimes convenient to speak of a retail price index,
which is a way of keeping track of the average change in the prices of
millions of items. But there is nothing for sale anywhere which costs
just that amount. As a measure it works well, provided one does not
take it literally. Science, in order to be possible for finite minds,
involves that kind of simplification or "abbreviation" (see, for
example, "Letter to Arnauld," 30 April 1687).
b. Little Perceptions

Leibniz is one of the first philosophers to have analyzed the
importance of that which is "unconscious" in one's mental life. That a
monad is a "mirror" of the whole universe entails that one's soul will
actually have an infinite number and complexity of perceptions.
Obviously, however, one does not apperceive (that is, one is not
conscious of) all these little perceptions, as Leibniz calls them.
Thus, perception for Leibniz does not mean apperception. (Leibniz
argues that this is a major error on Descartes' part.) Further, where
one is conscious of some perception, it will be of a blurred composite
perception. Leibniz's analogy is of the roar of the waves of the
beach: the seemingly singular sound of which one is conscious is in
fact made up of a vast number of individual sounds of which one is not
conscious–droplets of water smacking into one another.

For Leibniz, little perceptions are an important philosophical
insight. First and foremost, this relates to one of Leibniz's main
general principles, the principle of continuity. Nature, Leibniz
claims, "never makes leaps" (New Essays on Human Understanding, 56).
This follows, Leibniz believes, from the principle of sufficient
reason together with the idea of the perfection of the universe
(consisting of something like plenitude). But the idea of little
perceptions allows Leibniz to account for how such continuity actually
happens even in everyday circumstances. The principle of continuity is
very important for Leibniz's physics (see "Specimen Dynamicum") and
turns up in Leibniz's account of change in the monad (see below).

Second, little perceptions explain the acquisition of innumerable
minor habits and customs, which make up a huge part of one's
distinctiveness as an individual personality. Such habits accumulate
continuously and gradually, rather than all at once like decisions,
and thus completely bypass the conscious will. Further, these little
perceptions account for one's pre-conscious connection with the world.
For Leibniz, one's relation with the world is not one just of
knowledge, or of apperceived sensation. An individual's relation with
the world is richer than either of these, a kind of background feeling
of being-a-part-of. (Thus, a thorough-going skepticism, however
plausible at a logical level, is ultimately absurd.)

Finally, Leibniz's idea of little perceptions gives a phenomenal
(rather than metaphysical) account for the impossibility of real
indiscernibles: there will always be differences in the petite
perceptions of otherwise very similar monads. The differences may not
be observable at the moment, but will "unfold in the fullness of time"
into a discernible difference (New Essays on Human Understanding,
245-6).
c. Composites and Substantial Forms

According to Leibniz, everything one perceives which is a unified
being must be a single monad. Everything else is a composite of many
monads. A coffee cup, for example, is made of many monads (an infinite
number, actually). In everyday life, one tends to call it a single
thing only because the monads all act together. One's soul, however,
and the soul of every other living thing, is a single monad which
"controls" a composite body. Leibniz thus says that, at least for
living things, one must posit substantial forms, as the principle of
the unity of certain living composites. (See, for example, "A New
System of Nature." The term is derived from Aristotle: that which
structures and governs the changes of mere matter in order to make a
thing what it is.) One's soul, a monad otherwise like any other monad,
thus becomes the substantial form of one's otherwise merely aggregate
body.

Furthermore, according to Leibniz, such composite bodies must be made
of an infinite number of other inanimate as well as animated monads.
This follows from the universe being the most perfect possible, which,
again, seems to mean the richest in controlled complexity, in
"plenitude." Leibniz argues that it would be a great waste of possible
perfection to only allow living beings to have bodies at that
particular level of aggregation with which one is phenomenally
familiar. (Perhaps Leibniz was understandably impressed by the
different levels of magnitude being revealed by relatively recently
invented instruments like the microscope and telescope.) Leibniz
writes:

Every portion of matter can be thought of as a garden full of
plants, or as a pond full of fish. But every branch of the plant,
every part of the animal, and every drop of its vital fluids, is
another such garden, or another such pool. [...] Thus there is no
uncultivated ground in the universe; nothing barren, nothing dead.
(Monadology, §§67 & 69)

(Note: Although there is an extraordinary sublimity of such an image,
Leibniz is often accused of making rather too much of an inadequate
conception of the infinite.)

Further, the particular monads making up one's body are constantly
changing as one breaths in and out, sheds skin, etc., although not all
at once. The substantial form is thus a unified explanation of bodily
form and function. A mere chunk of stuff has, of course, an
explanation, but not a unified one–not in one monad, the soul. Leibniz
thus distinguishes four types of monads: humans, animals, plants, and
matter. All have perceptions, in the sense that they have internal
properties that "express" external relations; the first three have
substantial forms, and thus appetition; the first two have memory; but
only the first has reason (see Monadology §§18-19 & 29).
d. Innate Ideas

An innate idea is any idea which is intrinsic to the mind rather than
arriving in some way from outside it. During this period in
philosophy, innate ideas tended to be opposed to the thorough-going
empiricism of Locke. Like Descartes before him–and for many of the
same reasons–Leibniz found it necessary to posit the existence of
innate ideas. At the metaphysical level, since monads have no
"windows," it must be the case that all ideas are innate. That is to
say, an idea in one's monad/soul is just another property of that
monad, which happens according to an entirely internal explanation
represented by the complete concept. But at the phenomenal level, it
is certainly the case that many ideas are represented as arriving
through one's senses. In general, at least any relation in space or
time will appear in this way.

Thus, one could imagine Leibniz being a thorough-going empiricist at
the phenomenal level of description. This would amount to the claim
that the metaphysically true innateness of all ideas is
epistemologically useless information. Leibniz finds it necessary,
therefore, to advance the following arguments in favor of phenomenally
innate ideas:

(i) Some ideas are characterized by universal necessity, such as ideas
in geometry, logic, metaphysics, morality, and theology. But it is
impossible to derive universal necessity from experience. (Note that
this argument is hardly new to Leibniz.)

(ii) An innate idea need not be an idea consciously possessed (because
of "little perceptions," for example). An innate idea can be
potential, as an inclination of reason, as a rigid distortion in
Locke'stabula rasa. (Here, Leibniz provides the famous analogy of the
veins in the marble prior to the sculptor's work.) It requires
"attention" (especially in the form of philosophical thinking) to
bring to explicit consciousness the operation, and to clarify the
content, of these innate ideas.

(iii) Consider the possibility of foreseeing an event that is not
similar to (and thus merely an associated repetition of) a past event.
By using rational principles of physics, for example, one can analyze
a situation and predict the outcome of all the masses and forces, even
without ever having experienced a similar situation or outcome. This,
Leibniz says, is the privilege of humans over animals ("brutes"), who
only have the "shadow" of reason, because they can only move from one
idea to another by association of similars (see Leibniz's joke about
empiricists in Monadology, §28).

monad

Thus, at the phenomenal level, Leibniz can distinguish between innate
and empirical ideas. An empirical idea is a property of a monad which
itself expresses a relation to some other substance or which arises
from another internal property that is the expression of an external
substance. Although the difference between empirical and innate is in
fact an illusion, it does make a difference, for example, to the
methodology of the sciences. This is similar to the distinction made
above between the idea of truth (as the containedness of the predicate
in the subject), and the pragmatic/methodological issue of how one
comes to know that truth. The latter is not irrelevant, except to the
foundation and definition of truth. (Leibniz's most extensive
discussion of innate ideas, not surprisingly, is in the New Essays on
Human Understanding.)
10. Monadic Activity and Time

Correlate to the inter-connectedness of predicates in the complete
concept is an active power in the monad, which thus always acts out
its predicates spontaneously. Predicates are, to use a fascinating
metaphor of Leibniz's, "folded up" within the monad. In later writings
such as the Monadology, Leibniz describes this using the
Aristotelian/Medieval idea of entelechy: the becoming actual or
achievement of a potential. This word is derived from the idea of
perfections. What becomes actual strives to finish or perfect the
potential, to realize the complete concept, to unfold itself perfectly
as what it is in its entirety. This active power is the essence of the
monad. Leibniz has several different names for this property (or
closely related properties) of monads: entelechy, active power,
conatus or nisus (effort/striving, or urge/desire), primary force,
internal principle of change, and even light (in "On the Principle of
Indiscernibles").

This activity is not just a property of human souls, but of all types
of monads. This inner activity must mean not only being the source of
action, but also being affected (passivity), and of resisting
(inertia). Again, what one calls "passivity" is just a more complex
and subtle form of activity. Both a monad's activity and resistance,
of course, follow from its complete concept, and are expressed in
phenomena as causes and as effects. Change in a monad is the
intelligible, constantly, and continuously (recalling here the
principle of continuity discussed above) unfolding being of a thing,
from itself, to itself. "Intelligible" here means: (i) according to
sufficient reason, not random or chaotic; and (ii) acting as if
designed or purposed, as if alive–hence Leibniz's contribution to the
philosophical tradition of "vitalism."

It is important to understand that this is not just a power to act,
conceived as separable from the action and its result. Rather, Leibniz
insists that one must understand that power together with (i) the
sufficient reason of that power; (ii) the determination of the action
at a certain time and in a certain way; (iii) together with all the
results of the action, first as the merely potential and then as the
actual. (See "On the Principle of Indiscernibles," and Monadology
§§11-15.) One is not, therefore, to understand it as a sequence of
states, the individual bits of which are even ideally separable
(except as an object of mere description for science), nor a sequence
of causes and effects, again understood to be ideally separable (as if
there could have been the cause without the effect). All this follows
from the complete concept, the predicates of which are connected in
one concept. Each state therefore contains the definite trace of all
the past, and is (in Leibniz's famous phrase) "pregnant" with the
future.

But time, like space, is an illusion. How then is one to understand
change without time? The important question is: what conception of
time is being discussed? Just like space, Leibniz is objecting to any
conception of time which is exterior to the objects that are normally
said to be "in" time (time as an exterior framework, a dimension).
Also, he objects to time as mere chronology, a conception of time as a
sequence of "now points" that are ideally separable from one another
(that is, not essentially continuous) and are countable and orderable
separately from any thing being "in" them (that is, abstract).

However, in discussing relational properties above (and, in
particular, Leibniz's response to the Newton-Clarke argument about
non-linear motion), "space" was in a sense preserved as a set of rules
about the representative properties of monads. Here, too, but in a
more profound way, "time" is preserved immanently to the monad. The
active principle of change discussed above is immanent to monads, and
no one state can be separated from all the others, without completely
altering the thing in question into a thing that never changes (that
has only the one state for all eternity). For Leibniz, the past and
future are no more disconnected, in fact less, from the present than
"here" is from "there." Both distinctions are illusions, but temporal
relations in a substance form an explanatory, intelligible sequence of
a self-same thing. The principle of change becomes an original,
internal and active power of the thing constantly becoming the thing
that it is, as the spontaneous happening and internal principle of the
particular order of things which make up that substance. In other
words, substances unfold, become the things God always knew them to
be, in a time that is nothing other than precisely that becoming.

Time, then, has three levels, according to Leibniz

1. the atemporality or eternality of God;
2. the continuous immanent becoming-itself of the monad as entelechy;
3. time as the external framework of a chronology of "nows."

The difference between (ii) and (iii) is made clear by the account of
the internal principle of change. The real difference between the
necessary being of God and the contingent, created finitude of a human
being is the difference between (i) and (ii).
11. Influence

Leibniz's mathematics, in parallel to Newton's, made a significant
difference in European science of the 18th century. Other than that,
however, his contributions as engineer or logician were relatively
quickly forgotten and had to later be re-invented elsewhere.

However, Leibniz's metaphysics was highly influential, renewing the
Cartesian project of rational metaphysics, and bequeathing a set of
problems and approaches that had a huge impact on much of 18th century
philosophy. Kant above all would have been unthinkable without
Leibniz's philosophy, especially the accounts of space and time, of
sufficient reason, of the distinction between phenomenal and
metaphysical reality, and his approach to the problem of freedom.
Rarely did Kant agree with his great predecessor–indeed, rendering the
whole Cartesian/Leibnizian approach conceptually impossible–but the
influence was nevertheless necessary. After Kant, Leibniz was more
often than not a mine of individual fascinating ideas, rather than a
systematic philosopher, ideas appearing (in greatly modified forms) in
for example Hegelian idealism, romanticism, and Bergson.

In the 20th century, Leibniz has been widely studied by Anglo-American
"analytic" philosophy as a great logician who made significant
contributions to, for example, the theory of identity and modal logic.
In Continental European philosophy, Leibniz has perhaps been less
commonly treated as a great predecessor, although fascinating texts by
Heidegger and, much later, by Deleuze, show the continuing fertility
of his philosophical ideas.
12. Editions of Leibniz

As noted above, Leibniz did not publish much in his lifetime which
fits the familiar description of a philosophy book. Much was
published, however, shortly after his death. But there remained for
the dedication of future editors a huge estate of short papers,
letters, drafts of letters, and notes. The standard edition of the
works of Leibniz is the Akademie-Verlag of Berlin. The most
comprehensive collection of these in English, together with some
published material, is in Leibniz, Philosophical Papers and Letters,
translated and edited by L. E. Loemker, 2 volumes, University of
Chicago Press, 1956.

Several good, inexpensive and shorter anthologies of key texts:

* Philosophical Essays. Edited and translated by Ariew and Garber.
Hackett, 1989.
* Philosophical Texts. Translated by Francks and Woolhouse. Oxford
University Press, 1998.
* Philosophical Writings. Edited by Parkinson, translated by
Morris and Parkinson. Everyman, 1973.

Finally, editions in English of more specialized selections, the
longer texts, and correspondences of Leibniz:

* The Correspondence with Clarke. Edited by Alexander. Manchester
University Press, 1956.
* The Leibniz-Arnauld Correspondence. Edited and translated by
Mason. Manchester University Press, 1967.
* Logical Papers. Edited and translated by Parkinson. Oxford
University Press, 1966.
* The Political Writings of Leibniz. Edited and translated by
Riley. Cambridge University Press, 1972.
* New Essays on Human Understanding. Edited and translated by
Remnant and Bennett. Cambridge University Press, 1996.
* Theodicy. Edited by Farrer, translated by Huggard. Routledge and
Kegan Paul, 1951.