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The 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 provides an overview of Leibniz's metaphysic.
Consequently, this entry will 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. Remarkably, however,
the broad outline of his philosophy does remain constant.
This entry is predominately concerned with this broad
view of Leibniz's philosophical system.
Table
of Contents (Clicking on the links below
will take you to those parts of this article)
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 primarily because 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 could deduce 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 a
necessary 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 substance
is 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.)
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.)
- Truths of Essence
These come in two varieties:
- Primary/original truth: the law of non-contradiction,
for example.
- 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.
- Truths of Existence, of Fact, or of Hypothesis
Here, arguably, Leibniz sees four varieties:
- 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").
- 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.
- 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.
- 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" (see Discourse 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.)
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 an arbitrary
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.
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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).
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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.
A complete 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.
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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.
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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). The phenomenal
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).
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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's
tabula 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).
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
- the atemporality or eternality of God;
- the continuous immanent becoming-itself of the monad
as entelechy;
- 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.
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