Lecture Supplement
Introducing Leibniz
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1. Leibniz’ Life
and Interests [1646-1716]:
Gottfried Wilhelm Leibniz’ father was a Professor of Moral
Philosophy at the University of Leipzig, and as a young child he was largely
self-taught from the works in his father’s library.
His course of studies centered upon the Aristotelian and scholastic
“classics.” He entered the
University of Leipzig at the age of 15 as a law student, and there learned
something about the revolutionary ideas of Galileo, Bacon, Hobbes, and
Descartes. He concluded his studies
in five years, but was not granted his degree because of his age.[1]
He then attended the lesser-known University of Altdorf, and earned a
degree in law and philosophy in 1666.
While he was offered a faculty position there, he entered a life of
public service (like Hobbes and Locke in England), and occupied a number of
positions for noble men throughout his life.
Diplomatic assignments took Leibniz to Paris in 1672 (he also visited
England, and met with Spinoza on his way home in 1676), and on these travels he
became even more familiar with the “modern thinkers.”
Leibniz entered into a wide correspondence with many of the major
thinkers of his day, and he began publishing in important intellectual forums
such as the Journal des Savants.
Whereas Descartes and Spinoza were motivated to “build” intellectual
systems of thought which would
clearly and distinctly display certain “core ideas,” Leibniz is best seen as a
broad-ranging thinker whose primary wish was to bring many disparate elements
together: Christians of all sects, medical researchers, scientific researchers,
legal theorists, and mathematicians.
It is the latter field which is central to Leibniz’ thought, however (and
this should not be surprising when we remember that he is one of two individuals
credited with the development of calculus).
Like the other “continental rationalists,” Leibniz maintained that
reality is not only rational at its core, but like them he held that mathematics
helped us understand this rational core.
Perhaps we should pause and consider this point so that we don’t
misattribute our views to those of
the Early Modern thinkers. When we
think of science, we do not generally consider mathematics a science—after all,
it is an a priori rather than an
empirical (a posteriori), discipline.
But thinkers like Descartes, Spinoza, and Leibniz thought of mathematics
as not only a science, but as
the science.
In short they thought held that “what is real is rational” while holding
also that “mathematics is the paradigm of rationality,” and this leads fairly
directly (as we can see most clearly in Spinoza) to “reality is mathematical.”
In his Leibniz’s New Essays
Concerning Human Understanding: A Critical Exposition, John Dewey notes
that:
in the applicability of
mathematics to the interpretation of nature Leibniz finds witness to the
continuity and order of the world.
We have become so accustomed to the fact that mathematics may be directly
employed for the discussion and formulation of physical investigations that we
forget what is implied in it. It
involves the huge assumption that the world answers to reason; so that whatever
the mind finds to be ideally true may be taken for granted to be physically true
also. But in those days, when the
correlation of the laws of the world and the laws of mathematical reasoning was
a fresh discovery, this aspect of the case would not be easily lost sight of.[2]
Where geometry was the paradigm mathematical field for the
other rationalists, however, Leibniz is perhaps not best thought of along
geometric lines. He did not begin
with certain foundational beliefs in the manner of Descartes or Spinoza.
Where Spinoza was concerned with working out the deductive consequences
of the basic definition of substance, and Descartes was concerned with
discovering the foundations of knowledge, Leibniz wanted to
unify a large number of different
areas of thought. He wanted to
resolve paradoxes, problems, and inconsistencies by developing a coherent,
unified, overall theory that all individuals could rationally accept.
As Dewey notes,
Leibniz was a man of his
times...and was himself actively engaged in the prosecution of mathematics,
mechanics, geology, comparative philology, and jurisprudence.
But he was also a man of Aristotle’s times,—that is to say, a
philosopher, not satisfied until the facts, principles and methods of science
had received an interpretation which should explain and unify them.[3]
It is thus ironic, as Dewey notes, that Leibniz was
involved in so many divisive intellectual conflicts:
it is somewhat significant that
one whose tendency was conciliatory, who was eminently what the Germans delight
to call him, a “mediator,” attempting to unite the varied truths which he found
scattered in opposed systems, should have had so much of his work called forth
by controversy. Aside from the
cases just mentioned [contra the
Newtonians regarding the infinitesimal calculus; and
contra Bishop Clarke regarding the
nature of God, time, space, and freedom], his other chief work, the
Theodicy, is, in form, a reply to
Bayle....But Leibniz has a somewhat different attitude towards his British and
towards his Continental opponents.
With the latter he was always in sympathy, while they in turn gave whatever he
uttered a respectful hearing. Their
mutual critiques begin and end in compliments.
But the Englishmen found the thought of Leibniz “paradoxical” and forced.
It seemed to them wildly speculative, and indeed arbitrary guess-work,
without any special reason for its production, and wholly unverifiable in its
results....But Leibniz, on the other hand, felt as if he were dealing, in
philosophical matters at least, with foemen hardly worthy of his steel.
Locke, he says, had subtlety...and a sort of
superficial metaphysics; but he was
ignorant of the method of mathematics,—that is to say, from the standpoint of
Leibniz, of the method of all science.[4]
Nonetheless, Leibniz was a
firm believer in harmony, and this
meant that he looked for every opportunity to try to bring conflicting
orientations together. While he is
interested in so many different philosophical problems, if we are to understand
his orientation, we must pay special attention to two particular problems (in
part because they are not familiar to us): (i)
the problem of the continuum and motion
and (ii) the problem of fate and freedom.
Our understanding of Leibniz is hampered by the fact that there is no
central canonical text in his corpus.
As Roger Ariew and Daniel Garber note in their “Principle of Selection
and Rational for the Volume,” to their
G.W. Leibniz: Philosophical Essays:
there is nothing in Leibniz’s
enormous corpus that corresponds to Descartes’s
Meditations, Spinoza’s
Ethics, or Locke’s
Essay, no single work that stands as
a canonical expression if its author’s whole philosophy.
Although works like the “Discourse on Metaphysics” and the “Monadology”
are obviously essential to any good collection of Leibniz’ writings, neither of
these nor any other single work is, by itself, an adequate exposition of
Leibniz’s complex thought. Unlike
his more systematic contemporaries, Leibniz seems to have chosen as his form the
occasional essay, the essay or letter written about a specific problem, usually
against a specific antagonist, and often with a specific audience in mind.[5]
2. The Problem Of
The Continuum and Motion:
The Pythagoreans discovered that the side of the unit
square is incommensurable with its diagonal—they discovered what we call
irrational numbers.[6]
This led to problems because these numbers could not be assigned a place
on the number line and could not be readily fit into the Greek view of
mathematics which emphasized the study of
proportions (e.g., ratios of
rational numbers). Without a clear
understanding of infinity, however, paradoxes quickly develop as one talks about
the relationship of the rationals and irrationals.
Aristotle did not countenance the notion of an actual or completed
infinite totality, however, and he maintained that a totality could only be
potentially infinite—its finite
membership may be increased without limit but this does not mean there actually
is a completed infinitude.
Leibniz, on the other hand relied fundamentally upon the idea of a
completed infinitude.
He held to a principle of
continuity maintaining that everything in nature happens by degrees and that
there are no discontinuities or leaps in natural occurrences.
This was important to him as he grappled with the concept of
motion.
Throughout our Western history this has been an important concept.
In 600-500 B.C.E., early Greek philosophers like Anaximander and
Heraclitus took motion to be the essential characteristic of the natural world.
They did not inquire into its nature however.
In 500-400 B.C.E., Eleatic followers of Parmenides maintained that a
close philosophical analysis showed that motion is merely an apparent
phenomenon. Followers like Zeno
soon used various paradoxes to argue that motion was illusory: “traversing an
infinitude of points takes an infinitude of time,” “a body can move neither
where it is nor where it is not and, therefore, motion is impossible—a merely
apparent phenomenon,” etc.
Aristotelian science treated motion as a
change from a potentiality to an
actuality. That is, it was
treated
qualitatively and this makes any
mathematical study of motion most difficult—the most that can be done here is to
speak of ratios and proportions.
For Aristotle “all things that move are moved by something else.”
He maintains that motion is the
actualization of what exists potentially—a change in the
qualities of things:
Aristotle’s kinematics, like his
physics in general, was a qualitative
science, incapable of providing a precise definition of such motions as
velocity and acceleration. In fact,
Greek mathematics, with its insistence on the illegitimacy of proportions or
ratios between heterogeneous qualities, did not provide even the formal means of
defining velocity as the ratio between distance and time....[7]
Over time a problem arose in regard to the increase or decrease of
qualities—the question was how qualities like warmness or blackness could vary
in their intensities. As something
changes its qualities, it must change from one quality to another but this seems
to imply an infinitude of qualities between the grosser ones we usually note
(hot and cold, white and black).
Another problem was whether motion involved two qualities (the change of one and
the acquisition of another—the terminus or end) or whether it involved only a
gradual change of one quality. A
notable implication of Aristotle’s view is that it seemed to require that the
earth not move if the heavens were to move—there must be something that is
unmoved.
By
Galileo’s time we are back to the early Greek Atomists’ view of bodies in
motion. An important distinction to
Copernicus is that between relative and absolute rest and motion.
This allowed physicists to deal with the apparent rest of the earth while
accepting the traditional idea that movement required some fixed frame of
reference. Descartes recognizes the
importance of this distinction and would distinguish between vulgar views of
motion (change of place) and a scientific view (transfer of matter from the
vicinity of those bodies which it is in immediate contact into the vicinity of
other bodies).
As Roger Penrose notes,
the profound breakthrough that
the seventeenth century brought to science was the understanding of
motion.
The ancient Greeks had a marvelous understanding of things static—rigid
geometrical shapes, or bodies in
equilibrium (i.e. with all forces balanced, so there is no motion)—but they
had no good conception of the laws governing the way that bodies actually
move.
What they lacked was a good theory of
dynamics, i.e. a theory of the
beautiful way in which Nature actually controls the change in location of bodies
from one moment to the next. Part
(but by no means all) of the reason for this was an absence of any sufficiently
accurate means of keeping time, i.e. of a reasonably good ‘clock’.
Such a clock is needed so that changes in position can be accurately
timed, and so that the speeds and accelerations of bodies can be well
ascertained. Thus Galileo’s
observation in 1583 that a pendulum could be used as a reliable means of keeping
time had a far-reaching importance for him (and for the development of science
as a whole!) since the timing of motion could then be made precise.
Some fifty-five years later, with the publication of Galileo’s
Discoursi in 1638, the new subject of
dynamics was launched—and the transformation from ancient mysticism to modern
science had begun![8]
3. Contrasts
Between Descartes, Spinoza, and Leibniz:
Descartes maintained that:
all the variety in matter, or all the
diversity of its forms depends on motion.
There is therefore but one matter in the whole universe, and we know this
by the simple fact of its being extended.
All the properties which we clearly perceive in it may be reduced to the
one, viz. that it can be divided, or moved according to its parts, and
consequently is capable of all these affections which we perceive can arise from
the motion of its parts. For its
partition by thought alone makes no difference to it; but all the variation in
matter, or diversity in its forms, depends on motion.[9]
This view is one that becomes popular as the study of
dynamics provides the “direction” for the development of the physical sciences.
Whatever the merits of Descartes’ physical theories, however, his
philosophical world-view bifurcates the universe and runs into at least the
following problems:
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mind/body interaction,
different causal chains (for the
mental and the physical),
representationalism,
the number and nature of
substance(s), and
freedom.
As we have seen, Spinoza sought to avoid these difficulties with his talk
of the cause sui.
As we also saw, however, significant problems arise with his system
(including at least the following):
lack of freedom (nothing in the universe is contingent),
monism (only one substance), and
rejection of teleology and final
causes.
Leibniz’s philosophical system is significantly different
from both of these. He holds that
there is both a transcendent deity
and a created universe, and he holds
that there are an infinite number of substances (or monads).
He endeavors to avoid both the problems which Descartes has regarding the
interaction of substances in the created world, and the problems which Spinoza
has with determinism. He tries to
build a harmonious world-system which gives us
a fully deductive, completely rational,
created world which is fully explained by a necessarily existing deity who
freely creates a world which accords with the mechanistic physical laws while
allowing for free action and activity.
4. Leibniz’
Conception of Substance:
Thus Leibniz develops a “third” orientation:
like Spinoza and Descartes (and
unlike Pascal), he views the universe as
a harmonious, rational whole.
Unlike Spinoza, he asserts there are many substances (indeed, an infinite number
of them) and he speaks of a universal
harmony of this infinitude. He
felt that both Descartes and Spinoza were wrong to assume that extended things
were real (whether one treats them as substances or as attributes).
Once one makes extension real, he claims, one is forced to divide the
world into two substances or attributes and this makes it difficult to relate
these aspects of the universe to one another.
Leibniz hoped that he could show that extension, figure, and motion (the
things appealed to explain events in the “physical world”), as well as thoughts
could be explained as derivative—that he could find some concept that could be
used to explain both the physical
events and the mental ones.
His studies confirmed him in his opinion
that a different sort of account of
substance was needed—bare
extension, the essential characteristic of the physical according to the
others (whether treated substantially or as an attribute), could not explain
motion by itself. Galilean
mechanics explained motion in terms of successive states where a body occupies a
different position in each moment.
As the science become more and more satisfactory, it became necessary to appeal
to concepts like continuously increasing velocity, infinitesimal times and
distances, etc. Leibniz and Newton
devised calculus to deal with the attendant problems that such talk engendered
(if one treats motion as analyzable into successive discrete states, one must
allow natural objects to make “leaps” from one spot to another).
As long as one treats nature as
discrete, Leibniz believed, one can not escape the problems of the “continuum:”
now this is the axiom which I
utilize, namely, that “no event takes
place by a leap.” This
proposition flows...from the laws of order and rests on the same rational ground
by virtue of which it is generally recognized that
motion does not occur by leaps, that
is, that a body in order to go from one place to another must pass through
definite intermediate places....
I do not believe extension alone constitutes substance, since its
conception is incomplete....For we can analyze it into a plurality, continuity
and co-existence....I believe that our thought of substance is perfectly
satisfied in the conception of force and not in that of extension....[10]
In his A New System
of Nature, Leibniz says that:
but since having tried to lay the
foundations of the very principles of mechanics in order to give a rational
account of the laws of nature known to us by experiment, I realized
that the sole consideration of an
extended mass did not suffice, and that we must again employ the notion of force
which is very intelligible despite its springing from metaphysics.....it is
impossible to find the principles of a
true unity in matter alone or in that which is only passive, since
everything in it is only a collection or mass of parts to infinity....the
continuum cannot be composed of points.
Therefore...I was compelled to have recourse to a formal atom since a
material being cannot be both material and perfectly indivisible or endowed with
a true unity. It was necessary,
hence to recall...the substantial forms
so decried today....their nature consists in force....[11]
That is, the difficulties associated with the notion of a
continuum were instrumental in leading Leibniz to the view that motion itself
can not be a real entity because it never exists and only what exists in time
can be real. Where many felt
physical reality could be fully explained by appeal to
extension, figure, and motion,
Leibniz came to believe these were apparent rather than real, and that the basic
universal laws of nature could not be derived from such concepts.
In his “Introduction” to a collection of Leibniz’ essays, Paul Janet
provides a discussion which helps us come to understand Leibniz’ objection to
the notion of an extended substance:
...I think it can be shown
a priori that matter taken in itself
is something ideal and super-sensible, at least to those who admit a divine
intelligence. For it will readily
be granted that God does not know matter by means of the senses; for it is an
axiom in metaphysics that God has no senses and consequently cannot have
sensations. Thus: God can be
neither warm nor cold; he cannot smell the odor of flowers; he cannot hear
sounds, he cannot see colors; he cannot feel electrical disturbances, etc.
In a word, since his is a pure intelligence he can conceive only the
purely intelligible; not that he is ignorant of any of the phenomena of nature,
only that he knows them in their intelligible reasons and not through their
sensible impressions, by means of which creatures are aware of them.
Sensibility supposes a subject with senses, organs and nerves, that is,
it is a relation between created things.
From God’s point of view, therefore, matter is not sensible; it is, as
the Germans say, ubersinnlich.
The conclusion is easy to draw, namely, that God, being absolute
intelligence, necessarily sees things as they are, and conversely the things in
themselves are such as he sees them.
Matter is, accordingly, such in itself as God sees it, but he sees it
only in its ideal and intelligible essence, whence we see that matter is an
intelligible something and not something sensible.[12]
5. Leibniz’ Monads:
Leibniz calls his basic substances “monads” (from the Greek
‘monas’ meaning “unity” or “that
which is one”)—“metaphysical units” of force (“centers of psychic activity”).
Like Spinoza (and unlike Descartes) he holds there is
no possible interaction of substances
and, thus, for him the harmony between
substances must be imposed from without.
According to Leibniz, substances can not interact with one another, but
in a rationally-ordered world there must be correlations between the various
predicates which are true of one substance and those which are true of another.
If, for example, it is to be true of one substance, or monad, (call it
Bruce) that it is married, then there must be another monad (call it Laurie) of
which it is true that it is married to Bruce.
The truth of the first proposition requires that there be another true
proposition of the second sort.
For Leibniz, if the basic substances interacted, they would not truly be
substances (here we can see that he agrees with Spinoza, who argues that if one
substance caused something to be true of a second one, that second one would not
be a substance—it would be “conceived through another”).
Like Spinoza, then, he believed that
a major defect of Cartesian bare
extended matter was that it was conceived of as inactive—it could not
explain why anything happened and the
deity had to be brought into the picture as a constant source of action
(Descartes’ deity conserves as well as creates substances).
Leibniz felt we should consider activity to be a basic characteristic of
substances: “substance is a being
capable of action.”[13]
While Leibniz sees Spinoza as preferable to Descartes on these points, he
rejects Spinoza’s monism!
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Both Descartes and Spinoza thought of
substance as a subject in the
grammatical or logical sense—the attributes become the true predications of
substance, and it is supposed that these predicates can not exist without the
subject (though the subject could exist without the predicates).
Besides the logical/grammatical notion of a subject, however, there is
also the notion of an element that
persists through change. While
Leibniz agrees with Descartes and Spinoza that substances can only be subjects
and never be predicated of another thing, he holds that it is just as important
that they are “capable of action.”
Neither Descartes nor Spinoza developed a clear conception of
propositions and truth however. For
this reason, Leibniz’ “theory of propositions” and his “theory of truth” are
important. He held that the
subject-predicate form of proposition was basic—that all true propositions are
subject-predicate ones.
Moreover, to ensure that substances have the sort of “integrity” which he
felt was basic to them, he held that they could never be properly placed in the
predicate proposition. For him,
relational propositions (like “Bruce
and Laurie are married”) can not be real propositions then, they must be
analyzed into subject-predicate sentences (“Bruce is married” and “Laurie is
married”). Leibniz holds that a
substance is a logical subject of which many things may be attributed, but which
can not itself be attributed (or predicated) of anything else.
Moreover, he held that the concept of the subject contains all the
predicates that will be true of it.
His analysis of truth held that what makes a sentence true is that the
concept of the predicate of the proposition is contained within the concept of
the subject. Thus, really,
all sentences are analytic.[14]
Leibniz held, however, that some are finitely analytic (e.g., “A male is
a male,” or “My brother is a male”), and that some are infinitely analytic
(e.g., “Julius Caesar died in 44 B.C.E.).
According to Leibniz, monads have
an internal principle of change—he calls it “appetition
or desire.”
Monads are the fundamental real things, the subjects of change which
contain within themselves the principle of their changes.
His view of the universe is that it is filled with monads each reflecting
the universe from a different perspective.
6. The Role of
Leibniz’ Deity:
Leibniz’ deity plays an important role in his system for
two reasons. First the deity causes
the individual substances (monads), and provides for the pre-established harmony
between the changes of these substances; and, second, it is through the deity
that we get freedom or teleology in the world.
To have independent substances which act solely from their own nature,
Leibniz believes that he must allow that “...the notion of an individual
substance includes once and for all everything that can ever happen to it....”[15]
But if this is the case, how can there be freedom and teleology?
Well, he would avoid the deterministic picture of the universe which
Spinoza offers while holding on to the truth Spinoza accepts that substances can
not interact causally with one another without ceasing to be substances.
He does this by allowing that the events in the one causal chain which is
the harmonizing thread which runs through the universe are “certain,
but not necessary.”
7. Leibniz’ Central
Principles:
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To understand Leibniz, we will need to distinguish the
various central principles that are at the core of his theories:
the
principle of contradiction (or of
non-contradiction),
the
principle of sufficient reason,
the
principle of perfection (or of the
best).
Central to these principles is his distinction between
truths of reason and
truths of fact—but while his
distinction is somewhat like the one that is drawn now, we should be careful not
to attribute our view to Leibniz!
For him, truths of reason are
self-evident truths of reason, or they are easily reducible to such truths.
Except for the case of the deity’s existence, no existential propositions
are on this list. The denials of
such truths are contradictions and, thus, can not but be true.
Thus, these truths are guaranteed
by the principle of contradiction.
Truths of fact, on the other hand, require some
sufficient reason—there
must be some explanation as to why they are the case (are true).
Here we might distinguish the possible from the actual—some truths of
fact are not true because others are (they are
possible but nonactual)—it will be
convenient to speak of essences here.
The things of the world (the monads) have certain essences or natures
(certain things are true of them).
They need not have been the way they are, since other essences are
noncontradictory. Why, then, is the
world the way it is? For Leibniz,
the sufficient reason for the world being the way it is is the principle
of the Best!
Truths
of Reason |
Truths of Fact
(possible)
|
Truths
of Fact (actual) |
Principle of Non-Contradiction |
Principle of Sufficient Reason |
Principle of the Best |
Statements about essences |
Possible Worlds
Co-possibles (Sphere of the Possible) |
The Actual World
God could have chosen a different world (he is
metaphysically free yet
morally
constrained
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Finitely Analytic |
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Infinitely Analytic
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In addition, there are two other centrally important principles for
Leibniz:
the
principle of the identity of
indiscernibles: what distinguishes individual substances?
Only their characteristics/attributes.
the
principle of continuity: there are
no holes in the universe.
To further understand Leibniz’ world-view, we need to discuss the
phenomenal character of both causation and composites, but this introduction is
already over-long, and, instead, we will turn to the texts.
[1] Brief
biographies hint at some no longer understood
intrigue, but don’t identify it, while other
sources give the above explanation, which I
accept as the most reasonable.
[2] John
Dewey,
Leibniz’ New Essays Concerning Human
Understanding: A Critical Exposition [1888],
the citations are from selections reprinted
in From
Plato to Wittgenstein: The Historical
Foundations of the Modern Mind, ed. Daniel
Kolak (Belmont: Wadsworth, 1994), pp. 317-360,
pp. 323-324.
[3]
Ibid.,
p. 319.
[4]
Ibid.,
p. 334.
[5] Roger
Ariew and Daniel Garber, “Principle of Selection
and Rational for the Volume,”
in
G.W. Leibniz: Philosophical Essays, trans.
and eds. Roger Ariew and Daniel Garber
(Indianapolis: Hackett, 1989), pp. x-xii, p. x.
[6] That is,
a square whose sides are “one unit” long will
not have a diagonal which can be expressed as a
ratio of two “natural numbers” (p/q)—as we would
put it today, the diagonal has a length of the
“square root of 2.”
[7] Max
Jammer, “Motion,” in
The
Encyclopedia of Philosophy v. 5, ed. Paul
Edwards (N.Y.: Macmillan, 1967), pp. 396-399, p.
397.
[8] Roger
Penrose,
The Emperor’s New Mind (New York: Oxford
U.P., 1989), p. 162.
[9] Rene
Descartes,
Principles of Philosophy II, 23; in
The
Philosophical Works of Descartes, trans.
E.S. Haldane and G.R.T. Ross (Cambridge:
Cambridge U.P., 1969) v. 1, p. 265.
Emphasis added to passage.
[10] Letter
to De Volder in
Leibniz:
Selections, ed. P.P. Wiener (New York:
Scribners’, 1951), pp. 157-158.
Emphasis added to passage twice.
[11] G.W.
Leibniz,
New System of Nature [1695], in
The
Philosophy of the 16th and 17th
Centuries, ed. R.H. Popkin (N.Y.: Macmillan,
1966), pp. 324-325.
Also in
G.W.
Leibniz: Philosophical Essays, eds. Roger
Ariew and Daniel Garber,
op. cit.,
pp. 138-145, p. 139.
Emphasis added to passage four times.
[12] Paul
Janet, “Introduction,” in
Leibniz: Discourse on Metaphysics,
Correspondence with Arnauld, and Monadology
[1902], trans. George Montgomery (La Salle: Open
Court, 1968), pp. vii-xxiii, pp. xvii-xviii.
[13] Leibniz
G.W.,
Principles of Nature and of Grace, Based on
Reason [1714], in
The Light
of Reason, ed. Martin Hollis (London:
Fontana/Collins, 1973), p. 335.
[14] An
analytic
statement is one that is supposed to be true in
terms of the mere
meaning
of the terms involved.
For example “squares are four-sided
figures” is true because (a) ‘square’ means
‘four [equal]-sided figure’, and, thus, it
reduces to an “identity statement.”
Such truths are
conceptual truths.
These sorts of statements are to be
contrasted with
synthetic ones—they are truths that are
not
true simply in terms of the meanings of the
terms involved.
Here the truth of the statement depends
on the way the world is, rather than, simply, on
the way words are used.
The distinction between analytic and
synthetic truths or statements is, primarily, a
semantic
one.
[15] Leibniz,
Discourse
on Metaphysics, XIII,
in
Leibniz, trans. G.P. Montgomery (Chicago:
Open Court, 1968), p. 19.
Go to Lecture Supplement on Leibniz' Discourse and Monadology
Last revised on: 11/04/2014.